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Π⁰ detection using the CHAOS spectrometer : a feasibility study Ambardar, Anthony R. 1996

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71 Detection Using the CHAOS Spectrometer: A Feasibility Study by Anthony R. Ambardar B . S c , The Univers i ty of Br i t i sh Co lumbia , 1992 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F P H Y S I C S We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A February 14, 1996 © Anthony R. Ambardar, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia 6224 Agricultural Road Vancouver, Canada V6T 1W5 Date: Abstract The CHAOS spectrometer has demonstrated its success in the study of physics involving charged pions. Extending the capabilities of the spectrometer to allow studies with neutral pions would expand the range of potential experiments and permit a greater understanding of the phys-ics dealt with in the CHAOS collaboration's research. Since the spectrometer is sensitive only to charged particles, 7t°'s must be detected via pair conversion of their decay y's. In proceeding through the steps of a 7 t ° cross-section measurement, from the details of optimizing detection to aspects of analysis and normalizations, this thesis will help evaluate the suitability of CHAOS as a 7 t ° detector. February 14, 1996 ii Table of Contents Abstract i i Table of Contents i " L is t of Tables v i L is t of Figures v i i Acknowledgements x i i 1 Introduction 1 1.1 The Physics Program 2 1.1.1 The (7t,27t) Program 2 1.1.2 The 7tp Program 4 1.2 Theoretical Background '. 6 1.2.1 Chiral Symmetry 6 1.2.2 Chiral Perturbation Theory 7 2 The C H A O S Spectrometer 8 2.1 The Magnet 9 2.2 Wire Chambers WC1 and WC2 10 2.3 Wire Chamber WC3 11 2.4 Wire Chamber WC4 11 2.5 First Level Trigger 11 2.6 Second Level Trigger 14 3 Exper imenta l Setup & Data Acquis i t ion 15 3.1 Preliminary GEANT Studies 16 3.1.1 The Detector Model 16 3.1.2 Monte Carlo Setup 17 3.1.2.1 Beam Momentum 17 3.1.2.2 Converter Radius 19 3.1.3 Event Processing 19 February 14, 1996 iii 3.1.3.1 Evaluation Criteria 19 3.1.3.2 Single Event Procedure 20 3.1.4 Monte-Carlo Results 20 3.2 Experimental Setup 22 3.2.1 Beam Channel & Detector 22 3.2.2 Trigger System 22 3.2.3 Targets and Converter 24 3.3 Data Acquired 26 4 Data Analys is & Reconstruct ion 28 4.1 Analysis Setup 29 4.1.1 Chamber Calibrations 29 4.1.2 Particle Identification 29 4.1.3 Skimming 31 4.2 71° Reconstruction 33 4.2.1 Introduction 33 4.2.2 Procedure 36 4.2.2.1 Modifications For One-pair Events 39 4.2.3 Selection Criteria 41 4.2.4 Experimental Results 49 4.3 Normalizations 56 4.3.1 Beam Profile 56 4.3.2 Chamber Efficiencies 57 4.3.3 Beam Pion Content ?. 59 5 Cross section & Acceptance 60 5.1 Introduction 61 5.2 Normalizations 61 5.3 Detector Acceptance 62 5.3.1 Updated Monte-Carlo 63 February 14, 1996 iv 5.3.2 Reconstruction of Simulated Data 65 5.3.3 Simulation Results 66 5.4 Cross-section 73 6 Conclusions 76 6.1 Summary 77 6.2 Further Improvements 77 6.2.1 Experimental Setup 77 6.2.2 Track Reconstruction 78 6.2.3 Monte-Carlo 78 Bibl iography 80 A S C X Desiderata 81 A.l 71° Decay 82 A. 1.1 The y-y Opening Angle 82 A. 1.2 Invariant Mass 83 A.2 Pauli Blocking 83 A. 3 Geometrical Acceptance And Rates 84 February 14, 1996 v List of Tables Table 3.1 Properties and dimensions of targets used 25 Table 3.2 Summary of run logs for SCX tests 26 Table 4.1 Summary of selection criteria for good 7i° events 44 Table 4.2 Analysis yields for one-pair and two-pair 7t° events. 56 Table 4.3 Incident beam normalizations 57 Table 4.4 Wire chamber efficiencies for electrons and protons 58 Table 5.1 Details of cross-section normalizations 61 Table 5.2 Values of normalization constants 62 Table 5.3 Monte-Carlo 7t° data generated for each target type and 7t° out-of-plane angular window 65 Table 5.4 GEANT reconstruction yields for weighted and unweighted 7t° angular distributions 73 Table 5.5 Required quantities for the cross-section calculations, along with intermediate results of C H 2 and C D 2 cross-sections 73 Table 5.6 Major sources of error in the cross-section calculation. 74 Table A. l Approximate breakdown of geometrical acceptance 84 February 14, 1996 vi List of Figures Fig. 1.1 Flowchart describing the overall CHAOS physics program and the inter-relationships within 3 Fig. 2.1 A view of the magnet showing the two poles, return yokes (with the near one removed), and the central bore for target placement. The Cerenkov counters are visible between the coils, but the wire chambers are barely discernible between the pole faces 9 Fig. 2.2 Detector elements within the magnet pole faces, including WC.l, WC2, WC3, WC4, Cerenkov counters and scintillators, and related support electronics, shown with some components removed for clarity 10 Fig. 2.3 A section through the central region of the detector, showing details of the pole faces, four wire chambers, scintillators and Cerenkov counters 12 Fig. 2.4 A single CFT block, showing the AEi , A E 2 L , and AE 2 R scintillators, along with the Cerenkov detector. Also shown are the associated light guides 13 Fig. 3.1 The CHAOS detector as defined in the GEANT Monte-Carlo package. The CFT blocks are visible, as are the AE scintillators and the four wire chambers. At the center is an L H 2 cylindrical target. A section of the beam pipe and an in-beam scintillator can be seen 18 Fig. 3.2 A typical GEANT event showing the incident n+ entering the target and reacting to produce a 7 t ° , which then decays into two gammas 21 February 14, 1996 vii Fig. 3.3 GEANT histograms of gamma-gamma opening angles and e e" separations for each pair at WC1 23 Fig. 3.4 Placement of CHAOS with respect to the beam, as determined by RAY. CFT blocks 19 and 10 are removed to provide the beam entrance and exit 24 Fig. 3.5 Rough diagram of the lead converter's construction (top view), not to scale. The support bolt is used to both hang the target from the frame and hang the frame from an aluminum pole 25 Fig. 4.1 WC3 X(t) polynomials spanning the entire range of incident track angles. Though curves for some angles are difficult to resolve, it is apparent that significant nonlinearities exist 30 Fig. 4.2 Dot plots used in particle identification: AEj pulse height vs. momentum, Cerenkov pulse height vs. momentum, and Cerenkov vs. AEj pulse height 32 Fig. 4.3 Sample "one-pair" events showing the proton and the e+e" pair from gamma conversion in the lead converter. All chamber anode wires are shown, along with the AE's and CFT's. Blocks firing are marked, and pulse heights are indicated by relative sizes of bars placed outside the CFT's 34 Fig. 4.4 Sample "two-pair" events showing the products of both gammas converting in the lead 35 Fig. 4.5 Sample "two-pair" event, showing chamber hits. There are two possible ways of assigning e+'s and e"'s to each pair. The combinations are labelled "A" or "B" 36 Fig. 4.6 One-pair event where pair tracks do not intersect. Also shown are the proton and incoming beam tracks, and the target outline 37 February 14, 1996 viii Fig. 4.7 A one-pair event with a potentially misleading 2 e e" vertex located on the wrong side of the target 38 Fig. 4.8 Fourth order polynomial fit to determine proton energy losses in the lead converter. AE is taken as a constant for KE > 180 MeV. 41 Fig. 4.9 One-pair proton momenta histograms: (a) raw momenta, (b) momenta corrected for losses in the lead, and (c) momenta corrected for losses in the target and the lead 42 Fig. 4.10 Chi squared of track-sorting for good 1-pair and 2-pair events 43 Fig. 4.11 Histograms associated with cuts dealing with e+e" pair vertex information for good one-pair events from both experimental data and GEANT-generated data as described in section 5.3. Shown are the invariant mass, WC1 e+e" hit separation, and distance of closest approach of the e+ and e", with applied cuts corresponding to 50 MeV, 90 mm, and 10 mm respectively 45 Fig. 4.12 7 t ° vertex dotplot (good 1-pair events) showing a clear C H 2 target outline as well as background from a portion of the lead converter. The box used for the vertex cut is indicated. Dimensions are in the horizontal plane of CHAOS 46 Fig. 4.13 Opening angle distribution of gammas for one pair events with no cuts applied. The 2 n d y's momentum is inferred. There is no apparent structure at around 50° 47 Fig. 4.14 Opening angle spectra of gammas for two-pair events, for raw events (top) and good two-pair (all cuts applied) events (bottom). The effect of the Oyy cut is obvious. Note, however, that some events at larger opening angles are also rejected 48 February 14, 1996 ix Fig. 4.15 Sample of a reconstructed event that mimics a two-pair event, but is in fact due to a single initial gamma producing two e+e~ pairs in the converter. 49 Fig. 4.16 Plots of e+e" conversion positions (top) and conversion radius (bottom) for good one-pair and two-pair events (CH2 target). Visible are the lead converter outline and the WC1 position from tracks that share hits in that chamber. 50 Fig. 4.17 Proton and 7t° angles for good one-pair C H 2 events. Proton angles are skewed forward, 7C° angles slightly backwards, though mainly focussed on the lead. Peak asymmetries have been reproduced in GEANT. 51 Fig. 4.18 TC° angular distribution for good two-pair events in C H 2 51 Fig. 4.19 Plots of e+e" invariant mass vs. conversion radius for C H 2 for both (a) good events and (b) the same but without treating as a special case e+e" pairs that share WC1 hits. Both plots indicate the position of the lead converter, and show various structures due to aliasing effects. The position of WC1 is also apparent 52 Fig. 4.20 Example of a reconstructed event with selected e+e" vertex outside the WC1 radius, as indicated in the plot 54 Fig. 4.21 Reconstructed 7t° invariant mass distributions, and 71° and proton missing mass distributions for events on GH 2 (top four). Also' shown (bottom four) are the equivalent GEANT invariant mass and missing mass predictions from studies in section 5.3 55 Fig. 4.22 Plots of incident beam projection onto the target plane, for C H 2 and C D 2 targets, and gated on good 7t° events and sample beam events : 57 February 14, 1996 x Fig. 4.23 Incident beam timing with respect to a BL1A capacitive probe. Pion and protons are easily separable....: 59 Fig. 5.1 Out-of-plane 7t° angles from GEANT for good one-pair and two-pair reconstructed events. The plane of the detector corresponds to 90° 64 Fig. 5.2 GEANT gamma-gamma opening angles including Fermi-motion effects. The histogram is a little broader than Fig. 3.3 but a selection cut at 40° is still valid 66 Fig. 5.3 7T° scattering angles from GEANT for simulated first-level triggers and reconstructed one-pair and two-pair events, for both C H 2 and CD 2 targets 68 Fig. 5.4 GEANT-reconstructed counterparts to Fig. 4.16 and Fig. 4.17, for the C H 2 target. The e+e" vertex positions and radii (top four) reproduce the experimental distributions fairly well, as do the one-pair proton and 7t° scattering angles (bottom) 69 Fig. 5.5 One-pair 7t missing masses calculated from simulated data. The sequence of plots indicates the effects of corrections applied cumulatively to the missing mass calculations. Plot (a) is calculated using reconstructed momenta; plot (b) uses the in-plane components of the true momenta at the interaction vertex; plot (c) extends this to a three-dimensional calculation; and plot (d) further includes the target neutron's Fermi-momentum 70 Fig. 5.6 Energy and angular 7t° residuals for one- and two-pair events, based on summed C H 2 and C D 2 results 71 Fig. 5.7 Weighting function for reconstructed GEANT events. Squares are ratios of deuterium to SAID data 72 February 14, 1996 xi Acknowledgments I am indebted to a great many people, more than can be mentioned in this brief space. How-ever, I would be remiss if I did not acknowledge the following people in particular. I am grateful to my supervisor, Dr. Greg Smith, for his advice, guidance, and patience during the course of this thesis. My co-reader, Dr. Garth Jones, deserves special thanks for his unflagging support in all kinds of weather. In addition, I would like to thank Dr. Martin Sevior for first introducing me to and encouraging my work in this field. Thanks are also due to Pierre Amaudruz, Larry Felawka, Gertjan Hofman, Mohammad Ker-mani, and Rudi Meier, whose help at various stages of my project has been invaluable. Finally, I would like to thank my mother and father, Raj and Mike, for their support over the years. February 14, 1996 xii Chapter 1 In t roduct ion CHAPTER 1 Introduction February 14, 1996 1 Chapter 1 Introduction The purpose of this thesis is to examine the feasibility of using the Canadian High Accep-tance Orbital Spectrometer (CHAOS) in situations that require the detection of secondary 7t°'s. This entails simulation of the modifications necessary to allow rt° detection and optimization of the associated parameters, followed by analysis of real data taken during a test run in the Summer of 1994. The capability of 7 t ° detection would greatly enhance the utility of the spectrometer by providing opportunities for experiments that complement the goals of the existing CHAOS phys-ics program. 1.1 The Physics Program The experimental goals of the program, their inter-relationships, and the overall methodolo-gy are best summarized in Fig. 1.1. There is a natural division into a (7C,2TC) program and a 7cN program, although the underlying physics of the two are intimately related through diagrams of the type indicated in the figure, as well as higher orders which consist of n% scattering. The result-ing data are complementary. 1.1.1 The (7C,27r) Program The aim of this program is to investigate the reaction H(TTT,2K) at several incident pion bombarding energies.1 2-, 3-, and 4-fold differential cross-sections will be measured for the fol-lowing reactions: 7t"p —> TC+TC"n Tt"p -> 7C"7t°p 7t+p -> Tt+7t+n K + p -» 7t+7C°p These cross-sections will then be compared to theoretical predictions of several models, and the data phase-shift analyzed to extract the S-wave contribution to the cross-section. Exploiting the Chew-Low method, nn scattering amplitudes can then be extracted, leading to the determination of the S-wave isospin 0 and 2 nn scattering lengths and a^ . These values can provide a strin-gent test of chiral perturbation theory (%PT) through comparison with its predictions: 1. This is currently under study by M. Kermani as a Ph.D. thesis. February 14, 1996 2 Chapter 1 Introduction (K,2K) Program H(TC,2TC) 2-,3-,4-fold Phase do atot Space Models: Johnson Oset Bholokov Chew-Low 7tp Program 7ip d a ao. Filter PWA TCP A. a 0 a 0 a0 > a2 a(7C7C) , 5(TCTC) 0(7171) Tcp SCX & A an &Ay Charge Independence Violation W Tip CNI M I Term ss of p Fig. 1.1 Flowchart describing the overall CHAOS physics program and the inter-relationships within. February 14, 1996 3 Chapter 1 Introduction a° = (0.20 ±0.01) m^1 a° = (-0.042 ±0.002) m"1 These results also enhance investigations in the 7tp program. 