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Search for the rare charged decay kaon->pion neutrino antineutrino Roy, Jean 1994

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SEARCH FOR THE RARE CHARGED DECAYKAON-> PION NEUTRINO ANTINEUTRINOByJean RoyB. Sc., Université de Montréal, 1986M. Sc., The University of British Columbia, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESPHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIADecember 1994® Jean Roy, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shalt not be allowed without my writtenpermission.(Signature)_________Department of PiSLVS /c2SThe University of British ColumbiaVancouver, CanadaDate 9 —MWC I-f —I’1<DE-6 (2188)AbstractAn experimental search for the flavour-changing weak neutral current decay J(+ -+z)j7 wasperformed in the + kinematic energy range 60 < T+ < 100 MeV. The Standard Model theoretical prediction for the branching ratio is within the bounds (0.5—4.5) x 10—10. An observationat a rate significantly in excess of the prediction would be an indicator of new physics. Theexperiment was also sensitive to decays of the type J(+ +XO , where X° is a weaklyinteracting massive neutral particle with mass in the range 150 < Mxo < 260 MeV/c2.The search was carried out at Brookhaven National Laboratory, using an intense beamof positively charged kaons. A specialized detector selected candidate K+—lr+vE7 decaysamong a large background of other processes by identifying K+ decays at rest, measuring themomentum, kinetic energy and range of the + , recording its decay sequence for positiveidentification and vetoing photons from background processes. Data were collected in twodifferent periods in 1989 and 1991.After analysis of the 1989 data set, no events were observed, allowing a 90% confidence levelupper limit of 1.7 x 10—8 to be set for the branching ratio. This is a factor of 55 improvementover the previous experiment using the same region of phase space. Studies performed afterthe analysis was completed led to an estimated expected background of less than one event.In the 1991 data set, atotalof4 events were observed, with an estimated background of lessthan two events. The studies leading to this estimate were performed before the final analysiswas carried out, resulting in reduced bias. However, uncertainties in the background estimateprecluded the identification of the source of the events. Therefore, an upper limit of 5.0 x 108was set for the branching ratio, based on the observation of 4 events.11Table of ContentsAbstract iiTable of Contents iiiList of Tables xList of Figures xvAcknowledgement xxiDedication xxii1 The Experiment 11.1 Introduction 11.2 Theoretical considerations 31.2.1 The Standard Model 31.2.2 Weak Interactions 41.2.3 Quark mixing 71.2.4 Neutral currents 91.2.5 Three generations quark mixing 101.2.6 j+ _÷ i-+j,i7 branching ratio calculation 121.2.7 Long distance effects 151.2.8 Relationship to the CP violation problem 161.2.9 Estimate for K+ ÷ it.+v17 branching ratio 171.2.10 Non-Standard Model Physics K ; 191111.3 Experimental search 201.3.1 Background overview 251.3.2 Previous searches 272 The Apparatus 292.1 Kaon beam 292.2 Detector 312.2.1 Beam counters 362.2.1.1 Beam hole, B1 & B2 hodoscopes 362.2.1.2 Cerenkov counter 372.2.1.3 Beam wire chamber (BWPC) 392.2.1.4 Degrader, B3 & B3S counters 392.2.1.5 Lead-glass detector 402.2.1.6 B4 hodoscope 422.2.2 Target (TO) 432.2.3 I- and V-counters (IC and VC) 452.2.4 Drift chamber (DC) 452.2.5 Inner wire chamber (IWC) 492.2.6 Range stack (RS) 512.2.6.1 Transient digitizers (TD) 552.2.7 Photon veto system 572.2.7.1 Barrel Veto (BV) 602.2.7.2 Endcaps (EC) 613 Event Selection 633.1 Online selection 633.1.1 Level 0 653.1.2 Level 1 673.1.3 Level 2 68iv3.1.4 Level 3 693.1.5 Data Acquisition 713.1.6 Monitoring 723.1.7 Data Samples 743.2 Calibration 743.3 Offline selection 763.3.1 Event reconstruction 773.3.1.1 TARGET 773.3.1.2 DC-SETUP 783.3.1.3 DC-CHI2 803.3.1.4 RS-TRACK 813.3.1.5 RSPC 823.3.1.6 ICOUNTER 823.3.1.7 FIDUCIAL 843.3.1.8 ZDCTZ 853.3.2 Timing 863.3.2.1 PROMPT 863.3.2.2 TRKTIM 873.3.3 Photon Veto 883.3.3.1 INTIME 903.3.3.2 INTSE 913.3.3.3 INTEB 943.3.3.4 INT_RIV 943.3.3.5 PB-GLASS 973.3.3.6 B4TD 983.3.3.7 NDC 1013.3.3.8 DISENPI 1013.3.3.9 DISENK 101v3.3.4 Pion identification3.3.4.1 RGEMOM3.3.4.2 MASS3.3.4.3 KINSCORE3.3.4.4 DEDXRS3.3.4.5 FASFITPI and3.3.4.6 TDJVIDA... ELVETO3.3.4.8 TDFOOL. ELECTRON3.3.5 Beam cuts3.3.5.1 CERENKOV. BWPC . . BMHOLE3.3.5.4 B&CNTR3.3.6 Vertex Cuts3.3.6.1 TGTRACK.. NK3.3.6.3 TGFIT . . VTXYCA3.3.6.5 ZK.EK . . EB&EK101102102102103FITPI 1051081091111111121121131141141151151171171221251251261293. search region (KINCUT)Offline cuts summary3.4 First Analysis Pass 1294 Background Studies 1334.1 1989 Background studies 1374.1.1 K ,‘ 137vi4.1.2 Muons 1434.1.3 Beam piousirirev (Ke4)1989 Background summaryBackground studies._4.2.1.1 Method Method 2Radiative K.,r2Muons4.2.3.1 Kinematic Cuts5 Data Analysis and Results5.1 Final Analysis5.1.1 1989 Data5.1.1.1 1989 Pass25.1.1.2 1989 Pass35.1.2 1991 Data1471491491491501521551581591611641641651661691731771771791821841841841841851851454. 19914. TD cuts4.2.3.3 Muon background estimate4.2.4 Beam pions4.2.4.1 Two particle background4.2.4.2 Single particle background4.2.5 K+ ,. .+e+y (K4)4.2.6 Charge exchange4.2.6.1 “2 — K2—7reWe4.2.7 Hyperon production4.2.8 1991 Background summaryvii5.1.2.1 1991 Pass25.1.2.2 1991 Pass3. 1991 Pass45.2 Acceptance5.2.1 K,22 measurements5.2.1.1 1989 Jt’,22 measurements5.2.1.2 1991 K,22 measurements5.2.2 K,.2 measurements5.2.2.1 1989 K2 measurements5.2.2.2 1991 KT-2 measurements5.2.3 ir-scat measurements5.2.3.1 TD cuts5.2.3.2 Kinematic cuts5.2.4 Monte Carlo measurements5.2.5 Final Acceptance5.2.5.1 Scalar and tensor interactions5.2.5.2 11+ .‘5.3 Integrated kaon flux5.4 I( branching ratio measurement5.5 Final results5.5.1 K ,‘5.5.2 Scalar and tensor interactions5.5.3 K .‘6 Discussion6.1 Origin of the observed 1991 events6.2 K2 background6.3 K2 peak kinematics6.4 Photon Veto185188192198199199202206206206208208213214215218218219221223223225225227227229231232viii6.5 Other cuts 2346.6 Analysis method 2366.7 Consistency between 1989 and 1991 results 2377 Conclusion 2397.1 Possible improvements 240Bibliography 243A BNL E787 Collaboration 247B Analysis details 248B.1 Background studies 248B.2 Acceptance 256B.3 Integrated kaon flux 257B.4 K.2 branching ratio measurement 260C Monte Carlo Simulation 262D Contribution to BNL E787 264ixList of Tables1.1 Background processes to J(+ 263.2 Trigger levels rejection and execution time 643.3 Description of monitor trigger requirements 743.4 Summary of the irv7 data samples 743.5 Accidental rates in various detector subsystems for hits above 1 MeV 903.6 Parameters for INTIME cut (1991 data) 913.7 Parameters for INTSE cut (1991 data) 943.8 Photon veto cut parameters for 1989 data 943.9 Photon veto cut parameters for single end hits for 1989 data 973.10 Upper bound set for the K+ , kinematic search region 1273.11 Summary of all offline analysis cuts 1303.12 Summary of all offline analysis cuts (continued) 1313.13 Parameters for Passi photon veto cuts 1313.14 1989 Passi results 1313.15 1991 Passi results for one third of the data sample 1324.16 r0 detection inefficiency 1424.17 Effect of kinematic and TD cuts on 1989 muon background 144xSummary of 1989 background estimates.149Final analysis to determine,for K7r2 background estimation (Method 1) 151K,1-2 peak to tail event ratio for various levels of photon veto 153Analysis results for K2 background sample (Method 2) 153Event selection for data sample used to determine the rejection of the TGFIT cut.154Event simulation and analysis results for Ic’2 background 157Estimate of pion contamination in muon sample for muon background kinematicstudies. . 161TD rejection of muon backgroundPhoton veto rejection of muon backgroundTwo beam particle background analysisSingle beam particle background analysisInteraction products multiplicity and average energy for ir stoppingSummary of 1991 background estimates1989 Pass2 results1989 Pass3 results1991 Pass2 results5.34 Results of full analysis for 30% of the 1991 Pass2 sample 1895.35 Characteristics of the remaining events after full analysis of 30% of the 1991 datasample 1905.36 Results of full analysis for the entire 1991 Pass2 sample 1914. carbon. . 1721831851861885.37 Characteristics of the remaining 1991 events after full analysis of the entireirv77 data sample 1925.38 Parameters for tighter 1991 INTIME cut 1955.39 Parameters for tighter 1991 INTSE cut 1955.40 Acceptance of reconstruction cuts for 1989 data measured with K,2 decays. . . . 2005.41 Acceptance of photon veto, event reconstruction, timing and vertex cuts measured with I(2 decays for 1989 data 2015.42 Acceptance of event reconstruction cuts for 1991 data measured with K2 decays. 2035.43 Acceptance of photon veto and beam cuts measured with K,2 decays for 1991data 2045.44 Acceptance of delayed coincidence cuts and IC trigger cut measured with‘(p2 decaysfor 1991 data 2055.45 K2 event selection from 1991 Kir2(1) monitor data 2075.46 Acceptance of event reconstruction cuts measured with I(ir2 decays for 1991 data. 2075.47 Acceptance of FITPI and FASFITPI cuts for each range stack layer 2115.48 Acceptance of 1989 TD cuts other than FASFITPI and FITPI for each rangestack layer 2115.49 Acceptance of 1991 TD cuts other than FASFITPI and FITPI for each rangestack layer 2125.50 Muon escape correction 2125.51 Overall TD acceptance for 1989 data 2135.52 Overall TD acceptance for 1991 data 2135.53 Acceptance of kinematic cuts for 1989 data 214Xli5.545.555.565.575.585.595.605.61interactionsI(2 peak position and width for various data samplesNumber of events in J(7r2 peak region for 1991 dataBeam pion background analysis for 1989 data1991 K2 background sample for estimation method 1Analysis results for application of all cuts on 1991 events in the ‘cZT2 peak1991 Muon sample from 7rv17 levO data for kinematic cuts1991 Muon sample from KK2(1) data for kinematic cutsBeam pion background event selection from 1991 irv7 Passl data“e4 background simulation and analysisB.72 Kaon charge exchange background simulation and analysis for K —*decay.214215216217218221223225254KINSCORE cut acceptance for 1991 dataAcceptance factors determined with Monte Carlo simulation.Final K+ -+ vi7 acceptance table for 1989 analysisFinal K+ ,‘ K+7 acceptance table for 1991 analysisFinal calculated acceptance for K+ ÷ +j,7 via scalar and tensor interactions.Calculation of f3 for 1989 and 1991 dataCalculation of I(2 branching ratio for 1989 and 1991 dataCalculation of K+ ÷ +,j7 branching ratio 90% confidence level upper limit for1989 and 1991 data5.62 Branching ratio upper limit (90% C.L.) for K+ * K+y7 via scalar and tensor6.636.64B.65B.66B.67B.68B.69B .70B.71225232234249• . . . 250region. 251• . . . 252• . 252• 253253xiiiB.73 Kaon charge exchange background simulation and analysis for Kdecay 255B.74 + production background simulation and analysis 255B.75 K —* irv7 simulation and analysis (1991 data) 256B.76 Analysis of 1989 KJL2(1) data (real and Monte Carlo) for the f3 correction factor. 257B.77 Analysis of 1991 I(2(1) data (real and Monte Carlo) for the f8 correction factor.257B.78 Acceptance factors for 1989 I(,2 acceptance correction 258B.79 Acceptance factors for 1991 K2 acceptance correction 259B.80 Analysis of I(ir2(l) monitor data and Monte Carlo simulated data for the 1989K1-2 branching ratio measurement 260B.81 Analysis of Kir2(1) monitor data and Monte Carlo simulated data for the 1991K2 branching ratio measurement 261xivList of Figures1.1 Feynman diagrams for electron—proton electro-magnetic scattering 51.2 Feynman diagram for neutron decay in Fermi theory 61.3 Feynman diagram for neutron decay in the Standard Model 81.4 Second order Feynman diagrams for K+ ÷ +j47 for three generations of quarksand leptons 131.5 Relation between j+ . ir+,i and K+ ..+ 7jOe+ve decays 141.6 Examples of long distance effects 151.7 Unitarity triangle 161.8 Expected K+ .+l)7 branching ratio as a function of the top quark mass. . 181.9 7r+ momentum spectrum for K+ * +7 with Standard Model V-A couplingand hypothetical scalar or tensor couplings 191.10 Final state charged particle momentum distribution in the rest frame of theK+ for K+ * +p and the seven most likely K+ decay channels 211.11 Momentum, kinetic energy and range spectrum in the rest frame of the K+ forcharged particles in K+ +J)p,‘2 , K2 and K+ —* lr+7r decays 231.12 Historical progress in the experimental search for K+ ...* 282.13 Schematic diagram of the LESB1 beam line 302.14 Schematic side view of the E787 detector 32xv2.15 Schematic end view of the E787 detector 332.16 Detector display of a .‘ -+-° event 352.17 Schematic side view of the beam counters system for the 1991 run 362.18 erenkov counter schematic diagram 382.19 Schematic diagram of a section of one of the BWPC wire planes 392.20 Lead-glass detector schematic side view 412.21 Schematic end view of the target, I-counters and V-counters 452.22 Target and I-counters event display for K+ ÷ event 462.23 Schematic side view of the target, I-counters and V-counters 472.24 Drift chamber “jet” cell design 482.25 End view of drift chamber cell boundaries and fitted particle trajectory 492.26 -+ total momentum distribution for K2 events 502.27 Schematic end view of a section of the inner wire chamber (IWC) 512.28 Schematic end view of one range stack and barrel veto sector 542.29 Total measured energy and range distributions for the -+ from Jt’2 decays. . . . 542.30 Range stack counter pulses recorded with transient digitizers 582.31 Range stack counter pulses recorded with transient digitizers (expanded timescale) 592.32 Schematic design of one endcap module 623.33 Accepted fraction versus delayed time for the online delayed coincidence requirement 67xvi3.34 TD information from the stopping counter for events accepted by the online piondecay search 703.35 Schematic diagram of 1991 data acquisition system 733.36 Number of struck drift chamber wires outside of the reconstructed track 803.37 Geometry conventions used for ICOUNTER cut 833.38 Difference between measured and estimated I-counter energy 843.39 Kaon decay vertex z position and + track dip angle 853.40 ZT versus ZDC distribution for 1989 irvi7 Pass 1 data 863.41 T -T distribution for 1991 rvv events 873.42 Logarithm of the x2 probability for the TRKTIM cut for K2 events 893.43 Energy versus time distribution of hits in the various subsystems for the INTIMEcut for 1991 7rv7 data 923.44 Energy versus time distribution of hits in the various subsystems for the INTIMEcut for 1991 K2 events 933.45 Energy versus time distribution of hits for the various INTSE cut categories for1991 irv7data 953.46 Energy versus time distribution of hits for the various INTSE cut categories for1991 K2 data 963.47 TD multiplicity pulse from lead-glass counter 983.48 Lead-glass detector time versus delayed coincidence time for iriJi7 events 993.49 Tb4 — Trs versus log10xfor B4 counter TD fits (1991 data) 1003.50 KINSCORE results for pions and muons 104xvii3.51 Measured minus expected energy in range stack layers A, B and C for 1989irvi7 data (DEDXRS cut) 1053.52 TD information and fit results for a pion candidate 1063.53 E and variables from FITPI cut for pre-selected + 1083.54 Base 10 logarithm of the pion probability distribution for samples of pre-selected-+ and for 1991 data 1093.55 TD.MDA results for pions and muons 1103.56 Time of pion ierenkov hits with reference to Trs for 1991 7rv17 events 1123.57 Time of BWPC hits with reference to Trs for 1991 irzii7 events 1133.58 Energy measured in the B4 hodoscope for beam K+ and + 1153.59 Geometry conventions for TGTRACK cut 1173.60 Large angle scatter event rejected by the TGTRACK cut 1183.61 Large energy deposition by a rejected by the TGTRACK cut 1193.62 Photon conversion or multiple charged track K+ decay rejected by the TGTRACK cut 1203.63 Energy deposited by the in the target as measured by the TDs minus thevalues measured by the ADCs 1223.64 Target TD information and fit results for an event rejected by the TGFIT cut . 1233.65 VTXPCA components 1243.66 Relationship between Z, EK and EB4 for 1989 irz/i7 data 1253.67 Total range, energy and momentum of the lr+ for K2 background (solid line)and K+ ) +y7 Monte Carlo (dashed line) events 128xviii4.68 Example of background estimation.1364.69 Correlation between nuclear interactions and photon veto in J(i-2 background. . . 1414.70 background data sample with inverted photon veto cuts 1514.71 Kinetic energy spectrum of from decays 1564.72 Energy versus z-axis directional cosine for photons from ir0 decay in simulatedK1-2 and K27 events 1584.73 Total range versus total momentum for muon sample from irvi levO data 1604.74 distribution for muon background 1624.75 Total range versus total momentum for single beam particle background datasample 1684.76 Total range versus total momentum for Ke4 simulated background 1704.77 Kinetic energy at birth of the ir and e+ for simulated Ke4 events 1704.78 Energy deposited in scintillator by stopping 7r 1734.79 T -T distribution for K —* decays from charge exchange background. 1785.80 Kinematic distributions for 1989 events before the final cut 1875.81 Total range versus total momentum for 1991 events satisfying all Pass2 requirements 1895.82 Kinematic distributions for 1991 events before the final Pass3 cut 1935.83 Kinematic distributions for K+ ... +,)i7 Monte Carlo events before the final cut. 1945.84 Kinematic distributions for remaining 1991 events before the final cut for Pass4analysis 197xix5.85 Pion decay time distribution used to determine the acceptance of the FITPI andFASFITPI cuts (1991 data) 2105.86 Acceptance for K+ + as a function of Mxo, the mass of the recoilingsystem, for 1989 data 2195.87 Branching ratio upper limit (90% C.L.) for K .‘ as a function of Mxo,the mass of the recoiling system 2266.88 Upper limit on the number of 1991 K,.2 background events as a function of theTGFIT cut rejection 2306.89 VTXYCA components for events passing the cut 235xxAcknowledgementAs I finally bring this work to a conclusion after so many years of research, I look back andrealize how fortunate I was to interact with the people in the BNL E787 group. Pretty much allI have learned as an experimentalist I owe to them. I can honestly say that I benefited from theknowledge of each and every one of them. There were of course some key figures: My advisor,Jean-Michel Poutissou, who was always there to help me and communicate some of his greatpassion for research, even though his duties made him one of the busiest people at TRIUMF:Doug Bryman, on whom I could always count to put me back on the right track when I gotconfused, and who always made sure that our research environment was the best it could be:Finally, Akira Konaka, whose endless enthusiasm and insightful ideas were a constant source ofinspiration. Thanks to all.I was just as fortunate to have the support of some wonderful people outside of the academicworld. Even though they were so far away, my family managed to provide constant encouragement. They have taught me that even though it is nice to gain knowledge about the intricaciesof the Universe, there is no substitute for good values of honesty and determination. Merci dufond du coeur a mes parents Louise et Gilles, et ma soeur Line.My in-laws, Jean and Ian Beveridge, were always there to help and make me feel like theirson. Many thanks to them. Also thanks to the Norbies (who ever came up with that nameanyway?) for the soccer games and the long discussions about the space-time continuum (there,I said it) over a few (!!!) beers.And finally, I must thank my wife Jennifer, whose undying support pulled me through thegood and bad times. I cannot find the right words to express my gratitude to her, and howmuch it means to me to have her as my companion. I just hope that over the years I will beable to repay her for all she did for me.xxiTo the memory ofJ. Armand SamoisetteX)(iChapter 1The Experiment1.1 IntroductionThe current theoretical framework describing the interactions of elementary particles, knownas the Standard Model, is one of the most resounding successes of modern physics. Over thepast 60 years, knowledge of the basic constituents of matter and their interactions has evolvedthrough many experimental and theoretical breakthroughs; this knowledge is now embodied inthe Standard Model. In the past several years, essentially all results predicted by the StandardModel have agreed with amazing accuracy with experimental observations.Despite this great success, the Standard Model is lacking in some ways. To calculate physical observables, it requires a large number of quantities, such as elementary particles masses,to be taken as parameters and be determined experimentally. The model does not make anypredictions for these parameters as to their relationship or origin. Furthermore, elementaryparticles appear to be grouped in “families”, or “generations”; the Standard Model accommodates this very well by using mathematical group theory representations. However, thereis no indication as to the origin of these families and, in fact, no compeffing reason to havemore than a single family, other than perhaps to provide a mechanism for the violation of CP,the combined operation of charge conjugation (particle—anti-particle interchange) and parityinversion.For these reasons, recent experimental and theoretical efforts have centered on the search forphenomena that are not described by the Standard Model, or for deviations between calculatedobservables and the experimental measurements. The experimental effort has been directed at1Chapter 1. TheExperiment 2two fronts : the energy frontier and the precision frontier. By pushing the available energy inelementary particles coffisions to higher and higher levels, smaller and smaller distances can beprobed, potentially revealing structure hitherto undiscovered. The large available energy alsoallows for the production of new particles which might herald the discovery of new phenomena.Undiscovered interactions or particles can also be observed indirectly through their effects onlower energy processes; this requires the investigation of such processes using high precisiontechniques. This could be a search for processes not allowed by the Standard Model, or asearch for deviations from predictions for allowed but rare processes.This thesis describes one such endeavour, the experimental search for the decay of a positively charged K-meson (or kaon) into a positively charged ir-meson (or pion) and a neutrino—anti-neutrino pair, represented byirvi7. (1.1)This decay is allowed in the Standard Model, and is predicted to occur approximately oncein every 10 biffion kaon decays; it has never been observed experimentally. One of the mostattractive features of this process is the reliability of the theoretical calculation for its ratewithin the Standard Model. The decay rate is more commonly expressed as a branching ratio,the ratio of the decay rate for a particular process to the total rate for all possible decayprocesses. Some level of uncertainty remains in the calculation of the J(+ branchingratio due to the imprecise knowledge of some of the parameters required for the calculation. Ameasurement of the branching ratio would then allow the determination of these parameterswith very little theoretical uncertainty. Also, an observation of this decay at a rate deviatingsignificantly from the theoretical prediction would clearly be an indication of phenomena notaccounted for by the Standard Model.The remainder of this chapter will discuss the decay J(+ , +vj7 within the context ofthe Standard Model and present an overview of the experimental search. Chapter 2 describesthe apparatus and Chapter 3 the experimental procedure. Studies of background processes aredescribed in Chapter 4. Results are described in Chapter 5 and discussed in Chapter 6. Finally,a conclusion is given in Chapter 7.Chapter 1. The Experiment 31.2 Theoretical considerations1.2.1 The Standard ModelA full description of the Standard Model would require far too much space for inclusion in thisthesis. Extensive coverage of the subject can be found in the literature (see [1] for example);only a very brief overview will be presented here, introducing the key elements of the model.Because the decay K+ ._* .+i,iy proceeds via the weak force, more details on weak interactionswill be given below.In our present description of the basic building blocks of Nature, elementary particles areclassified in two groups, quarks and leptons. Both groups are spin 1/2 fermions; experimentsplace limits on their structure at the 10—17 cm level. There are currently six known leptons andfive quarks, with strong theoretical bias and some experimental evidence for a sixth quark. Inaddition, each quark or lepton has an anti-particle counterpart, with the same mass and spinangular momentum but opposite values for other quantum numbers. The leptons consist ofthe electron (e), the muon (j) and the tau (T), and their associated neutrinos, Ve, z and v.The e, t and T leptons each have unit electric charge; in fact, essentially all their propertiesare identical except for mass. The neutrinos are electrically neutral, and current experimentalevidence is consistent with them being massless. The quarks have fractional charges (in units ofthe electron charge); three have charge -1/3, the down (d), strange (s) and bottom (b) quarks,and three have charge +2/3, the up (u), charm (c) and the as yet unconfirmed top (t).Elementary particles interact via the four fundamental forces : electro-magnetism, weak,strong and gravity. These forces are mediated by the exchange of particles called intermediatevector bosons. Relativistic quantum field theory is the theoretical framework used to describethe interactions of elementary particles. The best example of such a theory is quantum electrodynamics (QED), developed in the early 1930’s, describing the interactions of charged particlesand photons. This theory has enjoyed tremendous success, and has been tested with greataccuracy; it served as a blueprint for theories describing other interactions.In 1933, Fermi proposed his theory of weak interactions to describe nuclear beta decay.Chapter 1. The Experiment 4The theory remains to this day, with a few modifications. A major breakthrough came inthe 1960’s by Glashow, Weinberg and Salam, who proposed a model unifying the electromagnetic and weak interactions into a single framework based on the mathematical groupSU(2) x U(1); it described the weak force as the exchange of massive bosons, and predictedtheir mass. Confirmation of the existence of these particles only came recently in investigationsof high energy proton—anti-proton coffisions [2]. This model became known as the StandardModel of electro-weak interactions. The Standard Model now also encompasses the descriptionof strong interactions by quantum chromodynamics (QCD), a theory based on the mathematicalgroup SU(3). Strong interactions involve only the quarks and the massless mediators of theforce, the gluons.1.2.2 Weak InteractionsThe weak interaction theory proposed by Fermi was analogous to QED in that it describedprocesses in terms of the interaction between two currents. Figure shows a graphicalrepresentation of the electro-magnetic interaction between an electron and a proton (assumedpoint-like) as the exchange of a photon, carrier of the force. Such representations, or Feynmandiagrams, are associated with terms in a perturbative series describing the interaction. Figure shows a first order term and figure shows an example of a second order diagramdescribing the same process. These terms are used to calculate the invariant amplitude for theprocess; the square of the amplitude is proportional to the probability for the process.The amplitude for the QED process in figure is given byM=(eyb) (4) (-ee7e) (1.2)where the and b are four-component spinors, solutions of the Dirac equation describingthe proton and electron, y1 are the Dirac matrices (j = 0, 1, 2,3), q is the momentum of theexchanged photon and e is the electric charge of the electron and proton. Here we have usedthe Heaviside—Lorentz convention for electro-magnetic units in which e0, the permittivity offree space, is set to unity, and “natural” units in which h and c are also set to unity. Withthese conventions, we have e2 = 4irc, where 1/137.036 is the fine structure constant. TheChapter 1. The Experiment 5Figure 1.1: Feynman diagrams for electron—proton electro-magnetic scattering;a) first order and b) example of second order interaction.amplitude M can be re-written ase2M=__JiJeq2 P(1.3)where J and J are the proton and electron electro-magnetic currents respectively; the squareof the electric charge e2 is the constant coupling the two currents.The Fermi theory was used to describe processes such as neutron decayn—p e 11e (1.4)The process, or its equivalent crossed reaction iwe —* pe , was viewed as a four particle pointinteraction, as shown by figure 1.2. The amplitude was given byM = G(’bp7n)( ebii)= GFJJJ, (1.5)where J and J’ are the neutron—proton and electron—neutrino weak currents respectivelyand GF is the coupling constant for the interaction, determined by experiment.This theory was successful at describing some properties of neutron decay and beta decays,but not all. One of the keys to solving this problem was the fact that Fermi had used only avector form for the weak interaction. The y term in equation 1.5 behaves like a vector underea)eepb) e eepJp; J1LChapter 1. The Experiment 6Figure 1.2: Feynman diagram for neutron decay in Fermi theory. The hashedcircle indicates the point interaction.Lorentz transformations. Other possibilities, namely scalar, tensor, axial vector and pseudoscalar, had to be investigated. The next twenty years saw attempts at finding the correctstructure of the weak interactions. One of the major stumbling blocks involved the decay of thenewly discovered strange particles (particles containing a strange quark); these particles wereproduced in strong interactions, but they displayed the relatively long lifetime characteristicof weak interactions. The problem, the so-called O—T puzzle, was that the positively chargedkaon, K+, was observed to apparently have two different decay modes, J(+ .... and—* , in which the final states have opposite parity. Originally it was thought thattwo different types of charged kaons existed, the 0 and T, since it was believed that parity (orspace inversion) was conserved in all interactions.In 1956, Lee and Yang [3] carefully reviewed all available information on the weak interactions and argued that the problems could be solved if these interactions violated parity, andthat this had never been tested experimentally. Experiments soon confirmed that this was indeed the case. It was eventually shown that the term in the weak current should be replacedby 71L(l — 75) [4]. The y1yS term transforms like an axial-vector under Lorentz transformation,hence the usual designation of weak interactions as having V — A structure.For many years, it was believed that although they violated parity (P), weak interactionswere invariant under the combined operation CP, where C is the charge conjugation operator, orparticle—anti-particle interchange. In 1964, a small CP violating effect was observed in neutral‘elfVeIiepJI4Chapter 1. The Experiment 7kaon decay [13]. To this date, it is still the only known system in which CP violation has beenobserved. It will be shown below how a measurement of the branching ratio for the processmay help to unravel the origin of this phenomenon.In the modern version of the theory [5], the weak interactions are viewed as the exchange ofmassive vector bosons between quarks and leptons and among themselves. This constructionreduces to the Fermi point interaction for low energy processes where the momentum of theexchanged boson is much lower than its mass. Quarks and leptons are grouped into doubletsof the mathematical group SU(2)(e’ (V,Li (VTe) ) rU C td) ) bsuggesting a “family” or generation structure to elementary particles. Doublets from eachgeneration are treated identically by the theory.In this framework, the example of neutron decay can be represented by the Feynman diagramof figure 1.3. The neutron and proton are identified as groups of three quarks, udd and uudrespectively. One of the d quarks of the neutron decays into a u quark with emission of a Wboson; the other quarks do not participate in the interaction and are referred to in this case asspectators. The emitted W then decays to an electron and an anti-neutrino.1.2.3 Quark mixingAnother problem of the theory of the weak interactions in the early days was the calculationof the decay rate for strange particles, which did not agree with experimental observations. Itappeared that the coupling constant GF, determined from beta decay, was not universal forall weak decays. In 1963, Cabibbo [6] proposed that the weak current for strongly interactingparticles (hadrons) was a sum of a strangeness conserving (j) and a strangeness non-conservingChapter 1. The Experiment 8e1Wd U)n d dpu u)Figure 1.3: Feynman diagram for neutron decay in the Standard Model.(j,) parts, related byJ = cos6j + sin 6j (1.6)where the angle O is now known as the Cabibbo angle. Therefore, for the decay of strange particles, the effective coupling was GF sin 8 instead of simply GF. Cabibbo obtained a consistentvalue for 8 from the available data on various weak decays. The currently accepted value is= 0.22.In the framework of quark interactions, and for a situation where only three quarks areknown (u, d and s), this formulation is equivalent to saying that the weak eigenstate for thecharge -1/3 quarks (d’) is an admixture of the d and s (quarks strong interaction eigenstates).The weak current can then be written as== u-y(1—75)(dcos9+ssinO) (1.7)where u and d represent the quark spinors. Because it transforms a quark of electric charge-1/3 into a charge +2/3 quark (and vice-versa), this current is referred to as the charged weakcurrent. In contrast, the electro-magnetic current of QED is neutral. This leads to a discussionof the possibility of weak neutral currents.Chapter 1. The Experiment 91.2.4 Neutral currentsIn the early days of weak interactions, there were no reason to consider weak neutral currentssimply because there were no experimental observation of such currents. This absence of observed weak neutral currents was a serious hurdle in the acceptance of a unified theory of theweak and electro-magnetic interactions [5]. Furthermore, we see that if we form the neutralcurrent between the weak interaction quark eigenstates using the formalism of Cabibbo, we get,recognizing only u and d’ as ingredients in the theoryJNC= u+JId’== iu + dd cos2 O + s sin2 8 + (ds + d) sin O cos (1.8)where the -y(1 — 75) factors have been omitted for clarity. In addition to neutral interactionsbetween the three types of quarks, or flavours, we have interactions where an s quark is transformed into a d quark, and vice-versa. Interactions of this type are known as flavour-changingneutral currents. Early searches for these interactions included K+ + 71.+e+e, K —and K+ + lr+1,Ti, but no evidence was found. The first search for J(+ — 1111 was in 1969,finding that the branching ratio was less than 1 x iO’ [32].In 1970, Glashow, fliopoulos and Maiani [7] proposed that there existed another charge+2/3 quark analogous to the u quark, which they named charm (c). The possibility of neutralcurrents remained, but the inclusion of the charm quark removed the flavour-changing neutralcurrents. This can be seen by arranging the quarks of same charge in column vectors U and V(u IdUEI I DEl\C)The Cabibbo mixing is then given by a unitary rotation matrix MD’=MD( d’ ( cos O sin 8 ‘\ ( d’\I I = I II I• (1.9)\ SI) — sin O cos O ) \ s )Chapter 1. The Experiment 10We can then write the neutral current as a generalization of the previous guess= iu+7v’= UU+DMMCD= uu+DD= Zu+ëc+dd+s (1.10)where the -y(1 — 75) terms have again been omitted for clarity. We see that all we have leftare neutral currents between quarks of the same flavour. This cancellation of flavour-changingneutral currents, shown here for first-order interactions, is exact to all orders; it is commonlyreferred to as “GIM mechanism”. This mechanism would prohibit decays such as *however, as will be discussed below, the mass of the different quark flavours being unequal,this exact cancellation is spoiled and a small non-zero amplitude remains at second order andbeyond.Neutral currents were also predicted for leptons. The first direct evidence for neutral currents came in 1973 in neutrino and anti-neutrino interactions in a bubble chamber [8]. Also, in1974 the charm quark was discovered simultaneously by two research groups [9, 10], establishingthe theory of weak neutral currents on firmer ground. In modern electro-weak theory, neutralweak current processes are viewed as the exchange of neutral weak bosons (Z°). As with thecharged weak bosons (W+ and Wj, the Z° was discovered only relatively recently [11].1.2.5 Three generations quark mixingThe unitary matrix M introduced above, was described by a single real parameter O, andcombined the charge -1/3 mass eigenstates to obtain the weak interaction eigenstates for twogenerations of quarks. In 1973, Kobayashi and Maskawa [12] realized that for a model withthree generations of quarks, the unitary matrix would be described by three real angles and onecomplex phase, and that this complex phase can describe for CP violation. This provides a natural link between the existence of three generations of elementary particles and the phenomenonof CP violation.Chapter 1. TheExperiment 11For three generations of quarks, we can write the 3 x 3 rotation matrix (usually referred toas the CKM, or Cabibbo—Kobayashi—Maskawa matrix) in the general formVudVusVubV= Vd V Vcb (1.11)Vtd V3 VtbNote that the cancellation of flavour-changing neutral currents by the GIM mechanism is stillvalid for the three generations case, guaranteed by the unitarity of the matrix V.In their original paper Kobayashi and Maskawa parameterized the matrix V asC1 —8[C3—8183V = s1c2 c123 —s23e8 c12s3+s2c3e (1.12)8182 C182C3 + C283e C182S3 — C2s3ewhere c cos 0, and s sin 0 and the parameters 01, 02, 03 and are real. These parametershave to be determinçd by experiment. In principle, all the elements Vj,j can be determinedindependently, over-constraining the four parameters describing the matrix. In practice, someelements, such as Vtd, are not accessible directly by current experiments. As will be seen below,processes like K+ _* 71.+1Jj7 can be used for an indirect determination of those elements.Current measurements of the elements of the CKM matrix show that it is nearly a unitmatrix, with the diagonal elements close to one and with small off-diagonal elements. Wolfenstein [14] introduced a useful and much simpler parameterization of the CKM matrix, in whichhe set V’L8 = sin 0 = A and expanded the other elements in powers of A. To order A3, thematrix has the form1—A2 A AA3(p—ii)—A 1 — ‘A2 AA2 (1.13)AA3(1—p—i) —AA2 1where A, p and 17 are real parameters. In this parameterization, i determines the CP violationphase.Chapter 1. TheExperiment 121.2.6 K j/j7 branching ratio calculationAs noted above, the decay K+ _* +/j7 is strictly forbidden at first order in the StandardModel. Inami and Lim [15] were the first to compute the branching ratio for a general casewith an arbitrary number of generations of quarks and leptons. Figure 1.4 shows the secondorder Feynman diagrams contributing to the amplitude : a box diagram and two so-calledpenguin diagrams. Note that each diagram involves a loop containing a charge 2/3 quark.These ioops have two quark vertices, one transforming an s quark into a charge 2/3 quark andone transforming the latter into a d quark. These vertices bring VVjd terms to the amplitude,where Vjj are CKM matrix elements, each multiplied by a function dependent on the massof the quark in the ioop. The overall amplitude is a sum of the contributions from all quarkflavours; if all had the same mass, the mass dependent functions could be factored out and theamplitude would contain a sum of the form VVid, where N is the number of generations.But this sum is simply the product of two columns of the CKM matrix, and is zero since thematrix is unitary. Therefore, the GIM mechanism makes the amplitude vanish if all quarkshave same mass.As this is not the case, we expect a small amplitude to remain at second order. For the caseof three generations of quarks, and assuming three light neutrino types, the formula obtainedby Inami and Lim for the branching ratio can be expressed asB(K —+ irvY) =3a2B(K-_*7r°eve) IVcdD(Xc)+VtsVtd1NXt)I2 (1.14)where a is the electro-magnetic fine structure constant, 8w is the Weinberg angle defined bycos8w = Mw/Mi, where Mw and M are the masses of the W and Z bosons respectively,and D(x) is given by1 3 (4_x)2 x 3 x.D(x) = [1 + (1— — (1— 2]xlnx. + —— ) (1.15)where x, with m the mass of the heavy quark in the ioop (charm or top). Inthe expression for D(x), it has been assumed that the mass of the charged leptons is smallcompared to the mass of the W boson [22].Chapter 1. The Experiment 13SUIU,C,tLI 1/+dU<1>0<0,zI<‘ U,C,t -,‘I+ss.. — ——>Figure 1.4: Second order Feynman diagrams for K+ +7 for three generations of quarks and leptons.< - 0<>VU)C,tSUSUVdiTULIVd +UChapter 1. The Experiment 14Effects due to strong interactions between the kaon in the initial state and the pion inthe final state of J(+ —* +1jj7 decay are taken care of by relating B(K+ —* 1r+v7) to thebranching ratio for the first order decay K+ O€+Ve [16]. This can be seen in figure 1.5:both decays contain a kaon in the initial state and a pion accompanied by two light leptons inthe final state. The two decays can be related easily by strong isospin. The branching ratio for. ir0ev has been measured to be (4.82±0.06)% [17]. Interactions between the initial andfinal state and effects due to the structure of the hadrons involved in the process often lead tocomplications in the theoretical calculation of the decay rate. The simple relationship allowingthe extraction of the relevant quantities from a known process is one of the main virtues ofirv271/+ +V01)Figure 1.5: Relation between K+ +,)i7 and K+ ...+ Oe+j, decays.The functions D(x) must be corrected for strong interaction effects in the quark loops.These corrections have been calculated to first order in QCD perturbation theory [18]; theresult was to reduce the charm quark contribution to the amplitude by about 35%. However,uncertainties in the calculation resulted in an uncertainty of 20—30% in the branching ratio. Arecent complete calculation to first order for the correction to the top quark ioop and a next-to-leading order calculation for the charm quark correction has reduced this purely theoreticaluncertainty to only about 7% [19].With these corrections made, the only parameters in equation 1.14 that are not well knownare the CKM matrix element Vtd and the mass of the top quark, assuming that IVtsI IVcbI.Recently, evidence has been reported for top quark production in proton—anti-proton coffisions,with a mass of 174 ± 10 GeV/c2 [20]. This value is consistent with the value determined2nd orderinteroction1st orderinteraction+ea) K-itv + 0+b) K -ir e VeChapter 1. The Experiment 15indirectly through electro-weak radiative corrections [21]. This would leave Vj as the only undetermined parameter in equation 1.14. Therefore, a measurement of the K+ _* +y7 branchingratio would provide a determination of Vtd with very little theoretical uncertainty. Other processes, such as B°—B° mixing and CP violation in the neutral kaon system can presently yieldvalues for Vd, but with considerable theoretical uncertainty. As will be discussed below, thesevalues can be used to estimate the K+ _ 1l.+j,j7 branching ratio.1.2.7 Long distance effectsThere are contributions to the amplitude for the decay K+ * +z,E7 from processes other thanthe second order diagrams of figure 1.4; the latter are usually referred to as short distanceprocesses. In long distance processes, the K+ decays through an intermediate virtual mesonstate which results in a final state containing a and two neutrinos. Figure 1.6a shows anexample of such a process where the decay is through a virtual muon. The rate for this andsimilar processes has been calculated [22, 23]; the sum of all contributions results in a branchingratio of order 10—13, which is significantly smaller than what is expected from the short distanceamplitude. A recent calculation of long distance effects based on chiral perturbation theory [24]essentially reached the same conclusion.++D +—b) K LFigure 1.6: Examples of long distance effects for a) K —* +i,i7 and b) KThis is in contrast to other second order weak processes such as —* . Figure 1.6bshows an example of a long distance process for this decay, which has been observed witha branching ratio of (7.4 ± 0.4) x 1O [17]. In this case, long distance effects contributesignificantly to the overall amplitude, making the extraction of meaningful quantities related1) 1)a) K-’iivi77,Chapter 1. The Experiment 16to short distance physics difficult. The absence of significant long distance effects is anotheradvantage of K+ 7r+vj1.2.8 Relationship to the CP violation problemOne of the main reasons for the importance of a measurement of Vtd is its relation to the CPviolation problem. As alluded to above, a non-zero complex phase in the CKM matrix wouldresult in CP violation. If we take the product of the first and third column of the CKM matrix,we obtain the following relationVudV+VcdV+VtdV=0 (1.16)which defines a triangle in the complex plane. This is known as the unitarity triangle, and isshown in figure 1.7a. Using the Wolfenstein parameterization of the CKM matrix and rescalingthe triangle by IViV*I, we get a triangle in the (p, ) plane, shown in figure 1.7b. Since is thecomplex phase, the position of the apex of the triangle defines the Standard Model contributionto CP violation. Currently, the position of the apex is not very well determined [25].a)Figure 1.7: a) unitarity triangle and b) same triangle rescaled by IVcdVI in the(p,i) plane.Writing the CKM matrix in terms of , A, p and , equation 1.14 can be recast to giveB(K+ +) 8 sin46w 1 — 2+ 1 +(1 — A2/2) D(x) 2 117B(K+_ir°e+v) 32 A48D2(x) — A2)4 D(x) —which defines a circle in the (p,17) plane, with radius proportional to the square root of the K+ ÷irvi7 branching ratio and center on the p axis slightly displaced from the point (1,0) [26]. Using‘7A b)itdtb(Ph?)C B (0,0) (1,0) pChapter 1. The Experiment 17this information combined with the ratio Vub/VcjI measured in B meson decays, which definesa circle centered at the (p,) origin, the apex of the unitarity triangle could be determined [27].Another way to determine the unitarity triangle would be to combine a measurement of theK+ +j4i branching ratio with a measurement of the neutral kaon decay K —*this determination would have almost no theoretical uncertainty [28]. Thus we see that ameasurement of the J( —* -+j,j7 branching ratio would greatly help in understanding theorigin of CP violation.1.2.9 Estimate for K —* rzi7 branching ratioAs noted above, present constraints on Vtd from other processes can be used to estimate thebranching ratio for K+ +7• Figure 1.8 shows the branching ratio for the sum of all knownneutrino flavours as a function of the mass of the top quark, taken from reference [29]. Theauthors obtained two different solutions for Vtd based on an analysis of the theoretical formulafor the experimentally determined CP violation parameter from neutral kaon decays. Thisanalysis was performed using experimental input for IVc&I and IVub/VcbI, both determined inthe decay of B mesons. Overlayed on the graphs is the one standard deviation range for thetop quark mass based on the reported evidence [20]. This restricts the allowed range for thebranching ratio toB(K —* rvI7) (0.5 — 4.5) x 10’° . (1.18)1.2.10 Non-Standard Model PhysicsThe predicted value of the K+ .+jj7 branching ratio in the Standard Model is quite firm,with the major limitation currently being the accuracy of the knowledge of Vtd and the mass ofthe top quark. Therefore, observation of this decay at a level significantly above the predictionwould be a clear indication for new physics. However, most of the possible scenarios for newphysics do not substantially increase the predicted rate. In reference [39], the authors reviewthe possibilities and conclude by describing K+ lr+z/17 as a “Standard Model standard”. Theleast exotic scenario would be the presence of a fourth generation of fermions with high mass.Chapter 1. The Experiment 18876t,30Figure 1.8: Expected K+ I.+i)i7 branching ratio as a function of the top quarkmass (Me), taken from reference [29]. The two graphs correspond totwo different solutions for Vtd. The dashed lines indicate the rangefor the top quark mass, assumed to be 174 ± 16 GeV/c2.This would enhance the decay rate if the couplings of the new charge 2/3 quark to the d ands quarks is not too small. Models such as multiple Riggs doublet, left-right symmetric andminimal supersymmetric produce no significant enhancement of the decay rate. In the caseof non-minimal supersymmetry and other exotics, enhancements are possible but the modelsmake no definite predictions for the rate.If non-Standard Model physics were involved in the decay K+ — lr+v7, it is likely that the-+ spectrum shape would be different than normally expected. Figure 1.9 shows the theoreticalr+ momentum spectrum in the rest frame of the K+ for K+ _* lr+z,i7, assuming a StandardModel V-A coupling and hypothetical scalar and tensor couplings. It is clear from this that adetermination of the i+ spectrum shape would be sensitive to non-Standard Model effects.An obvious change in the spectrum shape would also occur if the neutrinos had a finitemass. In the minimal Standard Model, neutrinos are assumed massless, but a small mass couldbe accomodated. The present limits of m,e < 5.1 eV/c2 (95% C.L.) and < 270 keV/c2(90% C.L.) [17] indicate that it would be very difficult to observe their effect on the K+I100 125 150 175 200 225 250 100 125 150 175 200M (GeV/c2) M (GeV/c2)225 250Chapter 1. The Experiment(I)C>,0-oFigure 1.9: + momentum spectrum for K+ +7 with Standard Model V-Acoupling and hypothetical scalar or tensor couplings.19lr+v17 spectrum. For the 95% C.L. upper limit is presently at 31 MeV/c2;a neutrino massof that order would affect the spectrum shape significantly, as well as its end-point. However,from various cosmological arguments must be less than a fraction of an MeV [17]. Therefore,until a very high statistics measurement of the spectrum shape of K+ * can be made,effects due to a finite neutrino mass are not likely to be observed by this experiment. K+ ,As will be discussed in the next section, the experimental signature for K+ * 71-+,)17 is K++ nothing. Therefore, this experiment is also sensitive to non-Standard Model processes ofthe type(1.19)where X° is any neutral weakly interacting particle or group of particles. The ir kinematicregion investigated in this experiment limits the mass of X° to the region 150 < Mxo <260 MeV/c2. Possibilities for X° include new bosons, a pair of Majorons [41] or a pair ofsupersymmetric particles. Some authors determined that the latter is not likely to contribute-T50 100 150 200Momentum (MeV/c)Chapter 1. The Experiment 20significantly [22]. Others have reported that the most favorable mass for new bosons producedin K+ ÷ is near 200 MeV/c2 [42]; also, the lower part of the 7r+ spectrum may beenhanced for Majoron production [43].The general theoretical conclusion about a non-Standard Model contribution to K++nothing is that although it is not likely, unexpected results are possible and should beinvestigated.1.3 Experimental searchBased on the expected K+ _* +z)i7 branching ratio, we see that a large number of kaons, of theorder of 10h1_1012, depending on the detection efficiency of the experiment, will be required foran experimental measurement. The experimental signature of K+ +j7 is very simple : acharged kaon decays to a charged pion and nothing else, since the two neutrinos in the final statecannot readily be detected. Figure 1.10 shows the ?r+ momentum spectrum for K+ 71.