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Construction of an ultra-thin cylindrical drift chamber for measurement of the rare decay K+ [formula] Pacradouni, Vighen 1993-09-22

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CONSTRUCTION OF AN ULTRA—THIN CYLINDRICAL DRIFT CHAMBERFOR MEASUREMENT OF THE RARE DECAY K+ ^vi7ByVighen PacradouniB.Sc., McGill University, 1989B.Eng., McGill University, 1991A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIASeptember 1993© Vighen Pacradouni, 1993In presenting this thesis in partial fulfilment of the requirements for an advanced degree at theUniversity of British Columbia, I agree that the Library shall make it freely available for refer-ence and study. I further agree that permission for extensive copying of this thesis for scholarlypurposes may be granted by the head of my department or by his or her representatives. Itis understood that copying or publication of this thesis for financial gain shall not be allowedwithout my written permission.Department of PhysicsThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1W5Date:17). /993AbstractThe branching ratio for the decay K+ —* r+v/7 has been measured at Brookhaven NationalLaboratory by the E787 collaboration to be 5.2 x 10 -9 . The best QCD calculations give aprediction of (.6 -4 6) x 10'. The theoretical equations for this calculation as well as theprevious experiment are reviewed. The experiment is in the midst of a major upgrade resultingin a new beam line and a modified detector. The ultra-thin cylindrical drift-chamber withhelical cathode strips for measurement of the axial coordinate of the charged particle track isdescribed. A design for charge pre-amplifiers to instrument the cathode strips is discussed. Thedesired gain was achieved for single amplifiers, however, the problem of ringing and cross-talkwhen mounted in close proximity remains.iiTable of ContentsAbstractTable of Contents^ iiiList of Tables^ viList of Figures^ vii12IntroductionTheory132.1 Role in Weak Theory ^ 42.2 G.I.M Mechanism 52.3 The CKM Matrix ^ 62.4 Theoretical Significance of the Decay K+^r+ vii ^ 62.5 Window on New Physics ^ 102.6 Determination of Vt d I 112.7 Determination of the CP violating phase ^ 142.7.1^Consistency of Standard Model parameters ^ 153 Experiment Overview 193.1 Introduction ^ 203.2 Strategy 203.2.1^Kinematics ^ 213.2.2^Particle Identification ^ 233.2.3^Photon Veto ^ 26iii3.3 Backgrounds ^ 273.3.1^K,2:^K+ -^ir+r°^...^.^.^..^.^.^.^.^.......^.^......^. 273.3.2^Kµ2 :^K+ -> ............................. 273.3.3^Scattered beam pions ^ 273.3.4^K+ -4 µ+vµ-y ^ 273.3.5^K+ -> 7r°Itt+vi, 283.3.6^K+ -> ir°e+ve ^ 283.3.7^K+ -- 7r+.71-+7- and K+ -> r+e+e- ^ 283.3.8^K+ -> r+er° 293.3.9^K+ + n -f p + K2;^K2 -> r+e - v nuclear reaction in stopping material 294 The Detector 304.1 Introduction ^ 314.2 Overview 314.34.4The Beam^..........^.........^..^..^....^..^..^............ ^The beam counters ......3544.5 The Target ^ 374.6 The Drift Chamber 384.7 The Range Stack ^ 394.8 The Photon Veto 414.9 Upgrades ^ 425 The Ultra-Thin Drift Chamber 435.1 Introduction ^ 445.2 Physical Description ^ 445.3 Thickness of the UTC 505.4 Operation of the UTC ^ 515.5 Comments on Design 53iv5.5.1 Mechanical ^  535.5.2 The Drift Gas  555.5.3 Drift Cells ^  585.6 The Momentum Resolution ^  596 The Read—Out Electronics 646.1 Introduction ^  656.2 Anode Pre—amplifiers ^  656.2.1 Description  656.2.2 Design Comments^. ......... . ^ 676.3 Cathode Pre-amplifiers  677 Conclusion^ 73Bibliography 75List of Tables5.1 Table of UTC components depicted in side view . . . . . . . . ...... 475.2 Table of UTC Electrode Layers ^ 495.3 Breakdown of radiation lengths in tracking volume of old drift chamber ^ 515.4 Breakdown of radiation lengths in tracking volume of the UTC ^ 515.5 Breakdown of radiation lengths in entire UTC ^ 525.6 Table of Optimized Potentials and Resultant Electrode Surface Fields ^ 60viList of Figures2.1 Feynman Diagram for K+ --* ee+v ^ 72.2 Feynman Diagram for forbidden 1st order K+ -4 r+vt7 ^ 72.3 2nd order Feynman Diagrams for K+ --+ r+vii ^ 92.4 Constraints in p — 77 Plane from Experiment 162.5 Constraints in p — n Plane with K+ ---÷ 71-+ //// Measurement ^ 183.1 Momentum spectrum of rare and background K+ decays 223.2 Range spectrum of rare and principal allowed K+ decays ^ 223.3 Energy spectrum of rare and principal allowed K+ decays 234.1 Cut-away view of E787 detector ^ 324.2 Scale drawing of E787 detector 334.3 Endview of detector ^ 344.4 Schematic representation of beam counters ^ 364.5 The Cerenkov counter ^ 374.6 Cross-sectional view of the target ^ 384.7 View of a sector of the range-stack 405.1 End View of UTC ^ 455.2 Side View of UTC 465.3 Drift Velocity vs Reduced Field for 50%-50% Ar-Ethane ^ 575.4 Momentum spectra with 2% resolution ^ 625.5 Momentum spectra with 1% resolution 626.1 Anode pre-amplifier circuit diagram ^ 66vii6.2 Schematic/Block Diagram of Charge Amplifier ^  686.3 Circuit diagram for charge amplifier ^  706.4 Scope trace of impulse response of charge amplifier .^...^71viiiChapter 1Introduction1Chapter 1. Introduction^ 2Experiment 787 at Brookhaven National Laboratory is a search for the second order weakdecay, K+ —> r+v17. The experiment is a BNL-Princeton-collaboration which has constructed,operates and maintains a detector optimized for the measurement of the above decay. Thedetector is located at BNL's Alternating Gradient Synchrotron facility.The last experimental run was in 1991, and while no candidate events have been found todate, an upper limit for the branching ratio of K+ 3 ir+iii7 has been set at 5.2 x 10 -9 at the90% confidence level [1]. The collaboration is now in the midst of upgrading the detector. Partof this upgrade consists of replacing the current central tracking drift chamber with a new onehaving a lower mass and an improved momentum resolution. The new drift chamber, calledthe ultra-thin chamber (UTC) is the topic of this thesis.Chapter 2 presents a cursory description of electroweak theory as it relates to K+It also describes the significance of the decay mode in the Standard Model and the extraction ofStandard Model parameters from a measurement of the K+ r+///7 branching ratio. Chapter 3describes the problems involved in the measurement of the decay and the general strategies andtechniques used in overcoming these difficulties. Chapter 4 presents an overview of the entireE787 detector giving brief descriptions of its various components. Chapter 5 deals with theUTC itself. It provides a physical description, an explanation of its operation, the motivationbehind its design, the results of studies of its momentum resolution, and finally the effects of animproved momentum resolution on the measurement of K+ —> r+v17. The UTC uses cathodefoil strip charge readouts to perform tracking in the axial direction, a feature not found in theexisting drift chamber. Although the existing pre-amplifiers can be used for the sense wires theyare certainly not optimal for the cathode strips. This is due to the electrical characteristicsof the cathode strips as well as the time evolution of the charge that they collect. Chapter6 provides a description of the existing anode amplifiers and presents a design for a chargeamplifier to instrument the cathode strips.Chapter 2Theory3Chapter 2. Theory^ 42.1 Role in Weak TheoryKaon decays have historically played an important role in the development of the theory ofweak interactions. In particular, a study of these phenomena contributed to the discovery ofparity violation and to the prediction of the existence of the charmed quark. The processK+ --+ 7r+v/7, a rare decay, offers the possibility of being a hunting ground for new physics or atest of the higher order predictions of the Standard Model.An attempt to develop a theory of a so-called weak interaction to describe the decay oflong-lived states such as nuclear beta decay, kaon decay, and muon decay produced the V-A theory of Feynman and Gell-Mann [26]. This was a Lorentz covariant theory of chargedcurrent interactions. The name V-A is derived from the fact that the currents contain termslike Ty' (1 — -y 5 )//) where 0,TP are the Dirac spinors and their adjoints, and the 7 0 and -yil-y 5parts transform respectively as vectors and axial-vectors under parity transformations.Although this theory accommodated parity violation, which had invalidated the Fermi the-ory, it nevertheless required different coupling constants to account for the differing rates ofdecay. In the context of quark theory, the nuclear beta decays and kaon decays correspondedto (d u) and (s u) transitions respectively. Cabibbo noticed that a lone universal con-stant would accurately describe transition rates in all three cases if one one were to treat theweak eigenstate, d', that is, the particle that participates in the weak interaction, as a rotatedsuperposition of d and s [27]. Thus, the weak isospin doublet becomes:(;) d cos 0, + s sin Ocwith 0, 13°.Now, given the presence of charged current interactions one was led naturally to expectneutral currents as well. In the Cabibbo theory with its sole doublet, the neutral currentconsisted of the transitions (u u) and d' ---* d'). This yields a neutral current of:JNC^+11'd'Chapter 2. Theory^ 5= Tin + dd cos t e + ss sin2 Oc (ds 3d) cos Oc sin ecclearly representing a non-zero, and non-suppressed amplitude for (s^d) transitions.Decays such as these, involving flavour changing neutral currents, of which the decayK+ —> 7r+ 07 is an example, were searched for but either not found or else were found to beextremely suppressed compared to their charged current counterparts.2.2 G.I.M MechanismIn 1970, Glashow, Illiopoulos, and Maiani, suggested a mechanism, subsequently named theG.I.M mechanism, to account for the suppression of these flavour changing neutral currents[25]. They proposed the existence of a second doublet and thus extended the Cabibbo modelto four quarks arranged in two orthogonal doublets:d')^s')with the weak eigenstate down-like quarks related to the strong eigenstates by a rotation matrix,( d' cos ec sin °c ) ds — sin 9 cos OcNow, the neutral current is composed of terms like:JNC = 'Tiu + + 37 cr + W sl(_ ) (d'= 'Yu + -c-c + cT 3/I^s= ttu + -ec + ( d Ts ) MIXd= Tiu^+ -aswith /d'i sbj(2.1))^)Vud Vits Vut,^d^= lica Ks Vcb^s^\ Vtd Vts Vtb^bChapter 2. Theory^ 6so that the flavour-changing part of the neutral current vanishes due to the unitarity of the mix-ing matrix, and this remains true for an arbitrary number of generations with the appropriatelydimensioned mixing matrix.2.3 The CKM MatrixIn the present-day six quark model we have three doublets [31]:u^c^tp ) ( , ) ( b')(••■■..■„..,.....