1.1.2 The 7ip Program This is a broad program encompassing several avenues of research. Currently under way is a study of T i p analyzing powers2 with the ultimate goal of determining the strange-quark content of the proton. The analyzing power Ay is defined by: da(T) -dr j ( i ) y ~ P( i )do(T) +P(T)da( i ) where the da's and P's refer to the cross-sections and target fractions corresponding to each target polarization state. It can be seen that Ay is insensitive to the absolute normalization that is re-quired in differential cross-section measurements. As. well, since the analyzing power essentially examines interference effects, it is particularly sensitive to smaller values of partial waves, more so than differential cross-sections. This feature will be exploited to help differentiate between conflicting existing low-energy cross-section data sets by comparing their predictions for Ay with that measured. Together with the analyzing power results, differential cross-section data may be used to de-termine the S and P wave isospin even scattering lengths aQ+ and a | + along with the T E N scatter-ing amplitude at v=0, t=0, where v = (s - u)/4m and t, s, and u are Mandelstam variables. The pion and proton masses are given by p and m. Chiral perturbation theory relates the TCN scattering amplitude, D + , to the TCN 2 term at the Cheng-Dashen point (v=0, t=p2) via the relation £ = F„ D+(2p2), where the pion decay constant Fn = 92.4 MeV [1]. Chiral symmetry is then invoked to link X to the rj-term matrix element a = ^ (pi m (uu + dd) |p> , where m = ^ (mu + m d). %PT predicts Z = rj + 15 MeV according to the latest calculations [2]. 2. This is being pursued by G.Hofman as a Ph.D. thesis. February 14, 1996 4 Chapter 1 Introduction Finally, SU(3)-symmetry can be used to relate the G-term to the observed baryon mass spec-trum and the so-called strange sea quark content of the proton via An analysis of cumulative TIN scattering data [2] yields a value of £ = 60 MeV, resulting in a val-ue of y ~ 0.2, and implying a 10% strange quark content. Another proposed area of study deals with 7irp elastic scattering in the Coulomb-nuclear in-terference (CNI) region. This takes advantage of the fact that nuclear interactions are effective over a large angular range while Coulomb forces become important at small angles. Hence there is an angular region within which the two forces have comparable strengths. Consequently, the re-sulting interference can be expected to have the most pronounced effects on cross-sections in this same region and, since the Coulomb interaction is well-understood, it is possible to use such a measurement to determine the magnitude and sign of the real part of the nuclear amplitude at for-ward angles. By comparison, typical larger-angle measurements rely on an extrapolation to for-ward angles from regions dominated by nuclear effects. In providing the real part of the riN forward scattering amplitude, CNI scattering data thus allow a direct determination of the £ term. As well, such data may be used to investigate the breakdown of charge independence. The final piece of the 7tp program, and the subject of this thesis, involves the study of pion-nucleon single charge exchange (SCX). Future experiments propose to measure da/dQ and Ay for 7t_p —» TC°n in an effort to detect charge-independence violation for the 7T.N coupling constant. By measuring the differential cross-section at t=0 and making use of forward dispersion relations, it is possible [3] to extract the product of the charged and neutral coupling constants without resort-ing to a PWA. Alternately, PWA's may be calculated in order to directly compare isospin-1/2 and isospin-3/2 amplitudes for 7rrp elastic and SCX reactions. As well, these data further enhance the database used to calculate the £ term by providing additional constraints on the PWA's used in its calculation. a = 35 + 5MeV i - y where y = 2(piss |p) (p| uu + dd |p> February 14, 1996 5 Chapter 1 Introduction 1.2 Theoretical Background Much of the theoretical background that motivates the CHAOS physics program and en-ables interpretation and analysis of its results is based on the formalism of chiral perturbation the-ory, essentially a low-energy perturbative description of quantum chromodynamics (QCD). As such, the theory warrants a brief description. 1.2.1 Chiral Symmetry At its lowest level, chiral physics deals with helicity related effects in the QCD regime. Re-call that helicity is defined as A = P S i.e. it is just the projection of spin in the particle's direc-tion of motion. Helicity states are typically characterized as left- or right-handed. Proceeding further, let us consider quark masses, limited for the time being to u and d quarks. Since they are usually "dressed" — surrounded by a cloud of virtual gluons and quark-antiquark pairs — there is a measurement distance implicit in any stated value of the mass. Thus, the dressed quark mass is termed as the constituent mass, while the undressed quark mass is termed the bare or current mass. Now, consider the quark mass contributions in a typical nucleon (~lGeV) where it is assumed the mass M(N) = Z(constituent quark mass). This implies that M(gluons + qq) ~ 300 MeV, whereas M(u) ~ 5 MeV and M(d) ~ 7 MeV. The strong suggestion here is that setting the u and d quarks masses to zero would not affect hadronic masses very much, and would have a small physical effect. First define a left- and right-handed quark doublet as = 2 d + Y 5 ) 7 * R = j d - Y S ) 7 L+R Projection Operators ^ Then, in the limit of vanishing bare quark masses (the chiral limit) the left- and right-handed terms in the QCD Lagrangian decouple to give L = -XVGuvk + W \ + v v V gluon field left-handed right-handed strength term term term February 14, 1996 6 Chapter 1 Introduction This Lagrangian obeys both SU(2) as well as SU(2) L® SU(2)R symmetry. Likewise for hadrons isotopic SU(2) symmetry still holds. However, nucleons are massive so they have definite helicity states, and therefore SU(2)L® SU(2)R symmetry no longer holds. The situation here is one in which the system's Lagrangian possesses a symmetry which the physical states do not. This is an example of what is termed Spontaneous Symmetry Breaking (SSB). 1.2.2 Chiral Perturbation Theory Goldstone's theorem posits that any SSB is accompanied by a vacuum excitation of mass-less zero-spin bosons. In the framework previously described these excitations correspond to the pions, which are considered to be lowest-energy modes of the QCD vacuum. At low energy, in the chiral limit, these Goldstone bosons dominate the behaviour of the system. As the quark masses are "turned on", the pions — pseudoGoldstone bosons — acquire mass which is still relatively small compared to other hadrons and, hence, their poles still dominate the low-energy behaviour. Whereas QCD is successful at describing high-energy interactions perturbatively in terms of the strong (running) coupling constant ocs, this approach fails at low energies since ocs becomes too large. Chiral perturbation theory manages to describe physics at large distances/lower ener-gies by taking advantage of chiral symmetry effects. The theory does this by essentially construct-ing an effective Lagrangian that possesses all the symmetries of QCD, but which treats the quark (pion) masses in a perturbative fashion, e.g. H X P T = H 0 + H l ' chirally quark-mass invariant expansion This is the framework of Chiral Perturbation Theory. It links the low- and high-energy QCD re-gimes, thereby providing opportunities for low-energy tests of QCD itself. February 14, 1996 7 Chapter 2 The C H A O S Spectrometer CHAPTER 2 The CHAOS Spectrometer February 14, 1996 8 Chapter 2 The CHAOS Spectrometer This chapter provides a brief overview of the major elements of the CHAOS detector and associated trigger systems, which are thoroughly explained in Refs [4], [5], and [6]. The spec-trometer is built around a large dipole magnet, and consists of a central target area, four self-sup-porting wire chambers used in track reconstruction, and an outer segmented ring of scintillators and lead glass Cerenkov counters for particle identification (PID). This arrangement is comple-mented by a sophisticated multi-level trigger system tailored to the requirements of the detector. 2.1 The Magnet The CHAOS magnet is a cylindrical dipole with poles 95 cm in diameter, capable of sus-taining magnetic fields up to 1.6 T. The central axis consists of a bore designed to facilitate inser-tion and removal of a variety of targets. In order to support a 360° range of scattering angles, an atypical magnetic field orientation was chosen, being perpendicular to the scattering plane. Gross elements of the magnet and detector are illustrated in Fig. 2.1. Fig. 2.1 A view of the magnet showing the two poles, return yokes (with the near one removed), and the central bore for target placement. The Cerenkov counters are visible between the coils, but the wire chambers are barely discernible between the pole faces. The bulk of the instrumentation is placed on a platform above the magnet, with access to the chambers gained via removal of the magnet's top. February 14, 1996 9 Chapter 2 The C H A O S Spectrometer 2.2 Wire Chambers WC1 and WC2 These two innermost proportional chambers are both situated at approximate radii of 115 mm and 229 mm respectively. WC1 has an anode pitch of 1 mm while WC2 has a pitch of 2 mm, with both chambers possessing a half-gap of 2 mm and containing 720 anode wires. Each cham-ber is also provided with cathode strips inclined at 30° with respect to the anode wire, for use in determining vertical track coordinates. The WC1 cathode pitch is 2 mm, the WC2 pitch 4 mm. Angular resolution in the scattering plane is better than 1/2° while the vertical resolutions of WC1 and WC2 are 2.4 mm and 0.7 mm respectively. Both chambers are designed to operate in high pion fluxes of up to 5 MHz. As well, they are constructed of low-density materials and are self-supporting in to order minimize multiple scatter-ing effects. These chambers are described in great depth in Ref. [4]. WC1 and WC2 are visible in Fig. 2.2, a view of the area between the magnet pole faces. Fig. 2.2 Detector elements within the magnet pole faces, including WC1, WC2, WC3, WC4, Cerenkov counters and scintillators, and related support electronics, shown with some components removed for clarity. February 14, 1996 10 Chapter 2 The C H A O S Spectrometer 2.3 Wire Chamber WC3 This drift chamber is designed to operate in the typically high magnetic fields associated with CHAOS, and provides spatial resolution of better than 200 pm. It is positioned at a radius of approximately 344 mm and has a half-gap of 3.75 mm. Anode and cathode wires alternate, each at a pitch of 15 mm, and the chamber overall comprises 144 nearly rectangular drift cells. Like WC1 and WC2, this chamber is also constructed to minimize multiple scattering effects. The high CHAOS magnetic field renders useless traditional methods of removing the left/right ambiguity associated with drift chambers. Thus, each drift cell is equipped with four cathode strips and the L/R ambiguity resolved by considering the induced signal on various combinations of these strips. The technique employed is described in detail in a previous publication [7]. Since the strips are vertical, they yield no z-coordinate information. Together, the three inner wire chambers pro-vide position information used by the second level trigger (2LT) in making its decision. 2.4 Wire Chamber WC4 In order to achieve a momentum resolution of -1% and to provide some redundancy for im-proving the robustness of track-sorting algorithms, WC4 is a vector drift chamber placed in the fringe field of the CHAOS magnet. The geometry consists of 100 trapezoidal cells, each covering a 3.6° angular range. Each cell contains 14 anode wires on a radial pitch of 5mm, with a 250 pm perpendicular stagger to aid in track L/R resolution. The first wire is positioned at a radius of -613 mm. The middle eight anodes of a cell provide a vector trajectory for an incident track, with each wire obtaining an average spatial resolution of -120 pm. Two anodes are -1 kQ resistive wires which provide vertical coordinate information with a resolution of -2.3 mm. Fig. 2.3 pro-vides a sectional view of the previously described four chambers as well as elements of the first level trigger. 2.5 First Level Trigger The Cerenkov counters together with their associated scintillators make up a cylindrical ar-ray of 20 blocks (an 18° span each) just outside the WC4 radius, as can be seen in Fig. 2.1. These CHAOS Fast Trigger (CFT) blocks serve a two-fold purpose: they provide energy-loss informa-February 14, 1996 11 February 14, 1996 12 Chapter 2 The CHAOS Spectrometer tion to be used in PID determination, and also determine the first-level trigger (1LT). Triggering is based simply on particle track multiplicity. Both these aspects are discussed in detail in Ref. [8]. Each CFT block consists of an inner scintillator AEi , two abutted scintillators AE 2 L (left) and AE 2R (right), and an outer Cerenkov detector. The arrangement of these elements is shown in Fig. 2.4. AEi is 3 mm thick and approximately 178 mm high and, as can be seen from Fig. 2.3, it defines the detector's out-of-plane angular acceptance of ±7°. Together the AE2's are 230 mm wide, 180 mm high, and about 12 mm thick. The lead-glass Cerenkov counter is trapezoidal, and about 125 mm thick. Two of the CFT blocks are typically removed to provide for the beam entrance and exit, with veto counters (V) covering the exit hole. In addition there exist two in-beam scintillators: a 3.2 mm thick hodoscope (SI) just at the beamline exit, and a 1.6 mm thick beam-defining hodo-scope (S2) at the entrance into the detector. F i g . 2.4 A single CFT block, showing the A E i , A E 2 L , and AE 2 R scintillators, along with the Cerenkov detector. Also shown are the associated light guides. Some illustrative dimen-sions are given as well. February 14, 1996 13 Chapter 2 The CHAOS Spectrometer The trigger logic is completely programmable via Lecroy ECL logic modules. In terms of scintillator hits, a single CFT's firing is typically defined as either CFT = AEj or CFT = AE, • (AE 2 L + AE 2R) Thus, the first-level trigger can be described as 1LT = Sj • S 2 • V • [*£ (CFTs) > n] assuming both in-beam scintillators are required in the coincidence. The parameter n is program-mable depending on the particle multiplicity desired. 2.6 Second Level Trigger The typically large experimental background expected can overwhelm data acquisition computers. The design of the second-level trigger (2LT) [5] is motivated by the need to bring the first-level event rate down to a manageable level. The 2LT is a programmable, essentially hard-wired computer formed from various Lecroy ECL modules (e.g. ALU's, stacks, look-up tables). With it, one can perform fast postprocessing of position information from WC1, WC2, and WC3. Basically, all chamber hit combinations are looped over and searched for matches to prepro-grammed specifications. This prior programming determines three stages of trigger requirements. The first stage requires a single track defined by three chamber hits be found. It must be of a given polarity, have momentum in a specified range, and be within a certain range of the detector origin. As well, to reduce muon contamination from in-beam pion decay, the track's incoming trajectory must be within programed limits. A further two optional stages may be employed: one implements a momentum vs. scattering angle correlation requirement, while the second requires two tracks in the main stage with a mo-mentum sum in a specified range. February 14, 1996 14 Chapter 3 Experimental Setup & Data Acquisition C H A P T E R 3 Experimental Setup & Data Acquisition February 14, 1996 15 Chapter 3 Experimental Setup & Data Acquisition In May of 1994 a short test run was carried out to help evaluate the detection characteris-tics of the CHAOS detector by studying the single charge exchange (SCX) reaction 7C+n —> 7t°p on C H 2 and CD 2 . Since it is so short-lived (see section A.l), detection of the it® usually involves detection of the two decay photons. As a magnetic spectrometer like CHAOS is useful only for charged particles, it is further necessary to induce the decay y's to pair-produce in the vicinity of a high-Z converter material, yielding e+e" pairs which can be detected. Reconstruction of the origi-nal 71° dynamics can then proceed via analysis of the tertiary e+e" pairs. This chapter begins by describing the Monte-Carlo studies carried out to optimize the detec-tor configuration, along with some of the guiding considerations. The actual experimental setup employed for the test run is then presented, followed by a summary of the data acquisition. 