+7 inthe rest frame of the kaon, typical of a three body final state. The end point of the distributionis at p+ = 227 MeV/c. Also shown are the charged particle momentum spectra for the sevenmost likely K+ decays channels.All other kaon decay channels are potential sources of background in a search for K+ *+i,E7. A survey of K+ decays with a in the final state reveals that except for K+ —* 1r+v7,and the rare and as yet unobserved decay J(+ , R-+Ty [31], the final state also contains atleast one neutral pion, which decays to two photons’ with a mean life of 8.4 x i’ s, or apair of charged particles. Decays with no in the final state involve either a or e+, inmost cases accompanied by a , photons or other charged particles. Therefore, decays otherthan K+ . become backgrounds when either photons or other charged decay productsare not detected, or a charged lepton is mis-identified as a , or both.The two most prominent potential background processes are K+ ÷ (K2 ) and K++0 (K.2 ), with branching ratios of 63.51% and 21.17% respectively. Because they are twobody decays, their charged particle spectrum is mono-chromatic in the rest frame of the K+‘The Dalitz decay ir0 —+ 7e+e also contributes with a branching ratio of -.4.2%.Chapter 1. TheExperiment 21— I I I I —!LU (.64irir,r (.056) 1r1r° (.21)(.01).048, /‘o 50 100 150 200 250Momentum (MeV/c)Figure 1.10: Final state charged particle momentum distribution in the rest frameof the K+ for K+ .. -+7 (dashed line) and the seven most likelyK+ decay channels (the branching ratio is indicated in parentheses).There are also potential sources of background which do not involve K+ decay. Pions producedin proton—nucleus coffisions contaminate the kaon beam and could fake a decay.Also, a K+ propagating through matter can interact and produce a neutral kaon through thecharge exchange reaction K+n K°p; the neutral kaon can then result in a final state includinga lr+.Based on these facts, the following strategy was used in the design of the experiment1. Positive identification of the K+ . This defines the initial state and guards against nonK+ decay backgrounds.2. Observation of K+ decays at rest in the laboratory. This ensures that the two most important background processes K,2 and K2 can be clearly identified by their mono-chromatickinematic peak, which would be smeared by the Lorentz boost if the K+ decayed in flight.3. Require a delayed decay of the K+ . This guarantees that the K+ decay is at rest andfurther suppresses nonK+ decay backgrounds.Chapter 1. The Experiment 224. Positive identification of the in the final state.5. High efficiency photon detection.These points affected both the design of the apparatus used in the experiment and the analysisof the collected data. The identification of the K+ can be accomplished by instaffing in theincoming particle beam detectors sensitive to the particle type. The K+ are brought to restby placing in their path a block of material of appropriate thickness. Decay products of theJ(+ have to be analyzed by a spectrometer. In particular, the kinematic properties of chargeddecay products should be well measured to help in the identification of the -+ . Figure 1.11shows the distribution of momentum, kinetic energy and range in plastic scintillator for the-+ j J(+ +z/j7 and for charged particles from three other prominent K+ decays. Typicalexperimental resolutions were included in these distributions. Also shown in the figure is thekinematic region investigated in this work; more will be said on this below.The range of a particle is equivalent to its path length in a material. For a charged particleof mass M >> me, where me is the mass of the electron, kinetic energy loss is primarily throughionization of atomic electrons. Due to the random nature of the coffisions between the chargedparticle and the electrons in the material, the path length will vary for particles with identicalkinetic energy. The mean range of a charged particle of kinetic energy E is given byR= I: _dE/dx (1.20)where dE/dx is the mean rate of energy loss of the particle in the material. The latter is afunction of the velocity of the particle in a given material. There is therefore a direct relationshipbetween the kinetic energy and mean range of a particle. In particular, particles of a givenkinetic energy will have a different mean range depending on their rest mass. Hence, any twoof the momentum, kinetic energy and range can be combined to determine the particle type.In practice, because of finite experimental resolution, the measurement of all three quantitiesis necessary. Because of the significant difference in mass and energy loss behaviour betweenelectrons and pions, mis-identification of an e+ as a is not a major concern. However, muonsand pions have similar masses and therefore similar kinematic properties; muons are essentiallyChapter 1. The Experiment 23— I • I • I IIL+Y,I•+1ToCD÷,r+lrIF0-I-,o so ioo 150 200 250 300Momentum (MeV/c)II —1T1t0—CD f10Iv+lfl’I../ \‘ I \‘ /0 50 100 150 2CKinetic Energy (MeV)4VC,,ED>•,T+7F+1T_0I-4-.0 10 20 30 40 50 60Range (cm)Figure 1.11: Momentum, kinetic energy and range spectrum in the rest frame ofthe K+ for charged particles in K+ * +1jj7 (dashed line), K,L2‘(2 and K+ irr decays. Typical experimental resolutionswere included for each quantity. The hashed area indicates the K+7r+vlJ kinematic search region used in this work.Chapter 1. TheExperiment 24the sole source of particle mis-identification background.Another way to positively identify the is to use its characteristic decay sequence. Approximately 99.99% of the time a pion will decay via lr+ with a mean life of 26 ns.This is then followed by the decay of the muon via ÷ e+vei7, with a mean life of 2.2 ,isand also nearly 100% probability. Therefore, by detecting the two secondary charged particlesresulting from the cascade decay of the primary 1i+ , positive identification can be made. Thisis in contrast to a primary + which results in only one secondary charged particle. Hence, thedetection of the decay sequence of the charged decay product of the K+ can also be used toreject background.Finally, the detection of photons should be as efficient as possible in order to reject thenumerous background processes which involve photons. The most prominent is K+ which the ir0 has a total energy of 245 MeV. The energy of the photons emitted the decayof the ir0 are distributed between 20 MeV and 225 MeV. The extremes correspond to the casewhere one photon is emitted in the direction of motion of the ir0 and the other in the oppositedirection. The minimum separation angle between the two photons is 67°; in this case, thetwo photons have equal energy (112.5 MeV). For other K+ decays involving O , the range ofphoton energies is not as wide and the minimum separation angle is larger. For K+ radiativedecays, in which individual photons are emitted, the photon energy is smaller and can be aslow as a few MeV. Typical inefficiencies for photon detection obtained in this experiment variedaccording to the energy and direction of the photon, and were between 10_i and i0. Thedetection also has to be accomplished in an environment with a high rate of accidental particles,which results from the intense incoming beam of particles and leads to accidental vetoing.Due to the limited photon detection capability, we see from figure 1.11 that the kinematicregion defined by the decay kinematic peak should be avoided in the search for K+The position of this peak at p,+ = 205.12 MeV/c defines two regions of the K+spectrum that can be exploited : one above the K,r2 peak up to the end point of the.+j/j7 spectrum and one below the K2 peak. The former region was the subject of arecent thesis [30]. The latter region was used in this work, and is indicated by a hashed regionChapter 1. The Experiment 25in figure 1.11. It is about a factor of two larger than the more “conventional” higher momentumregion, and in the case of a measurement would allow for a determination of the ir+ spectrumshape. It also involves backgrounds of a slightly different nature. The lower boundary ofthe region used was defined to some extent by the apparatus used and avoided most of theK+ — lr+lr+1r and K+ -+071-0 background processes. It is worth noting that the verticalscale on the graphs of figure 1.11 is entirely arbitrary, including the relative height of thedistributions for the different decay modes. The peaks of the K,2 and J(2 distributions are inreality some ten orders of magnitude higher than the maximum of the K+ K+l,17 distribution.The shape of the distribution for K2 and K,,.2 was assumed Gaussian for the figure; this is notnecessarily the case in practice.1.3.1 Background overviewThis section will give a brief overview of the background processes of concern for the searchfor K+ +j,i7 in the kinematic region below the K2 peak. Each will be discussed in detailin Chapter 4. Table 1.1 gives a list of these background processes. The most important is+0 (K2). It can mimic K+ _ +jjj7 if the photons from ir0 decay are not detectedand either the kinematic quantities for the are mis-measured or the + lost an undetectedamount of energy in a coffision. The latter effect is significant because the + can undergostrong interactions in matter. There is also a radiative mode, J(+ ,. .+O7 , in which theis naturally lower in momentum than the K2 mode; however, the photons from ir0 decayand the radiated photon have to be missed for this decay to be a background. Note that the7r+7I.°7 ratio indicated in the table is only for the kinematic region 55 < T+ < 90MeV [17]; for low energy radiated photons, most of the branching ratio is included in theK2 mode.The momentum spectrum of the from K+ ,‘ Op+i,1 (K3) decay covers the kinematicsearch region. The + must be mis-identified as a and the photons from ir0 decay missed.The decay K+ , with the largest of all K+ decay branching ratios, is not a concern forthis study because of the high momentum of the + (236 MeV/c). However, for the radiativeChapter 1. The Experiment 26Table 1.1: Background processes to the search for K+ _+ 7.+ij7 in the kinematicregion below the K2 peak. Also shown are branching ratios orprobabilities for the various processes and the maximum momentumof the or in the final state.Background Branching ratio Pmax (MeV/c)]K —* ir0 (K2) 0.212 205K R-07(K2) 2.75 x i0 205K —* r°pv (K3) 0.0318 215K —÷ (Kr) 5.50 X i0 236K —* rel’e (Ke4) 3.91 X i0 203Beam pions —Kn —f K°p Prob. = 0.0015 —K —* ri7, 0.135 216K—0.194 229K° —* K°, K°N + Prob = 0.024 —— irn 0.483 185mode K+ , the + spectrum does cover the K+ , +z,E7 kinematic search region.Again in this case, mis-identification and non-detection of the photon in the final state arenecessary for this mode to be a background.For the decay j+ ) (Ke4 ), both the ir and the e+ in the final state have tobe missed. There is also a similar decay, K+ r+1rCv,L, with a branching ratio about threetimes smaller than Ke4 . However, the maximum momentum for the in this decay is oniy151 MeV/c, and therefore its contribution to the overall background is not significant.Beam pions are a source of isolated pious which can simulate the final state of K+ ,SThe large number of pions which accompany kaons in the particle beam used in this experimentmakes this process a potential background. Beam kaons can also interact in matter as they arebeing brought to rest and produce a neutral kaon via the charge exchange process .÷ K°p.The neutral kaon is a superposition of the weak interaction eigenstates K and K. The K candecay semi-leptonically via Ic — irtW, where £ is either a muon or an electron. If the leptonis not detected, this decay can be a background to K+Finally, there is a finite probability that a neutral kaon produced in K+ charge exchangewill oscillate to an anti-kaon, or K° . The K° can interact in matter and produce a hyperon,Chapter 1. The Experiment 27which then decays 48% of the time to a lr+ and a neutron. The latter is difficult to detect.Therefore, if the interactions leading to the production of the are not detected, this processcan also be a background to K+ ÷1.3.2 Previous searchesFigure 1.12 shows the historical progress in the experimental search for K+ 7t.+z7 . Noevidence for observation has been reported; therefore, all results are 90% confidence level upperlimits. Each step on the graph represents a published measurement. The most recent resultB(I( —f rvE7) <5.2 x i0 (90%C.L.) (1.21)includes part of the work reported here, combined with an investigation of the higher momentumregion of the K+ +jJj7 decay ir+ spectrum [37]. The best result in the kinematic regionbelow the K2 kinematic peak previous to this experiment was [34]B(K—÷irvi7) < 9.4 x i0 (90%C.L.). (1.22)For j+ + via scalar and tensor interactions, the best previous limits were < 1.1 x 106and < 7.1 x i0 (90% C.L.) respectively. For K+ ÷ , the most recent published resultprevious to this experiment that included the mass region probed by this experiment here wasapproximatelyB(K —* irX°) <2 x 10 (90%C.L.) (1.23)with some dependence on Mxo [38].Chapter 1. The Experiment 2810_8—g10 — i I I I I I I I I I I —19 1970 1975 1980 1985 1990 19J5Publication dateFigure 1.12: Historical progress in the experimental search for K+ .+Jj7Each horizontal line represents a published result [32, 33, 34, 35, 36,37]. The dashed lines indicate the results using the apparatus of thisexperiment.Chapter 2The ApparatusThis chapter gives a description of the apparatus used for the experiment. This apparatus,located at Brookhaven National Laboratory (BNL) in Upton, NY, USA, was used to studyseveral different K+ decays. It was designed, constructed and operated by a collaboration ofphysicists from three institutions : BNL, Princeton University and TRIUMF (see appendix A).The experiment as a whole was identified as BNL Experiment 787. The following descriptionwill focus on the use of the apparatus in the search for K+ .. which was the main goalof the collaboration. Experimental data used in the work described in this thesis was recordedin two different periods of a few months in 1989 and 1991. There were some differences in theapparatus used in the two periods; they will be pointed out in the appropriate sections.2.1 Kaon beamKaons used for the experiment were produced in collisions between an accelerated beam ofprotons and a stationary target. The accelerator was the Alternating Gradient Synchrotron(AGS). Protons were first accelerated to 200 MeV with a linear accelerator and then injected inthe 807 m circumference synchrotron where they were accelerated to a momentum of 24 GeV/c.Approximately 1013 protons were stored in the synchrotron before being extracted over a timeperiod of 1.6 seconds; each extraction was referred to as a spill. The duration of one cycle ofacceleration and extraction was approximately 3.2 seconds.A portion of the extracted proton beam, typically 6 x 1012 protons, was directed on a 9 cmlong platinum production target. Particles of several types and of various energies are produced29Chapter 2. The Apparatus 30in the collisions between protons and platinum nuclei. Only a fraction of them were collected andguided towards the detector by the beam line, a series of dipole and quadrupole electro-magnetsand collimators. Figure 2.13 schematically shows the proton beam from the accelerator, theproduction target and the beam line, LESB1 (Low Energy Separated Beam). The integratedpath length of the particle beam from the production target to the final focus was 15.8 m. Thedipole magnets’ field polarity and strength was adjusted to select positively charged particleswith a momentum of 800 MeV/c. The rms resolution of the beam line momentum selectionwas approximately 1%. The first dipole had a total angular acceptance of 2.5 msr and collectedparticles emitted at the production target at an angle of 10.5° with respect to the proton beamdirection.Figure 2.13: Schematic diagram of the LESB1 beam line[44]. Dipole magnets aredesignated Dn, while quadrupole magnets are designated Qn.As was noted above, particles of several types emerge from the production target. Thecross-section for pion production in proton-nucleus coffisions is approximately 20 times thecross-section for kaon production. Also, a large number of protons are deflected via inelasticcoffisions with nuclei and can enter the beam line. Particle type separation was obtained usingan electrostatic separator, or Wien filter, tuned for 800 MeV/c K+ . Particles deflected by thecrossed electric and magnetic fields of the separator were blocked by the mass slit, an adjustableMass slitD3Chapter 2. The Apparatus 31coffimator installed following the separator.This particle separation significantly reduced the nonK+ components of the beam, butnot entirely. At the exit of the last magnet the beam consisted of a mixture of ii , protonsand K in the proportion 2 : 1 : 1. Approximately 106 K per AGS spill came through thelast magnet, were slowed by a degrader and came to rest in the target located in the center ofthe detector. This was the most intense kaon beam available in the world at the time1. Thedistribution of the K+ beam at the exit of the beam line was centered in the plane perpendicularto the beam axis, and occupied an area 12 cm wide (horizontally) and 4 cm high (vertically).The + beam was off center and more diffuse, with a full width and height of 18 cm and 5.5 cmrespectively.2.2 DetectorThe BNL E787 detector consists of a number of independent sub-detectors of various typesworking collectively to identify events consistent with a K+ 1r+yi7 decay. Each sub-detectoris dedicated to a particular aspect of either the precise identification of a K+ decaying at restto a or the rejection of the numerous background processes. Figure 2.14 shows a detailedside view of the entire detector. Figure 2.15 shows an end view of the detector as well as thecoordinate system used. The z axis is in the direction of the K+ beam, perpendicular to andinto the page in figure 2.15. Elements of the detector are often referred to in reference to theparticle beam direction; upstream is closest to the beam origin (in the direction of the negativez axis), and downstream is the opposite.The detector was designed based on the considerations discussed in Chapter 1. A set ofsub-detectors placed in the incoming beam, referred to collectively as beam counters, identifiedthe K+ and other particles. Charged particles were slowed by the beryffium oxide degrader; itslength was chosen such that kaons came to rest in a highly segmented target made of plasticscintillator, located downstream of the degrader. The high segmentation of the target allowedthe identification of the K+ decay vertex position and of the secondary charged particles.1LESB1 was replaced in 1992 by LESB3, providing a factor of improvement in K+ :lr+ ratio.Chapter 2. The Apparatus 32E787 DETECTORBARREL —VETOPHOTOTUBESRANGE STACKJ —— RANGE STACKPH OTO TU B ES—I-CDtlNTERFigure 2.14: Schematic side view of the E787 detector [45].Chapter 2. The Apparatus 33‘-VETEiRANGE STACKEND CAP- VETEII,V— CEIU NT ER SRANGE STACKCHAMBERSYxDRIFT CHAMBERE—787(END VIEW)Figure 2.15: Schematic end view of the E787 detector [45].Chapter 2. The Apparatus 34Surrounding the target was a series of detectors with cylindrical symmetry with respect to thez axis, designed to identify the K+ decay products. Precise position information about thecharged particles emerging from the target was obtained by a drift chamber. A static magneticfield directed along the z axis of the detector allowed the determination of the momentum ofcharged particles using the position information from the drift chamber. The field of 1 Teslawas provided by a 3 m diameter conventional solenoid magnet surrounding the entire detector.Note also that since all sub-detectors were permeated by the magnetic field, nearly all photo-multiplier tubes (or phototubes) used to measure the light output of scintillator counters wereinstalled outside of the magnet return iron.Surrounding the drift chamber was the range stack, a segmented stack of plastic scintillatorcounters designed to measure the kinetic energy and range of the charged particles emergingfrom the drift chamber. Two layers of proportional chambers were embedded in the range stackto provide additional position measurements for charged particles. Photons were vetoed byelectro-magnetic shower detectors arranged in three sub-systems, a barrel section surroundingthe range stack and two endcaps located on either side of the drift chamber. This systemcovered nearly 4ir sr, leaving only the beam—target axis and the region between the barrel andendcaps with limited coverage. The photon detection capability of the detector was augmentedby the use of all active elements not struck by the K+ or theThe electrical signals output by all sub-detectors were carried via 30—50 m long coaxial cablesto the counting house, where all electronic modules were located. The signals were processedwith discriminators, coincidence units, analog-to-digital converters (ADC) and time-to-digitalconverters (TDC). A description of the electronics systems will be given with the descriptionof the online event selection (section 3.1).Figure 2.16 shows an end view display of a 11+ r+r0 event based on information recordedby the detector. Only the counters with recorded energy are indicated, as well as the xy planeposition measurements from the drift chamber and the fitted trajectory. The is clearlyseen from its path through the target, I-counters, drift chamber and range stack. The twophotons from r0 decay were detected in the barrel veto. The numbers indicated in each counterChapter 2. The Apparatus 35represent the measured visible energy in units of MeV.7SCALE 1:15.0RUN 8108EVENT 3132Figure 2.16: Detector display of a K+ +7i event. See the text for explanations.A description of each sub-detector will be given in the following sections. Elements with themost impact on the search for K+ 7r+v7 will be emphasized. More technical details aboutall parts of the detector can be found in reference [46].7Chapter 2. The Apparatus 362.2.1 Beam countersThis system of detectors was used to monitor and identify beam particles from their exit fromthe beam line to the target at the center of the detector. Figure 2.17 gives a schematic side viewof the system used for the 1991 data run. The various elements of the beam counter systemwill be described in the order in which they are encountered by beam particles.SUPPORT ENDCAP ENDCAP MAGNET ENDCAP DRIFTTARGETCYLINDER PHOTOTUBE LIGHT GUIDE END PLUG MODULE CHAMBER—BEAM2.2.1.1 Beam hole, Bi & B2 hodoscopesThe first element is the beam hole counter. This counter consisted of two L-shaped plasticscintillator counters forming a square 23 cm to a side with an 18 cm wide (along the x axis)and 3 cm high (along the y axis) rectangular hole in its center, to accommodate the spatialdistribution of the incoming K+ beam. This counter was designed to identify beam particlesthat might be far off axis. All kaons should pass through the hole and traverse the Bi and B2hodoscopes, which were located immediately following the beam hole counter. B1 and B2 weregroups of plastic scintillator counters used to monitor the beam profile; they were not used inthe search for K+ ,Bi & 82 CERENKOVBEAM HOLE COUNTERS COUNTERCOUNTERDEGRADERHIGH FIELDPHOTOTUBES COUNTERFigure 2.17: Schematic side view of the beam counters system for the 1991 run.Also shown here are the upstream endcap, and part of the drift chamber and target.Chapter 2. The Apparatus 372.2.1.2 Oerenkov counterFollowing the Bi and B2 hodoscopes is the erenkov counter. This counter used erenkovlight emission resulting from the passage of beam particles through a dielectric medium, orradiator, for particle type identification; such counters have been used before in low energykaon beams [48]. The ierenkov light is emitted along the path of the moving charged particlewith a characteristic angle Oc with respect to the direction of motion of the particle. This angleis defined ascosOc = (2.24)where 3 = v/c is the ratio of the velocity of the charged particle in the medium to the velocityof light in vacuum (c), and n is the index of refraction of the medium. This defines a thresholdvelocity for emission of ierenkov light, /3 = 1/n. The radiator was a 2.54 cm thick and 15 cmdiameter acrylic disk. The index of refraction of acrylic is n = 1.49 in the frequency rangeof interest; therefore, the threshold velocity for erenkov light emission was = 0.67. For amomentum of 800 MeV/c, both + and K+ have a velocity above this threshold; protons donot.This counter also made use of the phenomenon of total internal reflection. The velocity atwhich (ierenkov light will be internally reflected in the radiator is defined as(2.25)For n = 1.49, we obtain 3 = 0.90; at 800 MeV/c, are above this threshold, but K+ are not.This leads to the arrangement shown in figure 2.18, where erenkov light emitted in responseto the passage of K+ exits the radiator from the circular face and is focused by a parabolicmirror onto a ring of ten phototubes (PMTs). Internally reflected light emitted in response tothe passage of r+ exits the radiator from the conical edge and is reflected onto another ring often phototubes.The output signals of the ten phototubes from each ring were sent to individual discriminatorchannels housed in two separate units. An output signal was available from these units providinga current proportional to the number of discriminator channels with an input voltage aboveChapter 2. The Apparatus 38Figure 2.18: ierenkov counter schematic side view. The dotted line shows thepossible path for Cerenkov photons emitted after the passage of abeam kaon; the dashed-dotted line shows the same for a passingbeam pion. Only two of the 10 PMTs in each ring are shown.Winston cones RadiatorConical ParabolicMirror MirrorChapter 2. The Apparatus 39threshold. The threshold was set at the level of a single photo-electron for each phototube.The output signals of the two units were sent to another discriminator where a minimum of sixphototube votes was required to define the passage of a or . In both cases the inefficiencyof detection was of the order of io——iO. Copies of the final pion and kaon ierenkov countersignals were sent to multi-hit TDCs for time measurement. Beam wire chamber (BWPC)Immediately after the erenkov counter was the beam multi-wire proportional chamber (BWPC),allowing precise monitoring of the beam profile and the identification of multiple incoming beamparticles. Figure 2.19 schematically shows the arrangement of one of the three wire planes usedin the BWPC. The gas used was an 80:20 mixture ofCF4—isobutane; the very fast response ofthis gas mixture allowed the operation of the BWPC in a high rate environment. The averagetime resolution was approximately 2.0 ns. In the first wire plane, 72 pairs of wires were positioned vertically. The other two planes consisted of 60 pairs of wires positioned at +45° tothe vertical. The active area of the planes was approximately 19 cm wide along the x axis and6 cm high along the y axis. The position resolution obtained was a 0.5 mm along the x axisand a 0.7 mm along the y axis. The efficiency of a single plane of the chamber was greaterthan 99%.////////////////////////////////////////////////////////I ///////A.1B mmANODES‘N CATHODE0 0 0 0 0 0 )12 m diameter ( 3 / 25 em thickGold plated / AluminTzed MylarTungsten 127 mmFigure 2.19: Schematic diagram of a section of one of the BWPC wire planes. Degrader, B3 & B3S countersBeam particles were slowed by a 535 mm long cylindrical beryffium oxide degrader. Thismaterial was chosen for its relatively high density (3.0 g/cm3)and low average atomic number,Chapter 2. The Apparatus 40resulting in a good stopping power while minimizing multiple Coulomb scattering effects. Thelow atomic number also reduced the probability of absorption of photons emitted in the decayof kaons in the target. Located immediately upstream of the degrader were two scintillatorcounters, B3 and B3S, used for beam flux and position monitoring purposes oniy. Lead-glass detectorIn 1991, a part of the downstream end of the degrader was replaced by a 10 cm long and11.2 cm diameter cylindrical piece of lead-glass, used primarily as a photon detector2. High-energy gamma rays traveling inside a medium can initiate an electro-magnetic shower. Auseful quantity in characterizing the ability of a material to interact with electrons and photonsis the radiation length. This length can be seen as the distance required for one layer ofmultiplication in the development of an electro-magnetic shower. The lead-glass used for thisdetector contained approximately 53% of lead oxide by weight (total density 3.85 g/cm3),substantially increasing the probability for photons to convert in it because of lead’s highatomic number; its radiation length was 2.84 cm.Very little scintillation light is produced by charged particles in lead-glass. However, becauseit is transparent in the visible and UV region, ierenkov light emitted in lead-glass can bedetected. The refractive index of the lead-glass used in this detector was n = 1.68, resultingin a threshold velocity of / = Vt/C 0.6 which corresponds to an electron kinetic energy of128 keV. The typical energy of photons incident on this detector is several MeV, which shouldresult in the production of ierenkov light if the photon initiates an electro-magnetic shower inthe lead-glass.A schematic side view of the lead-glass detector is shown in figure 2.20. The lead-glasscylinder was surrounded by a 1 cm thick cylinder of acrylic used to collect the Cerenkov lightand guide it by total internal reflection to a ring of 16 phototubes. The delicate focusing of theelectron’s trajectories in the dynode array of conventional phototubes is upset by the presenceof a magnetic field. Since this sub-detector was very close to the center of the detector assembly2More technical details will be given about this sub-detector since it was not described in reference [46].Chapter 2. The Apparatus 41where strong magnetic fields are present, high-field mesh dynode phototubes3were used. Thistype of phototube can provide gains of 1O—i0 when the axis of the tube coincides with themagnetic field lines, compared to gains of order for conventional phototubes in standardoperation without a magnetic field. The relatively small output signals from the high field tubeswere pre-amplified before being sent outside of the detector via coaxial cables. An alternativeto the use of high field phototubes would have been to install conventional phototubes outsideof the region of high magnetic field. However, the light attenuation in the very long light guidesrequired would have made this design impractical.High—field PMT Electra—magneticI Shower__y—rayBeam /Acrylic Lead—glassFigure 2.20: Lead-glass detector schematic side view. The dashed line indicatesthe path of a Cerenkov photon emitted by a beam K+ ; the dashed-dotted line indicates the same for a beam + . The dotted lineindicates the path of a Cerenkov photon emitted by an electron froman electro-magnetic shower, from production in the lead-glass to thephototube via the acrylic cylinder.As can be inferred from figure 2.20, Cerenkov light can be produced by beam and K+ inthe lead-glass. For most , the light produced exits the side of the lead-glass cylinder and aportion is trapped in the acrylic cylinder. For K+ , their lower velocity results in a ierenkovlight emission angle (see equation 2.24) too shallow to exit the lead-glass cylinder side; the2.5 cm diameter Hammamatsu R3432; the photo-cathode diameter was 1 cm.Chapter 2. The Apparatus 42light is totally reflected at that interface and exits from the end of the cylinder. To heightenthis effect, the side of the lead-glass cylinder was wrapped in a thin film of transparent Teflon(n 1.35), thereby decreasing the minimum angle for total internal reflection. Despite theseprecautions, light associated with beam K+ was observed, typically enough to be detected byone or two phototubes. For comparison, the mean number for beam pions was 8—9 phototubes,and for photon showers the light output was about 1 phototube/lO MeV. The light seen forK+ possibly came from cases where the K+ trajectory had a significant component in the xyplane, resulting in ierenkov light with a smaller incident angle with respect to the normal tothe lead-glass—acrylic cylinder interface than for kaons traveffing parallel to the z axis. Anothercontribution was from fluorescence in the lead-glass induced by the emitted ierenkov light.This effect was confirmed in beam tests performed at TRIUMF [49].Radiation damage also hindered the performance of this detector. The damage causes thenormally clear glass to acquire a yellowish tint, reducing the transparency and resulting ina lower light output per energy deposited. After a few weeks of operation, the performancestarted to degrade; near the end of the data collection period, the light output was only 30—40%of its initial value.Similarly to the Cerenkov counter, the output of the 16 PMTs was sent to a multi-channeldiscriminator unit which supplied an output current proportional to the number of channelsabove threshold. This signal was discriminated and sent to a multi-hit TDC, as well as atransient digitizer channel (see section The measurement of the response of the lead-glass detector as a function of time allowed the separation of signals from kaons and fromphotons or late beam pions (see B4 hodoscopeBetween the degrader and the target was the B4 scintillation counter hodoscope. It was usedto identify the passage of charged particles from the degrader to the target. Its segmentationallowed the monitoring of the beam profile in the zy plane at the entrance to the target.There were significant differences between the devices used in 1989 and 1991, although notChapter 2. The Apparatus 43in the purpose and general principle. In 1989, the B4 hodoscope consisted of three planesof scintillator counters. One was hexagonal in shape and covered the cross sectional area ofthe target; this counter was referred to as B4T. The other two planes each consisted of fourindividual rectangular counters arranged side by side to form a nearly square section coveringthe target front face. For one plane the individual counters were installed vertically while theywere horizontal for the other. In 1991, the B4T counter was removed. The other two planeswere replaced by two identical arrays of six individual counters forming a roughly hexagonalarea covering the front face of the target. The width of the counters decreased with proximityto the center of the array to compensate for the variation in beam intensity. The two planeswere installed at ±45° to the vertical.All counters in the B4 hodoscope were made of 6.25 mm thick plastic scintillator. Thelight emitted after the passage of a charged beam particle was collected with adiabatic lightguides and carried parallel to the beam direction outside of the region of high magnetic field.Conventional phototubes detected the light at the end of the light guides.2.2.2 Target (TG)The target defines the central detector region where K+ come to a stop and decay. On average,approximately 2 x iO K+ per accelerator spill came to rest in the target. It was designed withhigh segmentation to clearly identify the stopping K+ region and charged particles emitted inits decay, and with minimal non-active regions to avoid undetected energy losses from chargedparticles or electro-magnetic showers. Figure 2.21 shows a schematic view of the upstream endof the target in the zy plane. It was a hexagonal array of 378 triangular elements. Each elementconsisted of six 2 mm diameter scintillating fibres, held together with epoxy. Each individualfibre had a sputtered aluminum coating to protect the surface and eliminate cross-talk betweenfibres. Overall, 75% of the target consisted of active scintillator material.The fibres were approximately 3 m long, with the last metre in each element left withoutepoxy to allow more flexibility. The triangular elements were interlocked to form a hexagon10 cm flat-to-flat; a single cylindrical fibre occupied the center of the target, for a total of 379Chapter 2. The Apparatus 44elements. The upstream end of the target was located approximately 12 cm along the z axisupstream of the detector’s center of coordinates. An aluminum mirror was evaporated on thepolished surface of the upstream end to reflect scintillation light towards the downstream endof the elements, where each was viewed by a 10 mm diameter phototube. The output fromeach phototube was brought to the counting house and fed to a x 10 amplifier, the output ofwhich was connected to a passive circuit designed to divide the charge of the signals in threeparts. One part went to an ADC, one part to a discriminator which in turn fed a multi-hit TDCand a third part was summed with the output of all other elements. The resulting summedsignal was then discriminated at a voltage equivalent to an energy deposition of 5 MeV in thetarget. This discriminator output signal defined the presence of a particle in the target. Thedivision of the signal from each phototube to an ADC, a TDC and an analog sum is typical ofall sub-detectors using scintillator counters.Because of the large variation in the amount of scintillator crossed by charged particles ina given target element, the performance of the target was determined in terms of the numberof photo-electrons obtained per mm of path length for a minimum ionizing4 particle. Theoverall average was approximately one photo-electron per mm. The spatial resolution in the xyplane was 1.8 mm (rms) for a charged particle traveffing transversely to the target elements.Figure 2.22 shows an xy plane event display of the time and energy information recorded bythe target for the J,,2 event shown in figure 2.16. The K+ is clearly identified by its largeearly energy deposition in the target elements, because it travels mostly along the length of thescintillating fibres and it is near the end of its range where the rate of energy loss is largest. Incontrast, the -+ deposits a small amount of energy because of its high momentum and mostlytransverse trajectory; we also see the clear time delay between the K+ and , indicating thatthe K+ decayed at rest. The time resolution for individual elements was typically a 1.3 ns.4The mean energy loss rate of a minimum ionizing particle in plastic scintillator is approximately 1.7 MeV/cm.Chapter 2. The Apparatus 4510 cmV—cot.jnterFigure 2.21: Schematic view of the upstream end of the target, I-counters andV-counters. Shown in the upper right hand corner are details of atarget element.2.2.3 I- and V-counters (IC and VC)To define the target fiducial region along the z axis, six 6.4 mm thick and 24 cm long plasticscintillator counters surrounded the target, as shown on figure 2.21 and 2.23. Each counter wasconnected to a light guide and a phototube. Downstream of the I-counters were another sixscintillator counters called V-counters. These were 1.96 m long and 5 mm thick, and overlappedby 6 mm with the downstream end of the I-counters. Each of the six V-counters was viewedby a phototube. The V-counters were used to veto charged particles which might originatefrom kaons decaying downstream of the target fiducial region. They were also used to detectelectro-magnetic showers in the area between the target and the downstream endcap detector.2.2.4 Drift chamber (DC)Like multi-wire proportional chambers, drift chambers make use of the ionization caused bythe passage of a charged particle in a gas volume. However, in this case, the time required byI—counterSclntIIIatlrgFiberChapter 2. The Apparatus 46a)SCRLE 1: 0.5RUN 9109EVENT 3132SCRLE 1: 0.5RUN 9109EVENT 3132Figure 2.22: Target and I-counters event display for K+ event, a)shows the energy information in MeV and b) the time informationin nanoseconds.±±7Tb)Chapter 2. The Apparatus 47V—counterII YTargetIIzI—counter I—counterscintillotor light guideFigure 2.23: Schematic side view of the target, I-counters and V-counters.the ionization electrons to reach the anode wires (drift time) is used to determine the point ofclosest approach of the particle to the wire. The reference time is provided by a scintillationcounter external to the chamber and traversed by the charged particle.The drift chamber used in this experiment was a cylinder surrounding the target, withan inner and outer radius of 9.5 cm and 43.2 cm respectively. Its function was to accuratelydetermine the trajectory of charged particles emerging from the target and to measure theirmomentum. This was made possible by the presence of a 1 Tesla magnetic field in the directionof the z axis. The 50.8 cm long active volume of the drift chamber contained a gas mixtureof 50:50 argon—ethane; the argon was bubbled through ethanol at 0°C; this mixture provideda gain of io. The inner and outer radius walls were made of graphite-fibre epoxy 0.4 mmand 0.47 mm thick respectively, and the end plates of 9.5 mm thick aluminum. The cylindricalvolume was divided in five radial layers, which in turn were divided in 36, 40, 50, 60 and 70azimuthal cells respectively, in order of increasing radius. Figure 2.24 schematically shows thedesign of individual cells. The planes of cathode wires, shared by neighboring cells, were heldunder negative high voltage. Ionization electrons drifted towards the grounded anode wiresin the direction of the electric field thus created. However, the presence of the magnetic fieldtilted the trajectory of the electrons by an angle known as the Lorentz angle. This angle wasempirically determined for each cell and was typically 25°.Chapter 2. The Apparatus 48Anode sense wire (20 m diam.):45.7 mmo o Cathodeo a Wires(178 m diam.)o o- (300 m diam.)o a0 CAnode guard wire (100 m diam.)Figure 2.24: Drift chamber “jet” cell design. All cathode wires are made ofberyffium—copper alloy, as are the anode guard wires. The anodewires are made of gold plated tungsten.The wires in the innermost, middle and outermost cell layers (axial layers) were positionedparallel to the z axis of the detector. The wires in the other two layers (stereo layers) wereoffset by one cell in azimuth from one end plate to the other. This allowed the determinationof the position along the z axis. As shown in figure 2.24, the anode sense wires were staggeredalternately from the mid-plane, to resolve the left-right ambiguity in the position measurement.The innermost six anode wires were instrumented with pre-amplifiers, mounted on the chamberend-plates. Their output signals were carried to post-amplifiers located in the counting house,the output of which was fed to discriminators. These in turn fed multi-hit TDCs for drift timemeasurement.Figure 2.25 shows a schematic end view of the cell boundaries. Superimposed are theposition measurements for a positively charged particle and the fitted trajectory in the zyplane. A close-up of one of the cells crossed by the charged particle shows the effectiveness ofthe wire staggering in resolving the left-right ambiguity. The acceptance of the drift chamberwas approximately 2ir sr for charged particles of momenta greater than 150 MeV/c. The positionresolution achieved in the xy plane varied between 130 m and 250 m. Along the z axis, theresolution obtained was between 2.2 and 4.2 mm. Figure 2.26a shows the ir+ total momentumdistribution for K+ ,‘ 71+RO decays. Note that to obtain the total momentum, a correctionChapter 2. The Apparatus 49had to be applied for the energy lost by the in the target. The distribution was fit to asingle Gaussian function using a chi-square minimization method; the results are indicated onthe graph. The nominal value of the K,-2 momentum peak is 205.12 MeV/c. The non-Gaussiantails of the distribution are caused by a combination of tracking errors, multiple scattering in thedrift chamber and reconstruction errors, and scattering in the target. Based on the singleGaussian fit, the relative momentum resolution achieved was approximately a(p)/p = 2.2% atthe ‘(2 peak.Figure 2.25: End view of drift chamber cell boundaries and fitted particle trajectory. The squares represent the position measurements, includingmirror points due to the left-right ambiguity; the X’s indicate thepoints in the axial layers chosen by the fitting algorithm.2.2.5 Inner wire chamber (IWC)In 1991, a thin cylindrical drift chamber, called inner wire chamber (IWC) [50], was installedbetween the target and the drift chamber. Its main purpose was to provide additional trackingStereo layersAxial layersChapter 2. The Apparatus 50— I I I I I I I I—I I I I I I I I —mean= 203.67 ±0.19 b) mean= 204.24 ±0.18/ u= 4.57 ±0.16 u= 4.02 ±0.14102 -[ \(I)1 C10- -Jo 0() C.)101-100_ -10_1_ III I I I I I I I I I I I I I I I I — 10° I I I I I I I I I [I —140 10 1 0 20 2O 240 2o0 140 10 10 20 2O 210 2o0Momentum (MeV/c) Momentum (MeV/c)Figure 2.26: + total momentum distribution for I(2 events a) from the driftchamber and b) combining the IWC and drift chamber information.In both cases a correction was applied for the energy lost by theit-+ in the target.information to improve the resolution for position measurements of charged particles, primarilyalong the z axis. Figure 2.27 shows a schematic end view of a section of the IWC. It consistedof a single ring of axial wires located at a radius of 8.5 cm, between two concentric 50 im thickKapton foils. The wire plane was formed of 48 gold-plated tungsten anodes alternated with 48gold-plated aluminum cathodes. The anode wires were held at a positive high voltage whilethe cathodes were grounded. Copper coating on the Kapton foils maintained at ground voltagecompleted the nearly square drift cells around each anode. A copper coated 225 tm thick GlOcylinder5 at a radius of 7.6 cm and a copper coated Kapton foil at a radius of 9.4 cm formed theexternal walls of the chamber and defined the dimensions of the gas volume. These additionalcylinders also provided mechanical support and additional electrical shielding. The gas mixturewas the same as that used for the main drift chamber.The copper coating on the innermost foil was formed of 5.1 mm wide parallel strips angledat 45° with respect to the z axis and separated by 0.78 mm gaps. The center of gravity of5G10 is a trade name for a material made of 60% Si02 and 40% epoxy.Chapter 2. The Apparatus 51KaptonCopperstripsKaptonFigure 2.27: Schematic end view of a section of the inner wire chamber (IWC).the measured charge induced on the strips by the ionization in the gas, combined with theazimuthal information provided by the anode wires, allowed the determination of the positionof the ionization along the z axis. Measurements in the xy plane were obtained by measuringthe drift time of the electrons to the anode wires. Each anode wire and cathode strip wasinstrumented with pre- and post-amplifiers, analogous to the ones used for the drift chamber.A copy of the output signals from all post-amplifiers was sent to ADCs and another was sent todiscriminators which fed multi-hit TDCs. Figure 2.26b shows the total momentum distributionfor the same events as in figure 2.26a obtained by including the IWC information to the trackfit. As can be seen, the improvement in the momentum resolution was approximately 10%; thismatched the design expectation.2.2.6 Range stack (RS)The range stack was a cylindrical array of plastic scintillator counters surrounding the driftchamber. Its function was the measurement of the kinetic energy and the range of chargedparticles emerging from the drift chamber. The range stack was divided in 24 azimuthal sectorsand 21 radial layers, as shown in figure 2.15, and occupied the radial region between 45.1 cmIonizedelectrons Anode wirediam.)3.5 mmGasCharged particleChapter 2. The Apparatus 52and 89.6 cm. The innermost layer consisted of 52 cm long and 6.35 mm thick plastic scintillatorcounters, designated as T-counters. These defined the 2K sr fiducial acceptance region of therange stack for charged particles emerging from the target, and corresponded more or less withthe length of the drift chamber along the z axis. The other 20 layers consisted of 1.8 m long and1.9 cm thick plastic scintillator counters. The counters were supported at both ends by a web-like stainless steel frame, away from the fiducial region. This guaranteed that charged particlesaccepted in the fiducial region would encounter minimal amounts of non-active material, mostlyfrom wrapping of the counters. The range stack was constructed such that ir from K+7r+vl) decays would come to rest within it; this was also true of ir+ from K2 decays and a largefraction of the + from K2 decays.The kinetic energy of the charged particles stopping in the range stack was measured bydetecting with phototubes the scintillation light from each counter struck by the particle. However, in a scintillator counter, the light emitted by the passage of a charged particle is attenuatedaccording toI = 1 exp (d/Latt) (2.26)where I is the intensity of the light measured a distance d from the point of emission, 1 isthe intensity at the point of emission and Latt is the attenuation length. This length variessubstantially depending on the composition of the plastic scintillator, the physical dimensionsand the quality of the surfaces. For the scintillator counters used in the range stack, theattenuation length was of the same order as the length of the counters, meaning that this effectwas important. To avoid this position dependence of the energy measurement, phototubeswere installed at both ends of the counters. Since the measured energy is proportional to theamount of light detected, the measured energy at each end, denoted 1 and 2, for a chargedparticle crossing a counter of length L a distance x from end 1 can be expressed asE1 = E exp (/Latt)E2 = Eexp(—(L— )/Latt). (2.27)Chapter 2. The Apparatus 53From this, we can obtainI EE 1E= [exp (_L/Latt)j (2.28)giving the energy deposited by the particle as a function of the measured quantities E1 andE2, and independent of the position x. The constant exp (—L/Latt) can be determined bycalibration.The light from each end of the counters was collected with 0.9 m long acrylic light guidesand brought to PMTs outside of the magnet through holes in the iron end plates. Figure 2.28shows schematic details of one range stack and barrel veto sector; the latter is described insection Layers 2 through 10 of each sector of the range stack were read out in groups of4, 3 and 2 counters, designated as layers A, B and C respectively. This minimized complicationsin the installation of the PMTs, but adversely affected measurements for particles stopping inthat region. The arrival time of signals from each PMT were not measured with TDCs butrather by transient digitizers; these will be described below. The average number of photoelectrons per MeV per end for range stack layers 11 and above was approximately 11.0, and 7.0for layers A, B and C.Figure 2.29a shows the total 7r+ kinetic energy distribution for J(2 events. The total energyis obtained by adding the energy (measured via scintillation light) deposited by the chargedparticle in the target, I-counters and range stack. The nominal value of the K7r2 energy peakposition is 108.5 MeV. The relative resolution at the measured energy, based on a Gaussianfit, is 4.35%. The low energy tail is mostly due to inelastic scattering of the in the rangestack. This could be substantially reduced by requiring consistency between the momentummeasured in the drift chamber and the energy measured in the range stack. The high energytail is caused by MeV photons from r0 decay converting in the range stack on top of thecharged track.The radial segmentation allowed the measurement of the range of charged particles comingto rest in the range stack. For additional position information, multi-wire proportional chambers(RSPC) were installed in each sector, following layers C and 14 (see figure 2.28). The activelength of each chamber was approximately 1 m long. Axially positioned wires provided positionChapter 2. The Apparatus 54Ci)C0C-)ATBARRELVETORANGESTACKFigure 2.28: Schematic end view of one range stack and barrel veto sector.Figure 2.29: Total measured a) energy and b) range distributions for the lr+ fromK7-2 decays. Results of a chi-square minimization fit to a singleGaussian function are also shown.2120191817161514131211CBEnergy (MeV) Range (cm)Chapter 2. The Apparatus 55information in the zy plane. The z axis position information was obtained by measuring thecharge induced on the cathode by the ionization in the gas. The cathode was a serpentine-patterned copper trace on the wall of the chamber. The charge was measured at both ends andthe end-to-end time difference of the signals was proportional to the z position of the ionization.The RSPC position information, combined with the drift chamber position information,allowed the correction of the range measured in the range stack for the slope of the track inthe r — z plane. Figure 2.29b shows the total range in scintillator for J(2 events, obtained bysumming the measured range in the target, I-counters and range stack. The nominal value ofthe K2 range is 30.7 cm. The measured resolution is approximately 1.2 cm. As for the energydistribution, the low side tail is due to inelastic scattering of the lr+ in the range stack. Thehigh side tail is due to reconstruction errors. Transient digitizers (TD)One of the important tasks in the search for j+ _* +ii7 is the positive identification of theAs explained in the introduction, one way to do this is to identify the decay sequence ofthe . Since the charged particles emitted in the decay of kaons in the target and detected inthe fiducial region of the drift chamber come to rest in the range stack, this is where the decaysequence can be identified. In the scintillator counter where the 7r+ comes to rest, a first pulsewill be observed from the pion itself. It will be followed by a second pulse corresponding tothe mono-energetic muon from the + —÷ decay. The kinetic energy of the muon is only4.12 MeV, which corresponds to a mean range in plastic scintillator of 1.4 mm. Therefore, inmost cases the muon will deposit all its kinetic energy in the counter where the ir+ stopped andcame to rest. The muon will then decay according to + —* e+ve7 . The positron from thisdecay can have a kinetic energy between 0 and 53 MeV. Most of the time, it will generate a thirdpulse in the counter where the stopped and also deposit some energy in the surroundingcounters.To identify this decay chain, the time evolution of the output pulses of the range stack PMTswas recorded. The mean life of the + and the 26 ns and 2.2 jts respectively, the typicalChapter 2. The Apparatus 56range stack counter pulse width of 30—40 ns and the range of energy deposition in the counterwhere the -+ comes to rest, typically 0—30 MeV, defined the operating parameters required ofthe recording devices. The devices used were custom built transient digitizers (TD) [51], whichhad a sampling rate of 500 MHz, a dynamic range of 8 bits and a total time range of 10 s. Toreduce the number of such devices, the output pulses from four contiguous sectors of the rangestack were multiplexed for each end and all layers, for a total of 180 TD channels. A number ofadditional TD channels were used to monitor the PMT output of several other sub-detectors,notably the B4 hodoscope, the I-counters and the lead-glass detector. The TD channels werein groups of four on a double-width Fastbus [47] module; eight such modules were housed in astandard Fastbus crate.The output of discriminators monitoring range stack PMT pulses from each counter wasused to provide information on which of the four counters were contributing to the pulse in agiven TD channel. This information, digitized as a single bit at a frequency of 250 MHz, wasrecorded along with the pulse height information; it was referred to as “flags”.Figure 2.30 shows the PMT pulses digitized by TDs from both ends of a range stack counterin which a came to rest and decayed (stopping counter). Also showed are the digitized pulsesfrom both ends of the counter immediately below the stopping counter; a single pulse is visible,corresponding to the . On these graphs, X’s and 0’s represent the sampled points, separatedin time by 2 ns. Figure 2.31 shows the TD information for the same channels with an expandedtime scale, showing the pulse corresponding to the positron from muon decay. The positrondeposited energy in several surrounding counters, as showed by the TD information from twoadditional range stack layers.In addition to identification, the TDs were also used for all time measurements in therange stack. The time of a pulse was determined on its leading edge at the interpolated halfheight of the pulse. For 1991 data, this time value was then measured in reference to the timeof a sharp fiducial pulse (10 ns wide, 4 us rise time), generated by an external circuit andinjected in all TD channels near the end of the recorded time range for each event. Thesefiducial time pulses essentially synchronized all TD channels to an accuracy of better thanChapter 2. The Apparatus 5730 ps, removed time shifts which can occur in the TD system on an event by event basis andgreatly simplified•the time calibration. The intrinsic time resolution obtained for range stackcounters was o 0.35 ns. This was measured by comparing the time of individual countersthat were hit by a charged particle to the average of all other counters hit by the particle.In 1991, the PMT pulses from layers A, B and C of the range stack passed through anamplifier with a logarithmic transfer function before being input to the TDs. This effectivelyincreased the dynamic range of the TDs for those counters, to match the greater range of energydeposited by a ir+ coming to rest in those thick counters.2.2.7 Photon veto systemAnother important aspect in the search for J(+ ÷ .