Non UBC
DSpace
TRIUMF
McDonald, Steven Campbell
This thesis reports the first measurement of the radiative muon capture photon energy spectrum from hydrogen, performed at TRIUMF. The partial branching ratio for photons greater than 58 Me V is measured using a large solid-angle photon pair spectrometer. With this measurement, the strength of the weak pseudoscalar coupling, gp, of the weak hadronic current for the nucleon has been obtained. This was determined by comparing the measured photon rate with the most recent relativistic calculation of Fearing and Beder which included the affect of the Δ(1232) nucleon resonance in the process. When a muon is captured by a proton at densities of liquid hydrogn, it occurs predominantly from one of two states, the ortho molecular state and the para molecular state. The muon capture probability varies considerably between the two, with the ortho state the dominant. At present there is some contention over the rate of transfer between these two states, this rate, λ₀p, can effect the total rate of capture. This rate must be known for an accurate determination of gp· Consequently, two values of gp have been obtained. One, using the measured ortho to para transition rate, λ₀p = 4.1 x 10⁴ giving a value of gp = 11.2 ± 2.5, approximately 34% higher then the Goldberger-Treiman prediction. The corresponding partial branching ratio for photons greater than 58 MeV was measured to be 1.80 ± 0.3 x 10-⁸. The second value was obtained using the theoretical prediction for the transfer rate to the ground para state, λ₀p = 7.1 x 10⁴. This gives a value of gp = 10.5 ± 2.2 with the equivalent partial branching ratio of 1.82 ± 0.3 x 10-⁸, 26% larger than the PCAC prediction.
A MEASUREMENT OF THE WEAK PSEUDOSCALAR COUPLING BY RADIATIVE MUON CAPTURE IN HYDROGEN By STEVEN CAMPBELL McDONALD B. Sc. (Hons.) University of Melbourne, 1987 A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY ID THE FACULTY OF SCIENCE SCHOOL OF PHYSICS THE UNIVERSITY OF MELBOURNE DECEMBER 1993 TRIUMF LIBRARY JUL 1 2 1994 The work presented in this thesis was not performed by any other person, except where acknowledged. The material in this manuscript has not been submitted pre-viously, in whole or part, in respect of any other academi c award. All of the work has been carried out since the official commencement date of the program. Where this thesis contains material previously published or written by another person, due reference is made in the text. Signed: Date: lll Abstract This thesis reports the first measurement of the radiati ve muon capture photon energy spectrum from hydrogen, performed at TRIUMF. The partial branching ratio for photons greater than 58 Me V is measured using a large solid-angle photon pair spectrometer. With this measurement, the strength of the weak pseudoscalar coupling, gp, of the weak hadronic current for the nucleon has been obtained. This was determined by comparing the measured photon rate with the most recent relativistic calculation of Fearing and Beder which included the affect of the ~(1232) nucleon resonance in the process. When a muon is captured by a proton at densities of liquid hydrogn, it occurs predominantly from one of two states, the ortho molecular state and the para molec-ular state. The muon capture probability varies considerably between the two, with the ortho state the dominant. At present there is some contention over the rate of transfer between these two states, this rate, >.0p, can effect the total rate of capture. This rate must be known for an accurate determination of 9p· Consequently, two values of gp have been obtained. One, using the measured ortho to para transition rate, >.0 P = 4.1 x 104 giving a value of gp = 11.2 ± 2.5, approximately 34 % higher then the Goldberger-Treiman prediction. The corre-sponding partial branching ratio for photons greater than 58 Me V was measured to be 1.80 ± 0.3 x 1 o-s. The second value was obtained using the theoretical prediction for the transfer rate to the ground para state, >.0 P = 7 .1 x I 04 • This gives a value of gp = 10.5 ± 2.2 with the equivalent partial branching ratio of 1.82 ± 0.3 x 10- 8 , 26% larger than the PCAC prediction . V Acknowledgement There are many people who have been of great assistance to me during the time I have spent working on this thesis. I now wish to acknowledge and thank them for their contributions. I would like to begin by thanking my supervisor Dr. G.N.Taylor for his guidance and encouragement throughout my Ph.d Studies. I also thank him with my sincere gratitude and appreciation for providing the financial support necessary for the many and sometimes extended stays abroad, at the TRIUMF facility, Vancouver, Canada. I thank Dr. E.G.Muirhead and Professor A.G.Klein, successive heads of the school of physics, for the excellent research facilities provided during my graduate years . I thank all members of the RMC collaboration at TRIUMF, their extensive knowledge and expertise have provided me with a rich environment in which to learn and develop my skills as a fellow researcher. In particular I thank the group supervi-sor Prof. Mike Hasinoff for ~is enthusiasm and guidance, Dr. Peter Gumplinger and Dr. Brian Doyle for their many e-mail discussions, Renee Poutissou and Dorothy Sample for teaching me the many aspects of computing and data acquisition. I also wish to thank the assistance of Dr. Mark Munro for maintaining the computing facilities on which a lot of this work was performed and also for proof reading this thesis. I also wish to extend my deepest appreciation to Jane and David Armstrong and family. Their exceptional hospitality in opening their home and lives to me made my life in Canada like a second home. My time with them and the other residents of the 'Yellow Door', Kel, Joel, Craig, Leanne and the numerous guest Vl will be remembered with fondest memories. Especially those early morning walks to TRIUMF with Jane, Emily and dogs; Max and Cheers. During the course of my graduate years I was fortunate enough to share an office with fellow graduate researchers. They are Tony Bates, Sally Koutsoliotas and David Mclean. Over the years we have shared in many discussions and experiences and they have become my closest friends. To them I owe much and we shall always remain friends. Finally, I wish to express my deepest appreciation to my parents. They have provided me with the encouragement, love and support that has allowed me the opportunity to undertake my academic pursuits. For that I thank them with all my heart. y Contents Declaration Abstract List of Tables List of Figures Acknowledgements 1 Introduction 1.1 Introduction . 1.2 Weak Interactions . 1.2.1 The Leptonic Current 1.2.2 The Hadronic Current 1.3 Conservation Principles . . . . 1.3.1 G-Parity ....... . vu 11 IV X .. XU vu 1 1 2 3 5 7 7 1.3.2 The Conserved Vector Current Hypothesis 8 1.3.3 The Partially Conserved Axial-vector Current Hypothesis . 10 1.4 Probes for Measuring the Induced Pseudoscalar Coupling . 1.4.1 Nuclear /3-decay .......... . 1.4.2 Ordinary Muon Capture (OMC). 1.4.3 Radiative Muon Capture (RMC) 2 RMC Theory 2.1 Introduction . . . . . . . . 2.2 Radiative Muon Capture . 2.3 Muon Chemistry in Liquid Hydrogen 2.3.1 Introduction . . . . . . . . . . 15 15 16 19 23 23 24 28 28 2.3.2 2.3.3 Muonic atoms and molecules. Muon induced fusion 3 The TRIUMF RMC Facility 3.1 Introduction . . . . . . 3.2 Muon and Pion Beams 3.3 The Drift Chamber . . 3.3.1 Characteristics 3.3.2 Readout Electronics 3.3.3 Gas System . 3.3.4 Calibration 3.4 Inner Wire Chamber 3.5 Beam and Trigger Counters 3.6 Cosmic-Ray Counters . .. . 3.7 Magnet . . .. . ..... . 3.8 The Liquid Hydrogen Target . 3.9 Data Acquisition . . . 3.9.1 Trigger Logic . 3.9.2 Fastbus System 3.9.3 Blanking . 3.10 Run Summary . . 4 The Measured RMC Photon Spectrum 4.1 Introduction . . . . . . . . . . . . . . . . 4.2 Track Reconstruction . . . . . . . . . . . 4.2.1 Transverse Momentum of a Track 4.2 .2 Longitudinal Momentum of a Track . 4.3 2D or NOT 2D 4.4 Cuts 4.4.1 4.4.2 Quality Cuts Physical Cuts 4.5 The E>. perimental Photon Spectrum 4.6 Counting the µ and 1r Stops. . 4.6.1 Pile-up correction ... 29 33 37 37 40 43 46 47 48 50 52 53 55 57 57 60 62 67 70 70 73 73 74 75 76 79 81 82 85 . 106 . 109 . 110 4.7 4.6.2 . Beam counter efficiency correction . 4.6.3 Random veto correction ..... . 4.6.4 Scattering and absorption correction Summary . . 111 . 112 . 113 . 115 5 Determining g'P 117 5.1 Introduction . . . . . . . . . . . . . . 117 5.2 The Theoretical Photon Spectrum . . 117 5.3 Muon Chemistry Considerations . . . 121 5.3.1 The Atomic Singlet, Ortho and Para Molecular States. . 121 5.3.2 The Partial Branching Ratio . . . . . . . . 125 5.4 Predicting the Experimental Photon Spectrum . . 127 5.4.1 Detector Response . . . 128 5.4.2 Detector Acceptance . . 129 5.4.3 BCR Cut Efficiencies . . 132 5.4.4 Blanking Correction . 5.4.5 Checking the Monte Carlo Simulation . 5.5 Determining F(E) . . . . . . . . . . . . . . . . 5.6 Normalisation . ................ . 5.7 The RMC on H Partial Branching Ratio and gp 6 Conclusions 6.1 Summary of Results 6.2 Further Work Bibliography . 135 . 135 . 138 . 141 . 144 147 . 147 . 148 153 X List of Tables 1.1 The six coupling constants needed to describe the vector minus axial vector form of the weak hadronic current . . . . . . . . . . . . . . . . 10 1.2 Summary of the values of gp as determined from measurements of the 0 MC rate in hydrogen. . . . . . . . . . . . . . . . . . . . . . . . . 1 7 1.3 Muon lifetimes, capture and decay probabilities in various nulcei. 21 3.1 Drift chamber characteristics . 45 3.2 Drift Cell wire characteristics 3.3 Summary of theµ+ data taking 3.4 Summary of the µ- data taking 4.1 Summary of the Photon and Track cut parameters used in the DPLOT 47 72 72 routine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.2 Contribution to the RMC photon spectrum from the high energy tail 96 4.3 The estimated contribution from photons arising from RMC in the gold and surviving longe~ then 365 ns. . . . . . . . . . 99 4.4 Summary of the cosmic-ray background data analysis. . . 102 4.5 Estimated background contribution from cosmic-ray induced events for each data period and data type. . . . . . . . . . . . . . . . 103 4.6 Summary of the 3He contribution to the photon background. . 105 4. 7 Summary ofµ- data, with the estimated contributions from the most significant sources of photon background. . . . . . . . . . . . . . . . . 109 4.8 Correction factors due to the effect of multiple beam particles per beam pulse .................... . 4.9 Beam counter efficit acies and correction factors. 4.10 Correction factors arising from random vetoing of an event by the the . 111 . 112 inner veto counters ............................. 113 4.11 Fraction of muons 3topping in the various mater ial surrounding and before the liquid prdium target . . . . . . . . . 114 4.12 Summary of the corrected number of µatopa· • 115 5.1 The decay and transfer between the various atomic and molecular states of liquid hydrogen. . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.2 Partial branching ratio for RMC on hydrogen for various values of 9p with contributions from the singlet ortho and para states . 125 5.3 Summary of the Bit cut Efficiency. . . . . 134 5.4 Summary of the Random cut Efficiency. . 134 5.5 Summary of the Cosmic cut Efficiency. . . 134 5.6 BL correction, due to vetoing from a second beam particle. . 135 5. 7 Fraction of pions stopping in the various mater ial surrounding and before the liquid protium target. . . . . . . . . . . . . 138 5.8 Normalised acceptances for the ,r-p data. . . . . . . 143 5.9 Normalised number of muon stops for the µ-p data 5.10 Values for G~ss and gp using ,\OJI= 4.1 x 104 5.11 Values for G-?_ss and gp using Aop = 7.1 X 104 6.1 Summary of the investigation into the acceptance . . 143 . 145 . 145 . 152 Xll List of Figures 1.1 The semi-leptonic process, Ordinary Muon Capture, (OMC). . . . . . 4 1.2 The Three most dominant diagrams contributing to the amplitude if the axial vector current . . . . . . . . . . . . 12 1.3 Summary of all known measurements of gp.. 18 1.4 The sensitivity of the RMC and OMC rates to changes in the pseu-doscalar coupling constant, "gp . . . . . . . .. . . ·. . . . . . . . . . . . . 20 2.1 Feynman diagrams of the dominant amplitudes that contribute to the Radiative Muon Capture process in hydrogen .... ... . 2.2 Contributions to the RMC rate from the Delta resonance . 2.3 The dominate muon transfer channels. . . . . . . . . . 2.4 Flow chart of the princple channels for muon transfer .. 3.1 Projected view of th e! RMC pair spectrometer at TRIUMF .. 3.2 View of the RMC spectrometer along the beam axis . 3.3 The stopped 1r / µ beamline, M9A. . . . . . . . . . . . 3.4 RFS principle of operation . . . . . . . . . . . . . . . 3.5 x - y view of a photor. event in the RMC spectrometer . . 3.6 z view of a photon event in the RMC spectrometer. 3. 7 Drift cell characteristics . . . . . . . . 3.8 Schematic of the gas recycling system. 3.9 Schematic of the cosmic-ray veto counter positions 3.10 RM C liquid protium target. . . 3.11 Data acquisition configuration .. 3.12 Trigger logic. . .. . ..... . 25 28 31 34 38 39 41 42 44 44 46 49 56 59 61 63 4.1 Determination of the longitudinal component of momentum for a charged particle in a uniform magnetic field. . . . . . . . . . . . . . . 76 4.2 The Road Method procedure for locating tracks in a drift cell. . . . . 78 4.3 Figure (a) illustrates the charactdistics of a no wrap event, (b) illus-trates those of a wrap event. . . . . . . . . . . . . . . . . . . . . . . . 80 4.4 Histograms of the various parameters used to select well resolved photons. The histograms are ,r-p calibration data . . . . . . . . . . . 84 4.5 Photon energy spectrum from the µ+ 's stopping in the liquid hydro-gen (a) before cuts and (b) after the Photon and track cuts . . . . . . 86 4.6 The photon energy spectrum obtained by stopping a µ- beam in liquid hydrogen, ( a) no cuts, (b) after 1r cut . . . . . . . . . . . . . . 89 4. 7 The contributions to the muon decay photon spectrum from the three processes (i) radiative decay, (ii) bremsstrahlung and (iii) annihilation. 94 4.8 The magnitude of the ratio annihilation to bremsstrahlung plus ra-diative decay in positive muon decay at varicus photon energies. . . . 94 4.9 Decay curve for muons in Au for the data taking periods (a) January 1991, (b) December 1990. . . . . . . . . 97 4.10 An example of a Random photon event .. 4.11 Photon spectrum after Photon, Track and Bit cut s . 4.12 Photon spectrum after Random, Cosmic and Blank cuts. 5.1 Shape of the photon spectrum from the singlet state for different . 104 . 107 . 108 values of 9p· ............. . ....... . .•....... . 118 5.2 Shape of the photon spectrum from the ort .ho state for different values of 9p· ... . _ ........ . .. . . . • • . • ......••.. 119 5.3 Shape of the photon spectrum from the para stat e for different values of 9p·" . .• .•........•.•.•••••.•••••.•..•.