■"McThe matrix, Mc , is called the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The neutral cur-rents are:JNC = rtu + Tc + it + cTcr + Ws' -Fib'd \= rcu -Fec +it + ( d 3 6 ) 14 Mc sb 1= Ttu + Tc + it + Tld + .3.s + Aso that, once again the flavour-changing component vanishes.2.4 Theoretical Significance of the Decay K+ —> r+vi7We now consider the significance of the existence of the K+ ---> r+v17 decay mode. Figure 2.1shows the allowed decay K+ —> r°e+v which proceeds via a charged W+ current with abranching ratio (BR) of 5%. Figure 2.2 shows the first order Feynman diagram for the K+ --*Chapter 2. Theory^ 7v^e+WES ^uu ^  uFigure 2.1: Feynman Diagram for K+ -4 7r°e+vS ^0^.."Z.0".."vvd u ^  uFigure 2.2: Feynman Diagram for forbidden 1st order K+ —> r+v/7Chapter 2. Theory^ 8r+vi7 decay. From the above discussion one notices that it represents a flavour-changing neutralcurrent and is, therefore, forbidden.Figure 2.3 depicts the three second order processes that contribute to the decay. Consid-eration of the first two of these is sufficient, as the contribution of the third diagram has beenshown to be insignificant [2]. It is important to notice the internal quark lines. The diagramsbeside the Feynman diagrams for the first two processes highlight the internal quark verticespresent. The only constraints on the virtual quark are that they be of the up-like type ( withcharge 2/3). Thus the possibilities, u,c,and t, must be summed over. Now, the amplitude asso-ciated with each diagram depends on the quark mass through the propagator term as n4/M 2 ,where M is the mass of the exchanged vector boson. If the quark masses were equal, then theonly difference in the amplitudes would be due to the CKM couplings. Thus, the remainderof the amplitude could be factored out of the sum so that we would have, say, for the firstdiagram:mi = (- • .) E Vq*dVqsq=u,c,tThe summation corresponds to the inner-product of two columns of the unitary ( and thereforeorthogonal ) CKM matrix. Hence it is identically zero. Thus, if the quark masses were equalthe K+ r+vi, branching ratio would be zero and the G.I.M mechanism would be said to becomplete to all orders. Of course, the quark masses are different, and this spoils the cancellationat second order. The BR, then, obviously depends on the quark masses and the CKM matrixelements. A precise calculation was made by Inami and Lim [4] :^BR(K+ r+v/7)^a2 * E vqsvgdp(xol 2^(2.2)^BR(K+ —+ 71-°e+v) sin4 Owq=c,twhere1 ^3^(4 — x)2 x hi(x) + x4 43 x x 1 ]D(x)= —8 [1 + — x)2^— xand X q = m4/Myy.By calculating the rate relative to the measured and similar process, K+ —> 71-°e+v, oneavoids uncertainties in the hadronic wavefunctions. The calculation can be made in terms ofSSS(b)ddW+Chapter 2. Theory^ 9(C)Figure 2.3: 2nd order Feynman Diagrams for K+ r+vi7Chapter 2. Theory^ 10the above process due to the similarity of the two processes in figures 2.1 and 2.2. Both have akaon in the initial state and two leptons in the final state. The hadronic wavefunctions in thefinal state are related by a strong isospin rotation.With this parameterization, the BR for three neutrino generations is found to beBR(K+ —> r+vii) = (.6 —> 6) x 10-10 (2.3)for the top quark mass, mt  mw.The span is due both to uncertainty in elements of the CKM matrix as well as ignoranceof the top quark mass. Thus, in principle, a measurement of BR(K+ —> r+Vii) would allowlimits to be placed on the mass of the top quark. However, if one assumes the validity of theStandard Model then a direct measurement of m t is likely to occur before a signal is observed forBR(K+ —> r+vii). In this scenario, the known value of m t can be used to extract the magnitudeof the CKM matrix element, Vid, as well as the value of the CP violating phase described below.The latter may be used in conjunction with values derived from other experiments to performa detailed consistency test on the Standard Model.Before proceeding to a discussion of the extraction of IVtdI and the CP violating phase insections 2.6 and 2.7, mention should be made on the possibility of observing physics beyondthat predicted by the minimal Standard Model.2.5 Window on New PhysicsAs will be described in the next chapter, the search for K+ .— ir+v17 is, in fact, a search forK+ —.> r+ + nothing, so that the existence of additional decay modes of a kaon into a pion andlight weakly interacting particles will clearly affect the measured branching ratio.The simplest of such extensions would be extra generations of neutrinos [32]. However, theprecise effect of a fourth generation would depend on many unknown factors such as the massof the accompanying heavy lepton.Lepton flavour violating decays, which are strictly forbidden in the Standard Model withChapter 2. Theory^ 11massless neutrinos, comprise another possibility for new physics. These would be decays involv-ing presently known families of leptons as decay particles, e.g, K+ r+ve ym . However, it isalso possible that the additional decay modes give rise to amplitudes that interfere destructivelyso as to decrease the branching ratio.Also, although in extensions of the Standard Model, the Higgs is thought to have a massgreater than 10GeV/c2, there is still room for a lighter Higgs with mH < 350MeV/c2 whichwould contribute to the branching ratio through the process K+ r+H.Further candidates for unobserved decay particles are light supersymmetric particles. Theirexistence would also have an effect on the branching ratio by introducing more amplitudeswhere the supersymmetric particles would replace the intermediate states in the loops in theFeynman diagrams of figure 2.3 [28, 29, 30].Finally it should be noted that the current upper limit for K+ --> 71-1- vV is 5.2 x 10-9 whichis still at least an order of magnitude greater than the Standard Model prediction. An upperlimit has also been set for the process K+ r+X° where X° is any weakly interacting neutralparticle or system thereof with mass between 150 and 250 MeVIc2 . It is dependent on themass of the hypothetical particle but for the range mentioned is no greater than 2 x 10 -7.2.6 Determination of illtd1The discussion below follows [5]. The CKM matrix of equation 2.1 may be parametrized as:Si C3 S183Me = —si c2 ci c2 c3 — s2 s3 exp iS c1 c2s3 s2 c3 exp iS (2.4)s1 s2 — ci s2c3 — c283 exp —cis2s3+ c2c3 exp iSwhere ci = cos Oi and si = sin O. That is to say, the CKM matrix may be expressed in terms ofthree rotation angles and a phase. Comparing this with equation 2.1 one obtains the followingrelations:Vtd = S1 82^ (2.5)Vub^S183^ (2.6)Chapter 2. Theory^ 12and with the assumption that the cosines of small angles can be set to unity :Vcb :::.% 83 + S2 exp i5.^ (2.7)Taking the square of the magnitude one obtains:1Kb1 2 = s3 + s3 + 2s2s3 cos S^ (2.8)so that28283 cos (5 = IVcbI 2 — 83 — 83.^ (2.9)Using equation 2.2 for three neutrino generations and using the current values of 9w, Vus , a,BR(K+ —> 7r6e+v), and expanding, one obtains the expression:K+ —). r+vv = ID(x,) + 82(82 + 83 exp i(5)D(xt)12= Dc2 + 2DcDt (83 + 8283 cos 5) + M83182 + s3 exp i(51 2= Dc2 + DcDt(IVcbI 2 — s3 + s3) + DMIVcb1 2= M + DeDt(Mbl 2 — s3) + (DAIVcb1 2 )4 2.11 x 10-6(2.10)where De = D(x,) and Dt = D(xt). Solving this equation for .93 and substituting in equation2.5 one obtains the following expression for IVtdI 2 .IVtd1 2 = S21 DcDt + MIVcbi 2 x(BR(K+ —> ir+ vv)2.11 x 10-6 Dc Dc+ DtiVcb1 2 (1 —VubVcb2 1 )1)31^(2.11)It is evident from the above equation that the value of IVidI thus obtained will depend onother Standard Model parameters. These are :• a and O, which have been absorbed into the constant 2.11 x 10 -6• Vud through si = 1 — c? = 1 — Vu2d• ITicbl and the ratio IEdzi, Ir cbChapter 2. Theory^ 13• mc , mt, and mw through the kinematic functions D, and DtWhile the parameters in the first two items in the above list are known to good accuracy, thosein the latter two are not. In fact, there has been no experimental determination of m t to date.However, within the framework of the Standard Model, its value is constrained by the resultsof other experiments to lie within a certain range. An investigation of the sensitivity of theBR(K+ -+ r+vii) to Vtd based on the equation 2.11 using nominal values of m e = 1.5GeVand mt = 200GeV as well as Particle Data Group central values for the remaining StandardModel parameters while ignoring uncertainties leads to the following finding. A measurementof BR(K+ ---* r+vV) accurate to within 20% would yield a value for I Vtd I accurate to 13%.Furthermore, the sensitivity is not a strong function of mt . For example, at mt = 200GeV, ameasurement of BR(K+ -* r+vV) to 25% yields IVtd! to 17%.A consideration of the uncertainties in Standard Model parameters in the extraction of IVtdimodifies its uncertainty in the following manner. The uncertainties in a, 0,, mw, do not con-tribute significantly to the uncertainty in 1Vtdi. Although QCD corrections to BR(K+ -> r+vV)cause a variation of 15% to 30% in the branching ratio, these do not translate into a large un-certainty in IVtdi. A 10% uncertainty in mt contributes about 12% uncertainty in IVtd1. Anuncertainty of 0.1GeV in the determination of m e contributes about 4% to 8% uncertainty iniVtdi depending on the value of mt . However, unlike the uncertainty on mt which is an experi-mental problem, the uncertainty in m e is due to the theory underlying its extraction, and so isunlikely to diminish in the near future. Furthermore, although the uncertainty of 44% in theratio IY-uki, I contributes only 3% uncertainty to IVtd1, the 20% uncertainty in IVA contributescbroughly 20% uncertainty in I Vtdj. This seems to be the main source of error in the extraction ofIVtdI from BR(K+ -4 r+vij). It is theoretical in nature and not likely to improve in the shortterm. It thus sets a target of about 20 - 30% for the desired accuracy of the measurement ofBR(K+ -- r+07).Chapter 2. Theory^ 142.7 Determination of the CP violating phaseThe discussion below follows [6]. The CKM matrix has been parametrized by Wolfenstein [7]in powers of the Cabibbo angle (to third order) as follows:i VudVcd\ VtdVusVcsVtsVubVcbVtb=1 — A/2—AAA3(1 — p — iy)A1 — A 2—AA2AA3 (p — iy)AA21(2.12)where A = sin Oc -'-' 0.22.Substituting this parameterization of the CKM matrix into the theoretical expression forBR(K+ —+ 71-+vV) of equation 2.2 one obtains the following relation.BR(K+ ee+v)^3a2^(1 — A2 /2) D,^) 2^A4A8D? — 1/2 + (1 + A2A4 Dt PBR(K+ —* r+07) 8R-2 sin Ow4^1This describes a circle in the complex p — y plane centred at :1+ (1 — A2 12) Dcivts 1 2^Dt (2.14)and with a radius of :1  \IBR(K+ —+ r+vii) (2.15)1Vt,1 2Dt^2.11 x 10 -6where the following numerical values have been used: BR(K+ -- 7r°e+ v) = 0.0483, sin Ow =0.23, and a = 1/128.Therefore, a measurement of BR(K+ -- r+07) determines a circle in the p — i plane withcentre on the real, p, axis and displaced slightly from the point (1,0) by the charmed quarkcontribution to the branching ratio. It should be noted that the kinematic functions, Dc and Dt ,are both monotonically increasing functions of their respective quark masses. The displacementof the circle centre from the origin as well as its radius both decrease with increasing IV is i or Dt ,and hence increasing mt . The radius grows as the square root of the measured branching ratio.QCD radiative corrections to BR(K+ —> r+vv) have been calculated. There effect is to scalethe charmed quark contribution, Dc , by 0.71. This does not change the type of curve obtained(2.13)Chapter 2. Theory^ 15in the p - y plane, nor does it have an effect on the radius of the circle. It does, however, reducethe displacement of the centre from (1,0) by that same factor.Their remains the fact that the top quark mass is still unknown and that Iiits 1 is the CKMparameter with the greatest degree of uncertainty (20%) after Vtd. However, taking the limitof the PARTICLE DATA GROUP fit for IVts j as well as the lower limit on m t from the CDFcollaboration [8] of 89GeV/c 2, one can calculate an upper limit on the radius as well as anupper limit on the displacement of the centre from the point (1,0) along the real axis. Thus,an oval region in the p - n plane is circumscribed within which must fall the value chosen bynature. As the measurement of the upper limit on the BR(K+ .- r+v/7) improves the regionof allowed values becomes smaller.2.7.1 Consistency of Standard Model parametersOther constraints on the allowed region in the p-ri plane also exist. A review of such constraintsby Kim, Rosner, and Yuan [10] included the following:• The magnitude, KbI-V-Ika I 7 which, with la errors, defines an annular region centred on theorigin.• Circles centred on the point (1,0) with radius varying with top quark mass, determinedby B - B mixing.• Hyperbolas with a common focus at (1,0) determined by the parameter , e which describesthe main features of CP violation in the Kaon system.Figure 2.4 shows the curves based on central values of the above quantities as well as thosederived from the experimental 10 uncertainties. That is to say that uncertainties in otherStandard Model parameters have not been included in the uncertainties displayed in the figure.When the upper limit on BR(K+ ---> ir+ z/V) approaches the Standard Model predicted rangeit will appear on the figure as an oval region. Furthermore, when the mass of the top quark isknown and when an actual measurement of BR(K+ -3 r+ v17) is obtained, it can be displayedg•Chapter 2. Theory^ 16PFigure 2.4: Constraints in p — y Plane from ExperimentChapter 2. Theory^ 17on the graph in figure 2.4 as an annular region along with the previous results to see if the threegeneration Standard Model is adequate to explain the results of all of these experiments.The region defined by the measurement of BR(K+ —> 7r+v/7) will be subject to the followinguncertainties:• Statistical and systematic error in the experiment. An estimate for the uncertainty in theacceptance of the detector is 10% [9]. Thus, there is not much motivation for achieving astatistical error much better than that. One could therefore envisage a measurement ofBR(K+ —> 7+07) accurate to 20%.