+jj7 is the detection of photons emitted bybackground processes. Most of the photon detection was done with the photon veto system,consisting of three individual sub-detectors : the barrel assembly and two endcaps. All threewere electro-magnetic shower counters made of alternating layers of 5 mm thick plastic scintillator and 1 mm thick lead. The lead was used to convert incident photons into electron—positronpairs and the scintillator detected the ionization energy of electrons and positrons in the shower.The fraction of the total energy of the shower deposited in the scintillator, or visible fraction,was approximately 30%. Because only a portion of the energy deposited in these counters isdetected, they are commonly referred to as sampling calorimeters.There are three primary sources of inefficiency for the photon veto system1. Electro-magnetic shower fluctuations2. Photon escape3. Photo-nuclear absorption.The first item led to the choice of thickness for the scintillator and lead layers. Photons canescape detection through gaps in the system or regions where the number of radiation lengthsis not as large as others. The geometrical design of the detector was such that there were atleast 12 radiation lengths for 79% of 4ir sr and at least 2 radiation lengths for 99% of 4ir Sr.Chapter 2. The Apparatus 58120 — I I I I — 120 - I I I IStopping Stopping100- x counter - 100- counter0— 80- X + - 80- +- 0 TVTVa)60- - 60-a)(I)- xD 40- - 40-0 00 0 ++ 0x axx0 ,L1,20 - o - 20 -0 q,° ,0>— 0- ....i - 0o—2 0 20 40 60 80 100 — 0 20 40 60 80 100120-“‘‘‘‘“- 120- -ioo:- 100-o 0 0x80- - 80-+0 ÷ TV60- - 60-0 0- 0D 0040--40-0020— - 20-0— — 0——20 0 20 40 60 80 100 —20 0 20 40 60 80 100Time (ns) Time (ns)Upstream DownstreamFigure 2.30: Range stack counter pulses recorded with transient digitizers. Information from the stopping counter clearly shows the j-+ ,‘decay.Chapter 2. The Apparatus 59Upstream DownstreamFigure 2.31: TD information for the same event as figure 2.30 but with an expanded time and space scale, showing the positron from muon decay.403530,25 +e20a,1510500 200 400 600 800 10Time (ns)302520 +ea,•= 15a’a,- 10•>aC)aCl)ci)Ca 01a,a,a,03025÷20 e1510500 200 400 600 800 100Time (ns)302520 +e15 :10500 200 400 600 800 101Time (ns)120100 Stopping: counter :80aa60+ +e4020”n.h’0 200 400 600 800 101Time (ns)120 I I1008060 +• TV°:/20aU0 200 400 600 800 101Time (ns)100 I IStopping80counter60 +... + +e40• TV -+/J., li20:•(‘00 200 400 600 800 1OCTime (ns)100 I I IP080. 60a,4020+0 200 400 •600Time (ns)800 1000 0 200 400 600Time (ns)800 1000Chapter 2. The Apparatus 60Photo-nuclear absorption is dominated by giant dipole resonance excitation for photon energiesbelow 30 MeV. The de-excitation is often by neutron evaporation; some of those slow neutronscan be detected through their interactions in plastic scintillator. For photon energies above140 MeV, pion production becomes possible; those cases should be easier to detect.The other important design criteria for the photon veto system used in this experiment wasthe response time of the detectors. Because of the high beam intensity for this experiment,each detector element was subjected to a large random flux of particles over the duration ofthe accelerator spills. The rate in each counter was a function of its volume, its proximity tothe particle beam and the quantity of energy required to record a hit. For a veto system, theenergy threshold had to be balanced against the fact that random particles cause accidentalvetoing and result in a loss of acceptance. This can be mitigated by restricting the search forphotons to a small coincidence time window. This requires very fast response and is the mainreason behind the choice of plastic scintillator for the veto system. Barrel Veto (BV)The barrel veto consisted of a 1.9 m long cylindrical array surrounding the range stack. It wasdivided into 48 azimuthal sectors and 4 radial layers, as shown in figures 2.15 and 2.28. Allmodules were supported by a web-like frame of 1.5 mm thick stainless steel. The azimuthalboundaries were angled with respect to the detector’s radial direction such that they did notproject back to the target; this limited the effect of gaps and non-active material on photondetection. The modules in a sector consisted of 16, 18, 20 and 21 layers of lead and plasticscintillator, in order of increasing radius, for a total of 14.3 radiation lengths.As for the range stack counters, scintillation light was collected from both ends of themodules via acrylic light guides. Between the light guides and the modules were 15 cm longacrylic mixer blocks which made light collection uniform. Light was detected outside of themagnet at each end with conventional phototubes. Approximately 10 photo-electrons per MeVdeposited in the scintillator were obtained. The analog sum of all signals from barrel vetomodules was discriminated at a voltage level equivalent to 5 MeV (visible) to define a barrelChapter 2. The Apparatus 61veto signal. The time resolution for photon hits in the barrel veto compared to the time of thecharged particle measured in the range stack was o 1.4 ns. Endcaps (EC)The two endcap detectors, referred to as upstream and downstream endcaps, were positionedon either side of the drift chamber, as shown in figure 2.14. Each was divided in 24 azimuthalmodules, with each module consisting of 66 layers of lead and plastic scintillator wedge-shapedplates, for a total of 12.4 radiation lengths. The plates were installed perpendicular to the beamdirection so that the path of all photons emitted in the target crossed a significant thickness oflead and had a high probability to initiate an electro-magnetic shower. The inner radius of eachendcap was 10.3 cm, surrounding the beam region upstream and the target downstream. Theouter radius was 42.7 cm and 40.8 cm for the upstream and downstream endcaps respectively.The light emitted in the scintillator had to be transported along the z axis to the outside ofthe magnet where it was detected by phototubes. To accomplish this, the light was collected atthe wide end of the modules with a 6.5 mm thick plate of wavelength shifter. This material isessentially an acrylic substrate doped with a fluorescent compound; it absorbs light emitted byscintillator and re-emits it at a longer wavelength. The typical intrinsic efficiency of wavelengthshifter to re-emit an absorbed photon is high, 70—95%. However, taking into account theabsorption spectrum, the attenuation length in the materials and the geometry involved, asystem such as the one here has an efficiency of about 10% to detect light emitted in thescintillator [52]. To maximize this number, the wavelength shifter material was chosen suchthat its absorption spectrum overlapped as much as possible with the emission spectrum of thescintillator. Another important consideration in the choice of wavelength shifter material wasits response time to excitation, which had to be as fast as possible.Figure 2.32 shows a schematic picture of one endcap module. The wavelength shifter plateswere separated from the lead—scintillator modules by a 300 1um thick air gaps which preventedlight trapped in the wavelength shifter plate by total internal reflection to re-enter the scintillator plates and be lost. Light was collected at one end of the wavelength shifter plate by anChapter 2. The Apparatus 62adiabatic light guide connected to a 1.3 m long cylindrical light guide to reach the phototubeoutside of the magnet. An average of 8—10 photo-electrons per MeV deposited in the scintillator was obtained from these modules [53]. The energy resolution of individual modules wasmeasured with an electron beam at TRIUMF and determined to be o(E)/E = 6%/”, whereE is the energy measured in GeV.Adiabaticlight guideWavelengthshifter plate/Light guideLead & scintillatorplatesFigure 2.32: Schematic design of one endcap module.The discriminator threshold voltage for the analog sum of all modules in each endcap wasset at a level equivalent to approximately 10 MeV (visible). In 1991, x 10 amplifiers were addedbefore the signals were processed. This allowed a reduction of the voltage required to operatethe phototubes, in turn reducing the current drawn by the phototube base and improvingthe performance and stability of the system. The time resolution for individual modules was1.7 ns for hits above 1 MeV.Chapter 3Event SelectionThis chapter will describe how decays of individual kaons were observed with the help of thedetector, and how constraints applied to the digitized information from the detector were usedin selecting potential K+ lr+zn7 events among a large background of other processes.Constraints used to select events were divided in two groups, online and offline. The firstrefers to initial constraints used to select interesting K+ decays before the detector informationis recorded to a permanent medium. Some of these constraints were applied using electronicstechniques while others involved analysis of digitized information by dedicated micro-processors.These constraints were necessary for two main reasons : first, because of the limited ratecapability to record the detailed detector information and second, because only a small fractionof the incoming K+ are interesting in the search for K+ 11.+v17. The events selected onlinewere recorded for further study, usually on magnetic tape. The offline selection refers to allsubsequent constraints applied to the recorded data.3.1 Online selectionThe online event selection, or trigger, was designed to reject background events as rapidly aspossible while keeping the largest possible acceptance for signal events. The key elements toaccomplish this are• Stopping K identified• Delayed decay of the K+63Chapter 3. Event Selection 64• Single ir+ stopping in the range stack• Veto photonsThe trigger was arranged in three levels of increasing complexity and execution time. Table 3.2 summarizes the rejection and the execution time of each level for the two data collectionperiods in 1989 and 1991. A fourth trigger level was installed but not used in event selection; itwas used to compress the event information. At each level, a decision was taken as to whetheror not to further examine the detector information. Some information processing was requiredfor the trigger decision, and while these tasks were ongoing no other candidate event could besearched for, resulting in “dead time”. This was typically of the order of 25—30% of the 1.6second AGS spill. If at any level of the trigger an event was deemed uninteresting, all currentand subsequent operations in reference to the event were stopped and the system started thesearch for another candidate event at the lowest level of trigger. It was therefore advantageousto regroup the fastest operations at the earliest level of the trigger.Table 3.2: Trigger levels rejection and execution time.Level Rejection Execution Time89 91 89 910 1080 900 2Ons1 3.1 1.8 5[ts2 22 13 700sI 250sEach trigger level will be described below. Also described is the data acquisition system,which retrieved the digitized detector information and transferred it to magnetic tape. Finally,trigger conditions other than the ones used to select K+ +z/i7 candidate events will bedescribed briefly; these selected low bias events used for detector calibration and backgroundstudies.Chapter 3. Event Selection 653.1.1 Level 0The first trigger level (Level 0) used fast ECL logic circuitry. An event trigger consisted ofa coincidence between various detector signals. The requirements for the selection of K+ ÷+7 candidate events below the I(7,-2 peak for the 1989 data set can be represented asKT.IC.DC.(T•A).BCT•(12cT+...+18cT).(19+20+21).(ECM+ECP+BV).The 1991 Level 0 trigger had one minor difference which will be described below. This triggerand the events satisfying its conditions will be referred to as irvE7 in the remainder of this thesis.In the above expression, the (.) represents a logical AND, the (+) a logical OR and a line abovean item indicates that it was used as a veto. The individual requirements, to be described inmore detail below, are defined asKT incoming kaon (KT . B4 TG . spill)E Kaon erenkov counter hitB4 B4 hodoscope hitTG target hitspill AGS spill gateIC I-counter hitDC delayed coincidence(T . A) coincidence in first two RS layersBCT particle track reaches RS layer B(12CT + ... + 18cr) particle track veto for RS layers 12 to 18 (range veto)(19 + 20 + 21) veto for RS layers 19, 20 and 21 (muon veto)(ECM + ECP + BV) veto for endcaps and barrel vetoThe signal that initiated all events was (T A), a coincidence between the first two layersof a given sector of the range stack. Once a (T . A) coincidence had been identified, all otherdetector signals were looked at and trigger requirements were examined. Each (T . A) signalincurred about 20 ns of dead time. The irvi7 trigger required a single (T . A) coincidence todefine the start of a track in the range stack.Chapter 3. Event Selection 66The threshold for individual range stack counter hits was approximately 0.5 MeV. Hitmodules were considered part of a track if they were in the same sector as a (T A) coincidenceor in the next two sectors over in the direction of a positively charged particle curving in themagnetic field. The minimum range requirement was for the track to reach layer B of the rangestack (BCT). A veto was applied for tracks stopping beyond range stack layer 11 (range veto).This eliminated most of the K,2 decays as well as part of the IcZ,-2 decays. For the 1991 dataset, this requirement was modified to allow tracks to stop in range stack layer 12, changingthe range veto constraint to (l3cT + ... + lScT). The veto on the last three layers of the rangestack was referred to as muon veto because it vetoes the region of the range stack where mostmuons from K,2 decays come to rest. In this trigger, the muon veto primarily rejected photons.To identify incoming kaons (KT), a coincidence between hits in the kaon erenkov counter,B4 hodoscope and target during an AGS spill was required. Approximately 3.5 x i0 kaonsper AGS spill satisfied the KT requirement in 1991; in 1989, the rate was typically 15—20%lower. The delayed coincidence (DC) was between a kaon erenkov counter signal and any oneof the six I-counters. Figure 3.33 shows the fraction of events accepted by this requirement asa function of delay time for 1991 data. As can be seen from the graph, the average delayedcoincidence was about 2 ns. The requirement of at least one I-counter hit (IC) was essentiallyredundant with the delayed coincidence requirement, except for a small difference in energythreshold for the I-counters.Finally, ECM, ECP and BV represent the upstream and downstream endcaps and the barrelveto signals respectively. Analog sums of the signals from all modules from each of these subdetectors were formed and then discriminated individually. The threshold was approximately10 MeV for each endcap and 5 MeV for the barrel veto. As seen in table 3.2, the Level 0 triggerrejection was approximately a factor of 1000. The difference between 1989 and 1991 is simplydue to the maximum range requirement in the range stack (layer 12 stops were allowed in 1991).Chapter 3. Event Selection 671.2 I I I I I I I1.0 •4q••••I••e*fUUIUIS•I•0.80.6 f0 0,40.2 f0.0 111111—5 0 5 10 15 20Delay time (ns)Figure 3.33: Accepted fraction versus delayed time between the incoming kaonand the outgoing charged track for the online delayed coincidencerequirement.3.1.2 Level 1This trigger level consisted of three requirements for 1989 data. The first one required that thetotal number of target elements struck at the time of the event be less than 20. This reduced thenumber of K+ —* lr+lr+1r and K+ + 1r+e+ve decays satisfying the irtJi7 trigger conditions,as well as photon conversions in the target. For the same purpose, it was required that therebe only one cluster of I-counters sectors hit at the time of the event. A cluster was defined asany number of contiguous I-counters with a hit. The third Level 1 requirement was that nomore than two range stack hextants could be hit, and if two were hit they had to be adjacent.A range stack hextant was formed of all layers of four adjacent sectors. For example, hextant 1was the sum of range stack sectors 1 to 4. The threshold for a hextant hit was approximately10 MeV. This requirement was a form of photon veto, but it was used primarily to determinein which range stack hextant the charged particle came to a stop; this is necessary for the nexttrigger level.For 1991 data, only the hextant cut was included in the Level 1 trigger. Although the othertwo constraints did provide some background rejection at the trigger level, their significantChapter 3. Event Selection 68acceptance loss and the increased data taking rate capability available in 1991 made themunnecessary.3.1.3 Level 2This level consisted in a fast 7r+ decay search using the TD information. This search wasperformed by processors which directly accessed the TD information. In 1989, the devices usedwere the SSPs (SLAC Scanner Processor), which resided in each of the Fastbus crates housing32 TD channels. In 1991, the search was performed by the Smart Controllers (SC), dedicatedprocessors programmable in C language. These devices significantly reduced execution time ofthis trigger level, from 700 ts down to 250 s. The Smart Controllers each handled 16 TDchannels and performed a number of other operations on the TD data in addition to the r —*search, before transferring the information to the SSP controffing the Fastbus crate.The stopping layer and stopping hextant information from Level 0 and Level 1 was passedto all processors involved in the Level 2 trigger. The processor handling the stopping counterthen proceeded to retrieve the digitized TD data and performed the + decay search algorithmfor each end of that counter in succession. In order to reduce dead time, success of the searchfor the first end was required before the second end could be examined. This saved typically200 s in 1989 and 100 s in 1991. The search had to succeed for both ends of the stoppingcounter for the event to be accepted.Two different cases were handled by the search algorithm : a) two detached pulses and b)a double pulse. In case a) the integrated area of the second pulse was required to be consistentwith the energy deposited by a muon from + decay at rest. In case b), use was made ofthe linear relationship between the maximum height and the area of a pulse from a scintillatorcounter. For each TD channel, a slope and intercept were determined for this linear relationshipusing well identified single pulses. The maximum height and integrated area were computedfor each decay candidate pulse. From the pulse maximum, an expected pulse area wascalculated using the pre-determined constants and compared with the measured value. If thedifference between the measured area and the expected area was greater than a fixed threshold,Chapter 3. Event Selection 69the algorithm succeeded. An exception to this arose when the pulse reached the maximum ofthe TD dynamic range. In this case, the pulse height—pulse area relationship was unreliable, sothe event was rejected.Figure 3.34 shows the TD information for both ends of the stopping counter of two eventsaccepted by level 2. The efficiency of the search increased as a function of the decay time of the• The average efficiency varied as a function of the range stack stopping layer, from about70% to nearly 90%. The efficiency was lower in the thicker layers (B and C) because of thelarger size of the primary pulse from the stopping ir+ and their lower light collection efficiencyresulting in a poorer pulse resolution. The Level 2 trigger constraints were more demanding in1989 than in 1991, explaining the difference in rejection indicated in table 3.2. Another reasonfor the difference is the nature of the events reaching Level 2; the different Level 1 triggerconditions in 1989 and 1991 resulted in different emphasis of the various background processes.3.1.4 Level 3This trigger level operated in a farm of processors (ACP). Each processor, or node, was programmable in Fortran and could execute the same programs used in the offiine selection (seesection 3.3). A program executed in a host computer distributed individual events to availableACP nodes. The nodes analyzed the events and signaled the host program upon completion,returning the modified event information and the status of the analysis.The event rejection capability of this trigger level was not exploited. However, significantoperations were performed on the event information. The bulk of the 40 kBytes long events wastaken up by the TD information. It was realized that for part of the 10 is time range coveredby the TDs for the range stack channels, a small number of parameters from each pulse, suchas leading edge time, pulse height and pulse area, was sufficient information to keep. A fastalgorithm was developed to extract this information accurately and store it in an efficient way.The shortest pulses recorded by the TDs occupied four 32-bit words, and very long pulses tookup as much as thirty words or more; the algorithm stored the vital information in only twowords, regardless of the initial length. This compression was not applied to all range stack TDChapter 3. Event Selection 70160— — 4Q_ I•III•IrIIIIIrIIIIIIrII,I•IIIIIrII —0a) RS Sec 1—4 o b) RS Sec 1—4140- Lay B End 1 F 120- Lay B End 2°180- XXex0 X.4 0 x 0‘-f-LJ x - x00 o o20- -xX ox xXe 00 -IIIIIIIIlIIIIIIIIIIIIII...IIIIIIrt —— .IIIIIIIIIII,,IIII,IIIIrII,IIIIrII —u 10 20 30 40 60 70 10 20 30 40 50 60 70Time (ns) Time (ns)120— — 12()— —3<c)RS Sec 21—24 d)RS Sec 21—24100- Lay C End 1 - 100- x Lay C End 2X : 0080- - 80--= X - Xci)60- -60-0.) 0 ci :04QOXXo>b<20- XQ - 20- x 00 (3< ox (3< 0 X (3<:p :0- id i’6’ i idó’ ‘ib i-bTime (ns) Time (ns)Figure 3.34: TD information for both ends of the stopping counter for eventsaccepted by the online pion decay search for a) and b) double pulseand c) and d) detached pulse.Chapter 3. Event Selection 71channels; channels in the stopping hextant (used for trigger Level 2) were exempt. Also, forchannels outside of the stopping hextant, pulses in a 320 ns wide time region around the timeof the K+ decay were exempt.Another operation was performed by this trigger level for 1991 data. An algorithm determined the leading edge time of each of the fiducial time pulses injected in each channel near theend of the TD recording time. This leading edge time was stored in 16 bits. If the leading edgedetermination was deemed sufficiently accurate, the entire fiducial pulse was removed from thedata; otherwise, the full information was kept. The combined effect of the two algorithms, pulseinformation compression and fiducial time determination, was to reduce the average event sizeby about a factor of two.3.1.5 Data AcquisitionThe data acquisition system transfered the digitized information from the detector to magnetictape based on the decisions made by the trigger system. Figure 3.35 shows schematically howthe various electronics modules and dedicated processors were linked together and accessedby the computer coordinating the actions of the system in 1991. The main data acquisitionprogram resided on the host computer, a MicroVax II in 1989 and a Vaxstation 3200 in 1991.The primary link from the host computer to the detector was via the CERN Fastbus Interface(CFI). This allowed access to the master SSP located in a Fastbus crate. The master SSP waslinked to the secondary SSPs by a cable segment; each secondary SSP controlled one Fastbuscrate. One of these SSPs was linked to the trigger system and relayed the Level 0 and Level1 decisions to the SSPs located in the Fastbus crates housing the TDs. These SSPs thenperformed the Level 2 algorithm if necessary (or communicated with the Smart Controllers toperform the same task in 1991) and retrieved the digitized information from the TDs. Thetrigger SSP also recorded the status of all signals used by the trigger. This information wasrecorded with the data on magnetic tape, and could be used to apply some online constraintsduring the offline analysis. There were also SSPs in Fastbus crates housing the TDCs. TheADCs were located in CAMAC [54] crates; their information was retrieved via a high speedChapter 3. Event Selection 72bus by the Brookhaven FERA Interface (BFI).All secondary SSPs stored in memory the information from several events recorded during aspill from the AGS. In the intervening time between spills, the master SSP collected the information from the secondary SSPs and formed the events; typically, this operation took 10 ms perevent. The events were then transferred to the ACP system by the Fastbus Branch Bus Interface (FBBI). The ACP host program retrieved the events from the nodes once the level 3 triggeroperations were completed. The host computer then transferred the events to magnetic tape.In addition, copies of some events were also transferred via an ethernet line to another computerworkstation where the online monitoring program resided. Finally, information concerning thestatus of the high voltage system was periodically recorded to magnetic tape with the events.The information was provided by a Microvax II which controlled all CAMAC operations.3.1.6 MonitoringThe data acquisition system made it possible to examine a portion of the events as they wererecorded using the offline analysis program. An analysis program verified the integrity ofthe data and accumulated statistics related to the performance of all sub-detector and theirelectronics. If any element displayed a behavior outside of some preset tolerance, operatorswould be notified of the fault.Another very important aspect of monitoring involved other sets of events selected withdifferent trigger conditions than irvi7 data. These conditions were typically of low bias andwere designed primarily to select samples of the most common K+ decays such as K2 andK,2 . These events were recorded concurrently with the irvE7 events, hence providing excellentmonitoring of the experimental conditions. Because of the large number of events satisfyingthese simple trigger conditions, their numbers were controlled by applying a pre-scaling factor.The recorded events were analyzed offline to calibrate sub-detectors, estimate background levelsand determine the efficiency and acceptance of most of the online and offline constraints.Table 3.3 gives a description of the monitor triggers used. Note that the requirements forthe i-ii7 levO trigger are slightly different than for the irvi7 trigger described in section 3.1.1;Chapter 3. Event Selection 73Easibus CratesFgh speed busReadoutHost ComputerVaxstation 3200tCMMC Send Lii*Figure 3.35: Schematic diagram of 1991 data acquisition system.Chapter 3. Event Selection 74the former is less restrictive. This is because the irv7 levO trigger is the same as the one usedin the search for K+ _* K+7 above the K2 peak. To obtain a data sample corresponding tothe Level 0 trigger conditions used for the 7rvi7 search below the I(,,-2 peak, additional triggerrequirements were applied offline based on trigger information recorded with the data.Table 3.3: Description of Level 0 monitor trigger requirements. Conventions arethe same as the ones used in section 3.1.1. These triggers did notuse further trigger levels, except K-scat which used Level 1.Trigger ConditionsKt2(1) KT.(T.A).BCT .(19CT+20CT+21CT)Kir2(1) KT.(T•A)•BCT.(19CT+200T+21CT)_____________inñ7lev0 KT•IC•DC•(T.A).BCT.(19CT+20cT+21CT).(ECM+ECP+BV)ir-scat KB.ETG.DC.IC.(T.A).BCT.(19CT+20CT+210T).(ECM+ECP+BV)with KB (B1.B2)..B4.spill3.1.7 Data SamplesTable 3.4 summarizes the data samples collected in 1989 and 1991.Table 3.4: Summary of the 7rv1 data samples.Year Time period (days) # of events1989 33 1.4 x 1061991 59 6.0 x 1063.2 CalibrationA calibration of the time and energy measurements of the sub-detectors was necessary beforeoffline analysis could proceed. For some of the sub-detectors, the calibration required specialdata sets or trigger conditions designed specifically for the calibration. In most other cases,use was made of monitor events (see section 3.1.6). This provided for a calibration directlyapplicable to the experimental conditions of the KVV data set. All sub-detectors were calibratedChapter 3. Event Selection 75using events from the common K,2 and K2 decays, except for some of the beam counters whichwere calibrated using beam pions, and the barrel veto energy calibration which was performedusing cosmic ray muons. A set of trigger conditions was specifically designed for the latter;data were recorded for each year immediately after the accelerator operations had ceased.To calibrate the drift chamber, muons from J(2 decays were used. Data were taken bothwith the spectrometer magnet on and off; turning off the magnet removes the complicationof the Lorentz angle for the drift electrons’ trajectory. The energy calibration of calorimetersand other scintillator counters used well identified kaons, pions or muons. The expected energydeposition by particles in the various detector elements was determined either by Monte Carlosimulation or integration of the Bethe-Bloch formula [17]. These expected values were then usedto calibrate the detector response. The energy calibration of a sub-detector was independentof the others.The time calibration of sub-detectors other than the drift chamber and beam countersproceeded in several steps linking the different sub-detectors. The target, in which both theK+ and its charged decay products were observed, was calibrated first. The kaons defined timezero. Because the time measurements in the range stack had the best resolution, it was themost important part of the time calibration. Well reconstructed muon tracks from K2 decayswere used. Each counter was calibrated with respect to the A-counter in the same sector (orone sector over). The time of the A-counters were aligned by using the average time of thetarget elements struck by the muon.Once the range stack time calibration was completed, photons from 1’i,-2 events were usedto calibrate the barrel veto and endcap elements. The + track was reconstructed in the rangestack and its time (Trs ) was determined. The barrel veto and endcap elements struck by photonshowers were then calibrated with respect to Trs . Finally, the I-counters time calibration wasperformed using + from K2 decays.Chapter 3. Event Selection 763.3 Offline selectionThe events satisfying all trigger requirements were recorded to magnetic tape in YBOS [55]format. Each event was formed of several data banks, each one containing specific information.To retrieve the events from tape and have access to the YBOS data banks, a dedicated programcalled KOFIA [56] (Kaon OFfline Interactive Analysis) was used. For each event retrieved themain program called a user supplied subroutine which accumulated information about theevents and took a decision on whether or not the event should be set aside for further analysis.The user supplied analysis subroutine made use of many other subroutines to retrieve databanks, provide calibrated detector information and perform analysis on the data.The offline selection requirements were based on the same general criteria as the onlinerequirements. The approach that was followed in the design of these constraints, or “cuts”,was different for the two data sets. For 1989 data, the “standard” method typically used indata analysis performed towards the search of rare decays was chosen. In this method, simplecuts are initially applied to the data to reduce the size of the sample. These cuts are usuallywell established and can be set up with relative ease. Based on examination of the remainingdata, more elaborate cuts are designed to reject background events and are then applied tofurther reduce the sample size. Any number of such iterations can be performed until the setof cuts is deemed final. There is however a problem with this method : if the last steps of theprocess involve only a small number of events, and they often do, there is a significant dangerof biasing the result. Because a large amount of information is available for each event, it iseasy to design cuts which reject all events while apparently maintaining a large acceptance forthe signal searched for. This could lead to an overestimate of the sensitivity of the experiment.It could also have the unfortunate consequence of preventing the observation of a real signal.To avoid these pitfalls, for 1991 data the design of all cuts beyond the simple initial set wasaccomplished using data samples that could not contain potential signal events. In this way,bias was minimized for the final result. However, this method brought the additional difficultyof finding appropriate data samples to prepare the cuts. These samples had to be representativeof the background processes that the cuts were designed to reject. The worst scenario wouldChapter 3. Event Selection 77be a cut which appears very effective when applied to the “background” data sample but turns•.outto have no rejection. at all for true background. Furthermore, some criterion had to beestablished to determine the effectiveness of a cut. For example, a cut which rejects half ofthe background sample but has an acceptance of only 50% for the signal would be obviouslyineffective. It was decided that the fraction of events rejected by each cut had to be at least twicethe fraction of events rejected because of acceptance loss. Obviously, there is some dependenceon the data sample used for this test; the data has to be representative of the background beingaddressed by the cut.The design of cuts and the estimation of the level of contamination from all backgroundsources was an iterative process. The following section describes all cuts and the next chapterwill describe the study of all background sources. In the description that follows, cuts weregrouped in several categories : track reconstruction, timing, photon veto, pion identification,beam, target vertex and signal region. Most of these categories contain several different cuts.Each of them was identified by a short word or mnemonic for easy identification later on inthe description of the background studies and analysis. A summary of all cuts is given insection Event reconstructionThe cuts described in this section pertain to the identification of a stopping kaon in the targetand a positively charged particle leaving the target and passing through the I-counters arrayand the drift chamber and finally coming to rest in the range stack. TARGETThis cut used a set of subroutines to do pattern recognition in the target and attemptedto identify target elements hit by a K+ and ones hit by an outgoing + from kaon decay.Because they travel mostly parallel to the scintillating fibres, kaons typically had large earlyenergy depositions in the target elements. The decay pions tend to travel transversely to thescintillating fibres and therefore had more modest energy losses at later times. The calibratedChapter 3. Event Selection 78ADC and TDC information was used to classify the struck target elements as or Tofirst order, kaon elements had to have a measured time relative to the kaon erenkov countersignal between -10.0 and +10.0 ns and an energy greater than 3 MeV, while the pion elementstimes had to be between -10.0 and +75.0 ns and their energy less than 3 MeV. These initial listsof kaon and pion elements were used to initiate the pattern recognition. Based on their positionin the xy plane, neighboring elements were grouped to form clusters, which in turn were usedto form the stopping kaon track and the outgoing pion track. For the latter, struck I-counterswere also used as a guide to identify the track. During the pattern recognition process, theassociation of an element as kaon or pion could be changed in order to improve the pattern.This algorithm had a very high efficiency(‘-S.’99%) in identifying a kaon and its decay chargedparticle, at the cost of keeping some obviously flawed events. A more restrictive target trackingalgorithm, combining information from the drift chamber with the target information, will bedescribed later.The specific requirements of this cut were simply that a kaon track be successfully reconstructed in the target; no demands were made on the pion track. More restrictive constraintswere applied by other cuts which used quantities determined by the target track reconstructionsubroutine. This included lists of the identified kaon and pion elements and the energy-weightedtime and summed energy of the kaon and pion track. DC-SETUPOne of the primary requirements for a * +z,i7 candidate event is that a single positivetrack be reconstructed in the drift chamber. In addition to providing the track momentummeasurement, the drift chamber tracking information is the key element in identifying the K+.The good position resolution helps in linking track segments identified in the target and rangestack, where resolution is inherently poorer.The first step in identifying a track in the drift chamber was to convert the TDC timeinformation from the hit wires into a hit position. A pedestal was subtracted from the rawtime value to obtain the drift time of the hit. Using the calibrated value of the drift velocityChapter 3. Event Selection 79the drift time was then converted into a drift distance. From this distance and the calibratedvalue of the Lorentz angle, two positions in the xy plane were determined for each hit due tothe left-right ambiguity. Only in the process of track fitting were mirror hits discarded fromthe list.The list of cells from the three axial layers with wire hits was then scanned. In each cellan attempt was made to fit the hit positions to a straight line. The minimum number of hitsrequired was three. The straight line fits in the cells gave a vector position and direction. Thesevectors were used to identify a crude circular track. The points from the chosen vectors werethen used to fit a circle in the xy plane, with the radius of curvature giving the xy componentof the track momentum. Other points not initially chosen were included or discarded from thefit on the basis of the change in the chi—square value of the circle fit.In the event of a successful X7J fit, the information was used in combination with the hitpositions on the two stereo layers to obtain z-position information. In the turning angle-zposition space the track trajectory is a straight line, with the slope giving the z component ofthe momentum. The minimum number of points required for a successful z fit was three, withat least one in each of the two stereo layers.The specific requirements for the drift chamber track reconstruction were that one and onlyone track be identified by the fitting procedure, with successful fits in both the zy and z planes.For 1991 data, other requirements were added. The track had to be positively charged, andthere had to be at least one hit in each of the five wire layers. This last requirement ensuredthat the particle did not exit the drift chamber fiducial volume via one of the end plates, wherea large energy loss could go undetected. Finally, as a form of photon veto, the number of hitwires other than the ones used to form the track was limited to be less than or equal to 45.Figure 3.36 shows the distribution for this number for “p2 and irv7 data. For K,2 events thereshould be no activity at the time of the K+ decay other than the ,+ , except for accidentalparticles. For irvi7 data, all background sources are included. This requirement eliminatedevents in which photon conversions created a large amount of ionization in the drift chambergas, but did not get reconstructed as tracks. A similar cut was included in the 1989 analysisChapter 3. Event Selection 80but as a separate entry; it appears in the photon veto cuts category (3.3.3).3500 4000030003000025002D00 U)—C CD Do 001500 01000100005000 00 20 40 60 80 100 0 20 40 60 80 100# of wires # of wiresFigure 3.36: Number of struck drift chamber wires outside of the reconstructedtrack for a) K2 data and b) irvi data. The dashed line indicatesthe cut position.In 1991, additional tracking information was available from the inner wire chamber (IWC);it was not used in order to identify the track. However, the IWC tracking was performed afterthe drift chamber track fitting procedure succeeded, and if the chi—square value of the overallfit either in xy or z was improved by the inclusion of IWC information, the results of thecombined DC-IWC fit were used for the rest of the event analysis. Therefore, no additionallosses of acceptance were incurred by using the IWC, but the analysis benefited from the 10%improvement in z-position resolution (see section 2.2.4). DC-CHI2In 1989, some events satisfying the basic track fitting criteria had very poor x2 probabilities,sometimes identically zero. These cases resulted from unstable fits; hence, a cut was appliedto eliminate these events. The drift chamber track fitting algorithm was improved for the 1991data analysis, and therefore this cut was not necessary.‘‘‘‘III’’’’’’a)I . . .Chapter 3. Event Selection 813.3.1.4 RS-TRACKTo find tracks in the range stack, a list of counters for which the geometrical mean of thecalibrated energy at each end of the counter was greater than 0.5 MeV was used. A track wasinitiated by hits in the T and A counters of a given sector. Each subsequent layer was examinedfor a hit, first in the same sector as the T . A coincidence and then in the next sector over if nohit was present in the same sector. Both positive and negative track options were considered,with the former being the first choice. Once the charge of the particle had been established thesearch continued only in that direction, until a layer was found with no hit counter connectedto the track.Each of the tracks thus identified was then compared to the list of drift chamber tracks bydetermining which T-counter was intersected by each drift chamber track. Only the range stacktracks for which a match was obtained with a drift chamber track were considered for furtheranalysis. The subroutine then summed up the energy deposited by the particle in the rangestack and computed its range. For the latter, the drift chamber information was extrapolatedto correct for the curvature of the track and the component of the range along the z axis. Forthe tracks which intersected one or both of the range stack proportional chambers (RSPC),their zy and z position information was used to refine the range measurement.A correction was needed for the range in the stopping layer. Here, the observed energy inthe last layer was used to determine the range, by interpolating an empirical table of range asa function of energy. This implied that a hypothesis had to be made about the particle type.The correction was computed for both a and a p,+ hypothesis and both results were madeavailable. In the case of the hypothesis, since most of the time the pion decay occuredwithin the ‘-‘100 ns long ADC integration gate, a value of 4.12 MeV appropriately corrected forsaturation [57j was subtracted from the stopping layer energy before the range was determined.One unfortunate consequence of this method for measuring the range is that for tracks stoppingin the thicker layers of the range stack the track energy and range are highly correlated. Thisis particularly important for this analysis because of the high acceptance of range stack layerB for K+ .SChapter 3. Event Selection 82This cut required that one and oniy one track matching the drift chamber track be reconstructed in the range stack. For 1991 data, the stopping layer had to be within layers 3 and6 (inclusive) and the stopping counter energy had to be greater than 4.0 MeV. This is theminimum expected in the case of a stopping pion decaying to a muon and a neutrino withinthe ADC gate. RSPCIt is possible for particles to stop in the walls of the proportional chambers (RSPC). The particlemight even curl and re-enter the range stack scintillator layer preceding it. To eliminate suchpossibilities, activity in the RSPC above the stopping counter for tracks stopping in range stacklayer C was examined. If hits were recorded by the chamber, the event was rejected. This cutwas not applied to 1991 data; no evidence was found for such activity after all other trackreconstruction and kinematic cuts were applied. ICOUNTERIn the I-counters, energy is deposited by the charged particle leaving the target. If the particleis a , it can undergo a nuclear interaction in the I-counter, possibly leaving more energy thanexpected. It is also possible for kaons, other beam particles or photon conversions to depositenergy. Again, the energy measured in the I-counters wifi be greater than what is expected. Toreject some of these cases, it was required in 1989 data that the total measured energy be lessthan 5.0 MeV in the I-counter struck by the + track identified in the target.A subroutine using the drift chamber track fit information determined which of the six Icounters was hit by the charged particle, the range of the particle in that I-counter and estimatedthe energy deposited, based on the range and assuming the particle was a . The subroutinehad to succeed in finding an intersection between the drift chamber track and the inner andouter faces of the I-counters array. The range was computed as the arc length between the twointersection points, corrected for the component along the z-axis using the drift chamber trackinformation. The estimated energy deposition was then computed, using the + expected rateChapter 3. Event Selection 83of energy loss at the measured momentum. The energy loss rate was computed by interpolationin a table of empirical values.The expected energy loss was then compared to the measured ADC energy. In the casewhere the track crossed two adjacent I-counters, the measured energy in both counters wassummed. Because of the finite position resolution of the drift chamber, this was also done inthe case where the track was close to the boundary between two I-counters. Figure 3.37 definesthe geometry for this requirement. For each event, the angle 8 between the center (dashed line)of the counter and a vector from the center of the target to the intersection point of the trackwith the inner face of the counter (CP) was found. If the absolute value of sin8 was greaterthan 0.4, the energy of the adjacent counter was added. The maximum possible value of I sin Owas 0.5, defined by the I-counters geometry. The difference between the measured energy andthe estimated energy had to be less than or equal to 2.0 MeV. Figure 3.38 shows this quantityfor a sample of K,-2 events.+•1CFigure 3.37: Geometry conventions used for ICOUNTER cut.Chapter 3. Event Selection 84600050004000U)3000200010000Figure 3.38: Difference between measured and estimated I-counter energy for the-+ for J(i,2 events. Events outside of the region defined by the dashedlines were rejected. FIDUCIALThis cut ensured that the K+ decayed in the fiducial volume of the target and that the chargedparticle trajectory was contained within the geometrical acceptance of the drift chamber andthe T-counters. Two quantities were used : the z position of the kaon decay vertex (Z) andthe sine of the dip angle of the -+ trajectory (sin Odjp), measured at the decay vertex. Thedip angle is defined as the angle between the particle track and the xy plane, with positivevalues in the same direction as the positive z-axis. This angle is equivalent to the directionalcosine along the z-axis. Z.., was determined by extrapolating the DC track in the target andfinding the point of closest approach with the position of the decay vertex in the xy plane givenby the target track reconstruction routine. The cut positions were set at IZtI 10 cm andsin Sdjpl 0.5 ; events outside of these limits were rejected. Figure 3.39 shows the distributionof these two variables for a sample of 1991 K2 events.—4 —2 0 2 4(MeV)Chapter 3. Event Selection 85800 600500600400a)400 3002002001000 0—20 10 20 —1.0 —0.5 0.0 1.0sIn 0 dpFigure 3.39: Kaon decay vertex z position and 7r+ track dip angle for K),-2 events.Cut positions are indicated by the dashed lines. ZDCTZIn 1989, it was not required that the track in the drift chamber include hits in all five cell layers.The result of this is that some particles exited the chamber by traversing one of the aluminumend plates, thereby losing some undetermined amount of energy. To remove such events a cutwas applied on the position of the track along the z-axis at the outer radius of the drift chamber(ZDC); the cut position was —22.0 < ZDC <24.0 cm.An additional measurement of the track position along the z-axis was obtained by comparingthe energy measured at each end of the T-counter struck by the track. The position along thez-axis is given byZT = ln(-) (3.29)where .