• • 119 5.4 Shown are the photon contribution of the singlet, ortho and para states to the total photon spectrum for gp = 1. . . . . . . . . . . . . . 120 5.5 Partial photon rate (Emin = 58 MeV) versus 9p· •••••••••••• 120 5.6 The population of the various atomic and molecular states in liquid hydrogen over time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5. 7 The probabilty of RMC in liquid hydrogen per muon capture as a function of time. . . . . . . . . . . . . . . . . . . . . 5.8 Partial branching ratio (Emin = 58 MeV) versus 9p· . 5.9 The response function for various photon energies E...,. . 124 . 126 . 129 5.10 Acceptance curve for mono-energetic photons ... . . . .... . ... 130 5.11 Shape of RMC spectrum between 58-100 MeV. . . . . . ....... 131 5.12 The (1r-p) Monte Carlo spectrum generated using the RMCGEANT v5.207 compared with the measured (1r-p) photon spectrum .. . ... . . . 136 5.13 The Function F(E) for January 1991. This represents the difference between the acceptance determined by a Monte Carlo calculation and the measured acceptance for the 1r-p process. . ...... . .. . . . 141 5.14 (1r-p) acceptance data. . . ... . .. . .... . .... . ...... 142 5.15 Determination of 9r,· The dashed curve was obtained using the cal-culated ortho to para transition rate of Aop = 7.6 x 104 • The solid curve uses the experimentally determined rate of Aop = 4.1 x 104 • • 145 6.1 All measurements of 9r,· • . . • . . . . . • . . . • . . • . • . . . . . 149 1 Chapter 1 Introduction 1.1 Introduction In 1965 Rood and Tolhoek [I] indicated that the radiative muon capture (RMC) process is especially sensitive to the strength of the pseudoscalar coupling. This coupling, commonly labeled as g.,, arises from the influence of the strong force on the electroweak interaction. An understanding of g.,, provides information about how these two forces interact at energies where QCD is not calculable, and the theory of weak interactions fails to completely describe the weak behaviour of hadrons. The RMC process has a small branching ratio, (- 10-s per stopped muon). Consequently, in the preceeding 35 years only a handful of attempts have been made to measure this process. Until now nobody has attempted the most elementary process, RM C on the proton (I.I) Only now, with the advent of accelerators capable of producing high-flux muon beams and with the development of suitable detector technology, is it feasible to attempt a measurement of the fundamental process, RMC on hydrogen. This thesis describes such an experiment. This chapter reviews the familiar Standard Model of weak interactions. It de-scribes the present understanding of weak hadronic currents in terms of the "V -A interaction". It then reviews the concept of induced weak currents which have been 2 Chapter 1. Introduction adopted to account for the effects of the strong interaction. A brief summary of each of the induced currents is presented, with particular emphasis on the experimentally least known, the induced pseudoscalar current. A review of the attempts and the .methods used in the past to determine 9p is presented, summarising the advantages and disadvantages of each technique. Finally, the radiative muon capture process in hydrogen is presented as the preferred probe for determining ~he strength of the induced pseudoscalar coupling , 9p· 1.2 Weak Interactions The electroweak theory, SU(2)®U(l), of Weinberg-Salam-Gia.show [2, 3, 4) pre-dicts very well the behaviour of the electroweak interaction of leptons and quarks. For pure leptonic processes the theory is exact. In contrast, weak interactions in-volving hadrons are more difficult to calculate. This arises because hadrons are composite objects and while individual weak quark currents could be described ad-equately by the Standard Model, the effects of the spectator quarks carrying the strong interaction cannot be calculated. Until a comprehensive theory for all electroweak and strong interactions at all energies can be established, phenomenological extensions to the Standard Model are used to bridge the understand ing of the interaction between these two forces. By applying observed conservation properties, invariance principles and the introduc-tion of form factors it is possible to provide a basis for understanding the underlying structure of the lesser known and calculable semi-leptonic processes. It will be the aim of this thesis to provide a better understanding of the least known of these form factors, namely the pseudoscalar form factor . Extensive theoretical and experimP,ntal work over the past 60 years has pro-vided a detailed understanding of the conservation properties and , he form factors of weak interactions at low energies . The earliest of these studies began in 1934 when Enrico Fermi [5, 6) presented the first comprehensive theory of nuclear beta 1.2. Weak Interactions 3 decay. Formulated in close analogy with the gauge theory of quan-'.um electromag-netic interactions, Fermi proposed four fermion currents interacting at a point. The next major step forward came from the work of Feynman and Gell-Mann in the late 1950's [7]. This was based mostly on experimental observations of parity violation and revealed the underlying "V -A" nature of the weak process. What finally culmi-nated in the late 1960's was the comprehensive theory of weak and electromagnetic foteractions by Weinberg, Salam and Glashow [2, 3, 4]. It was shown that a weak inter~tion Lagrangian for the charged weak current can be constructed with the form: For beta decay and muon capture, q2 Mlv (Mw BOGeV). In this low energy limit, the non-local effects due to the vector boson propagator are negligible and the current-current description is adequate [8]. This is given by: ~elf ( ) ,..,, L,weak X = - J1(x)J'\x) + Hermitian conjugate, (1.3) with the effective weak coupling constant GF given by GF = y2g 2 /Mlv, and J>.(x), a vector current which can be decomposed into hadronic and leptonic components, (1.4) A pure leptonic interaction consists entirely of the leptonic component to J >. (x), while a semi-leptonic process contains both hadronic and leptonic terms. In this work we will consider the semi-leptonic process of muon capture by a proton. 1.2.1 The Leptonic Current Figure 1.1 represents the capture of a muon by a proton, a semi-leptonic pro-cess. In the left portion of the diagram, leptons are the only participating particles 4 µ Leptonic current w 2 q =0 Weak Hadronic current Chapter 1. Introduction (n) d d 1l udu (p) Figure 1.1: Ordinary muon capture (OMC) is a semi-leptonic process, consisting of both a leptonic and a hadronic current . The hadronic current has a composite quark structure, consequently the additional strong interactions can interfere with the bare weak hadronic current, giving rise to extra structure . This additional structure is represented by the enlarged vertex. (excluding the propagator of the interaction). They contain no observable internal structure, consequently the interaction vertex is point-like and has a pure vector minus axial vector (V -A) form. The weak leptonic current for this interaction can be represented by: (1.5) Where ,>. are the Dirac gamma matrices, with ,s cl.efined as 15 = i, 0111213. The Viep = ,>. and A1ep = "(>. "(s form of the interaction is evident . This is a dir, ct consequence of weak processes coupling only to left handed (negative helicity state) particles and right handed (positive helicity state) antiparticles. 1.2. Weak Interactions 5 1.2.2 The Hadronic Current In the case of the weak hadronic current the Standar d Model does not specify the composite structure of the hadron and therefore cannot provide a complete description of the hamiltonian. However, if one were to examine the hadronic current at the quark level (right side of Fig. 1.1 ), the essential process is the transformation of an up quark to a down quark, (or on the hadron level, a proton into a neutron). If it were possible to turn off the additional strong interactions between the spectator quarks, the weak hadronic current can be written with a similar form to the leptonic current, namely (1.6) Once again the-V-A form of the interaction is evident. The additional cos 0c factor is the Cabbibo angle which accounts for the mixing between the quark generations [9]. No mixing has been observed in the lepton generations. If the strong interaction is now allowed to be turned on, the above expression for the hadronic current, Eq. (1.6) becomes (1. 7) where, (1.8) and The terms Fv(q2) and F11(q2) are the familiar vector and axial-vector form factors respectively, of the hadronic current. The four additional form factors Fm(q2 ) 'weak magnetic', Fa(q2 ) 'scalar', Ft(q2 ) 'tensor' and Fp(q2 ) 'pseudoscalar' are constructed to account for the effects of the strongly interacting particles on the 'bare' weak hadronic current. The extra terms are called 'induced' weak currents because they are induced by the presence of strong interactions between the confined quarks. They do not arise naturally from electroweak theory but are constructed to account 6 Chapter 1. Introduction for the compositeness of the hadron. In general these are complex form factors which are functions of the momentum transferred between the proton and muon, q2 ( defined by q>. = P>. - n>., where P>. and n>. are the proton and neutron four-momenta). In the region q2 m; relevant to RMC, the q2 variation is small for all form factors except Fp(q2). Consequently, a related set of coupling 'constants' is constructed: 9v(q2) = Fv(q2 ) 9m(q2) = 2MFm(q2) 9a(q2) = m1Fa(q2) 9a(q2) = Fa(q2) 9p(q2 ) = m1Fp(q2 ) 9t( q2) = 2M Ft( q2 ), where M is the nucleon mass and m1 the mass of the lepton. (1.10) (1.11) (1.12) (1.13) (1.14) (1.15) The induced terms are all proportional to the square of the momentum transfer q>., Consequently in /3-decay, contributions from the induced current terms are neg-ligible and are difficult to observe in experiment. For muon capture, the momentum transfer is considerably larger and the induced current terms cannot be ignored. Invariance principles and conservation laws constrain the structure of these form factors [10, 11]. For example, time-reversal invariance requires that all the 9i ( i = v, m, s, a, p, t) be real. The presence of the 9a and 9t terms imply the presence of second class currents. The conserved vector current ( CVC) hypothesis relates 9m to the usual electromagnetic form factors, while the partially conserved axial-vector current (PCAC) hypothesis together with the Goldberger-Treiman relation constrains 9p· These principles are examined in detail in the following section. 1.3. Conservation Principles 7 1.3 Conservation Principles 1.3.1 G-Parity The operator, G, is defined by (1.16) where C is the charge conjugation operator and ei1rT2 generates a rotation of 180° around the Traxis in isotropic spin space (i.e. translates n -+ p and vice versa). Strong interaction processes are invariant under a G-parity transformation . It is reasonable to assume that currents induced by strong interactions might also con-serve their G-parity. Both the bare vector and axial vector terms transform with a definite G-parity, ava- 1 = v, GAa-1 = -A, (1.17) (1.18) even for the vector and odd for the axial vector. Both 9m and gp transform with the same G-parity as the bare vector and axial vector terms respectively; the vector and magnetic being even and the axial vector and pseudoscalar being odd . These are by definition 'first-class' currents. The 9a and 9t induced currents transform with opposite G-parity, i.e. ava- 1 = -v, GAa-1 = A. (1.19) (1.20) Currents with this property have been classified by Weinberg [10] as 'second-class' currents. It is generally accepted that second-class currents do not exist. They do not arise naturally in gauge theories and there has been no convincing evidence for 8 Chapter 1. Introduction non-zero values [11, 12, 13, 14, 15]. For the purpose of this investigation, second-class currents will be neglected and so one can write: F.(q2) = 0, Ft(q2) = 0. 1.3.2 The Conserved Vector Current Hypothesis (1.21) (1.22) The electromagnetic current of the proton and neutron can be given by the expressions [16, 17], (1.23) and (1.24) where Fl( q2 ) and F:( q2 ) are the Dirac and Pauli form factors of the proton re-spectively. F{'(q2) and F2(q2) are the same for the neutron. The form factors are normalised to unity at q2 = 0, except Ff( q2) which is zero. The form of the vector part of the weak hadronic current as defined by Eq. ( 1.8) is similar to Eqs. (1.23) and (1.24), with the exception of the additional F. scalar term, which is zero with the assumption of no second-class currents. This subsequently led Feynman and Gell-Mann [7] to postulate the isovector current hypothesis. The isovector current hypothesis (IVC) states that the isovector part ' of the electromagnetic current and the vector parts of the charge raising ( n -+ p) and charge lowering (p -+ n) weak current, form an isotriplet vector of current operators, 1.e. (1.25) Assuming a similarity with the electromagnetic current, Feynman and Gell-Mann postulated that the weak vector current will also be conserved. This is the conserved 1.3. Conservation Principles 9 vector current hypothesis or eve and it can be simply expressed by the following relationship, (1.26) With this divergence condition and the IVe hypothesis expressed by Eq . (1.25), the weak vector, F,,(q2 ), and weak magnetism, Fm(q2 ), form factors can be related to the Dirac and Pauli form factors of the electromagnetic current for the proton and neutron. In the limit q2 -+ 0 these reduce to (1.27) for the vector form factor , and to (1.28) for the weak magnetic form factor. The values µp and µn are the proton and neutron anomalous magnetic moments (18] in Bohr magnetons, µp - 1.793 (1.29) and µn = -1.913. (1.30) The conserved vector current ( eve) hypothesis is a natural consequence of the Standard Model and has been well supported by experimental evidence (19] (see table 1.1 ). It should be pointed out that if the eve condition is applied directly to Eq. {1.8) then eve requires F.( q2) to be zero, consistent with the exclusion of second-class currents. It remains to describe the axial vector, F4 (q2), and the pseudoscalar, Fp(q2 ), form factors. 10 Chapter 1. Introduction Coupling Theoretical Experiment Technique Constant Prediction Measurement 9v(0) 1.0 1.000 ± 0.002 µ-decay [20) 9m(0) 3.706 3.78 ± 0.20 /3-decay, µ-capture 9a(0) -1.32 -1.261 ± 0.004 neutron lifetime [21] gp(0.88m!) -8.5 -8.7 ± 1.9 µ-capture on H 9t(0) 0 0.03± 0.21 /3-decay, A=12 [13] 9s(0) 0 < 0.003 /3-decay [22] Table 1.1: Summary of the six coupling constants needed to describe the form of the vector and axial vector currents of muon capture. The theoretical values are obta ined from known conservation properties such as eve, PeAe, G-parity and time-reversal invariance. 1.3.3 The Partially Conserved Axial-vector Current Hypothesis Assuming no second-class currents, the general form of the axial vector current between nucleons can be written as [16), (1.31) The matrix element in Eq . (1.31) can be mostly attributed to three processes. These processes are illustrated in Fig . 