3.1 Preliminary GEANT Studies Of critical importance is the design of the converter used to induce pair-production. It was decided for this test to use a cylindrical lead converter placed around the 7C° production target and within the WC1 radius, with segments cut out to provide for a beam entrance and exit. The most important information required prior to the test was the optimal converter thickness and radius, along with a rough idea of the detector acceptance. To this end, extensive use was made of a CHAOS spectrometer model implemented using the GEANT [9] Monte-Carlo package. 3.1.1 The Detector Model A GEANT-based body of code (termed CHAOSSIM) has been developed by the CHAOS user group. It is constantly being updated and improved, with the ultimate goals of providing an accurate physical simulation of the detector, and producing equivalent-to-online data for testing of analysis methods and software. At the time of these 7t° tests (May 1994), the code was at the stage of nearly completely simulating the physical aspects of the detector. All the wire chambers were implemented, including the various construction materials but excluding the wires them-selves. The CFT blocks were included as well, along with major elements of the magnet. A choice of target types was available, with the inclusion of any extra materials required for cryogenics. Using this version of CHAOSSIM, a cylindrical lead converter was added to the geometry, and extensive modifications to the code were made to facilitate monitoring of vP decays. On a per February 14, 1996 16 Chapter 3 Experimental Setup & Data Acquisition event basis, this involved the run-time storage of all dynamical information for n s and all their daughter particles. This was necessary in order to later distinguish actual (pair-produced) e+e" pairs from accidental pairs. The GEANT-based detector model can be seen in Fig. 3.1. The fact that this model uses a cylindrical L H 2 target is of little importance, since the 7t° decay photons easily pass through it with low interaction probability. The Monte-Carlo results should be valid for another target material of differing geometry. Also note that the definition of the target is used primarily for energy-loss purposes; the actual reaction taking place at the interaction vertex is user-defined. 3.1.2 Monte Carlo Setup An earlier 7t° detection test run was inconclusive. Recurring wire chamber problems made it impossible to judge the suitability of chosen beam, detector, and converter parameters. It was de-cided for the May 1994 test run to err on the side of caution by choosing test parameters designed to yield the highest event rate possible. 3.1.2.1 Beam Momentum The simulation beam energy was chosen to be -180 MeV. The reasoning behind this deci-sion is three-fold. First, the SCX cross-section is peaked around this energy [10], helping to max-imize the event rate. Secondly, this energy severely limits the phase space available to a pion production reaction such as 7t+n —> 7t+7t°n, allowing the analysis to concentrate on the quasi-elas-tic SCX reaction 7t+n -> 7t°p. The third reason involves consideration of electron ranges in the detector and how this var-ies with incident beam energy. In a magnetic field B an electron's radius of curvature is given by P e R e = > where P e is the electron momentum in MeV/c, B is the field strength in Tesla, and dis-tances are in cm. It can then be shown that for a converter radius R^., the electron's maximum range — its greatest radial distance from the converter — is given by D = R e + JR2, + R g - R c , where the electron is assumed to be from an e+e" pair of small opening angle. This maximum range essentially determines whether or not a pair will be reconstructible i.e. whether the range will allow it to reach WC4. It can further be assumed that R c « R e since, by the detector's geome-February 14, 1996 17 Chapter 3 Experimental Setup & Data Acquisition Fig. 3.1 The CHAOS detector as defined in the GEANT Monte-Carlo package. The CFT blocks are visible, as are the AE scintillators and the four wire chambers. At the center is an L H 2 cylindrical target. A section of the beam pipe and an in-beam scintillator can be seen. The panelling evident in the three inner chambers is purely an artifact of the 3D rendering. Not shown are the chamber wrapping materials, the lead converter between WC1 and the target, and the magnet. February 14, 1996 18 Chapter 3 Experimental Setup & Data Acquisition try, R c must be less than the WC1 radius and R e must be -70 cm. This assumption yields 3B Ideally, one would choose the highest beam energy and lowest magnetic field that still per-mitted good track reconstruction/sorting. However, the May 1994 test was a short run inserted into a larger data-taking program and, as such, major changes to the detector configuration were not possible. While the incident pion momentum PK was easily changed, rearrangement of CFT blocks was precluded, resulting in the beam entrance and exit regions remaining fixed, with a beam deflection of 18° within CHAOS. This constant deflection implies a constant ratio P^/B, with consequences for the maximum pair range D. Since the incident beam energy is shared among four electrons/positrons first through a two-body process, followed by a decay, followed by two pair-productions, one expects P e to change more slowly than Pn. To maintain constant beam deflection however, B must change at the same rate as Pn, resulting in a decreasing pair range D as PK is increased. Hence, a greater event rate can be obtained with lower incident beam momentum. 3.1.2.2 Converter Radius The constraint of fixed beam deflection limits what can be done to improve the pair range D. However, simply reducing the distance pairs must travel to reach WC4 will increase the event rate. One cm less of distance is roughly equivalent to a few MeV more of total pair energy. As-suming it would not hinder offline track-sorting, the best converter radius is as close to WC1 as possible. During the May 1994 test run this was not possible, as it would have required removal of the top of CHAOS, a major operation. Thus the radius was chosen to be 6 cm, close to the radius of the central bore. 3.1.3 Event Processing 3.1.3.1 Evaluation Criteria Since, just prior to the test run, the simulation code used did not yet permit offline analysis using the standard CHAOS software packages, the best one could do to optimize converter pa-rameters was to study the types of events which are potentially reconstructible offline. Unambigu-February 14, 1996 19 Chapter 3 Experimental Setup & Data Acquisition ous determination of a K decay is possible only if both decay photons convert in the lead, and the secondary e+e" pairs pass through all four wire chambers. Converter optimization is then a matter of maximizing the number of these so-called "two-pair" events for a given number of incident beam particles. 3.1.3.2 Single Event Procedure A GEANT Monte-Carlo event, of which Fig. 3.2 is an example, develops as follows: 1. A single incident beam particle is created in the beam pipe, with a gaussian spread in momentum and initial position typical of the channel. It is then tracked by GEANT into the detector. 2. Upon entering the target, an interaction is forced a random distance within. The reac-tion products of 7U+n —> 7U°p are produced according to two-body kinematics, and the resultant particles are tracked through the detector. 3. Details of the Tt° formation and decay are stored, as well as subsequent pair-production information for the decay photons. Position, momentum, energy-loss, and historical data is saved for electrons and positrons passing through each of WC1, WC2, WC3, WC4, the converter, and any other detector elements defined as "sensitive." 4. Once all particles have been tracked, the stored information is analyzed to check if the current event is potentially reconstructible offline i.e. if two e+e" pairs reach the mid-point of WC4 while passing through all the inner chambers. Determination of a valid pair is made by sorting through the stored data and attempting to match arbitrary e+ and e" origin points to each other and to the recorded gamma conversion positions. 3 . 1 . 4 M o n t e - C a r l o R e s u l t s The optimal thickness of lead was determined to be roughly between 2 and 3 mm. As the thickness falls below 2 mm, the number of reconstructible events decreases in keeping with the reduced conversion efficiency. Likewise, thicknesses greater than 3 mm result in e+e" pairs losing too much energy to successfully reach WC4. These losses would be the greatest factor limiting energy resolution in the offline analysis. Tuning the converter thickness is thus a trade-off be-February 14, 1996 20 Chapter 3 Experimental Setup & Data Acquisition Fig. 3.2 A typical GEANT event showing the incident 7t+ entering the target and re-acting to produce a 7t°, which then decays into two gammas. One gamma converts into an e+e" pair in the lead converter, while the other continues through and eventually cre-ates a shower in the magnet's steel. The dotted straight tracks are photons, mainly from bremsstrahlung, which is the dominant source of energy loss in lead for these e+e" pairs. February 14, 1996 21 Chapter 3 Experimental Setup & Data Acquisition tween good event statistics and good energy resolution. Again, in an effort to gain the maximum event rate, it was decided to use lead 3 mm thick for the May 1994 test run. For this thickness, the average AE/E of pairs that reach WC4 is -9%. Brief simulations were also performed to verify the arguments on page 19 regarding the most advantageous incident beam momentum and converter radius. Maintaining a constant beam deflection within the detector, incident beams of 200 MeV and 300 MeV were compared, and bore out the decision to use a lower incident beam momentum. The benefits of a larger converter radius were also verified in a comparison of simulations for converter radii of 6 mm and 9 mm. Some GEANT histograms useful in later offline analysis are shown in Fig. 3.3. The gamma-gamma opening angles have a clear minimum at 50°, and e+e" tracks are separated at WC1 by typ-ically less than 9 or 10 cm. 3.2 Experimental Setup 3.2.1 Beam Channel & Detector The channel was tuned for 287.5 MeV/c (180 MeV) TU+'S, and the slits adjusted to provide a beam rate of -3.5 MHz. In order to be able to use the lowest magnetic field possible, the program RAY was used to help choose the best translation and rotation of CHAOS within the experimental area, as illustrated in Fig. 3.4. Instead of passing through the centers of the entrance and exit holes, the beam is allowed to "crowd" the edges slightly. The final magnetic field used was 0.3 T. The translation is expressed perpendicular to the beam line, while the rotation is counter-clock-wise, with 0° corresponding to the CHAOS x-axis parallel to the beam. The target angle is mea-sured clockwise from the CHAOS x-axis to a line normal to the plane of the target, and is needed to ensure a constant depth when using a rectangular target. 3.2.2 Trigger System The first-level trigger system was set up to require a coincidence between the in-beam scin-tillators, no hit in the veto counter, and three or more CFT blocks firing (using AE^AE^). This CFT multiplicity was chosen to help reduce the event rate from elastics and, at the same time, ad-February 14, 1996 22 Chapter 3 Experimental Setup & Data Acquisition 5000 4 0 0 0 3000 2000 1000 0 1600 1400 "i r ^ 1 1 1 1 1 1 1 1 1 1 1 r 50 100 150 7 — 7 O p e n i n g A n g l e [cleg.] _1 I I I I I I I I I I I I I I I I I I I I I l I I I I I L 200 ~i 1 1 1 1 1 1 1 I j 1 1 1 1 1 1 1 1 1 1 1 1 1 r 1 1 1 1 r 5 1 0 + _ 15 20 25 WC1 e e S e p a r a t i o n [ c m ] Fig. 3.3 GEANT histograms of gamma-gamma opening angles and e+ e" separations for each pair at WC1. These will be useful in establishing cuts to be used later in the of-fline analysis. February 14, 1996 23 Chapter 3 Experimental Setup & Data Acquisition 1 000 CHAOS Position Translation = -5.21 cm Rotation = 19° Target Angle = 9.1° -50 0 -1 00! Fig. 3.4 Placement of CHAOS with respect to the beam, as determined by RAY. CFT blocks 19 and 10 are removed to provide the beam entrance and exit. mit the possibility of an e+ and an e" going into the same block. One problem is that such a trigger requirement is biased towards background events that produce large showers. Configuration of the second-level trigger required some care, as the high particle multiplici-ty and the presence of the lead converter were atypical of previous 2LT use. The two optional stages placing constraints on the momentum sum and momentum vs. scattering angles were dis-abled, leaving only the primary stage decision based on polarity, momentum range, and impact parameter i.e. closest track distance to the origin. It was required that a single negative polarity track be found, of momentum between 11.9 and 8000 MeV/c, passing within 80 mm of the origin. This radius included both the converter and target within its bounds. 3.2.3 Targets and Converter Two targets were used for the test run: one of polyethylene (CH2) and one of deuterated polyethylene (>99% CD 2). The C H 2 target was fairly thick in an effort to gain a high event rate, February 14, 1996 24 Chapter 3 Experimental Setup & Data Acquisition while the C D 2 target was useful because of its larger fraction of loosely bound neutrons. Note that gammas are expected to pass through these targets with low interaction probability; hence, target thicknesses will have negligible effect on gamma resolution. Properties of the targets used are summarized in Table 3.1. Also, the C H 2 data may be used as background for the CD 2 data, thus enabling the rough estimate of a deuterium cross-section in the final TC° analysis. Target Thickness (cm) Width (cm) Height (cm) Density (g/cm*) N t 2 (moles/cm ) C H 2 3.81 5.0 25. 0.93 0.253 CD 2 0.584 5.0 6.0 1.079 0.0393 Table 3.1 Properties and dimensions of targets used in the May 1994 test run. The construction of the converter is illustrated in Fig. 3.5. It consists of two halves of a lead cylinder of radius -5.4 cm and 3 mm thickness, made up of individual sheets 1 mm thick layered Lead Sheets Beam Window Fig. 3.5 Rough diagram of the lead converter's construction (top view), not to scale. The support bolt is used to hang either target from the frame and hang the frame from an aluminum pole. February 14, 1996 25 Chapter 3 Experimental Setup & Data Acquisition and suspended from an circular aluminum support, which in turn hangs from an aluminum pole capable of being lowered down the central bore of CHAOS. The support mechanism is the same one used in an earlier vP test, and was reused in the May 1994 test for expedience's sake. The C H 2 target is drilled near the top and hung from a support bolt through the aluminum ring, while the C D 2 target, being smaller and costlier, sits in a thin aluminum frame which in turn is hung from the support bolt. Since the bore pole and targets share the same support bolt, thick targets are pushed off center in order to keep the converter centered. This resulted in the C H 2 target being shifted upstream approximately 2.75 cm. The widths of the beam entrance and exit windows are approximately 4.5 cm and 3.5 cm respectively. 3 . 