\ is the attenuation length of light in the scintillator counter and E is the energymeasured at end i. For good tracks, there is a linear relationship between this measurementand ZDC. Figure 3.40 shows the distribution of ZT versus ZDC for a sample of 1989 rvE Passidata. The dashed lines show the cut used; also shown are the limits for the cut on ZDC. Notethat the scale for ZT was not calibrated in centimetres.—10 0z vertex (cm)0.5Chapter 3. Event Selection200150 -100500—-50—100—150 H—200i-i-i--r I,,,IH,—30 —20 —10 0Z0 (cm)86Figure 3.40: ZT versus ZDC distribution for 1989 irzJi7 Passi data. The eventsinside the dashed and dotted lines were accepted.3.3.2 Timing3.3.2.1 PROMPTThis cut ensured that the K+ decayed at rest in the target by requiring a delay between themeasured time of the K+ track in the target (T ) and the measured time of the + track(T). Each quantity was an energy-weighted average of the time of individual target elementspart of the K or track. The time difference T -T was required to be within the bounds2.0 < (T -T ) < 50.0 ns. The late time constraint originated from the fact that for lateK decays a significant part of the energy deposited by the + could be missed by the ADCintegration gate and therefore reduce the total measured track energy. Figure 3.41 shows thedistribution of T -T for a sample of 1991 irz’E7 events. The spectrum is formed of threecomponents : a peak near time zero from K+ decays in flight, an exponential decay part fromJ(+ decays at rest and a flat component over the entire spectrum from beam pions. Note thatthe early part of the exponential spectrum is deformed by the acceptance of the online delayedcoincidence (see figure 3.33).For 1989 data, several other requirements were included in this cut. The time of the charged-NJ:::.§. ..:“ .:.10 20 30Chapter 3. Event Selection 871 tI I I I I I III I I I I I I12 I10+0C,)DoC)420I—- II 11111111 I III I—20 0 20 40 60 80TIMEP—TIMEK (ns)Figure 3.41: T -T distribution for 1991 7rvE events. Events outside of theregion defined by the dashed lines were rejected.particle track in the range stack (Trs ) was determined by taking the mean of the time measuredat the two ends of the A-counter struck by the track. The following cuts were applied usingthis time measurementTrs > —1.OnsTrs — T> 1.OnsIT — TrsI <4.5ns. (3.30)For 1991 data, additional requirements on the time of the charged particle track were re-groupedin another cut, described next. TRKTIMThis cut was concerned with the time information of the in 1991 data. The time of their+ track in the target (T ) was defined earlier. The I-counter time (T) was the time of theI-counter identified as part of the track by the ICOUNTER cut. If the information was reliable,the time value as measured by the TDs was used; otherwise the TDC based time was used.In the case where the track crossed two I-counters or was close to the boundary between twoChapter 3. Event Selection 88counters, the earliest of the two time measurements was chosen.The time of the range stack track (Trs) was determined by averaging the times of the countersbelonging to the track, determined from the leading edge of the TD pulses. For each counteron the track, a list of calibrated times from each end was scanned for end-to-end coincidences.The difference between the times at each end had to be less than 7 ns. A list was made of theaverage time of the two ends for counters with a coincidence, thereby removing the dependenceof the time measurement on the position of the energy deposition in the counter. This list wasthen scanned to find times within 10 ns of the T-counter time. The overall track time was aweighted average of all counter times found in coincidence with the T-counter, with the weightgiven by the pre-determined time resolution of the hits.The three different measurements of the time of the charged particle track were then compared to each other. A x2 quantity was formed, using Trs as the reference because of its betterresolution2 — (T — Trs — zS)2 (T — Trs —X +with z and a the measured mean and standard deviation of the (T — Trs) and (T— Trs)distributions for irvi7 data. The standard deviation for (T— Trs) was a = 0.81 ns, and for(T1 — Trs) it was a = 1.15 ns and a = 0.59 ns for TDCs and TDs, respectively.The x2 probability P(x2) was determined for two degrees of freedom. Figure 3.42 showsthe distribution of the base 10 logarithm of the x2 probability for K,2 events. On this graph,all counts below -10.0 are accumulated in the leftmost bin; these are mostly events for whichno outgoing track elements were found in the target, hence no Ttg value was available. Eventswith a probability P(2) less than iO were rejected, as indicated by the dashed line on thefigure.3.3.3 Photon VetoIn the search for K+ 7r+v7 below the K2 peak, most backgrounds involve photons. Thehigh rate environment created by the intense incident beam of kaons and pions makes it difficultto effectively reject photons while keeping accidental vetoing at an acceptable rate. Cuts haveChapter 3. Event Selection 89250020001500(1)CD0(-)10005000Figure 3.42: Logarithm of the x2 probability for the TRKTIM cut for K,2 events.Events to the left of the dashed line were be designed to balance these two factors. Some cuts indirectly veto photons, usually becausea photon conversion shower perturbs some measurement. This section will describe cuts thatare designed specifically to reject events with photons.The most straightforward approach to photon veto is to search for energy deposition incoincidence with the ir detected in the drift chamber and range stack; the search shouldencompass the entire detector, except for the regions where the identified j+ deposited energy.A subroutine performed such a search in the electro-magnetic calorimeter (barrel veto andendcaps), the range stack, I-counters and V-counters. Table 3.5 gives the average accidentalrate for hits above 1 MeV for the different subsystems (constant background). Note that thereis some correlation between the rates; for example, a single random particle can deposit energyin both an endcap and the range stack.For the barrel veto and the range stack, time and energy information was required fromboth ends of the counters. Another subroutine handled cases where partial information wasavailable. For 1989 data, a cut was setup for the endcaps and barrel veto (INT_EB) and onefor the range stack, I-counters and V-counters (INTJtW). For 1991 data, a separate cut wassetup for the range stack and barrel veto energy depositions found with information from one—10 —8 —6 —4 —2 0log10 P(2)Chapter 3. Event Selection 90Table 3.5: Accidental rates in various detector subsystems for hits above 1 MeV.The endcaps entry is the sum of both the upstream and downstreamendcaps.Subsystem Rate (MHz)Range stack 2.6Barrel Veto 1.1Endcaps 6.8I-counters 0.33V-counters 0.89end missing (INTSE); all other events with some photon energy were handled by a single cut(INTIME). INTIMEAs mentioned above, this cut looked for energy in the detector in coincidence with the chargedtrack, but away from the regions struck by that track. The time of the track measured in therange stack (Trs ) was taken as the reference time. The leading edge times of hits in all countersin the search regions with measured ADC energy were compared to the reference time. If thetime difference was within a pre-determined time window, the energy of that counter was addedto a sum. In the case of the barrel veto and the range stack, time and energy information wasrequired from both ends of the counters; the absolute value of the end-to-end time differencein a module had to be less than 30 ns.Individual energy sums were taffled for each sub-detector, and a cut was applied on eachsum. Table 3.6 lists the time windows and energy thresholds used. Figure 3.43 shows thedistribution of energy versus time for hits in the various subsystems for irv7 events. The searchwindows are indicated on the graphs. For the barrel veto graph, a late tail can be observed.This is attributed to slow neutrons resulting from photo-nuclear interactions. Figure 3.44 showsthe same graphs, but for pre-selected K,2 events. Since in this case no activity is expected atthe time of the + , it is a measure of the level of accidental vetoing expected in the case of_+ +jj7 events; as will be seen in the section describing the acceptance calculation, the lossChapter 3. Event Selection 91is significant. The prompt peak in the range stack plot is due to counters that are part of thecharged particle track but have less than 0.5 MeV and to &rays emitted by the charged particle.Because of the energy threshold chosen for the cut, only the latter incurs an acceptance loss.There is also a prompt peak in the I-counter plot. There are two contributions to this peaktracks which hit two adjacent counters at an angle shallow enough to avoid identification as asector crossing and photon conversions in the target depositing energy in the I-counters. Thelatter contribution is about twice the former and is probably due to photons radiated by the,+. It should be noted that losses due to the I—counters account for only about 2.5% of thetotal INTIME cut acceptance loss.Table 3.6: Parameters for INTIME cut (1991 data).Subsystem Time window Threshold[Min,Max] (ns) (MeV)RS [-2.0,+13.0] 0.5BV [-5.0,+15.0] 0.4EC [-4.5,+4.5J 0.6IC {-5.0,+5.0j 0.2VC {-6.0,+5.0] INTSEIt was noted in the description of the previous cut that for the range stack and barrel veto,information from both ends of the counters was required. However, in the case where a photonconverts very close to one end of these counters, it is quite possible for the other end to missthe hit completely, especially if the energy deposited is small. Also, hardware or software errorscan result in a wrong measurement of the time of a hit at one end. The INTSE cut looked forcounters in the range stack and barrel veto for which either the energy or the time informationfrom one end was missing. The hits were categorized according to which information wasavailable, and search parameters similar to the ones for the INTIME cut were determined foreach category. Table 3.7 lists the categories that were found to provide some photon rejectionand the time windows and thresholds for each. Figures 3.45 and 3.46 show the distributions ofChapter 3. Event Selection 9225-BV20->‘ I”.510• I....I....oo—20 —10 0 10Time (ns)25- 20n>- 15>‘• 10•.U. I. .-.,9•-i—30 —20 —10 0Time (ns)Figure 3.43: Energy versus time distribution of hits in the various subsystems forthe INTIME cut for 1991 iriii7 data.I. . . . I.. . I ... . IRSII.—£•%120 -15>•‘10U300 —20 —10 0 10 20Time (ns)I02520>11) 15>.‘0’10CU5.20 30ECGDoaIC-.00G.-I—30 3 )—20 —10 0 10 20Time (ns)A—30 —20 —10 0 10 20 30Time (ns)2015>‘ii 10•CU5.vCIib 2b 30Chapter 3. Event Selection 93I IIIIIIIII:iI..Ii.:::::.:. :::::. :1: .rimriri—20 —10 0 10 20 30lime (ns)I,,II,I,,III,,II,::—20 —10 0lime (ns)I tii,iIipiiByOn.BUIUODiQ.000iCiQej.D.00000.Qinne.W..j..fl000000rfl-7-rr-1-rrrVTrT-;—20 —10 0lime (ns)Figure 3.44: Energy versus time distribution of hits in the various subsystems forthe INTIME cut for 1991 IE,2 events.2520->0 15->‘10CU50.—30c2520n>cv:515>‘Q10CU5025 -20 -15>1C,:5 10CU5..I. ./..ib 213 30.I.20>05 15>‘C,i3 o•CU5,Lj0 o 10 20 —30 ‘0 6 ‘ib 20 So’lime (ns) Time (ns)vo2520>0a15>‘—30 10 20 30Chapter 3. Event Selection 94time versus energy of hits in the different categories for iriiE and K,2 events respectively, afterthe INTIME cut had been applied.Table 3.7: Parameters for INTSE cut (1991 data).Subsystem Ends hit Time window ThresholdEnergy Time [Min,Max] (ns) (MeV)RS both single [-7.O,+7.0] 0.0RS single both [-5.O,+5.0] 0.0RS single single [-10.0,+10.0] 0.6BV both single [-8.0,+8.0] 0.0BV single single [-14.0,0.0] INT..EBThis cut looked for activity in the endcaps and barrel veto for 1989 data. The time windowsand energy thresholds are listed in tables 3.8 and 3.9. Included in the single end hits parameters(table 3.9) is an entry referring to the endcaps. This cut requires the number of endcap moduleswith a time hit within the coincidence window but with no measured energy to be less thantwo.Table 3.8: Photon veto cut parameters for 1989 data.Subsystem Time window Threshold[Min,Max] (ns) (MeV)RS [-4.2,+13.81 0.5BV [-4.3,+11.7] 0.3EC [-5.9,+6.1] 0.5IC [-4.75,+3.25] 1.0VC [-6.4,+5.6] INT.J{IVThis cut dealt with the range stack, I-counters and V-counters, and completed the photon vetocuts for 1989 data. Tables 3.8 and 3.9 give the parameters used. In addition, for the IC and VCChapter 3. Event Selection 954>>‘01CIn423>‘0’CInU.4>a)>00’CUi1-i...0000.,.000t.0...0.flfl..•0nn On .1 n.1•0 i o000[D:Ioonooaa On 0 IIOD 00.000nO.0,.n4-n>a)23>001CIn ::•00000.00I. .1. I. I. I.. I• .—I..—07nynDOa.0....0..n.0.OD0O.,n...n. l.a0,.oOnn. aaOa0QQOO0flaa.a.aflno. D.0•000O....0.On.O?...0Q00flfl.nI0.0OOn. .00000—10 0 10Time (ns)5 IIIIII,II,.... 5 &a-JZi,i.000..—10 0 10 20Time (ns)I N 0 I,0 1m9—20 —10 0 10 20Time (ns)-t-o,,... r ,l,o.1_H.rl,r,, -0:.::::.:::;::::::::::::::::i:::.:::::nfl..... Inon. ... 006 • 000. a000000aD 00, • 03 •,D , no nonaooonnoo.nnoQodtflJ5fforodnooonooaoo0oDana,. .n.ooooanooo0000ofloooo.ono..oooao05-4->a)23->001CLi1-0-—20sJ0 I0 ib 2Time (ns)D00l...0000.,0.06—n 0-00-G09-0090ft-0 ln0.000. .1000000.1000oa000 a aoO:uJoQo 00 cOo uOoo 0 00 000 a 000 0 DO20Figure 3.45: Energy versus time distribution of hits for the various INTSE cutcategories for 1991 irvi7 data. Going from left to right and top tobottom the graphs correspond to the categories listed in table 3.7.—20 —10 a ib 20Time (ns)Chapter 3. Event Selection>ci)>‘0’C4.>a)>.0’CIn96!IIIIIIII4• DII1 ..•1 ... ..1.....I Y1.P ,11rrmI .I00a.Ooa . a..a .aLo oaaD,.á.o. ‘0.0.0 “0oo.000.jJUOn.q.000.oa000 ...000.00000o •0a aaa Ia10 aa a ca00 aO 0 000 aaIDaa’a,54.n>a)3.>,C,CIn1•554.>‘C,CIn10-54.1—an00aa0aa—; ib 26 ib 20Time (ns)aa a . oanaaaaoooo.ooaaQ000o. .. .Qaoao.aao. . ..JTime (ris)I C• a•0 • .. .‘: .. ::°. .a.J aaaa • ••a’•fl.. • •aaOO 000 COCOa. • ailioC. • oa .00aa.jJao •.flqa..flc.o. ‘a •iji. .aa.a..fl.IJo.aa a,a.Oo aa•’afla a . • •na0 I I—20 —10 0 10 20Time (ns)Time (ns)Figure 3.46: Energy versus time distribution of hits for the various INTSE cutcategories for 1991 K,2 events. The graphs correspond to the same054n>a)>1a,CIn—iO 0 10 20Time (ns) .-aaa-.o-o.-.a.-ath,ooaa.aoa 00.Oa a000Q000000DaaaaaflU0000000aQflaa0000oa—20 —10 0 10 20categories as in figure 3.45.Chapter 3. Event Selection 97Table 3.9: Photon veto cut parameters for single end hits for 1989 data. Alsoincluded is a cut on endcap energy hits with no recorded time.Subsystem Ends hit Time window ThresholdEnergy Time [Min,Max] (ns) (MeV)RS both single [-5.0,+5.0] 0.5RS single both [-6.5,+6.5] 0.5RS single single [-6.5,+6.5] 0.5BV both single [-5.0,+5.0] 0.3BV single both [-11.0,1.0] 0.3BV single single [-11.0,1.0] 0.3EC 2 hits none [-4.0,12.0] —subsystems, cases where there were no time hits found in a ±400 ns time window but energywas measured were rejected. PB-GLASSAs described in section, the primary purpose of the lead-glass counter was to detectphotons originating from the target and heading in the direction opposite to the K+ beamclose to the beam axis. It was also designed to be sensitive to incoming beam pions, but not tokaons. As was seen in section, the kaons sometimes do leave a signal, mostly ascribedto fluorescence in the lead-glass. This made the detection of low energy showers more difficultthan expected.To help in this task, the multiplicity signal from the lead-glass counter recorded by a TDchannel was used. For each multiplicity pulse identified, the leading edge time was measuredfor pulse heights corresponding to each number of phototubes hit. Because of the narrow widthof the signals (r.. 15 ns), sometimes a single TD pulse resulted in several time values at a giventhreshold. Figure 3.47 shows a TD pulse for the multiplicity of the lead-glass counter formedof several hits. The horizontal dotted lines show the pulse height positions at which the timeis evaluated for rising portions of the pulse, corresponding to the number of phototubes hit.The list of time values for a given minimum number of phototubes threshold was comparedto the time of the track in the range stack (Trs). The time value closest to Trs was thenChapter 3. Event Selection 98selected as TPbG. Figure 3.48 shows the distribution of TpbG — Trs as a function of the delayedcoincidence time measured in the target for 7rzñ data, for minimum thresholds of one, two andthree phototubes. The vertical band identifies the hits due to photons and the diagonal bandis due to the incoming kaons; the latter becomes more important as the minimum threshold islowered.1 2— 1111111111111 11111111111 liii —iOOH80- °60-40-:20-I I I I I I I I I I I I I I I I I I I I I ——z0 20 40 60 80 1(0Time (ns)Figure 3.47: TD multiplicity pulse from lead-glass counter. The dotted lines indicate the pulse heights at which the time is evaluated for a risingpulse, corresponding to the number of phototubes hit.Based on these distributions and similar ones for I(2 data, a coincidence time window wasset at -6.0 to +8.0 ns. If the delayed coincidence time (T -T ) was greater than 15 us aminimum threshold of 1 phototube was used; otherwise, a threshold of 3 phototubes was chosen.Note that a single phototube hit corresponded to about 10 MeV deposited in the lead-glass.The presence of a hit in the coincidence time window vetoed the event. B4TDIn 1989 the lead-glass counter was not available. It was possible for photons with a trajectoryopposite to the incoming beam to convert in the B4 hodoscope or convert in the degrader withsome products from the electro-magnetic shower depositing energy in the B4 hodoscope. For70xx 6xx 3x 0cI<° x°>Pc4 1oxQoCD 00I‘CD.oCD CDCD0,I-CD_CD —.CDCD.CCDCDCD ..CDTIMEP—TIMEK(ns)0a-,.*...-.—.—..aII flmmar\)(.J-00000c.J 0 0 0H-O 0 0I o0-D C),0-t.’J 00H0-10.(0 C’,TIMEP—TIMEK(ns)k)C.i-01a)00000.1,,,I..I...1D H -a CD a,C_.J-ti HC),dJioIIJiiia0r\JC1000010)00TIMEP—TIMEK(ns) 01 00) 0H -a CD (I, -o H0 00 F.!J.0 0H 0 0 0 -10.(0 =5a,0 0 C-?).H -aCDC),.F’.J-UHC?).IJuID“3 0•1.?)C.?)0Chapter 3. Event Selection 1001991 data, it was seen in the previous section that the PB-GLASS cut had some limitationsfor low energy photons, because of the light given off by incoming kaons. Some sensitivity forthese low energy showers was obtained by searching for energy deposition in the B4 hodoscopeat the time of the K decay.The output of the B4 hodoscope phototubes was recorded with TD channels. For 1989data, the output of the B4T counter was used for this cut. In 1991, the sum of the phototubeoutput from the six elements of each of the two B4 hodoscope planes was used. Single anddouble pulse hypothesis fits (see section were performed independently on the outputof each channel. Figure 3.49 shows the time of the second pulse compared to Trs as a functionof log10 x for 1991 data. The variable x is related to the residual of the single pulse fit; adouble pulse therefore has a large value of x . If the value of log10,was above 1.8 (2.0) and asecond pulse was found with a time with respect to Trs within a coincidence window of ±6.0 ns(±5.0 ns) for 1989 (1991) data, the event was rejected.11111111 III 11111111111 :I1rI10 1 2 3 4 5logFigure 3.49: Tb4 — Trs versus log10 x for B4 counter TD fits for 1991 irv7 data.Events inside the dashed box were rejected.Chapter 3. Event Selection 1013.3.3.7 NDCThis cut looked at the total number of hit wires in the drift chamber for each event. In 1991it was included as part of the DC-SETUP cut, but in 1989 it was an individual cut. Also, in1989 the hits selected by the track fitting procedure were not excluded from the total. Eventswith a number of hit wires greater than 50 were rejected. DISENPIThis cut looked at activity in the target at the time of the K+ decay. The time reference wasT . The energy of all target elements not part of the or J(+ track with a time withinthe window [-6.0,+7.0] us was summed. If the sum exceeded 5.0 MeV the event was rejected.It should be noted that the TGTRACK cut (see section includes essentially the samerequirements but with a lower energy threshold. This cut was not used for 1991 data. DISENKSimilarly to the above cut, the energy in target elements not part of the lr+ or the K+ trackbut in coincidence with the K+ track was summed up. The time window chosen was —4.0 <t— T( < 2.0 ns, where t is the time of the element considered, and the energy threshold was5.0 MeV. This was primarily directed at beam pion backgrounds. It was not applied to 1991data.3.3.4 Pion identificationThis section describes the cuts designed to positively identify -+ tracks in the range stack.Primarily, these cuts differentiate between 7r+ and + , but they also have a significant contribution in the rejection of lr+ nuclear interactions. Cuts are applied on the kinematic information(range, energy and momentum) from the track, and several cuts relate to the +decay chain identification in the range stack using the TDs.Chapter 3. Event Selection 1023.3.4.1 RGEMOMThis cut required consistency between the + momentum measured with the drift chamber andthe + range measured in the range stack. Based on the momentum, the range of the K+ inscintillator was inferred from an empirical table. A cut was applied on the difference betweenthe measured range and the expected value. The cut was +5 cm for particles stopping in layersB and C and +6 cm in layer 11. This cut was oniy used for 1989 data. MASSIn this cut the consistency between the 7r+ momentum measured with the drift chamber andthe 7r+ energy measured in the range stack was verified. Using those two quantities the massof the particle can be determined according to the formulap2 T2M = DC — RS (3.31)2TRSwhere Frc is the momentum and TRS is the kinetic energy and the speed of light c has beenset to 1. If the measured mass was outside of the range 105 < M < 175 MeV/c2 the event wasrejected. As for RGEMOM, this cut was only used for 1989 data. KINSCOREFor 1991 data, the three independent kinematic quantities (momentum as measured by thedrift chamber, range in the range stack and kinetic energy as measured in the range stack)were used for a single cut. In reality, these three quantities were not completely independent.As described in section, the range in the last layer of the range stack hit by the trackwas computed using the measured energy. This computation was made for both a and ap,+ hypothesis. Also, a small amount of energy was lost by the charged particle in the driftchamber carbon fibre outer wall. This loss was calculated using the measured momentum,assuming the particle was a , and was included in the range stack track energy. However,the effect of this correction on the correlation should be negligible.Any two of the three kinematic quantities available should be sufficient to determine theparticle type. However, because of finite resolutions, it was necessary to use all three to obtainChapter 3. Event Selection 103adequate separation. The range stack range was compared to the range expected accordingto the measured momentum for both a and a hypothesis. The differences between themeasured and the expected value for both hypotheses were used. The third quantity used inthe cut was the mass of the particle, determined according to equation 3.31.The three quantities, pion hypothesis range—momentum correlation, muon hypothesis range—momentum correlation and particle mass were combined to form a Fisher discriminant, usingmultiple discriminant analysis [58]. This type of analysis assumes that the data consists of twodistinct populations, and finds the linear combination of the input variables (Fisher discriminant) which provides the maximum separation between the two populations, in this case piousand muons. The coefficients needed to form the Fisher discriminant were determined usingtraining samples, well identified groups of events belonging almost entirely to one of the twopopulations. The muon training sample was taken from rviY 1ev 0 monitor data and the piontraining sample from 7r-scat monitor data. Figure 3.50 shows the distribution of the Fisherdiscriminant for the two training samples. To avoid systematic effects due to the average rangeand energy of pious stopping in different range stack layers, the linear coefficients and cut positions were determined for individual range stack stopping layers. The cut positions for eachrange stack layer are indicated in figure 3.50; events within the dashed lines were accepted. DEDXRSThis cut looked more closely at the charged particle energy deposition in the range stack. Basedon the track position and momentum measured with the drift chamber, the energy deposition ineach range stack counter struck by the track was computed by summing the estimated energyloss in small steps. The radius and the center of curvature of the track (and therefore themomentum) were re-calculated at each step. The energy deposition of each step was calculatedbased on the step size and the energy loss rate (dE/dx) in plastic scintillator obtained from atable of empirical values, assuming the particle was a . This computation was performedfor RS layers A, B and C; it followed the particle until either its kinetic energy was 1.0 MeVor less or it exited range stack layer C. This estimated energy deposition in each range stackChapter 3. Event Selection 104Figure 3.50: KINSCORE results for pre-selected samples of pions (open histograms) and muons (shaded histograms) for the different stoppinglayers. The individual histograms were normalized to the total sample size for each particle type.—30 —20 —10 0 10Fisher discrimincirit20 30 —30 —20 —10 0 10 20 30Fisher discriminantChapter 3. Event Selection 105layer struck by the + , except for the layer in which it came to a stop, was compared to theenergy measured with the AD Cs. Figure 3.51 shows the distribution of measured energy minusexpected energy for each range stack layer for 1989 Passl data. Events outside of the regiondefined by dashed lines were rejected.150to:30C)50Figure 3.51: Measured minus expected energy in range stack layers A, B and Cfor 1989 7rzñ7 data (DEDXRS cut). Events outside of the regionsdefined by dashed lines were rejected.The effect of this cut was to reject muons, pions which undergo nuclear interactions in therange stack and photons which converted on top of the track in the range stack. It was notused for 1991 data; the background studies indicated that no significant gains in backgroundrejection could be made by including it in the data analysis. Other cuts addressing the samepotential background processes provided adequate rejection. FASFITPI and FITPIThese two cuts made use of a subroutine designed to perform single and double pulse fits onthe TD information from both ends of the range stack counter in which the charged particlecame to a stop. The pulses recorded by the TDs in a time window 100 ns before and 150 nsafter the time of the charged track were examined by the subroutine. Using pre-determinedsingle pulse shapes, the data was fit with the CERN MINUIT minimization program [59] forboth a single and double pulse hypothesis. For a single pulse, the two fit parameters were a200100—10 0 10(KIeV)—10 0 10 —10 0F—f (MeV) E—E (MeV)Chapter 3. Event Selection 106time offset for the beginning of the pulse and a scale factor for the pulse height. For the doublepulse hypothesis, the fit used four parameters : the time offset of the first pulse, the time delaybetween the first and second pulse and a scale factor for each pulse. Figure 3.52 shows the fitresults for both ends of the stopping counter for a-cci,a)U,Figure 3.52:Time (ns) Time (ns)TD information and fit results for a candidate for both ends ofthe stopping counter. The dashed line indicates the double pulse fitresult; the full line and the shaded area indicate the first and secondpulse respectively.Listed below are quantities obtained from the fits that are used to constrain the results.Chapter 3. Event Selection 107C(i) : single pulse hypothesis residual for end ix : 0.5 x log10 (C(1) x C(2))double pulse hypothesis residual for end iC,(i) : C,(i) / C,T.(i)C,(1) x C(2)E(i) : second pulse area for end iiJE,(1) x E(2)T(i) : time delay between first and second pulse for end iT,(1)—T,(2)0.5 x (T,(1) + T,(2))The FASFITPI cut was a quick version of the cut in which only a single pulse hypothesisfit was performed. Cuts were applied on C,(i) and x . The FITPI cut compared the resultsof the single and double pulse fits; cuts were applied on C(i) , P , E(i) , E andThe latter quantity was a measure of the distance separating the point of origin of the twopulses along the z-axis in the range stack counter. Figure 3.53 shows the distribution of E andLT,L for a pre-selected sample of pious. Note that the default cuts were already applied to thissample. The rms resolution for E,L was approximately 30 counts, corresponding to 0.6 MeV.LT is proportional to the difference between the z-axis position of the energy deposition ofthe first and second pulse; the resolution was 1.4 ns, corresponding to approximately 20 cm.To further constrain the result for 1989 data, tighter cuts were applied on some quantitiesobtained from the fits : ITI < 3.5 ns, P, > 20 and 9 < T, < 60 us. For 1991 data, severalquantities were combined in a chi-square quantity, defined byx2fl(x)2where the x were x , log10P , E, /.TL and min(E(1),E(2)), and and o were the meanand standard deviations of each quantity, determined from a sample of pre-selected + . Becausethe difference in counter thickness influences the resolution for fit results, parameters weredetermined individually for layers B, C and 11+12. The probability for the x2 value obtainedChapter 3. Event Selection 108‘1):30()was determined for the appropriate number of degrees of freedom; events with a probability lessthan 0.01 were rejected. Figure 3.54 shows the base 10 logarithm of the probability distributionfor samples of pre-selected + and + TDMDAThe five quantities combined to form a x2 value in the FITPI cut for 1991 data were alsocombined to form a Fisher discriminant (see section, along with the energydeposited in the last range stack layer struck by the charged particle track. To determine thelinear coefficients necessary for this cut, a muon training sample was selected kinematically outof the irv7 data sample using the KINSCORE cut; in this case, the cut position was chosen toselect muons instead of pions. The pion training sample was taken from 7r-scat monitor data.This cut was designed to primarily reject cases where a fluctuation in a large single pulse wasmistaken for a double pulse. This effect was greater for early delay times; therefore, the cut wasapplied only if T was less than 26 ns for tracks stopping in layers B and C and less than 40 nsfor tracks stopping in layers 11 and 12. Events with a Fisher discriminant greater than 0.0 inlayers B and C and 0.3 in layers 11 and 12 were rejected. Figure 3.55 shows the distribution ofT (ns)1’Figure 3.53: E and zT,L variables from FITPI cut for pre-selected lr+Chapter 3. Event Selection6010912001000800(1)6004002005040PionsC0- (_)2010—6 —4Iog,0(TD X2 prob.)0— 1111111111 I 111111111 — 0—10 —8 —6 —4 —2 01og0(TD x2 prob.)Figure 3.54: Base 10 logarithm of the pion probability distribution for samplesof pre-selected -+ and j+ for 1991 data. Events to the left of thedashed line were rejected (probability < 0.01).the Fisher discriminant for + and + samples. The dashed lines indicate the cut positions. ELVETOA significant fraction of the muon background surviving the two-pulse constraints in the stopping counter originated from accidental hits providing the second pulse or from early + decays.In both cases, it was possible for the particle responsible for the second pulse to also depositsome energy in the area surrounding the stopping range stack counter. The ELVETO cut lookedat time hits in coincidence with the time of the “muon” pulse in a search region surrounding thestopping range stack counter. The region covered three sectors on either side of the stoppingcounter and the minimum number of layers forming a thickness of at least 3.9 cm above andbelow the stopping counter. Any time hit found at least 5 ns after the + track time and within5 ns of T,rejected the event.Chapter 3. Event Selection 110Figure 3.55: TDJVIDA results for pre-selected samples of 7r+ (open histograms)and p+ (shaded histograms) for the different stopping layers. Theindividual histograms are normalized to the total sample size for eachparticle type.—0.5 0.0 0.5Fisher discriminant—1.5 —1.0 —0.5 0.0 0.5 1.0 1.5Fisher discriminantChapter 3. Event Selection 1113.3.4.8 TDFOOLThe range stack time hits used by the ELVETO cut were derived from the leading edge ofpulses recorded by the transient digitizers. For the range stack layer immediately precedingthe stopping layer, a second pulse in coincidence with the one in the stopping counter could beobscured by the pulse corresponding to the passage of the stopping charged particle. For thisreason, a double pulse fit identical to the one performed in the stopping counter was performedin the preceding layer. In the cases where a hextant crossing occured in that layer, both hextantswere examined. For successful double pulse fits, if the time of the second pulse was within 3 nsof the one in the stopping counter, the event was rejected. This cut was only used for 1991data. ELECTRONThe final step in identification was to identify a positron from the + ,‘ e+ decaychain. Positron candidates were searched for in the range stack in a region ±1 sector and +2layers from the stopping counter. The electro-magnetic shower from a positron can depositenergy in several range stack counters. Time measurements from the two ends of counters inthe search region were scanned for coincidences; the mean and difference time for each wasrecorded, as well as the mean pulse height. Groups of counters with a mean time within 5 nsof each other were selected; a minimum of two counters was required to form a group. A groupwas selected as a positron candidate if the average time of the counters in the group was atleast 20 ns later than the + decay time, at least one counter had a pulse height greater than100 counts (‘ 2.5 MeV) at each end, the total pulse height for the group was greater than750 counts and the average end-to-end time difference was within 3.5 ns of the ir — timedifference ). Finally, the summed area of all range stack pulses with a time within 5 nsof the positron candidate time had to be less than 7000 counts. This considerably reduced fakepositron signals due to accidental tracks.Chapter 3. Event Selection 1123.3.5 Beam cutsBecause of the trigger requirement for a kaon ierenkov signal, and the target track reconstruction constraints, specific offline requirements for an incoming K+ were not necessary. However,the identification and rejection of beam pions scattering into the range stack was very important.Several detector elements were used for this purpose. CERENKOVThe time values of the pion Cerenkov counter multiplicity signal pulses, measured with a TDC,were compared to the measured time of the charged particle track in the range stack (Trs). Thetime value closest to Trs was selected as the pion ierenkov time (Ta). A cut on T,, — TrsI wasset at 6.0 ns (5.0 ns) for 1989 (1991) data; events within those bounds were rejected. Figure 3.56shows the T — Trs distribution for 1991 7rIiL events. This requirement provided most of thebeam pion background rejection.i0410C,,c 2D 100C-)10110°Figure 3.56: Time of pion Cerenkov hits with reference to Trs for 1991 irvi7 events.Events inside the dashed lines were rejected.Chapter 3. Event Selection 1133.3.5.2 BWPCThe pion erenkov counter has a limited efficiency in detecting beam pions, as well as limitedgeometrical coverage. The radiator only covers a circular region 15 cm in diameter, which canbe exceeded by the beam pion halo. The multi-wire proportional chamber (BWPC) providesa wider geometrical coverage for beam pions. Hits in at least two of the three planes of thechamber were required to identify a particle; however, nearly 99% of the time a hit was foundin all three planes. The measured time of a particle in the chamber was the average of thecalibrated times of the individual hits. A subroutine searched for time hits near zero identifyinga , and then looked for later hits which would indicate the presence of another beamparticle. The list of hits was compared to Trs and the closest one was chosen as Tb. Eventsfor which —4.0 < Tj,w— Trs < 12.0 ns were rejected. Figure 3.57 shows the time distributionfor irt/17 events. This cut was only used for 1991 data.i041o(02:, IL)0C)101100Figure 3.57: Time of BWPC hits with reference to Trs for 1991 irv7 events. Eventsinside the dashed lines were rejected.TbT (ns)Chapter 3. Event Selection 1143.3.5.3 BM..HOLEThe beam hole counter was described in section As mentioned above, the halo of beampions tends to be wider than the K+ beam, due to the beam line optics. The entire K+ beamshould be well within the acceptance region of the hole counter. Beam pions can strike thescintillator counters forming the hole. For 1991 events in which a beam hole counter ADC hitof more than 10 counts was recorded, the list of TDC times was scanned and compared to TrsThe beam hole counter time closest to Trs was chosen as Tbh. Events with Tbh— TrsI less than5.0 ns were rejected.In 1989, the BM_HOLE counter cut was used for a different purpose. It was used to detectcharged particles which might originate from photon conversions in the degrader. The TD Ctime scale of the beam hole counter was calibrated such that the time of a beam particle withrespect to Trs was zero. Particles resulting from a photon conversion related to the decay of aK+ in the target would appear with a delay corresponding to the time of flight of the J(+ to thetarget and the photon traveling towards the beam hole counter, approximately 20 ns. Eventswith a beam hole counter ADC energy greater than 50 counts and a time with respect toTrs within a [-16.0,+24.0] ns window were rejected. No evidence was found for such hits in 1991data. B4_CNTRThis cut required that the energy deposited in the B4 hodoscope be consistent with that expected from a slow K+ about to enter the target. It was only used for 1991 data. The calibratedADC values of the energy deposition in each of the six fingers of the two B4 hodoscope planeswas summed. The average of the sum from each plane was taken as EB4. Figure 3.58 showsthe distribution of EB4 for K2 events and beam pion-scattering events, where it is clear thata faster moving deposits much less energy than a stopping K+ . Events with EB4 less than1.8 MeV were rejected. This constraint was particularly effective against events in which aK+ passed through the ierenkov counter and subsequently decayed in flight to a whichscattered in the target and stopped in the range stack.Chapter 3. Event Selection 1150 1 5 6Energy (MeV)Figure 3.58: Energy measured in the B4 hodoscope for beam K (shaded histogram) and -+ (open histogram). Events to the left of the dashedline were rejected.3.3.6 Vertex CutsThe cuts described in this section are concerned with the quality of the K+ decay vertex inthe target. Any anomalous energy deposition must be identified in order to reject ii-+ nuclearinteractions or additional K+ decay products. Information from the drift chamber and the B4hodoscope supplemented the target information to improve the background rejection capability. TGTRACKThis cut used the drift chamber track information to define a track in the target. Target elementswith ADC information were categorized as pion or kaon hits according to their measured time.The list of kaon and pion elements as provided by the target track reconstruction subroutine(see section, which used primarily energy information to categorize hits, was used as astarting point. To be considered part of the pion track, an element had to have a measured timewithin 5 ns of Trs and closer to Trs than T . A cut was placed on the number of kaon (NK)and pion (N,!-) elements at 1 < NK 10 and 1 N < 30. A 0.8 cm wide swath centered onthe extrapolated drift chamber track defined the + trajectory in the target. Using the centerChapter 3. Event Selection 116of curvature of the drift chamber track in the zy plane and an axis parallel to the x-axis as areference, a rotation angle was found for each kaon and pion element based on a vector betweenthe center of curvature and the center of the target elements. The rotation angle decreased asthe particle exited the target. Figure 3.59 shows the geometry conventions used. Using thisinformation, the following cuts were applied1. At least one kaon element was on the swath.2. The maximum pion rotation angle was less than or equal to the maximum kaon rotationangle ax).3. If 4 > the pion element with q’ had at least one pion element neighbor.4. Groups of kaon elements not on the swath could not have elements on both sides of theDC track. This removed events where the pion originated from the middle of the kaoncluster.5. The maximum pion element energy, corrected for the dip angle of the -+ trajectory, hadbe less than or equal to 3.5 MeV.6. Pion elements on the swath could not have a neighboring pion element off the swath.7. The energy of pion elements off the swath and disconnected from other elements wassummed up (Er). A cut was placed at EISC < 1.5 MeV.8. The minimum distance between the pion element with 1/1ax and the kaon elements(MINDIS) was computed. A cut was placed at MINDIS 2.0 cm.9. The distance covered by the extrapolated drift chamber track in the kaon elements wascomputed (DPATHK). A cut was placed at DPATHK < 1.2 cm.This cut eliminated a large number of pion interactions in the target, as well as photonconversions. Figures 3.60, 3.61 and 3.62 show examples of events rejected by the TGTRACKcut.Chapter 3. Event Selection 117Figure 3.59: Geometry conventions for TGTRACK cut. An angle was determined for each target element on the swath defined by the ir+ track. NKThis cut required the total number of target elements struck by the K+ to be less than 10. TheTGTRACK cut described above restricted this number to be less than 11, and therefore thiscut had little impact. It was only applied to 1989 data. TGFITThis cut used transient digitizers to identify large energy depositions at the time of the K+ decayin the target elements struck by the K+ . In the element where the K+ comes to rest, onlya few MeV are expected at the time of the K+ decay from the outgoing + . However, ifthe j.+ undergoes a nuclear interaction or travels a significant distance along the z axis beforescattering towards the range stack, more energy will be deposited. Also, the could travel inthe target elements struck by the K+ in a way that makes part of its path undetected.Three TD channels were used in 1991 to view the target phototubes’ output. Each TDchannel covered one third of the target elements, distributed in a random but known fashion.Unconstrained single and double pulse hypothesis fits, similar to the ones performed on therange stack information for the ir —* t decay search, were performed independently in eachx,Chapter 3. Event Selection 118SCALE 1: 0.5RUN 10017EVENT 48509SCALE 1: U.SRUN 10017EVENT 48509Figure 3.60: Large angle scatter event rejected by the TGTRACK cut. The topdisplay gives the energy information (MeV) and the bottom displaygive the corresponding time information (ns). The extrapolated DCtrack trajectory is also indicated.0. 4Energy (MeV)Time (ns)Chapter 3. Event SelectionEnergy (MeV)SCflLE 1: 0.5119Time (ns)Figure 3.61: Large energy deposition by a ir rejected by the TGTRACK cut.The displays are as in figure 3.60. Note the energy deposition of7.2 MeV in a single ir target element.RUN 9181EVENT 42685SCALE 1: 0.5RUN 9181EVENT 42665Chapter 3. Event Selection 120cz_E_z___cRLE1• 0. 15 2.96.9Energy (MeV)9.5RUN 9400EVENT 54280SCALE 1: 0.61721—, 24IS‘S—t 19 19Is16 1922ISIS2121ISII1920 Time (ns)20291920RUN 9400EVENT 54280Figure 3.62: Photon conversion or multiple charged track K+ decay rejected bythe TGTRACK cut. Displays are as in the previous two figures.Chapter 3. Event Selection 121of the three channels. The overall time scale of each channel was calibrated such that thestopping K+ time was zero. The pulse area in each channel was also calibrated. For the fit,pulse information was considered up to only 35 ns beyond the known + time in the target(T ), obtained from the target track reconstruction subroutine. This prevented late accidentalhits from disrupting the fits. The quality of the single and double pulse fits was compared; ifthe single pulse fit was the best and the time of the pulse was within 5 ns of T the energy wasassigned to the pion. If the double pulse fit was the best, the time of both the first and secondpulse was compared to T. If the time was within 5 ns of T , the energy was assigned to thepion.From the list of pion elements and the known assignment of target elements to TD channels,the pion energy expected in each TD channel measured with the ADCs was summed up. Thisnumber was compared to the energy measured with the TDs for the cases where a successfulfit occured. For the individual channels, if the energy measured with the TDs exceeded theenergy measured with the ADCs by 3 MeV or more, the event was rejected. A cut was alsoplaced at 3 MeV on the sum of the differences between TD and ADC measured energy forthe three channels. Figure 3.63 shows the distribution of this sum for K,.2 background events,both from the K2 kinematic peak region and from the K+ .* lr+z)E7 kinematic search region.The excess of events in the high side tail in plot b) identifies events in which the lost asignificant amount of energy in the target elements struck by the K+ . Figure 3.64 shows theTD information as well as the fit results for the three TD channels of an event rejected by theTGFIT cut. There is a very large energy deposition at the time of the K+ decay in channel# 2. The single pulse fit for channel # 3 is not very good. This is most likely due to the factthat the pulse shape used for the fit is an average for all target elements included in each TDchannel and is expected to be less accurate for some target PMTs. The rejection of the TGFITcut was limited by the double pulse resolution of the fits. Pulse shape accuracy is one of thefactors contributing to this limitation.Chapter 3. Event Selection 122300250200C,,D0C)100500Figure 3.63: Energy deposited by the r+ in the target as measured by the TDsminus the values measured by the ADCs. The TD energy value is thesum of the three channels (see text). Both plots are for J(,,-2 eventsrecorded in the 7r11i7 data. Figure a) is for events in the K,-2 peakand figure b) is for events in the rvv signal region. VTX..PCAAs for the previous cut, the VTX_PCA cut was designed to reject events in which a large energyloss by the ir+ was hidden in the K+ track. The method consisted in comparing three differentmeasurements of the energy assigned to the K+ in the target. The first measurement was thedirect measurement of the K+ energy in the target, i.e. the sum of the measured energy in allelements identified as belonging to the K+ track. The second energy measurement was derivedfrom the measured range of the K+ in the target. It was determined by extrapolating the driftchamber track back to the decay vertex to obtain the range along the z-axis and combining itwith the range in the xy plane as measured by the target track reconstruction subroutine. Atable of energy as a function of range for K+ was then interpolated to obtain an estimate ofthe K+ energy deposition based on the measured range.The third energy measurement was obtained from the K+ energy loss rate (dE/dx) inthe B4 hodoscope, given by dividing the measured energy deposition by the known counter—10 0 10Energy (MeV)—10 0 10Energy (MeV)25 .1. I, I I 1, IIC 3 EKPDC=2O.2 MeV 16.5 MeV0o1b2b3o 5b 60Time (ns)Figure 3.64: Target TD information and fit results for an event rejected by theTGFIT cut. The dashed line shows the double pulse fit, the full lineshows the first pulse and the shaded area indicates the second pulse.For channel 3 only a single pulse fit is shown.Chapter 3. Event Selection 12325ci) 20Ici)C,):50500ci) 40Ici) 30ci):3a 20Time (ns)-cci)Ici)ci)0—20Chapter 3. Event Selection 124thickness. A table of K+ energy as a function of energy loss rate was interpolated to obtain theestimated K energy deposition. The values of the difference between the direct measurementand the two expected values of the J(+ energy deposition were then combined in a principalcomponent analysis [58]. In this type of multi-variate analysis, new variables are formed as linearcombinations of the input variables. The coefficients are chosen such that the output variablesare uncorrelated and have maximum variance. The output variables are then rescaled such thattheir variance is unity. For n input variables, there will be n output variables, correspondingto the principal components. For VTX.YCA, a cut was applied in the space defined by the tworesulting normalized variables. Figure 3.65 shows the distribution in this space for two samplesof K2 background events; the events identified as “peak” are from the K,.2 kinematic peakregion and the ones identified as “tail” are from the K+ .+ +j7 kinematic search region.6— III I — ii iL_4.inir1hjU1’’iIii,h1jtiir iii —Peak Tail4 4-0)g 0 — :::.___...... . ..- —4-—6— III 1111111 111111 1111111 —6— 1111111 1111111111 III I1PI111I1—6 —4 —2 0 2 4 6 —6 —4 —2 0 2 4 6Component 1 Component 1Figure 3.65: VTX_PCA components for ‘(p2 events. Events below the dashed linewere rejected.This cut was used for 1991 data only. For 1989 data, cuts were applied individually onthe consistency of the extrapolated K+ decay vertex position with the K+ energy and the B4hodoscope energy with the I energy. These cuts are described below.Chapter 3. Event Selection 1253.3.6.5 ZKJKThis cut was based on the relationship between the position of the J( decay vertex along the zaxis (Z) and the measured K+ energy in the target (EK). Events not satisfying the relation(Zt + 10.0) < (.)3 (3.32)were rejected. Figure 3.66a shows the relationship between Ejç and Z. for 1989 7rv1 Passldata; the events to the right of the dashed line were rejected.15——160 ,i,n’T.i.rmn.rni.n, —ci) f” b)I..140- -10— ,‘ :120—,‘ :5 — , .,,,. , . . : C’::. “:;‘::t:::’..•.__100 -. ..“E I 101,10.0 > : .C.) I-I ,liii-—C - 0 -0 — -“- •o•- 80 —0IIll0Il’D I%_._ . . .“ —- 00 /-— . - .10 Li_i - a1.01 •.,, / 60 — .—5 — i. :4...’e - . -tl,,’/ Afl. . aI- ‘.,..,t - -—10 : ‘,20——— I I I II II I II I I II 0 11111111111111111.1 I0 50 100 150 200 0 100 200 300 400 500Ek (MeV) E84 (MeV)Figure 3.66: Relationship between Z, EK and EB4 for 1989 irW data. a) showsversus 1K and b) shows EK versus EB4. The dashed linesindicate the cut positions. See text for details. EBtEKSimilarly to the previous cut, consistency was demanded between the K+ energy in the targetand the energy deposited in the B4 hodoscope by the Ic . Figure 3.66b shows the distributionof EK versus EB4 for 1989 Pass2 data (see section; the events above the dashed linewere rejected.Chapter 3. Event Selection 1263.3.7 Kinematic search region (KINCUT)This cut selected the ii+ kinematic region where K+ ..