1.2. If the strong interaction is again imagined to be turned off, diagram 1.2(a) represents the capture of a muon by a bare proton, and contributes the term ;>..;sin Eq. {1.31). If the strong interaction is now turned on, pion vertex corrections must be added (see Figure 1.2(b )). Pion vertex correc-tions are responsible for renormalising the magnitude of 90 from the naked value of 1 to 1.26, the measured value. The final diagram 1.2(c), represents the contribution from one-pion exchange (OPE). The amplitude for this term can be written, using 1.3. Conservation Principles the Feynman diagram approach as with OPE Amplitude= (p -+ n1r) x ( 1r propagator) x (µ- -+ 1rvµ), · (p-+ n1r vertex)= iG1rNN(q2)../2. (1Pn'Y51Pp), 1 ( 1r propagator) = .( 2 2 ), i q +m1r (µ- -+ 1r-vµ vertex)= °;_if1rq>.(1P11,. 1>.(l - 1s)t/Jµ), 11 (1.32) (1.33) (1.34) (1.35) The parameter G1rNN is the pion-nucleon coupling constant and /1r is the pion decay constant. The amplitude for one-pion exchange is constructed by combining all three of the above to yield the following expression, The above amplitude contains the factor qµ15. A comparison between this am-plitude and the term containing Fp( q2 ) in Equation (1.31) gives, (1.37) The additional factor H(q2 ) has been added to account for all the vertex cor-rections associated with one-pion exchange. H(q2 ) is normalised such that H(q2 = -m!) = 1 and is a smooth function of q2 • Multi-pion exchange would give a further additive correction to Eq. (1.37), but these diagrams are second order effects and have been neglected . Substituting Eq. (1.37) into the equation for the axial vector current, Eq. (1.31 ), yields (1.38) 12 p µ Chapter 1. Introduction ff n p 0 n p .. ff-1 w - w -w-: - -v,,. µ v,,. µ a) b) c) Figure 1.2: The three most dominant diagrams contributing to the terms in the axial vector current . (a) Bare muon capture , (b) muon capture with pion vertex corrections and (c) one-pion exchange. n ... In section (1.3.2) the eve hypothesis was used to relate the vector and magnetic weak form factors to the Dirac and Pauli form factors of the electromagnetic cur-rent. The axial vector has no electromagnetic analogue . However , it has just been shown that one-pion exchange contributes to the axial vector current . The pion is a pseudoscalar particle, J1r = o-. The only four vector available to the matrix element (OIAl1r) is the pion momentum vector, q, such that : (1.39) where f 1r is the pion decay constant and <P1r the pion field. Taking the divergence of Eq. (1.39) yields the result, (1.40) Since neither m1r nor /1r are zero, the axial current is clearly not conserved. However, a partial conservation of the axial vector current, PeAe [23, 24] can be considered, namely, (1.41) 1.3. Conservation Principles 13 which in the limit of m1r 0 recovers conservation. Applying the PCAC condition Eq. (1.41) to Eq. (1.38) and using the Dirac equation,"'(µ ,,8 tp = -mt/J, gives, v:z:µ {1.43) Taking the limit as m1r 0 gives (1.44) Evaluating Eq. {1.44) at q2 = 0, with f1r = 130.8 ± 0.3 [18], G1rNN = 13.40 ± 0.8 [25]and using the normalisation condition H(q2 = 0) H(q2 = -m;) = 1, yields the Goldberger-Treiman [26] relation for Fa, {1.45) Using the Goldberger-Treiman relation and the general equation for Fa ( q2) (Eq. ( 1.44)) yields a prediction for the induced pseudoscalar coupling, {1.46) where, (1.47) The value of f has been estimated using a monopole form of G1rNN [27]. For small q2 , f = 0.006. The smallness of this value is due to the similar q2 dependence of Fa and G1rNN for small q. Neglecting f and in terms of the coupling constants, 14 Chapter 1. Introduction the pseudoscalar coupling may be written as (1.48) for the muon capture process. The pseuodoscalar coupling term is an induced cur-rent, consequently its magnitude will vary for different processes. The q2 dependence of g'P is clearly dominated by the pion pole, indicating that the pseudoscalar contribution is dominated by pion exchange. For ordinary muon capture the two body final state kinematically constrains q2 to 0.88m!. Substituting this into Eq. (1.48) yields the Goldberger-Treiman prediction for g'P/ 9a.· or g'P = 6.78, 9a. g'P = 8.56. (1.49) (1.50) The value of 9a. has been taken to be the measured value of 1.261 ± 0.004. The 5% discrepancy between the measured value of 9a. and the value determined on theoretical grounds is attributed to the size of the chiral symmetry breaking. This discrepancy is addressed in references [25] and [28]. Of all the form factors required to describe the weak hadronic current, the pseu-doscalar coupling, g'Pl is clearly the least tested to high precision. The world average of the five measurements in the last 30 years carr ies an uncertainty of 22%, with the single most accurate measurement in excess of 40%. In contrast, measurements of other coupling constants 9v,9m and 9a. at q2 = 0 are better than 0.3% (see table 1.1). Theoretical calculations claim a value of g'P=6.8ga. with an uncertainty of just 3%. Clearly a more precise experimental determination of g'P is required. It is the goal of this work to improve the measured accuracy of the pseudoscalar coupling strength, gp, of the weak hadronic current. The discussion that follows describes the different probes that have been used in the past to measure 9p· The advantages and 1.4. Probes for Measuring the Induced Pseudoscalar Coupling 15 disadvantages are addressed along with the reasons for choosing RMC as a preferred process for the measurement of 9p· 1.4 Probes for Measuring the Induced Pseudoscalar Coupling Many probes have been used in the past to test the form of the weak hadronic current. Generally one has been limited in these tests, not by theoretical consider-ations, but rather by the formidable experimental requir ements. It has long been recognized that RMC is particularly sensitive to the pseud oscalar coupling, but it is only now with the high muon fluxes achievable at the modern meson factories and with the development of detector technologies that such a measurement is feasible. However, it is instructive to examine the probes that have yielded measurements of gp in the past. 1.4.1 Nuclear /3-decay Nuclear beta decay has been an exceptional probe for examining semi-leptonic weak interactions. It was the first evidence that prompte d Fermi in 1934 to formu-late his theory of weak interactions. It has been the basis of extensive experimental tests of weak interactions, in particular, the vector (gv), axial-vector (ga) and weak magnetism (gm) form factors. However, in nuclear beta-de cay the momentum trans-fer, q2 , is fixed and very small, (q2 (M; - MJ)). Consequently, the weak induced pseudoscalar coupling is extremely difficult to measure. The ratio of gp to 9a is, (1.51) The result of the Bhalle and Rose experiment [29] can only put a limit of gp/ 9a < 90 for electron capture. The related radiative electron capture process ep nv 1 has not revealed significant information either [30]. Clearly a different approach was needed. 16 Chapter 1. Introduction 1.4.2 Ordinary Muon Capture (OMC) An alternative process for obtaining information about induced currents is ordi-nary muon capture (OMC) . The larger mass of the muon ("' 205 times me) enables a larger momentum transfer (q2 = 0.88m!)- The ratio of the pseudoscalar to axial-vector coupling constant becomes gp = 7 9a, 140 times larger than in electron capture; a considerable enhancement compared with nuclear beta decay. Therefore, ordinary muon capture offers to be a more sensitive probe for determining the strength of the induced pseudoscalar current. In any discussion of weak hadronic currents it is important to distinguish between the form factors associated with a bare nucleon and those of a nucleon embedded in a nucleus. The observed quenching of the axial-vector 9a in (p, n) reactions (31] has long indicated possible "renormalisation" effects of the nuclear medium . More recently, it has been shown [32] that the quark momentum distributions ( or structure functions) of a free proton , differ from those of a proton in a nucleus. This is the well known EMC effect. Intuitively, it is not unreasonable to expect some renormalisation of the axial and pseudoscalar couplings. To illustrate this, reconsider the three diagrams in Figure 1.2. The first diagram (1.2a) represents the transition of a nucleon without considering the hadronic structure, (i.e. a pure weak vertex) and gives a contribution of 1 to 9a· The second diagram (1.2b) exchanges a pion (via the strong interaction) between two nucleons. This strong pion vertex correction gives rise to the well-known, renormalised axial vector, 9a = l.26g:ure . Finally, diagram (1.2c) contributes to the pseudoscalar, gp term, by turning up as a pion propagator proportional to l/(q 2 + m!), bringing a pion-pole into the process. It is then readily seen how a renormalisation of 9a and gp for a nucleus could be explained by a renormalisation of the l- ,onic field, ¢,,,,. In a nuclear medium the exchanged virtual pion can be scattered by the surrounding nucleons. This has the effect of reducing the effective range of the pion by polarizing the nuclear medium. It is therefore reasonable to 1.4. Probes for Mea.suring the Induced Pseudosca.lar Coupling 1. ( - Target gp 9p/9a Reference -l.quid H2 6.0 ± 8.0 4.8 ± 6.3 Bleser et al. 1962 (34] liquid H2 11.0 ± 4.3 8.7 ± 3.4 Rothberg et al. 1963 (35] gas H2 10.3 ± 3.9 8.2 ± 3.1 Alberigi Quara nta et al. 1969 (36] gas H2 7.9 ± 5.9 6.3 ± 4.7 Bystritiskii et al. 1974 (37] liquid H2 7.1 ± 3.0 5.6 ± 2.4 Bardin et al. 1981 [38] 8.7 ± 1.9 6.9 ± 1.5 World Average Table 1.2: Summary of the values of Up as determined from measurements of the OMC rate in hydrogen. The values presented have been corrected for the affects of th ,i ortho to para transition rate as determined by Bardin et al. [39]. 17 replace the free pion field with an effective pion field, ¢>':, for a pion in a nuclear medium. The conseyuence is a renormalisation of the weak hadronic currents 9a and gp in nuclei. Evidence for a renormalised axial-vector comes from Gamow and Teller [31, 33]. Typically, the best shell model calculations require a 20% renormalisation of the nucleonic value, 9a ,.._, 1.26, to 9a ,.._, 1 in the presence of a large number of nucleons. To study modifications of gp in a similar way, it is first necessary to extract gp for the nucleon, where one is free from nuclear structure uncertainties. The obvious system to use is the hydrogen nucleus, consisting of a single proton. Theoretical calculations are precise and there are no approximations of the nuclear structure . Experimentally, the single nucleon system presents an en ormous challenge to the experimentalist, having to compete with low rates and large backgrounds. For hydrogen, the branching ratio for the elementary process µp -+ nvµ is ,.._, 10- 4 , Consequently, only a handful of measurements of OMC in hydrogen exist. A summary of all OMC measurements in hydrogen is compiled in table 1.2. The results in this table are also illustrated in Fig. 1.3. These measurements represent the only direct information available on gp for the nucleon . While the rate of OMC in hydrogen has been measured to high accuracy (- 4%) it is relatively insensitive to the value of gp, yielding uncertainties of at least 42% on individual measurements of 9p· 18 Chapter 1. Introduction 15-+----'----L-------''--------'-----'----'----+-12 9 1i Ill .. II ,0 II ... 1:1 II .. II ::I a - - - - - - - -.a- - - - -1i .. II II s ... Ill 0 ,:: p:; II :2 ,-c - - - --;; - - - PCAC Value -3-------.----.----,.----.----,----..----t-1962 1963 1969 Year 1974 1981 1993 Figul'e 1.3: This figure is a summary of the measurements presented in table 1.2. The dashed line indicates the Goldberger-Treiman theoretical prediction for gp/9a using the PCAC hypothesis. 1.4. Probes for Measuring the Induced Pseudoscalar Coupling 19 1.4.3 Radiative Muon Ca'pture (RMC) Radiative muon capture (RMC), unlike OMC, liberates an inner-bremsstrahlung photon with an energy below the muon rest mass (- 105 MeV), i.e. µ- + N ( Z) -+ N ( Z - 1) + 11" + , . (1.52) Consequently, the momentum transferred between the muon and proton can vary from -m! (radiated by the proton), up to 0.88m! (rad iated by the muon). Ex-amination of Eq . (1.48) shows the q2 dependence of 9p· For q2 approaching -m! ( corresponding to the high end of the photon spectrum) the pion-pole dominance becomes important. At high photon energies, an enhan cement of 3.5 in the rate compared with OMC makes RMC a preferable process for determining gp to higher precision. Additionally, the high energy photons from RMC are generally easier to detect than the 5 MeV neutrons in OMC. The conceptual advantage of the increased sensitivit y of gp to RMC is almost eliminated by the very low rate of the elementary process, µ- + p-+ n + 11µ + ,, (1.53) which occurs only once for every 108 stopped muons, four orders of magnitude smaller than the OMC rate . Consequently, the elementary process of radiative muon capture by a proton has, until now, eluded experimental investigation. In ad-dition, only photon energies above E..., 2:: mµ/2 are accessible to observation. Below this threshold the RMC photon spectrum is indistinguishable from the unavoidable electron outer-bremsstrahlung spectrum from muon decay, and the radiative muon decay processes: 98% 1.4% (1.54) {1.55) ~-20 Q) ro 0:: 0 ..... Q) tlD 0 ro ...0 CJ Chapter 1. Introduction 20 15 10 5 --- -- --- --0 -5 -10 ---µ +p_. v+n+-y (RMC) --- --- ---µ +p--+ v+n (OMC) ---15-t---,---,r-r-,--r---,--r--r-,----r----r--,---,r-r-----r--r---,--r-,-~ -20 -10 0 10 % change in gP Figure 1.4: The sensitivity of the RMC and OMC rates to changes in the pseudoscalar coupling constant, g1 . 20 1.4. Probes for Measuring the Induced Pseudoscalar Coupling Nucleus z Lif ~time (µs) Capture% Decay% H 1 2.195 0.1 99.9 C 12 2.026 7.8 92.2 Ca 40 0.333 84.9 15.1 PB 82 0.072 96.7 3.3 Table 1.3: Muon lifetimes, capture and decay probabilities in various nulcei [45]. 