3 D a t a A c q u i r e d n test data were gathered over a 20 hour period in May 1994. Table 3.2 is a condensation of the experimental log for that period of time. The column "Passed to 2 Level" indicates the Run Number Target Type Incident Beam 1st Level Triggers Passed to 2nd Level LAM's Events To Tape 730 5.9xl009 625406 560083 305901 305895 731 3.4xl008 35755 31933 17502 17502 732 7.50xl009 711866 659118 361290 361072 733 C H 2 7.55xl009 788033 704271 386892 386855 734 1.95xl009 205437 183267 100958 100952 735 2.32xl009 246694 219401 120793 120780 736 8.75xl009 936620 834967 457668 457507 737 1.03xl010 1109959 986825 540785 540651 T O T A L S 4.48xl010 4659770 4159721 2291789 2291214 738 1.29xl010 985875 923181 394357 . 394275 739 C D 2 9.6xl009 722937 676833 290581 290581 740 4.2X10 0 9 281012 278411 12842 12842 T O T A L S 2.67xl010 1989824 1878425 697780 697698 Table 3.2 Summary of run logs for 7t SCX tests. February 14, 1996 26 Chapter 3 Experimental Setup & Data Acquisition number of 1st level triggers that were successfully processed by the 2nd level trigger. For the trig-ger setup employed in this experiment, the ratio of the two is essentially the computer live time. February 14, 1996 27 Chapter 4 Data Analysis & Reconstruction CHAPTER 4 Data Analysis & Reconstruction February 14, 1996 28 Chapter 4 Data Analysis & Reconstruction This chapter describes the preparation and methods used in analyzing the May 1994 SCX data, along with results of the 7 t ° reconstruction and some related quantities useful later. 4.1 Analysis Setup 4.1.1 Chamber Calibrations Correct track reconstruction is predicated on having accurate knowledge of the positions of all wire chamber hits. For the inner chambers WC1 and WC2 this requires only translation and ro-tation offsets for each. WC3 and WC4 however, being drift chambers, require in addition calcula-tion of the relationship between TDC (time-to-digital converter) values and drift distances, summarized as X(t) polynomials. WC4 is the more straightforward of the two to calibrate, as it is located in a fringe-field area and comprises several wire planes. Calibration of WC3 is more in-volved since it is located in a region of high magnetic field. The nonlinearity introduced into the X(t) relations by this field must be dealt with by parametrizing the drift distance in terms of both time and incident track angle. All these quantities are determined using the standard CHAOS iterative calibration software [11]. The X(t) polynomials for a range of incident track angles are summarized in Fig. 4.1. The importance of the WC3 calibrations is underscored by the fact that the majority of the track-sort-ing problems seen in the preliminary offline analysis disappeared with the use of calibrated WC3 X(t) relations. For ease of calculation, drift distances are represented as angles. Recall from section 2.3 that each WC3 drift cell is instrumented with four cathode strips used in left/right determination. Previous CHAOS experiments operated at sufficiently high mag-netic fields that the best left/right resolution was gained by reading diagonal — as opposed to ad-jacent — strips. Comparison of the two methods for the 0.3 T magnetic field used in the May 1994 SCX test indicates that use of adjacent strips provides better left/right resolution. 4.1.2 Particle Identification The particle identification scheme used here [8] determines PID's by testing correlations be-tween particle momenta and energies deposited in the A E i and Cerenkov counters. It's primary goal is the identification of pions with as few false rejections of pions as possible. The algorithm February 14, 1996 29 Chapter 4 Data Analysis & Reconstruction Fig. 4.1 WC3 X(t) polynomials spanning the entire range of incident track an-gles. Though curves for some angles are difficult to resolve, it is apparent that sig-nificant nonlinearities exist. February 14, 1996 30 Chapter 4 Data Analysis & Reconstruction separates protons fairly easily, as they typically deposit large amounts of energy, but in the case of pions and electrons, distinction requires more care. What is done is to successively, conservative-ly, remove electrons and label what remains as pions. The scheme is modified slightly for SCX as we are interested in not falsely rejecting electrons. Proton separation remains the same, but cuts on electrons become fairly loose, with the remaining unidentified particles assumed to be elec-trons. While this method lumps together pions and electrons, there are no adverse effects, because the 7T° selection criteria used in the analysis make it extremely unlikely for a pion to successfully mimic an e+ or e" from a pair. This is helped by the fact that the beam energy is close to the pion production threshold, and so the majority of observed pions are n+ elastics as opposed to what might seem to be n+n pairs. Fig. 4.2 shows the momentum, AEj, and Cerenkov dot plots used for particle identification, comparing those for raw events against those for good events as deter-mined by the criteria of section 4.2. Notice how n+ elastics are rejected by the "good 7t°" selection criteria. At beam energies where pion production becomes a factor, the PID methods must be de-termined more carefully. 4.1.3 Skimming The relatively loose trigger constraints used in the test run lead to a bias in the recorded data towards "noisy" events containing a large number of CFT blocks firing. Reducing this data to a manageable amount for analysis requires reasonably efficient skimming criteria that do not reject good 7t° events. All the track reconstruction routines currently in use by the CHAOS group assume that each track is associated with a vector (track) in WC4. Since a valid WC4 track requires hits in at least three of the eight wire planes and typical anode efficiencies are greater than 85%, WC4 may be taken as nearly 100% efficient. Thus, the number of WC4 tracks in an event is a useful measure for skimming, since it helps define what can and cannot be reconstructed. As proton energy losses in AEi and A E 2 are much bigger than electrons and pions over a large momentum range, the PID efficiency for protons may also be taken as 100%, allowing pro-ton identification to be used in skimming with little fear of rejecting good 7t° events. In the offline analysis there are two classes of events that in principle provide enough infor-mation to reconstruct 7t° information. The first is a "one-pair" event in which a proton and e+e" February 14, 1996 31 Chapter 4 Data Analysis & Reconstruction W 400 < All Events i . . . . i ... i i .... i Good 7t° Events Pions Electrons Protons W 400 < Protons Electrons -400 -200 0 200 P (MeV/c) 400 600 -400 -200 0 200 P (MeV/c) 400 600 V 100 • Electrons Pions Protons o a <D 100 U • I Electrons Protons / -400 -200 0 200 P (MeV/c) 400 600 1 1 1 I 1 1 1 1 I 1 1 1 1 I 600 -400 -200 0 200 400 P (MeV/c) 2o 0 J Electrons o 1 5 0 a 1)100 Pions Protons > o a 1> too Electrons « . . . :fj| Protons 400 AE, —i— 200 40 0 AE, Fig. 4.2 Dot plots used in particle identification: AEi pulse height vs. momentum, Cerenkov pulse height vs. momentum, and Cerenkov vs. AE] pulse height. Protons are well separated because of large pulse heights, and most pions are identified as electrons due to loose PID cuts. This misidentification causes no problems in the analysis since almost all these "fake" electrons are rejected by 7t° event selection criteria, as can be seen in the PID histograms associated with good 7t° events deter-mined by the reconstruction algorithms. February 14, 1996 32 Chapter 4 Data Analysis & Reconstruction from a single photon conversion are detected, and the second is a "two-pair" event consisting of two e+e" pairs with an optional proton. To accommodate both these classes the skimming test was defined as [S(WC4 tracks) = 3] • [I (protons) = 1] OR [Z(WC4 tracks) > 4] • [E (protons) < 1] The first term selects only clean "one-pair" events, while the second selects all "two-pair" events along with any noisy "one-pair" events. This test combination rejected -64% of raw events. Other pion scattering analyses have made use of a skimming cut based on the scalar sum of the momenta of all tracks in an event. However, the momentum sum spectra of known good one-and two-pair events is fairly broad, and thus diminishes the effectiveness of this type of cut. 4.2 TC° Reconstruction 4.2.1 Introduction The reconstruction code attempts to build up a likely 7t° event from the information at hand, namely the predetermined PID's and sorted particle trajectories. The track sorting is accom-plished using code developed by Martin Sevior, employing an oc-|3 tree-pruning algorithm (called "tree_sort") to search for valid particle tracks, and requiring a track to have hits in all four wire chambers. Other track sorting routines exist that can do without some hits in the inner three cham-bers, thus potentially improving the overall experimental acceptance, but for the purposes of this test a four-hit requirement helps to remove any ambiguities arising from the high-multiplicity events under study. As well, it also simplifies wire-chamber efficiency normalizations later. The only exception to this requirement is that hits in WC1 may be shared by two tracks, which is nec-essary because preliminary GEANT studies indicated that many e+e" pairs had very small track separations at the WC1 radius and would produce overlapping chamber hits or clusters. Of the two types of 71° events being reconstructed, the "two-pair" variety is most useful as it provides sufficient information to fully identify the 7t° decay, while "one-pair" events require the inference of missing track parameters. Examples of reconstructed events of both types are giv-en in Fig. 4.3 and Fig. 4.4. February 14, 1996 33 Chapter 4 Data Analysis & Reconstruction J 1 L _ I I I I I I I I I I I I L L Fig. 4.3 Sample "one-pair" events showing the proton and the e+e" pair from gamma conversion in the lead converter. All chamber anode wires are shown, along with the AE's and CFT's. Blocks firing are marked, and pulse heights are indicated by relative sizes of bars placed outside the CFT's. February 14, 1996 34 Chapter 4 Data Analysis & Reconstruction J I I J I 1 I I 1 I I I I I I L L Fig. 4.4 Sample "two-pair" events showing the products of both gammas con-verting in the lead. February 14, 1996 35 Chapter 4 Data Analysis & Reconstruction 4 . 2 . 2 P r o c e d u r e The description of the procedure used to reconstruct 7t° information will focus primarily on "two-pair" events, with occasional reference made to the simpler methods used with "one-pair" events. The obvious first step in analyzing an event such as that in Fig. 4.5 is determining which Fig. 4.5 Sample "two-pair" event, showing chamber hits. There are two possible ways of assigning e+'s and e"'s to each pair. The combinations are labelled "A" or "B". opposite-polarity particles are associated with each pair. One possibility is to quickly determine this from the track sorting information at hand, such as clustering of WC1 hits for a given pair. However, these hits are not always closely spaced and, moreover, this method might ignore other potentially useful information. Thus, it was decided instead to calculate all the desired quantities for all combinations of e+'s and e"'s, and then use this information to select the combination rep-resenting a valid 7t° event. Fig. 4.5 illustrates these combinations. The sequence of calculations for a given combination is summarized as follows: 1. A circle is analytically determined from the three inner-chamber hits of each electron and positron track. The field here is sufficiently uniform that this is possible. February 14, 1996 36 Chapter 4 . Data Analysis & Reconstruction 2. Using these fits, intersections of the e+'s and e"'s are calculated for each pair. Also re-corded for each pair are the WC1 hit separation, the radial distance of the intersection from the lead converter, and the distance of closest approach of the e+e" tracks. There are four cases to be handled: a. If the tracks intersect at exactly one point, then that is taken as the gamma con-version point. b. If the tracks do not intersect at all, their distance of closest approach is calculated and, together with the circle information, used to determine the midpoint be-tween tracks at their closest approach. This point is recorded as the vertex. An example of this type of event is Fig. 4.6. Fig. 4.6 One-pair event where pair tracks do not inter-sect. Also shown are the proton and incoming beam tracks, and the target outline. c. If the tracks share a WC1 hit, then this hit is taken as the intersection point. This is the most reasonable interpretation, as there are many events of this kind and it is not likely that a pair is formed in the lead, scatters and crosses over, and then intersects once more at exactly the WC1 radius. Moreover, GEANT studies have shown such closely spaced tracks to be common. Treating this case as a "two-in-February 14, 1996 37 Chapter 4 Data Analysis & Reconstruction tersection" event results in misleading aliasing effects when trying to determine the intersection radius. This will be discussed and demonstrated later in section 4.2.4. d. The most common case provides a choice of two intersections. The vertex cho-sen is that which is closest to the lead converter radius and on the same side of the target as the pair's WC1 hits. This effectively requires that the e+e" pair and the original gamma be emitted in the same direction. The reason for this latter re-quirement is that sometimes the distance between the two intersections is suffi-ciently great that the vertices are on opposite sides of the target. It is often just a matter of chance then which vertex is closer to the lead radius. Accidentally pick-ing an opposite side vertex makes any TC° reconstruction meaningless. Fig. 4.7 il-lustrates a potential problem event if the correct vertex is not chosen carefully. 3. Once the correct intersections are worked out for each of the pair combinations, further calculations are made as follows: a. The e+ and e" vector momenta are worked out at each intersection and used to calculate the opening angle and invariant mass of each pair. For a true pair pro-, duction event the invariant mass at an e+e" vertex is expected to be close to zero. \ Fig. 4.7 A one-pair event with a potentially misleading 21 e+e" vertex located on the wrong side of the target. nd February 14, 1996 38 Chapter 4 Data Analysis & Reconstruction b. The total (vector) e e" momentum yields the momentum of the original gamma giving rise to the pair. This allows calculation of the gamma-gamma opening an-gle and invariant mass, which is expected to be close to the vP mass of 135 MeV. c. The TU° decay vertex is taken as the average of the two beam-gamma intersec-tions. This is done to improve position resolution. The method of selecting the better event combination, for example A or B in Fig. 4.5, was derived largely empirically. What is done is to choose the combination that minimizes the sum of e+e" vertex invariant masses. The small number of good two-pair events in the data set makes it possible to check this selection by visually inspecting events and verifying that the correct combi-nation was chosen. Of 200 events inspected in this way, none were seen to choose the wrong com-bination. One reason this criterion works well is evident from studying Fig. 4.5 once again. The wrong combination — tracks 3 and 4 as one pair and tracks 1 and 2 as the other — results in some very large opening angles and therefore correspondingly large invariant masses, which are then penalized. 