+ +i)iy candidates were searched for.This region excluded the I(2 peak region where background events were expected due to thelimited r0 rejection. The three quantities used, total range, total momentum and total energy,were determined as follows : the total range was the sumR0 = RTG + R10 + + R0 + RRS (3.33)where RTG is the measured + range in the target, Ric the range in the I-counters, andR0 the range in the inner and outer radius drift chamber carbon fibre walls respectively andRRS is the range in the range stack. The range in the target is the path length in the zyplane determined from the target elements struck by the + , corrected for the dip angle ofthe + trajectory determined by the drift chamber. The determination of the I-counters rangewas described in section 2.2.3. The range in the drift chamber walls was based on the knownthickness of the walls and the measured particle trajectory. The measurement of the rangestack range was described in section 2.2.6.To obtain the total momentum, the measured drift chamber momentum had to be correctedfor the energy lost by the + before entering the chamber. This was done by first converting themeasured drift chamber momentum to a range (RDC), by interpolation in a table of empiricalvalues relating momentum and range in scintillator for a . This range value was summedwith the ir+ range before the drift chamberR’Dc = RTG + Ric + + RDC (3.34)and R’Dc was re-converted to a momentum value (P0) using the same empirical range versusmomentum table.The total + energy was given by= ETG + Ei + Ej + E0 + ERS (3.35)where ETG is the measured + energy in the target, Ei the energy measured in the I-counters,E and E0 the energy deposited in the drift chamber walls and ERS the energy measured inChapter 3. Event Selection 127the range stack. The energy deposition in the drift chamber walls was determined by convertingthe measured range to an energy using the known energy loss rate for a in carbon fibre.Each of the three kinematic quantities were constrained independently. The three are alsodirectly related; therefore, the cut position on one quantity could be fixed and the other twoadjusted accordingly. For 1989 data, the total energy cut was fixed based on the distributionof K,,-2 background events. The total momentum and total energy cut positions were thenadjusted by requiring that the ratio of acceptance for K+ 71+z,17 events and rejection forIc2 events be the same as for the total range cut. For K+ * Monte Carlo generatedevents were used, while real data was used for‘1it2For 1991 data, the total range cut was set first, at the same position as for 1989 data. Thiswas to ensure some level of consistency between the accepted regions for the two data sets. Thetotal range cut was chosen because of its stability, due mainly to its geometric nature. The totalmomentum and energy are more susceptible to calibration variations; their cut positions wereset to the same ratio of acceptance versus rejection as the range cut. The final cut positionsfor the two data sets are given in table 3.10. Figure 3.67 shows the distributions used to setthe 1991 cuts.Table 3.10: Upper bound set for the J(+ ,‘ +ii7 kinematic search region.Quantity Year1989 1991Total energy (MeV) 98.0 99.0Total range (cm) 27.0 27.0Total momentum (MeV/c) 190.0 195.0The cut at the lower end of the spectrum was determined implicitly by the minimumrange requirement of the iriii7 trigger. Based on the Monte Carlo K+ ÷ distributionin figure 3.67, we see that this roughly corresponds to R0 = 11 cm, E0 = 52 MeV and= 140 MeV/c.Chapter 3. Event Selection(I,C:30C)CoC:30C)Cl,C:30C)Figure 3.67: Total range, energy and momentum of the ir+ for K2 background(solid line) and K+ +yj7 Monte Carlo (dashed line) events. Thenumber of Monte Carlo events in the histograms is arbitrary.128iso 200Momentum (MeV/c)Chapter 3. Event Selection 1293.3.8 Offline cuts summaryTables 3.11 and 3.12 list all the offline analysis cuts used and a brief description for each.3.4 First Analysis PassThe offline event selection proceeded in several stages, or “passes”. The first one (Passl),consisted of a subset of the cuts described in the previous section. The cuts chosen had highacceptance for signal events and reduced the size of the data sample for subsequent analysis.Because the resulting sample was used in studies of the possible background sources for 1991data, which will be described in Chapter 4, the results of Passl will be given here. Results offurther analysis passes will be described in Chapter 5.Several of the cuts were less stringent at Passl than the final versions described in section 3.3.In particular, the photon veto time windows and energy thresholds were different than for thefinal cut. Table 3.13 lists the photon veto parameters used at Passl for 1989 and 1991 data.Also, the PROMPT cut only required T -T > 1.5 ns for both 1989 and 1991 data.Tables 3.14 and 3.15 give detailed statistics for the various cuts; for 1991 data, statistics arefor approximately one third of the data sample. Note that the cuts in 1991 were more restrictivethan in 1989, by about a factor of 7. In these tables, as well as all other tables describing dataanalysis in this thesis, the number indicated next to the entry identifying each cut representsthe number of events satisfying the cut requirements. In many cases, the rejection (R) oracceptance (A) of each cut will also be indicated, as is the case here. The rejection is definedasR (3.36)where Ne is the number of events examined by the cut and N is the number of events passingthe cut requirements. The acceptance is simply the inverse of the rejection.Chapter 3. Event Selection 130Table 3.11: Summary of all offline analysis cuts.Cut DescriptionEvent reconstructionTARGET K and ?-+ track reconstruction in targetDC-SETUP Drift chamber track reconstructionDC-CHI2 Drift chamber track fit chi-squareRS-TRACK Range stack track reconstructionRSPC Activity in RSPC if RS stopping layer = 11ICOUNTER ii+ I-counter energy and rangeFIDUCIAL K decay vertex along z axis, ir trajectory dip angleZDCTZ + track position along z axis at outer DC radiusTimingPROMPT Time delay between K and ir in targetTRKTIM Consistency of + track time in TG,IC and RSPhoton VetoINTIME Photon veto in RS, BV (both ends) and EC, IC, VCINTSE Photon veto in RS, BV (single ends)INT..EB Photon veto in EC and BVINT..RIV Photon veto in RS, IC, VCPB-GLASS Lead-glass detector hits in coincidence withB4TD Second pulse in B4 in coincidence with ir in RSNDC Number of DC wires hitDISENPI Energy in target outside of and K+ tracks at time ofDISENK Energy in target outside of ir and K+ tracks at time of K+Pion identificationRGEMOM RS range and DC momentum correlationMASS RS range and energy correlationKINSCORE RS range, RS energy and DC momentum correlationDEDXRS Energy deposition pattern in RSFASFITPI Single pulse hypothesis TD fit (ir —* ti search)FITPI Comparison of single and double pulse hypothesis TD fitTDMDA Multiple discriminant analysis of TD fit resultsELVETO Veto in RS at ir —* p, timeTDFOOL TD double pulse fit in RS layer previous to stopELECTRON Search for positron from ir —* —* e decay chainBeam cutsCERENKOV Pion erenkov counter vetoBWPC Beam wire chamber veto at time of in RSBMHOLE Beam hole counter vetoB&CNTR Energy deposition in B4 hodoscopeChapter 3. Event Selection 131Table 3.12: Summary of all offline analysis cuts (continued).Cut DescriptionVertex cutsTGTRACK Refined track reconstruction in targetNK Total number of target elements struck by K+TGFIT Double pulse fit of target TD informationVTX_PCA Correlation of TG K energy, TG K range and B4 energyZKEK Correlation of target K+ range and energyEB4_EK Correlation of B4 energy and K+ target energyKinematic search regionKINCUT Total range, energy and momentum cutTable 3.13: Parameters for Passi photon veto cuts. The time column refers tothe coincidence time window.Subsystem 1989 1991Time (ns) Threshold (MeV) Time (ns) Threshold (MeV)RS [-4.3,3.7] 1.0 [-1.0,1.0] 2.0BV [-5.2,4.8] 1.0 [-3.0,3.0] 2.0EC [-4.9,5.1] 1.0 [-2.0,2.0] 5.0IC [-4.75,3.25] 1.0 — —VC [-6.4,5.6] 1.0 — —Table 3.14: 1989 Passl results. The number of events showed next to each cutis the number satisfying the cut requirements.Cut # events Rejection1382868TARGET 1270154 1.08874 ± 0.00028PROMPT 780919 1.6265 + 0.0011DISENPI 649167 1.20296 ± 0.00061INT_EB 324314 2.0017+0.0025DC-SETUP 176448 1.8380 + 0.0030RS-TRACK 160763 1.09756 ± 0.00082INT_RIV 87215 1.8433±0.0042FASFITPI 34901 2.499±0.010FITPI 15911 2.194±0.013ELVETO 12554 1.2674 ± 0.0052Total 110.15± 0.98Chapter 3. Event Selection 132Table 3.15: 1991 Passl results for one third of the data sample.Cut # events] Rejection2062081TARGET 1988477 1.0370 ± 0.000 1PROMPT 1363512 1.4583 + 0.0007DC-SETUP 834914 1.633 ± 0.001RS-TRACK 802423 1.0405 ± 0.0002TRKTIM 800332 1.0026 1 ± 0.00006INTIME 460984 1.736 ± 0.002FASFITPI 362892 1.270 + 0.00 1FITPI 131113 2.768+0.006Total 15.73± 0.04Chapter 4Background StudiesThe most difficult task in the search for K+ + +p7 is the rejection of the large numberof background processes that can mimic it. In the search for rare processes, the possibilityalways exists that a signal could be observed, regardless of the theoretical predictions. To haveconfidence in the final result, the expected contributions from background processes have to bedetermined. Since it is expected in the case of this experiment that background contributionswill be relatively small, the estimation of the expected levels of background is likely to require anextrapolation beyond the sensitivity to the process r+z. This can make the reliabilityof the estimates difficult to ascertain.Background levels can be estimated in two ways: using Monte Carlo simulations and usingreal data. The former involves lengthy simulations which can necessitate days or weeks ofcomputer usage. This can limit the usefulness of this method, although the introduction inthe last few years of inexpensive and powerful computer workstations somewhat mitigated thisproblem. A more important limitation of the Monte Carlo method is the reliability of thesimulation of the various physical processes involved. For K+ + +jJ7 background processes,uncertainties in nuclear and photo-nuclear total and differential cross-sections can lead to largeuncertainties when extrapolating to sensitivities of the order of 10—8 — i0. Nevertheless, insome cases this method is the only one available.For these reasons, real data was used whenever possible to determine background levels.This has the advantage that any instrumental effect not properly reproduced in a Monte Carlosimulation is taken into account. Both the irvE and monitor data samples are suitable for such133Chapter 4. Background Studies 134studies, although the iri/i7 data sample is generally preferable since it is the one with the largestintrinsic sensitivity to all background processes. To study a particular background, cuts can beapplied to a data sample to select a sub-sample dominated by this background. Other cuts canthen be designed and their effectiveness studied.A useful way to select a background data sample is to invert one of the cuts designed toreject it, i.e. select the events which fail the cut. This has the advantage that none of theevents used in the background study could be a candidate event, and is of great importance ineliminating potential bias in the search for a K+ ..+ .+i,E7 signal. Assuming that the rejectionof the inverted cut is independent of the others, the expected number of background eventsfrom the source studied is thenTIT iirtot evt 1 1.LVbgdIVK >< ----X—XIVKwhere Nk9t and NK are the number of kaons (or some other suitable normalization) in theirvi7 data sample and in the background study sample, respectively, Nevt is the number ofevents remaining after all cuts are applied to the sample selected by inverting a cut, E is theefficiency of the inverted cut to select the background events and R is the rejection of theinverted cut. The last two quantities have to be determined with an independent data sample.Equation 4.37 is quite general. In practice, the data sample used to study the backgroundis often the irvii sample; in this case, NOt and NK are equal. Also, the selection criteria of theinverted cut are often the same as the ones used in the final analysis. In this case the efficiencyof selecting background events (E) is simply related to the rejection of the cut(4.38)Taking both of these cases into consideration, we can rewrite equation 4.37 asNbgd = . (4.39)Finally, in some cases some of the cuts applied to the sample selected by inverting a cut areknown to be independent of each other. Their rejection can be determined separately and thenChapter 4. Background Studies 135factored out in order to increase the statistical power of the procedure. We would then haveNbgd 1evt < fi (4.40)where R, is the rejection of the ith of n cuts factored out of the analysis, and is thenumber of events left after applying all cuts to the sample selected by inverting a cut, exceptthe cuts whose rejection is factored out in the expression. By factoring out several cuts withlarge rejection, it becomes possible to reach levels of background sensitivity that would nototherwise be attainable.The success of this method depends on two points1. the rejection of the inverted cut and the others designed to reject the background ofinterest are independent.2. the rejection of the inverted cut can be reliably estimated by using another data sample.To demonstrate this, consider the following simple example, in which a single background sourceis present, there are no signal events and we have three cuts (or groups of cuts) designated A,B, and C. Figure 4.68 illustrates this situation; there is a total of N0 events, the number ofevents which pass all cuts is N0 and the terms N in each region represent the number of eventsrejected by cut i. We now wish to estimate the number of background events, N0, before weperform the final analysis which will result in N0 events. We can select a sample of backgroundevents by inverting cut A, and then apply cuts B and C which results in NA events. Followingthe method described above, we have= NA (4.41)RA-1where BA is an estimate of the rejection of cut A. For this, we can select a different sample byinverting cut B and then apply cut A. We then have- NABC+NAB+NBC+NBRA=NBC+NB. (4.42)Substituting this back in equation 4.41, we get- NBC+NBN0 = NA x . (4.43)‘ABC + IVABChapter 4. Background Studies 136N0Figure 4.68: Example of background estimation. See text for explanations.We see from this that to validate the method, we needNBC+NB N0 (NABC+NABNAwhich expresses the fact that the fraction of events accepted over rejected by cut A is independent of the sample chosen, which means that the rejection of cut A has to be independent ofthe other cuts.A variation of this generic method makes use of the fact that K+ + +jJj7 events aresearched for in a specific region of phase space. Events faffing outside of this region can beexamined extensively without introducing bias for the events inside the search region. A cutcan be inverted to enhance a particular background source as described above, but here theratio of events seen inside and outside of the search region is exploited. The assumption ismade that the ratio of the number of events outside of the search region to the number insideis the same for the sample selected by inverting a cut as for the data remaining after all cuts.This is expressed as,Tinv )T.Lvout _•, lvOUtTT1flV 1ST.inwhere the subscripts “in” and “out” refer to the number of events inside and outside of thesearch region respectively, and the superscript “mv” refers to the events selected by invertingN0Chapter 4. Background Studies 137a cut. The factor N0 can be obtained by applying all cuts to the events outside of the searchregion. The estimate for the number of background events can then be calculatedN?’Nbgd = = N0 X (4.46)outEquation 4.45 can be rearranged to giveN1 NoutArmy — 1’riflVin outwhich simply expresses the fact that the rejection of the cut used to select the backgroundmust be the same for the events inside and outside of the search region. The categorization ofthe events in two kinematic regions is effectively a cut; what is expressed above is equivalentto saying that the rejection of the two cuts considered must be independent. A correlationbetween the two can significantly affect the result obtained in the background estimation.The following sections describe in detail the studies of the various background sources forthe search for K+ — lr+v17 , performed using the methods just described. For 1989 data,the studies were not very extensive and were performed after the final analysis was completed.This is because the analysis method used (see section 3.3) did not require a priori backgroundstudies. The background was studied as the analysis cuts were prepared and the overall levelwas estimated afterwards. It was subsequently realized that this method could lead to bias inthe final result. Therefore, for 1991 data detailed estimates for each possible background sourcewere made before the final analysis was performed.4.1 1989 Background studies4.1.1 K+ ,‘This decay is the primary source of background for this search. For I2 decays to be mistakenfor K+ ÷ 7j-+7 decays, the photons from r0 decays have to be missed (or one photon and ane+e pair from K° Dalitz decays). The r0 rejection inefficiency of the detector for .O ‘s fromK2 decays has been measured to be 1 x 106 [60]. We can therefore expect some K2 eventsto remain in the data sample after applying all the photon veto cuts. The kinematic searchChapter 4. Background Studies 138region for J(+ lr+ j47 was chosen such that most of the remaining K,,.2 events are rejected(see section 3.3.7). The background comes from the low energy tail of the + distribution. Onecomponent of the tail comes from resolution effects and measurement errors. In this case, allthree kinematic quantities have to be mis-measured in a correlated way since a cut is applied onthe consistency of the three quantities with a hypothesis. The other more serious componentto the low energy tail comes from nuclear interactions. The interaction can occur eitherin the target, I-counters or in the range stack. The latter case is not as serious since themomentum measurement is not affected. However, if the interaction occurs in the target closeto the K+ decay vertex, the energy loss will have occured before the -+ kinematic quantitiesare measured. The rejection of K,,.2 background therefore relies heavily on the ability to detectj+ nuclear interactions in the target.One other possibility is decay in flight of the pion, with the resulting ,+ from -+ _÷continuing more or less in the direction of the initial ii- . The time of flight in the detectorof a from K,,.2 decay is only a few nanoseconds, compared to its mean life of T,.+ = 26 ns.A simple Monte Carlo simulation showed that of those K,,.2 decays which satisfied the trackreconstruction requirements, only about 2% had decayed in flight. Because the kinetic energyavailable for the final state particles in this + decay is so small, and the direction of the isessentially the same as the initial + to satisfy the track reconstruction requirements, the energyof the charged particle track is most of the time about equal to that expected from K,,.2 decay.Also, an accidental hit in the stopping counter is required to satisfy the + + decaychain requirement. A more complete Monte Carlo simulation showed that the decay in flightbackground is at least a factor of 50 less than the case where the + undergoes a nuclearinteraction. Therefore, this contribution to K,,.2 background was considered negligible.In plastic scintillator, the can interact either with a hydrogen (single proton) or a carbonnucleus. In the energy regime of this experiment, +—p interactions are entirely elastic, witha maximum energy loss for the + of about 58 MeV; the cross section is approximately 70 mbat 108 MeV. Interactions with carbon nuclei are more complex, since several inelastic channelsare open [61]. The total ii+ —‘2C interaction cross section of nearly 600 mb at 108 MeV can beChapter 4. Background Studies 139divided into three parts : elastic, inelastic and absorption, with each part contributing aboutone third of the cross section [621. The absorption part includes “true” absorption and alsocharge exchange (ir+ ‘2C —* r°p “C), which contributes about 20% of the absorption crosssection. Since there is no in the final state for absorption, it does not contribute to thisbackground unless the interaction is in the range stack, in which case two accidental pulsesmust be present in the stopping counter to fake the + decay chain. The maximum energy lossin an elastic coffision with a carbon nucleus is about 7 MeV, implying that the contribution tothe low energy tail of the K2 peak from -+ —C elastic coffisions is small.In inelastic coffisions, the simplest interaction is the case where the carbon nucleus is left inan excited state and returns to ground state via gamma or alpha emission. If gamma emissionoccurs, the probability of detecting the interaction increases substantially. Typical excitationenergies are 4.4 MeV, 7.7 MeV, 9.6 MeV and 12.7 MeV, but many higher energy states alsoexist [63]. The energy levels with the largest share of the cross section are the 4.4 MeV and9.6 MeV levels [61]. The first one decays exclusively by gamma emission, while the seconddecays almost exclusively via alpha emission. In the case of alpha emission, the 8Be residualnucleus decays to two alpha particles with a half-life of about 0.07 fs. The rest mass of 8Beis only about 90 keV higher than the summed rest mass of two alpha particles, resulting invery little kinetic energy for the decay products. Therefore, the probability of detecting thisinteraction in the target is very small.If the energy transferred to the carbon nucleus by the is sufficiently large, it becomespossible to knock out a nucleon from the nucleus, leaving either a “B or nucleus, possiblyin an excited state. The thresholds are 16.1 and 18.7 MeV for proton and neutron emissionrespectively. If the emitted nucleon is a proton, the probability of detecting the interactionincreases significantly, but strongly depends on the energy and direction of the emitted proton.Neutrons knocked out or emitted through evaporation of an excited nucleus can also be detectedif they collide with protons in scintillator, as long as the interaction occurs within the coincidencetime window of the INTIME or INTSE cuts; this will not necessarily be the case since someof the neutrons will be emitted at very low energy and therefore will move slowly through theChapter 4. Background Studies 140detector.Since the two important effects in background are photon and nuclear interactiondetection, they are obvious choices for cuts used in selecting data samples to be used in abackground study, especially since naively the two types of cuts should be independent. Inreality, the correlation between the two is quite large. This is related to the non-uniformityof the photon veto coverage of the detector and is illustrated in figure 4.69. In this figure,the -+ from J(,-2 decay initially travels in the direction of the beam axis and scatters in thetarget towards the range stack through a nuclear interaction, satisfying all the particle trackingrequirements of the analysis. The energy deposited by the before it scatters towards therange stack overlaps with the energy deposition of the incident K+ , making its detectiondifficult. The ir0 is emitted back-to-back with the ir and promptly decays to two photons.The most likely angle for the decay photons is along the direction of the r0 , which in thiscase points back to the beam hole, the region with the least number of radiation lengths in thedetector. For K2 decays in which the + does not scatter in the target, the photons tend tobe emitted in the direction of the barrel veto, where coverage is maximal. As can be seen, thiseffect will strongly correlate nuclear interactions and photon detection. This was the primaryreason for the installation of the lead-glass detector in 1991.The K2 background contribution was estimated by making use of the ratio of events insideand outside of the K+ ,S K+147 kinematic search region. This method is the second backgroundestimation technique described in the introduction to this chapter. In what follows, since theyare dominated by the K2 peak, the events outside of the K+ + kinematic search regionwill be referred to as “peak” events; the events inside will be referred to as “tail” events. Theratio of the two numbers will be designated by i:#Peak events= .. (4.48)#Tail eventsTo measure ‘ii, use was made of a monitor data sample collected using special trigger conditions. The EC and BV veto requirements were removed from the 7rviY Level 0 trigger, andall other trigger requirements the same as for 7rv7; this considerably enhanced the number ofK2 decays recorded. A total of 15523 events were available for further analysis. All offline cutsChapter 4. Background Studies 141K+ItFigure 4.69: Correlation between nuclear interactions and photon veto inK2 background.except direct photon veto cuts and the final kinematic cut were applied to this data sample; atotal of 2451 events survived all cuts, of which 14 were in the K+ —* search region. Thisresulted in243717=—h— = 174+ (4.49)where the error is statistical. As will be described in section, application of all cuts to theevents outside of the J(+ ... +1fj7 search region resulted in 49 events. Assuming that the ratioi remains the same after application of photon veto cuts, we can estimate the K.,.2 backgroundcontribution49 + 7Nbgd174 + 47= 0.282 + 0.086. (4.50)However, we just saw that we can expect a correlation between the photon veto cuts and thefinal kinematic cut, namely that the photon veto cuts are not expected to be as effective forthe tail events as they are for the peak events. Therefore, this estimate is not expected to becorrect.To estimate the effect of this correlation, a Monte Carlo simulation was used (see appendix C). First, the angular and energy dependence of the inefficiency of the photon vetoLead—Glass TargetDegrader 1’ NuclearHodoscope InteractionChapter 4. Background Studies 142system was determined by simulating a large number of photons with a uniform distribution inenergy (0—250 MeV) and direction (—1.0 cos 8 < 1.0), where cos 8 is the z-axis directionalcosine of the photon. The distribution was also uniform in the xy plane. The point of originof these photons was in the target and chosen according to the distribution of K+ stoppingpositions determined experimentally. A simulated photon was considered to be missed if lessthan 1.0 MeV of energy was deposited in the active regions of the detector.Using this information as a lookup table, the detection inefficiency for neutral pions with atotal energy of 245 MeV, as in Ic2 decays, was determined. Again, the angular distributionwas uniform and the point of origin of the ‘r0 in the target was chosen according to the realK+ stopping distribution. The r0 was allowed to decay and based on the direction and energyof the two decay photons the probability of not detecting the r0 was calculated. Table 4.16gives the inefficiency for different parts of the angular distribution. Because in I(,-2 decaysthe ir0 is emitted back-to-back with the + , the range —0.5 cos 8o 0.5 corresponds tothe fiducial region accepted by the inJi7 trigger. Note the large differences observed betweenthe different angular ranges, which simply reflects the non-uniformity of the photon detectionsystem.Table 4.16: ir0 detection inefficiency. The angle O,,o is the angle between theK0 direction and the z-axis.Angular range Inefficiency—1.0< cosO,,.o —0.9 55 x iO—0.5 < cos8o < 0.5 1.5 x iO0.9< cos9o 1.0 41 x iO—1.0 < cosOo 1.0 6.9 XThe final step was the simulation of K,r2 decays satisfying the irzJiY trigger requirements.As for the real data sample described above, the online photon veto requirements were notincluded, but the rest of the Level 0 and Level 1 KVE7 trigger requirements were simulated. Thesimulation included nuclear interactions and decay of the ir+ , but the ir0 was not allowed todecay to save computer time. All offline analysis cuts that could be applied to the simulatedChapter 4. Background Studies 143events were applied. At this stage, the ratio of events in the ‘(2 peak region to the events inthe tail region was consistent with what was observed in real data. The ir0 angular distributionfor the remaining events in the peak region was almost entirely in the —0.5 cos 8o < 0.5range, as could be expected. For the events in the tail, the distribution was more or less flat incos Oo. All of the tail events had undergone a nuclear interaction in the target, indicating thestrong correlation expected. Using the information obtained on the r° detection inefficiencyto weight the K.7r2 simulated events remaining after all cuts, the effect of the correlation wasdetermined. The correlation factor measured was 3.7 + 0.5, where the error is statistical only.If we correct the estimate for the number of K2 background events expected for thiscorrelation factor, we getNbgd = (0.282 ± 0.086) X (3.7 + 0.5) = 1.04 + 0.35. (4.51)The study of the simulated It2 events remaining after all cuts and located in the K+kinematic search region indicated that additional rejection could be expected for thisbackground from the BMHOLE and EB&EK cuts. These were not included in this studybecause the B4 hodoscope and the beam hole counters are not simulated properly by theMonte Carlo program. However, it was clear that additional rejection could be expected fromthose cuts. Therefore, it was concluded that the number of K2 background events was lessthan one.4.1.2 MuonsThe muon background involves two different kaon decay modes : ÷ +v4 ) andK+ * Oj+ (K3 ). These are the only two direct sources of muon background in thekinematic region considered in this search. Another possible source would be I(2 decays.However, a muon from such a decay would have to suffer an undetected energy loss of at least50 MeV in order to be a background; the probability for such an occurrence is extremely remote.This study also includes a portion of the pion decay in flight background, which was brieflydiscussed in section 4.1.1.Chapter 4. Background Studies 144For and I(3 decays to be backgrounds to K+ ÷ , the + has to be misidentifiedas a and photons have to escape detection. Therefore, there are three groups of independentcuts that can be used to select and study muon background : particle identification cuts, whichinclude kinematic and TD cuts, and photon veto cuts. This study used the first two groups.The first step in the study was to apply all cuts except TD and kinematic cuts to the Passidata sample. Only 22 events remained after application of those cuts. One reason for such lowstatistics is that at Passi FASFITPI, FITPI (without tighter constraints on zT , P,, and )and ELVETO were applied, which reduced muon background contamination considerably. Thesample of 22 events should contain mostly muon background events. Table 4.17 shows the effectof the remaining cuts on this sample. The first observation from this table is that the TD cutsappear to be far more effective than the kinematic cuts. Examination of the remaining eventsshows that for all three events satisfying the TD cuts the K+ stopped in RS layer C, while for9 of the 11 events satisfying the kinematic cuts the + stopped in layer B. The distribution ofparticle mass for the latter shows that most of them are more likely to be pions than muons.One explanation is that they are pions which underwent a nuclear interaction in the range stack.The requirement by the TD cuts for a complete + + e+ decay chain is very effectiveagainst such events. Therefore, the rejection of the kinematic cuts was determined using onlyevents with a stop in RS layer C, resulting in = 3.5 + 2.1.Table 4.17: Effect of kinematic and TD cuts on 1989 muon background. At thisstage the FITPI cut did not include a cut on T,Kinematic cuts # events22RGEMOM 14DEDXRS 12MASS 11TD cuts # events22FITPI 9ELECTRON 3For the FITPI cut applied in table 4.17 there were no specific requirements on T , theChapter 4. Background Studies 145average of the time delay between the first and second pulse in the stopping range stack layer(see section The decision to apply the requirement 9 <T < 60 ns was based on examination of a different sample of muon background. In this case, cuts on the range—momentumcorrelation and the mass of the charged particle were used to select muons in the Pass 1 datasample. Beyond Passi, only the RSPC, TGTRACK and KINCTJT cuts were applied to thissample in order to increase the number of events available. Despite this precaution, only 7events remained after application of the TD cuts used in table 4.17. However, the muon background was concentrated at early and late T values. The cut on T1 provided an estimatedadditional rejection of R— = 3.5 ± 2.1.The estimate for the number of muon background events was based on the three eventsremaining after TD cuts in table 4.17 and the estimates for and Ri—:Nbgd = (3.0 ± 1.7) X (3.5 ± 2.1) X (3.5 + 2.1) = 0.24 + 0.24 (4.52)where the error is statistical only. Obviously this estimate suffers from low statistics. However,the very fact that so few muon background events could be extracted from the irvi7 data samplewas an indication that the contribution from muon background was not very large. Becauseof possible contamination by pion background, the estimate was probably conservative andtherefore judged acceptable.4.1.3 Beam pionsThe large content of the particle beam used for this experiment can be a source of backgroundwhen a scatters inelastically in the target. The trigger requirements that an incoming K+ beidentified and that there be a delay between the incoming and outgoing particles in the targetsignificantly reduced the contribution from this source. Nevertheless, it was necessary to designadditional offline constraints to further reduce this potential background. The main assumptionmade in this study was that a potential background event occured only if the beam scatteredin the active target and was the particle of choice in the drift chamber and range stack. Casesfor example of a emerging from the degrader and stopping in the range stack without hittingthe target were assumed to be negligible after all analysis cuts are applied.Chapter 4. Background Studies 146Beam pions come from three sources : primary production by proton—Pt target coffisions,decay in flight of a kaon, and nuclear interaction of a kaon, primarily in the degrader. Thereis also the possibility of protons in the secondary beam line interacting in the degrader andproducing pions. However, a proton with a momentum of 800 MeV/c is just about at thresholdfor production, and therefore this contribution can be neglected. The particle identificationcapability of the terenkov counter allowed the classification of the beam pion background intotwo groupsA) Two particle background. This group can be divided in two subgroups1. A K+ and a K+ crossed the erenkov counter.2. Two K+ crossed the ierenkov counter. One of the two decayed or interacted resulting in a ir+.B) Single particle background. In this case, a single K+ crossed the ierenkov counter anddecayed or interacted resulting in a track which scattered in the target.In each case the trigger conditions can be satisfied; in case B, a fluctuation due to finitetime resolution is required for the event to pass the delayed coincidence requirement. The beampion background study performed for 1989 data only considered case A-i; the other cases wereconsidered to be negligible. A sample of rvE7 events which satisfied the Passi requirements,failed the CERENKOV cut and were located in the K+ * 1r+ii7 kinematic search region wereselected. This sample of 3005 events was dominated by beam pion background. All other cutswere then applied to these events; the analysis ran out of events before all cuts could be applied.Full results of this analysis are given in table B.65.To estimate the beam pion background contribution, the rejection of the CERENKOV cuthad to be measured. A sample of beam pion background was selected out of the 7rv17 databy requiring that two particles be identified in the beam wire chamber and that the energydeposition in the B4 counter be consistent with a single + . Using this sample, the rejectionof the CERENKOV cut was determined to be R = 11.6 + 1.3.Chapter 4. Background Studies 147Because no events remained after analysis of the sample of events which failed the CERENKOVcut, an upper limit on the number of background events was set. From Poisson statistics, if theobserved number of events is 0, the 90% confidence level upper limit on the mean number ofevents is 2.3. Therefore,2.3Nbgd <-LC2.3<< 0.22 (90% C.L.). (4.53)4.1.4 K+ , K+e+j, (K4)The decay Ke4 , a four body decay with three charged tracks and with a branching ratioof 3.9 x iO, may appear at first to be rather benign as a background to K+ ,‘However, it is kinematically possible for both the ir and the e+ to be emitted with a verysmall amount of energy. Both of them can conceivably hide in the active target in the regionwhere the K+ stopped; in particular, a low energy ir coming to rest in plastic scintillator willbe captured with almost 100% probability by a carbon nucleus. The end point of the kinematicspectrum for from Ke4 is 203 MeV/c, just below the ‘(2 peak, resulting in a large kinematicacceptance for the ir+ by this search.A slightly different scenario for this background is the case where the -ir is absorbed inthe target in flight, instead of coming to rest and be captured by a carbon nucleus. The trueabsorption cross section for 7t on 12C is 100 mb for a ir momentum of 170 MeV/c. ForKe4 decays in which the + momentum is in the 7rzJU search region, the momentum of the ir isalmost always below 170 MeV/c, peaking around 80 MeV/c. To go undetected, the interactionshould take place within a short distance from the decay vertex, say 2 cm. The probability ofir absorption in plastic scintillator at 170 MeV/c within 2 cm is about 1%. Therefore, theportion of Ke4 background in which the ir was absorbed in flight is quite small comparedto the case where the r interacts at rest, and can be neglected. Note that at 80 MeV/c, acharged pion has a range of about 2 cm in plastic scintillator.Chapter 4. Background Studies 148The signature of Ke4 decays as a potential background to K+ 7I.+Y is essentially identical to K,r2 decays in which the undergoes a nuclear interaction in the target and thephotons from the r0 decay were not detected. Energy deposited in the K+ target elements byKe4 charged decay products other than the must be identified. Techniques to do this weredeveloped for K2 background. What is needed here is to determine how often Ke4 decayshave this decay pattern in the target. Note that for most Ke4 decays, multiple tracks will beidentifiable in the target and cuts such as TGTRACK will reject these events very effectively.To select a sample of Ke4 background events, all cuts were applied to Pass2 data (seesection with the exception of TGTRACK and ZK_EK. A total of 51 events were left.Inspection of these events indicated that many were likely to be Ke4 decays, although it wasnot possible to clearly distinguish Ke4 background from I(,2 events with a 7j+ undergoing anuclear interaction in the target. The assumption was made that most of the events in thesample were Ke4 decays. The remaining task was to determine the rejection of the two cutsnot applied to the sample. To determine the rejection of the TGTRACK cut, a large numberof Ke4 decays were simulated with a Monte Carlo program. The matrix element used to weighthe kinematics of Ke4 decay in the simulation was as described in references [67] and [68].A complete simulation of ir interactions in scintillator was not available; therefore, only theionization energy loss was taken into account for the r . Cuts simulating the ones appliedto the real data were applied to the simulated events. A total of 670 events remained beforeapplication of TGTRACK. All but three events were rejected by the cut, resulting in a rejectionof RTGTRACK = 223 ± 129.After application of TGTRACK on the simulated events, the ones remaining had a verylow energy r stopping in the target. The ZK_EK cut should be reasonably efficient at detecting the energy released by the capture of a ir at rest in the target. But since ir nuclearinteractions were not simulated by the Monte Carlo program, another method was needed todetermine the rejection of ZK_EK. Based on studies of ir interactions in carbon described inthe literature [69, 70], the rejection was estimated to be RZKEK = 2.0 ± 0.5. More detailedstudies of ir interactions performed for 1991 background estimates confirmed that this numberChapter 4. Background Studies 149was appropriate.The estimate for the number of Ke4 background events was then calculated to be51 + 7.1Nbgd —RTGTRACK RZKEK— 51+7.1— (223 + 129)(2.0 + 0.5)= 0.114+0.074 (4.54)where the error is statistical only.4.1.5 1989 Background summaryTable 4.18 summarizes the estimates for the background sources studied. Errors given arestatistical only; systematic errors on these numbers were not very well known, particularly forK2 background. Based on these results, it was estimated that the sum of all contributionswas one event or less. Other potential background sources discussed in section 1.3.1 and notstudied here were considered negligible.Table 4.18: Summary of 1989 background estimates.Background Estimate (# events)]J(+ ,‘ (K2) < 1.0Muons (K3,‘ii2y ) 0.25 ± 0.25Beam pions < 0.22 (90% C.L.)K ,‘ (Ke4) 0.114 + 0.0744.2 1991 Background studies4.2.1 K+ ,‘Two different methods were developed to estimate the K2 background contribution in 1991data. Each used the irvi data sample, but systematic effects were very different for the twomethods. No Monte Carlo simulations were used.Chapter 4. Background Studies 1504.2,1.1 Method 1This method is essentially the same as the one used for 1989 data. First, the ratio of eventsfound outside of the K+ * +7 kinematic search region to the number inside (ii) was determined. The background sample was selected by inverting the photon veto cuts applied afterPassl; all other cuts were then studied, particularly cuts which reject nuclear interactions inthe target, and was measured. In a separate analysis, all cuts were applied to the peak eventsfrom the entire irvE7 data sample. From the number of remaining events, and assuming themeasured value of applies to the case where all cuts are used, the number of K2 backgroundevents inside the kinematic search region could be estimated.The data sample selection started with the Pass 1 data sample. Note that this means that theINTIME cut was partially applied. All cuts were applied except the cuts specifically designedto reject interactions in the target, namely TGTRACK, TGFIT, VTX_PCA, PB-GLASS andB4TD, KINCUT and the photon veto cuts (INTIME and INTSE). The latter were inverted,i.e. all events which failed either of these two cuts were selected. Inverting the photon vetocuts after the Passl cuts were applied resulted in a sample of events for which only a smallamount of energy was visible outside of the 7r+ track, which is very close to the full analysiswithout actually performing it. A total of 27512 events were selected; full details are givenin table B.66. Table 4.19 shows the effect of the remaining cuts on this sample, separated inpeak and tail events, as well as the value of at each step. The value of after all cuts is30.8 + 3.5. Figure 4.70 shows the lr+ momentum spectrum for the events in the first and lastlines of table 4.19, highlighting the effectiveness of the cuts applied at reducing the tail eventsrelative to the peak. This can also be seen quantitatively in table 4.19: the value of i increaseswith the application of every cut. It should be noted however that the open histogram samplein figure 4.70 contains a number of events from Ke4 decays, which are heavily suppressed bythe TGTRACK cut (see section 4.2.5).The number of peak events remaining after all cuts for the entire rvi7 data sample was 159.Details of this analysis are given in table B.67. Based on this result, the expected number ofChapter 4. Background Studies 151Table 4.19: Final analysis to determine i for K2 background estimation(Method 1).Cut Peak II Tail# Rejection II # RejectionSelected 21119 6393 3.3TGTRACK 3876 5.45 + 0.08 419 15.3 ± 0.7 9.25TGFIT 3485 1.112 + 0.006 250 1.68 ± 0.07 13.9VTX_PCA 3057 1.140 + 0.007 191 1.31 ± 0.05 16.0PB-GLASS 2259 1.35 + 0.02 78 2.4 ± 0.2 29.0B4TD 2191 1.031 + 0.004 71 1.10 ± 0.04 30.81 c4 I I Ii03E__________120 140 160 160 200 220 240 260Momentum (MeV/c)Figure 4.70: J(,t2 background data sample with inverted photon veto cuts beforeapplication of remaining cuts (open histogram) and after (shadedhistogram).Chapter 4. Background Studies 152background events from K2 decays wasNpeaic 159 + 13Nbgd 30.8 + 35 = 5.16 + 0.72 (4.55)where the error is statistical oniy. This number is quite large and seems to indicate that theanalysis cuts are not sufficient at removing background events.Further studies of the ratio offered a possible explanation for this large number of background events. The ratio was determined for two other levels of photon veto. Table 4.20summarizes the results. The first line comes from analysis of Kir2(1) monitor data to which all7rv7 trigger conditions were applied, except the photon veto. All offline cuts were also applied,with the exception of direct photon veto cuts. This resulted in a very large value of , and isthe value that could be expected if there was no correlation between photon veto and nuclearinteractions, since in this case there are almost no constraints on the photons from ir0 decay.The second entry gives the value of measured after only online photon veto cuts were applied.These cuts correspond to a threshold of approximately 5 and 10 MeV in the barrel veto and theendcaps respectively. The data sample consisted of about 4% of the full data sample. It canbe seen that is almost the same as for the data sample selected after Passl photon veto cutsdiscussed above and displayed as the third entry in the table. These results clearly demonstratethe strong correlation between photon veto and nuclear interactions. It could be argued thatsince the value of i appears to be constant after online photon veto cuts have been applied,the extrapolation can be made to the level at which no prompt energy is visible. However, thevery large correlation makes this extrapolation somewhat uncertain. Furthermore, it is possiblethat by requiring detection of a small amount of photon energy, the number of tail events isenhanced compared to the case where nothing can be seen, since in many nuclear interactionslow energy photons are emitted by excited nuclei. For these reasons, the background estimatefrom this method was considered unreliable. Method 2This method was based on the assumption that the most important component of the ‘c,-2 backgroundcame from events in which a nuclear interaction occured in the target and interaction productsChapter 4. Background Studies 153Table 4.20: K2 peak to tail event ratio for various levels of photon veto.Condition Peak Tail] 77No photon veto 3815 9 424+141Online photon veto 485 16 30.3 + 7.5Passl photon veto 2189 71 30.8 + 3.6were hidden by the K+ track in the target. In order to select such background events, theTGFIT cut was inverted. The first step in the event selection was the application of all cutsto the Passi data sample, except TGTRACK, VTXYCA, PB-GLASS, B4TD, TGFIT andKINCUT. This corresponds to the events passing the BWPC cut in table B.67, a total of 1464events. Of these, 745 failed TGFIT and were used to study the other cuts. Table 4.21 shows theanalysis results. As can be seen, all the events in the K+ —* lr+v77 search region (or tail) wererejected before the last cut was applied. The rejection of B4TD was estimated by applying itto the 9 tail events passing the TGTRACK cut. Only one event was rejected, giving a rejectionof RB4TD = 1.12+ 0.13.Table 4.21: Analysis results for I(,2 background sample (Method 2).Cut Peak Tail# Rejection # RejectionSelected 1202 262Fail TGFIT 599 146TGTRACK 26 23.0 ± 4.4 9 16.2 + 5.2VTX_PCA 21 1.24 + 0.12 5 1.80 ± 0.54PB-GLASS 10 2.10±0.48 0—B4TD 10 1.00 + 0.00 0 —The last factor needed for the background estimation was the rejection of the TGFIT cut,which was used to select the background sample. For this, a data sample representative ofthe K2 background was needed, but selected in a different way than the one used above. TheVTXPCA cut was designed to reject the same kind of background as TGFIT, and so should beappropriate for the selection. The primary limitation of TGFIT is the double pulse resolutionChapter 4. Background Studies 154of the TDs covering the target. Therefore, its efficiency is a strong function of the K+ decaytime; the later the decay, the better the chance of identifying the pulse. VTXYCA, on theother hand, only uses summed energy and geometric quantities and is limited by the resolutionof the measurement of these quantities. By using a sample of events which fail the VTX_PCAcut, we should be able to measure the rejection of TGFIT in a reasonably accurate way.The application of VTXYCA and TGFIT only really makes sense after TGTRACK hasbeen applied. The sample of events after TGTRACK in table 4.21 would be appropriate, butthere are only 9 events available in the K+ ÷ +i,Y search region. Removing the photon vetocuts beyond Passi increased the statistics. The events satisfying the BWPC cut requirementsin table B.66 were used for this purpose. Table 4.22 describes the additional cuts applied forthe sample selection. The TGFIT cut was then applied, and 60 events survived, for a rejectionofRTGFIT = 2.02 + 0.18. (4.56)From this, the measured value of RB4TD and the fact that no events which failed TGFITsurvived the full analysis, we can set a 90% C.L. upper limit on the number of backgroundevents expected from this sourceNbgd <2.3X1= 2.0 (4.57)RTGFIT — 1 RB4TDwhere the factor of 2.3 corresponds to the 90% confidence level upper limit for a Poissonstatistical process in which no events were observed.Table 4.22: Event selection for data sample used to determine the rejection ofthe TGFIT cut.Cut # events RejectionSelected 28522TGTRACK 4501 6.336 + 0.087KINCUT 432 10.42 ± 0.48Failed VTX..PCA 121 —This result, indicating that the background from K,.2 decays is less than two events atthe 90% confidence level, is not consistent with the result obtained with Method 1. The twoChapter 4. Background Studies 155methods used different techniques and different data samples, and therefore should be sensitiveto different systematic effects. Method 2 is obviously limited by statistics. This cannot beremedied as the entire iriñ data sample was used.Two assumptions have to be validated to make the estimate from Method 2 correct1. The potential K,T-2 background consists of events in which the energy lost by the 7+ in anuclear interaction in the target overlaps with the energy deposited by the K+2. The rejection of the TGFIT cut for this type of background can be correctly measuredusing a data sample selected by inverting the VTX_PCA cut.If there is a significant component to the K2 background for which a nuclear interaction inthe target leaves no visible energy, then both assumptions will be invalid. These assumptionsappeared reasonable, and therefore the estimate from Method 2 was believed to more accuratelyrepresent the actual expected background from J2 decays.4.2.2 Radiative Kr2The radiative decay J(+ 1l.+rO7 (K2, ) provides a simple mechanism for the + to loseenergy compared to the non-radiative K.2 decay: emission of a photon. The most importantcontribution is from inner bremsstrahlung, in which the photon is emitted by the r+ . There isalso the possibility of direct photon emission, in which the photon is emitted by an intermediatestate particle. This contribution to the decay rate has been measured and is about 15 timesless than the inner bremsstrahlung part [17].The signature of K1-2.. background is practically the same as K1.2 decays with nuclearinteractions. It is therefore very difficult to disentangle the two components in the real data.Considering the J7l-2-), branching ratio and the presence of another photon compared to K2 , itcan reasonably be expected that the contribution of K.27 will be smaller than K2 . To provethis, a Monte Carlo simulation was used. The method consisted in the determination of theexpected number of K1,.2 events in the K+ i.+,jy kinematic search region as a function ofthe number of K2 peak events observed outside of the search region.Chapter 4. Background Studies 156In order to normalize the number of events to the number of K2 peak events, it isnecessary to know the branehing ratio for each decay. The branching ratio for is a functionof the region of phase space considered. In fact, most of the branching fraction for verylow photon energy is included in the K2 branching fraction. Experimental measurementsof the I,T-2 branching ratio have been made using the region of + kinetic energy between55 and 90 MeV [64, 65], significantly below the J(,2 peak energy of 108.5 MeV. Figure 4.71shows the + energy spectrum for iO decays generated with a Monte Carlo program. Thecorrect matrix element, including a direct emission contribution, was used to weigh the eventsgenerated. A cutoff on the + kinetic energy was placed at 106 MeV. The ratio of the integralof the spectrum in figure 4.71 for the ranges 55—90 MeV and 0—106 MeV gave the correctionfactor for the effective It’2.. branching ratio for the full energy range up to the cutoff:11O6 dNBR(K2..)) = JOdNx (2.93 ± 0.16) x i0 = (1.11 ± 0.06) x 10 (4.58)‘55where the sum of the accepted values for the inner bremsstrahlung and the direct emission partsof the branching ratio in the energy region 55—90 MeV has been used [17].(IC0C.)10’1000 20 40 60 80 100 120Energy (MeV)Figure 4.71: Kinetic energy spectrum of + from K2.