21 In an attempt to overcome the inherent low rate of muon capture by a bare nucleon, previous collaborations (as with OMC measure ments) have concentrated their experimental efforts on nuclear radiative muon capture [40, 41, 42, 43, 44). While extraction of gp is more difficult because of the lack of understanding of the nuclear physics involved, the rate of capture is significantly enhanced. For a large nucleus like Pb, the muonic Bohr orbit is approximately 3 fm. The corresponding nuclear half-density radius is "' 6.5 fm. Consequently, the overlap of the muon and proton wave function is sufficiently large to allow muon capture to compete with the more frequent muon decayµ-+ evellµ process. This is illustrated in table 1.3 where typical decay and capture probabilities for various nuclei are presented . Additionally, a study of RMC in nuclei of Z > l offers insight into possible renormalisation effects of gp as a result of the surrounding nuclear medium, for example, meson exchange currents (MEC) and medium polarizations. Despite how interesting the prospect of a renormalised gp may be, it remains essential to the basic understanding of weak hadronic currents, that the naked nucleonic value of gp be determined. While it seems clear from the body of evidence from nuclear RMC experiments that gp is being renormalised by the nuclear medium, the bare value of gp remains hidden in only a few experiments with large uncertainties . The goal of the work described in this thesis was to measure the branching ratio for RMC on hydrogen and provide a determination of gp more accurate than previous measurements. This will thereby test the well known and accepted Goldberger-Treiman relation for the bare nucleon. A review of the theoretical developments that have culminated in our present understanding of RMC are presented in Chapter 22 Chapter 1. Introduction 2. Chapter 3 discusses, in detail, the experimental facility and technique used to measure the rad iative muon absorption process in liquid hydrogen . In chapter 4, the · photon backgrounds from competing processes are examined along with the methods developed to identify and eliminate them . Finally, in chapter 5 the method used to extract gp from the RM C rate in hydrogen is presented. 23 Chapter 2 RMC Theory 2.1 Introduction The first discussion of internal bremsstrahlung in muon absorption was presented by Huang et al. in 1957 (46]. It was only a few years later, in 1962, that the first photon from radiative capture in iron was observed by Conforto et al. (47]. In 1965 the theoretical work was again taken up by Rood and Tolhoek [1], where they showed that RMC was especially sensitive to the magni tude of the pseudoscalar coupling, 9p· The intervening 30 years have seen an exhaustive theo retical effort, with several different approaches to calculating the elementary RMC amplitude investigated. All recent calculations agree, to within a few percent of each other, in their prediction of the RMC rate for the nucleon. In contrast, the exper imental situation still re-mains unclear . Until the measurement discussed in this thesis, there had been no attempt to investigate the rare elementary radiative capture process on the proton . Previously, measurements were restricted to nuclear RMC, leaving gp hidden in the description of the nuclear structure. It is only now that th e gap between theory and experiment can be bridged, thereby testing the theoreti cal predictions that have existed since the early 1960's. This chapter presents a review of the theoretical progression that led to the de-velopment of the present understanding of RMC. This thesis is primarily concerned with the elementary amplitude µ-+p ---4 n+vµ+ 1 . A discussion of the consequences 24 Chapter 2. RMC Theory of embedding the elementary amplitude in a nucleus is not presented, though for completeness, reference is given to the excellent review article by Gmitro and Truol [48]. 2.2 Radiative Muon Capture Three approaches have been used to calculate the radiative muon capture am-plitude for a proton. The first historically and perhaps the most intuitive, is the diagrammatic treatment [1, 49, 50]. In this approach the elementary amplitude for RMC on a free nucleon is constructed by considering the Feynman diagrams de-picted in Fig 2.1. A radiated photon line is attached to each of the participating particles carrying either charge or magnetic moment. The first diagram (a) is the dominant contribution to the overall rate, accounting for as much as 20-40% alone, and up to 60% when additional interference terms are considered. It is dominant be-cause the muon mass, mµ, is small in the denominator of the propagator, compared with the nucleon mass, MN, of the other diagrams (b), (c) and (d). Diagrams (c) and ( d) describe radiation through interaction of the anomalous magnetic moment of the neutron and proton with the electromagnetic field. The diagrams {e) and (f) are required to maintain gauge invariance. They arise if the minimal substitution q>,. --+ q>,. - eA>. is made for q-dependent vertices. Diagram ( e) accounts for the weak magnetism coupling and similarly (f) for the induced pseudoscalar coupling. The minimal substitution in the pion propagator leads to diagram (g) which can be in-terpreted as bremsstrahlung from the virtual pion propagator. The RMC amplitude is calculated by summing each of the matrix elements for the Feynman diagrams . An alternative approach was undertaken by Adler and Dothan [51]. Starting with the Born terms of the radiative amplitude (i.e. the first four Feynman diagrams of Fig. 2.1), they have extended the low-energy theorems (LET) of Low [52] to the case of the axial-vector interaction. Noting that LETs are actually based on current divergences rather than current conservation, Adler and Dothan sought to 2.2. Radiative Muon Capture {c} 1 {e} ] 7 ff (f) {g) Figure 2.1: Feynman diagrams of the dominant amplitudes that contribute to the Radiative Muon Capture process in hydrogen. 25 26 Chapter 2. RMC Theory use the PeAC hypothesis, which has a non-zero axial-current divergence for finite moment1:1m transfer, to construct the leading terms in the photon momentum , k, of the RMe amplitude. Recently this method was reviewed by ehristillan and Servadio [53] to include leading terms linear in both the transferred momentum, q, and the photon momentum, k. Their work is in full agreement with that of Adler and Dothan . The LET approach is also in agreement with the diagrammatic approach to a few percent . Neglected is a numb~r of terms arising from minimal electromagnetic substitution (i.e. the substitution q>. --+ q>. - eA>.) in the momentum dependent form factors other than 9p· The q2 dependence in these is small and they can be considered as constants . Some of these additional terms have been considered by Manacher and Wolfenstein [54], and by Adler and Dothan, and are small(~ 5%). In the methods described so far, all begin with an initial set of Feynman dia-grams or a relativistic Hamiltonian which reproduces these diagrams . Hwang and Primakoff [55, 56, 57] attempted to calculate the RMe amplitude solely from conser-vations laws eEe, eve , PeAe and a very general Hamiltonian. The conservation laws provide a set of constraint equations which are applied to a general Hamiltonian formed from available vectors and multiplied by unknown form factors. However, the constraints are not sufficient to determine all unknown form factors. An ad-ditional hypothesis, the linearity hypothesis fixed the functional dependence of the form factors, requiring that they be linear in the various couplings. The result was a RM C photon rate a factor of two smaller than that predicted by the early approaches. This was somewhat puzzling since all three approaches satisfy eve, PeAe and require gauge invariance. The discrepancy was eventually recognised to be the fault of the linearity hypothesis, in particular the q2 dependence of the form factors was ignored for the hadron radiating diagram, which is where the largest contribution to the rate is expected from the pseudoscalar term . In addition, the pion radiating diagram was not considered . The corrections were later a dressed by Gmitro and Ovchinnikova (58] and full agreement with the diagrammatic and LET approaches was regained. 2.2. Radiative Muon Capture 27 In summary, the calculations of the elementary amplitude for radi,.tive muon capture seems to be well understood. Variations of less th an a few percent between the methods can be most likely attributed to higher order terms in k and q which have been neglected. There is one other aspect of these calculations that so far has not been addressed. In all these approaches to calculate the RMC amplitude, non-relativistic approximations have been used. The approxim ations follow the line of a Foldy-Wouthuysen (59) transformation, which is effectively an expansion in powers of (1/M), where M is the nucleon mass. The matrix elements of the Hamiltonian are then squared. The end result should be accurate to order (1/M). Recently, Fearing [60) has performed a fully relativistic calculation of the RMC rate using the diagrammatic approach and found a difference of 10% compared with the no~-relativistic calculation of Opat [50). The results of the measurement presented here will therefore be compared with the full relativistic ·calculation of Fearing. This will be discussed in detail in chapter 5. Furthermore, to determine the value of the pseudoscalar coupling constant, gp, one generally relies on a comparison between experimental rates for large photon energies, m,.,/2 E-r mµ., with theoretical amplitudes containing hadronic and leptonic currents. However, this method is-only reliable if one is assured that no significant amplitudes have been omitted from the calculation. Until 1986, all calculations of the elementary amplitude had neglected to include contributions from the intermediate excited state of the nucleon, (the ~(1232) MeV resonance). Such contributions· to µp nvµ.-y are shown in Fig. 2.2. This was rectified by the work of Fearing and Beder [61) in which they found that the contri-bution from the diagrams can increase the rate by as much as 20% of the dominate amplitudes. The effect is largest in the singlet µ-p atomic state. At densities of liquid hydrogen the lifetime of this state is short. Consequently, the net effect of the ~(1232) exc·tation is only a 7-8% increase in the RMC rate. l Although no nuclear state complications exist for RMC by hydrogen, the neg-ligible rate of the elementary process (- 10- 8 ) per stopp ed muon, necessitates the 28 Chapter 2. RMC Theory µ 7 a) b) Figure 2.2: Contributions to the RMC rate from the Delta resonance . use of hydrogen in high concentrations, namely in its liquid state. Consequently, one must be aware of the atomic and molecular effects pertaining to the liquid state of hydrogen. The radiative capture rate is particularly sensitive to the spin orientation of the muon and proton. A discussion of the muon chemistry in hydrogen is thus warranted. 2.3 Muon Chemistry in Liquid Hydrogen 2.3.1 Introduction It has been shown [62) that the muon capture rate by a proton can be described by: (2.1) For antiparallel muon and proton spins (o-p · 0-1,1} = -3, while for parallel spins it is + 1. Consequently the muon absorption process is very sensitive to the particular spin orientation of the participating particles. There are essentially two effects which need to be considered in the analysis of muon capture experiments. They are, 2.3. Muon Chemistry in Liquid Hydrogen 29 (i) the scattering processes with transitions from one hyperfine state to the other, (ii) the formation of molecular ions. It is essential to know the transfer rates between these species and their popula-tions before the capture rates can be interpreted correctly. · 2.3.2 Muonic atoms and molecules A negative muon when slowed down in hydrogen is eventually trapped by the Coulombic field of a proton. A neutral muonic atom (µp) is formed and in a very short time (less than a few nanoseconds [63)) the muon cascades down into the lowest ls orbital. Muon capture by the proton can proceed from one of two hyperfine states. The singlet state Fa, in which the proton and muon spins Sp and Sµ are antiparallel , or the spin triplet state Ft, where Sp and Sµ are parallel. In the former case the resultant spin Fa = 0 and in the latter Ft = I. For a pure V - A interaction the capture probability in the spin triplet state is zero, At = 0. Capture proceeds entirely from the spin singlet state. When hadronic currents are present the pure V - A interaction is modified by the induced current terms . The capture probability from the triplet state becomes finite, but still much smaller than the singlet state, A5 • For hydrogen in concentr ations of</>::; 10-5 (where </> = NJ N0 and N0 is the density of liquid hydrogen) the statistical population of the hyperfine states is preserved [64). The probability of capture is then (2.2) In the case of more moderate concentrations of hydrogen molecules, the statistical weighting in Eq. (2.2) can be drastically altered . The energy difference between the two hyperfine states is !iE = 0.18 eV, consequently collisions with neighboring hydrogen atoms and molecules may result in the exchange of a proton with opposite spin direction . This is the so-called "jump mechanism" [65). The thermal energy 30 Chapter 2. RMC Theory ( only 0.0035 e V) is too small compared to the separation energy to induce transitions to the upper hyperfine state. Consequently, the spin singlet state is energetically favourable and not reversible. Subsequent collisions will result in the triplet state converting rapidly to the singlet state. The rate of this conversion depends on the concentration of protons participating in these collisions. In liquid hydrogen, the half-life of the triplet state does not exceed approximately 0.01 % of the free muon lifetime (2.2 µs). Practically, all muon captures from the µp atom proceed from the spin singlet state. A further and more important consideration is that the µp atom can undergo a further collision, (µp)F=O + (pp)-+ (pµp)+ + p + 135eV. (2.3) At the density of liquid hydrogen, the rate of collision is expected to be high, with ,.._, 95% (66) of captured muons being in a (pµp) molecule. The capture in (pµp) differs from capture in (µp) in two points. First, the overlap of the muon-proton wavefunctions is different. Second, the additional proton spin orientation has a significant effect on the rate of muon capture. It is therefore important to know the probability of muon capture from the rotationally excited ortho-state (proton spins parallel) and the ground para-state (proton spins anti-parallel), see Fig.2.3. It has been shown (67), that the ortho pµp-state is dominant over the ground para-state~ ,.._, 0.0002. Not only is the formation of the ortho-pµp dominant, it is "PM stable from transition to the ground para-state. This stability has been confirmed by the experiment of Bardin et al. (39). Weinberg (67) relates the pµp molecular capture rate as a linear combination of the µp atomic singlet and triplet states. For the ortho-molecular state the rate is given by (2.4) 2.3. Muon Chemistry in Liquid Hydrogen µ, triplet 1s singlet µp Atom pµp Molecule Figure 2.3: The dominate muon transfer channels . and for the para-molecular state by AT"1.ra - 2 (!A ~A] pµp - "'(p 4 a + 4 t ' 31 t t ppµ, 1=1 ortho L=O para ppµ t t (2.5) where the 1's are the ratios of the probability of the muon being found at the position of either proton in the (pµp) molecule and the probability of the muon being at the position of the proton in the (µp) atom. For the ortho molecule 2"Yo = 1.01 ± 0.01 and for the para molecllle 2"'(p = 1.15 ± 0.01 (68, 69, 70, 71]. The value T/ allows for the possibility that the meso-molecular formation can occur from muonic hydrogen in the triplet state. On the basis of the argument given earlier we expect most of the molecular formation to take place with the (µp) atom in the singlet state . Neglecting the spin-orbit effects from the triplet state, T/ = ¾. Calculations (34, 72] indeed show the mixing is small and 'f/ departs from the value ¾ by only a few percent . 