4.2.2.1 Modifications For One-pair Events In the case of a one-pair event there is no choice of combinations to make — there is only one possible pair available. The case where the e+ and e" come from different gammas is equiva-lent to the situation described previously for a two-pair event if the wrong track combination is chosen. Here the single e+e" vertex opening angle is expected to be large, and will be rejected by the cuts described in section 4.2.3. The 7 t ° decay vertex is whichever of the beam-proton or beam-gamma intersection has the greater intersection angle. A 7 t ° invariant mass may be calculated by inferring the momentum of the missing gamma from the momenta of the proton, incident beam, and the single detected gam-ma. Then all the other calculations proceed as for a two-pair event. One problem with this inference is that it folds together errors associated with pair energy losses and proton energy-loss straggling. Also, it assumes the proton and vP momenta are in the plane of the detector. The proton being almost an order of magnitude more massive than the TU° February 14, 1996 39 Chapter 4 Data Analysis & Reconstruction implies that the it s out-of-plane angular range is larger than the proton's. Thus, detection of the proton does not constrain the 71° very much. A simpler, more reliable quantity to calculate is the 7t° missing mass (MM), defined as M M = J ( E 7 i + - E p ) 2 - ( P J C + - P p ) 2 where E + , P +, E„, P n refer to the total energies and momenta of the incident beam and detected proton. Note that the Fermi motion of the target neutron is neglected. By contrast, the two-pair Tt° invariant mass calculation is a direct measurement; it is not af-fected by target Fermi motion or proton energy losses. Also, the assumption that the 7C° is close to the plane of the detector is much more realistic for two-pair events. Detection of both e+e" pairs implies that both gamma momenta are close to the plane, and that therefore the 7t° momentum is in turn. The only other modifications involve compensating for proton energy losses in both the tar-get and the lead converter. Energy losses in the lead are determined from a polynomial fit to the proton energy loss in 3 mm of lead vs. the final proton kinetic energy. Both quantities are taken from GEANT simulations, and the resulting fit is graphed in Fig. 4.8. Calculation of energy losses in the target is more involved. A box of the same dimensions as the target is manually fit to a 7t° vertex plot, under the assumption the proton and 7t° originate at the same point. The proton curvature is typically very slight, so a straight-track approximation is made from the 7t° vertex to where the track intersects a side of the box. The proton energy loss in the target is determined by integrating the Bethe-Bloch equation backwards along this path. The energy loss is not calculated for the CD 2 target because its dimensions are similar to the 7t° vertex resolution. Overall improvement in the proton momentum spectrum with energy loss compensa-tion is demonstrated in Fig. 4.9. The raw peak has a a ~ 72 MeV/c while the final corrected peak has a ~ 44 MeV/c. From the GEANT studies of section 5.3, the natural width of this peak is found to be o ~ 41 MeV/c, arising primarily from kinematic broadening and Fermi motion effects. February 14, 1996 40 Chapter 4 Data Analysis & Reconstruction 4 . 2 . 3 S e l e c t i o n C r i t e r i a Once the choice of combination is made, further cuts are made to select good 7 t ° events. In-dividually, the cuts are meant to be a little "loose," becoming more effective when applied togeth-er. This is motivated by a fear of losing good events from an already small population, especially since the type of event under study and the analysis method are atypical. The various cuts em-ployed are summarized in Table 4.1, followed by a brief description. The track-sorting cuts essentially clean up the worst of the "garbage" tracks. As can be seen in Fig. 4.10 for good 1-pair and 2-pair events, the cuts are fairly superficial. As well, referring to Fig. 4.2 shows that the cuts on momentum are fairly loose. Here a "good" event describes a recon-structed event that passes all selection cuts. The pair vertex cuts reject events based on three criteria. Firstly, the preliminary GEANT studies in section 3.1.4 showed that the distance between pair hits in WC1 is fairly well-bounded in order for the pair to reach the outermost chamber. This is reasonable since the separation is re-lated to the gamma energy, and hence to the maximum radial range of the e+ and e~ in the detector. AE = 39.06 - 0.716 • KE + 7.55xlO~3 • K E 2 - 3.86xl0~5 • K E 3 + 7.45xl0~8 • K E 4 0 50 100 150 ' 200 Final Proton KE [MeV] Fig. 4.8 Fourth order polynomial fit to determine proton energy losses in the lead converter. AE is taken as a constant for KE > 180 MeV. February 14, 1996 41 Chapter 4 Data Analysis & Reconstruction 350 _| i i I_J I i_i—i—i—L_i—i—i—i—I—i—i—i—i—I—i—i—i—i—l—i—i—i—i—I—i—i—i—L ( a ) 0 100 200 300 400 500 600 700 500 _| i i i i I i i i i I i i i i I i i i i_l i_i i i I i i i i I—i—i—i—L 0 100 200 300 400 500 600 700 500 —| • > >—' I i—' • • I—' ' ' 1 I i >—1 1 I '—1—1—I—1—1—1—1—I—1—L—1—L 0 100 200 300 4-00 500 600 700 Proton Momentum [ M e V / c ] Fig. 4.9 One-pair proton momenta histograms: (a) raw momenta, (b) momenta corrected for losses in the lead, and (c) momenta corrected for losses in the target and the lead. February 14, 1996 42 Chapter 4 Data Analysis & Reconstruction February 14, 1996 43 Chapter 4 Data Analysis & Reconstruction Level of Cut Type of Cut Details Track Sorting Track Momentum -300 MeV/c < P < 800 MeV/c Track %2 X2<0.25 Pair Vertex Invariant Mass m i n v<50 MeV WC1 Hit Separation AWCj <90 mm Distance of Closest Approach (DCA) D.C.A. < 10 mm 7i° Decay Vertex y-y Opening Angle 0^ > 40° (2-pair only) 7 t ° Vertex Origin Reject 7t°'s not originating in the target. Table 4.1 Summary of selection criteria for good TC events. Secondly, the distance of closest approach of e and e" tracks in a pair should not be unrea-sonable large, otherwise it is likely the tracks are not related at all. There is no GEANT prediction from earlier studies for a suitable value of the cut. It was determined empirically from raw D.C.A. histograms. However, this choice is borne out by the work of section 5.3, which deals with offline analysis of more recent GEANT data. The third pair vertex cut is on the e+e" vertex invariant mass, which is expected to be low for a true pair-production event. Histograms of the quantities associated with these e+e" pair vertex cuts are shown in Fig. 4.11, along with the same plots made by analyzing GEANT data, as described in section 5.3. These histograms are for good one-pair events, meaning one-pair events reconstructed with all applicable cuts. Distributions for good two-pair events are similar, but lack appreciable statistics. It is apparent from the figure that the experimental and simulated distributions are consistent with each other. Also, the values of pair vertex cuts from Table 4.1 are seen to reject events from the tails of the distributions shown, further emphasizing the looseness of the criteria. The spike seen at 0 MeV invariant mass is due to non-intersecting e+'s and e"'s being as-signed a zero-degree opening angle, and hence a small invariant mass. The spike at 0 mm separa-tion results from pairs in which the e+ and e" share a WC1 hit. Plots of the e+e" invariant mass and February 14, 1996 44 Chapter 4 Data Analysis & Reconstruction Good 1-Pair G E A N T Good 1-Pair 20 40 60 80 e e Invariant Mass [MeV] i— 1— 1— 1— 1—i— 1— r^— 1—i— 1— 1— 1— 1—r 20 40 60 80 e e Invariant Mass [MeV] o u i—1——I—1—'—1—1—r 40_ 60 80 WC1 e e Separation [mm] i 1 1 1 1 I 20 +40_ 60 80 WC1 e e Separation [mm] "i—1 1 1 1—r 5 10 15 Distance of Closest Approach [mm] 5. 10. 15. Distance of Closest Approach [mm] Fig. 4.11 Histograms associated with cuts dealing with e+e" pair vertex information for good one-pair events from both experimental data and GEANT-generated data as described in section 5.3. Shown above are the invariant mass, WC1 e+e" hit separa-tion, and distance of closest approach of the e+ and e", with applied cuts correspond-ing to 50 MeV, 90 mm, and 10 mm respectively. February 14, 1996 45 Chapter 4 Data Analysis & Reconstruction separation also do not show a smooth transition going from the origin's spike out to the tail. The observed dips are thought to be due to finite WC1 position resolution. For example, this finite res-olution means that the distribution of e+e" vertex opening angles would not be continuous around zero degrees, thus leading to a discontinuity in the invariant mass distribution near 0 MeV. The highest level of cuts deals with parameters of the n° decay vertex. The most straightfor-ward cut to make is on the 7t° vertex position as shown in Fig. 4.12, ensuring it originates in the target and not another background source such as the lead converter. The second nP cut is on the opening angle of the two reconstructed gamma momentum vec-tors. In the CMS frame of the decay 71° the gammas are emitted back-to-back, while in the lab frame we can expect them to be emitted in a cone with a minimum angle (see section A. 1.1). From Fig. 3.3 in section 3.1.4 we know this angle to be -50°, and thus impose a loose cut on the opening angle of 40°. The validity of this cut depends on the gamma-gamma opening angle resolution, O"(0yy), be-ing less than 10°. We can estimate this by relating it approximately to the 7t° angular resolution, 150 100 50 a a o n -50--100--150 _ i i i i L _j i i i _ _j i i i_ C H 2 Target Vertex Cut Box Lead i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|— 150 -100 -50 0 50 100 150 X [ m m ] Fig. 4.12 7t° vertex dotplot (good 1-pair events) showing a clear C H 2 target outline as well as background from a portion of the lead converter. The box used for the vertex cut is indicated. Dimensions are in the horizontal plane of CHAOS. February 14, 1996 46 Chapter 4 Data Analysis & Reconstruction G(QK°), according to o"(8yy) = 2rj(87C°). From section 5.3.3 the 7 t ° angular resolution is known to be 3.5°. Hence, o"(6yy) is approximately 7°, indicating that the opening angle cut is valid. For one-pair events this cut is not used since the opening angle distribution is smeared out, as shown by Fig. 4.13. It will be shown in section 5.3.3 that this is largely due to the target nucle-on's Fermi momentum. For two-pair events, however, this cut provides the best test of all of a valid 7 t ° decay. Look-ing at Fig. 4.14 (top), there is a clear demarcation between the two areas straddling the cut. The minimum opening angle requirement alone is responsible for rejecting approximately half the events that might otherwise be taken as valid. With all two-pair selection cuts in place, the gam-ma-gamma opening angles compare favourably with the spectrum predicted earlier by GEANT in Fig. 3.3. Inspection of earlier GEANT events has shown that two-pair events with smaller gamma-gamma opening angles are almost always associated with bremsstrahlung,processes taking place in the lead converter. Typically these are one-pair events. However, in travelling through the lead the pair loses energy through radiation. It is possible for these bremsstrahlung photons to further 300 _j i i i i I i i i i I L i i J I i i i i I 0 [ I I I I j I I I ! | I I I I j 1 I I I j 0 50 100 150 200 7—7 O p e n i n g A n g l e [deg.] F ig . 4.13 Opening angle distribution of gammas for one pair events with no cuts ap-plied. The 2 n d y's momentum is inferred. There is no apparent structure at around 50°. February 14, 1996 47 Chapter 4 Data Analysis & Reconstruction 20 15 H w -t-> § 10 O o _J I I l_ _1 I L_ _J I I 1_ Due to Bremsstrahlung i r T ~i 1 r~ n nun pn Finn 50 100 150 7 — 7 Opening Angle [deg.] _i 1 1 1 I 1 1 1 1 I 1 1 1 i_ 200 50 100 150 200 7 — 7 Opening Angle [deg.] F ig . 4.14 Opening angle spectra of gammas for two-pair events, for raw events (top) and good two-pair (all cuts applied) events (bottom). The effect of the 0yy cut is obvious. Note, however, that some events at larger opening angles are also rejected. February 14, 1996 48 Chapter 4 Data Analysis & Reconstruction convert in the lead and thus mimic a two-pair event. The opening angle cut is the only means of distinguishing this type of event, of which Fig. 4.15 is an example. Roughly equal numbers of bremsstrahlung and real two-pair events are observed in the experimental data. This is consistent with both event types requiring that two gammas convert in the lead and each e+e" be emitted near the plane of the detector. Fig. 4.15 Sample of a reconstructed event that mimics a two-pair event, but is in fact due to a single initial gamma producing two e+e" pairs in the converter. 4 . 2 . 4 E x p e r i m e n t a l R e s u l t s The reconstruction algorithm employed seems to work reasonably well. The calculated e+e" vertices clearly outline the lead converter, as seen in Fig. 4.16. Both conversion radius histograms show a fairly sharp peak at a converter radius of 5.4 cm and FWHM of 14 mm, although the sta-tistics for two-pair events is admittedly poor. The silhouette of WC1 is apparent in Fig. 4.16, due to the way tracks that share WC1 hits are handled. Recall from section 4.2.2 that these tracks are assumed to intersect at the WC1 hit position. As seen on the following page, the conversion positions for one-pair events seem more skewed towards backwards angles, while for two-pair events no forward/backward bias is evi-dent. This is because the large proton energy losses in the lead converter and in the target make February 14, 1996 49 Chapter 4 Data Analysis & Reconstruction Good One-pair Good Two-pair o o 1 , , , , 1 Converter • j A , Mis-sorting. rrr*^ >—•—i—1—1—' M ^ ' 1 1 i ^ - i 1 1 — i 1 1 e e Conversion Radius [mm] 50+ _ 100 150 200 e e Conversion Radius [mm] Fig. 4.16 Plots of e e" conversion positions (top) and conversion radius (bottom) for good one-pair and two-pair events (CH 2 target). Visible are the lead converter outline and the WC1 position from tracks that share hits in that chamber. proton detection more likely at forward proton angles, where their energy is greatest, and thus de-tected 71°' s will be skewed towards backwards 7t° angles, though primarily directed towards the halves of the converter. The effect is illustrated in Fig. 4.17. Notice also the proton angular gap due to the beam exit region. The GEANT generated counterparts to Fig. 4.16 and Fig. 4.17 are presented in section 5.3.3, and show good agreement with the figures here. The 71° angles for two-pair events, as shown for C H 2 in Fig. 4.18, suggest less constraint to-wards the position of the lead, which is reasonable for a multi-step event such as this, as one would expect holes in the detector acceptance to be somewhat "smeared" out. Also, any effects due to the detection of the proton are absent. February 14, 1996 50 Chapter 4 Data Analysis & Reconstruction -200 -100 0 100 Proton Angle [deg.] 7TU Angle [deg.] Fig. 4.17 Proton and 7t° angles for good one-pair CH2 events. Proton angles are skewed forward, 7t° angles slightly backwards, though mainly focussed on the lead. Peak asymmetries have been reproduced in GEANT. A useful indicator of reconstruction algorithm performance has been a plot of the e+e" in-variant mass vs. the conversion radius, as shown in Fig. 4.19(a). There is a structure due to the converter at ~5 cm radius. It narrows towards the top because larger invariant masses are correlat-ed to larger e+e" opening angles, and hence improved position resolution. The band located across 0 MeV invariant mass arises from pairs with non-intersecting tracks and correspondingly poor po-sition resolution. There are also two bands that extend out at an angle from the structure on either side. It is significant that their projection on the x-axis is at ~5 cm; this indicates they are related to the lead converter. Inspection of the pairs in this region shows that they are comprised of fairly symmetric tracks with two intersections, both of which would appear to be good choices for the pair produc-tion vertex. -200 -100 0 0 100 200 n Angle [deg.] Fig. 4.18 7t° angular distribution for good two-pair events in CH 2 . February 14, 1996 51 Chapter 4 Data Analysis & Reconstruction 60 > CD 50 co 40 cd C 3 0 cd • r-H cd > 20 CD CD 10 Converter Position WC1 Position Mis-sorting Aliasing 1 r- 1 i 1 1 r—i r -50 100 Conversion Radius [mm] ~ i — 1 — 150 200 ~i 1—1—1—1—r 0 50 100 150 200 Conversion Radius [mm] F i g . 