• Uncertainty in the top quark mass. A 1% uncertainty has been estimated for m t assumingthe top quark is discovered at SSC with a mass between 89 and 200GeV.• Uncertainty in the value of IITts l. The latter is equivalent to Mb! and the its error is dom-inated by theoretical uncertainties. It is estimated to be 10 - 20% [10], which translatesdirectly into an error on the displacement and radius.Figure 2.5 shows the central value and 1cr limits due to the variation in 1V ts i for a top quarkmass of 140GeV/c2 and an imagined measured BR(K+ —> 71-+///7) of 2 x 10-10 . Comparing thescales of figures 2.4 and 2.5 it would seem that a 20% measurement of BR(K+ --* r+vV) is bothadequate and interesting.Chapter 2. Theory^ 18I)Figure 2.5: Constraints in p — ri Plane with K+ ---). 7 + 1111 MeasurementChapter 3Experiment Overview19Chapter 3. Experiment Overview^ 203.1 IntroductionSince neutrinos are exclusively weakly interacting they are, for all practical purposes, directlyunobservable. Consequently, the search for the decay K+ --7r+v-ii is, in effect, a search forthe decay K+ 7r + nothing. Any real detector system is prone to misidentifying or missingemerging particles. Moreover, since K+ —+ r+07 is a rare process, it will be accompanied bybackgrounds leaving similar signatures in the detector at very high rates. The combination ofthe above two facts poses serious difficulties in making an unambiguous measurement of thedecay K+ 7r+vP.This chapter first briefly describes the method used by the E787 collaboration to searchfor the rare decay K+ r+07. It then proceeds to examine in greater detail the backgroundprocesses and describes the manner in which they can confound the measurement.3.2 StrategyThe general strategies used to overcome the difficulties mentioned above are kinematics, effec-tive particle identification, and extremely efficient photon detection. The tools used in imple-menting these strategies are those that are standard in nuclear and particle physics, a beam ofaccelerated particles, a target, drift chambers, scintillation detectors, high speed electronics andcomputing power. Furthermore, the implementation of these strategies is greatly facilitated bythe simplifying assumption that the decaying kaon is at rest. This assumption is rendered validby using an active target to stop a beam of kaons and requiring a time delay between the kaonand the appearance of the pion. This requirement for triggering is called "delayed coincidence".The stopped kaon ensures the monochromatic nature of the spectrum of the charged particlefrom the two—body decays, Kir2 and Ko described below. It also fixes the initial momentumand energy which allows one to make the assumptions described in the subsections below.Chapter 3. Experiment Overview^ 213.2.1 KinematicsThe following processes comprise the background in the measurement of K+ —> r+v-g:1. Kr2: K+^ir+7r° —> 27 (BR 0.21)2. Kin : K+ —> itt+vi, (BR = 0.64)3. scattered beam 7r+4. K+ —> ,u,+vm-y (BR = 0.0055)5. K+ —> 70,a+v,, (BR =0.032)6. K+ —> ee+ve (BR = 0.048)7. K+ —> i+70- 7r — (BR = 0.017)8. K+ —> 7r+ e+ e-9. K,3 : K+^+roe10. K+ +n—> p+ K2; K2 7r+e — vFigure 3.1 shows the momentum spectrum of the principal background modes as well as thesought rare processes. The numbers in parentheses give their respective branching ratios. Themethod used and the design of the detector itself are both motivated by the rejection of thesebackgrounds. The modes Kµ2 and K,r2, with branching ratios of 0.64 and 0.21 respectively areof particular concern. By confining the search to the region between the Kii2 and Kir2 peak, or213 < (M eV Ic2 )^ < 237, a high degree of background rejection is achieved while still acceptingabout 20% of the phase space. Figure 3.2 and Figure 3.3 depict the spectrum of the range inscintillator and of total energy for the same processes. The kinematic separation between theKir2 and IC2 peak is even greater than for the momentum Similar cuts are made on the basisof energy and range, and events are depicted on a three dimensional cartesian plot of energy,range, and momentum. The kinematic limits due to the Kr2 and Kµ2 peaks on each axis define1120"Fri Tr'6040Chapter 3. Experiment Overview ^ 220^50^100^150^200^250^300Momentum (MeV/c)Figure 3.1: Momentum spectrum of rare and background K+ decays14.3 mg^( q ic frb: in sr;niillotorFigure 3.2: Range spectrum of rare and principal allowed K+ decaysChapter 3. Experiment Overview 230^50^100^150^200^250Kinetic Energy (MeV)Figure 3.3: Energy spectrum of rare and principal allowed K+ decaysa box in this three-dimensional space. Events are then said to fall inside or outside the boxwith an event inside the box representing a signal for the decay.3.2.2 Particle IdentificationParticle identification is achieved in two completely different ways. The first involves combiningthe measurements of particle momentum and range to test a particle mass hypothesis, whilethe second consists of observing the decay chain 7r+ —> p+ --- e+.Range—Moment urnThe average differential energy loss per unit length due to Coulomb interactions of a particletravelling through a medium is given by the equation shown below called the Bethe—Blockequation:dX^A132 In— —K ---Z p { 2mc2,32 Em 202}12 (1 —13 2 )dE (3 .1)0Rpr ed =//pl c ±m?—mi A E(E Mi)dE (3.4)Chapter 3. Experiment Overview^ 24with27rNz2e4me2where N is Avogadro's number, m and e are the electron mass and charge, Z,A, and p arethe atomic number, atomic mass, and density of the medium, respectively, and I is its effectiveionization potential; z is the charge and the velocity (in units of the speed of light) of theionizing particle. The quantity EM is the maximum energy transfer allowed in each interaction.Simple relativistic two—body kinematics yields that EM = 2 m c 2 2 / (1 /3 2 )For a given particle type and medium, the rate of energy loss can be rewritten as a functionof particle velocity only:dX = Av(v)•dE^ (3.2)The kinetic energy of a particle of mass M is E K = M E(V), where E(v) is a function ofvelocity only. Therefore, by inverting c(v) and substituting for v in equation 3.2 one can writethe energy loss in terms of E and M :dX = AE(E/M).Hence the range of the particle may be obtained by integrating the above equation fromthe starting kinetic energy to zero. The predicted range will depend upon the type of particleone assumes through the variable M. To denote this the variable M is replaced by Mi withi = 71- depending on the hypothesis. The predicted range for a given hypothesis is given by:dE (3.3)where ppc refers to the momentum as measured before entry into scintillator.A Gaussian distribution of the measured ranges about the predicted range (plus an offset,SR due to systematic measurement errors) is assumed. A likelihood function of the formed wirt ea s^R)2Li = exp ^ (3.5)20-RChapter 3. Experiment Overview^ 25is calculated for each hypothesis (pion,muon). The particle is identified as the one correspondingto the hypothesis with the greater likelihood. Moreover, cuts are made requiring thresholdvalues of the relative likelihood, Lir /L/2 , for accepting candidate stopped particles as pions.TD Waveform FittingThis is a method of distinguishing between muons and pions. A more detailed descriptionof the detector components is given in chapter 4, however, for the purposes of this section itis suffient to know that the target, (and central tracking drift—chamber) are surrounded by aseries of scintillating elements collectively known as the range stack. Light is collected from thescintillator by photomultiplier tubes which are instrumented with transient digitizers (TD's)which record the output waveforms.Particle identification is achieved based on the following effect. A stopped 7r+ will decay viathe process ir+ itt+v/h . A itt+ will decay via it+ —÷ e+ ve zT,(7). Since particles deposit a largeportion of their energy just before stopping, a large pulse is observed in the photomultiplieroutput when the pion stops in the scintillator. It then decays to a 4.12MeV ,a+. The muonwill, in turn, stop in the same scintillating element producing a second, smaller pulse. Thestopped muon then decays into a positron. However, the positron—muon mass difference islarge so that the emerging positron will have sufficient energy to escape the element in whichit originated and register hits in adjacent elements.Therefore, in order for a hit in the range stack to be identified as pion the following criteriaare sought. The pulse shape from the original stopping element must have two peaks — onefor the pion stopping and one for the muon stopping. In addition, energy must be deposited inadjacent elements to show evidence of the it+ —> e+. The latter requirement provides furtherrejection of backgrounds where the first, double pulse was due to a it+ —> e+ decay followed byan accidental hit.Chapter 3. Experiment Overview^ 263.2.3 Photon VetoThe Kir2 decay is a two-body decay with the r+ and r° emerging back to back with well-defined and roughly equal energies and momenta. As the 7r° does not interact via the Coulombinteraction and, as its lifetime is too short to allow its detection directly, the principal methodfor detecting it and thus suppressing the background due to the Kr2 is the detection of thephotons that emerge from its subsequent decay. The two photons from the decay range in energyfrom 20 to 225 MeV. However conservation of energy yields that if one photon is of low energyand difficult to detect the other will be of high energy and easily detectable. Furthermore,conservation of the 7r° momentum guarantees that there be at least one energetic photon withits momentum roughly parallel to that of the parent r° and therefore anti-parallel to the 7r+from the kaon decay.The same principle holds true for IG3 decays as well, although in a more complicatedmanner and to a lesser extent. The daughter particles from this decay are a 7r+ and two r °'s.If the r+ is not energetic then the event will fail the kinematic requirement, therefore, in thefollowing it is assumed that the 7r+ has significant energy and momentum. By conservation ofmomentum, there must therefore be at least one energetic 7r° with momentum anti-parallel tothat of the r+. From there the reasoning proceeds as for the IC2 case to guarantee that therebe at least one energetic photon anti-parallel to the r+.Although the entire detector is encased in scintillator dedicated to photon vetoing over 4rof solid angle, the anti-correlation of the photon momentum with that of the 7r+ allows one tomake use of other scintillating elements by vetoing also on the basis of all energy collected intime with the kaon decay but spatially separated from the charged track.Chapter 3. Experiment Overview^ 273.3 Backgrounds3.3.1 K7,2 : K+^7r+7r°Since the charged particle is in fact a 7r+ just like for K+ —> 7r+vii, the only qualitative differenceis the detection of the photons from the subsequent 7r ° decay. Therefore, background arises dueto the photon detection inefficiency. However, to further suppress backgrounds kinematic cutsare made on momentum, range, and energy which suppress Kr2 by a factor of 105 but reducethe acceptance by a factor of 1.5 x 10 -3. This represents an improvement in signal to noise bya factor of 150.3.3.2 Kul: K+ —>Given the discussion of muon and pion particle identification given in the previous section, inorder for a Ko background event to appear the following must occur. The muon range inscintillator must be measured in the range 35 — 42 g/cm2 (see figure 3.2). There must be nophotons detected. After the initial stopping pulse, either an accidental pulse must simulate thetwo—peak shape of 7r+ —> e+ decay chain or the muon must decay to a 4MeV electronand another, accidental decay must occur to simulate the 7r+ it+ —> e+ sequence.3.3.3 Scattered beam pionsThis background arises from the difficulty of producing pure K+ beams. The ratio of pionsto kaons in the purest of beams is about two to one. Hence, backgrounds arise when a beam7r+ arrives in the target just after the kaon and scatters into the tracking volume giving theappearance of a decay product.3.3.4 K+ —>This process is similar to its non-radiative cousin, K+ —> it+vi,, and so will arise under the sameconditions plus that of failure to detect the emerging photon. It is interesting to note, however,Chapter 