32 Chapter 2. RMC Theory· In summary, the only two states in which the muon spends any appreciable frac-tion of its lifetime are the atomic singlet state and th e ortho-molecular state. The transition between these two states has been measured with considerable accuracy [73]. The result indicates that ,..., 85% of µp atoms undergo transfer to the pµp ortho-molecule. The total muon capture rate for liquid hydrogen ( assuming there is no transition from the ortho-molecular state to para-moelcular state) is then given by, (2.6) The validity of Eq. (2.6) depends on the value of ).op (the ortho to para transition rate). A recent experiment [39] quotes, ).op= (4.1 ± 1.4) X 104 .s-1• (2.7) The same experiment determined that with the >.0 P correction applied, g; = 8. 7 ± 1.9. This agrees with the PCAC prediction of g; = 8.56 ± 0.25, but would disagree significantly if it was assumed ).op= 0 (gt = 12.6 ± 1.5). Clearly it is important to take into consideration the ).op rate when making a precise determination of 9p· In the non-relativistic limit the electromagnetic ortho-para transitions in the pµp molecule are forbidden by the selection rule~/= 0. However, closer inspection [64] reveals that a fully relativistic treatment allows for a finite ortho to para transition rate. The rate from ortho to para is expected to be ).op= (7.1 ± 1.2) X 104. (2.8) Clearly this latest theoretical prediction by Bakalov for the ortho to para. transi-tion rate is not in agreement with the measured ortho to para rate given by Bardin. Because of this lack of agreement and the effect that the ).op rate has on the deter-mination of gp, this work will not neglect the contribution ,from the para-molecular state to the total capture rate. In chapter 5 the theoretical photon spectrum will be 2.3. Muon Chemistry in Liquid Hydrogen 33 calculated using both the theoretical value for >.0 P Eq. (2.8) as well as the measured value Eq. (2.7). 2.3.3 Muon induced fusion Another and very important process is the transfer of the muon to deuterium . When muonic atoms form they appear as small neutr al objects, there passage through matter can resemble that of a neutron. The Bohr orbit of one of these muonic atoms is 207 times smaller than their electronic counterparts, given by, 1i a ---"' - m e2 µ 250/m. (2.9) Consequently, the charge of the hydrogen nucleus is shielded for distances larger then aw The muonic atom can then approach and penetrate the Coulomb barrier of a neighboring atom to interact with the nucleus. If the second nucleus is a deuteron or an impurity in the hydrogen with Z l, the transfer process is irreversible. For this reason, high purity liquid hydrogen is essential. Impurity levels of a few ppb (parts per billion) for all elements other than hydrog en is essential to keep the photon background from muon capture by heavier nuclei safely below "' 10% of the hydrogen RMC rate. A further, and perhaps the most interesting process to be aware of is muon capture from 3He. The 3He is produced through the muon induced fusion of a (pµd) molecule. The final state can either be a µ3He atom in which the muon can capture, µp + d (pµd) µ3He + 'Y, (2.10) or normal 3He with the muon set free to catalyse further fusions. µp + d (pµd) ~ 3 He + µ. (2.11) The use of normal liquid hydrogen, which contains 140 ppm deuterium, would 34 + Ortho Chapter 2. RMC Theory Signal _J_ Para + ® "- = (1.89 ±0.20) X 101 S - 1 /\d = (1.43 ±0.13) X 101:> S _, = (5.6 ±0.2) X 101 S -I ~. 1 = (0.46 ±0.03) X 101 s-1 ~" = (0.06 ±0 .006) X 109 S-l 11 -1 A.z ,., x 10 s }.op= (4.1 ±0.14) X 104 S- 1 Figure 2.4: Flow chart of the principle channels for muon transfer.] result in an RMC signal from µ3He 10 times larger than the hydrogen signal. Hydro-gen with a deuterium concentration ($ 2ppm) called protium is necessary. At this level the probability of RMC on 3He is reduced to...., 2% of the RMC on hydrogen signal level (74]. Figure 2.4 illustrates the principle channels to which the muon can be transferred. In summary, at the density of liquid hydrogen, radiative muon capture arises predominantly from two quantum states, the (µp) atomic singlet state - 15% and the ortho (pµp) molecular state - 85% of the time. In addition it has been shown that the ortho-para transition rate, although small , is not negligible and must be included in any determination of 9p· All of the considerations just discussed, full relativistic calculation, inclusion of the Ll resonance and the significance of the ortho-2.3. Muon Chemistry in Liquid Hydrogen 35 para transition rate, have been addressed in the calculatio ns of Fearing. The work of this thesis will use this most recent calculation to extract 9r, from the experimental RM C photon spectrum. 37 Chapter 3 The TRIUMF RMC Facility 3.1 Introduction Although the RM C photon spectrum extends from 0-100 Me V, only the portion above 53 Me V is distinguishable from the intense and unavoidable background of bremsstrahlung (internal and external) by µ-decay electrons. With this in mind , a detection system capable of detecting photons from 50-1 00 Me V was constructed. The detector must have a good acceptance (to contend with the low rate....., 1 RMC photon per 108 stopped muons) and good energy resolutio n at the µ-decay endpoint (to discriminate against the µ-decay photon background). In addition, it should be insensitive to the enormous flux of neutrons from the much more frequent process of ordinary muon capture (roMc/rRMC ....., 104 ) and electro ns from muon decay. Also desirable is the ability to distinguish RMC photons originating from the target, from photons due to background processes such as pion capture and cosmic-ray induced events. These requirements have been achieved with the construction of a large solid-angle (....., 21r) photon pair spectrometer. Photons emerging from the hydrogen target undergo pair conversion in a thin (1.08 mm) cylindric al lead sheet surrounding the target. The electron and positron pair is then tracked through a large-volume cylindrical drift chamber. Axially segmented scintillato r layers are used to veto the high flux of charged particles coming from the target and provide a trigger on photons which convert in the layer of lead. The spectrometer is positioned inside 38 L 0,) +-' 0,) E 0 L +-' uu 2~ er:: (/) Cl) • Q) Cl) ..oc :J·--+-' u 0 Cl) +-' o-_c<( Q_<( Chapter 3. The TRIUMF RMC Facility . rn ...µ C . Cl) -+-' C L Q) ..Q E 0 . ..c Cl) u rn E "a) 0, ..Q -+-' u Uc t Cl) m 1- <( m o o E 0 Figure 3.1: Projected view of the RMC pair spectrometer at TRIUMF . 3.1. Introduction 39 a region with a uniform axial magnetic field of 2.4 kG. The magnet is surrounded by multiple layers of scintillators and planar wire drift chambers to identify cosmic-ray induced photon events. Figure 3.1 shows a detailed illustration of the detector assembly, while Fig. 3.2 illustrates a simpler, cross sectional view along the beam axis. This chapter describes, in detail, the de.sign of the RMC spectrometer, the liq-uid protium t.argeL the trigger and data acquisition system. The production and transport. of the muon beam will also be discussed. Be~m., BMuuo---=--Target IWC -----++-''?" DC 1m Figure 3.2: View of the RMC spectrometer along the beam axis 40 r-.'Chapter 3. The TRJUMF RMC Facility 3.2 Muon and Pion Beams The pair spectrometer and magnet were positioned at the end of the M9A stopped-1r/µ channel at TRlUMF . A primary beam of 500 MeV protons {typically 140 µA} from the TRJUMF cyclotron bombards a 10 cm long berylli~m target . The opening to the M9A channel is positioned at 135° to the incident proton beam . This reduces the contamination of the ,r / µ beam by electrons and high energy neutrons, both of which are peaked in the forward direct ion. The pion production cross sec-tion at~ 150 MeV /c is approximately isotropic . Figure 3.3 illustrates the system of . . dipole and quadrupole lenses used to focus and direct the beam into the target . Slits located after the dipole Bl, select the channel momentum (typically 65 MeV /c) so as to stop the muons in the centre of the liquid hydrogen target. More information on the TRlUMF cyclotron, primary and secondary beamlines can be found in the TRlUMF users handbook [77]. The muon beam is obtained from the pion decay channel (1r - 11.11µ), with branching ratio of approximately 100%. The raw beam composition at the target (if left unseparated} contains roughly equal numbers of muons and pions and about 10 times as many electrons (1r/µ,.., 1 and e/µ- 10). This 1r-e contamination must be reduced for two reasons. Firstly, the large flux of electrons would result in a saturation of the beam and trigger counter electronics, incurring a large dead time iD. the detector. Secondly, the pions would produce photon backgrounds from both radiative pion capture in the target ( 1r-p - ni giving a monoenergetic photon at 129 MeV) as well as ,r-p - n1r0 ; 1r0 - ii producing photons over the range 55-83 MeV. Therefore it is essential to suppress the pion and electron content of the muon beam in a measurement of RMC. Suppression of the pions and electrons was achieved by implementing a radio fr:equency r micle separator (RFS) 9.5 m upstream of the liquid _hydrogen (LH2) target. The RFS makes use of the fact that the time-of-flight for each of the three beam components (w,µ,e) is different. The principle of the RFS is illustrated in 3.2. Muon and Pion Beams 41 • Figure 3.3: The stopped / µ beamline, M9A. 42 Chapter 3. The TRIUMF RMC Facility Momentum = 77 MeV/c "--- RF Waveform • 50 60 70 80 90 100 Time of Arrival (ns) Figure 3.4: RFS principle of operation Figure 3.4, which shows the time-of-flight structure of the secondary beam relative to the RF electric field at the position of the separator. The muons (,8.....,0.6) arrive approximately one-half an RF period (.....,20 ns) ahead of the pions (,8.....,0.5) from the same proton pulse and electrons (,8.....,1.0) from the following pulse. The phase of the RFS is adjusted so that the peak of the RF voltage coincides approximately with the muon time of arrival.· The force of the transverse electric field is then exactly compensated by the force qv x B from a horizontal DC magnetic field. Thus, the muons pass through undeflected. By the time the pions and electrons arrive at the separator the electric field has been reversed and the magnetic and electric force components work in the same direction deflecting them from the beam. A full description of the RF separator can be found in Blackmore et al. (78]. The separated beam composition was measured to be 1r/µ.- 10-3 and e/µ.;...; Sx10- 2 at the target. The negative muon flux was typically 6x10 5µ.s-1 with a beam momentum spread 6P/P = 8% and a spot size of <rs~ 3.4cm by u11 4.4cm at the target. A positive muon bt: ,m was used to study the effects of the bremsstrahlung back-ground from muon decay. This will be discussed in detail in Chapter 4. Production 3.3. The Drift Chamber 43 of a 65 MeV /c µ+ beam was achieved simply by reversing the polarity of the mag-nets in the M9A beamline. The flux of positive muons is 5 times greater then that for negative muons and so slits are used to reduce the beam intensity to a rate comparable to the rate for a µ- beam. In addition to the µ- and µ+ beams a negative pion beam was also used. When pions stop in the target they will undergo radiative pion capture with a branching ratio of 0.39. The monoenergtic photon emitted has an energy of 129 MeV and can be used to check the energy resolution of the detector. The remaining pions that capture (branching ratio of 0.61) result in the production of the neutral pion which subsequently decays into two photons. The photons from this decay have a uniform energy distribution between 55 and 83 Me V and can provide information on the d~tector acceptance . Pions have a shorter range than the muons and so a higher beam momentum, 81.5 Me V / c, was needed to stop the pions in the same region of the target . Slits were used to maintain stopping rates in the target similar to the rates when tuned to a µ- beam . At this higher beam momentum, the particle separation is not as clean as it is for a 65 Me V / c beam. Beam components are 96% 1r- , 3% e- and 1% µ-. 3.3 The Drift Chamber The principal tracking device of the RMC spectrometer is a large-volume cylin-drical drift chamber [77, 78). It was designed to analy se the momentum of the electron and positron produced by the conversion of an RMC photon in the lead foil. Figure 3.5 displays a reconstructed photon event viewed in the plane x-y, trans -verse to the incident beam. Figure 3.6 displays the same event as seen along the beam axis, y-z plane . Table 3.1 list further characteristics of the spectrometer. The detector covers a large solid angle (- 21r ), has an energy resolution of"" 12% at 129 MeV and a position resolution of"" 154 µmin the transv erse plane . 44 Drift Chamber : +Gas Ar/ethane (50/50) +length 90 cm +t.R 2B cm +13 stereo {7°) +272 drift cells +a 117 = 154µm ( 1 o = 21T Chapter 3. The TRIUMF RMC Facility - -- -rwc B scints. Pb converter C scints . RUN 21B1 EVENT 73 Figure 3.5: z-y view of a photon event in the RMC spectrometer . ' D scints. ' /'\ \. I ' .\ Stereo layer (7°) I '\ \ '\ \ ... \\ ' IWC Pb converter RVS Z Figure 3.6: z view of a photo11 event in the RMC spectrometer . 3.3. The Drift Chamber 45 Item Radius (in) I Comments Magnet coil 24.000 vertical D Scint . 16 panels 23.835 1/4" thick 37.000" long Drift chamber outer radius 22.835 Carbon fiber cylinder D Scint. PMT's 21.125 2" tubes Layer Cells Cell center Cell half-width at center 4 80 20.866 0.8194" 3 72 18.465 0.8057" 2 64 16.063 0. 7885" 1 56 13.661 0.7664" Total 272 Total wires 7888 Drift chamber Inner radius 11.890 Carbon fiber cylinder IWC Outer 11.120 Cathode 10.856 IWC Anode 10.640 IWC Inner 10.159 Cathode 10.425 C Scint. PMT's 9.500 1 1 /8" tubes B Scint. PMT's 7.000 1 1 /8" tubes C Scint. 12 Panels 6.220 1/8" thick, 18.00" long Lead Converter 6.102 .04 7" thick, 10.00" long B Scint. 12 Panels 5.984 1/8" thick, 19.00" long Magnet Hole U.S. and D.S. 5.250 10.5" Diameter A' Scint 4 sectors 4.961 1/8" thick, 20.00" long A Scint 4 sectors 4.803 1/8" thick, 20.00" long Target Vacuum Flask 4.134 0.059" aluminum Target Flask 3.150 D.C. active length 33.460 35.40" overall Stereo angle layer 3 70 13° rotation Table 3.1: Drift chamber characteristics 46 Chapter 3. The TRIUMF RMC Facility TRACK-DRIFT LINE PLOT Cell IO-wall1, layer 1 Gao 10 -Argon .!lox Ethane _,_..,..--,..--,-,,-,,-, r--1r--i--.--.--.---.