4.19 Plots of e+e~ invariant mass vs. conversion radius for C H 2 for both (a) good events and (b) the same but without treating as a special case e+e" pairs that share WC1 hits. Both plots indicate the position of the lead converter, and show various structures due to aliasing effects. The position of WC1 is also apparent. February 14, 1996 52 Chapter 4 Data Analysis & Reconstruction The most likely explanation is that uncertainty in track resolution causes the e+ and e" tracks from a pair to be reconstructed as slightly overlapping, instead of providing a single intersection. The resulting two vertices are typically equally good candidates in that they are roughly the same distance from the expected converter radius. The choice then becomes arbitrary, giving rise to a variation in conversion radius. Just as a greater overlap produces vertices farther away from the converter radius, so too does it produce larger vertex opening angles, and thus larger invariant masses. The observed bands are an aliasing effect that stems from e+e" tracks having a variable overlap. The invariant mass vs. conversion radius plot has also been useful in diagnosing reconstruc-tion problems. For example, recall from section 4.2.2 how the e+e" vertex is chosen. According to step 2-c, if one of the possible intersections of a pair is due to shared WC1 hits then that intersec-tion is taken as the e+e" vertex. Ignoring this step, and treating such events as in step 2-d (generic two-intersection event), produces the plot in Fig. 4.19(b). Here there is a clear band extending across the plot, with an x-axis projection at the WC1 radius, thus indicating the aliasing is a phe-nomenon associated with WC1. This situation arises when, notwithstanding a more correct inter-section at WC1, there exists a fictitious vertex that is chosen because it is closer to the lead converter radius, as per step 2-d. Consider as well the region indicated in the plot outside the WC1 radius. Its projection onto the x-axis also seems to indicate that it is a WC1 -related effect, and inspection of reconstructed events in this region appears to bear this out. Such an event is displayed in Fig. 4.20, where the chosen e+e" vertex is outside the WC1 radius. The suspicion in this example is that the WC1 hit assignments for the e+ and e" tracks might be flipped to improve things, and in fact if this is done manually then the %2 of the e+e" tracks decreases marginally. Thus, these relatively rare events are an artifact of track mis-sorting. Other large-radius vertices can as well be ascribed to severe scat-tering in the lead converter. Ultimately, the best indicator of valid 7t° decays for the case of two-pair events is the calcu-lated invariant mass, which is expected to be peaked near 135 MeV and gaussian in form, with a low-energy tail corresponding to energy losses in the lead. Fig. 4.21 shows, for the C H 2 target, the reconstructed n° invariant masses for good one- and two-pair events; the 7t° missing mass for one-pair events; and the proton missing mass for two-pair events. Also shown are the corresponding February 14, 1996 53 Chapter 4 Data Analysis & Reconstruction histograms from GEANT simulations. All the one-pair distributions are broad and smeared out, both the 7t° invariant mass, which was not expected to be too useful, and the 7t° missing mass, which, stemming from a more straightforward calculation, was thought to be more reliable. The breadth of these distributions can be attributed to target-nucleon Fermi-motion (see section 5.3), as is suggested by the good agreement between the experimental one-pair histograms and those calculated from simulated GEANT data, which models Fermi-motion effects. The two-pair experimental distributions are also consistent with their GEANT counterparts. The experimental K° invariant mass histogram is peaked at 125 MeV, close to the true mass of 135 MeV, with a FWHM (full width at half max.) of -25 MeV, as determined by fitting it to a gaussian with exponential tail. The GEANT distribution is peaked at 126 MeV, with a FWHM of -26 MeV. The final yields of the analysis are summarized in Table 4.2. The statistics for two-pair events are admittedly poor, but should still enable a later cross-section calculation to be made. Note that the ratios of one-pair to two-pair yields (referred to as R12) are different for each target type used. R12(CH2) ~ 100 while R12(CD2) ~ 330. A likely explanation for this discrepancy Fig. 4.20 Example of a reconstructed event with selected e e" vertex outside the WC1 radius, as indicated in the plot. February 14, 1996 54 Chapter 4 Data Analysis & Reconstruction Good One-pair Good Two-pair 0 50 100 Q 150 300 250 300 350 0 50 „ 100 150 200 250 TT Invariant Mass [MeV] TT Invariant Mass [MeV] 0 50 100 150 200 250 300 360 600 700 BOO 900 1000 1100 1200 TT Missing Mass [MeV] Proton Missing Mass [MeV] F i g . 4.21 Reconstructed n invariant mass distributions, and 7t and proton missing mass distributions for events on C H 2 (top four). Also shown (bottom four) are the equivalent G E A N T invariant mass and missing mass predictions from studies in section 5.3. The one-pair histograms are smeared out due largely to Fermi-motion effects. Overall agreement between experimental and simulated data is good, within the statis-tics available. February 14, 1996 55 Chapter 4 Data Analysis & Reconstruction comes from the fact that for one-pair events, proton energy losses are larger in the thick C H 2 tar-get than in the thin C D 2 target, while for two-pair events, the gammas are fairly insensitive to tar-get thicknesses. Hence, relative to two-pair events, fewer one-pair events are expected for the C H 2 target. Thus, one would expect R 12(CH2) < R 12(CD2). Event Type Good n° Yield CH2 CD2 One-pair 24406 15026 Two-pair 248 46 Table 4.2 Analysis yields for one-pair and two-pair 7t° events. 4 . 3 N o r m a l i z a t i o n s In addition to the yields, calculation of a cross-section would also require several efficien-cies to be known. Of these, three are determinable from the offline analysis: the fraction of inci-dent beam particles counted that actually strike the target, as determined from a profile of the beam; detection efficiencies of the wire chambers; and the overall fraction of pions in the incident beam. 4 . 3 . 1 B e a m P r o f i l e The incident beam fraction impinging on the target is determined by calculating the projec-tion of the beam onto the plane of the target. Horizontal (radial) and vertical bounds of the target are found by looking at the projection gated on good 7C° events. These, bounds are then applied as cuts to an unbiased incident beam distribution to determine the fraction within bounds. The unbi-ased data used for this purpose is from a set of sample events. The vertical projection distributions for sample events and JC° events are equally broad, and hence can be ignored. Projections in the horizontal plane, however, provide bounds for placing cuts. Fig. 4.22 shows the sample-gated and 7T°-gated projection histograms used in determining the beam fraction on target, while Table 4.3 summarizes the beam profile calculations. The change in beam fraction on target going from the C H 2 to the CD 2 is due mainly to a shift in the beam profile, which is seen clearly in the figure. February 14, 1996 56 Chapter 4 Data Analysis & Reconstruction Target Type Total Incident Beam Fraction On Target CH2 4.48xl010 0.851 CD2 2.70X1010 0.698 Table 4.3 Incident beam normalizations. 4.3.2 Chamber Efficiencies The various wire chamber efficiencies are of critical importance in a cross-section calcula-tion, and more so in the case of 7t° studies. For instead of dealing with two or three scattered par-ticles, for two-pair events one deals with four tracks, each required to go through four chambers. Assuming WC4 is 100% efficient, this introduces a variation in the detector efficiency that goes as CH -100 - 5 0 0 50 Rad ia l Beam Project ion [mm] 1000 800 600 o 400 200 100 -100 71° Events - 5 0 "~0~ 50 Rad ia l Beam Pro jec t ion [mm] 100 2000 1500 1000 500 H -100 - 5 0 0 50 100 -100 - 5 0 0 50 R a d i a l Beam Pro jec t ion [mm] Rad ia l Beam Pro jec t ion [mm] Sample Events Fig. 4.22 Plots of incident beam projection onto the target plane, for CH2 and C D 2 targets, and gated on good 7 t ° events and sample beam events. 100 February 14, 1996 57 Chap te r 4 Data A n a l y s i s & Recons t ruc t i on the twelfth power of the chamber efficiency. This is compounded by the fact that the electrons are minimum-ionizing. One procedure for determining the electron efficiencies is as follows. Using an unbiased data set, good one-pair events are searched for using a track-sorting routine that disallows hit-sharing and does not require hits in all four chambers. Further requirements are that the events have no unassigned hits that might potentially confuse the track-sorting algorithm, and that no tracks pass through any dead sections of the chambers. Statistics are then gathered on the number of events having e+'s and protons with hits in all chambers, and e"'s with up to one chamber hit missing. Then, if £ is the relative track-sorting efficiency with a chamber hit missing, and N(m) is the number of events with m hits missing, the efficiency for a single chamber is given by e = 1 i + M N(0)£ Unfortunately, as the May 1994 data were taken with the 2LT in place, the only unbiased data is available from sample-gated events. While this procedure has been applied to the samples data, the statistics are poor. Proper determination of efficiencies requires a dedicated calibration run. However, concurrent analysis of T i p data [12] from immediately before and after the SCX run has yielded pion and proton efficiencies for the same chamber voltages. In the energy ranges under study the pions are also minimum-ionizing and have similar stopping powers as the SCX electrons. Thus, it is reasonable to substitute these pion efficiencies for the electron efficiencies necessary in later calculations, as summarized in Table 4.4. Chamber Particle e+, e~ P WC1 96% 99% WC2 94% 99% WC3 92% 98% WC4 100% 100% Table 4.4 Wire chamber efficiencies for electrons and protons. Typical uncertainties are +2% February 14, 1996 58 Chapter 4 Data Analysis & Reconstruction 4 . 3 . 3 B e a m P i o n C o n t e n t The incident beam is expected to have a non-negligible proton fraction [13] which must be compensated for in the beam normalizations, while electron and muon contamination is expected to be negligible compared to overall statistical uncertainties. This fraction is determined by look-ing at the incident beam timing (TCAP) with respect to a BLIA capacitive pick-up, for sample-gated events. TCAP represents the time-of-flight of particles from the % production target to the SI in-beam scintillator at the spectrometer's entrance. Fig. 4.23 shows the TCAP timing spectrum for samples acquired over the entire run. The observed pion fraction is 0.942. 3 0 0 0 J L j L j L j I 1 I 1 L 3 1 5 0 0 -O u ; m 2 5 0 0 H 2 0 0 0 H Pions 1 0 0 0 - \ Protons 5 0 0 - \ 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 TCAP Timing Fig. 4.23 Incident beam timing with respect to a BLIA capaci-tive probe. Pion and protons are easily separable. February 14, 1996 59 Chapter 5 Cross section & Acceptance CHAPTER 5 Cross section & Acceptance February 14, 1996 60 Chapter 5 Cross section & Acceptance The practicality of carrying out TC° studies ultimately lies in the feasibility of determining cross-sections. The aim of this chapter is to carry out a calculation of the total cross-section for the reaction T C + d —> TC° p p and compare this to the results of a recent measurement [14]. The C H 2 data will be used for background subtraction from the CD 2 data. 5.1 Introduction The small yields of this study make any calculations of differential cross-sections impossi-ble. It is realistic only to determine the total cross-section, O", defined as o - Y N beam N tgt e where Y is the analysis yield and N b e a m is the number of incident beam particles. The parameter £ is an overall efficiency defined as 6 = eWC edet eiive eTC Etgt where the individual efficiencies are described in Table 5.1. The fraction of doubles in the beam is Normalization Detail e W C Wire chamber efficiencies. elive Computer live-time. Pion fraction of beam. £tgt Beam fraction incident on target. edet Overall detector efficiency. Table 5.1 Details of cross-section normalizations. omitted as it is expected to be negligible on the scale of other normalizations and the overall sta-tistical uncertainty. 5.2 Normalizations All the normalizations are available from the experimental data with the exception of the detector efficiency, which requires Monte-Carlo calculations and offline analysis. The chamber February 14, 1996 61 Chapter 5 Cross section & Acceptance efficiencies for one-pair and two-pair events can be determined from Table 4.4. One-pair events require one proton and two electron hits in each of WC1, WC2, and WC3, with WC4 taken as 100% efficient. Two-pair events require four electron hits in each of the chambers. In both cases incident beam hits are needed in WC1 and WC2, for which the corresponding efficiencies are the same as for electrons since the incoming pions are minimum-ionizing. The computer live time is essentially given by the ratio of numbers of second-level triggers processed to first-level triggers generated. This information is available from the experimental scalers, and is summarized in Table 3.2. The pion fraction and target-incident fraction of the beam are calculated offline from sample events, as shown in section 4.3. Values of the normalization parameters described so far are sum-marized in Table 5.2 for both target types and both event types, whichever is relevant. Normalization Target Type Event Type CH2 CD2 One-Pair Two-Pair ewc N/A N/A 0.597 0.429 elive 0.893 0.944 N/A . N/A . 8tgt 0.851 0.698 N/A N/A • £ K 0.942 Table 5.2 Values of normalization constants. 5.3 Detector Acceptance The detector acceptance, e,jet, is meant to incorporate information about the detector geom-etry, data-acquisition electronics, and reconstruction software. The detector model reflects the ac-tual position and orientation of CHAOS during the test run, and incorporates the lead converter and two target geometries used. The event generation routine simulates a target-nucleon Fermi-motion. Photon conversion and geometrical efficiencies are accounted for by GEANT's internal physics models and explicit tracking of particles. The experimental first-level trigger is simulated in the CHAOSSIM code, while the second-level trigger is simulated in the offline event recon-struction, as are the effects of any dead chamber electronics observed during experimental data acquisition. A newer version of the CHAOSSIM software than that described in section 3.1 is February 14, 1996 62 Chapter 5 Cross section & Acceptance used to generate equivalent-to-online data, which is then analyzed using the standard offline anal-ysis software. Analysis software efficiencies can thus also be accounted for. 5.3.1 Updated Monte-Carlo The CHAOSSIM software has been extensively modified since the preliminary GEANT studies. Changes have been made to the geometry specifications and output formats that more closely link it to the experimental setup. The various changes can be summarized as follows: 1. Nearly full digitization of event data is implemented in the YBOS output format, the same format as online data, thus allowing the same event selection criteria to be used for real and simulated data. By using information from online calibration files, holes in the various chambers can be simulated as well. The raw GEANT event information is also available to the analysis package, enabling straight-forward calculations of resolu-tions. The chamber z-coordinate information is not currently being digitized. 