3. Experiment Overview^ 28that suppression of this background is aided by the following effect. At high muon momentum,the process is almost exactly like K1,2 decay where events are suppressed through particleidentification and kinematics, with the low—energy photon being difficult to detect and of littleconsequence. As the muon momentum decreases, the kinematical suppression decreases but thecorresponding increase in the photon momentum due to momentum conservation facilitates thephoton vetoing.3.3.5 K+ --> ir°p+vi,This background can arise from misidentification of the muon as a pion combined with thefailure to detect the photons from the subsequent ir° decay. It thus bears resemblance to Kr2and K,12 backgrounds except that it is a three-body decay and hence not monochromatic. Thishinders suppression of it through purely kinematical considerations. However, the advantageof redundancy is gained in that both photon vetoing and muon identification are applicable.3.3.6 K+ —> 71-°e+veThis background is very similar to K+ —> ir°p+v,, except that misidentification of the electron'scharged track as that of a pion is less likely.3.3.7 K+ 7r+7r+7r — and K+ —> r+e+e -This background is easily identifiable by the multiplicity of charged tracks. Due to conservationof momentum, the stopped kaon requirement precludes the production of a sole long-distancecharged track. Only two out of potentially three charged tracks need be detected. In factdetection of a single charged track may be sufficient to distinguish this from K+ r+in7 ifthat track is due to the 7r — with its negative curvature in magnetic field.Chapter 3. Experiment Overview^ 293.3.8 K+ , r+roroThis background is similar to K7r2 except, once again, in that it is not monochromatic. Thiskinematical disadvantage is offset by the fact that there are potentially twice as many photonsto detect.3.3.9 K+ + it -* p + la; 1,72_4 r+e — v nuclear reaction in stopping materialThe combination of kaon charge exchange followed by a semi-leptonic decay can give rise tobackgrounds according to the following scenario. The incoming K+ undergoes kaon chargeexchange as it interacts with a neutron in the nucleus of the stopping material producing alow—energy proton. The low—energy proton goes undetected as it may not even by emittedfrom the nucleus. The K2, lives for a while then decays to simulate the delayed coincidencetrigger giving rise to a low—energy electron which goes undetected (along with the neutrino).The long—range 7r+ recoiling off the leptons could then be mistaken as having emerged from theprocess K+ —> r+vii.Chapter 4The Detector30Chapter 4. The Detector^ 314.1 IntroductionThis chapter provides a brief general description of the entire detector used by the E787 col-laboration to measure the branching ratio of K+ —> 7r+vTi. The first section gives an overviewof the entire system, and the sections that follow it briefly describe the various sub—systems.4.2 OverviewA low-energy separated beam line (LESB I) provides a source of charged kaons which passthough a fine-grained multi-wire proportional chamber and a series of scintillators and ho-doscopes used to define the beam. These particles of approximately 800MeV/c are slowed bya beryllium—oxide degrader. A Cerenkov counter before the degrader establishes particle typewhich is confirmed by a dEldX measurement after the degrader. The particles stop in a highlysegmented scintillating fiber target which sits in the centre of a cylindrical composite detectorentirely contained in a conventional solenoidal magnet. The magnet provides a uniform 10kGfield pointing in the positive z—direction which is parallel to the direction of flow of the beam andcollinear with the axis of cylindrical symmetry of the detector. Figure 4.1 provides a cut—awayview of the detector and figure 4.2 is a scale drawing of the configuration of the sub-systemscirca the 1990 experimental run.Decay products emerging within a 27r solid angle are tracked in a drift chamber beforeentering the range stack. This is a cylindrical shell of plastic scintillator segmented both az-imuthally and radially. The pulse shape from the element in which the decay particle stops,in itself, provides a basis for particle identification as explained in section 3.2.2 In addition therudimentary level of tracking provided by the segmentation, which is augmented by two lay-ers of thin cylindrical multi-wire proportional chambers (RSPC's) interspersed between layersof scintillator, is sufficient for a range measurement which also serves as a basis for particleidentification.Finally, the range stack is enclosed by a barrel—shaped electromagnetic calorimeter made ofE-787 DETECTOR CB^1.4.10END CAP PHOTON VETO COUNTERSIWO DEGRADERBEAM dE COUNTERRANGE STACK-IRONBARREL PHOTON VETO COUNTERSRANGE STACK SUPPORT BOKCENTRAL DRIFT CHAMBERIRON END PLATEPHMONuL/IPLIER TUBES(BARREL PHOTON VETO)PHOTOMULTIPLIERTUBES (TARGET)PHOTOHULTIPLIERTUBES (RANGE STACK)E-787 (END VIEWEND CAPi - VETOTARGETChapter 4. The Detector^ 34Figure 4.3: Endview of detectorlead—scintillator sandwich and two-endcaps providing almost 47r coverage of photon detection.Figure 4.3 shows and endview of the detector depicting the various elements mentioned above.4.3 The BeamThe beam of K-1- 's is produced in the following fashion. A beam of 28 GeV protons extractedslowly from the Alternating Gradient Synchrotron (AGS) is made to strike a platinum tar-get thereby producing a plethora of secondary particles. Among these particles are protons,Chapter 4. The Detector^ 35lambdas, pions, and, of course, kaons. Low energy particles produced at 10.5° with respect tothe incident beam are extracted by a dipole magnet. Two quadropole magnets then focus thebeam onto a second dipole that spatially disperses the particles according to momentum. Thebeam then passes through an electrostatic separator. This is a device using crossed electric andmagnetic fields to transform the one—dimensional spatial dispersion of the particles in the beamwith respect to momentum into two-dimensions with respect to particle mass and velocity. Twomore quadropole magnets focus this dispersed beam onto the mass slit which selects particlesby transmitting only particles in a narrow mass band. A final pair of quadropoles focuses theselected particles into the detector. The length of the beamline is 15.5 meters. By this methodit has been possible to produce beams with one kaon for every two pions.The slow extraction of the primary AGS beam leads to 2-3 x 10 5 kaons stops in the targetdistributed smoothly in time over 1.4 seconds. This low instantaneous rate is important becauseit does not flood the detector and electronics. Barring an accidental pile-up, this rate ensuresthat the detector is tracking only one kaon at a time.4.4 The beam countersThe beam counters define the geometrical acceptance into the detector for beam particlesand they provide the accurate timing information for triggering. In addition, they serve as adiagnostic for tuning the beam. The system of beam counters is depicted in figure 4.4 below. Itconsists of four scintillating detectors, B1 — B4, a multi-wire proportional chamber (MWPC),and a C erenkov counter.B1 is a simple scintillation counter placed immediately downstream of the final quadropolebeam—focusing magnet and is used for beam tuning. It is followed downstream by B2, also usedfor beam tuning, which is a hodoscope. B3 is composed of two concentric scintillator discs ofdifferent radii placed one after the other. A comparison of their rates provides a measure of thetightness of focus of the beam before entry into th degrader. B4 is a three-layer scintillationdetector. Two of the layers make up a X — Y hodoscope and the final layer, just before theChapter 4. The Detector^ 36Figure 4.4: Schematic representation of beam counterstarget, provides part of the beam signal for triggering. Also, photons produced from a decayin the target escaping in the upstream direction will register a hit in B4 in coincidence withthe charged track. Thus, this counter also serves to plug what would otherwise be a hole inthe photon veto in the upstream direction. The hodoscope part of the counter, in additionto providing information on the beam particle multiplicities, provides a dE/dX measurementbased on the pulse height by exploiting the different ionization rates for pions and kaons. Thisprovides confirmation of beam particle identification just before entering the target.The initial beam particle identification is provided by the aerenkov counter. In the mo-mentum band 750 — 800 MeV/c kaons and pions produce Cerenkov light in lucite which lie oneither side of the critical angle for internal reflection. Pion light produced at the shallower angleis internally reflected, leaves by the side of the disc where it is collected by a conical mirror andreflected onto the PMT's recording pions. The light from the kaon is emitted forward, leavesthe downstream end of the disc and is reflected by a parabolic mirror onto PMT's recordingkaons. This is depicted in figure 4.5 below. Immediately downstream of the aerenkov counter isa three—layer MWPC that serves as a check on the beam profile before entry into the degraderand provides redundancy on beam particle multiplicity.PMTK^ PARABOLIC ^MIRRORCONICAL4odiIRRORibo„‘11.1.111111.V4/LUCITERADIATORP MTTTChapter 4. The Detector^ 37Figure 4.5: The C erenkov counter4.5 The TargetThe kaons stop in a live fiber target consisting of 378 triangular scintillating elements arrangedin a hexagonal array. Each element is composed of six fibers, 2 millimeters in diameter and 3meters in length, which have been glued together. One ADC and one TDC per six fiber cluster,or triangle, serve to record the scintillation light pulse shapes.The spatial segmentation of the target as well as the good timing information allow forearly tracking of decay particles and hence reconstruction of the decay vertex. This helps toflag events having a detached vertex where the apparent decay pion did not emerge from thecharged kaon, as happens in the case of kaon charge exchange backgrounds and scattered pionbackgrounds. Also, it is the good timing information that makes possible the implementation ofthe "delayed coincidence" requirement of a time delay between the kaon entering the detectorand the appearance of the pion.The fiducial volume of the target is defined by two additional scintillation detectors, theChapter 4. The Detector^ 38Figure 4.6: Cross—sectional view of the targetI—counter and the V—counter. These are shown in figure 4.6. By requiring a hit in the I—counterand no hit in the V—counter a limit is placed on the maximum amount of obliqueness of anacceptable track emanating from the target. This is done to validate the rough measurement ofthe range obtained from the range stack (described in section 4.7) based on the stopping layerof the track.4.6 The Drift ChamberThe drift chamber occupies the region between the target and the range stack. Its primarypurpose is to measure the momentum of the decay particle.The existing drift chamber consists of 5 radial layers with each layer being azimuthallysegmented into 36,40,50,60, and 70 cells respectively from inner to outer layer. The first, third,and fifth layers have six instrumented anode wires oriented axially. The second and fourthlayers have six wires oriented at angles from 3.1 to 4.0 degrees with respect to the axis of theChapter 4. The Detector^ 39chamber. The drift gas used was an argon,ethane, ethanol mixture in the ratio 49.9:49.9:0.2 atatmospheric pressure.This existing chamber will be replaced by the UTC which is the main topic of this thesisand discussion of it is deferred to the next chapter where it is presented in some detail.4.7 The Range StackAs its name suggests the range stack provides the first quick estimate of the range of emergingdecay products. In addition to this, however, the range stack provides an energy measurementwhich is used in photon vetoing, as well as tagging of the subsequent decays of muons and pionsas discussed in section 3.2.2.The range stack is a cylindrical shell of plastic scintillator surrounding the drift chamber andinterior to the barrel veto. It is segmented into 24 azimuthal sectors and 21 radial layers. Anenlargement of one of the sectors is shown in figure 4.7. The innermost layer, called a T-counter,having a shorter