---.. ao E u - er -x - - ~- - )( 4.5cm - - - -e - - - X - - - - -e-- - - - -x ------ar-----x - - - - - ti:> -w - - - - - - X uo -4cm Drift " cell: •sense wire 20µm <p W+Au •cath. wire 150µm <p Al+Au •staggering ±254µm •Efield 2kV / cm 1 vd,ift - so µm/nsec Figure 3.7: Drift cell characteristics 3.3.1 Characteristics The drift chamber consists of four super-layers of cells, each cell possessing 6 sense wires. The wires of layers 1, 2 and 4 are axial to the beam and those of layer 3 are inclined at a stereo angle of 7.0° (relative to the axis). The third layer provides a z-coordinate position for each track ( x - y coordinates from the stereo layer are not used in the i - y fitting of a track). The four layers have 56, 64, 72 and 80 cells respectively. The sense wires are staggered alternately left and right of the cell mid-plane by 254 µm so as to resolve the local left/right ambiguity of the track. The geometry and characteristics of a drift cell are illustrated in Fig. 3. 7. Table 3.2 lists the w ;re characteristics of the anodes and cathodes. Gold-plated aluminium cathode and anode guard wires minirnisec. the scattering of the converted e- e+ pairs. This correspondingly decreases the high energy tail of the spectrometer response function, thereby reducing the contribution of the photon background from 3.3. The Drift Chamber 47 I Item I Dimern ion I Comments I Cell height 1.800" Sense wire 6 per cell 20µm W+Au Non-Sense wire 2 per cell 25µm W+Au Sense guard wire 2 per cell 150µm Al+Au Field wire 32 per cell 150µm Al+Au Field wire 2 per cell 178µm Al+Au Field guard wire 4 per cell 300µm Al+Au Table 3.2: Drift Cell wire characteristics µ decay bremsstrahlung. To maintain a uniform electric field throughout the wedged shape of the drift cell, a resistor chain on each cathode plane provides a voltage gradient. Voltage gradients of 31.0, 33.6, 36.4 an 39.2 Volts/wire are used within each cell of layers 1,2,3 and 4 respectively . The increase in the voltage gradient compensates for the increase in cell size from the inner super-layer to the outer. The sense wires are held at ground while -5.0, -5.1, -5.2 and -5.3 kV is applied to the high end of the resistor chain in layers 1,2,3 and 4 respectively. The drift chamber is enclosed by an inner and outer carbon fiber fitted between the two end-plates. The inner fiber has a thickness of 0. 75 mm and the outer carbon fiber of 1.0 mm. To maintain high field uniformity near the inner radial wires of layer 1 and the outer radial wires of layer 4, the surface of the carbon fiber facing into the chamber was electrically isolated with cathode foils of copper at -3.25 kV. 3.3.2 Readout Electronics Of the 10 anode wires per cell only the inner 6 are available for readout. Pream-plifier cards are mounted on each cell of the downstream end-plate. Signals from the anodes are carried along 6 metres of ALPHA 9374 coaxial cables to postampli-fier / discriminator modules located beside the spectrometer magnet. The postampli-fier / discriminators have an ECL iogic output for signals over threshold and parallel analogue outputs [79]. These outputs were used for diagnostic purposes such as the 48 Chapter 3. The TRIUMF RMC Facility monitoring of the RF noise on the DC wires. The logic output from the postam-plifier / discriminator modules was sent down ECL "twist and flat" cables to LeCroy · 1879 Fastbus pipeline TDCs (80]. Multi-hit time information over 1 µsec with 2 ns resolution on each wire was recorded. The 17 Fastbus TDCs (each 96 channels) monitored a total of 1632 anode sense wires. In the Fastbus crate, where the TDCs reside, trigger cards are mated to each of the 17 TDCs at the auxiliary backplane connector. These cards perform a majority logical OR of the 6 wires in each cell. If at least two wires in a cell fired, the cell is registered as hit. These "OR boards" are then interrogated by a SLAC Scanner Processor (SSP) which, for a specific pattern of hit cells, decides whether to accept or reject the current event. The OR boards are des~ribed in more detail in (81]. The readout of the OR boards can only be performed after the Fastbus TDCs have been scanned and converted. This could take up to 1 µsec before the SSP makes a decision on the event. To access the hit information on the OR boards more readily and consequently make a quicker trig-ger decision, provision was made to readout the OR boards through TTL converters into an analogue hit counter (AHC). The AHC then performed the pattern search that was previously performed by the SSP. The effect was to decrease the trigger rate from 600s- 1 to 100s- 1 and decrease the dead-time by 8%. 3.3.3 Gas System A gas mixture of argon/ethane/ethanol (49.9%/49.9%/0.2%) was chosen to pro-vide a drift velocity of"' 52 µm/ns at electric fields near 2 kV /cm. The gas mixture was regulated by a recycling system, a schematic of which is shown in Fig. 3.8. Typically 90% of the gas mixture is recycled. Active filters remove 0 2 (R3-11 copper catalyst) and H20 (3.A mole~ular sieve) to levels of less than 5 ppm. The 0.2% ethanol is added by bubbling half of the argon through eL anol at -2.9° C. The flow rate through the chamber is approximately 2 litres/minute, while the 10% argon and ethane vented is replaced from cylinders through mass flow controllers 3.3. The Drift Chamber 49 Ii -+-' z (I.I ::::, C I _c J1; X L-w Q) u I >- -+-' u en I- u ·-C ti => Q) C .c 0 0::: => (/) illl: z (I.I C (!) f I-=> '1 0 L-Cl) .0 • E !!I C 0 .c IL u Q) C -+-' C u !t .c -+-' t z L-w -~ 0::: 0 ' on C .. 0 C"I 0::: L-<( l~ w 0 rn L[) illl: it 2 ' 0 <( L[) :r: -+-' 0 ·c u >- => u _J i L- 0 I- Q) 0 0... ..... - ,.,, LL 0... t I - f ::::, 0::: :::> ! z CD 0 Cf) N I I i u Cf) i 2 <( 1 0::: c., Figure 3.8: Schematic of the gas recycling system. 50 Chapter 3. The TRIUMF RMC Facility which regulate the gas mixture to better than 1 %. The temperature and humidity around the drift chamber can affect noise levels in the pre-amplifiers mounted on the downstream end-plate of the chamber. To cool the interior of the magnet, dry nitrogen gas was vented in from gas cylinders outside the magnet . The temperature and pressure in the chamber were monitored by 8 thermocouples and 1 pressure transducer mounted on the end-plate inside the chamber. The temperature outside of the chamber and around the pre-amplifiers was also monitored. 3.3.4 Calibration Pedestals: The purpose of the drift chamber is to provide spatial coordinates (x,y,z) of charged-particle tracks passing through its volume. The particle momenta associated with those tracks can then be calculated and the initial photon energy determined . To obtain accurate coordinate information, the drift time of the ionised electron cloud to the anode wire must be determ ined. The drift distance d, is given by: (3.1) where vd is the drift velocity, t is the drift time measured in the TDCs and t 0 is the earliest possible time relative to the TDC START at which electrons can arrive at the sense wire (t0 is called the time pedestal). It is essential to obtain the time pedestal to high accuracy if high spacial resolution is to be achieved. Each of the 1632 sense wires in the chamber will have its own time pedestal; these values are obtained from calibration runs. A calibration run consists of tuning the beam to 1r-(most of the triggered events are good photons). Those photons that undergo pair production in the lead foil will produce an electro:u-positron pair that follow helical paths in the magnetic field of the spectrometer: (x - Xc)2 + (y - Yc)2 = R2, (3.2) 3.3. The Drift Chamber 51 z =a</>+ b, "' t -1 (y - Ye) 'f' = an ( ) , X-X e (3.3) where Xe and Ye are the coordinates of the centre of track circle and R is the radius of the track circle. A measure of the position resolution of the spectrometer is the degree to which the reconstructed hit information agrees with the above track parameterisation. This is quantified by determining the residual for each track. A residual is the distance of a reconstructed track point from the parameterised track , which is a least squares fit to all the track points. For N points assigned to a• track , the sum of the residuals is given by (3.4) where Xi and Yi are the reconstructed hit coordinates . The goal of a calibration run is to find the values of t0 , the time pedestal for each wire, vd, the drift velocity, and a, the Lorentz angle that minimises Sr. The standard deviation of the Sr distribution for all tracks in a calibration run gives the average position resolution of the spectrometer . This was typically"' 154µm. Drift velocity and Lorentz angle: In principle, the drift velocity and Lorentz angle can be determined for a specific gas mixture, E and B field strength . In practice , these can be difficult to monitor at a level necessary for high accuracy. It is better to measure the Lorentz angle and drift velocity directly rather than rely on tabulated values. For different drift velocities the residuals in the track fitting are calculated. The drift velocity that minimises the residual s is taken to be the correct drift velocity Vd, Further discussion of track residuals will follow in chapter 5, where track reconstruction will be explained in detail. Because of the axial magnetic field from the spectrometer magnet the electrons drifting towards the anodes deviate from the line of the electric field. The Lorentz angle a is a measure of the extent of this drift from the electric field lines. By using a minimum x2 search in the track fitting, a value of a 5.2° was found. Drift 52 Chapter 3. The TRIUMF RMC Facility velocities and Lorentz angles were dtermined for each of the 24 radial wire positions. Regular checks of the time pedestals , drift ve]ocities and Lorentz angles are made throughout each data taking period. When variations were observed, separate calibration sets were used for the corresponding data sample . 3.4 Inner Wire Chamber For reconstruction of the photon momentum along the z-direction { axial to the beam) both of the tracks from the e+c pair must pass through an inner wire chamber (IWC) and the third super-layer of the drift chamber. The inner wire chamber is a cylindrical, dual co-ordinate, multi-wire proportional chamber of the type described by Bird et al. [82]. It is positioned inside the inner radius of the drift chamber . It is 2.4 cm thick and consists of 3 wire planes; an inner anode plane of 768 wires {20 µm diameter Au-W) parallel to the beam direction, and two cathode planes. Each plane has 384 aluminised mylar strips {110 µm thick). The 384 strips of the outer cathode plane lie at an angle of +45° to the anode plane while those of the inner cathode plane lie at -45°. The IWC provides an (x,y,z) coordinate for each track, the x-y coordinate is obtained from the position of the hit anode wire and the z coordinate from the intersection of the hit anode and the cluster centroid from at least one of the cathode planes. The anode wires have an angular separation of 2.13°; typically only one anode will fire per hit. If two anodes fire, the x-y position is taken to be the midpoint of the arc between the two wires. The resolution of the x-y position of the track from the IWC is considerably worse than that from the drift chamber and is not used in the x-y fit of the track. The IWC uses a gas mixture of 77.6% argon, 22.2% isobutane and 0.2% freon bubbled through methylal. With the anodes at 3.4 kV and cathodes at ground, the efficiency is ,.._, 98%. The z-position resolution is 1.2 mm. Electronic readout of the IWC consists of 4 receiver memory hybrid {RMH) crates with 12x32 channel RMH receiver modules storing information from the 1536 anode and cathode wires. Readout of the RMH modules 3.5. Beam and Trigger Counters 53 is performed by the SSP-Fastbus system. A full description of the readout, encoding, and decoding can be found elsewhere [83]. 3.5 Beam and Trigger Counters Four scintillation counters (BM1_4 ) were fixed 17 cm upstream of the target centre to monitor the content of the beam and define a "muon stop". Each measured 16 mm in thickness and was read out by two separate lightguides and photomultiplier tubes to afford maximum light gathering efficiency. Each counter, with the exception of the third, was better than 99% efficient. The thlrd was suspected of having a weak joint at one of the lightguide-scintillator boundaries and was 97% efficient. A muon stop was defined as 4-fold coincidence between all of the four counters. The output pulses from these counters were sent to both a Fastbus 1820 multi-hit TDC allowing beam information up to 500 ns both before and after the photon event to be recorded as well as a CAMAC TDC on a 10 µsec range. Timing information from the beam counters was used to reject pion-induced events which occur in prompt coincidence ~ith a beam particle stopping in the target. In addition, the output pulse was sent to CAMAC ADCs, whereby pulse height information could be used to discriminate between pion- and muon-induced photon events. Surrounding the target was a package of 5 concentric layers of scintillators. The first two layers each consisted of four arc segments forming two cylinders with radii of 12.20 cm and 12.60 cm respectively, and each 50.8 cm in length. The thickness of the scintillator was 0.32 cm. The inner layer (A1_ 4 ) was covered by the outer layer (A;_ 4) offset by 45° to cover the gaps between the scintillator joints. Signals from ea.ch of the scintillator quarter arcs were sent via lightquides through a 25.4 cm hole in the rear of the magnet to photomultiplier tubes mounted on the exterior rear face • of the magnet. These two layers provided an efficient veto against the copious flux of charged particles (mostly muon-decay electrons) coming from the target. The next two scintillator layers (B1-12 and C1_12 ) consisted of polygon tubes 54 Chapter 3. The TRIUMF RMC Facility with radii of 15.20 cm and 15.80 cm. Each of the polygons was made up of 12 flat panels 0.32 cm thick and a length of 48.3 cm and 45. 7 cm for the B and C layers respectively. Between the two layers was a thin sheet of lead 1.08 mm thick. This layer acted to convert photons from the target into the e+ e- pair that was subsequently tracked through the volume of the drift chamber. The B ring served both to support the lead sheet and to act as an additional charged-particle veto. The C ring was used to identify the production of charged particles in the lead before they entered the IWC and drift chamber. Finally, outside the drift chamber at a radius of 59.4 cm was a fifth scintillator layer, the D ring. This consisted of a polygon tube of 16 flat panels 0.64 cm thick and 94.0 cm in length. Together the C and D counters accomodate the geometrical pattern characteristic of an e+e- pair. Each scintillator segment in each of the 5 layers was optically isolated from its neighbours and read out by lightguides to photomultiplier tubes mounted on the outside front or rear face of the spectrometer magnet. Test runs of the spectrometer in early 1990 found a large number of e+e- wrap-ping around in th~ volume of the magnet to re-enter the drift chamber. Events of this nature made tracking the event in software difficult. Only (x,y,z) points up to the track leaving the drift chamber were used in track reconstruction. To reduce the number of tracks re-entering the spectrometer, 3 mm of aluminium, 4 mm of lead and another 3 mm of aluminium sheeting was placed around the outside of the D rmg. The thickness of the lead converter between the B and C ring was important. While a thicker layer would afford a higher conversion efficiency it would decrease the energy resolution. The end-point of the photon spectrum from the bremsstrahlung of the electron from muon decay is 53 MeV. A decrease in the resolution would smear this endpoint up into the region of the photon signal from RMC. With the muon decay process eight orders of magnitude more frequent than the RMC signal, the high-energy tail from this background would reduce the likelihood of detecting 3.6. Cosmic-Ray Counters 55 any photon signal from RMC. Monte Carlo studies aided in finding a compromise between conversion efficiency and energy resolution. A lead thickness of 1.08 mm of-fered a 10% conversion efficiency and acceptable energy resolution ("' 12% resolution at 129 MeV which improved at lower photon energies). 