2. The geometrical placement of the simulated detector can be defined by the output pa-rameters of the RAY program, as shown in Fig. 3.4. While this is not important in get-ting a rough estimate of the detector acceptance, it is absolutely necessary when modelling individual cell and wire inefficiencies, since there must be a strict correspon-dence between the real and simulated detectors. 3. Much of the TC° decay information described in section 3.1.3 is written out to YBOS banks and made available to the analyzer for comparisons. 19 4. The original two-body phase space event generator now includes a typical C Fermi-momentum distribution [15] based on a spherical density dependant Hartree-Fock cal-culation that is parametrized by 3 6 n- 2 P(q) = X a { M ) exp(-njq ) where n{ = apJ i=l and {a1;...,a6} = {0.00053,-0.15912, 1.6313,-0.57563,0.25868,-0.15587} {a, (3} = {0.69179, 1.4412} for which the momentum q is in units of fin"1.. This is more significant for one-pair events, as two-pair events would share the extra momentum over more particles. February 14, 1996 63 Chapter 5 Cross section & Acceptance 5. The converter model has been updated to reflect the geometry used during the test run, including the correct entrance and exit widths. Likewise, both the CH2 and CD 2 target geometries are implemented. The 1LT was simulated in GEANT and set up as a triple coincidence based on AE1»AE2. YBOS event information was then only written out for first-level triggers. Many GEANT runs were performed for both target types over a several-month period. However, because of continual improvements, optimizations, and bug fixes during the course of running, only the latest batch of simulations is used for the acceptance calculations. The only speed optimizations applied to these runs are based on limiting the out-of-plane 7t° angle. Reconstructed GEANT information (with no angular limits) shows that one-pair events oc-cur for 7t° angles up to 40° out of the plane, and for two-pair events up to 12° out of the plane. Thus, aborting the tracking for events outside these windows does not alter the number of good events finally reconstructed. However, for acceptance calculations care must be taken to ensure that the number of events tracked is normalized to that of runs not employing windows. Illustra-tive angular distributions are shown in Fig. 5.1. 3 o u "i—1—1—'—1—r 50 100 „ 150 Good 1-pair GEANT fl(m ) [deg.] ,0 50 100 150 Good 2-pair GEANT 0(TT ) [deg.] Fig. 5.1 Out-of-plane 7t angles from GEANT for good one-pair and two-pair recon-structed events. The plane of the detector corresponds to 90°. The useful GEANT data generated are summarized in Table 5.3. The "Events Tracked" re-fers to those generated Monte-Carlo events that are within the TT,0 angular windows, and are passed to GEANT for tracking. Data created with one-pair Monte-Carlo windows are usable in two-pair acceptance calculations, but yield fewer good events. Note that including optimizations outlined previously, typical simulation rates were approximately 3-4 events-tracked/second. February 14, 1996 64 Chapter 5 Cross section & Acceptance Detector Configuration Approx. Events Tracked Monte-Carlo Events Generated C H 2 One-pair , 1 100 000 1 661 000 C H 2 Two-pair 4 000 000 16 616 783 C D 2 One-pair 1 400 000 1 928 045 C D 2 Two-pair 3 700 000 15 730 160 Table 5.3 Monte-Carlo TC data generated for each target type and TC° out-of-plane angular window. 5 . 3 . 2 R e c o n s t r u c t i o n o f S i m u l a t e d D a t a The reconstruction software used to analyze the G E A N T data is essentially identical to that used to study experimental data, with some modifications to accommodate both the extra infor-mation available from G E A N T and the lack of some information that has not been or cannot be simulated in any easy way. These modifications involve the PID system, second-level trigger, GEANT YBOS banks, and detector electronics. The particle identification used in reconstruction is the known ID available from GEANT. The discrepancy between this 100% PID efficiency and the experimental one is thought to be small, especially since the experimental PID cuts were somewhat loose, with the selection criteria of section 4.1.2 themselves doing a good job of proton and electron selection. Use of the PID test system for experimental data would require GEANT to know absolute gains, light-gathering effi-ciencies, and pulse-height characteristics for each of the CFT blocks and AE counters, which is beyond the scope of this work. The YBOS data output by G E A N T is based on a fully functional model of the detector. The output contains position and drift-time information for all possible channels. However, it is im-portant to take into account any dead channels, as this may make appreciable holes in the accep-tance. This simulation is possible in the reconstruction by using information from online data acquisition. Use of experimental WC3 and WC4 TDC drift-time-to-distance calibration files in the analysis allows modelling of dead TDC channels. Furthermore, code has been written that ef-fectively deadens regions of WC1, WC2, and WC3 as per dead channels recorded during online acquisition. February 14, 1996 65 Chapter 5 Cross section & Acceptance The effects of the second-level trigger's inclusion in data-taking need to be accounted for, as there is little experience in using the 2LT for 7 t ° decay reactions. There is analysis code in place (after deadening of appropriate chamber regions) that simulates the functioning of the 2LT, allow-ing accept/reject decisions in the simulation to be based on the same polarity, momentum, target-range, and beam-window requirements as online data. The 7t° selection criteria is basically that of section 4.2.3 with small modifications to some TC° vertex boxes defined in the tests. While the inclusion of Fermi-momentum effects in the GEANT event generation can be expected to alter slightly the gamma-gamma opening angle dis-tribution, the original cut at 40° is still applicable, as can be seen from Fig. 5.2. 5 . 3 . 3 S i m u l a t i o n R e s u l t s There is generally good agreement between analysis results for experimental and recon-structed GEANT data. As well, the availability of raw GEANT information allows verification of aspects of the reconstruction, and permits easy calculation of various kinematics residuals (i.e. the differences between reconstructed quantities and their true values known by GEANT). 2 0 0 7—7 O p e n i n g A n g l e [deg. ] Fig. 5.2 GEANT gamma-gamma opening angles including Fermi-motion effects. The histogram is a little broader than Fig. 3.3 but a selection cut at 40° is still valid. February 14, 1996 66 Chapter 5 Cross section & Acceptance Several details of the analysis were checked. The proton energy-loss correction for the lead converter assumes all reconstructed protons pass through the lead. This was verified via GEANT information. It was also possible to determine what fraction of reconstructed events were due to the secondary 7t° decay channel vP —» y e V (branching ratio -1.2%). All reconstructed two-pair events were found to originate from 7t° —> yy decays, and approximately 0.5% of one-pair events originated in 71°—> ye+e~ decays. The GEANT 7t° scattering angles for both simulated first-level triggers (events causing 3 CFT blocks to fire) and reconstructed events are shown in Fig. 5.3. First-level triggers appear to be distributed over almost the entire angular range, diminishing at forward and backward angles most likely due to acceptance holes in the lead, WC3 dead sections, and the CFT beam entrance and exit. For good one-pair events forward-angle 7t°'s are somewhat suppressed since they would compete for energy with forward-going protons that typically undergo large energy losses in the target and lead. Furthermore, at backward angles Tt°'s usually have less kinetic energy and thus, the single pair required for the event may not have sufficient energy to reach WC4 and the CFT's. Note that for the detector configuration used, each e+ or e" needs a minimum of -25 MeV energy to be detected. Hence each gamma requires -50 MeV. Since there are no protons competing for energy, two-pair events are observed for smaller 7t° angles than one-pair events. Though backward-angle Tt°'s are suppressed as for one-pair events, the two-pair large-angle tail is shifted more towards forward angles. This can be explained by the fact that these events require detection of two gammas, implying the Tt°'s require -50 MeV more energy than the corresponding one-pair events. The forward shift of Tt° angles accounts for this larger energy requirement. The GEANT-reconstructed histograms and dotplots corresponding to Fig. 4.16 and Fig. 4.17 are shown in Fig. 5.4. Although the statistics involved are limited, the experimental and re-constructed distributions for e+e" conversion positions and and proton angles are fairly close and have similar asymmetries. Recall from section 4.2.4 the experimental 7t° missing mass distribution for good one-pair events, seen in Fig. 4.21. The breadth of this distribution was attributed to target-nucleon Fermi motion and out-of-plane momentum components which are neglected in the reconstruction. Using February 14, 1996 67 Chapter 5 Cross section & Acceptance CD, 50 0 100 150 6(n ) [First-Level Triggers} 50 100 150 0(TT ) [First-Level Triggers] 50 100 150 B(n ) [Good One-Pair] 50 100 150 e(n ) [Good One-Pair] 1 — 1 — 1 — 1 — 1 — r 50 100 150 B(n ) [Good Two-Pair] 200 0 i — 1 — • — 1 — 1 — i — 1 — 1 — • — 1 — r 50 100 150 0(TT ) [Good Two-Pair] Fig. 5.3 TC scattering angles from GEANT for simulated first-level triggers and recon-structed one-pair and two-pair events, for both C H 2 and C D 2 targets. Angles are mea-sured in degrees. February 14, 1996 68 Chapter 5 Cross section & Acceptance One-Pair Two-Pair i i 50 100 150 e e Conversion Radius [mm] 50 100 150 200 e e Conversion Radius [mm] 200 Fig. 5.4 GEANT-reconstructed counterparts to Fig. 4.16 and Fig. 4.17, for the C H 2 tar-get. The e+e" vertex positions and radii (top four) reproduce the experimental distribu-tions fairly well, as do the one-pair proton and nP scattering angles (bottom). February 14, 1996 69 Chapter 5 Cross section & Acceptance GEANT information about an event's exact reaction kinematics, it is possible to determine the source of this broadening. Fig. 5.5 shows plots of the one-pair TC° missing mass calculated in four different ways, starting with reconstruction in the same way as for experimental data. The same calculation is then made using the GEANT beam and proton momenta at the interaction vertex, in both two and three dimensions. Finally, this last calculation is modified to include the target neu-tron Fermi momentum. It is apparent from the figure that the smearing observed is due largely to Fermi-motion effects. Shown in Fig. 5.6 are reconstruction residuals of TC° kinetic energy and scattering angle for both C H 2 and C D 2 data. The residual is defined as the difference between a reconstructed quantity and its true value (which is available in GEANT). Applying Gaussian fits to both plots result in an 0 50 100 0 150 200 250 300 350 0 50 100 0 150 200 250 300 350 TT Missing Mass [MeV] n Missing Mass [MeV] Fig. 5.5 One-pair it® missing masses calculated from simulated data. The sequence of plots indicates the effects of corrections applied cumulatively to the missing mass cal-culations. Plot (a) is calculated using reconstructed momenta; plot (b) uses the in-plane components of the true momenta at the interaction vertex; plot (c) extends this to a three-dimensional calculation; and plot (d) further includes the target neutron's Fermi-momentum. February 14, 1996 70 Chapter 5 Cross section & Acceptance angular resolution of a ~ 3.5° and an energy resolution of a ~ 22 MeV. The mean of the energy residual, (l ~ -21 MeV, is consistent with the GEANT prediction of up to 10 MeV loss for each pair in the lead converter. The detector acceptances needed for the cross-section calculations are basically the analysis yields of reconstructed one-pair and two-pair GEANT events normalized to the number of origi-nal Monte-Carlo events generated, as per Table 5.3. However, these numbers are based on a two-body phase-space distribution in GEANT, and are essentially valid for SCX on free neutrons. SCX on deuterium is suppressed at forward angles due to Pauli-blocking effects arising from the two final-state protons (see section A.2). One-Pair Two-Pair T—•—•—•—•—i—1—1—1—1—r -50 0 0 50 TT Energy Residual [MeV] 100 -100 1 >~> r—' 11 ••' ' " ' I 50 0 0 50 7T Energy Residual [MeV] F i g . 5.6 Energy and angular residuals for one- and two-pair events, based on summed C H 2 and CD 2 results. The non-zero mean of the two-pair energy residual is consistent with pair energy-loss predictions in the converter, while the near-zero mean of the one-pair residual is likely due to smearing from Fermi-motion effects. February 14, 1996 71 Chapter 5 Cross section & Acceptance It is possible to compensate approximately for this effect by weighting the reconstructed events and the total number of Monte-Carlo events generated. This is achieved by making use of recent differential and total cross-section data [14] for SCX on deuterium at 164 MeV. The deute-rium data must also somehow be scaled to 180 MeV incident pion energy. Short of carrying out a relativistic three-body Faddeev calculation, which is beyond the scope of this thesis, a reasonable scaling estimate can be made by comparing total cross-sections at these energies as determined from the SAID program [10]. Since these values differ by less than 0.2%, no scaling attempt will be made. The number of GEANT Monte-Carlo events are weighted according to the ratio of total deuterium cross-section at 164 MeV [14] to that of SAID at 180 MeV, given by aD(164 MeV)/o"SAID(180 MeV) = 0.6176. Reconstructed events are weighted by TC° angle ac-cording to the ratio of the two differential cross-sections in 10° bins. Shown in Fig. 5.7 is a plot of this ratio and the third-order polynomial fit to it. The results of raw and weighted analyses of re-constructed GEANT events are summarized in Table 5.4. i 1 i 1 i 1 i 1 i 1 r 0 20 40 60 80 100 120 140 160 180 3T A D [deg.] LAB L b J Fig. 5.7 Weighting function for reconstructed GEANT events. Squares are ratios of deuterium to SAID data. The solid line is a polynomial fit. February 14, 1996 72 Chapter 5 Cross section & Acceptance Weighting CH2 Target CD2 Target One-Pair Two-Pair One-Pair Two-Pair Raw 8.88 79 2232 54 Weighted 675.3 48.5 1674 34.5 Table 5.4 GEANT reconstruction yields for weighted and unweighted Tt- angular distributions. 5.4 Cross-section With the detector acceptance information of the previous chapter there is now sufficient in-formation to carry out a cross-section calculation. The values summarized in Table 5.5 are used to determine cross-sections with respect to numbers of C H 2 and C D 2 molecules, which are then sub-tracted to yield D 2 results. This calculation is done for both one-pair and two-pair data as a consis-tency check. Note that this subtraction is still valid even though an experimental i\P angular distribution is being used for the acceptance calculations, since the same distribution is being ap-plied to carbon in both C H 2 and CD 2 . The final cross-section for deuterium is given by 0-(CD7) - a(CH-) o-(D) = -Quantity CH2 Target CD2 Target One-Pair Two-Pair One-Pair Two-Pair Yield 24406 248 15026 46 ^beam 44831869388 26998671804 N t g t [CX2/mb] 0.000152 0.0000233 e W C 0.597 0.429 0.597 0.429 edet 6.58xl0~4 4 . 