active length in the z—direction serves to restrict the angular acceptance to 2r.This is done to eliminate tracks which are oblique with respect to the detector midplane andmay be the result of scattering off the drift chamber endplates or the steel support structurethat protrudes part way into the stack.There are two layers of multi-wire proportional chambers interleaved at two radii in therange stack to provide more accurate tracking which is used for offline corrections to the range.Within each sector the 21 layers of scintillator are actually read out as 15. Because of spatialconstraints at small radii the inner layers are optically coupled thus reducing the requirednumber of phototubes. No significant loss in range resolution is caused by this arrangementsince the tracks of interest have longer range.Light is collected by phototubes at each end of the range stack and the the signals fromthese are processed as follows. Analog—to—digital converters integrate the pulse height for theenergy measurement. Transient digitizers (500 MHz) record the pulse shapes for decay sequenceidentification, and discriminators provide fast signals for triggering. The cost of TD's prohibitsFigure 4.7: View of a sector of the range—stackBVRSChapter 4. The Detector^ 40Chapter 4. The Detector^ 41instrumentation of each PMT individually so at present every four PMT's are multiplexed toone TD channel.4.8 The Photon VetoThe last line of photon detection is provided by a detector with many radiation lengths com-prised of alternating sheets of 5mm scintillator and 1mm lead sheets. This combination isconfigured in the shape of a cylindrical shell, called the barrel veto (By), placed outside therange stack, as well as in the shape of two discs, called the endcap veto (EC) which are parallelto and cover the drift chamber endplates. In this manner almost 47r solid angle coverage ofphoton detection is achieved.The barrel veto is made up of counters arranged in 48 azimuthal sectors and 4 radial layerssupported along their entire length by a stainless steel frame built into the interior of themagnet. In order to prevent photons escaping through the gaps between sectors these have allbeen placed skewed with respect to the radial direction so that none of the gaps point backto the target (see figure 4.7). A mixer block couples the scintillator sheets within a modulewhence light is brought out through the magnet end—plate by Incite light guides which feed aPMT sitting outside the magnet.The endcap modules are composed of 24 azimuthal petals. The signal is collected by acompact fluorescent wave shifter bar placed on the outer radial face of each petal. Scintillationlight from the petal excites the wave—shifter, and the light from the latter is brought out bylight guides through the magnet endplate and feeds a PMT sitting outside.Barrel and endcap veto elements are instrumented by ADC's and TDC's for precision offlineanalysis, as well as by summers for the purpose of forming fast analog total energy sums. Thesesums are discriminated and used for online vetoing of events containing photons. Althoughthe online vetoing suffers from errors due to accidentals, it is instrumental in suppressing theK7,2 background and reducing the number of events written to tape. A more precise veto,which takes energy deposited in other scintillating elements as well as timing into account, isChapter 4. The Detector^ 42subsequently performed offline.4.9 UpgradesBetween the 1990 and 1991 runs a few modifications to the detector were made. A 10cm portionof the BeO degrader at the downstream end was replaced with lead—glass read out with high—field phototubes thus making that part of the degrader active. Also, beam counters B3, B3S,and B4T were removed. Finally, a small single—layer cylindrical drift chamber, called the innerwire chamber (IWC), was placed in the air gap between the target and the main drift chamber.There are a number of further upgrades to the detector, in addition to the UTC, beingmade for the next experimental run. A new beamline (LESBIII) has been constructed with animproved production target, two separators, and improved beam optics. This will result in anK+/ir+ ratio of about 2, which represents a fourfold improvement over LESB I, as well as atwofold increase in K+ flux. The beam counters have been modified to fit inside the smalleraperture of the UTC and an extra MWPC has been added. The number of x and y fingers inthe B4 counter has been increased from 6 to 8, and the third layer B4T has been removed. Inaddition, B1 and B2 will be used for beam tuning but will be removed during actual runningbecause they scatter kaons away from the target. A new target has been constructed withsquare fibers instead of round ones in order to minimize the amount of dead material betweenthe scintillating fibers. The range—stack will have layers A,B, and C demultiplexed and straw—tube chambers will replace the range—stack MWPC's. At least one of the endcap photon vetoes,currently composed of lead—scintillator sandwich, will be replaced with pure CsI read out withhigh—field phototubes. Two sets of "collar detectors" (of lead—scintillator sandwich) will beadded. One set will be placed between the endcap vetoes and the magnet steel at the upstreamand downstream ends. A second narrower one will be placed at the downstream end to justsurround the target between it and the magnet steel. This will be done to plug holes in thephoton veto for photons escaping along a path almost parallel to the beam.Chapter 5The Ultra—Thin Drift Chamber43Chapter 5. The Ultra-Thin Drift Chamber^ 445.1 IntroductionThe function of the drift chamber is to provide precise tracking of decay particles. The radiusof curvature of the track in the magnetic field is used to make a precise determination ofthe decay particle momentum. Also, extrapolation of the particle trajectory out of the driftchamber volume back into the target and out into the range stack aids in pattern recognitionfor interpreting target element hits and allows for offline corrections to particle range based onthe angle of entry into the scintillator. The new chamber has been designed to have as fewradiation lengths as possible and, for this reason, is called the ultra-thin chamber or UTC.The main reasons for the desirability of a low-mass or thin chamber are the following.Multiple Coulomb scattering of the particle in the chamber gas and in the wires decreases themomentum resolution of the chamber. Monte-Carlo calculations indicate that the current driftchamber's resolution is, in fact, limited by multiple Coulomb scattering and that a factor of2 improvement in momentum resolution could be achieved by a factor of 5 reduction in thenumber of radiation lengths coupled with a 20% increase in size. This is what the UTC isdesigned to achieve and is the primary motivation for its construction. Also, it is desirable toreduce the amount of inactive material because short—range charged particles stopping in it willnot be detected.5.2 Physical DescriptionThe UTC consists of 5 cylindrical concentric chambers. The first, third, and fifth are driftchambers containing axially strung sense and field-shaping wires and an Argon-Ethane gasmixture. These are called the first, second, and third superlayers respectively. The second andfourth chambers serve merely as spacer volumes and are filled with Helium gas. The chambersare separated from one another by copper clad Kapton foils which serve as cathode planes andas gas seals.In what follows, a description of the composition of the chamber is given starting from theSUPERLAYER 1(TARGET)SUPERLAYER 2Chapter 5. The Ultra—Thin Drift Chamber^ 45Figure 5.1: End View of UTCinner radius and working outwards, and the reader is asked to refer to figures 5.1 and 5.2.The innermost component is a cylinder made of G10 clad with copper which will be groundedin an effort to produce a quiet RF environment for the sense wires. It is this cylinder alongwith the outermost carbon-fibre cylinder which supports the load placed on the endplates by thetension in the wires. A cathode foil is glued onto the cylinder. The foil is made of a substancesimilar to mylar having the trademark name Kapton clad with strips of copper coated withnickel which run at an angle with respect to the axis of the cylinder. At one end of thechamber, the downstream end, the strips are glued onto copper pads on a plastic shim usingconductive epoxy. Traces from these copper pads are soldered to inline connectors onto whichare mounted the pre—amplifiers that read out the charge on the strips. Aside from the numberChapter 5. The Ultra—Thin Drift Chamber ^ 46Figure 5.2: Side View of UTCChapter 5. The Ultra—Thin Drift Chamber^ 47Table 5.1: Table of UTC components depicted in side viewRea WWI mw1 FON. SUPPORT RING E-31014 1,0MIL 7.r1 12 FON. SUPPORT RING E-31015 ORYL 731 13 CRIMP PIN 111-3914 Cu 00644 INNER TUBE MST 0 ,33340 IL/0-1C 15 EXPANSION SUPPORT ROD 0-333500 AL. 6COMPRESSION SUPPORT ROD D-3335012 AL.7 EXPANSION SUPPORT ROD D•3335013 K. 60 COMPRESSION SUPPORT ROD D-2325014 IL. 6B EXPANSION SUPPORT ROD D-333300 AL. 2010 COMPRESSION SUPPORT ROD D-3335001 PL. 2011 EXPANSION SUPPORT ROD D-333501712 COMPRESSION SUPPORT ROD D-333500 IL. 2013 EXPANSION SUPPORT ROD 0-333500 IL. IS14 COMPRESSION SUPPORT ROD 11..33350110 IL. 1816 COMMON SUPPORT ROD 0-33350111 PL. IS16 COMPRESSOR SUPPORT ROD D-33350#12 IL. 1817 ONIP.R00 END PIECE 0.43350113 AL. Be18 EXP. ROD END PIECE 0-333501114 ST. Be19 SUPPORT RING 0-33365 AL 120 SUPPORT RING E-31033 AL 121 SUPPORT RING E-31034 AL. 122 SUPPORT RING 0-33358 AL. 12.3 FOL SUPPORT RIND 0-33370 ORYL 731 124 FON. SUPPORT RING E-31040 ORYL 7:1 125 FOL SUPPORT RING E-31041 ORYL 731 126 WIRE SUPPORT RING 0-33371 ORYL 731 127 WIRE SUPPORT RING E-31D42 ORYL 731 1 ,28 WIRE SUPPORT RING 0-33300 ORYL 731 129 WIRE SUPPORT RING E-31D43 ORYL 731 130 WIRE SUPPORT RING E-31045 ORYL 721 131 WIRE SUPPORT RING E-31040 ORYL 731 132 FON. SUPPORT RING 0-33404 ORYL 731 133 FOL SUPPORT RING 0-33405 ORYL 7.31 134 FOL SUPPORT RING E-31054 OM 731 136 OUTER TUBE ASS'Y E-31066 AL/C.F. 135 #1 FOIL CYLINDER KAFTAN 137 #2 FOIL CYLINDER KAFTAN 138 #3 FOR. CYLINDER KAFTAN 130 #4 FOIL CYLINDER ICAPTAN 140 0 FOIL CYLINDER KIPTAN 141 0 FOIL CYLINDER KAFTAN 142 FUMMACHSCR. #4-40 UNC X 3/8 LO. WM 10043 PMAIONACHSCR. #4-40 UNC X 5/16 LO. SS 18844 PANHEM1CHSCR. #4-40 UNC X 3/4 LO. SS 17045 SKIAIDAMCHSCR. #4-40 UNC X 3/4• .G. SS 17046 PM HOSCHIOR. 14-40 UNC X 5/8 LO. SS 17847 PANAIDMACHSCR. 0-40 LINO X 1/2 Uk SS as46 DOWELS B-30023 BRASS 3249 0-RING 3/32 W OA X 848 LOA. BUt4P0A 250 0-RING 3/32 W DIA. X 708 LOIA BUNA-N 151 • •^•^ma •^• • 152 • •^•^•^560 • • • 153 • •^•^•^555 • • • 154 • •^•^•^418 •^• •55 • •^•^•^400 • • • 1as • •^•^•^280 • • 157 • •^•^272 • • 156 • •^•^•^874 •^• • 1so • •^•^•^590 • • • ISO • •^•^382 • • • 161 • •^•^•^308 •^• • 1Chapter 5. The Ultra—Thin Drift Chamber ^ 48of strips, radius, and length all of the cylindrical foils mentioned are similar At either end ofthe support cylinder are glued two annular endplates made of a plastic having the trademarkname Ulteml . These endplates have small holes drilled in concentric circle patterns or layersat seven different radii. These holes house gold-plated pins crimped around the cathode andsense wires which populate the drift region between the plates. The high-voltage distributioncards are attached to the pins on the upstream endplates, and the pre-amplifiers which readout the anode wires are attached to the pins on the downstream endplates.There are two types of wires. The anode wires are 20 pm in diameter and are made ofgold-plated tungsten. These are maintained at high voltage and are read out through fastanalog preamplifiers. The cathode wires are 100 pm in diameter and made of gold-zinc platedaluminium. They are grounded and not read out. The anodes and cathodes are strung undera tension of 50g and 100g respectively. The wires are arranged in the seven layers as follows.The innermost layer is populated by both anode and cathode wires in an alternating pattern.The second layer is composed entirely of cathode wires, as are the fourth and the sixth. Thethird,fifth, and seventh layers are similar to the first.However, the anode wire positioning between these layers is staggered so that an anode wirein any of these layers lines up radially with a cathode wire in the