3.6 Cosmic-Ray Counters The rate of photons from RMC on hydrogen is small. Only 5-7 RMC photons . ( E-r 58 Me V) are recorded per 24 hours of data taking. Because of the long periods of data collecting along with the low rate of photons from RMC, cosmic-ray-induced events constituted a large portion of the photon spectrum between 58-100 MeV. Therefore, it was essential to identify and reject these event s. This was accomplished by a set of 12 large-area planar drift chambers and 6 large scintillators. The drift chambers are all 5 cm thick with the smallest 90 cm wide and 260 cm long. The scintillators are 1.27 cm thick and arranged to match the area of the drift chambers. The top and upper part of all four sides of the magnet were covered by a double layer of drift chambers and a single layer of scintillator. Figure 3.9 illustrates the positions of the cosmic-ray veto counters around the magnet. While the cosmic-ray veto counters are very efficient at rejecting charged cosmic-rays, there remains a neutral component which was not identified. These neutral cosmic-rays can shower in the magnet yoke and produce a photon background in the spectrometer. For large Z nuclear targets, the RMC rate is much higher (in-creasing ex: Z4 ) and the photon background from the neut ral cosmic-ray component was found to be negligible ( 1 % [841). For hydrogen it can be as large as 20%. Approximately 500 hours of data taking with "beam on" provided a measure of the extent of the photon background from the neutral component of the cosmic-rays. This was measured to be (-1 per day). The term "beam on" implies that aµ beam was delivered down the M9A channel and into the RMC spectrometer. Some of this data taking was with the liquid hydrogen target in position, some without. Details 56 Chapter 3. The TRIUMF RMC Facility a) Beam axial view • , ' ' , ~- Magnet b) Top view l ____ _ Scintillator Drift chamber Drift Chamber Figure 3.9: Schematic of the cosmic-ray veto counters positions around the magnet. 3.7. Magnet 57 of how this was measured and subtracted from the photon spectrum will be reviewed in Chapter 4. 3.7 Magnet A large-volume solenoid magnet was used to supply a uniform axial magnetic field (2.4 kG) over the drift region in the spectrometer. The available space within the magnet measured 152 cm (horizontally), 122 cm (vertically) and 117 cm (along the beam axis). This enclosed the drift chamber, inner wire chamber, target, beam counters, both the outer trigger scintillator ring and the inner trigger, and lead converter package. Both the front and rear of the magnet has a 25.4 cm diameter hole along the beam axis. The upstream hole permits access of the beam collimator and the four beam scintillator counters as well as the beam. Also, in the front face of the magnet are 40 holes for the lightguides of the segmented B(12), C(12) and D(16) scintillator layers. The downstream hole provides access for the hydrogen target and its cryostat, as well as the segmented veto scintillator layers A and A'. Gaps, both at the rear left and right of the magnet, allow readout cables for the 1672 channels of the drift chamber and 1536 channels of the inner wire chamber as well as various high voltage lines. A field of 2.4 kG provided the best compromise between resolution and acceptance. The magnetic field had a uniformity of SB/ B 0.5% and was constantly monitored with a NMR probe located at the front face. 3.8 The Liquid Hydrogen Target Because of the long muon lifetime (2.2 µsec), the µ-p atom survives long enough to become involved in a chain of atomic and molecular interactions before it captures or decays. It may even become a part of a different atomic or molecular species. The potentially large background rate from RM C on higher Z material therefore places stringent requirements on the purity of the liquid hydrogen target. 58 Chapter 3. The TRIUMF RMC Facility If natural {unpurified) liquid hydrogen, having a deuterium contamination of 140 ppm , were used a muon in the singlet atomic state would quickly transfer to the deuteron in about 500 ns and to any larger (Z,A) contaminant much more rapidly [85). The neutral µd atom can form a pµd molecular ion which may undergo muon induced fusion. The final state can either be a µ- 3He atom in which the muon can capture or normal 3He with the muon set free. At the natural deuterium contamination of 140 ppm, RMC on 3He would swamp the signal from RMC on hydrogen. For this reason isotopically pure liquid hydrogen (protium), with less than 2 ppm deuterium was used . The liquid hydrogen was contained within a cylindrical gold flask, 16 cm m diameter and 15 cm in length, with a domed front face. The gold walls were 154µm thick. The short lifetime of the muon in the gold walls ( muon disappearance time of 73.5 ns [45)) allowed radiative muon capture in the gold to be identified from RMC in the hydrogen. Deta ils of this procedure will be explained in chapter 4. Surrounding the gold flask were two silver heat shields ( disappearance t ime 88.1 ns) and a silver vacuum jacket 1.0 mm thick. The vacuum permitted the hydrogen to be kept at 17°K. The upstream face of the inner heat shield was a single layer of aluminised mylar 2.5µm thick; the corresponding front face of the outer heat shield consisted of nine layers of aluminised mylar with a total thickness of 22.5µm. The front face of the vacuum jacket was 254µm thick aluminised mylar . Immediately upstream of the target and attached to the outer heat shield was a silver beam collimator. It was composed of two cylinders, the smaller with a radius of 5.0 cm and the larger with a radius of 8.43 cm. Each had a 762µm thick wall · and they were connected at the upstream end by a silver annulus, 762µm thick. The purpose of the silver collimator was to prevent muons scattered from the beam scintillation counters from stopping in the low-Z scintillator material surrounding the target. The target design is shown in Fig. 3.10 The protium was obtained by electrolysis of ultra-pure water (~ 1.4 ppm deu-terium). Samples of the protium were periodically drawn from the target and tested 3.8. '-':The Liquid Hydrogen Target RF~C TARGET SPECFICA TION MARCH 19~1990 59 SUPER JNSULATll 9 LAYERS ----~n--~,:.._- SLPER JNSULA TIC r£1..D • • 010 0.064 :3 'STAIN..E:SS STEAL 8/32 SCR£\IS SIL VCR • Jl40 . 2 STAJ .... £SS STEAL VASHCRS 3/8 x l/16 SILVER RETAINER Figure 3.10: RMC liquid protium target. l LAYER - ·- -·- - - --- - -- -- ~--- "--- - - - . . ____ .. - - ·-- --·· --- -·---- ·--- -60 Chapter 3. The TRIUMF RMC Facility for Z > 1 contaminants using mass spectroscopy. Typical deuterium concentrations are about 2 ppm. Heavy contaminants are prevented from getting into the protium by a palladium filter and are kept at a level less then 10- 9• A full description of the protium production and bake-out procedure is given in {88]. 3.9 Data Acqvisition The data acquisition ~ystem was designed to collect data from all of the spec-trometer components and to monitor their performance. The system had to be able to cope with high trigger rates and as much as 4 kbytes of data per good photon event. The high number of data channels that had to be monitored, particularly in the drift chamber, made it necessary to use both fast and high density electron-ics. Standard NIM and CAMAC ECL modules provided the front-end trigger logic. The Anolog Hit Counter (AHC) and Fastbus system provided the higher level trig-ger and fast electronic readout while data recording and monitoring was handled by a MICRO VAX. Figure 3.11 shows a schematic of the data acquisition system configu_ration. Because of the expected length of the experiment of 3-4 years, and the large number of electronics necessary, a dedicated counting room {M9A) was setup to house the dat.~ taking and transfer system. The data acquisition system can be divided into several subsystems . They are the: 1. the front-end trigger electronics, ( CAMAC and NIM), 2. higher level trigger and readout electronics, (Fastbus, AHC and $SP-MASTER), 3. buffering system and data recording equipment, (Fastbus and SSP-SLAVE), ~- monitoring system, (CAMAC and VAX 3200). 3.9. Data Acquisition 8 mm VCR VAX-3200 DECNET VAX-3100 CFI CERN Fostbua Interface F astbus 2 SLAVE SSP - Data Buffering SSP 2 SL.AC Scanner Processor f2 Calibration and Timing module SSP 8D TDCs Comae 1 Comae 2 Comae 3 Comae 4 SL.AC Scanner Proceaaor f 1 MASTER SSP - data readout Branch Driver ECL Trigger Logic ADCs, TDCs ond Registers DACS and rwe readout Cosmic-ray readout Figure 3.11: Data acquisition configuration. 61 62 Chapter 3. The TRIUMF RMC Facility 3.9.1 Trigger Logic Three · t rigger conditions were implemented in this experiment . 1. The Photon Trigger btrigger ): This was the standard trigger for normal data taking. It was designed to trigger on a photon emerging from the target, converting in the lead sheet and producing an Ce+ pair of which at least one passed through the drift chamber into the outer ( "D") scintillators. The pho-tons may originate from a number of processes: radiative 1r-capture, radiative µ-capture or cosmic-ray-induced photons. 2. The Charged Trigger (Qrate): Designed to provide samples of the charged particles {mostly electrons from muon-decay in the target), this trigger was set by a variable width gate Qrate to take approximately 1 % of the triggers during normal muon running. During "beam off" periods, this trigger was fully enabled and would trigge r on charged cosmic-ray events that passed through the C counter layer. This permitted efficiencies of the drift chamber and scintillato rs to be measured. 3. The Random Trigger {R,.ate): This is a trigger that was enabled for approx-imately 3% of the total triggers. Whenever two or more of the beam counters fired during an open R,.ate gate pulse, the event was recorded. This permitted a sample of the beam's composition. The last two triggers were usually enabled in parallel with the photon tr igger but inhibited by a gate-delay generator so that they constituted only a few percent of the total triggers. A schematic diagram of the trigger logic is shown in Fig 3.12. Signals from the segmented A1-4, A;_4 , B1-12, C1-12 and D1-16 scintillators are sent to a splitter box. Duplit ate copies of the analogue signals are sent to ECL 4413 discriminators and CAMAC ADCs. Each 4413 discriminator module responds to the signals from one of the scintillator rings and produces a majority output of 2 mA per hit segment "tj oq· = ... (1) c..:, -~-0 ()q r,· 0--------------C ------------1 MLU [D >10 [C 8 ----1 [8 >1A A • I [A Moster Veto __ __. OR boor signals from 272 drift cells AHC >0 cells layer 2 1--------1 I clumps1----~ layer 3 ____ _, I clumps1-----1 layer 4 Computer I Busy E = Event S = Strobe Computer Busy t-------, Strobe· to OR Boards Slow Blank 'Y • AHC Fast Clear SSP Start Moster Veto t:, (") .0 i:: .... c,, .... ..... g· 0) 64 Chapter 3. The TRIUMF RMC Facility for that ring. The resulting outputs are sent to NIM discrimin~t~rs, where the output signals can be made to represent each of 6 conditions by setting appropiate thresholds. These conditions are: 1. the sum of A and A', (E(A + A'). 4. sum of C (EC). 2. more than one of the A or A',(> l(A + A'). 5. sum of D (ED). 3. sum of B, (EB). 6. and more than one D, (> lD). These signals are then sent to NIM coincidence modules to form the appropriate trigger. For the charged trigger two conditions are allowed: Ql = EB · EC · ED · Q Q2 = > l(A +A')· EC· ED· Q (3.5) (3.6) where Q is the Qrate gate whose frequency controls the fraction of charged triggers allowed during normal muon data taking. The photon trigger requires the coinci-dence: 1 = E(A +A')· EB· EC· 2:: lD (3.7) That is, no hits in the veto scintillation counters inside the radius of the lead con-verter, at least one hit in the C scintillators, indicating a photon conversion, and at least one D scintillator hit. These conditions can be met_ in less than 60 nsec, and provide a signal, STROBE, which is used to gate the CAMAC ADCs and registers, start the CAMAC TDCs, and stop the Fastbus TDCs. The Fastbus TDCs are free running; a STROBE stops them. In addition specific patterns between the C and D hit counters are looked for, producing an EVENT pulse (this is described in detail below). A STROBE-EVENT coincidence begins the Fastbus TDC read cycle, while a STROBE-EVEN 'r resets them. At this level of the logic the 1 trigger still accepts a large number of non-photon events. At a typical beam rate of 6 x 105 s-1, the STROBE rate is 1300s- 1 . 3.9. Data Acquisition 65 In addition to · he hardware· coincidences indicated above, signals from the seg-mented scintillator counters and various oth~r NIM pulses ( Q and R rate gate pulses, prompt and non-prompt bits as well as pulses representing the 6 conditions described above) are converted to ECL logic pulses and passed through pattern recognition modules . An LRS CAMAC 4508 programmable logic unit (PLU), duplicates the NIM coincidence conditions (Eqs. (3.5), (3.6) and (3. 7)) as well as tagging the event as being prompt (in coincidence with the beam counters firing, 1r induced) or non.-prompt. The output of the 4508 identifies the type of event; charged; cosmic; prompt photon; or non-prompt photon. The 4508 takes about 60 nsec to output a decision. During this time, signals from the C scintillator segments are sent to a LRS CAMAC 2372 memory lookup unit (MLU). The MLU was progra mmed to output a specific D pattern for each C counter. (The 12 input channels to the MLU represented the 12 C counters, while the 16 output channels represented the D counters that could have fired). The output D pattern corresponded only to those D counters that could have been hit by an electron or positron of minimum momentum having caused a particular C counter to fire. The allowed D pattern from the MLU was then put in logical coincidence with the actual D pattern via an ECL 4516 lookup unit (LU). The 16 output channels from the LU passed into a 4413 discriminator whose output was 2mA into 50!1 for each correct D that fired. A threshold on a NIM discrim-inator could be set to accept the event for a predetermined number of "correct " D counters . For the previous experiment (RM C on nuclear targets) this was set at two, requiring both electron and positron tracks to reach the outer D ring. For this experiment it was reduced to allow events where only one of the tracks reached the outer D counters . While this had the advantage of increasing the detector ac-ceptance, those tracks that did not make it to the outer D scintillator, but instead, wrapped around in the chamber, generally had a poorer fit , and consequently poorer energy resolution. The consequences of this "JD trigge r' will be discussed in the following chapter . A coincidence between the "Valid Number of Ds" output pulse and the 4508 event type ( charged, cosmic or photon) forms a valid "EVENT" pulse. 