- decays simulated by MonteCarlo. A total of decays were generated.102Chapter 4. Background Studies 157K-2 and events were generated with the Monte Carlo program. The photon vetorequirements were not included in the irzJi trigger simulation since the overall r0 rejection oforder 105_lOG would force the simulation of a prohibitive number of events. The simulationprimarily determined the relative acceptance of the analysis for the ir+ for the two decays.Table 4.23 summarizes the results of the simulation and subsequent analysis for both decays.The number of events was normalized to the number of stopped kaons. From these numbersand the branching ratio for each decay, the ratio K of K7,-2 events in the kinematic peak overevents in the K+ _ +,ji7 search region was determined=><B(K712)><N#1(,r27 B(K,,-2..) NKT— 1976+44 0.2117+0.0016 71312— 776 + 28 (1.11 + 0.06) x 10 67941= 510 ± 35 (4.59)where NT and NKT are the number of kaons satisfying the KT trigger requirement in theI(ir2y and the K,,.2 simulation respectively.Table 4.23: Event simulation and analysis results for K,r2 background.I Requirement K,,-2 BKT (stopped kaon decay) 67941 71312Passed trigger simulation 5209 4890Passed offline analysis 1976 776Figure 4.72 shows the energy versus directional cosine along the z-axis for the photons from.O decay for simulated I,2 and K-,,-27 events satisfying all offline analysis cuts. The distributionsare clearly very similar; therefore, it was assumed that the r0 rejection of the photon veto systemis the same for both decays. For K-27 decays, the presence of an additional photon increasesthe rejection. The single photon detection inefficiency of the detector has been measured asa function of energy and angular distribution [66]. From these measurements, and the energydistribution of the extra photon for the 776 Monte Carlo K.27 events satisfying all the analysisrequirements, the photon veto inefficiency was estimated to be = (7.83 ± 0.78) x 10—2, fromChapter 4. Background Studieswhich the rejection due to the detection of the radiated photon was determinedR.=4-=12 8+L3158(4.60)Finally, from the known number of Kr2 peak events remaining after all cuts were appliedto the irz47 data sample (table B.67), we can estimate the number of background events fromKir2j decaysN1ç2Nbga= K—159+13— 510+ 35 12.8+ 1.3= 0.0244+0.0036 (4.61)where the error is statistical only. This estimate is significantly less than the expectation fromI2 background, justifying the initial hypothesis.Figure 4.72:4.2.3 Muons0-—1.0 —0.5Energy versus z-axis directional cosine for photons from K° decay insimulated K2 and K,,-2-. events.This study of muon background was similar to the one performed for 1989 data. However, it wasK—’rrrr°250200150100>ci)>‘a)CU,‘i-i —5Q • .1>ci)>•.ci)CUi2S0 ccc’I ccc -K—’nrr°y200150-. :100-.;.:.;. k••. :.::.50 - 1=0— I—1.0 —0.5 0.0 0.5Z dir. cosine0.0 0.5Z dir, cosine1.0done in a more systematic fashion. The kinematic cuts were studied first, using monitor data.Chapter 4. Background Studies 159A sample of muon events was then selected out of irvl7 Passl data using inverted kinematic cuts;this sample was used to study TD cuts. The photon veto cuts were factored out of this studyto improve the statistical power. The muon background was then estimated by combining theresult of the TD cuts study and the estimated rejection of the kinematics and photon veto cuts.The effect of correlation between the cuts involved in this study was considered. The selection criteria for the data samples used could have resulted in biasing of the relative importanceof the two decay modes involved; for instance, the photon veto cuts should affect Ic,7 andK,3 in a different way. Examination of the phase space distribution of the data samples usedshowed that the differences between the samples were minor and therefore correlations shouldnot be very important in this study. Kinematic CutsSamples of muons suitable for a study of kinematic cuts were obtained from monitor data. Inthe absence of any cuts placing requirements on the lr+ e+ decay chain, the kinematicregion below the K2 peak is rich in muon background events. Two different types of monitordata were used to select muon samples : irziU levO data and Kw2(1) (see section 3.1.6). Theirv7 levO data sample was the one used to prepare the kinematic cuts. All requirements of therv Level 0 trigger were applied to this data, based on the trigger information recorded withthe events. Also applied were track reconstruction cuts in the target, drift chamber and rangestack, TRKTIM, PROMPT and KINCUT. Full details are given in table B.68. Only 219 eventssatisfied all these requirements. Figure 4.73 shows the distribution of total range versus totalmomentum prior to the final cut for this sample. This shows that the sample is dominatedoverall by‘(T-2 events but that in the kinematic region selected the sample is dominated by aclear band of muons.This sample, and a sample of pions selected from ir-scat monitor data by applying TD cuts,were used to determine the parameters of the KINSCORE cut. As described in section,this cut combined the independent measurements of the momentum, range and kinetic energyChapter 4. Background Studies 16050--40.::-EU V :.a)300’ .. :.iCV .20 I10 I ii I TTIT100 150 200 250 300Momentum (MeV/c)Figure 4.73: Total range versus total momentum for muon sample from irvi7 levOdata. The events below the dotted line were identify the particle type. Because of the small number of muon events available, the parameters and cut position were determined for all range stack stopping layers combined. Afterexamination of a larger sample of pions, the cut positions were re-adjusted to the values givenin section measure the rejection of the KINSCORE cut, another sample of muons was selected.This time the K7r2(1) monitor data was used. A total of 440 events were selected; table B.69gives the details of the selection. The main difference between the sample selected from irv7lev0data and this one is that there were no direct photon veto cuts for the latter; this should enhancethe presence of K,LV.-)/ and K,3 decays, but also enhance the number of K2 decays as well. Byapplying the TGTRACK cut, the number of ir+ from J(2 decays in the K+ R.+l)7 kinematicsearch region should be significantly reduced. The shaded histograms in figure 3.50 are fromthis data sample; it is clearly dominated by muons.Applying the KINSCORE cut to this sample resulted in 59 events, for a rejection of R1d =7.46 + 0.90. However, even though the sample was dominated by muons before the applicationof the KINSCORE cut, a small pion contamination could dominate the sample after the cutwas applied and significantly affect the value of Therefore, an estimate of the pionChapter 4. Background Studies 161contents of the sample was required. TD based pion identification cuts (FITPI, ELVETO andELECTRON) were applied to the 440 events; nine events survived. This number had to becorrected for the acceptance loss of the TD cuts used, and then corrected for the acceptanceloss of KINSCORE to estimate the number of pions remaining. The acceptance was taken fromsections and Table 4.24 summarizes the estimation of the pion contamination;as can be seen, the effect is significant.Table 4.24: Estimate of pion contamination in muon sample for muon background kinematic studies. ATD is the combined acceptance of theFITPI, ELVETO and ELECTRON cuts and A1d is the acceptanceof the KINSCORE cut.Layer JJ # events ATD # pions AIdE i # PiOflSB 5 0.360 ± 0.015 13.1 + 6.1 0.8498 + 0.0074 11.8 ± 5.2C 3 0.445 ± 0.020 6.7 + 3.8 0.8286 + 0.0094 5.6 ± 3.2• 11+12 1 0.509 ± 0.019 2.0 + 2.0 0.8354 + 0.0093 1.7 ± 1.7• Total 9 J 22.6 ± 7.4 19.1 ± 6.3Based on these numbers, the kinematic rejection for muons was measured to beR— (440 + 21) — (22.6 + 7.4)— 10 5 + 2 7 4 62kin (59 + 7.7) — (19.1 + 6.3) — . ( . )where the error is statistical. TD cutsTo study the effect of the TD cuts on the muon background, muons were selected out of theirv7 Passl data sample based on kinematics. The selection used the Fisher variable fromKINSCORE; the cut position was [5.0,+15.0]. Using the second muon data sample describedin the previous section, the efficiency of this muon selection was measured. Out of 440 events,328 were accepted. This had to be corrected for the pion contamination, both before and afterthe selection. In the previous section, the pion contamination before the cut was estimatedto be 22.6 ± 7.4 events. Based on the large pion rejection of the muon selection cut (50—200),the pion contamination after the muon selection was negligible. Therefore, the muon selectionChapter 4. Background Studies 162efficiency was= (440 + 21)—(22.6 ± 74) = 0.786 ± 0.060 (4.63)Other cuts were also applied in the selection to eliminate other backgrounds that mightcontaminate the sample. All cuts except TD cuts, the 4.0 MeV minimum energy requirementin the stopping counter and explicit photon veto cuts (INTIME, INTSE, PB-GLASS and B4TD)were applied; this included the signal region cut on total momentum, range and energy. A totalof 575 events were selected. Figure 4.74 shows the T, distribution for those events, clearly notconsistent with the exponential distribution expected from + decay.1 c I I I I I I I —80 -60 -(I,C0C)40 -0 1Irf 11111111111—20 0 20 40 60 80 100 120T (ns)Figure 4.74: T,. distribution for muon background.Three components can be identified in this time spectrum: a large group concentrated atsmall T, values, a flat component and a rise of the flat component at late values of T. Thefirst group corresponds to cases where fluctuations of the primary pulse were mistaken for asecond pulse. These are rejected by tightening constraints on the results of the double pulsefits. The second component corresponds to accidental hits providing the second pulse in thestopping counter and early + decays. These can be rejected by searching for other relatedactivity in the detector at the same time or by demanding that the z-axis position of the secondpulse be consistent with the z position of the primary pulse. For the case where the secondChapter 4. Background Studies 163pulse originates from the early decay of the , a large rejection is obtained by demanding athird pulse consistent with the ii — ,S + chain. Finally, the rise in the flat componentat late times is attributed to the edge of the ADC integration gate (about 75 ns) for the rangestack. For earlier times, the presence of an accidental hit can disrupt the range stack trackreconstruction, and therefore more of these events are rejected.This sample of events was used to develop the various TD based cuts other than FASFITPIand FITPI described in section 3.3.4. Table 4.25 shows the effect of these TB cuts on themuon sample. In this table, the RS-TRACK cut only includes the 4.0 MeV requirement inthe stopping counter, and the FITPI cut only includes the x2 cut on the fit results; the otherrequirements for these two cuts were already applied at Passi.Table 4.25: TD rejection of muon background.Cut # events RejectionMuons 575RS-TRACK 540 1.065 + 0.0 11FITPI 280 1.929±0.080TDMDA 221 1.267 ± 0.039TDFOOL 138 1.601 + 0.084ELVETO 30 4.60 ± 0.74ELECTRON 15 2.00 ± 0.36RTD 38.3 + 9.8As was noted earlier, explicit photon veto cuts were not applied to this sample in order toincrease the statistical power of the study. In fact, the photon veto cuts reject all 15 eventsremaining after application of the TD cuts. The rejection of the photon veto cuts for the muonbackground can be measured by applying them to the entire muon sample. Table 4.26 showsthe effect of these cuts.It should be emphasized that the rejection measured here for the TD cuts and the photonveto cuts only includes the effect of the cuts applied after Pass 1. The total rejection of the TDand photon veto cuts was effectively much higher since a large background rejection occurs atthe trigger level and at Passi.Chapter 4. Background Studies 164Table 4.26: Photon veto rejection of muon background.Cut # events RejectionMuons 575INTIME 143 4.02 + 0.29INTSE 95 1.505 + 0.089PB-GLASS 58 1.64 + 0.13B4TD 57 1.018 + 0.018R— 10.1± Muon background estimateThe estimate for the total number of events expected from muon sources for the 1991 datasample is thenNevt 1 1NbgdE R— 15±3.9 1 1— 0.786 ± 0.060 10.5 ± 2.7 10.1 + 1.3= 0.180 ± 0.071 (4.64)where Nevt is the number of events remaining in the kinematically selected muon sampleafter all cuts except explicit photon veto cuts. The error quoted is statistical only.4.2.4 Beam pionsThe various sources of beam pion background were described in section 4.1.3. In this study,none of the cases listed were considered negligible. Events matching the characteristics ofeach category were selected out of the wvi7 Passl data sample and studied separately. Asa first step, all cuts except the ones specifically directed at beam pion backgrounds and the*.+jj7 kinematic search region cut were applied to the Passl irv7 data sample. Thisprovided a sample of 12818 events, dominated by beam pion background. Table B.70 gives thedetails of the selection.Chapter 4. Background Studies 1654.2.4.1 Two particle backgroundThe multi-wire proportional chamber was the ideal device to select the two beam particlebackground. It was equally sensitive to K+ and + , was located immediately next to theterenkov counter and had large acceptance for both the focused kaons and the more diffusepions. Out of the data sample described in table B.70, events which failed the BWPC cut wereselected. To remove a possible contamination from K2 decays with an accidental hit in theBWPC, the kinematic search region cut (KINCUT) was also applied; a total of 3284 events wereselected. Applying the remainder of the cuts resulted in no events. A large part of the rejectionwas provided by the TGTRACK cut. Therefore, to improve the sensitivity of the backgroundestimate, the target vertex cuts (TGTRACK, TGFIT and VTX_PCA) were removed from theanalysis and their rejection estimated separately. Table 4.27 shows the result of the analysiswithout these cuts.Table 4.27: Two beam particle background analysis.Cut # events RejectionTwo particle bgd 3284PROMPT 2590 1.268 ± 0.011ICOUNTER 1821 1.422 + 0.018TRKTIM 453 4.02 + 0.16FIDUCIAL 353 1.283 ± 0.032BMJIOLE 328 1.076 ± 0.016B4_CNTR 282 1.163 + 0.026CERENKOV 33 8.5 + 1.4PB-GLASS 10 3.30 + 0.87B4TD 5 2.00 ± 0.63[ Total 657 + 294Using the same sample of two beam particle background, the rejection of the cuts left outwas measured. Here, care had to be taken to avoid over-estimating the rejection. Even thoughthe intrinsic rejection of the cuts constraining the track in the target and the rejection of allother cuts are independent of each other, in practice there is some overlap in the rejectionChapter 4. Background Studies 166of some of those cuts. For this reason, the TRKTIM and FIDUCIAL cuts were applied before measuring the combined rejection of TGTRACK, TGFIT and VTX.YCA. The measuredcombined rejection wasRTG = = 134+60, (4.65)dominated by the TGTRACK cut.The final piece of information that was needed was the rejection of the BWPC cut. Tomeasure this, a sample of events with a hit in the pion erenkov counter as well as a hit in thelead-glass counter at the time of the track in the range stack was selected. This sample wasextracted from the sample described in table B.70 ; a total of 7822 events were selected, andthe BWPC cut was applied to these events. This resulted in a measured rejection of7822RBWPC = = 15.0 ± 0.6. (4.66)The estimate for the number of background events from two beam particle sources after allcuts in the irvi7 analysis was then1 1Nbgd = Nevt X XRBWPC — 1 RTG= (5.0+ 2.2) x (15.0+0.6)—i (134+ 60)= 0.0027 + 0.0017. (4.67) Single particle backgroundThis type of background occurs when a single J(+ , already identified in the Cerenkov counter,decays or interacts resulting in a before reaching the target. The simplest way to selectthis type of background was to identify a single in the B4 hodoscope. Figure 3.58 showedthe energy distribution of lr+ and K+ in the B4 counter; there is clear separation between thetwo particle types. Using the sample described in table B.70, single pions were selected byinverting the B4_CNTR cut. To remove background events involving two beam particles, theCERENKOV and BWPC cuts were applied as well. Only 93 events out of the entire irtJi7 Passidata sample satisfied all the analysis criteria. Table 4.28 describes the analysis of this sampleusing the remaining cuts.Chapter 4. Background Studies 167Table 4.28: Single beam particle background analysis.Cut # events RejectionSingle particle bgd 93PROMPT 74 1.257 + 0.066ICOUNTER 39 1.90 + 0.21TRKTIM 15 2.60 ± 0.53FIDUCIAL 10 1.50 ± 0.27TGTRACK 0 —TGFIT 0 —BMHOLE 0 —VTX.YCA 0 —PB-GLASS 0 —B4TD 0 —KINCUT 0 —Obviously, this measurement suffers from low statistics. The main reason for this is that theonline delayed coincidence as well as the offline PROMPT cut applied at Passi had a very largerejection for the background studied here. In order to increase the sensitivity of the estimate, itwas necessary to determine the rejection of the cuts which were not necessary in table 4.28. Ofthese, the only cuts that can be expected to provide a large rejection factor are PB-GLASS andKINCUT. For the former, the beam pion can be identified as it passes through the lead-glassdegrader. For the latter, figure 4.75 shows the total range versus total momentum distributionfor the selected sample of single beam particle background. The distribution is clearly uniform,with no significant contamination from I(2 events; only the part of the distribution in thesearch region will contribute to the background. The rejection of PB-GLASS and KINCUTwas measured using the selected sampleRPbG = = 2.82 + 0.39 (4.68)RKINCUT = = 3.21 ± 0.49. (4.69)The rejection of the B4_CNTR cut, which was used to select the background sample, wasdetermined using a sample of ir-scat monitor data. For this data sample, a beam pion wasidentified in the Oerenkov counter, ensuring that only a lr+ entered the target passing throughChapter 4. Background Studies 16850——40- -D- •O. =C)30 -=20-..10— I I I I I I I I I rrrr1100 150 200 250 300Momentum (MeV/c)Figure 4.75: Total range versus total momentum for single beam particle background data sample. Events above the dotted lines were rejected bythe KINCUT cut.the B4 counter. The rejection was measured to beRB4 = = 5.68 + 0.39. (4.70)Neglecting the rejection of other unnecessary cuts in table 4.28, the background from singlebeam particles was estimated asNbgd Nevt X1X1X1 (4.71)RB4 — 1 RPbG RKINCUTBecause in this case no events were observed after applying the remaining cuts to the selectedsample (table 4.28), an upper limit was setNbgd < 2.3 X (5.68— 1) X 2.82 = 0.05 (9o%c.L.) (4.72)Obviously, this component of the beam pion background dominates. However, it is clear thatthe estimate is conservative and is also limited by statistics. It is possible that the rejection ofthe TGTRACK cut was significantly more than what can be estimated from reducing 10 eventsto none. Nonetheless, the estimate is at a comfortable level for this analysis, ensuring that theprobability of observing a background event from beam pion background was sufficiently low,and in reality was probably much lower.Chapter 4. Background Studies 1694.2.5 K —* rreve (Ke4)As was seen in the 1989 study of Ke4 background, because of the similarity between the signatures of the Ke4 and K,2 backgrounds, it is very difficult to extract a sample of events fromthe available real data that is unambiguously dominated by Ke4 . It is however reasonableto expect that the Ke4 background contribution should be small, at least compared to K1r2For these reasons, a more detailed Monte Carlo simulation was used to estimate the level ofbackground from Ke4 decays in 1991 data; no real data were used.Ke4 decays satisfying the 7rviY trigger conditions were simulated with the Monte Carlo program. Since only a portion of the Ke4 phase space is of any interest for this study, immediatelyafter the K+ decay the kinematic variables of the decay products were examined. Severalconditions had to be met for the simulation of the event to proceed further1 + momentum > 140 MeV/c2. + z-axis directional cosine w.+ < 0.63. ir kinetic energy T_ < 50 MeV4. If 20 < Tir— <50 MeV, w71.— > 0.55. e kinetic energy Te+ < 80 MeVThese conditions saved a large amount of computer time and did not bias the result of thestudy, as will be shown below. As for the simulation used for 1989 data (section 4.1.4), nuclearinteractions for the ir were not simulated. Their effect was taken into account separately.A total of 1 >< i07 K4 decays were simulated. Offline cuts applied were event reconstructioncuts, INTIME, TGTRACK and KIN CUT. Details of the simulation and analysis are given intable B.71; a total of 19 events satisfied all criteria. Figure 4.76 shows the total range versustotal momentum for these events. As can be seen, they are confined to the lower part ofthe K+ ÷ -+j,7 kinematic search region; this was caused by the constraints imposed by thetrigger and the analysis. Figure 4.77 shows the kinetic energy distribution of the r and e+immediately after the J(+ decay for the remaining events. Clearly, the constraints applied atChapter 4. Background Studies 170simulation time did not bias the distributions; all remaining events are well below the cutoffsof 20 and 80 MeV for the ic and the e+ respectively.‘I— 0— I I I —30--E(_)020- .10— i I I II I I I 11111100 150 200 250Momentum (MeV/c)Figure 4.76: Total range versus total momentum for Ke4 simulated background.All events are found in the search region (inside the dotted line).I I I I I I— 6 I I I I I —6-- 55---4—— — -C CD—o o03- -02-2--05152D 020 46BDir Energy (MeV) e Energy (MeV)Figure 4.77: Kinetic energy at birth of the ir and e+ for simulated Ke4 eventspassing all analysis criteria.Chapter 4. Background Studies 171To estimate the expected number of background events from this source after analysis of alldata, several other factors were required. The number of background events was expressed as:N 1 fDNbgd=XB(Ke4)XAana1XXNKX (4.73)gen 1r Jswhere N2, is the number of simulated events satisfying all analysis criteria, Ngen is the numberof events generated in the simulation, B(Ke4) is the Ke4 branching ratio, Aai is a correctiontaking into account the real data acceptance and the acceptance loss of cuts not applied in thisanalysis, R.— is the rejection due to nuclear interactions of the stopping r , NK is the totalnumber of K+ observed in the real data analysis and f and f are the fraction of incidentK+ that stopped in the target for the Monte Carlo simulation and the real data respectively.From the analysis of Monte Carlo generated data described above, we have Nevt 19 andNgen 1 x io. The accepted value of the branching ratio is B(Ke4) = 3.9 X i0 [17].Aanai was calculated from the measured acceptance of the individual cuts for real data (seesection 5.2.5) and corrected for the intrinsic acceptance of cuts applied to Monte Carlo data.A value of Aanai = 0.0390 ± 0.0021 was obtained. From data analysis of the iri/i7 sample,NK = 1.436 x 1011 (section 5.5.1). From section 5.3, f = 0.6422 ± 0.0085, and from MonteCarlo event generation we have = 0.9059 + 0.0011.The rejection due to stopping negative pions was more difficult to determine. Negativepions can interact in flight in the same manner as ‘s, but the most significant effect is theircapture at rest by nuclei. As a result of the interaction at rest of a negative pion with a carbonnucleus, a large variety of fragments can be produced [69, 70]; this is commonly referred to asa “ir star”. Table 4.29 gives the multiplicity and average energy of stopped 7f interactionproducts. There will also be gamma rays produced as a result of the de-excitation of the heaviernuclear fragments or from absorption of neutrons by carbon nuclei.Data were obtained from a TRIUMF test experiment which measured the energy depositedby 20 MeV negative pions stopping in a block of plastic scintillator [71]. The block was 4 cmhigh, 4 cm wide and 3 cm thick and viewed by a single photomultiplier tube. Figure 4.78 showsthe energy distribution observed. The primary peak at 20 MeV corresponds to r absorptionwith no detectable reaction products; the smaller peak around 14 MeV is due to negative muonsChapter 4. Background Studies 172Table 4.29: Interaction products multiplicity and average energy for r stoppingin carbon. Entries for charged decay products are from reference [69]and for neutrons from reference [70].Particle Multiplicity Average energy(particles/ir ) (MeV)proton 0.45 + 0.04 10.4 ± 1.8deuteron 0.33 + 0.03 6.3 ± 1.1triton 0.22 + 0.02 3.0 + 0.53He 0.03 ± 0.005 0.5 ± 0.24He 0.62 + 0.06 5.5 + 1.0Li 0.13 + 0.02 1.2 + 0.3neutron 2.44±0.18 31.8+3.1which contaminated the beam.In this setup, the probability of interaction for neutrons or gamma rays is not very large.The mean free path of a 30 MeV neutron in scintillator is about 19 cm. It was assumed that thelarge energy tail in figure 4.78 is from charged particles. There are therefore two contributionsto R—Rir-. = Rchg X (4.74)where Rthg is the rejection from charged particles and is the rejection from neutrons andgamma rays. We assume that the two factors are independent.For Rthg, the assumption was made that it was necessary to get at least 10 MeV fromthe ir absorption in order to detect the interaction and reject the event, with cuts such asTGTRACK, TGFIT and VTXY CA. Based on the data shown in figure 4.78, the additionalrejection from r nuclear interaction is Rchg = 1.776 + 0.016, where the error is statistical only.To estimate neutrons with an appropriate energy distribution were simulated in thedetector. The visible energy deposited in the detector within a time coincidence window corresponding to the INTIME cut parameters was summed, to simulate the effect of the INTIMEcut. It was found that the probability of detecting the presence of a neutron from ir absorptionwas 0.1961 + 0.0040, where the error is statistical only. According to table 4.29, the mean number of neutrons emitted in ir absorption in carbon is 2.44; therefore, the rejection expectedChapter 4. Background Studies 173500400300U,CD00200100020 40 60 80Energy in scintillator (MeV)Figure 4.78: Energy deposited in scintillator by stopping ir . The small peak at14 MeV is due to contamination in the test beam.due to neutrons is = 1.638 + 0.018. It is possible that residual nuclei emitting gammarays contribute to the rejection; due to the complicated nature of these excitations and lack ofa proper simulation program, this contribution was neglected. Hence, the total rejection dueto the absorption of negative pions in the target was estimated to be= (1.776 ± 0.016) x (1.638 + 0.018) = 2.909 + 0.041. (4.75)Finally, substituting this value and the ones for all other factors in equation 4.73, we obtainthe total number of background events expected from K4 decaysNbgd=X (3.91 ± 0.17)>< 10 X (0.0390 ± 0.0021) X (2.909 + 0.041) X11 0.6422±0.0085x(1.436 x 10 ) x 0.9059 ± 0.0011= 0.101 ± 0.024. (4.76)4.2.6 Charge exchangeKaons interact via the strong force when they propagate through matter. One possible interaction for a charged kaon is charge exchange, in which it interacts with a nucleon, resulting inChapter 4. Background Studies 174a neutral kaon and a nucleon. In the case of a positively charged kaon, the reaction isKn —* K°p. (4.77)The neutron will obviously be bound in a nucleus. In the case of this experiment, if theinteraction occurs in the active target, the energy loss from the proton can easily overlap withthe energy loss from the incident K+ and be missed. The neutral kaon is a superposition of thetwo mass eigenstates K (K-long, mean life 51.7 ns) and K (K-short, mean life 8.92 x 10_us).The K-short decays essentially 100% of the time to two pions, with a small amount of radiativetwo pion decay. The three pion decay mode of the K-short has yet to be observed, withbranching ratio upper limits of a few times i0. On the other hand, about 65% of the K-long’s decay semi-leptonically (K —* 7r±tFve). Since this is a three body decay, the leptonin the final state can have very little energy and be difficult to detect if the K-long decaysbefore exiting the target. Both the muonic and electronic branch contribute to this potentialbackgroundK —* tiY1 BR = 13.5% (4.78)K —* ireEe BR 19.35%. (4.79)Just as was the case with K+ * +e+ve , this background is indistinguishable fromK.1.2 background : a single + originates from the target and the energy deposited by theproton and the decay lepton in the target overlaps with the energy deposited by the incidentIf the lepton has a significant amount of energy it will easily be detected. The estimate ofthe background contribution from this source hinges on the determination of the rate at whichparticles other than the K+ and the remain hidden. Because of their very different masses,the energy loss behavior of electrons and muons is quite different. For a given energy, it willbe easier to detect an electron, so we can expect the muonic branch to contribute more to theoverall background rate. In addition, the kinematic end point of the muonic branch is lowerthan the electronic branch, resulting in a larger kinematic acceptance by the v7 trigger.No reliable way of selecting data samples representative of this background was found,and the estimate had to rely on a Monte Carlo simulation. The first step in setting up theChapter 4. Background Studies 175simulation was to obtain the charge exchange cross section as a function of energy. This is nottrivial since no measurement exists of this cross section at the relatively low energies involved inthis experiment, except for a nuclear emulsion measurement averaged over C, N and 0 nucleifor a energy of 60 MeV [72]. A few measurements exist of the charge exchange crosssection for K+ on deuterium at low energy [73, 74]. The assumption was made that the crosssection for ‘2C is six times that of deuterium, appropriately corrected for nuclear shadowingand electro-magnetic effects. The cross section is typically a few mb, which results in an averageprobability of interaction of 1.5 x i0 for K+ incident on the target.The reliability of the cross-section used in the Monte Carlo simulation was checked using aspecial data set [75]. Trigger conditions were arranged to select K-short decays to two chargedpions. This study unequivocally demonstrated the presence of neutral kaons in the target. Thefraction of observed K-short per incident K+ was determined for both the real data and theMonte Carlo. The ratio of the two numbers gives a correction factor for the charge exchangerate=Iv eaio= 2.44 ± 0.98 (4.80)The simulation for the study of charge exchange as a K+ .+ K+147 background startedwith a K+ at the front face of the scintillator target. The total probability of charge exchangeinteraction for each event was calculated based on the K+ energy at the start of the eventand recorded in a data bank. The energy at which the interaction occurred was chosen basedon the theoretical distribution calculated from the charge exchange cross section and the kaonenergy loss energy dependence. The K+ was then allowed to propagate in the target and whenits energy dropped below the pre-selected value, the charge exchange reaction was forced, witha K-long being produced. The two semi-leptonic decay channels of the K-long were studiedseparately.In most cases, the K-long was produced with an energy large enough for it to leave thetarget before it decays. For example, a K-long with a kinetic energy of only 10 MeV has avelocity of 6 cm/ns ; considering the K-long lifetime of 51.7 ns, the probability is small that itwill decay within the active target. Therefore, the K-long was forced to decay within the targetChapter 4. Background Studies 176and the probability for this to occur was recorded for each event. Forcing every K+ simulatedto undergo charge exchange and each K-long produced to decay within the target significantlyimproved the efficiency of the simulation.The events satisfying the simulated irvi trigger were analyzed with the same program usedfor the real data. The number of background events expected from this source iii the real datawas expressed asN8 1 1Nbgd=X X fi X BR X Aanai X X NKT X fK1 (4.81)IVK ç L-‘otherswhere is the weighted number of events surviving the analysis, NK1 is the number ofkaons started at the front face of the target which satisfy the KT trigger requirement, is asdefined above by equation 4.80, fKo is the fraction of the K°’s produced in strong interactionsthat are K-longs, BR is the branching ratio of the K-long decay mode studied, Aaj is asdefined in section 4.2.5, Rothers is the additional rejection expected from cuts not applied,NKT is the total number of events satisfying the KT trigger requirement in the data andfKinc is the fraction of counts recorded as KT in the real data that are actual K+ incidenton the front face of the target. The latter was determined by a Monte Carlo simulation tobe = 0.8742 ± 0.0023; losses come from a K+ either decaying in flight or interacting inthe degrader and still satisfying the KT requirement. As mentioned in the previous section,NKT = 1.436 X 1011. Aaj was calculated in the same way as for Ke4 background; the valueobtained was Aj = 0.0458 ± 0.0081. fK = 0.5 since a Ko is a superposition of the two masseigenstates K-long and K-short, each with equal probability.Rothers is dominated by the VTXYCA cut. It might be expected that TGFIT would alsoprovide a significant rejection factor; however, as will be seen below, 7r+ tracks from chargeexchange background emerge from the target typically a few nanoseconds from the arrival timeof the K+ , which renders the TGFIT cut essentially ineffective. The VTXYCA cut was notapplied to the simulated data because the B4 hodoscope is not simulated properly by the MonteCarlo program. By inspecting the distribution of K+ energy in the target as a function of thedecay vertex position extrapolated from the drift chamber track, the rejection expected wasestimated to be Rothers = 2.0 + 0.5. Substituting for the known values in equation 4.81, weChapter 4. Background Studies 177obtainNbgd= xBRx(5.9+3.0)x 108. (4.82) K —*A total of 2.0 x 106 events were simulated for K2 —* ; of these, 1993776 satisfied theKT trigger requirements. The offline cuts applied were the same as for the Ke4 backgroundstudy. Table B.72 gives the details of the simulation and analysis; 37 events remained after allcuts were applied. Each event had a weight given by the product of three probabilities1. Probability of j(+ charge exchange2. Probability of decay of the K in the target3. Probability of satisfying the online delayed coincidence.The third item was calculated based on the measured value of T -T and the distributionshown in figure 3.33. The sum for the 37 events was 4.96 x ion. Figure 4.79 shows the T -T distribution before the PROMPT and KINCUT cuts were applied; note that each eventwas weighed appropriately in the histogram. The large count in the bin near 4 ns is dominatedby a single event with a very low energy K-long, which has a high probability of decay in thetarget.Using equation 4.82, the numbers from table B.72 and BR(K —+ jri7 ) = 0.135 ±0.002 [17], the background contribution was estimatedNbgd=X (0.135 + 0.002) X (5.9 + 3.0) X 108= 0.20 ± 0.10 (4.83)where the error is statistical only. This background is obviously non-negligible. K —*The simulation and analysis for the decay K —* K+eve proceeded in exactly the same wayas for K —* . A total of 6 x events were simulated, of which 598053 satisfied theChapter 4. Background Studies 178.0020.00 15C,).00100C-).0005.0000Figure 4.79: T -T distribution for K —* ri7, decays from charge exchangebackground.KT trigger requirements; only 6 events remained after offline cuts were applied, with a summedweight of 1.04 x io. Details are given in table B.73. When compared to —*the obvious difference between the two analyses was with respect to the trigger acceptance,which is a factor of 3.7 times less for j0 ,‘ . The electron from K —* 7r+e ismore easily detected than the muon in J( —* . This is also reflected in the rest of theanalysis, with the INTIME cut having a much greater rejection. The other important point isthat the PROMPT cut was not applied in this analysis. If it had been applied, all the eventswould have been rejected. To avoid the time consuming task of generating perhaps an orderof magnitude more events for a background process which was obviously less significant than—, use was made of the results of the study of the latter process to estimate therejection of the PROMPT cut. The time delay in the target should be independent of the Kdecay mode, and hence no systematic effect should be introduced.Of the 901 events passing the TGTRACK cut in table B.72, 596 were found in the searchregion. The weighted sum of these events was 1.38 x 102. Therefore, the rejection of theChapter 4. Background Studies 179PROMPT cut was estimated to be1.38 x 10—2RPROMPT= 4.96 x 10—= 2.78. (4.84)To determine the background contribution, equation 4.82 was modified to take into accountthe rejection of the PROMPT cutNbgd= Npassx1x BR x (5.9 + 3.0) x 108. (4.85)RPROMPTSubstituting the appropriate numerical values, it followed thatNbgd = X X (0.1935 ± 0.0025) X (5.9 ± 3.0) X 108= 0.0071 + 0.0036 (4.86)where the accepted value of the K ,‘ +e76 branching ratio was used [17]. The error isonce again statistical only. This background contribution is nearly 30 times less than the onedetermined for J.2 —* L17L decay.4.2.7 Hyperon productionSemi-leptonic decay is not the oniy possible j+ +i7 background process for a neutralkaon produced via K+ charge exchange. Through the well known process of oscillation, theJ(0 produced in a nuclear interaction has a time dependent probability of being a K° [76].Since it contains a strange quark as opposed to a strange anti-quark, the K° can interact witha nucleon and produce a strange baryon through the reactionK°N — YTr (4.87)where N is either a proton or neutron and Y is a or A hyperon; the latter can in turn decayto a charged pion and a nucleon. For the specific case of this experiment, interactions on thesingle proton of hydrogen nuclei in scintillator can be neglected since the likelihood of detectingboth interaction products or their decay daughters is very large. For nucleons bound in carbonnuclei, there is a significant probability that one of the interaction products will be immediatelyabsorbed by the carbon nucleus, and therefore be difficult to detect.Chapter 4. Background Studies 180The process which a priori appeared to be the most significant was studied with a MonteCarlo simulation. The first part of the simulation was identical to the simulation of K+ chargeexchange background. Instead of allowing the neutral kaon to decay, it was forced to interactin the target via the reactionK°N (4.88)assuming it had evolved in a K°. The probability for this was calculated based on the Ko timeevolution and stored in a data bank. The total cross section for the interaction of I2 withcarbon and hydrogen has been measured for relatively low incident energies [77]. By combiningthese data, the total interaction cross section of Ic in scintillator was determined. The crosssection for equation 4.88 has not been explicitly measured however. To estimate it, use was madeof the Kp —+ cross section [78], which should be similar except for some isospin differencesand electro-magnetic effects. Based on this information, an energy independent cross sectionof 50 mb/nucleon was assumed, corrected by a factor of 0.5 for the nucleon screening effect incarbon nuclei. From this cross section, the probability for the J(O to interact was calculatedand stored. The pion in the final state was assumed to have been absorbed by the carbonnucleus, and therefore was not tracked in the event simulation. This was corrected for, as willbe described below. The distribution of the cosine of the angle of the interaction products withrespect to the direction of the K° was assumed to be flat in the center of momentum frame.After the interaction, it was assumed that the hyperon escaped the carbon nucleus,propagated in the target and decayed via the process7r+fl (4.89)This decay has a branching ratio of 48%. In the rest frame of the E+, the -+ and neutronmomentum is 185 MeV/c ; for the neutron, this corresponds to a kinetic energy of 18 MeV,making its detection difficult. Because of its large rest mass of 1189 MeV/c2, the E particletypically has a very short range in the target. The kinematic acceptance for the decay isvery large, even taking into account that some of the ‘s decay in flight. The mean life of theE is (0.799 + 0.004) x 10° us ; this implies that it+ tracks from this background process willappear more or less prompt, as for the charge exchange background.Chapter 4. Background Studies 181A total of 2 x io events were simulated. Of these, 193105 satisfied the KT requirementand 81 remained after all cuts had been applied. Table B.74 gives detailed results. The weightfor each event was the product of four factors1, Probability of I( charge exchange2. Probability of Ko K°3. K° interaction probability4. Online delayed coincidence probabilityThe sum of the weights for the remaining events was 3.15 x i0.If we compare the results of table B.74 to the ones obtained for charge exchange background,it is clear that the acceptance is much larger for this process. The probability of K° interactionand the probability of detection of the interaction products determine the importance of thisbackground relative to the charge exchange background. The number of background eventsfrom this source was estimated with the following formulaNbgd= NpassfKo x x pabs X Aanai X X B( ,‘ q) x NKT x (4.90)NK L RMany of the factors in this equation are the same as for the charge exchange background, fi, Aanai, NKT and fK1. The accepted value of the branching ratio is B(E — irn) =0.4830 + 0.0030 [17]. The factor Rothers we had for the charge exchange background has beenreplaced by R. Inspection of the extrapolated z-vertex as a function of K+ energy in thetarget showed that no significant additional rejection could be obtained from cuts such asVTX_PCA. However, the pion produced in the interaction is absorbed by the carbon nucleus,but is not simulated. As calculated for Ke4 background, we can expect an additional rejectionof R7, = 2.91 + 0.04 from neutrons and other interaction products from ‘r absorption.Appropriate values for the two remaining factors, pEesc and 7’ are not obvious. Fortunately, a bubble chamber experiment investigated Kp interactions and reported values forthese factors [79]. They determined pEesc = 0.52 ± 0.10 and plrabs = 0.10; no error was quotedfor the latter. With N5 = 3.15 x i0 and Njc1 = 193105, and substituting all the otherChapter 4. Background Studies 182factors, we obtain the estimate for the number of background events from this source usingequation 4.90Nbgd = 0.33 ± 0.16. (4.91)This number is quite large, and raised serious concern. Inspection of the simulated eventssatisfying all analysis criteria showed that about one third of them had a large gap in the xyplane in the target between the elements struck by the K+ and the elements struck by the +.The target track reconstruction algorithm assigned the elements struck by the + to the “kaon”,and ignored the elements struck by the K+ . Such a signature was looked for in several realdata samples, but no evidence was found. The other main characteristics of this backgroundare early times in the target and a ir+ momentum peaked around 185 MeV/c; again, no clearevidence was found in various data samples chosen to enhance these characteristics. This is incontrast with K4 background for which even though the background estimate relied upon aMonte Carlo simulation, such events could be identified by scanning events at various stages ofbackground studies using real data. For charge exchange, the independent study by other E787collaborators clearly identified the presence of Ic particles in the target. There is thereforeno doubt that Ic particles are also produced; their decay can be reliably simulated by theMonte Carlo program. In the case of hyperon production following K+ charge exchange, theinteraction cross section is not very well known, and the simulation relied on necessarily crudeassumptions. For all these reasons, it was concluded that this background contribution, eventhough it cannot be ruled out, is likely overestimated by the simulation.4.2.8 1991 Background summaryEstimates for all the background sources for 1991 data are summarized in table 4.30. Becausesome of the estimates are given as an upper limit, it is difficult to add all of them to obtain atotal background estimate. If we neglect the one particle beam pion background, the sum for allbackground sources other than Jt’,-2 is 0.84 ± 0.20 events. According to the Poisson probabilitydistribution, the probability of observing one event if the mean of the distribution is 0.84 isP = 0.36 and the probability of observing no events is P = 0.43. This means that there was aChapter 4. Background Studies 183non-negligible probability of observing at least one background event after analysis of the entiredata sample, particularly considering the estimate for the K7r2 background. However, uponcareful examination of the background data samples available, no additional constraints couldbe found that reduced the background expectation significantly while satisfying the rejectionversus acceptance loss criterion of effectiveness.Table 4.30: Summary of 1991 background estimates.Background Estimate (# events)K —* ii.i° (K2) < 2.0 (90% C.L.)K —+ 7r7r°7 (K27) 0.0244 + 0.0036Muons (K3 ,K,27 ) 0.180 + 0.071Beam pions (two part.) (2.7 + 1.7) x i0Beam pions (one part.) < 0.05 (90% C.L.)K —* reve (Ke4) 0.101 ± 0.024Charge exchange (K —* E7) 0.20 ± 0.10Charge exchange (K —* 7reE7e ) 0.0071 ± 0.0036Hyperon production 0.33 + 0.16Chapter 5Data Analysis and ResultsThis chapter describes the analysis steps beyond the first pass, the determination of the acceptance for K+ _ +jj7 and J(+ _÷ +XO , the determination of the total integrated kaon fluxand the final results. A discussion of these results will be deferred until the next chapter.5.1 Final Analysis5.1.1 1989 DataThe final stage of the 1989 data analysis proceeded in two steps, Pass2 and Pass3. Details ofeach step are given in the sections below. 1989 Pass2The second analysis pass on 1989 data consisted in five cuts applied to the events satisfying allPassl requirements. The cuts were the CERENKOV cut, the remainder of the PROMPT cut requirements except for T -T <50 ns, the ELECTRON cut, the RGEMOM cut and the MASScut. For the latter, the calculated particle mass had to be within the range 100—180 MeV/c2,which is slightly less restrictive than the final cut. Table 5.31 gives the detailed statistics ofthis analysis pass. The remaining data sample contained a mixture of most background eventtypes.184Chapter 5. Data Analysis and Results 185Table 5.31: 1989 Pass2 results.• Cut # events RejectionPassl 12554CERENKOV 9459 1.3272 + 0.0068PROMPT 4042 2.340 + 0.028ELECTRON 1889 2.140 + 0.036RGEMOM 1258 1.502 + 0.024MASS 1160 1.0844 + 0.0089Total 10.82 ± 0.305.1.1.2 1989 Pass35.1.2 1991 Data5.1.2.1 1991 Pass2For Pass3, the remaining cuts and final versions of cuts partially applied in earlier passes wereapplied to the Pass2 data sample. Table 5.32 gives the detailed statistics of this analysis. Noevents remained after all cuts were applied. Figure 5.80 shows the kinematic distribution forthe events before the application of the last cut (KINCUT). The group of events above theK+ .+,)i7 search region corresponds to K.2 decays in which the photons from ir0 decay werenot detected.The 1991 data analysis beyond Passl proceeded in three steps, Pass2 to Pass4. Pass3 consisted of two separate steps, each involving analysis of a portion of the events satisfying Pass2requirements. Details for each pass are given below.For the second pass of the 1991 analysis, all cuts except the ones expected to have the largesteffect on the most serious background sources, namely TGTRACK, TGFIT, VTXYCA, PBGLASS, B4FIT, were applied to the Passl data sample. Several of the cuts applied were thefull versions of cuts partially applied at Pass 1. Table 5.33 gives the result for each cut appliedin succession. Of the remaining 1464 events, a total of 262 were in the J(+ ÷ .+j7 kinematicsearch region. Figure 5.81 shows the ir+ range versus momentum distribution for the remainingChapter 5. Data Analysis and Results 186Table 5.32: 1989 Pass3 results.Cut # events RejectionPassi 1160BM_HOLE 1140 1.0175 ± 0.0040B4TD 1036 1.100 + 0.010NK 1025 1.0107 + 0.0033PROMPT 1002 1.0230 ± 0.0048DISENPI 989 1.0131 ± 0.0037DISENK 976 1.0133 + 0.0037INT_EB 527 1.852 + 0.055NDC 470 1.121 + 0.017DC-CHI2 451 1.0421 ± 0.0099ICOUNTER 400 1.128 + 0.019RSPC 399 1.0025 + 0.0025INT_RIV 293 1.362 + 0.041FITPI 203 1.443 + 0.056TGTRACK 88 2.307 + 0.018FIDUCIAL 70 1.257 + 0.068ZDCTZ 64 1.094 + 0.040ZK_EK 59 1.085 + 0.039EB4_EK 52 1.135 ± 0.054DEDXRS 50 1.040 + 0.029MASS 49 1.020 ± 0.021KINCUT 0 —Chapter 5. Data Analysis and Results 18735+30 + : ++++:;+ ++ +t*% ++,+.t+ii. +÷++I +1510.1,,140 160 180 200 220 24Momentum (MeV/c)240 I I I I I220o +++•-I- +÷+++ :÷200 + +÷---\%÷ +÷++ t .II- +S — —-I—-’ IOnC “-flJ II)S I0160 I140 I I I I60 80 100 120 140Energy (MeV)35 I I+30 + ÷+$ +++ ++ ++ ._+4t1. ++ ++_÷ ++* + + ÷25 : +V I0’ ICon0 I1510 I I I I I I60 80 100 120 140Energy (MeV)Figure 5.80: Kinematic distributions for 1989 events before the final cut. Thedashed lines indicate the upper limits of the K+ * lr+vv searchregion.Chapter 5. Data Analysis and Results 188events. A clear peak from K,.2 events can be observed, as well as a flat low energy tail in the_ search region.Table 5.33: 1991 Pass2 results for the entire data sample.Cut # events RejectionPassi 399958PROMPT 348794 1.14669 ± 0.00069DC-SETUP 260033 1.3413 + 0.0013RS-TRACK 239065 1.08771 + 0.00063ICOUNTER 165311 1.4462 + 0.0020TRKTIM 100537 1.6443 + 0.0032INTIME 18952 5.305 + 0.035INTSE 14677 1.2913 + 0.0051FITPI 10255 1.4312 + 0.0078TDJVIDA 9366 1.0949 + 0.0033TDFOOL 7113 1.3167 + 0.0076ELVETO 5219 1.3629 ± 0.0097ELECTRON 3991 1.308 + 0.010FIDUCIAL 3199 1.2475 + 0.0098KINSCORE 2813 1.1372 + 0.0074BM_HOLE 2700 1.0418 ± 0.0040B4_CNTR 2544 1.0613 + 0.0051CERENKOV 1604 1.586 ± 0.024BWPC 1464 1.0956 + 0.0084Total 273 + 1991 Pass3Pass3 consisted in the application of the remaining cuts to the events satisfying the Pass2requirements. Because of the large uncertainties in the background estimates, it was decidedto initially perform Pass3 on 30% of the data sample. If any events remained, they could beinvestigated and appropriate action taken before the remainder of the data was analyzed. Inthis way, if a certain feature of the background had been overlooked, improvements could bemade that would potentially benefit the remaining 70% of the data sample without bias.Table 5.34 shows the results of the analysis of 30% of the Pass2 sample with all cuts.Separate statistics are given for the kinematic search region events (tail) and events outside ofChapter 5. Data Analysis and Results 18940- -10— i I I100 150 200 250Momentum (MeV/c)Figure 5.81: Total lr+ range versus total momentum for 1991 events satisfying allPass2 requirements. The dashed line indicates the upper limit of the_+j,7 search region.that region (peak), as well as the overall total. As can be seen, two events satisfied all analysiscriteria.Table 5.34: Results of full analysis for 30% of the 1991 Pass2 sample.Cut # Events Peak Tail# Rejection RejectionPass2 420 351 69TGTRACK 89 80 4.39±0.43 9 7.7±2.4TGFIT 79 73 1.096 + 0.038 6 1.50 + 0.35VTX_PCA 71 65 1.123 ± 0.046 6 1.00 + 0.00PB-GLASS 49 46 1.41 + 0.11 3 2.00 + 0.82B4TD 47 45 1.022 + 0.022 2 1.50 ± 0.61KINCUT 2 0 2 1.00 ± 0.00The two events were carefully examined for any obvious flaw that might have been missed bythe analysis procedure; none was found. The possibility of software errors was also considered,but all aspects of the events had been correctly analyzed. Table 5.35 lists some importantcharacteristics of the events. The first observation is that the momentum of the -+ for theChapter 5. Data Analysis and Results 190two events is similar and relatively high. In both cases the + energy is lower than what couldbe expected based on the momentum; this is reflected in the high calculated rest mass. Thesame can be said of the total range. The total energy and total range match very well. Thisis not unexpected however, since the range in the last range stack layer struck by the + trackis determined using the measured energy in that layer. It should also be noted that bothevents are well within the K+ ir+v7 kinematic search region. They are at least 3.5 standarddeviations below the K,,-2 peak position in all three kinematic quantities.Table 5.35: Characteristics of the remaining events after full analysis of 30% ofthe 1991 data sample.Quantity ] Event 1 Event 2RS stopping layer 3 4RS stopping sector 21 24Total ir momentum (MeV/c) 188.8 189.1Total + energy (MeV) 87.0 90.8Total + range (cm) 22.6 24.6Rest mass (MeV/c2) 147.5 143.6K decay time (ns) 2.7 4.9ir decay time (ns) 47.2 55.8The + momentum for both events is close to the value expected for + decay (185 MeV/cat rest). The relatively early K+ decay time in the target is also somewhat suggestive. Event1 had a 0.58 MeV energy deposition in one endcap module within the time window of theINTIME cut. This is just below the cut position of 0.6 MeV. No other activity was observed atthe time of the + track. Finally, the + decay time in the stopping range stack counter is quitelate. This might be expected if the “muon” pulse was a random hit, as opposed to a true muonfrom pion decay. However, the evidence is rather slim. The estimate of the background frommuon sources was quite firm and did not support this hypothesis. All other background sourceswere revised, and the only possible background explanations were K,,-2 , charge exchange andhyperon production.All cuts were re-examined to determine if additional rejection could be obtained. Onlythe offline photon veto cuts INTIME and INTSE and the cut on the summed energy of pionChapter 5. Data Analysis and Results 191time target elements not connected to the + track (part of TGTRACK) could be tightenedto reduce the background by a factor of two above the reduction due to acceptance loss. Noparticular feature of the background samples allowed the design of new cuts. It was thereforedecided to complete Pass3 on the entire data sample with the existing cuts, and apply thetighter cuts as Pass4. Details about those cuts and their effect on the Pass3 data sample willbe given in the next section.Table 5.36 shows the results of the final analysis, including the 30% discussed above. Anadditional five events satisfied all analysis criteria, bringing the total to seven events. This isentirely consistent with the two events observed in 30% of the sample, but inconsistent withthe background estimates. Table 5.37 lists the characteristics of all seven events; in this table,events B and F were events 1 and 2 in the 30% initially analyzed.Table 5.36: Results of full analysis for the entire 1991 Pass2 sample.Cut Events Peak Tail_______# Rejection #] RejectionPass2 1464 1202 262TGTRACK 306 279 4.31 ± 0.23 27 9.7 ± 1.8TGFIT 272 254 1.098 ± 0.021 18 1.50 ± 0.20VTX_PCA 246 231 1.100 ± 0.022 15 1.20 ± 0.13PB-GLASS 174 165 1.400 + 0.058 9 1.67 ± 0.35B4TD 166 159 1.038 ± 0.016 7 1.28 ± 0.23KINCTIT 7 0 — 7 1.00+0.00The delayed coincidence time distribution is consistent with the K+ mean life. The decaytime for these events still appears somewhat stretched out, but not excessively so. Contraryto the first two events observed, the additional events are spread out in the kinematic space.Figure 5.82 shows the kinematic distribution of the events before the final cut was applied. Thelarge group of events immediately above the K+ lr+zñ7 search region is again due to K2 peakevents for which the photons from ‘r0 decay were not detected. The smaller group about 20 MeVhigher in energy than the K2 peak corresponds to K.2 events in which a low energy photon (h.’20 MeV) from r0 decay converted in the range stack on top of the ii+ track. Such events wereChapter 5. Data Analysis and Results 192Table 5.37: Characteristics of the remaining 1991 events after full analysis of theentire irv7 data sample.Quantity EventA B C D E F GRS stopping layer 4 3 3 3 4 4 4RS stopping sector 11 21 21 10 10 24 16Total momentum (MeV/c) 174.0 188.8 176.6 164.2 184.6 189.1 186.9Total energy (MeV) 85.3 87.0 86.0 73.2 92.2 90.8 93.5Total ir range (cm) 21.6 22.6 22.6 16.6 24.3 24.6 25.8Rest mass (MeV/c2) 133.1 147.5 142.0 153.6 137.4 143.6 135.5K decay time (ns) 14.7 2.7 21.3 10.0 12.3 4.9 2.1j- decay time (ns) 28.6 47.2 28.9 13.9 58.6 55.8 15.2not observed in the 1989 data sample because of the application of the DEDXRS cut, whichrejected events with an anomalous energy deposition pattern for the track in the range stack.Background studies in 1991 showed that such a cut would have no effect other than acceptanceloss on the background events in the J(+ ÷ K+7 search region. Indeed, the application ofsuch a cut to the Pass3 sample rejected almost all the events in the sateffite peak above theK+ 71-+1jj7 search region but none of the events in the search region.Figure 5.83 shows the same distributions as in figure 5.82 for a large number of K+lr+vET Monte Carlo events satisfying the simulated iriñ7 trigger and the offline analysis cuts,indicating the shape of the signal from K+ 7.