previous or next odd layer.Within a superlayer, there are the same number of wires in each layer, however, the number ofwires varies between superlayers. Otherwise, the number of layers and the arrangement of anodeand cathode wires is the same for all three superlayers. The number of anodes and cathodes ineach wire layer as well as the number of strips on each foil are summarized in table 5.2.Surrounding the first superlayer is a cathode strip foil (foil 2). At the downstream end thereis an additional G10 2 ring screwed and glued to the wire endplate. The foil is mounted on theinside of a Nory13 ring which is pushed up against the G10 ring and fastened with screws. An0-ring is used to provide a gas seal between the Noryl and G10 rings. At the upstream end'Intern is a registered trademark of General Electric2 G10 is a trade name for an insulating glass—epoxy composite3 Noryl, a machinable plastic, is a registered trademark of General ElectricChapter 5. The Ultra—Thin Drift Chamber ^ 49Table 5.2: Table of UTC Electrode LayersLAYER SUPER—LAYERTYPE RADIUS [cm] ANODEWIRESCATHODEWIRESCATHODESTRIPS1 1 Foil 80.00 482 1 A or C 85.60 48 48 -3 1 C or C 91.20 0 96 -4 1 C or A 97.59 48 48 -5 1 C or C 103.98 0 96 -6 1 A or C 111.26 48 48 -7 1 C or C 118.54 0 96 -8 1 C or A 126.84 48 489 1 Foil 135.14 7210 2 Foil 214.00 10811 2 A or C 221.24 96 96 -12 2 C or C 228.48 0 192 -13 2 C or A 236.21 96 96 -14 2 C or C 243.94 0 192 -15 2 A or C 252.19 96 96 -16 2 C or C 260.44 0 192 -17 2 C or A 269.25 96 96 -18 2 Foil 278.06 14419 3 Foil 359.58 18020 3 A or C 367.46 144 144 -21 3 C or C 375.48 0 218 -22 3 C or A 383.86 144 144 -23 3 C or C 392.22 0 218 -24 3 A or C 400.72 144 144 -25 3 C or C 409.72 0 218 -26 3 C or A 418.86 144 144 -27 3 Foil 428.00 216Chapter 5. The Ultra—Thin Drift Chamber^ 50the foil is glued directly to the wire endplate. Aluminium flanges attached to the G10 extenderring at the downstream end, and to the endplate at the upstream end, extend the next sectionsof the chamber out in the axial direction as well as providing spacing in the radial direction.This is done to maintain the solid angle covered by the detector. Another cathode foil is gluedonto the outer edges of two Noryl rings. At the downstream end the ring partially overlaps thealuminium flange and is fixed to it by screws. At the upstream end the overlap is complete andonce again, screws are used to fix the Noryl ring to the aluminium flanges. At both ends an0—ring seal is made between the aluminium flange and the Noryl ring.Two more endplates, this time made of Noryl, surround foil 3. At the downstream end, theendplate is fastened to the foil ring with radial screws. At the upstream end, the endplate issupported by the aluminium flange to which it is fixed by axial screws. The second superlayer isstrung similarly to the first and is surrounded by another cathode foil (foil 4). This foil is gluedto a Noryl ring which seals up against another aluminium extender flange screwed directly to theupstream endplate of superlayer 2. At the downstream end, the foil is glued to the outside edgeof the downstream endplate. The connector shim is epoxied to it and another Noryl extenderring fastened to the endplate with radial screws. To this is fastened another aluminium flange.From here the inner foil for superlayer three (foil 5), the foil rings and endplates are assembledas for superlayer two. The outer foil for superlayer 3 (foil 6) will be glued onto a carbon-fibrecylinder padded with ROH—A—CELL, a styrofoam-like substance. The carbon—fibre cylinderwill be fixed to it with radial screws.5.3 Thickness of the UTCThe amount of material in the chamber is important for two reasons. Firstly, multiple scatteringin the tracking volume itself will cause the tracks to deviate from the ideal circular paths,resulting in larger experimental errors on the radius of the circle fit. This is discussed morequantitatively in section 5.6 below. For these purposes one need only consider the materialthrough which the particle must pass once it has entered the tracking volume. That is, one8.4 x 10 -3TOTALArgon-Ethane gaswires2.0 x 10 -36.4 x 10 -3COMPONENT^NO. OF RAD. LENGTHSChapter 5. The Ultra-Thin Drift Chamber^ 51Table 5.3: Breakdown of radiation lengths in tracking volume of old drift chamberTable 5.4: Breakdown of radiation lengths in tracking volume of the UTCCOMPONENT NO. OF RAD. LENGTHSfoils 2,3,4,5 0.37 x 10 -3Argon-Ethane gas 1.05 x 10-3Helium gas 0.03 x 10-3wires 0.20 x 10 -3TOTAL 1.65 x 10-3may ignore the inner and outer support tubes as well as the innermost and outermost foils. Thenumber of radiation lengths of the various components as well as the total number of radiationlengths in the tracking region have been calculated for the old drift chamber [24] as well asfor the UTC. They are presented in tables 5.3 and 5.4 below. They have been calculated fora trajectory proceeding radially outward in a plane transverse to the cylindrical axis of therespective chambers.The scattering in the inner support tube will not affect the circularity of the track and sowill not reduce the quality of the fit but it will, of course, alter the trajectory of the particlebefore it enters the chamber. The outer support tube simply comprises more dead materialthrough which the particle must pass before entering the range-stack. The breakdown of theradiation lengths for the whole chamber is presented in table 5.5.5.4 Operation of the UTCThe arrangement of anode and cathode wires and cathode foils described above results in theestablishment of roughly square drift cells which may be thought of as individual proportionalcounters. Physically, each cell is centred on an anode wire and defined by the square formedChapter 5. The Ultra-Thin Drift Chamber^ 52Table 5.5: Breakdown of radiation lengths in entire IJTCCOMPONENT NO. OF RAD. LENGTHSfoils 1 and 6 0.19 x 10-3inner gnd plane 1.18 x 10 -3inner support tube 0.20 x 10-3outer support tube 2.55 x 10-2tracking region 1.65 x 10-3TOTAL 2.87 x 10-2by linking its neighbouring cathode wires, or its neighboring cathode wires and adjacent foil.As previously mentioned, the anode wire is held at high potential thus creating an electricfield emanating from the wire. When a charged particle passes through the drift-cell region itionizes the gas, and electrons from the ionization drift toward the anode wire. When they cometo within a few wire diameters of the anode they undergo significant acceleration and obtainsufficient kinetic energy to ionize the gas themselves. Both the original and newly liberatedelectrons are again accelerated and cause further ionization. This process is repeated until allthe electrons reach the surface of the anode wire and are captured. In this manner, and withsufficiently high electric fields, electron multiplication factors of up to 10 5 can be attained. Thepositively charged ions drift toward the cathode wires and foil strips. However, current pulsesoccur on the cathode strips due primarily to the charge induced by the anodes. The currentpulses or induced charges are read out and enhanced by electronic amplifiers connected to theanode wires and cathode strips.Since there is no electric field component applied in the axial, or z, direction, the liberatedelectrons, do not drift axially. Thus the avalanche on the wire will be localized in the z direction.This localized electron swarm induces charge on the nearby cathode foil strips, with cathodestrips nearer the avalanche having larger induced charge than those further away. Since thecathode strips run at an angle with respect to the wires, the intersection of the wire and cathodestrip defines a range in z with some central value. By taking an average of these central zvalues of hit strips weighted by the relative induced charges one can infer the z coordinate ofChapter 5. The Ultra-Thin Drift Chamber^ 53the trajectory of the charged particle which gave rise to the ionization.The time of passage of the particle through a given drift cell can be estimated from hits inthe I and V counters mentioned in section 4.5. Given the speed of the charged particles andthe distances involved, the delay between entering the UTC and passing through any given cellis presumed to be insignificant. Measuring the time of onset of the anode current pulse withrespect to the estimated time of the passage of the particle through the cell permits estimationof the radial distance from the anode of the point of closest approach of the particle trajectory.This estimate translates into contours about the anode wires to which the trajectory must havebeen tangent. To the degree that the electric field is purely radial in direction and isotropicwith respect to the x and y coordinates, these contours will approximate circles. However, therelationship between wire hit times and drift distances in various directions can be calculated indetail based on electric field, gas pressure and gas characteristics. In practice they are calibratedbased on a set of test data with a uniform spread of particle trajectories over the volumes ofthe drift cells.Given the speed of the particles the drift chamber seeks to track, it is assumed that thepredominant interaction they undergo is with the axial magnetic field. This leads to a helicaltrajectory, whose projection is a circle in the x—y plane. Therefore, the particle trajectory isinferred by fitting the best circle which is tangent to the above calculated contours. The pitchof the helix is derived from the z measurements from the cathode foils.5.5 Comments on Design5.5.1 MechanicalThe chamber consists of many pieces and is quite complex mechanically. Aside from the labourinvolved in assembly, the drawback to such a design is the problems it presents in obtainingprecision alignment of its various components. Fortunately, alignment between superlayersdoes not affect the resolution and so these translational and rotational offsets from an ideal,cylindrically symmetric chamber system can be calibrated out. The justification for this designChapter 5. The Ultra—Thin Drift Chamber ^ 54is that it renders the entire chamber accessible for the purposes of maintenance. Indeed, thevarious superlayers can be removed individually, have their foils replaced, and be entirely orpartially restrung. It was originally planned to have the foils glued to their support rings whichwould then be screwed in place. However, for purposes of providing good gas seals they wereglued to the endplates. Nevertheless, experience has shown that it is still possible to removethem without damaging the superlayer.The foil material was chosen to be Kapton primarily due to its low leak rate for He gas.Leakage of the Helium gas from the spacer volume into the drift—cell superlayers would reducethe gas gain. The use of 2cm of water equivalent pressure differential from the interior toexterior volume of each foil combined with a 40g/cm tension has been calculated to maintainthe cylindrical shape of the foil to within lmm [12]. According to field calculations of the driftcell, a uniform field can be achieved with a 1mm tolerance between the anode and the cathodefoil. The tensions on the wires are to prevent deformation due to electrostatic and gravitationalforces. The sense wires are tensioned at 50g and the cathodes at 100g for a total load on theendplates of 300kg. This is much less than the 880kg loading of the old drift chamber allowingthinner and lighter endplates to be used.The choice of Noryl was made for the endplates and foil rings in order to reduce the radiationlengths in the chamber. It is a low—density plastic with good dimensional stability and isrelatively easy to machine. It is also a good insulator and thereby at once resolves the problemof isolating the anode pins protruding from the endplates. On the other hand, a groundedaluminium endplate would have produced extra shielding against RY noise. Previous experiencewith Noryl had confirmed its good dimensional stability, however, this experience had been forrelatively small pieces. With the TJTC some problems with creeping and warping of the largerendplates have tended to hinder efforts at aligning and positioning them properly.Chapter 5. The Ultra—Thin Drift Chamber^ 555.5.2 The Drift GasThe drift gas used is an argon (49.9%), ethane (49.9%), ethanol (0.2%) mixture. The reasonsfor this choice are the ability to operate at