7 3 X 1 0 - 6 1.41X10"3 3.55xl0~6 l^ive 0.893 0.944 8tgt 0.851 0.698 ETC 0.942 £ 2.82xl0~4 1.45xl0~6 5.21 x lO - 4 9.45x10 7 G(CX2) [mb] 12.7 25.1 45.8 77.3 Table 5.5 Required quantities for the cross-section calculations, along with intermediate results of C H 2 and CD 2 cross-sections. February 14, 1996 73 Chapter 5 Cross section & Acceptance One troubling feature of the intermediate results is that one-pair and two-pair cross-sections differ by a factor of roughly two. The interactions involved in simulating a two-pair event are purely electro-magnetic, for which GEANT is believed to be quite accurate. One-pair events, however, require the tracking of trigger-defining protons that lose large amounts of energy, and GEANT is thought to be less reliable for low-energy interactions of hadrons. As well, since two-pair events are multi-step processes that share CMS energy among four particles, they are less likely to be affected by Fermi-motion or other energy modifying effects. In any case, two-pair events are thought to be much more reliable for determination of a final deuterium cross-section. The variation of E^t m a Y be explained in terms of the larger proton energy losses occurring in the CH2 target, as was done for the experimental yields in section 4.2.4. In a similar fashion, one can also calculate ratios of one-pair and two-pair E^t values for each target, yielding R12(CH2) ~ 140 and R12(CD2) = 400, compared with the values calculated from experimental yields of 100 and 330 respectively. For both experimental and simulated data, it is observed that R12(CH2) < R12(CD2), as was expected. Table 5.6 summarizes the major sources of error used in this cross-section calculation. All the uncertainties are statistical, and treated as uncorrected. The uncertainty in overall chamber ef-ficiency is determined by adding in quadrature the chamber efficiency uncertainties for either the 14 hits required by a two-pair event or the 11 required by a one-pair event. Uncertainties in both £,j e t and the yield are calculated by first assuming a Poisson distribution and then taking where n is the experimental yield or, in the case of E ^ , the yield of events recon-structed from GEANT data. The total errors given are calculated by adding in quadrature the ma-jor error sources listed. Error Source CH2 Target CD2 Target One-Pair Two-Pair One-Pair Two-Pair Yield 0.006401 0.06350 0.008158 0.1474 e W C 0.06633 0.07483 0.06633 0.07483 edet 0.03846 - 0.1429 0.02444 0.1690 Total 0 [mb] 0.98 4.4 3.3 18 Table 5.6 Major sources of error in the cross-section calculation. All addition is in quadrature. Values quoted are fractional errors, except for the totals, which are statistical a values. February 14, 1996 74 Chapter 5 Cross section & Acceptance With the total error (a) in the deuterium cross-section given by where a C H and G C D are total uncertainties from Table 5.6, the final cross-section result for a[d(TC+,TC°)pp] is (26 + 9) mb based on two-pair events. This compares favourably with the (29.8 + 0.8) mb result of [14]. Errors associated with experimental yields and detector efficien-cies may be minimized through longer data-taking and simulation runs, but global chamber effi-ciencies are not expected to be as straightforward to improve. However, chamber efficiencies associated with specific TC° angular bins — as may be needed for a differential cross-section mea-surement — will likely be more accurate since they do not incorporate overall chamber varia-tions. February 14, 1996 75 Chap te r 6 C o n c l u s i o n s CHAPTER 6 Conclusions February 14, 1996 76 Chapter 6 Conclusions 6.1 Summary The detection and interpretation of 7C° decay events has proven to be feasible, albeit with an associated detector acceptance on the order of IO" 6. Tools ( C H A O S S I M ) exist and have been shown to function properly in determining optimum detector setup characteristics. Analysis tech-niques exist to select TC° events (in particular the two-pair variety) with a high degree of confi-dence, and provide typical 7t° resolutions of o~ ~ 3.5° in angle and rj ~ 22 M e V in energy for the geometry chosen in this study. The detector is well-simulated, allowing realistic determination of absolute acceptances. However, precision of total cross-section measurements is limited primarily by global wire-chamber efficiencies, and the 14-chamber-hits requirement for detecting a two-pair event. Analyzing power measurements, on the other hand, would suffer far less from such normalization concerns. 6.2 Further Improvements The detector's operation as a TC° spectrometer would benefit from improvements in the areas of physical configuration, analysis and reconstruction, and simulation methods and software. 6.2.1 Experimental Setup A s determined in section 3.2 the detector acceptance can be improved by maximizing the radius of the converter used, as this effectively adds several M e V of energy to each electron or positron, and covers a larger gamma angular range i f the linear dimensions of the beam entrance and exit openings in the converter are maintained. The effects on the pair reconstruction of mov-ing the converter close to the W C 1 radius must be studied, as e+e" tracks w i l l then always share W C 1 hits and the W C 2 e+e" track separation may become an issue. Pair energy losses may be compensated for by use of an active converter such as B G O . Knowing the minimum expected gamma-gamma opening angle would allow the converter to be segmented, thus allowing separation of A E information for each gamma. The other alternative in minimizing losses is to reduce the converter thickness, but this is only acceptable i f the resulting reduced conversion efficiency is feasible. February 14, 1996 77 Chapter 6 Conclusions Unlike the May 1994 test run, a dedicated SCX experiment would not be bound by a fixed value of P/B, the ratio of incident-beam momentum and CHAOS magnetic field. Pair ranges may be increased by minimizing B and maximizing P, subject to the track reconstruction routine's con-tinuing functioning as typical tracks become suffer. As well, any acceptance gains must more than compensate for the reduced cross-section as P is moved away from the A resonance. The optimal target geometry employed depends on the event type under study. Since pro-tons undergo large energy losses, a thin target is called for when analyzing one-pair events. How-ever, since the 7t°-decay gammas do not interact strongly with low-density target materials, two-pair event yields may be maximized by using a thick target without adversely affecting energy and angular resolution. Note that with a sufficiently large target, TC°'S may see the detector's geo-metrical acceptance vary significantly depending on their decay position; hence, increasing the target size may only be effective up to a point. 6.2.2 Track Reconstruction Yields of the offline analysis may be improved by relaxing the requirement that all tracks pass through all chambers. However, TT.0 events are typically of high multiplicity, so care must be taken to ensure that this modification does not generate fictitious tracks or promote excessive mis-sorting. By using a track-sorting routine that allowed WC3 hit omission, for example, one could expect the analysis yields to increase by a factor of 1/0.924- 1.4 . 6.2.3 Monte-Carlo Monte-Carlo simulations are easily the most time-consuming part of the overall analysis, and of commensurate importance in the interpretation of results. Thus, it is critical to be able to achieve good Monte-Carlo statistics. To this end, there are two modifications to the CHAOSSIM software which would significantly increase the yield of reconstructible events: 1. Force conversion of a TC° decay gamma at a random depth if it intersects the converter, and weight the event accordingly. Typical conversion efficiencies for this study are -22%, hence forcing both gamma conversions would improve yields by a factor of -20. February 14, 1996 78 Chapter 6 Conclusions 2. Restrict the e+e" out-of-plane angles to a range known to cause first-level triggers, and again weight the event appropriately. This is estimated to improve yields by a factor of -50. -5 Considering only the case for two-pair events, an increase in yields of approximately 10 is not unreasonable. However, the implementation must be done carefully, as it deals with the low-level functioning of GEANT. As well, forcing particular reactions and kinematics may require the creation of extra vertices within the GEANT tracking structure. Since the code to digitize YBOS output makes some assumptions in this regard, care must be taken to ensure it is not affected by any modifications. With the code changes outlined previously and associated improvements in yields, it then becomes feasible to calculate detector acceptances on the basis of angular bins, thus enabling dif-ferential cross-section measurements to be interpreted. February 14, 1996 79 Bibliography [I] B.R. Holstein, Phys. Lett., Vol. B244, 1990, pp. 83. [2] J. Gasser, H. Leutwyler, M.E. Sanio, Univ. of Helsinki Preprint: HU-TFT-90-55, 1990. [3] G. Hohler, TtN Newsletter No. 2, May 1990, pp.1-14. [4] M.A. Kermani, "The CHAOS Detector and Commissioning Results", Master's thesis, U.B.C., 1993. [5] S.J. McFarland, "The CHAOS Second Level Trigger", Master's thesis, U.B.C., 1993. [6] G.R. Smith, et al., "The CHAOS Spectrometer for Pion Physics at TRIUMF", Nucl. Instr. Meth., A362, 1995, pp. 349-360. [7] G.J. Hofman, J.T. Brack, P.A. Amaudruz, G.R. Smith, "Left-right resolution in high mag-netic fields for the CHAOS inner drift chamber", Nucl. Instr. Meth., A325, 1993, pp. 384-392. [8] F. Bonutti, et al., "The CHAOS Fast Trigger: An array of telescopes for e, rc, and p mass identification in the intermediate energy region", Nucl. Instr. Meth., A350, 1994, pp. 136-143. [9] CERN Computing Division, GEANT Detector Description and Simulation Tool, Geneva, Switzerland, 1993. [10] R. Arndt, SAID scattering database, version SM95, 1995. [II] G.J. Hofman, Internal CHAOS documentation, 1992. [12] M.A. Kermani, Private communication, Aug. 1995 [13] E.L. Mathie, editor, TRIUMF Users' Handbook, TRIUMF, 1987. [14] H.T. Park, "Pion Single Charge Exchange on the Deuteron", PhD dissertation, M.I.T., 1995. [15] M. Sandel et al., "Pion production in nuclear collisions with Fermi motion effects", Phys. Rev. C, Vol. 20, No. 2, 1979, pp. 744-756. February 14, 1996 80 Appendix A S C X Desiderata APPENDIX A SCX Desiderata February 14, 1996 81 Appendix A SCX Desiderata A.l 71° Decay The TC° is a light neutral meson of mass m^„ = 134.97 M e V , which decays primarily (-98.8%) via the reaction TC° —> yy, the next most likely decay branch (-1.2%) being TC° —» y e+e". — 17 -—8 It has a lifetime of x = 8.4x10 sec, with C T = 2.5x10 m. Hence, for all practical purposes the TC° may be considered as decaying at the position it is formed. A.l. l The y-y Opening Angle In its rest frame the TC°'S decay is isotropic, the gammas being emitted back-to-back. How-ever, when boosting to a lab frame, the opening angle between these gammas may decrease, de-pending on their orientation in the TC° rest frame and the TE°'S energy. The minimum lab angle between gammas, Qmm, will occur when, in the TC° rest frame, they are emitted perpendicular to the 71° momentum, which is assumed to be along the x-axis. Assuming this orientation, the x- and y-components of a single photon's momentum in the 7 t ° rest frame are P x = 0 and P y = E y , * * r> where we have used the fact that P^ = E y = m „ /2 . Taking y and p to be defined as usual, the lab-frame momentum components are P x = y • B • and P y = E y , and thus 0 m j n is given by P i 0 . = 2 • tan"1 -1 = 2 • tan - 1 — ^ min p 7 ' P For a particular 7C° kinetic energy, T 0 , y = h 1 and, since y • B = Jy - 1, this yields JC m o jt = 2 • tan - 1 + 1 2 -^1/2 To be applicable to SCX on deuterium, this 0 m j n must be further minimized over the range of available 7 t ° energies. Since 0 m j n decreases as T 0 increases, it is only necessary to consider the maximum 7 t ° energy. Taking this as the incident beam energy of 180 MeV yields 0 m j n = 51°, in agreement with the GEANT results of section 3.1.4. February 14, 1996 82 Appendix A SCX Desiderata A. 1.2 Invariant Mass For purposes of effecting cuts, useful quantities in the analysis are the invariant masses of the two Tt°-decay gammas, and the e+ and e" at a pair vertex. For two identical particles of mass m, energies Ej and E 2 , and momenta P i and P 2 , the invariant mass squared is defined as, 2 m i n v = ( E , + E 2 )2 - (P\ + P 2 ) 2 2 m i n v = E2 + 2EjE 2 + E 2 - p] - 2P, P 2 - P 2 2 m i n v = 2(m2 + E 1 E 2 - P 1 - P 2 ) 2 m i n v = 2(m2 + E 1 E 2 - | p 1 | | p 2 | c o s e 2) where 6j 2 is the angle between the two momenta (i.e. the opening angle). For photons, m .= 0 and E = |p|, in which case, m 2 n v = 2E]E 2 (1 - cos6]2) . This also holds approximately for the electrons detected in this study, since they typically have |p|/m > 46. Note that there is a strong dependence here between opening angle and invariant mass. A . 2 Pauli Blocking Suppression of the forward deuteron SCX cross-section is known to occur as the result of the Pauli exclusion principle applied to the two final-state neutrons. The deuteron has isospin 0 and is primarily in a Sj state, while the final-state nn system has isospin 1 and, restricting our-i 3 selves to relative angular momenta / = 0 , 1, may occupy the S 0 and P states. These are the only states that may be anti-symmetric under particle interchange. The S Q wave function is anti-symmetric since the neutron spins are anti-parallel. As the P state has parallel spins, the neutrons must occupy different regions of momentum space in order to be anti-symmetric under interchange. In the case of small momentum transfer from the incident pion (i.e. small 7t° scattering angles), the neutrons are likely to compete for the same momentum states since they are expected to have similar Fermi momentum distributions. The resulting sup-pression at small 7t° angles is termed Pauli blocking. February 14, 1996 83 Appendix A SCX Desiderata A . 3 G e o m e t r i c a l A c c e p t a n c e A n d R a t e s This section provides an approximate breakdown of various factors entering into the geo-metrical acceptance of the detector, as determined from the studies of section 3.1 and section 5.3, and for the beam, detector, converter, and target configurations described in this study. As well, a yield rate estimate (two-pair) will be made for 7t +d —> 7t°pp on LD 2 . Geometrical requirements for detecting a two-pair event are that the 7 t ° , y's, and e+e" pairs be emitted close to the plane of the detector, and that the two y's both convert in the lead. Table A. l summarizes estimates of these factors, yielding a total acceptance of about 5x10 6 , which is consistent with the result from section 5.4 of £, ^ ~ 4x10 6 . Description Geometrical Factor 7t° emitted in plane of detector 0.10 Decay y's emitted in plane of detector 0.10 1st y converts in lead 0.22 2 y converts in lead 0.22 1st e+e" emitted in plane of detector 0.10 2nd e+e" emitted in plane of detector 0.10 TOTAL 5xl0-6 Table A . l Approximate breakdown of geometrical acceptance. Using the overall two-pair detector efficiency for a thin C D 2 target calculated in section 5.4, £ = 9.45x10 1 , one can determine an event rate for 7t +d —> 7t°p on L D 2 , where the liquid deuteri-um density is assumed to be p = 0.163 g/cm . This yields a rate of approximately 4.6x10 5 counts/sec , per mb cross-section, per MHz incident beam, per cm of target thickness. For rj ~ 30 mb, a 3 MHz beam rate, and 5 cm thick L D 2 target, one would expect an event rate of -1.2 counts/minute. Note that this rate applies to two-pair events only and is based on the detector and converter setup of the May 1994 test run. February 14, 1996 84 

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