+jJ7 assuming a V-A weak interaction coupling. 1991 Pass4As mentioned above, after analyzing 30% of the Pass2 data sample using all cuts and findingtwo candidate events, the offline cuts were re-examined. Based on the available backgroundsamples, it was found that the INTIME, INTSE and TGTRACK cuts could be made morerestrictive while satisfying the condition that the rejected fraction be at least a factor of twolarger than the acceptance loss. Tables 5.38 and 5.39 list the new parameters for the INTIMEand INTSE cuts respectively, to be compared to tables 3.6 and 3.7. For the INTIME cut, inaddition to widening the coincidence time window and lowering the energy threshold, a cut wasChapter 5. Data Analysis and Results 19335 ‘‘‘‘i’.’’+30-+15 I10 I i.140 160 180 200 220 240Momentum (MeV/c)21—c .‘ I I I I I I220t÷.* 4;200 — — ÷ + + + + ++E +++ I+ ICE0 I160 I140 Iii I I I60 80 100 120 140Energy (MeV)35 I I I I I÷60 80 100 120 140Energy (MeV)Figure 5.82: Kinematic distributions for 1991 events before the final Pass3 cut.The dashed lines indicate the upper limits of the Jç[+ ÷ .j+j,jy searchregion.CD cz•1—.‘CD bCDrI-.•.,—.CDri—.+ 21’Range(cm)&iC010010010.11.1.11..1•.IIIIIIIIIIIIIIII00II••‘‘110001.•...ein 000001..0000000I•...00000,..ooflflo..•IOoIJotJDoI••‘..aLEJJnoo...•aOULIJ000n0000mon••..nooflorjin0nEooofl000onnnnofl00.Iiiiflfl00no..0UI5o00cI00o1JLIQ..-ror000000nn..ni0IJ00000..00000000n.nn000000000000.100000.00.0.0010.....InnIn,,.,.•11011..0000.Momentum(MeV/c)--r’JF••.)0)I01’.)oo00I,I.I.11111111111111_I—IOn.100.00.•.1108011I•‘‘noofl“DEjD0•.000000’nI•‘‘oOUOOoo’’••...0OOJnu.”I..,I0000nJo0000000‘ottIoooo’I...•...ooafloo.ooflOflflo00O0fl00‘‘‘OoOOào00oo0O,.•••o.00000000...0OflOOn0fl0o‘.000000Ofl,fl 0000000.•00’•.0’’•0000’InODInInoon....00000n000nn’..I..nfln•.‘niuloInuDUono•.‘noJflnOflofloI..Iuo..onflflI.UOUU000..In000000•000EIIIln000000‘o’oUUflonUIj1fl..’-naaUOo‘.IJUUOonn00flO0I000000’.‘.00000...onQJJOOnnnjfl5.o DOG...0001.1Gill0Range(cm)-‘F\)F\)CJ(i010010(TI0.000 0 -s 0 0 0 0m :5 CD -S CD <I CD—so0 0) 00-s dcxiCD°:5 I-, C Ct’0 F’) F’) 0 F..) 00.0 0P1 :5 (TI -S‘<0,-,0CD <‘-I-5 F’) 0 00oI•...I......I......II....I.....I.••..1...,.,liiiII,1lIII1I,IIIiiCDChapter 5. Data Analysis and Results 195placed on the energy in the V-counters measured by the ADCs for cases where no time valuewas recorded in the TDCs for the same module in the range [-400,+200] ns. For INTSE, somewindows and thresholds were changed and new categories were added : barrel veto single endADC hits with TDC hits at both ends, barrel veto single end ADC hits with no TDC hits andendcap time hits with no energy measured with the ADCs. For the latter, at least two moduleswith time hits within the coincidence time window are required.Table 5.38: Parameters for tighter 1991 INTIME cut, to be compared to table 3.6.Subsystem Time window Threshold[Min,Max] (ns) (MeV)RS [-2.0,+16.0] 0.5BV [-8.0,+15.0] 0.4EC [-4.5,+8.0] 0.0IC [-6.0,+6.0] 0.2VC {-6.0,+5.0] 0.1VC No time 0.8Table 5.39: Parameters for tighter 1991 INTSE cut to be compared to table 3.7.Subsystem Ends hit Time window ThresholdEnergy Time [Min,Max] (ns) (MeV)RS both single {-1O.0,+10.0] 0.0RS single both [-5.0,+5.0] 0.0RS single single [-10.0,+10.0] 0.25BV both single [-12.0,+8.0] 0.0BV single both [-6.0,+12.0] 0.0BV single single [-14.0,0.0] 0.4BV single none 1.0EC none 2 hits [-2.0,+10.0] 1.0The parameters for these two cuts were adjusted by examining the events remaining afterthe cuts were applied with the previous set of parameters. For the rejection, a sample ofirvi7 events failing the TGTRACK cut and located in the K+ * +j,7 signal region was used,while for the acceptance a sample of K,2 events was used.Chapter 5. Data Analysis and Results 196For TGTRACK, the cut position for ESC was moved from 1.5 MeV to 1.0 MeV. ESC isthe energy sum for the target elements off the swath defined by the drift chamber track andnot connected to the other track elements but in coincidence with the time of the track. This isa form of photon veto. The sample used to adjust the cut was the sample of events failing thephoton veto cuts beyond Passi and located in the j+ +jJj7 kinematic search region (seetable 4.19). Of the 71 events in the sample, 3 were rejected by tightening the TGTRACK cut.The tighter cuts described here gave an additional rejection factor of 1.58, primarily againstK,.2 background, with an acceptance relative to the Pass3 cuts of 0.83. They also affectedthe background estimates. In most cases the change was small and came primarily from theacceptance loss of the additional cuts. For K2 background, the estimate from Method 1changed significantly. The value of the peak/tail ratio was updated to= 2231= 30.1 + 3.5. (5.92)As will be seen below, the number of events remaining in the K2 peak region after all cuts is117. Therefore, the K2 background estimate using Method 1 becomesNbgd== 3.89 + 0.58 . (5.93)The change in the K.2 background estimate from Method 2 is more difficult to assess, since noevents remained after Pass3 cuts were applied to the selected background sample. If we assumethat the estimated additional rejection factor of Rpass4 = 1.58 applies fully to K,.2 background,we can then calculate the background estimate asNbgd < X X = 1.3 (5.94)RTGFIT — 1 RB4TD Rpass4where we modified equation 4.57.The application of these tighter cuts on the events satisfying all Pass3 requirements resultedin the rejection of three of the seven events in the K+ +jjj7 search region. Outside of thesearch region 117 of the 159 events analyzed satisfied all requirements. Figure 5.84 shows thekinematic distributions of the events before the final cut.Referring back to the designation of table 5.37, the three events rejected were events B,C and D. Event B, as mentioned before, had a 0.58 MeV energy deposition in one endcapChapter 5. Data Analysis and Results 19735__%30 —— -:—25 +a) +01g20 I15 I10 I • I • I. •140 160 180 200 220 240Momentum (MeV/c)240‘ I ‘ I ‘ I220C) + ++ • . +t 4f.%÷. ++ + + 420D +4•4 +1180 +++160 I140 I I I ‘I I I60 80 100 120 140Energy (MeV)35 I • I30 •a:.:+ +4544+*•+#+ + 4+:+ •+$+ + + +25- ++ I •ci)01C -C15 - I H10 I I ii I I I60 80 100 120 140Energy (MeV)Figure 5.84: Kinematic distributions for remaining 1991 events before the finalcut for Pass4 analysis. The dashed lines indicate the upper limits ofthe K+ 21+zji signal region.Chapter 5. Data Analysis and Results 198module with a time within the coincidence window. It might be argued that rejecting thisevent somewhat biased the analysis since the endcap energy deposition had been observedbefore the cut was adjusted. However, the energy threshold of the endcap cut was not adjustedbased on this event but rather by looking at the background sample. All other INTIME andINTSE energy thresholds and time windows were re-adjusted in order to tighten the photonveto cuts as much as possible. Therefore, the bias introduced by rejecting this event is mostlikely negligible. Event C failed the TGTRACK cut with ESC = 1.25 MeV. Event D hadtwo endcap TDC hits within the coincidence time window but with no measured ADC energy.Further discussion about the result and the nature of the remaining events will be reserved forchapter 6.5.2 AcceptanceThe combined acceptance of the detector, trigger and offline analysis must be determined inorder to calculate a branching ratio. The calculation relied as much as possible on real datato take into account all the experimental conditions. The low bias monitor data were wellsuited to this task, since they were collected in the same conditions as the 7rv1 data sets. Someacceptance factors, such as the detector geometrical acceptance and the effects of nuclearinteractions cannot be determined using real data; for those items a Monte Carlo simulationwas used.Three monitor data samples were used to measure the acceptance factors : Kt2(1), Kir2(1)and 7r-scat. A description of the trigger requirements for these data sets was given in table 3.3.As their designation would suggest, these data sets contained primarily K,2,Ic and beampions respectively. The following sections describe the analysis of each of those data sets and theacceptance factors derived from each. As much as possible, cuts were applied in the same orderas in the final analysis, particularly for groups of cuts which address the same backgrounds.This method should minimize systematic effects and possible double counting of acceptancelosses.Chapter 5. Data Analysis and Results 1995.2.1 K,2 measurementsBy their nature, K,2 decays are ideal for measurements that require a single charged trackand no other particles, one of the important features of K+ ,S +7 decays. The drawbacksof K,2 decays are the high momentum of the charged particle, which is substantially higherthan the upper limit of the accepted region of kinematics for this search, and the fact that thecharged particle is a as opposed to a 7r+ . Nonetheless, the acceptance of several cuts wasmeasured with a sample of K2 decays. They are well suited for measuring the acceptance ofcuts affected mainly by accidental losses, such as photon veto, beam and reconstruction cuts.The I(j2(1) trigger is very efficient at selecting K2 decays. Therefore, with minimal additionalconstraints clean samples were selected. 1989 K,2 measurementsTwo separate samples of K2 events were selected out of the I(2(1) monitor data sample.The first was selected by requiring that the events satisfy the online delayed coincidence cutand that there be a single track in the range stack, identified without the use of drift chambertracking information. The delayed coincidence is not part of the KJL2(1) trigger, and so itwas required offline by looking at the trigger information recorded in the data. This samplewas used to determine the acceptance of target and drift chamber track reconstruction cuts, aswell as Level 1 trigger cuts and some beam counters cuts. After the target and drift chambertrack reconstruction cuts had been applied, a ±1.5a cut on the total range, kinetic energy andmomentum of the + was applied to improve the purity of the sample. The values of the meanand width (a) of the K,2 kinematic peak were from fits to a Gaussian function pius a fiatbackground component for all three quantities. Table 5.40 gives the details of the analysis aswell as the acceptance of each cut considered.Further explanations are necessary for the DC-SETUP cut. The low value of the acceptanceis the result of a broken wire in the drift chamber. The wire broke about 65% into the 1989 datataking period. Because of the significant amount of time needed for a repair, it was decided topostpone it until data collection was complete for the year. Since the broken wire could haveChapter 5. Data Analysis and Results 200Table 5.40: Acceptance of reconstruction cuts for 1989 data measured withK2 decays.Cut # events Acceptance24686TARGET 24108 0.97658 +0.00096DC-SETUP 17084 0.7086 +0.0029Pt0t cut 8666Level 1 NTG < 20 6992 0.8068 +0.0042Level 1 IC, Hextant cut 6813 0.9744 ±0.0019CERENKOV 6649 0.9759 ±0.0018BMJIOLE 6551 0.9853 +0.0015B4TD 6476 0.9886 +0.0013curled around several other wires, the high voltage was turned off for a section covering one thirdof the drift chamber active volume, resulting in the low acceptance of the track reconstructioncut. Furthermore, the acceptance obtained here is for charged particles with a momentum of236 MeV/c, which is significantly higher than the momentum in the K+ + kinematicsearch region. A correction based on the ratio of the DC-SETUP cut acceptance for K2 and* events simulated with a Monte Carlo program was applied to the number givenin table 5.40. The corrected value was ADC_SETUP = 0.672 ± 0.003.The second sample of I2 decays was selected by applying the target and drift chambertrack reconstruction cuts, the CERENKOV and B4TD cuts to reduce beam pion contaminationand by requiring that the track not reach the outermost layer of the range stack. The latterrequirement was applied using the trigger information recorded with the events and was toensure that the muon did not deposit energy in the barrel veto, since this sample was usedto determine the acceptance of all photon veto cuts. Also determined with this sample werethe acceptance of the range stack and other track reconstruction cuts not determined with theother K,2 sample, as well as timing cuts and vertex cuts. A total of 8011 events were selected.Table 5.41 gives details of the analysis and the acceptance of each cut. Cuts applied to the othersample of K2 events were also applied here to minimize possible double counting of acceptancelosses.Chapter 5. Data Analysis and Results 201Table 5.41: Acceptance of photon veto, event reconstruction, timing and vertexcuts measured with K,2 decays. The values used in the final K+ ++jj7 acceptance calculation are indicated by a check mark. For theothers, the acceptance was measured by other means.Cut j events Acceptance j_UsedEvents selected 8011ICOUNTER (Ej < 5 MeV) 7765 0.9693 +0.0019RS-TRACK 7731 0.99562 +0.00075 /Pt0t cut 4917 —Level 0 Del. coinc. 4081 0.8300 ±0.0054Level 0 Photon veto 3899 0.9554 +0.0032Level 1 NTG < 20 3069 0.7871 ±0.0066Level 1 IC, Hextant cut 3006 0.9795 ±0.0026BM_HOLE 2955 0.9830 ±0.0024NK 2946 0.9970 +0.0010PROMPT 2512 0.8527 +0.0065DISENPI 2496 0.9936 +0.0016DISENK 2475 0.9916 +0.0018INT_EB 1995 0.8061 ±0.0079NDC 1881 0.9429 ±0.0052DC-CHI2 1825 0.9702 ±0.0039ICOUNTER 1795 0.9836 ±0.0030INT_RIV 1574 0.8769 +0.0078TGTRACK 1223 0.777 +0.010FIDUCIAL 1169 0.9558 +0.0059ZDCTZ 1126 0.9632 ±0.0055ZK_EK 1106 0.9822 ±0.0039EB4_EK 1060 0.9584 +0.0060Chapter 5. Data Analysis and Results 202Because of the dependence of energy deposition on particle type and momentum, theICOUNTER cut acceptance measured here was not used; it was rather determined with asample of K2 decays (see section 5.2.2). Also, a correction was necessary for the cut onthe maximum energy deposition in target elements struck by the outgoing charged particle (part of the TGTRACK cut). This correction amounted to 0.962 ± 0.003, resulting inATGTRACK = 0.747 + 0.010. The acceptance of the FIDUCIAL and ZDCTG cuts was corrected for the momentum dependence of the charged particle track in the same way that theDC-SETUP cut was corrected. The values obtained were AFIDUCIAL = 0.932 + 0.004 andAZDCTG = 0.923 + 0.006.Finally, the acceptance of the RSPC cut was determined by counting the number of eventswith a hit in the chamber located in the sector diametrically opposite to the sector in which themuon from It2 decay came to a stop. The value measured was ARSPC = 0.98321 ± 0.00097. 1991 K2 measurementsA sample of K2 events was selected by applying the online delayed coincidence cut, based onthe trigger information recorded with the events. This selected K+ decays and ensured that acharged particle passed through one of the I-counters and was contained in the DC/RS fiducialregion. Since the data sample was to be used to measure the acceptance of the photon veto cuts,muons that reached the last layer of the range stack were rejected using the trigger information.Table 5.42 gives the statistics of the sample selection and shows the results of the applicationof the track reconstruction cuts, along with the value of the acceptance for each cut. Note thatfor the RS-TRACK cut, the minimum energy deposition requirement of 4 MeV in the lastcounter of the track was not included; only the track reconstruction part of the cut was used.Because of a possible dependence on the momentum of the track, the acceptance of the DCSETUP, RS-TRACK and ICOUNTER cuts was not taken from this analysis. It was rathermeasured with + tracks from K1,.2 decays, which have a momentum closer to the one of ii+ from+jj7 decays accepted in this analysis; this will be described in next section 5.2.2.In principle, the acceptance of the TRKTIM cut could be taken directly from this analysis,Chapter 5. Data Analysis and Results 203Table 5.42: Acceptance of event reconstruction cuts for 1991 data measured withJc2 decays. Only the value of the acceptance for the TARGET cutwas ultimately used in the final acceptance calculation.Cut # events Acceptance73766Online del. coinc. 49198 —Online RS layer 21 veto 20360 —20360 —TARGET 20107 0.98757 + 0.00078DC-SETUP 17127 0.8518 + 0.0025RS-TRACK 17051 0.99556 + 0.00051ICOUNTER 16105 0.9445 + 0.0018TRKTIM 15027 0.9331 ± 0.0020but there is one caveat. Because this cut requires consistency between the time of the trackmeasured in the target, I-counter and range stack, events which have no pion element in thetarget will be rejected by it. By selecting muon tracks which do not reach the last layer ofthe range stack, the K+ decay vertex distribution of the events selected was biased towardsthe center of the target in the xy plane. This implied that the number of events rejectedbecause there were no target elements struck by the muon track was less, thereby increasingthe acceptance of the TRKTIM cut. The I(2(1) monitor events were re-analyzed in the sameway as in table 5.42, but this time without rejecting the events reaching the last layer of therange stack. From this analysis, the acceptance of the TRKTIM cut was obtainedATRKTIM = = 0.8824 ± 0.0017. (5.95)The acceptance of the other event reconstruction cuts was the same as in table 5.42 withinstatistical errors.The next step was to determine the acceptance of photon veto cuts and beam cuts. Beforeproceeding, the data sample satisfying all cuts in table 5.46 was purified by applying a cuton the total momentum, range and energy of the + . The cut was applied at +2 for eachquantity, based on Gaussian fits of the distributions. Table 5.43 shows the results of the analysis.As in the case of event the reconstruction cuts, the acceptance of cuts that might depend onChapter 5. Data Analysis and Results 204particle type or momentum of the charged particle was not taken from this analysis, but ratherfrom analysis of a sample of I(2 decays. This included FIDUCIAL, TGTRACK, TGFIT andVTX.YCA. Also, the acceptance of the PROMPT cut was not measured with this sample, butrather was measured along with the acceptance of the online delayed coincidence cut, whichwas used to select this sample. All cuts were nonetheless applied, even if their acceptance wasnot being measured, to avoid possible double counting of acceptance losses.Table 5.43: Acceptance of photon veto and beam cuts measured with ‘2 decaysfor 1991 data. The values used in the final K+ _* +y acceptancecalculation are indicated by a check mark.Cut # events Acceptance Used]Events selected 10646Online EC & BV veto 9654 0.9068 + 0.0028Hextant cut 9448 0.9787 + 0.0015PROMPT 8836 0.9352 + 0.0025INTIME 6008 0.6799 ± 0.0050INTSE 4824 0.8029 ± 0.0051FIDUCIAL 4604 0.9544 ± 0.0030TGTRACK 3318 0.7207 + 0.0066TOFIT 3060 0.9222 + 0.0046BM_HOLE 3021 0.9872 ± 0.0020B4_CNTR 3011 0.9967 + 0.0010VTX_PCA 2735 0.9083 ± 0.0053CERENKOV 2729 0.99781 + 0.00089 /BWPC 2633 0.9648 ± 0.0035PB-GLASS 2330 0.8849 ± 0.0062B4TD 2243 0.9627 + 0.0039The acceptance of the delayed coincidence, both online and offline, was also measured withK,2 decays. A series of cuts not including the delayed coincidence requirement were applied tothe KJL2(1) monitor data sample to select a clean sample of K2 events; the delayed coincidencecuts were subsequently applied to determine their acceptance. The cuts used to select thedata sample were: online RS layer 21 veto, TARGET, DC-SETUP, RS-TRACK, ICOUNTER,TRKTIM, FIDUCIAL and a ±2u cut on the total range, momentum and energy as in table 5.43,Out of the total of 73766 events analyzed, 12363 satisfied all selection criteria. Table 5.44 givesChapter 5. Data Analysis and Results 205the measured acceptance for the online and offline delayed coincidence cuts. Also measuredwith this sample is the acceptance of the online IC requirement, which in principle should beredundant with the delayed coincidence. However, because of slightly different discriminatorthresholds for the two requirements there is a small additional acceptance loss from the ICrequirement.Table 5.44: Acceptance of delayed coincidence cuts and IC trigger cut measuredwith ‘(p2 decays for 1991 data.Cut # events AcceptanceEvents selected 12363Online del. coinc. 10052 0.8131 + 0.0035Online IC cut 10003 0.99512 ± 0.00069PROMPT 9336 0.9333 ± 0.0025The acceptance loss due to accidental hits of two other trigger cuts, (13CT + ...+18cT)(range veto) and (19 + 20 + 21) (muon veto), were also determined with K1t2(1) monitor data.These factors could not be determined directly based on the trigger information recorded withthe data since all + tracks from I(ii2(1) triggers reach at least layer 19 of the range stack.The +20 ns coincidence time window of the trigger had to be simulated using the range stackinformation from the ADCs and TDs. A region seven sectors wide centered on the stoppingrange stack sector was excluded from the search in order to avoid hits related to the + track.Acceptance losses from both cuts overlap with acceptance losses from the INTIME and INTSEcuts. Therefore, the measurement was made with the K,2 data sample after all photon vetocuts were applied. The events satisfying all cuts in table 5.43 were used.For the muon veto cut, the measurement was done by simply counting the number of eventswith a hit in either layer 19, 20 or 21 of the range stack in the region away from the p+ track.This number was corrected for the fact that 7 sectors out of 24 were excluded from the search.The measured acceptance wasAmuveto = 0.9877 + 0.0025. (5.96)For the range veto, losses occured when accidental hits appeared in layers 13 to 18 in theChapter 5. Data Analysis and Results 206sector with the T• A hit or up to two sectors over from the T A sector in the direction of acurling positively charged particle. For the events remaining after application of the muon vetocut above, layers 13 to 18 of the range stack were scanned for hits in a region three sectors widediametrically opposite to the + track. The measured acceptance wasArgeveto = 0.99848 + 0.00076. (5.97)5.2.2 Ic2 measurements5.2.2.1 1989 Kr2 measurementsFor 1989 data, the only cut whose acceptance was measured with IcZ,,-2 decays selected outof K7r2(1) monitor data was the ICOUNTER cut. The value obtained was AICOUNTER =0.943 + 0.002. Many more measurements were done with J(7,. decays for 1991 data; these aredescribed in the next section. 1991 K2 measurementsK.7,-2 decays have two advantages compared to I(2 decays for the determination of K+-+jJ7 acceptance factors: the charged particle is a pion, and its momentum is reasonably closeto the values allowed in the search for K+ lr+vE7. The drawback is of course the presenceof photons from r0 decay. This can be remedied by requiring that both photons from ir0 decaybe detected in the barrel veto, essentially “puffing” them away from the central region of thedetector. In this way, acceptance measurements can be made using the clean + track.Kir2(1) monitor data were used. This trigger is not as efficient at selecting J.’2 decays as theIEi2(1) trigger is at selecting K,2 decays, primarily because of the large number of K2 decaysthat can stop in range stack layers below 19. However, requiring the presence of two clearlyidentified clusters of energy in the barrel veto consistent with a ir0 from K.7-2 decay selecteda fairly pure sample of K7,-2 events. The TARGET and PROMPT cuts were also applied toimprove the purity of the sample. Table 5.45 shows the results of the selection; a total of 9882K.,,-2 events were selected out of the entire Kir2(1) monitor data sample.Chapter 5. Data Analysis and Results 207Table 5.45: K2 event selection from 1991 Kr2(1) monitor data.Cut # events RejectionKir2(1) monitor events 166726TARGET 163048 1.02256 + 0.00038PROMPT 97428 1.6735 ± 0.0034ii photons in BV 9882 9.859 ± 0.094The sample was then used to determine the acceptance of event reconstruction cuts andsome vertex cuts. Table 5.46 shows the results of the analysis. Note that for the RS-TRACKcut, the 4 MeV minimum requirement in the last counter was not included; it was accountedfor together with the TD cuts acceptance factors.Table 5.46: Acceptance of event reconstruction cuts measured with K2 decaysfor 1991 data. Numbers used in the final K+ ...+ acceptancecalculation are indicated by a check mark.Cut # events Acceptance ]_Used9882DC-SETUP 8573 0.8675 + 0.0034RS-TRACK 8559 0.99837 ± 0.00044ICOUNTER 7948 0.9286 ± 0.0028TRKTIM 7587 0.9546 + 0.0023FIDUCIAL 7158 0.9435 ± 0.0026TGTRACK 4458 0.6228 ± 0.0057TGFIT 4087 0.9168 ± 0.0041VTXPCA 3636 0.8896 + 0.0049The momentum spectrum for K+ * +j,7 events accepted by this experiment is not thesame as that for K2 events. The possibility that a correction was required to take into accountthis momentum dependence was investigated. Use was made of Monte Carlo simulated eventsfor both K+ ....* +j77 and K.2 decays. The ratio of the acceptance of each cut as measuredwith Monte Carlo events for the two types of data should give the appropriate correction. It wasfound that some cuts needed a downward correction while others needed an upward correction.The overall correction was consistent with unity, so this effect was neglected in the acceptanceChapter 5. Data Analysis and Results 208calculation.5.2.3 7r-scat measurementsThe ir-scat trigger is a good source of isolated pions of various momenta emerging from thetarget and stopping in the range stack. With minimal event reconstruction cuts, a relativelypure sample of pions can be selected and then used to determine the acceptance of _*e+ (TD) and kinematic cuts. TD cutsSimple event reconstruction cuts were applied to 7r-scat monitor events to select beam pionsstopping in the range stack. In principle, the combined acceptance of FASFITPI and FITPIcould simply be obtained by taking the ratio of events passed to events analyzed. However,even if kinematic cuts are applied to it-scat data it is very difficult to obtain a pure sampleof stopped + . In many cases the is absorbed in a nuclear interaction at the very end ofits trajectory in the range stack and hence satisfies all kinematic requirements. Losses due tonuclear interactions are taken into account separately; we do not want to include them here aswell.An alternative method, based on the fact that most of the acceptance losses for the FITPIcut are due to early decays of the + , was used to determine the acceptance. The timeresolution of the TDs coupled with the finite rise and decay time of the scintillator pulseslimited the ability to separate the decay muon pulse from the primary + pulse. Therefore,by fitting the late part of the distribution of it+ decay times measured by FITPI, where theacceptance should be very high, and extrapolating the fitted curve to the early time region, theacceptance loss could be estimated. Losses not due to early decays were taken into account byindividually scanning a portion of the failed events and estimating the fraction of events thatshould have been accepted.Both FITPI and FASFITPI were applied to the selected sample of pions. 1 The resulting1Note that here the FITPI cut does not include tighter requirements on , etc.Chapter 5. Data Analysis and Results 209.+ decay time spectra was used to perform the fits. Individual measurements were made forrange stack layers B, C and 11; because of their different thicknesses, it can be expected that theacceptance will differ in each layer. For 1991 data, the acceptance of layer 12 was determinedtogether with layer 11. Figure 5.85 shows the fit results for 1991 data. The depletion of eventsat early times can be clearly seen. The data was fit using a x2 minimization method to thefunction y = Aet/T, where y is the number of counts in a bin, t is the time value of a bin,A is the normalization factor and r is the mean life of the + . The value of A is also theextrapolated number of events for the entire time range. The time range used for the fit wasthe one giving the best x2 per degree of freedom and resulting in a 7r+ mean life consistent withthe accepted value of r,1.+ = 26.030 + 0.024 us [17]. For example, the values obtained for thegraphs in figure 5.85 were 26.83 ± 0.97 ns, 26.4 ± 1.0 ns and 26.1 + 1.1 ns for layers B, C and11—12 respectively. Adding a constant term to the function used for the fit did not improvethe results. To determine the value of A, the fits were one parameter fits with r fixed to theaccepted value.A pre-scaled sample of events failed by FITPI was hand scanned to correct for other losses.Since it is difficult to judge early decays, only events with a decay time of at least one lifetimewere considered; therefore the number observed had to be corrected by e10. The acceptancefor a given layer was expressed asNpAFITpI = (5.98)NE+XNFXewhere Np is the number of events passing the FITPI cut, NE is the extrapolated numberof events based on the fit, NF is the number of events which failed the FITPI cut, NHS isthe number of failed events hand scanned and NFH is the number of hand scanned events thatshould have been accepted by FITPI. Table 5.47 gives the final calculated value of the acceptancefor each layer for 1989 and 1991 data. There are two reasons for the lower acceptance in 1991compared to 1989 : first, the higher beam rate in 1991 caused more mistakes by the fittingprocedure due to random activity in the stopping counter. The effect increases with proximityof the stopping counter to the beam area. And second, the use of logarithmic amplifiers forrange stack layers B and C is likely to have worsened the double pulse resolution.Chapter 5. Data Analysis and Results 210COUNTS = 2226i03 I. I I I ILayer BA = 3276.2 82.52 8 x2/d.o.f. = 0.73D• f2bb6b”8b’1do1,,rr decay time (ns)COUNTS 144710:3 I I I I ILayer CA 1892.1 ± 55.4102 2/d,o.f. = 0.843:..decay time (ns)COUNTS = 1309i03. I.. I .1 I ILayers 11+12 A = 1699.8 50.7102 2/dof = 0.980J1,JII1f,I,,,—20 0 20 40 60 80 100 120decay time (ns)Figure 5.85: Pion decay time distribution used to determine the acceptance of theFITPI and FASFITPI cuts (1991 data).Chapter 5. Data Analysis and Results 211Table 5.47: Acceptance of FITPI and FASFITPI cuts for each range stack layer,calculated according to equation 5.98.Year LayerB C 11+121989 0.764 ± 0.025 0.767 ± 0.025 0.771 + 0.0231991 0.581 ± 0.022 0.667 ± 0.028 0.712 + 0.024Once the FITPI cut had been applied, the purity of the data sample was very high. Therefore, the acceptance of all other TD cuts was determined simply by applying the cuts to the datasample in succession and taking the ratio of events passed over events analyzed. Tables 5.48and 5.49 show the results of the analysis for individual range stack stopping layers and givesthe overall acceptance for all TD cuts except FITPI and FASFITPI.Table 5.48: Acceptance of 1989 TD cuts other than FASFITPI and FITPI foreach range stack layer.Cut LayerB C 11Selected pions 513 302 187Online ir —* t cut 0.793 + 0.018 0.679 ± 0.027 0.850 ± 0.026FITPI (/.T1. ,P ) 0.744 ± 0.022 0.810 + 0.027 0.887 + 0.025ELECTRON 0.739 + 0.025 0.741 + 0.034 0.858 ± 0.029ELVETO 0.978 + 0.010 1.000 ± 0.000 1.000 ± 0.000FITPI (T,) 0.879 ± 0.022 0.860 + 0.031 0.848 + 0.032[ Total 0.375 + 0.021 0.350 ± 0.027 f 0.549 ± 0.036One additional acceptance factor had to be accounted for. There is a finite probability thatthe muon from + decay will leave the counter in which the lr+ came to rest. For a rectangularcounter of length £, width w and thickness t, the probability for a particle traveling a distanced (d < t < w <) to exit the counter is(5.99)where higher order terms were neglected. For the case of range stack counters, the 1/ termcan be neglected. The 1/w term represents the fraction of muons leaving from the side of theChapter 5. Data Analysis and Results 212Table 5.49: Acceptance of 1991 TD cuts other than FASFITPI and FITPI foreach range stack layer.Cut LayerB C 11+12Selected pions 2228 1447 1309Online ir —* t cut 0.6934 ± 0.0098 0.770 + 0.011 0.8732 ± 0.00924 MeV in last RS counter 0.9683 + 0.0044 0.9767 ± 0.0045 0.9904 + 0.0029FITPI x2 0.9044 + 0.0076 0.9237 + 0.0080 0.9037 ± 0.0088TDJvIDA 0.9298 + 0.0069 0.9094 ± 0.0090 0.9883 + 0.0034TDFOOL 0.9594 + 0.0056 0.9617 ± 0.0063 0.9693 + 0.0054ELVETO 0.8956 + 0.0088 0.9135 ± 0.0095 0.9837 + 0.0040ELECTRON 0.765 ± 0.013 0.8082 + 0.014 0.850 ± 0.012Total 0.371 ± 0.010 0.448 ± 0.013 [ 0.626 ± 0.013counter. This is only a loss if the stopping counter is at the boundary between two range stackhextants, since the TDs digitize the signals from a whole hextant and no flag information wasrequired for the muon pulse. Therefore, the muon escape probability is(5.100)The minimum energy deposition required by the FITPI cut for the muon is approximately2 MeV, which translates into a range d = 1.37 mm. Table 5.50 summarizes the calculation ofthe correction for muon escape.Table 5.50: Muon escape correction.Layer t (cm) w (cm) ‘P’(%) CorrectionB 5.85 14.4 1.29 0.9871C 3.90 15.7 1.86 0.981411+12 1.95 17.0 3.61 0.9639The TD acceptance for individual range stack layers is the product of the FASFITPI+FITPIacceptance, the acceptance of all other TD based cuts and the muon escape correction. The finalacceptance was obtained by taking a weighted sum of the acceptance for individual layers. Theweights were obtained from the range stack stopping layer distribution for K+ 71.+z,E7 MonteChapter 5. Data Analysis and Results 213Carlo events. Tables 5.51 and 5.52 summarize the calculation of the overall TD acceptance forthe K+ 7i.+v; analysis.Table 5.51: Overall TD acceptance for 1989 data.Quantity LayerB C 11FASFITPI + FITPI acceptance 0.764 ± 0.025 0.767 ± 0.025 0.771 + 0.023Other TD cuts acceptance 0.375 + 0.021 0.350 + 0.027 0.549 + 0.036Muon escape correction 0.9871 0.9814 0.9639Total acceptance 0.283 + 0.018 0.263 + 0.022 0.408 + 0.029Stopping fraction 0.6798 + 0.0075 0.2561 + 0.0070 0.0641 ± 0.0041Final TD acceptance 0.285 + 0.014Table 5.52: Overall TD acceptance for 1991 data.Quantity LayerB C 11+12FASFITPI + FITPI acceptance 0.581 + 0.022 0.667 + 0.028 0.712 ± 0.024Other TD cuts acceptance 0.371 ± 0.010 0.448 + 0.013 0.626 + 0.013Muon escape correction 0.9871 0.9814 0.9639Total acceptance 0.213 ± 0.010 0.293 ± 0.015 0.430 + 0.017Stopping fraction 0.6381 ± 0.0076 0.3046 ± 0.0073 0.0573 + 0.0037Final TD acceptance 0.2498 ± 0.00855.2.3.2 Kinematic cutsUsing a sample of K-scat monitor data selected with TD cuts, it was straightforward to determine the acceptance of the kinematic cuts by simply counting the number of events passing eachcut. As for the TD cuts acceptance, the measurements were made for individual range stackstopping layers. Tables 5.53 and 5.54 describe the results of the application of the kinematiccuts on the selected samples, and the calculation of the acceptance for 1989 and 1991 datarespectively. As in the case of the TD acceptance, the final result is the weighted sum of theacceptance for each RS layer. The weights were obtained by taking the weights used in the TDChapter 5. Data Analysis and Results 214acceptance calculation and correcting them for the TD acceptance of each layer. This is to takeinto account the fact that the final stopping distribution is different than the one determinedby the Monte Carlo after the application of the TD cuts.Table 5.53: Acceptance of kinematic cuts for 1989 data.Quantity LayerB C 11Events selected 571 334 265RGEMOM 0.9685 ± 0.0073 0.949 + 0.012 0.955 + 0.013DEDXRS 0.9620 + 0.0081 0.946 + 0.013 0.9921 ± 0.0056MASS 0.942 + 0.010 0.967 + 0.010 0.9880 ± 0.0068Acceptance 0.877 + 0.014 0.868 ± 0.018 0.936 ± 0.015Stopping fraction 0.674 + 0.042 0.235 ± 0.021 0.091 + 0.009Final acceptance 0.880 ± 0.043Table 5.54: KINSCORE cut acceptance for 1991 data.Quantity LayerB C 11+12Events selected 2331 1616 1574Pass KINSCORE 1981 1339 1315Acceptance 0.8498 ± 0.0074 0.8286 ± 0.0094 0.8354 + 0.0093Stopping fraction 0.543 + 0.026 0.351 ± 0.020 0.106 ± 0.008[ Final acceptance 0.841 ± 0.0295.2.4 Monte Carlo measurementsThe geometrical and phase space acceptance, as well as the acceptance loss due to nuclearinteractions and decay-in-flight of the + were determined with a Monte Carlo simulation. Thefirst two factors were determined by simulating K+ ..+ +j/j7 decays without decay and+ nuclear interactions. A comparison of this simulation with another in which -+ decay andnuclear interactions were turned on allowed the determination of the acceptance loss from thelatter two effects. In both cases the 7rvE trigger was simulated and the offline analysis appliedChapter 5. Data Analysis and Results 215to the events satisfying the trigger cuts. Table B.75 shows the results for both simulations for1991 data; similar numbers were obtained for 1989 data. Differences between the two weredue to the different K+ decay vertex distribution in the target and the different momentumresolution for the two years.Table 5.55 summarizes the acceptance factors obtained from Monte Carlo simulation. Thegeometrical acceptance (Ageom) is simply the fraction of events passing the T. A requirementfor the sample simulated without + nuclear interactions and + decay. The phase spaceacceptance (Ah.p.) is the product of several factors : the acceptance of the BCT and rangeveto (Argeveto) trigger requirements (see section 3.1.1), and the acceptance of the KINCUT cut(total energy, range and momentum):= ABCT X Argeveto X AKINCUT (5.101)The acceptance factor taking into account losses from + decay and nuclear interactionsis simply the ratio of the combined trigger and analysis acceptance for the simulations with andwithout t+ decay and nuclear interactions.Table 5.55: Acceptance factors determined with Monte Carlo simulation.Factor Year1989 1991Ageom 0.4199 + 0.0018 0.4086 ± 0.00220.3008 ± 0.0035 0.3003 + 0.00380.721 ± 0.018 0.706 + 0.0175.2.5 Final AcceptanceTables 5.57 and 5.56 list all the acceptance factors used in calculating the overall K+ *+jjj7 acceptance for 1989 and 1991 data respectively. All errors quoted in the tables arestatistical only. The final values for the overall acceptance areA, = (2.57 ± 0.20) x i0 (5.102)= (1.77 ± 0.11) x i0. (5.103)CzC) Tj CCD S IIz C)Ci) zCD S C)HCrJ Tjz H-4 z H0 CD -4 -4 0I-0 H0 -4 0 CD -4 0Cl) C)-4 C) C HCl) H C)C) I:Tj H0 CD -4 0cj CD CDC) CD C S CD -4 -iCD -4 CD 0 -4 -4 0CD CD -4 -4 C) CD -4 -4 C. -4CD CD 0 C CD CDCD CDCD CD C) CD -4 0C) I-4 CD C) -4 0 CD CCD 0’01 C) + + C CD Ibz,zC)C)C)-4+0C)C)C)CCC&CCCCCCCCCCCCCCCCPP-EoccPPPboPPPCCP-ccPP-401CC-CCCC-4C01CCCCCC0)Cl’-40)0)-4C010)CCC)Cri-01Cl’X(XI—0)1>3C)C)1>31>30)C)C-401CCC)01CCCCCCC0)CC41>3C—4CCl’C)C)CCC)CC—10)>30)sD1>31>30’CCCCCCD+H-H-++H-H-+H-H-H-H-+++H-++++H-H-H-+++H-++++SCCCCCCCCCCCCCCCCCCCCCCCPCPPCCPP><CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCI—CCCCCCCCCCCCCCCCCCCC—CCC)0)C0)Cl’-—4C)C)1>3CC0)0)CL>30)00)C.)Cdl’CCCCC)1>3C.)00CCCl’CC-4CCCCC)1>31>34Cl’00C!ø-4010)C)C) HC) CCH rj HCD S C,)H C)ICID C) 0— z H Cl)z HC,) CD CD C,)00 ... CD 00 0 CD 0C)C) 0 HCl) H C)HC, C CD0 CD CCD CD CC)CD CD 0 Cl) ...0CD C CDCC CD CC C, CD2- CD C, C CD C, CDCD C, CD CICD 0 S CD Cl) CD Cl) CD I.CD C, I-IC Cl) + CDCD ± 1 + C, C, CD C, CD 1+ C- CD CD CD Cl) Cl))l.Z)L)3ppl.Zb3lZtZ3.)))C)C)C)+--0 DI.C)C)C)C)C).C).C)C)C)C)C)C)C)C)C)C)C)C)C)C)•C).C)C).C)C).C)C).CD..............CD.CD..CD..CD-1CDCDCDCD00CDC)•CD0000C)00CDCDCDCD0000CDCDCD00CDCD.C)-CD0000:•t’Z00C)00©-0000C)C)C’:00CD-C)C)ri-00C)—CDC)CDCDCC00C—IC00C)I—CCCC)C)0000i•—a)C)0000I00—CDCDCDCC?’C)-IC?’—1-cj00——CD—+H-++H-H-+H-H-H-H-H-H-++H-H-H-H-H-H-H-H-H-H-H-H-H-H-I—©C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C),XC)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)I•C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)C)I.C)C)I.C?)C)It)4C?’CD00C?)C)C?iC?’‘.)C)C?)C)IC)C?)C)-IC)C)C?’00C)C)CDI—aC?’CDt)IC)-C?’C)004C?’-aC?’00C)C?’CD-I00C!)CD00CDC)--aChapter 5. Data Analysis and Results 2185.2.5.1 Scalar and tensor interactionsThe acceptance for non-Standard Model 11+ .+a7 mediated by scalar or tensor interactionswas obtained using a Monte Carlo simulation. Events with the appropriate kinematic distribution were generated; the riii7 trigger was simulated and offline analysis cuts were applied.The first order acceptance relative to A was obtained for each process by taking the ratio ofthe number of surviving events to the number of surviving events from an identical simulationin which the kinematic distribution was based on the Standard Model (V-A). The number ofevents was normalized to the number of stopped K+ in each simulation.This acceptance had to be corrected for the fact that the + stopping layer distributionin the range stack is different for each process. The distribution can have a significant effecton the TD acceptance (see section The correction was calculated for each process for1989 and 1991 data; it typically reduced the acceptance by a few percent. Table 5.58 gives thefinal calculated acceptances.Table 5.58: Final calculated acceptance for K+ ÷ via scalar and tensorinteractions.Interaction Year1989 1991Scalar (1.95 ± 0.15) x iO (1.299 + 0.081) x i0Tensor (3.14 + 0.24) x iO (2.11 ± 0.13) x iO5.2.5.2 K .‘The acceptance for J(+ K+XO was calculated in the same manner as scalar and tensorinteraction K+ ‘, , but had to be calculated as a function of Mxo, the mass of therecoiling system. In this case, the effect of the + stopping distribution in the range stack wasmore significant, as much 25%, and increased or decreased the acceptance, depending on Mxo.The acceptance was calculated assuming that the particles (or system of particles) representedby X° are stable. Figure 5.86 shows the total acceptance for 1989 data in the range where it issignificant, 150 < Mxo <260 MeV/c2. A similar curve was obtained for 1991 data.Chapter 5. Data Analysis and Results 2191 — I i Ici)C)C0-I-..0C)00iü- -140 280Figure 5.86: Acceptance for K+ +XO as a function of Mxo (1989 data).5.3 Integrated kaon fluxThe other important ingredient needed to determine a branching ratio is the total number ofK+ observed by the detector. In principle, this number would simply be the total number ofcounts accumulated for the KT trigger requirement, which defines the presence of a K+ in thedetector. This sum should only be accumulated when the data acquisition system was “live”and not busy analyzing or transferring to tape the digital information from an event satisfyingtrigger conditions.However, there are several ways in which an incoming K+ can satisfy all KT trigger requirements without decaying at rest in the target. The K+ could interact or decay in flight inthe degrader and its products pass through the B4 counter and the target. The K+ could alsoscatter in the target and decay elsewhere in the detector. These types of events should not becounted, since what we want is the total number of K+ which decayed at rest in the target.Hence, a correction factor must be determined to take into account the incoming K+ which donot stop and decay in the target.To determine this important correction, use was made of the Ki2(1) monitor data, outof which can be selected Jt’2 events with relatively few offhine requirements. If we wanted to160 180 200 220 240 260M. (MeV/c)Chapter 5. Data Analysis and Results 220measure the K2 branching ratio with such an analysis, we would use the following expression:BK,2= (5.104)fs NKT AK2where N is the number of events satisfying all the analysis criteria, NKT is the total KTcount, f3 is the fraction of counts in NKT which are stopped kaons in the target, and AK2 isthe combined acceptance of online and offline cuts for K2 events. If we can measure the latter,we see that by using the known value of BK2, the value of the correction f3 can be determinedeasily.The acceptance AK2 was determined with a Monte Carlo simulation, and was correctedfor various effects due to experimental conditions; it was therefore expressed asAK2 = AMC X Acor. (5.105)Results of the analysis of Kt2(1) monitor data and Kt2(1) simulated events for 1989 and 1991are given in tables B.76 and B.77 respectively. Event reconstruction cuts were applied, as wellas a cut on the total j range (43 < R0 < 61 cm) for 1989 data and on the total ,+ rangeand momentum (46 < R0 < 61 cm , 215 < P0 < 255 MeV/c) for 1991 data. For real data,the online and offline delayed coincidence cuts were also applied, as well as the CERENKOVcut. A total of 13801 and 27531 events remained after analysis of real data, for 1989 and1991 data respectively. For the Monte Carlo simulation, there were a total of 47924 and 28529stopped kaons for 1989 and 1991 data, respectively, before application of the simulated triggerrequirements. Therefore, the uncorrected acceptance wasAjc 0.3152 + 0.0021 (5.106)A}c = = 0.3196 + 0.0028. (5.107)The acceptance correction for the 1991 analysis was expressed asAD AD AD AD AD ADA — AD rITG AD ‘DC ‘RS IG TRK FID ADIlcor— LODe1c X X ‘De1c X 4P X X X AM X AM XTG DC RS IC TRK FIDwhere the superscripts D and M refer to real data and Monte Carlo events acceptance respectively, and the subscripts refer to the different cuts. A similar expression was used for theChapter 5. Data Analysis and Results 2211989 analysis. The values of the various acceptance factors used to compute the acceptancecorrection for 1989 and 1991 data are given in tables B.78 and B.79. Table 5.59 summarizesthe calculation of the f8 factor for both 1989 and 1991 data. Use was made of equations 5.104and 5.105, as well as the accepted value of BK2 = 0.6351 ± 0.0019 [17].Table 5.59: Calculation of f for 1989 and 1991 data. Refer to equations 5.104and 5.105 and the text for a description of the terms in the table.Quantity 1989 1991N 13801 ± 117 27531 ± 166NKT 220357 367963AMC 0.3152 + 0.0021 0.3196 + 0.0028Acor 0.4962 + 0.0058 0.5740 + 0.0042f8 [ 0.630 + 0.010 [ 0.6422 ± 0.00855.4 K branching ratio measurementAs a partial check of the acceptance calculations and integrated kaon flux measurement, ameasurement of the K2 branching ratio was made using I(ir2(1) monitor data. A minimal setof cuts was applied in order to select K2 events : event reconstruction cuts, delayed coincidence,TD cuts, and the CERENKOV beam cut to eliminate any residual beam pion contamination.The branching ratio was obtained using the formulaBK1r2= N (5.109)f3 NKT AK2where N is the number of events satisfying all analysis requirements and AK2 is the acceptanceof the online and offline cuts for K2 decays. The other factors in the equation were defined inthe previous section. The acceptance was again determined by a combination of Monte Carlosimulation and corrections taking into account experimental conditions; it was defined asAK2 = AMU X Acor. (5.110)For the analysis of both real and simulated data, event reconstruction cuts were applied, aswell as a cut on the total 7r+ range. For real data, the online and offline delayed coincidenceChapter 5. Data Analysis and Results 222cuts were also applied, as well as the CERENKOV cut and TD cuts. Furthermore, for both1991 real and Monte Carlo data, the RS-TRACK cut included a restriction on the range stackstopping layer to 3 < Stop lay. < 6. This explains the smaller acceptance for ‘(2 decays ofthe 1991 analysis.Tables B.80 and B.81 give detailed analysis results for 1989 and 1991 datarespectively.For the Monte Carlo simulated data, there were a total of 28586 and 14535 events satisfyingthe KT (stopped K ) requirement for 1989 and 1991 data respectively. This resulted inuncorrected acceptances ofAc = = 0.1766 ± 0.0032 (5.111)= = 0.1434 + 0.0021. (5.112)The acceptance correction was analogous to the one used in the calculation of f3 (see equation 5.108). For the TD acceptance, the calculation of section was re-done to takeinto account the different stopping layer distribution of the rF from K2 decays compared to-+j,7 decays. The values obtained for the corrections were:Ar = 0.265 + 0.013 (5.113)Ar = 0.312 ± 0.010. (5.114)Table 5.60 summarizes the calculation of the I(,-2 branching ratio for 1989 and 1991 databased on equations 5.109 and 5.110. The errors given are statistical only. Both measurementsare consistent with the accepted value of 0.2117 + 0.0016 [17]. This result gives some confidencein the simulation of the detector geometric acceptance and of + nuclear interactions, as wellas in the measurement of the acceptance of TD, delayed coincidence and event reconstructioncuts.Chapter 5. Data Analysis and Results 223Table 5.60: Calculation of ‘(,,2 branching ratio for 1989 and 1991 data. Refer toequations 5.109 and 5.110 and the text for a description of the termsin the table.Quantity 1989 1991N 1748 ± 42 6830 ± 83NKT 282057 1103889AMC 0.1766 + 0.0032 0.1434 + 0.0021Acor 0.265 ± 0.013 0.312 + 0.010f5 0.630 + 0.010 0.6422 + 0.0085K2 branching ratio 0.210 ± 0.012 0.2153 + 0.00855.5 Final results5.5.1 J(Using the calculated values of the acceptance and the total integrated kaon flux, the branchingratio can be calculated. It is expressed asNBK+.+ = f TT A (5.115)is IVKT irvi7where N,j is the number of events selected by the analysis, NKT is the total KT count, f5 is thefraction of counts in NKT which are stopped kaons that decayed in the target (see section 5.3)and is the combined acceptance of the trigger and analysis for j+ ,S .+j47 events (seesection 5.2). The inverse of the product of f5, NKT and A is defined as the sensitivity (orsingle event sensitivity).The observation of the number of events satisfying all analysis criteria is a Poisson statisticalprocess. After the analysis of the 1989 data, no event was found. For 1991 data, the uncertaintyin the background estimates precluded the assignment of the 4 events observed asdecays. Hence, an upper limit on the number of K+ j.