high gas gain, the reasonably fast drift velocity, andthe saturation of the drift velocity (explained below).Avalanche multiplication occurs in noble gases at much lower fields than in complex molecules.This is due to the fact that the latter have many non-ionizing modes of energy dissipation. Thechoice of argon from among the noble gases arises from the high specific ionization coefficient.This is the average number of ions produced by a minimum—ionizing particle. The specificionization coefficient of argon is exceeded only by those of xenon and krypton which are ruledout by their expense.A chamber filled solely with pure argon cannot operate at gas gains higher than 10 3 or 104for the following reasons. During avalanche excited and ionized atoms are produced. An excitednoble gas atom can only dispose of its energy and return to the ground state by emitting aphoton. For argon the minimum energy of such a photon is 11.6eV which is greater than theionization potential of any metal used in the cathodes. Thus, photoelectrons are extracted fromthe cathode which, in turn, avalanche causing spurious signals. Also, the ionized argon atomsmigrate to the cathode where they are neutralized. The energy released from the electron cap-ture is either radiated as a photon or by the ejection of another electron from the cathode metal.Both of these lead eventually to another spurious avalanche. Furthermore, the probability ofthese events is great enough as to result in permanent discharge even for moderate gains.Polyatomic molecules, on the other hand, especially those composed of greater than fouratoms, have many non-radiative excited states (rotational and vibrational). They can thusabsorb photons emitted from argon ions and dissipate the energy through elastic collisions ordissociation into simpler radicals. This is the role of ethane in the gas mixture; it is said tobe a polyatomic quencher. In addition, when ionized polyatomic molecules neutralize at thecathode secondary emission is highly unlikely; they either recombine into simpler molecules orform larger complexes (polymerization).Chapter 5. The Ultra—Thin Drift Chamber ^ 56For this reason, polyatomic quenchers, used as the sole additive, are detrimental to thelifetime of the chamber. This is because the created polymers deposit on the anode and cathodeforming an insulating layer. Positive ions created from further avalanches continue to drift to thecathodes, settle on the the polymer surface and slowly diffuse through. Eventually, the positiveions build up on the surface of the polymer due to the excess of the rate of ionization over thatof neutralization. Thus, a strong dipole electric field is created which extracts electrons fromthe cathode and sets off a permanent discharge. This is known as the Maher effect.In order to avoid this problem it is possible to make use of quenchers which do not polymer-ize. These are substances such as alcohols, aldehydes, and acetates. The problem with these,however, is that their vapor pressure is low compared to that of hydrocarbons. As a result theiroverall efficiency in quenching against photoionization and secondary emission when mixed inwith the drift gas is also low.Nevertheless, these non-polymerizing quenchers are used in the following manner to greatadvantage. By choosing a non-polymerizing agent with an ionization potential lower than theother components in the gas mixture, which includes a polymerizing hydrocarbon quencher forefficiency, use is made of an efficient charge exchange mechanism whereby the excess electronsare transferred from one species to the other such that all ions are removed except the onewith the lowest ionization potential. Thus the ions arriving at the cathodes will be of thenon-polymerizing type. This is the role of the ethanol in the gas mixture. This combinationallows operation of the chamber reliably at a gas gain of about 8 x 10 4 .Finally, another desirable characteristic of this gas is that its drift velocity "saturates".That is to say that above a certain value of reduced field, the drift velocity of the gas is roughlyconstant. Reduced field refers to the ratio E/P, where E is electric field in V/cm and Pis gas pressure in torr. The relationship between drift velocity and E/P, as calculated byGARFIELD, a program for modelling multi-wire chambers, E/P, is depicted in figure 5.3.It is seen that at the upper values of E/P, such as 340 kV/cm • torr at which the UTCoperates, the drift velocity does not vary much. Note that the plot is logarithmic in the reducedI r11^1^11 111Gem 15 mArgen 50% nhone 50%n^ (^-AOnI.Chapter 5. The Ultra—Thin Drift Chamber ^ 57IZ^3 4 i r T E. I 1^J^A. il 0 9 g i10E/p [vicrn i.orrjFigure 5.3: Drift Velocity vs Reduced Field for 50%-50% Ar—EthaneChapter 5. The Ultra–Thin Drift Chamber^ 58field. In calculation of drift distances from the times of the pulses a constant drift velocity is notassumed, but rather a space-time relation is inferred from calibration data taken at intervalsassuming a uniform distribution of ionizing tracks. This takes into account non-uniformity inthe electric field but still assumes that the drift properties of the gas are constant over time.Since the electric field at each point in the drift cell is due to the well controlled potentials onthe wires the only remaining variable is pressure. Therefore, the saturation of the gas insuresthat the space-time relations do not depend strongly on the pressure. This avoids the need forclose monitoring and control, in absolute terms, of the pressure in the drift chamber.The use of helium in the spacer regions between superlayers is obvious. It is a light inorder to reduce multiple scattering—non-flammable gas used to blow out and shape the foils.5.5.3 Drift CellsThe layout of the wires leads to drift cells which are physically adjacent, non-overlapping, androughly square in shape. Its shape leads to a field which is approximated well over a large areaof the drift cell by the field due to an infinitely long cylindrical shell of charge. The latter hasthe following cylindrically symmetric form:E(r) = ^Vr In b/a (5.1)where a is the radius of the anode and b is some average radius to the edges of the cell whichare at almost zero potential. It follows that the isochrones, or contours of equal drift time fromthe wire, will be roughly circular. The values of potential to be applied to the anodes werecalculated subject to the following constraints. The field on the surface of the anodes is kept ator below 260kV/cm in order to prevent spontaneous field emission around the anodes. This isstill on the conservative side. Also, the surface field on the cathodes is kept below 30kV/cm inorder to prevent "whisker growth", the polymerization of trace impurities in the gas onto thecathodes. The calculation was done using GARFIELD. It was not assumed that cells in thesame layer or superlayer were perfectly isolated from one another. Thus, the potentials for anChapter 5. The Ultra—Thin Drift Chamber^ 59entire superlayer were optimized together and different values of potential were found for eachlayer. These are summarized in table 5.5.3 below.As can be seen, none of the anode wire surface fields exceed 260kV/cm, in fact, they arebacked off somewhat from that value. The surface fields at the cathodes are nowhere near30kV/cm so it can be seen that the anode surface fields are the limiting factor.5.6 The Momentum ResolutionThe momentum resolution of the UTC was studied prior to its construction in two differentways. The first way was by a Monte—Carlo study which used a specialized program, calledUMC, based on the EGS package, which can generate events and model their effect on all thecomponents of the detector to produce data that can be subsequently analyzed by the analysispackage, KOFIA [13]. The measure of resolution used was AP = Pmeas — Ptrue of the particlesin the drift chamber.The momentum derived from equally spaced measurements of a charged track in the x — yplane, transverse to the magnetic field, is given byPay = 0.3 MekG.Vc/mc qBR (5.2)where q is the charge in units of the electron charge, B is the magnetic field and R isthe radius of curvature of the track. Neglecting non—uniformities in the magnetic field, theerror in the momentum arises from errors in obtaining the radius of curvature of the track, orequivalently its inverse, k, called the curvature. The curvature error is due to two components,6kpos , the error in measuring points on the track, and Ok,,,, the error due to deviation of theparticle trajectory due to multiple scattering. These are given bySkpos —^N +720 L25o-xy16MeV/c /—Skins = iipvi3 Vf(5.3)(5.4)where axy is the x — y measurement uncertainty of the wires, L is the path length of track, NChapter 5. The Ultra-Thin Drift Chamber^ 60Table 5.6: Table of Optimized Potentials and Resultant Electrode Surface FieldsLAYER SUPER-LAYERANODES CATHODESAPPLIEDPOTENTIAL [kV]SURFACEFIELD [kV/cm]SURFACEFIELD [kV/cm]1 1 .92 1 1.807 259.4 13.4 -3 1 15.1 15.34 1 1.947 259.6 17.75 1 16.6 16.36 1 1.988 259.5 17.5 -7 1 14.7 15.08 1 1.914 259.4 12.4 -9 1 .610 2 .711 2 1.881 259.2 12.9 -12 2 14.9 15.013 2 2.010 259.6 17.614 2 16.5 16.315 2 2.030 259.3 17.5 -16 2 14.8 15.017 2 1.935 259.3 12.518 2 .619 3 .720 3 1.907 259.2 12.6 -21 3 14.9 14.922 3 2.034 259.0 17.523 3 16.5 16.624 3 2.053 259.5 17.5 -25 3 14.7 14.826 3 1.945 259.4 12.427 3 .6= 16MeV/c VILqB13 0.3 (5.5)Chapter 5. The Ultra—Thin Drift Chamber ^ 61is the total number of measurements, f is the number of radiation lengths traversed, and /3 isthe speed of the particle in units of the speed of light.Propagating these errors through one obtains the following contributions to the momentumerrors.Pxy ) ms(46 Pxy (613n )^_ a- P^720^ (5.6)Pay^0.3BL2 N + 5xy xy posAn average value of f -= 1.65 x 10-3 has been estimated by looking at the various materialstraversed by the particle. Putting B = 10kG, L = 0.43m, /3 = 0.82 , and P = 185MeV/c forKr2 pions in the chamber a value of §,- = 1.24MeV is obtained. This amounts to the bulk ofthe value obtained from the Monte—Carlo. Consideration of the position resolution contributionto the momentum uncertainty, leads to an improvement by a factor of 0.64 due to the increasedtrack length measured by the UTC ( 36.3 cm instead of 29.0 cm ).The total momentum resolution as measured at the drift chamber is worsened by targetcontributions. When these were included in the Monte—Carlo a value of 2.3 MeV/c was obtained.The second way in which the momentum resolution was studied was by actual constructionof a prototype chamber by the Princeton group [14]. This chamber resembles the actual UTCexcept that it comprises only a sector of a cylinder and so does not cover the same solid angleand has fewer wires. Also, the cathode foil strips for the prototype chamber run at 90° to thewires whereas they run at roughly 45° to the wires in the UTC. The chamber was installed inthe detector, a run was made and the results analysed using code written for the UTC. Themomentum resolution obtained on the Princeton prototype chamber was 2.42 MeV/c.The motivation for the construction of the UTC was primarily to increase the kinematicbackground rejection by improving the momentum resolution (roughly from 2% to 1%). Fig-ure 5.4 depicts the sought and principal background spectra smeared with a Gaussian to accountfor the 2% resolution of the current chamber. Figure 5.5 depicts the same spectra smeared for1% resolution corresponding to the UTC.Chapter 5. The Ultra-Thin Drift Chamber^ 62100^150^200^250Momentum (MeV/c)Figure 5.4: Momentum spectra with 2% resolutionFigure 5.5: Momentum spectra with 1% resolutionChapter 5. The Ultra-Thin Drift Chamber^ 63It should be noted that the overlap between the K02 spectrum and the K+ --> 71-1- vTi spec-trum is reduced significantly. For the purposes of background rejection the separation of therange spectra of KA2 and K+ --). r+vii is much greater. Thus it is possible to eliminate essen-tially all the Ko background by making cuts solely on the basis of range. Nevertheless, theimprovement in momentum resolution will allow the momentum cut to be tightened addingfurther redundancy while still increasing the acceptance.Chapter 6The Read—Out Electronics64Chapter 6. The Read-Out Electronics^ 656.1 IntroductionThe hits on wires and cathode strips caused by a charged track appear as current pulses orcharge