+j/i events was set based onthe observed number for both data sets. The Poisson probability distribution is defined asf(n,)= ‘ n=0,1,2,... (5.116)n!with n the observed number of events and i the mean of the distribution. We are looking forthe mean N such that the probability is at least 1 — a (confidence level) that the outcome ofChapter 5. Data Analysis and Results 224another similar experiment will yield a number of events greater than the number observed,defined as n0. Therefore,1 — a = f(n, N) (5.117)n=no+1or equivalentlya = f(n,N). (5.118)For a 90% confidence level upper limit (or a = 10%) and n0 = 0, the solution is N = 2.3; forn0 = 4 the solution is N = 7.99.The error on the result of each analysis is dominated by statistical fluctuations. However,the overall error on the sensitivity should be included in the result. The relative statisticalerror is 6—8% for the overall acceptance and only about 1.5% for f3. The measured value ofthe K2 branching ratio agreed with the accepted value within the statistical error for bothanalyses; however, this is not in itself proof that the systematic error is small. Because ofuncertainties in the K+ stopping distribution and the simulation of nuclear interactions, it isbelieved that a conservative figure of 10% for the systematic error is more appropriate. A formalway of incorporating the systematic error in an upper limit can be found in the literature [81].The upper limit is then given byN’ = N{1 + [1 — — o(N — no)2]/N} (5.119)where N and n0 are as defined above and is the relative error on the sensitivity.The branching ratio upper limit for the process K+ +7 can then be calculated according to the formulaB(K+,‘ +) < f3 Nj< A (5.120)Table 5.61 summarizes the calculation of the 90% confidence level upper limit for each of thetwo analyses. The result from 1989 data has already been published [37], and is a factor of 55improvement over the previous published result using the same kinematic region [34].Chapter 5. Data Analysis and Results 225Table 5.61: Calculation of K+ ... +7 branching ratio 90% confidence levelupper limit for 1989 and 1991 data, based on equation 5.120. Referto the text for a description of the items in the table.Item 1989 1991no 0 4os 0.1 0.1N’ 2.33 8.16f3 0.630 + 0.010 0.6422 ± 0.0085NKT 8.6648 x 1010 14.3613 X 1010(2.57 ± 0.20) x i0 (1.77 + 0.11) x i0B(I( upper limit 1.7 x 108 5.0 x 10 ]5.5.2 Scalar and tensor interactionsTable 5.62 gives the 90% confidence level upper limits from 1989 and 1991 data calculated usingthe acceptance given in table 5.58. The 1989 results represent an improvement of a factor ofapproximately 50 over the previous published results [34].Table 5.62: Branching ratio upper limit (90% C.L.) for K —* .+jJ via scalarand tensor interactions.Interaction Year1989 1991Scalar 2.2 x 10—8 6.8 x 108Tensor 1.4 x 10—8 4.2 x 10—85.5.3 K ‘Figure 5.87 shows the 90% C.L. upper limit on the branching ratio for J(+ iI.+XO , asa function of Mxo. Also shown is the previous published result covering the same region ofMo. This limit assumes that X0 is a stable weakly interacting massive particle, or system ofparticles.Chapter 5. Data Analysis and Results 226—IlIllil,, IiIIIII,IIIIIIIIIIIIIIIII -tlo-6140 160 180 200 220 240 260 280M. (MeV/c)Figure 5.87: Branching ratio upper limit (90% C.L.) for 11+ irX° as a function of Mxo, the mass of the recoiling system. The fuli and dashedcurves are from 1989 and 1991 data respectively. The dotted curveshows the previous published limit coveriug this range of Mxo [38].Chapter 6DiscussionThe single event sensitivity to K+ lr.+z,E of the 1989 analysis was 7.3 x i0 and no eventswere observed, whereas for the 1991 analysis the sensitivity was 6.2 x i0 with 4 eventsobserved. There is an obvious mismatch between the results. The first thing to understand isthe origin of the events observed in 1991 data. This leads to a re-examination of the backgroundestimates, and to further studies of the data. Furthermore, the analysis method used for thetwo data samples has to be compared in assessing the consistency between the results.6.1 Origin of the observed 1991 eventsThe events remaining after all cuts were applied to the 1991 data sample are certainly notfrom Standard Model J(+ +j7 decay, considering the expected range for the branchingratio based on current information about Vtd (see figure 1.8). An analysis of 1989—1991 datain the kinematic region above the ‘-2 peak set a 90% C.L. upper limit of 3.7 x iO for thebranching ratio for J(+ 7I.+7 [30], lending further credence to the theoretical estimate. Onepossibility is that the observed events are from a non-Standard Model source. As was discussedin section 1.2.10, some theories predict an enhancement in K+ ,S + nothing for the kinematicregion below the KR-2 peak, but there are no firm predictions. This is not reason enough toeliminate the possibility that new physics is responsible for the observed events. However,the potentially large systematic uncertainties in the background estimates do not allow us tosupport or rule out the new physics hypothesis.227Chapter 6. Discussion 228If the remaining events are background, we have to identify the sources (or source) responsible and why the a priori studies underestimated the contribution. Muon and beam pionbackground are the least likely candidates. The studies for these background sources made useof real data and no large correlation between cuts was observed. Background sources that wereestimated using Monte Carlo techniques are always suspect, considering that subtle effects notsimulated can become significant at the 10—8 level. For I.(e4 , the kinematic distribution of the+ for the simulated events satisfying all cuts, shown in figure 4.76, is significantly differentfrom the one for the final events from real data (figure 5.84). The Ke4 background events are located in the lowest part of the K+ * +)j7 kinematic search region, contrary to the final eventsobserved. Hence, it is unlikely that the Ke4 background contribution was underestimated.As stated in the description of the background studies, K+ charge exchange simulationis inherently poor due to the lack of detailed knowledge of the processes involved. This isparticularly true of charge exchange followed by hyperon production. However, the signature ofthese background processes is fairly clear; it should be possible to enhance those characteristicsat some level in real data and identify events of this type. All such attempts failed, indicatingthat the estimates cannot be grossly underestimated, and perhaps were rather overestimated.The validity of the background estimate for radiative ‘(-2 decays hinges on the differencebetween the distribution of photons from ir0 decays for Jt.2 compared to K-2 and on thedetection of the extra photon. In section 4.2.2, it was shown that the energy and directiondistribution of photons from ir0 decays in I2-y is very similar to the one from K2 decaysbefore the application of any photon veto cuts. It is conceivable that subtle differences in thedistributions not visible at that level become significant once photon veto cuts are applied. Thismay in turn affect the distribution of the radiated photons, resulting in a rejection lower thancalculated. However, this effect would have to be some two orders of magnitude to push theestimate of 0.024 + 0.004 events up to a number of events comparable to the total observedafter all cuts; this is not very likely.This leaves K2 background as the most probable background origin for the observed events.Chapter 6. Discussion 229In the following sections the estimates given in section 4.2.1 are re-examined and further investigations are described.6.2 I(2 backgroundThe 1991 K-2 background estimate that was considered most trustworthy was from the so-calledMethod 2, even though it suffered from low statistics. The method relied on the hypothesis thatthe K.2 background is dominated by events in which the + undergoes a nuclear interaction inthe target. There is no doubt that such events do occur. However, if a significant portion of thistype of background cannot be detected by either the TGFIT or VTX_PCA cuts, the estimateis not valid. Figure 6.88 shows the 90% C.L. upper limit on the number of background eventsas a function of the rejection of TGFIT, calculated according to equation 5.94. The rejectionof TGFIT was estimated to be 2.02 + 0.18 using a sample of events failing the VTX.YCAcut. Looking at table 5.36, we see that the rejection of TGFIT for the final data sample was1.50±0.20, lower than estimated. This would place the upper limit for the number of backgroundevents at 2.6 events, which still does not explain the four observed events. The rejection is ofcourse a function of the sample used to measure it. For example, if TGFIT is applied as thevery last cut for irvi events in the J(+ +,JE7 signal region, it rejects no events at all. Thisindicates some level of correlation between TGFIT and the other cuts applied at Pass3 andPass4, and makes the estimate even more uncertain. Because TGFIT and VTXYCA wereboth inverted to select data samples used in this background estimate, their combined effectshould encompass most of the K2 background for the estimate to be reliable. In the end, itappears that these cuts did not have sufficient rejection to provide this.The estimate from Method 1 was not trusted because of the large correlation observedbetween photon veto cuts and cuts designed to reject + tracks with nuclear interactions inthe target. Because the number of events predicted by that estimate is reasonably close to theobserved number, it is tempting to consider it as correct after all. The value of the ‘cZ,r2 peak/tailratio (ii) was determined using a sample of events failing the full photon veto cuts (after Pass 1).Measuring with a sample of events with no photon veto cuts other than the online cuts gaveChapter 6. Discussion 23015-J(-). 10Eci)00ci)>ci)0Figure 6.88: Upper limit on the number of 1991 K2 background events as afunction of the TGFIT cut rejection. The upper limit is calculatedaccording to equation 5.94.a similar value. It was unclear whether or not i would remain the same after all photon vetocuts were applied. Based on the numbers in section, the value of i after all cuts is= 30 ± 15, which has a large statistical error but is nonetheless consistent with 30.8 + 3.5, thevalue used to estimate the expected background.As a test of this estimation method, 1989 data was re-analyzed to select events which failthe photon veto cuts. All cuts were applied except the photon veto cuts beyond Passl. Notethat the photon veto cuts applied at Passl in the 1989 data analysis were considerably tighterthan for the 1991 data Passl. For 1989 data, cuts were applied with an energy threshold of1.0 MeV in the RS, BV, EC, IC and VC, while for 1991 the energy threshold was 2.0 MeV forthe RS and BV and 5.0 MeV for the EC; no photon veto cuts were applied on the IC and VC.The number of 1989 data events failing the photon veto cuts beyond Passl in the peak and tailwere 85 and 17 respectively, for a ratio = 5.0 + 1.3. There were 49 events left in the It’,-2 peakafter all cuts. If we use these numbers, the prediction for the number of background events inthe 1989 analysis isNbgd= 5M+L3 = 9.8 ± 2.92.0TCFIT Rejection(6.121)Chapter 6. Discussion 231No events were observed in the 1989 analysis after all cuts, about an order of magnitude lessthan this prediction, which is obviously wrong. This simply shows that the strong correlationbetween photon veto cuts and the number of events in the K2 peak and tail regions makesthis method unreliable. This casts serious doubt on the validity of the 1991 prediction, eventhough it is close to the final number. The agreement may just have been fortuitous.The value of i measured for 1989 data is significantly worse than all numbers measured for1991 data. One difference noted above is the level of photon veto. To attempt a more accuratecomparison, the 1991 data sample failing the full photon veto cuts was re-analyzed to bring itto a level similar to 1989. Photon veto cuts were applied at an energy threshold of 1.0 MeVon the RS, BV, EC, IC and VC using the final coincidence time windows. For the RS andBy, the late edge of these windows is significantly later than the windows used for 1989 Passi;the windows are comparable for the EC, IC and VC. With these additional constraints, therewere 267 events in the K7.2 peak and 7 in the tail, compared to 2191 and 71 previously (seetable 4.19). To compare to the 1989 sample, these numbers have to be corrected for the factthat in 1989 tracks ending in range stack layer 12 were not accepted. The 1991 numbersfor the sum of range stack layers B, C and 11 were 177 and 7 in the peak and tail regionrespectively, for a ratio = 26.3 ± 9.7. This is still significantly better than the value measuredfor 1989 data. One very likely reason for this difference is the addition of the lead-glass degraderand the use of TD cuts in the target; these two cuts clearly reject more events in the tail regionthan in the peak, thereby improving the ratio. The more troubling part is that even though again was made in background rejection by using these cuts, the level of background appears tobe higher in 1991 than it was in 1989. Some other effect (or effects) must be responsible forthe increased background level.6.3 K7r2 peak kinematicsIt was observed in the search for K+ ..+ 7I.+7 in the kinematic region above the K2 peak [30]that the position and width of the Jc-2 peak in total range, energy and momentum was differentafter all cuts than what could be expected based on the background samples. Such an effectChapter 6. Discussion 232was looked for in this analysis. Table 6.63 gives the mean and sigma of Gaussian fits of the7r+ range, energy and momentum distributions for various data samples. There is no significantdifference between them, implying that the events observed in the K+ _* +l)77 search regionafter application of all cuts are are not the result of a systematic shift or broadening of theK2 peak. This result might have been expected by simply looking at the kinematic distributionof the remaining events, and noticing that they are well within the search region. Some physicalprocess must be responsible for their presence in the K+ lr+i’E7 search region, rather thanan instrumental systematic effect.Table 6.63: K2 peak position and width for various data samples. The meanand sigma are from Gaussian fits with a flat background component.Sample ] Quantity Range (cm) Energy (MeV) Momentum (MeV/c)No 5 Mean 29.78 ± 0.05 106.00 ± 0.16 204.36 ± 0.18(553 events) Sigma 1.06 + 0.04 4.06 ± 0.15 3.92 + 0.16Fail Pass3 7 Mean 29.50 + 0.04 105.47 + 0.12 203.90 + 0.13(2191 events) Sigma 1.27 ± 0.04 4.20 ± 0.10 4.07 ± 0.11Pass3 Mean 29.56 ± 0.07 105.87 ± 0.25 203.78 + 0.34(159 events) Sigma 1.09 + 0.06 4.29 ± 0.23 4.25 + 0.316.4 Photon VetoOne possibility for the increased level of background in 1991 data compared to 1989 is that thephoton veto system did not perform as well. A good indicator of the photon veto performanceis the number of events remaining after all cuts in the J(,2 peak kinematic region. No particulareffort is made in the preparation of the analysis cuts to reject the events in that region, since itis known that they will be rejected by the final kinematic cut. They are therefore an unbiasedindicator of the photon rejection. It is important to note however that these events do not givean absolute measurement of the photon rejection for I(2 background events for which the isin the K+ * .+jjU kinematic search region. The distribution of photon direction and energyfor the latter could be significantly different than for events in the J2 peak region, affectingthe photon veto performance. This study is a simple way of diagnosing a possible degradationChapter 6. Discussion 233of the performance of the photon veto system.For 1989 data, there were 49 events remaining in the I,i-2 peak after all cuts. To compareto this, the number of events observed in 1991 had to be corrected for the fact that range stacklayer 12 stops were accepted by the rvE1 trigger; only the events in range stack layers B, Cand 11 should be counted for comparison. Table 6.64 shows the number of events observed inthe K2 peak region for 1991 data for several different conditions. Also given for each case isthe number of peak events in the 1989 analysis corrected for the differences in acceptance andintegrated kaon flux, and the ratio of the numbers for 1991 and 1989 analysis.In table 6.64, the ““ indicates that the TGFIT and PB-GLASS cuts were not used; thesecuts were not available for use in 1989. The final row in the table refers to the analysis ofirzñ data without the use of online or offline photon veto cuts. These numbers provide thereference to which other numbers are compared. For 1989 data, use was made of a specialdata set taken with a modified 7rv17 trigger in which the online photon veto cuts had beenremoved. After full analysis, a total of 2437 events were observed in the IZ72 peak region,with a KT sum of 1.106 x For 1991, the K7r2(1) monitor data sample was used; theiri47 trigger requirements were applied offline based on the recorded trigger information, exceptfor the photon veto cuts. All offline analysis cuts were applied except direct photon veto cuts(INTIME, INTSE and PB-GLASS). A total of 553 events remained in the K1.2 peak region, ofwhich 292 stopped in range stack layers B, C and 11. The KT sum, corrected for the onlinepre-scale, was 1.104 x 106.The only entry in table 6.64 not consistent within one standard deviation with the casewhere no photon veto was applied (last row) is the case where the PB-GLASS and TGFITcuts were removed from the Pass3 analysis (first row). It should also be noted that the resultwithout any photon veto shows an excess of events in 1991, about 25% more. Some of thisdiscrepancy may due to the fact that in 1991, cuts were not applied on the energy depositionpattern of the in the range stack. Such cuts would reject events in which a low energyphoton converted on top of the + track. However, examination of the kinematic spectrum ofthe 553 events remaining after the analysis performed without direct photon veto cuts showsChapter 6. Discussion 234that this effect is likely to be small. The effect is only enhanced after photon veto cuts areapplied. As can be seen in figure 5.84, about 10% of the 1991 events remaining in the K,.2 peakafter Pass4 fall into that category.It is difficult to attribute the excess of K2 peak events in the 1991 analysis without directphoton veto cuts to one cut or group of cuts in particular. This effect may be partly responsiblefor the larger background level in 1991. However, the study described in this section shows thatthe 1991 Pass4 set of cuts provides as much photon rejection for I(i2 peak events as the 1989analysis.Table 6.64: Number of events in peak region for 1991 data for various conditions. The number only includes stops in range stack layers B, C and11. The “89 equivalent” number comes from the number of eventsobserved in 1989 corrected for differences with the 1991 analysis inacceptance and integrated kaon flux.Conditions Peak events 89 equivalent 91/89 ratioPass3* 155 87 ± 0.15 1.79 ± 0.33Pass3 101 70 ± 12 1.44 ± 0.28Pass4* 109 72 + 12 1.51 ± 0.29Pass4 72 58.3 ± 9.9 1.23 ± 0.25No7 292 237± 22 1.23±0.136.5 Other cutsBecause the likelihood was low that muons and beam pion backgrounds were responsible for theobserved events in 1991, only photon veto and target vertex cuts offered potential for increasedbackground rejection. These cuts were therefore examined with more scrutiny. For photon vetocuts, tighter versions of INTIME and INTSE were described in section The PB-GLASSand B4TD cuts could not be tightened further. For target vertex cuts, one of the parametersof TGTRACK was tightened, as described in section The rejection of the TGFITcut could not be improved beyond simple acceptance loss. Based on the available backgroundsamples, tightening VTX_PCA did not improve the rejection by the nominal factor of two aboveI I I I I I I I I I ii’ I—1 0 1 2 3 —3 —2 —1 0 1 2Component 1 Component 1VTXYCA components for events passing the cut for a) backgroundsample (crosses), events satisfying only Pass3 requirements (triangles) and events satisfying all Pass4 requirements (circles) and b)K2 events (density distribution). The dashed lines indicate the cutposition.Figure 6.89 a) shows the distribution for the background sample (crosses) and the sevenevents remaining after Pass3; the four events passing all Pass4 cuts are shown as circles whileevents rejected by Pass4 are shown as triangles. Figure 6.89 b) shows the density distributionfor K,.42 events. irvi events satisfying the Pass3 requirements tend to be towards the edge ofChapter 6. Discussion 235acceptance loss.One important point that was made in the section on background studies is that the background samples used in designing the cuts must be representative of the background studied forthose cuts to be effective. For VTX_PCA, the background sample used to set the cut positionwas a sample of events failing the photon veto cuts beyond Pass 1 and with range, energy andmomentum in the K+ ,. +7 signal region. Figure 6.89 shows scatterplots of the two normalized components of the VTXY CA principal component analysis for the events satisfyingthe cut. Remember that events for which the measured “kaon” energy in the target is in excessof what was expected based on the range of the K+ in the target or the energy deposited bythe K+ in the B4 counter tend to have negative values for component 2.3. lillIll 1111111111 Iiiiilii ii — 3 111111 11111111 IllIllillI III —c’J00.E0C-)2-1—0-—1 -—2 -—3+++ ++ ++++. +++ +4.++•++*++1+ + + ++4 + +IS,. +•:• + +•. --•..I;a)- 2-— 1—c.’JIZII)- 0-00— —1 —- —2-,on,o,DaDoQ@o VrIDDDDDDDDflUUDDODVVDDDOD77. • .7• 0 .1•‘...000a00000..a• •1b)—3 —2Figure 6.89:3Chapter 6. Discussion 236the accepted region, whereas it is clear that the background sample has a distribution similarto K,2 events. None of the seven Pass3 events appear near the center of the distribution, theregion most densely populated by I(2 events. It is therefore quite possible that this cut wasnot optimized to obtain the best possible background rejection because the background sampleused was not adequate.A review of all available variables for the seven events remaining after Pass3 showed thatthe cut parameters of all cuts other than photon veto and target vertex cuts were properlyset. A pile-up of events near the edge of a cut position would have been a clear signature for aparticular background; no such effect was observed.6.6 Analysis methodThe observation that the background sample used to set the cut position for VTX_PCA may nothave been the ideal sample to work with brings up the more general question of the effectivenessof the analysis method used for 1991 data. The entire approach was based on the realization thatthe standard analysis method, used for 1989 data, had problems. Designing cuts by examiningdistributions of various quantities extracted from the residual events at each step could lead toa biased result, particularly if the data sample used was small. This was not the ideal way tosearch for a small potential signal. The approach used for 1991 data removes concern aboutbias. It works well as long as the background data samples used allow the cuts to be set at ornear their optimum effectiveness.If the background level to contend with is relatively high, small fluctuations in the cuts mayhave significant effects on the final result. Of the 4 events remaining in the K+ lr+v17 searchregion after 1991 Pass4, it is quite likely that a few and perhaps even all of them would havebeen rejected if the cuts had been set using data samples which included the candidate events,as demonstrated in the previous section. The standard analysis method allows for a betteradjustment of the cuts to the real background than the new method, unless the backgroundlevel is intrinsically low and small variations in the cuts are not important. For the search for_* .+z,j7 below the K,,-2 peak, this is not the case; the detector was pushed to its limit inChapter 6. Discussion 237terms of background rejection.This is not an indictment of the philosophy of the analysis method used for 1991 data. Itwas extremely important to develop the techniques necessary for such an analysis and uncoverits weak points to make further improvements. Two main weaknesses were identified1. If the intrinsic level of background is high, the choice of background samples representative of the true background is crucial in order to set the cuts appropriately2. Systematic uncertainties in the background studies must be kept as small as possible inorder to identify an unexpected signal. The corollary to this is that the correlation between cuts used to study background processes must be kept to a minimum.6.7 Consistency between 1989 and 1991 resultsThere are two extreme scenarios explaining the mismatch between the results from the twodata samples1. The 1989 result is entirely correct and the events observed in 1991 are from backgroundsources. The background rejection in 1991 was poorer either because of a degradation ofthe performance of the detector or because the analysis method did not allow the cuts tobe optimized.2. The 1991 result is correct, and analysis bias is responsible for the elimination of all theexpected events in 1989.The true explanation is likely to be a combination of the above two cases. It is certainlypossible that one or two events should have been observed after analysis of the 1989 data,either because of analysis bias or statistical fluctuation. The dominant KJT-2 background wasestimated using a combination of real data analysis and Monte Carlo simulation to be at thelevel of one event or less, but as was the case in 1991 the systematic uncertainty was not known.Chapter 6. Discussion 238As discussed in the previous section, the method used in 1991 to prepare the offline analysis cutswas likely responsible for the presence of a few events. Therefore, considering the low statisticsinvolved and the unknown and potentially large systematic uncertainties, the two results arenot obviously inconsistent with each other.Chapter 7ConclusionThe result from the analysis of the 1991 7rvE data set is most certainly disappointing, becauseno clear explanation for the observation has been found. Based on the result obtained with 1989data, a significant gain in sensitivity was expected with 1991 data because of the larger numberof kaons observed and the addition of the lead-glass degrader and the inner wire chamber. TheIWC was to provide a modest improvement in tracking resolution, mostly for the z-axis component, so its impact was not expected to be very large; it performed as expected. The lead-glassdetector was introduced to primarily reject photons from the component of K2 backgroundthat was thought to be dominant. Its performance degraded significantly during the course ofthe 1991 data run because of radiation damage. In addition, light emitted by incoming kaonshindered the detector’s ability to identify low energy electro-magnetic showers. Despite theseproblems, photons were clearly detected and as expected the rejection of events in the low energy K2 tail was larger than for events in the K7r2 peak region. However, the overall rejectionobtained with the lead-glass detector was not as high as was initially expected.The analysis technique used in 1991 likely reduced bias in the final result but may have hadthe unfortunate side effect of not providing a set of cuts pushing the rejection capability of thedetector to its maximum. In some sense this method worked very well : a small number ofevents which were not examined at any point beforehand remained after all cuts were applied.The events satisfied all requirements for what would be expected of a signal. However, thelarge uncertainty in the background estimates does not allow us to differentiate signal andbackground. Further studies of the final results offer some indication, albeit flimsy, that the239Chapter 7. Conclusion 240remaining events are background, most likely from I(w2 decays, with a chance of kaon chargeexchange possibly followed by hyperon production and decay contributing as well.The correct upper limit for K+ —* in the kinematic region below the I2 peak setby this experiment is likely somewhere between the values obtained in 1989 and 1991. The1991 background rejection was not optimized because of the analysis techniques used while the1989 result was probably at or beyond the best that could be achieved, depending on the levelof bias in the analysis. It would not be strictly correct however to add the sensitivity of thetwo results for a combined upper limit. Even though the two data sets were collected usingthe same detector, there were differences not only in the sub-detectors themselves, but also intheir performance and calibration, which might influence the results. The difference in kaonbeam intensity may also have had an effect on the outcome, and certainly affected the detectorperformance.The work presented here showed that the BNL E787 detector did not have sufficient sensitivity for the search for K+ in the kinematic region below the I,,-2 peak. It leaves openthe question of the origin of the events observed in the 1991 data set. More data collected in1994 with a significantly upgraded detector may shed some light on this question. The upgradesand possible further improvements are discussed in the next and final section.7.1 Possible improvementsThe most important improvement necessary is to obtain more accurate background estimates,particularly for J2 and charge exchange. For Iir2 , the correlation between lr+ nuclearinteractions and photon veto must be reduced substantially. The simplest improvement is toenhance the photon veto capability of the detector and make it more uniform over the entiresolid angle. In addition to reducing the correlation this would also improve the K2 backgroundrejection. Some steps have already been taken in that direction. The endcap lead—scintillatorsandwich detectors have been replaced by fully active arrays of pure cesium iodide crystals. Thegeometric coverage of the new endcaps, both at the inner and outer radius, is greater than theold ones. Small lead—scintillator detectors were installed on the magnet iron behind the newChapter 7. Conclusion 241endcaps as close as possible to the beam axis, and another group of lead—scintillator detectorsfills the gap between the V-counters and the magnet iron. The lead-glass cylinder was replacedby a more radiation resistant type of lead-glass, and the light collection efficiency was improved.These changes should significantly enhance the photon rejection in the beam axis direction,where the most improvement was needed. The other crucial region is between the outer radiusof the endcaps and the barrel veto near the ends of the detector. This would be improvedby adding photon detectors between the range stack and the barrel veto. Several options arepresently considered, but actual improvements will not be installed before 1996.The other way to reduce correlations is to improve the nuclear interaction detectionin the target. A new target with less non-active materials and using scintillating fibres withbetter light output performance has been installed. The output of each target channel will beindividually recorded with 500 MHz gaffium arsenide CCD transient digitizers [86], substantiallyimproving the detection capability for large energy depositions overlapping with the energy fromthe stopping K+ in the target. In the future, it might be possible to operate the digitizers ata frequency of 1 GHz; this would further improve the double pulse resolution.For K+ charge exchange, the main uncertainty in the background prediction is the rate atwhich this process occurs. It should be possible to select data samples, possibly using a specialtrigger, which would allow the study of this process in detail. The present estimation using thebest available information for the Monte Carlo simulation is uncertain and at an uncomfortablyhigh level. This background source cannot be ignored in future searches, and efforts should bemade to understand it better. The improvements made to the target and its electronics willdirectly benefit any such study. Also beneficial will be the new central drift chamber, whichwill provide a factor of two improvement in momentum resolution, but most importantly willimprove the z-axis position resolution by a factor of 2 to 3. 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Santamaria, Nuclear Physics B315, 558 (1989).[44] The scale drawing of the magnets in this figure was provided by G.S. Clark, TRIUMF,and was based on information provided by J. Doornbos, TRIUMF.[45] Figure provided by K. Li, Brookhaven National Laboratory.[46] M.S. Atiya et al., Nuclear Instruments and Methods in Physics Research A321, 129 (1992).[47] IEEE Standard FASTBUS Modular High-Speed Data Acquisition and Control System,IEEE, New York, 1985.Bibliography 245[48] V. Fitch and R. Motley, Physical Review 101, 496 (1956).[49] D.A. Hutcheon, A. Konaka, Y. Kuno, J.A. Macdonald and Y. Yoshimura, BNL Experiment787 Technical Note #223.[50] V.A. Kujala, An Inner Wire Chamber for the E787 Detector, M.Sc. Thesis, Departmentof Physics and Astronomy, University of Victoria, 1991.[51] M. Atiya, M. Ito, J. Haggerty, C. Ng and F.W. Sippach, Nuclear Instruments and MethodsA279, 180 (1989).[52] G. Keil, Nuclear Instruments and Methods 87, 111 (1970).[53] J. 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Good, Physical Review 113, 352 (1959)[65] K.M. Smith et al., Nuclear Physics B 109, 173 (1976).[66] T. Nakano and Y. Kuno, BNL Experiment 787 Technical Note #256.[67] A. Pals and B. Treiman, Physical Review 168, 1858 (1968).[68] L. Rosselet et al., Physical Review D 15, 574 (1977).[69] G. Mechtersheimer et al., Physics Letters 73B, 115 (1978).[70] R. Madey et al., Physical Review C 25, 3050 (1982).Bibliography 246[71] M. Sevior, private communication.[72] Ya.A. Berdnikov, S.N. Polishchuk, and S.G. Smith, Soviet Journal of Nuclear Physics 55,1470 (1992).[73] W. Slater et al., Physical Review Letters 7, 378 (1961)[74] R.G. Glasser et al., Physical Review D 15, 1200 (1977).[75] D. Wright and D. Marlow, BNL Experiment 787 Technical Note #269.[76] D.H. Perkins, Introduction to High Energy Physics, Third Edition, Addison-Wesley ed.,1987, pp. 243-246.[77] G.A. Sayer et al., Physical Review 169, 1045 (1968).[78] A.D. Martin, Low and Intermediate Energy Kaon-Nucleon Physics, E. Ferrari and G.Violini eds., 97-114 (1981).[79] H. Davis et al., Nuovo Cimento 53A, 313 (1968).[80] D. Akerib, D. Marlow and P. Meyers, BNL Experiment 787 Technical Note #168.[81] R.D. Cousins and V.L. Highland, Nuclear Instruments and Methods in Physics ResearchA320, 331 (1992).[82] D.R. Marlow, P.D. Meyers, W.C. Louis, L.S. Littenberg, G. Azuelos and A. Stevens, UMCMonte Carlo Programme, Version 1.0.[83] W.R. Nelson, H. Hirayama and D.W.O. Rogers, The EGS4 Code System, SLAC-265 UC32, 1985.[84] T. Gabriel and R. Alsmiller, Physical Review 182, 1035 (1969).[85] R. McPherson, L. Felawka, J. Roy, D.S. Akerib, M.A. Selen and P.D. Meyers, UMC MonteCarlo Programme, Version 4.0.[86] D. Bryman, J.V. Cresswell, M. LeNoble and R. Poutissou, IEEE Transactions in NuclearScience 38, 295 (1991).[87] M.S. Atiya et al., Physical Review Letters 66, 2189 (1991).Appendix ABNL E787 CollaborationListed below are the names of the physicists who were members of the BNL E787 collaborationat the time the experiment reported in this thesis was performed.S. Adler, M.S. Atiya, I-H. Chiang, J.S. Frank,J.S. Haggerty, T.F. Kycia, K.K. Li, L.S. Littenberg,A. Sambamurti, A. Stevens, R.C. Strand and C. WitczigBrookhaven National LaboratoryW. C. LouisLos A lamos National LaboratoryD.S. Akerib, M. Ardebili, M. Convery, M.M. Ito,D.R. Marlow, R. McPherson, P.D. Meyers, M.A. Selen,F.C. Shoemaker, and A.J.S. SmithPrinceton UniversityE.W. Blackmore, D.A. Bryman, L. Felawka, P. Kitching,A. Konaka, Y. Kuno, J.A. Macdonald, T. Nakano,T. Numao, P. Padley, J.-M. Poutissou, R. Poutissou,J. Roy, R.A. Soluk, and A.S. TurcotTRIUMF247Appendix BAnalysis detailsThis appendix contains full analysis results used in background studies and acceptance calculations.B.1 Background studies248Appendix B. Analysis details 249Table B.65: Beam pion background analysis for 1989 data. The data sample usedwas selected out of the Pass 1 data.Cut j # events RejectionFail CERENKOV 3005BMJ{OLE 2853 1.0533 + 0.0044B4TD 2413 1.1823 + 0.0094NK 2296 1.0510+0.0048PROMPT 129 17.8 + 1.5DISENPI 127 1.016 + 0.011DISENK 117 1.085 ± 0.028INT_EB 76 1.54 ± 0.10DC-CHI2 61 1.245 ± 0.071NDC 55 1.109 ± 0.047ICOUNTER 26 2.12 + 0.30RSPC 25 1.040+0.041INT_RIV 17 1.47±0.20FITPI 9 1.89+ 0.43ELECTRON 6 1.50 ± 0.35TGTRACK 3 2.00 + 0.82FIDUCIAL 2 1.50+0.61ZDCTZ 1 2.0 + 1.4RGEMOM 0 —Appendix B. Analysis details 250Table B.66: 1991 K2 background sample for estimation method 1.Cut # events RejectionPassl 399958PROMPT 348794 1.1467 + 0.0007DC-SETUP 260033 1.341 + 0.001RS-TRACK 239065 1.0877 + 0.0006ICOUNTER 165311 1.446 + 0.002TRKTIM 100535 1.644 ± 0.003FITPI 82235 1.222+0.002TDJVIDA 76194 1.079 + 0.001TDFOOL 68605 1.111 + 0.001ELVETO 60919 1.126 + 0.002ELECTRON 49398 1.233 ± 0.002FIDUCIAL 41513 1.190±0.002KINSCORE 37999 1.092 ± 0.002BM_HOLE 37153 1.0228 ± 0.0008B4_CNTR 36186 1.0267 + 0.0009CERENKOV 30283 1.195 ± 0.003BWPC 28522 1.062 ± 0.002Fail 7-veto 27512 1.037±0.001Appendix B. Analysis details 251Table B.67: Analysis results for application of all cuts on 1991 events in theK2 peak region.Cut # events RejectionPassi 399958PROMPT 348794 1.1467 ± 0.0007DC-SETUP 260033 1.341 + 0.001RS-TRACK 239065 1.0877 ± 0.0006ICOUNTER 165311 1.446 ± 0.002TRKTIM 100535 1.644 ± 0.003INTIME 18952 5.30 + 0.03INTSE 14677 1.29 1 + 0.005FITPI 10255 1.431 ± 0.008TDJVIDA 9366 1.095 ± 0.003TDFOOL 7113 1.317 + 0.008ELVETO 5219 1.363 ± 0.010ELECTRON 3991 1.308 + 0.010FIDUCIAL 3199 1.248+0.010KINSCORE 2813 1.137 ± 0.007BMJIOLE 2700 1.042 ± 0.004B4_CNTR 2544 1.06 1 + 0.005CERENKOV 1604 1.586 + 0.024BWPC 1464 1.096 + 0.008Fail KINCUT 1202TGTRACK 279 4.3 + 0.2TGFIT 254 1.10 + 0.02VTXYCA 231 1.10 ± 0.02PB-GLASS 165 1.40 + 0.06B4TD 159 1.04 ± 0.02Appendix B. Analysis details 252Table B.68: 1991 Muon sample selection from irv)7 levO monitor data. The “Trigger” cut refers to the application of the (13CT + ... + 18c) and(19 + 20 + 21) Level 0 requirements, based on the trigger informationrecorded with the data.Cut # events Rejection7rvvlevO 112702Trigger 5116 22.0± 0.3TARGET 4997 1.024 + 0.002PROMPT 3746 1.33 + 0.01DC-SETUP 1840 2.04 + 0.03RS-TRACK 1608 1.14 + 0.01TRKTIM 1271 1.26 + 0.02KINCUT 219 5.8 ± 0.4Table B.69: 1991 Muon sample selection from Kir2(1) monitor data.Cut # events RejectionKir2(1) 166726Trigger 41981 3.97± 0.02TARGET 40866 1.0273 ± 0.0008PROMPT 22118 1.848 ± 0.008DC-SETUP 14689 1.506 ± 0.007RS-TRACK 13914 1.056 + 0.002ICOUNTER 12325 1.129 + 0.003TRKTIM 11521 1.070 ± 0.002FIDUCIAL 10518 1.095 ± 0.003KINCUT 1000 10.5 ± 0.3TOTRACK 440 2.27 + 0.08Appendix B. Analysis details 253Table B.70: Beam pion background event selection from 1991 irv7 Passi data.All cuts are as described in section 3.3.[ Cut events RejectionPassl 399958DC-SETUP 301922 1.325 + 0.001RS-TRACK 301922 1.0829 + 0.0006INTIME 53609 5.20 ± 0.02INTSE 43836 1.223 ± 0.002FASFITPI 43723 1.0026 ± 0.0002FITPI 33810 1.293 ± 0.003TDJVIDA 31107 1.087 ± 0.002TDFOOL 25633 1.214 + 0.003ELVETO 21209 1.208 ± 0.003ELECTRON 16849 1.259 ± 0.004KINSCORE 12818 1.314 ± 0.006Table B.71: Ke4 background simulation and analysis. The RS-TRACK cut included a requirement that the true + stopping counter be identicalto the one found by the range stack tracking algorithm.Cut # events Rejection1.0 xPass kinematic constraints 725059 13.792 + 0.016Level 0 trigger simulation 102472 7.076 ± 0.020Level 1 trigger simulation 92411 1.1089 + 0.001192411TARGET 90695 1.0 1892 + 0.00046PROMPT 70940 1.2785 ± 0.0022DC-SETUP 58749 1.2075 ± 0.0021RS-TRACK 49308 1.1915 ± 0.0022ICOUNTER 45959 1.0729 + 0.00 13TRKTIM 45550 1.00898 ± 0.00044INTIME 4101 11.11±0.16ir decay at rest 4066 1.0086 + 0.0015FIDUCIAL 3764 1.0802 ± 0.0048TGTRACK 19 198±45KINCUT 19 1.00 ± 0.00Appendix B. Analysis details 254Table B.72: Kaon charge exchange background simulation and analysis for K —*decay. Offline analysis cuts are the same as in table B.71.Cut # events Rejection2.0 x 106Satisfy KT requirement 1993776 1.00312 ± 0.00004Level 0 trigger simulation 382364 5.2143 ± 0.0076Level 1 trigger simulation 271658 1.4075 + 0.0014271658TARGET 233747 1.16219+0.00090DC-SETUP 105250 2.2208 ± 0.0051RS-TRACK 81100 1.2978 + 0.0022ICOUNTER 74574 1.0875 + 0.0011TRKTIM 64688 1.1528 + 0.00 16INTIME 31561 2.0496 ± 0.0082+ decay at rest 30595 1.0316 ± 0.00 10FIDUCIAL 24280 1.2601+0.0037TGTRACK 901 26.95 + 0.88PROMPT 47 19.2 + 2.7KINCUT 37 1.270 ± 0.096Sum of weights 4.96 x i0Appendix B. Analysis details 255Table B.73: Kaon charge exchange background simulation and analysis for K2 —*7r+e7e decay, to be compared with table B.72.Table B.Cut j # events Rejection6.0 x_i05Satisfy KT requirement 598053 1.00326 + 0.00007Level 0 trigger simulation 33654 17.771 + 0.094Level 1 trigger simulation 22042 1.5268 + 0.006022042TARGET 19249 1.1451+0.0029DC-SETUP 10263 1.876 ± 0.013RS-TRACK 7093 1.4469 ± 0.0095ICOUNTER 6485 1.0938 ± 0.0040TRKTIM 5673 1.143 1 + 0.0054INTIME 513 11.06 ± 0.46+ decay at rest 497 1.0322 + 0.0082FIDUCIAL 381 1.304+0.032TGTRACK 14 27.2 ± 7.1KINCUT 6 2.33 + 0.72Sum of weights 1.04 x iO74: production background simulation and analysis.Cut # events Rejection200000Satisfy KT requirement 193105 1.03570 + 0.00044Level 0 trigger simulation 47137 4.097 + 0.0 16Level 1 trigger simulation 40218 1.1720 + 0.002240218TARGET 35851 1.1218+0.0020DC-SETUP 34712 1.03281 ± 0.00099RS-TRACK 28687 1.2100 + 0.0030ICOUNTER 27711 1.0352 ± 0.0011TRKTIM 23523 1.1780 ± 0.0030INTIME 13871 1.6958 ± 0.0092.+ decay at rest 13611 1.0191 ± 0.0012FIDUCIAL 11284 1.2062+0.0047TOTRACK 1322 8.54 ± 0.22PROMPT 101 13.1 ± 1.2KINCUT 81 1.247 ± 0.062Sum of weights 3.15 x i0Appendix B. Analysis details 256B.2 AcceptanceTable B.75: K —* simulation and analysis (1991 data). The OFF and ONcolumns refer to events simulated without and with ir+ decay andnuclear interactions turned on, respectively.[ Cut OFF ON]Events generated 50000 50000KT (stopped kaon) 47556 47501T• A 19434 19407BCT 16049 13485Del. coinc. 15972 13152(13CT+...+18CT) 11012 10028(19+20+21) 11012 9935(BV + EGM + EGP) 11012 9917Hextant cut 11012 990611012 9906TARGET 10952 9858DC-SETUP 10674 9442RS-TRACK 9914 7693ICOUNTER 9751 7571TRKTIM 9321 7155INTIME 9264 6893+ decay at rest 9264 6729FIDUCIAL 8587 6251KINSCORE 8365 5742TGTRACK 7507 4984KINCUT 3906 2792Appendix B. Analysis details 257B.3 Integrated kaon fluxTable B.76: Analysis of 1989 Kt2(1) data (real and Monte Carlo) for the f3correction factor.[ Cut Data MC45698 17476Online del. coinc. 32221 —CERENKOV 30558TARGET 29925 17393PROMPT 23503 —DC-SETUP 16543 17105ICOUNTER 16308 16892RS-TRACK 16120 16880FIDUCIAL 15068 15808ZDCTG 14878 15556R0 13801 15107Table B.77: Analysis of 1991 K2(1) data (real and Monte Carlo) for the f3correction factor.Cut Data MC73766 10941Online del. coinc. 49198 —TARGET 48561 10839PROMPT 41016 —DC-SETUP 35144 10683RS-TRACK 33545 10670ICOUNTER 31910 10376TRKTIM 30553 9691FIDUCIAL 28988 9294CERENKOV 28246 —27531 9118Note for tables B.78 and B.79.The acceptance factors for Monte Carlo data were simply calculated from the numbersin tables B.76 and B.77, since the sample is pure J(2 . For the real data, the acceptanceAppendix B. Analysis details 258factors were taken from section 5.2.1; however, the acceptance of 1991 cuts other than theonline and offline delayed coincidence was measured by re-analyzing the data sample withoutthe PROMPT cut. This is because events with no target element struck by the charged trackare rejected by both the PROMPT and TRKTIM cuts, and this acceptance loss is not countedin the acceptance for the PROMPT cut given in section 5.2.1. The acceptance factors obtainedby analyzing the 1991 data without the PROMPT cut were consistent with the ones obtainedin tables 5.42 and 5.43, except for TRKTIM and CERENKOV. The reason for the latter beingdifferent was that the other beam and target cuts were not applied in this case; there is someoverlap in the rejection of accidental beam particles for the various cuts.Table B.78: Acceptance factors for 1989 Jc2 acceptance correction. The ZDCTGcut used here only included a cut on ZDC.Factor Data ] MCALODe1c 0.8300 + 0.0054 —ATG 0.97658 ± 0.00096 0.99525 ± 0.00052ADelc 0.8527 + 0.0065 —ADC 0.7086 + 0.0029 0.98344 + 0.00097Aic 0.9836 + 0.0030 0.98755 + 0.00085ARS 0.99562 + 0.00075 0.99929 + 0.00020AFID 0.9558 + 0.0059 0.9365 + 0.0019AZDC 0.98739 + 0.00091 0.9841 + 0.0010Ac 0.97338 ± 0.00091 —Total correction 0.4962 0.0058Appendix B. Analysis details 259Table B.79: Acceptance factors for 1991 K2 acceptance correction.Factor Data MCALODe1c 0.8131 + 0.0035 —ATG 0.98705 + 0.00051 0.99068 + 0.00092ADelc 0.9333 ± 0.0025 —ADC 0.8519 ± 0.0016 0.9856 ± 0.0011ARS 0.99531 ± 0.00034 0.99878 ± 0.00034Ai 0.9418 ± 0.0012 0.9724 ± 0.0016ATRK 0.8824 ± 0.0017 0.9340 ± 0.0024AFID 0.9491 ± 0.0012 0.9590 ± 0.0020Ac 0.97338 + 0.00091 —Total correction 0.5740 ± 0.0042Appendix B. Analysis details 260B.4 K2 branching ratio measurementTable B.80: Analysis of K7r2(1) monitor data and Monte Carlo simulated datafor the 1989 K2 branching ratio measurement.Cut # eventsData MC41817 5295Online del. coinc. 24701 —CERENKOV 23315 —decay at rest — 4439TARGET 22698 4387PROMPT 18147DC-SETUP 12167 4029ICOUNTER 11825 3912RS-TRACK 11490 3853FASFITPI 4059 —FITPI 2519 —ELECTRON 2138 —ELVETO 2127 —Stop. counter match — 3352FIDUCIAL, ZDCTG 1916 291925.5 < R0 < 35.0 1748 2567Appendix B. Analysis details 261Table B.81: Analysis of K7r2(1) monitor data and Monte Carlo simulated datafor the 1991 K2 branching ratio measurement.Cut # eventsData MC166726 10496TARGET 163048 10348PROMPT 97428 —DC-SETUP 71922 9023RS-TRACK 29804 5502ICOUNTER 26778 5375TRKTIM 25232 5196FASFITPI 19684 —FITPI 10095 —ELVETO 9638 —ELECTRON 8058 —+ decay at rest— 4944FIDUCIAL 7503 4555CERENKOV 7297 —26.0 < R0 < 34.0 6830 4099Appendix CMonte Carlo SimulationA computer program, written specifically for the BNL E787 experiment, was used for all MonteCarlo simulations. Several members of the E787 collaboration contributed to the first version ofthe program [82]. It defined a detector geometry as close as possible to the actual detector. Thepropagation of photons and electrons through the various materials was handled by subroutinesfrom the EGS4 Monte Carlo program, a well known and extensively used simulation code [83].For heavy charged particles (M >> m) the energy deposition was determined by adding theenergy losses due to collisions with atomic electrons in the medium (ionization or excitation).Each particle was propagated through the detector in small steps; the number of coffisionsin each step was determined by dividing the total average energy deposited along the step,obtained using the Bethe-Bloch formula [17], by the minimum energy a particle loses in acollision. All unstable particles were allowed to decay to appropriate final states. For kaons,specific decay modes could be selected.Subroutines were available to treat nuclear interactions of positively charged pions andkaons in plastic scintillator. Total and differential cross-sections for the various processes weretaken from the available literature. Also, the program included a package of subroutines namedPICA [84], for the treatment of photo-nuclear interactions.The flow of the program was handled by several user supplied subroutines, giving access tothe output variables generated by the code at every step. In this way, a significant amount ofcomputer time could be saved by generating only interesting events. The version of the MonteCarlo program used in this thesis included a simulation of the Level 0 and Level 1 trigger, and262Appendix C. Monte Carlo Simulation 263the ability to record the response of the sub-detectors for each event in YBOS format [85].The recorded events could then be analyzed with the same program (KOFIA) that was used toanalyze real data.In typical simulations, a was initially started at the front face of the target. The positionand momentum of the K+ were chosen such that the distribution of stopping coordinates for alarge number of K+ matched the distribution observed in real data. The K+ was then allowedto decay, and all particles in the final state were propagated in the detector. Once the particlepropagation was complete, the energy deposited in each part of the detector as a function oftime was examined to simulate the operation of the trigger. If the event satisfied the triggerrequirements, it was recorded for further analysis. In addition to the information simulating thereal detector response, the full information about the propagation of each particle was recordedwith the event.Some aspects of the detector response were not simulated, notably the segmentation ofthe B4 hodoscope and the lead-glass detector. These sub-detectors had a small effect on thesimulations. Also not simulated was the response of the transient digitizers. To simulate theireffect in selecting -+ decays, the lr+ stopping in the range stack were required to stop inscintillator and to decay at rest. In addition, the stopping range stack counter determined bythe range stack tracking algorithm had to be the same as the true stopping counter.Appendix DContribution to BNL E787Modern particle physics experiments are often performed by medium to large groups of physicists, with significant support from engineering and technical staff. It is sometimes difficult toassess an individual’s contribution to the experiment. Therefore, at the request of my Ph.D.committee, this appendix describes my specific contributions to the BNL E787 collaboration(see appendix A).I was first involved as a Masters degree student (1986—1988), when I contributed to thedesign, construction, installation and calibration of the endcap calorimeters. This work wasreported in a thesis [53]. From October 1988, I contributed as a Ph.D. student. I was on siteat BNL for the entire data collection periods in 1989, 1990 and 1991. Data for this thesis werecollected in 1989 and 1991. While at BNL I was specifically responsible for the maintenanceand calibration of the endcap calorimeters and the determination of the transfer function oflogarithmic amplifiers installed on some range stack channels. My tasks also included overallmaintenance of the detector and its electronics as well as data taking shifts. In addition, Ideveloped software to be used on-line in the ACP system for the analysis of monitor events usedin calibration, for the reduction of the transient digitizer information and for the determinationof the TD fiducial time.For off-line software used by the whole collaboration, I contributed improvements to theTD data analysis and prepared low level analysis and calibration software for the inner wirechamber installed in 1991. For 1989 data, I was a member of the three-person team in chargeof the initial sorting of events according to trigger types. The 1989 data analysis for the search264Appendix D. Contribution to BNL E787 265for K+ —* 71-+,j7 below the K2 peak reported in this thesis was done in collaboration withAkira Konaka. Both of us developed the high level software necessary for this analysis, morespecifically for refined -+ tracking in the target, I-counters and range stack, and for the searchfor photon hits with incomplete time and energy information in the range stack and barrel veto.I actively participated in the preparation of the publication reporting this analysis [37] and wasresponsible for communications with the editors of the journal. I was also a member of an E787internal review committee for the publication describing a search for the decay ir0 —* v17 [87].For the 1990 and 1991 data I was in charge of the preparation of off-line software used forthe combined first analysis pass of all events, including triggers other than 7t-iJi. This meant theintegration into a single program of software developed by other members of the collaborationfor specific physics analyses. For 1991 irvi7 data, I performed all the analysis and backgroundstudies reported in this thesis, and developed the techniques necessary to attempt an unbiasedanalysis. Improvements to the analysis software were built on the experience acquired with the1989 analysis. More specifically, the refined + tracking in the target and the photon veto cutswere improved, multi-variate analysis techniques were introduced for TD, kinematic and vertexcuts, and software was developed to perform pulse fits on the target TD information.


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