deposits on the electrodes in the chamber These must be converted into analog anddigital signals which then drive ADC's and TDC's. This is implemented in two stages, pre-amplifiers and post—amplifiers.Post—amplifiers take analog signals from the pre—amps and perform some further ampli-fication and pulse—shaping to produce an analog signal which is fed into the ADC's. Theyadditionally provide discriminated signals which drive the TDC's.Preamplifier cards are mounted directly onto the anode pins on the downstream endplateand onto connector pins soldered to the copper pads on the shims surrounding the foils, whichmake electrical contact with the strip through conductive epoxy. It is the task of these pre-amplifiers to convert the current or charge into voltage signals which are propagated down longcables to the postamplifiers located away from the detector. As a result, the design of the pre-amplifiers must take into consideration the inherent electrical characteristics of the electrodesand chamber, and it is their design which is discussed in this chapter.6.2 Anode Pre-amplifiers6.2.1 DescriptionThe pre—amplifiers that will be used to read out the anode wires will be the same as for theold drift—chamber. A schematic diagram is given in figure 6.1. It is a discrete—design feedbackamplifier based on the BFT25 transistor manufactured by Motorola. It is composed of fourclassic transistor amplifier stages. The first stage is a common—base current buffer which servesas a low impedance input. The importance of this is discussed below. The next three stagesprovide the open loop gain for the feedback amplifier. The second and fourth transistor (fromthe left of the figure) are used as buffers for the purposes of impedance matching. They serveto isolate the third transistor which used in the common—emitter configuration and providesChapter 6. The Read-Out Electronics 66Figure 6.1: Anode pre-amplifier circuit diagramChapter 6. The Read—Out Electronics^ 67most of the voltage gain. The entire circuit may be thought of as a current—to-voltage amplifierwith a typical gain of 10mV/yA.6.2.2 Design CommentsThe origin of the signal on the anode wire is due to the measurement of a charge in a systemof total capacitance between anode and cathode of C, which given by [16]:dV — ^Q dV dr.CV° dr (6.1)where Q is the charge, Vo is the potential between anode and cathode, r is the distance fromthe anode, and V is the potential at that distance.Since the ions are generated near the anode and drift all the way to the cathodes theircontribution to the induced signal is dominant at later times. Thus, if the anode were electricallyisolated the voltage at the anode would increase as more and more ions drifted to the cathodes,until such time as all the ions had reached the cathodes. When the anode is read out, adifferentiator is formed of time constant RC, where R is the input impedance of the amplifier(and C is still the inherent capacitance between anode and ground). To the degree that Rcan be made small, the differentiator becomes ideal, and short, sharp pulses are obtained. Ashorter time constant does yield a signal with a lower peak value but the effect is minimal sincethe time growth of the voltage induced at the anode is very fast at the beginning, reachinghalf its final value in one—thousandth of the total time. Furthermore, since very little analoginformation from the anode pulse heights is used, the improvement of rate capability of thechamber outweighs the slight loss of pulse height. Such is not the case for the cathode stripsas will be seen below.6.3 Cathode Pre-amplifiersThe tracking of the z—coordinate of the particle is achieved with the cathode strips in thefollowing manner. Clusters of cathode strips are first sought out. Then, for each hit strip,Chapter 6. The Read—Out Electronics^ 68FROMTOIL STRIPTOPOST-AMPRFigure 6.2: Schematic/Block Diagram of Charge Amplifierthe intersection is found between it and a wire hit which was roughly coincident with the hiton the strip. The intersection between the strip and such a wire yields a z—coordinate. Thesez—coordinates are weighted by the charge read out from their corresponding strips and averagedover the strips in the cluster to produce a centre of gravity for the charge which is taken to bethe z—position of that portion of the track. Thus, the z—coordinate resolution of the chamberis dependent upon good signal to noise ratios for the cathode strip pulses read out. Timingconsiderations cannot be neglected altogether, since rate and coincidence with wire hits arestill important. However, pulse height, in contrast with the situation for anodes, is of greaterimportance.For this reason, the anode amplifiers described above are not optimal in this situation.Rather, what is required is a charge amplifier of the form depicted in figure 6.2.This can be thought of as a current integrator, with integration time RC, or equivalentlyas a charge amplifier with gain 1/C. The idea is to have the output remain significant over alarge portion of the total ion drift time thereby collecting a larger signal, or charge, over thegate time of the ADC.At present, an improvement in gain for the the foil strip read-outs on the inner two foils iscrucial for the following reason. Due to the chamber geometry, the foil strips themselves have acapacitative coupling to the ground plane on the inner support tube. At the high frequencies ofChapter 6. The Read—Out Electronics^ 69these induced pulses the coupling acts to short out these signals thereby reducing the input tothe (present anode) amplifiers and hence the overall gain. This effect is particularly pronouncedfor the first two foils as would be expected from the geometry and the measured strip—to—groundplane capacitances.To compensate for this, high gain must be achieved by the read—out amplifiers themselves.In order not to exacerbate the problem mentioned above, the basic amplifier in figure 6.2 musthave low input capacitance and be fast enough to cope with the high—speed signals involved.An implementation of such a charge amplifier which was prototyped is presented in fig-ure 6.3 below. The design is based on the NE253 series Gallium—Arsenide dual—gate MESFET.Referring to figure 6.3, the top MESFET, Ql, is configured as a constant—current source forbiasing and provides a high signal impedance to the drain of the second MESFET, Q2, whichis used as common—source amplifier. The choice of the NE253 is motivated by the fact thatwhen the second gate terminal, G2, is grounded the input capacitance at G1 is reduced to afraction of the a picofarad despite the high gain between the gate and drain. It does not sufferfrom the Miller effect. The common—source amplifier stage is followed by two buffers, BFT92BJT's (Motorola) which serve to isolate the feedback path and the output. It should be notedthat there is no actual feedback capacitor in this circuit. This is due to the fact that there isalready about 1pF capacitance inherent in the 150K resistor.The circuit was tested by connecting a 1pF capacitor to the input and applying a 1V voltagestep to the other terminal of the capacitor. This was done to simulate the charge on the cathode.An oscillator trace of the output is displayed in figure 6.4. The output signal has a rise—time ofroughly lns and a time—constant of 62ns and a peak output of 1.58V. This represents a gain of1.58 x 1012 V/Coul. With the space limitations and configuration of the connector pins on thechamber. It is necessary to place six such amplifiers on one small PC board. The effect of thiswas studied by prototyping four such circuits in close proximity on a copper ground plane. Theresult was that the cross—talk positive feedback between them led to oscillations. It may bepossible, however, to eliminate this effect through the use of RF chokes on the power suppliesChapter 6. The Read—Out Electronics^ 70Figure 6.3: Circuit diagram for charge amplifierChapter 6. The Read—Out Electronics^ 71Figure 6.4: Scope trace of impulse response of charge amplifierChapter 6. The Read—Out Electronics^ 72and by proper layout of the circuits.Chapter 7Conclusion73Chapter 7. Conclusion^ 74The UTC is a low—mass cylindrical drift chamber using signals on axial anode wires as wellas helical cathode strips to measure the x,y, and z coordinates of charged partide tracks. Itis intended to replace the present drift chamber in the E787 detector in order to improve thecharged particle tracking and enhance the momentum resolution of the detector from 2% to 1%.The lower mass of the UTC is achieved through the use of zinc—gold plated aluminium cathodewires instead of Be—Cu wires, the use of cathode foil strips for z—position measurement ratherthan extra layers of stereo sense wires, the use of helium filled spacer regions, and through theuse of plastic (Noryl) for the endplates and foil rings.The time development of the signal on a cathode strip differs from that on an anode wire.Thus, while it is possible to use the pre—amplifiers that instrumented the stereo wires on theold drift chamber to read out the foil strips, these would not be optimal. Superior gain andsignal—to—noise can be achieved with the use of a charge amplifier such as the one presented inchapter 6. Furthermore, capacitative coupling of the foil strips to the ground plane is causingattenuation of the signals on the inner two foils. Thus, improved signal gain from the pre-amplifiers would serve to remedy the situation. The alternative to this would be to to increasethe field in the first superlayer and use the increased gas gain to compensate for the reducedsignal on foils 1 and 2. The drawbacks to this would be spurious field emission and acceleratedageing of the chamber.The desired gain has been achieved using one amplifier in isolation. However, when severalare placed in close proximity on a single board problems with cross-talk leading to oscillationwere observed. These problems are currently under study.Bibliography[1] M.S Attiya et. al. (The E787 Collaboration), Phys. Rev. Lett. 70 (1993) 2521[2] J. Ellis, J. Hagelin, Prog. Part. Nucl. Phys. 23 (1983) 1[3] S.L Glashow, J. Biopoulos, and L. Maiani, Phys. Rev. D2 (1970) 1285[4] T.Inami, C.S Lim, Prog. Theor. Phys. 65 (1981) 297[5] L.S Littenberg, E787 Technical Note 179 (18 October 1990, unpublished)[6] J. Haggerty, E787 Technical Note 196, (6 November 1990, unpublished)[7] L. Wolenstein, Phys. Rev. Lett. 51 (1983) 1945[8] F. Abe. et. al. ( The CDF Collaboration), FERMILAB-PUB-90-137-E (July 1990, unpub-lished)[9] D. Akerib, D. Marlow, P. Meyers, E787 Technical Note 1986 (8 August 1990, unpublished)[10] C.S Kim, J.L Rosner, C.-P. Yuan, Phys. Rev. D42 (1990)[11] M.S Attiya et. al. (The E787 Collaboration), Nuclear Instruments and Methods in PhysicsResearch A321 (1992) 129[12] E. Blackmore, D.Bryman, Y. Kuno, P. Padley, T. Numao, E787 Technical Note 182 (12February 1991, unpublished)[13] Y. Kuno, E787 Technical Note 200 (23 January 1991, unpublished)[14] R.A MacPherson, M.R Convery, M.M Ito, D.R Marlow, W.R Sands, E787 Technical Note212 (7 August 1991, unpublished)[15] A. Konaka, private communication[16] F. Sauli, Principles of Operation of Multiwire Drift and Proportional Chambers CERNreport 77-09, May 3, 1977[17] D. Bryman, International Journal of Modern Physics 4 (1989) 79[18] J.V Cresswell et al., IEEE Transactions on Nuclear Science 35 (1988) 460[19] Rob Veenhoff, A drift chamber simulation program v2.02, CERN (1990)[20] P. Renton, Electroweak Interactions, Cambridge University Press, Cambridge, 1990, 596p.75Bibliography^ 76[21] E. Segre, Nuclei and Particles, 2nd ed., W.A Benjamin Inc., Reading, Massachusets, 1977,966p.[22] V. Kujala, Master's Thesis, University of Victoria, 1991[23] D.S Akerib, Ph.D Thesis, Princeton University, 1991[24] W.0 Louis, E787 Technical Note 150 (12 May 1988, unpublished)[25] S.L Glashow, J.Illiopoulos, L. Maiani, Phys. Rev. D2 (1970) 1285[26] R.P Feynman, M. Gell—Mann, Phys. Rev. 109 (1958) 193[27] N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531[28] J. Ellis, J.S Hagelin, Nucl. Phys. B217 (1983) 189[29] M.K Gaillard, Y.0 Kao, I—H. Lee, M. Suzuki Phys. Lett. 123B (1983) 241[30] S. Bertolini, A. Masiero Phys. Lett. 49 (1986) 1549[31] M. Kobayashi, T. Maskawa, Prog. Theor. Phys. 49 (1972) 282[32] U. Turke, Phys. Lett. 168B (1986) 296

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