66 Chapter 3. The TRIUMF RMC Facility The EVENT rate was typically 600s- 1 . The next level of the trigger examines the pattern of hit cells in the drift chamber. The OR-boards which were described earlier perform a "majority logic OR" for each group of six sense wires associated with each cell. When two or more wires in a cell register as hit, that cell is tagged as hit. The OR-boards pass on this hit-cell information to the Anologue Hit Counter or AHC (87]. The AHC produces output voltages proportional to the number of cells, or clus-ters of cells, hit on each layer of the RMC drift chamber. A cluster is any group of two or more consecutive cells in a layer. The AHC may be manually switched to count either individual cell hits or clusters of hits for each layer. The analog outputs are 0-1 volt into 50 n, in steps of approximately 0.1 volt per hit. Each layer of the chamber is counted separately permitting elementary pattern restrictions on the hit cells in the drift chamber. The AHC hit pattern tests reduces the coincidence STROBE·EVENT·AHC rate to 100s- 1 . This coincidence identifies a valid event. Subsequently the Fastbus TDCs are converted and the SSP is sent a request to start reading all information from the various pata acquisition sub-systems. An EVENT signal indicates an incorrect CD pattern, a AHC signals an incorrect DC pattern. Upon receiving a STROBE-EVENT a fast clear is sent to the SSP, ADCs, TDCs, and registers. The final stage of the trigger applies further pattern tests in the "SLAC Scanner Processor" (SSP) to reduce the trigger rate to less than 50 s- 1 , for recording to tape. At this rate the experimental dead time is 10%. An important part of the logic is the identification of a beam particle as a muon ( or 1r for pion calibration runs) and to count accurately the number that stop in the target. Each of the four beam counters is read out by two phototubes whose linear signals are summed and monitored by CAMAC ADCs. The discriminated pulses are sent to scalers and CAMAC TDCs of 200 ns full range and Fastbus pipelined TDCs of 1 µsec full range. The pipelined Fastbus TDCs allow beam timing information up to 500 ns both before and after an event is signalled. An 3.9. Data Acquisition 67 ADC and TDC pulse in coinci<:1ence with an event is an efficient indicator of a pion induced event. These events are tagged by setting a PROMPT bit when 2 or more of the 4 beam counters are hit. While these events could be vetoed, they are recorded to tape and later rejected in software by examining the beam counter ADCs and TD Cs and the PROMPT bit. The advantage of recording these radiative pion events is that they provide valuable information on the detector acceptance and resolution . A valid µ-stop is defined as a coincidence between all four beam counters together with the RF separator phase for muons and no master veto, MV, µ11top11 = l.2.3.4.RFwMV. (3.8) Finally, the livetime (LT) must be determined . This is measured by running a pulser at 10 kHz, and recording the number of pulses in a register, while no master veto has been set. In an experiment such as this, where a large number of electronic modules and timing pulses are necessary, it is an essential requirement that all of its components be available for testing via computer generated pulses with a minimum of alteration to the electronics. This was achieved in the software control ,of the ECL 4413 discriminators, a NIM driver and a Struck 320 Camac Branch Driver . All trigger scintillators are monitored by the 4413s. By downloading a software mask into the ECL 4413s via Camac and firing the NIM driver, all possible patterns of trigger scintillator firings can be simulated, thereby allowing a te st of the entire electronics chain. 3.9.2 Fastbus System After a valid trigger (STROBE-EVENT-ARC) was generated by the trigger elec-tronics, the process of collecting all relevant information from the detector sub-systems and outputting it to magnetic tape was initiate d. The front-end data ac-quisition consisted of a Fastbus crate containing a SLAC Scanner Processor (SSP) 68 Chapter 3. The TRIUMF RMC Facility > [88], 18 Lecroy 1879 pipelined TDCs and a Struck 320 CAMAC Branch Driver [89] connected to 4 parallel CAMAC crates. Th e first CAMAC crate contains the programmable ECL logic modules which generate the first-level hardware trigger, as well as ECL scalers monitoring scintillator rates. The second crate contains CAMAC ADCs and TDCs which record the beam counter and trigger counter pulse heights, TDC times and various NIM registers . The third crate contains DACs which control and monitor high voltages, temperature sensors and beam line parameters such as the quadrupole currents and beam rate. It also houses the IWC readout module for the RMH system. These three crates are located in the counting room . The fourth CAMAC crate is located in the meson hall beside the spectrometer magnet and contains the readout for the cosmic-ray drift chambers and scintillators . The first SSP serves as the MASTER, controlling all CAMAC operations and requests to and from a second SSP (the SLAVE), located in a second Fastbus crate and connected via a Fastbus cable segment . The SLAVE SSP is responsible for buffering data between the MASTER SSP and the VAX 3200. The SSP micropro-cessor emulates the IBM 360 instruction set and is programmed in assembler using a VAX-based crossassembler and loader. When a candidate event is found , the trigger sends a request to the SSP. The SSP first begins reading the OR-boards. Further pattern searching of hit cells in the drift chamber is performed. If no correct "'hit cell" pattern is found the SSP is fast-cleared and the hardware trigger re-enabled. The SSP next reads the IWC information, if the number of IWC words is less then a minimum number (23) then the event is rejected, ( to reconstruct the longitudinal component of the momentum an IWC point must be included in the event data set) Twenty-three words of IWC data was found to be the minimum number of words that contained at least one anode and one cathode cluster crossing. For good events further readout of the pipelined TDCs and of all Camac modules is done. The SSP continues gathering events until its 512 kB ( a.ta memory is filled, at which point it signals the buffer subsystem . The buffer subsystem consists of a second Fastbus crate with a second SSP 3.9. Data Acquisition 69 (the SLAVE) and a CERN Fastbus Interfac,~ module [90]. During data taking, the SLAVE monitors the cable segment, waiting for a signal that the front-end SSP is full. Upon such a signal it copies the full data buffer over the cable segment to its own memory using a high speed("' 20 Mbytes/sec) 32-bit word block mode trans-fer. As soon as the transfer is complete, it re-enables the MASTER SSP and signals an interrupt to the VAX-3200. The second SSP and Fastbus crate were initially intended as replacement spares. However, during data ta king in the preceding nu-clear RMC measurement, a large fraction of the dead-tim e was due to the readout between the the front-end SSP and the VAX-3200. This was primarily due to the I µsec read cycle of the VAX. The 20 Mbytes / sec transfer rate between the two SSPs allows the MASTER SSP to quickly transfer its data buffer, re-enable the trigger and continue to take events. This data buffering procedure reduced the dead-time by - 15%. The final stage of the data acquisition process involves the transfer of data from the second SLAVE SSP to the VAX-3200 via the CERN Fastbus Interface. Data are collected and stored on the VAX-3200 in a shared memory segment. From here it is copied to 8-mm data cassettes. An independent process passes a fraction of the events over DECNET to another VAX node running analysis and histogramming software. The DECNET process is run at a priority that will not allow it to interrupt or interfere with the data transfer to tape. By performing the online analysis on a second VAXstation {usually a VAX-3100), there is no contribution to experimental dead-time from online analysis. The online software is identical to the offiine data analysis and is capable of sampling "' 30% of the events tak en to tape. In addition to the full track searching and fitting performed by the online analysis code RMCOFIA (Radiative Muon Capture OF:fline Interactive Analysis), several other processes are run on the VAX-3200 periodically to monitor the performance of the many d~tector components. 70 Chapter 3. The TRIUMF RMC Facility 3.9.3 Blanking A master veto (MV) signal is used to disable the front-end trigger electronics. This can be enabled for a number of reasons: (a) it can be initiated by the STROBE signal which indicates a possible "GOOD" event ( either charged, cosmic or photon) and kept on by the gate ( G 1) if the EVENT signal is satisfied. This allows the data acquisition time to readout all the subsystem information into the SSP buffer. (b ), it can be initiated due to equipment failure i.e. RF separator, spectrometer magnet trip, high voltage trip on the drift chamber, wire chamber, cosmic-ray chambers or any of the scintillators, low or high trigger rates . . In addition ~o the automatic blanking due to failures in the experimental system, a software monitoring system (MONITOR) was installed on the VAX-3200 which alerts the operator to any divergence of important experimental parameters from their nominal values. Such parameters include the detector high voltages, beamline magnet currents, chamber temperatures, gas flow, magnetic field, RF separator phase, and beam rates. The monitor program examines the shared memory and extracts relevant information at specific time intervals. Parameters that remain constant such as the high voltages, magnetic field and beamline magnet currents are monitored every 15 minutes while trigger rates are scanned approximately every 20 buffers. This method of selective monitoring reduced the amount of dead-time. In the event of any parameter exceeding the limits set by a calibration file, the MONITOR program sends out an audible alarm and displays the failed parameter. The alarm continues until the condition is corrected and, if necessary, data taking is suspended. 3.10 Run Summary Data for this experiment were taken over several period ~ of time beginning in Au-gust 1990. Prior to this, the performance of the drift chamber and trigger electron-ics was tested. In December 1988, the drift chamber was installed in the "Chicago 3.10. Run Summary 71 magnet " and tracks from cosmic-rays were first obserw ,d. During 1989, a num -ber of measurements of RMC on nuclear targets (27 Al, 28Si, 4°Ca, natMo, natsn and natpb) was investigated [84]. Studies of these experiments, in particular the 4°Ca measurement which had been previously investigated by a number of authors [84], provided valuable insight on the performance and characteristics of the drift chamber and related trigger electronics. The measurement of RMC on the purified hydrogen began with 2 weeks of data taking in August 1990. Further beam time was allocated during 4 weeks in November -December 1990 with a following 3 weeks in January-February 1991. This thesis has examined the data collected from these times. Further data taking has continued and is expected to be completed by early 1994. Summaries of the number of muons stopped and the experimental livetime for each of the µ- and µ+ data tak-ing periods examined in this work are shown in tables 3.3 and 3.4. During "beam off" periods, measurement of the efficiencies of the various detector components was studied using cosmic-rays. Additionally, more than 500 hours of background measurements of the photon rate from cosmic-rays were investigated. At the completion of the data taking, a statistical precision of 5% (or 400 RMC photon events) is anticipated . This data will have the potential of yielding a mea-surement of the pseudoscalar coupling strength, gp, for the bare nucleon to an ac-curacy of 10%. The results presented in the next chapter constitute data taken up to the end of January 1991, approximately....., 30% of the expected total. 72 Chapter 3. The TRIUMF RMC Facility Data Taking Number Livetime Beam particle Period of Files Days (hrs) Stops x 1010 August 1990 68 1.18 (28.32) 5.10912 December 1990 92 1.83 (43.81) 9.66849 January 1991 80 1.73 (41.53) 10.90230 Total 240 I 4.74 (113.66) I 25.67991 Table 3.3: Summary of the µ+ data taking Data Taking Number Livet ime Beam particle Period of Files Days (hrs) Stops x 1010 August 1990 228 4.20 (100.80) 19.9729 December 1990 292 8.07 (193.36) 39.1135 January 1991 489 13.51 (324.19) 83.4094 Total 1009 I 25.18 (618.35) 1 142.4958 Table 3.4: Summary of the µ- data taking , 73 Chapter 4 The Measured RMC Photon Spectrum 4.1 Introduction The expected event rate for RMC photons in this experiment is 6-7 per day. However, the front-end trigger rate is 1300s- 1 events per second. Various hardware and software conditions which were described in the previous chapter reduce this rate to 50 events per second which are written to tape. Clearly, the majority of these events, are not photons from the RM C process. They can be from the various photon backgrounds, s~ngle tracks (principally from muon decay) or simply be random noise in the spectrometer which has satisfied the front-end trigg er logic. The tighter and more intelligent the front-end decision making is, the lower the rate of false, non-RM C events. This has the advantage of a more compac t data set to work with. However, complex decision making at the front-end usuall y incurs large . dead-time . A compromise is necessary. The expected data collecting time for this experiment was 60 days of livetime ( 2-3 years of experiment time). Consequently, it was decided that a reduced dead time was more important than having to manage vast amounts of data. With an experimental dead time of "' 10%, event by event data were recorded to 2.3 Gigabyte 8mm tapes. Approximately 1,000,000 raw triggers were written onto each tape in 4 hours. On average only one of these was expected to be from the RMC process in hydrogen. This chapter describes the process of reducing the raw data. The ultimate goal is to reconstruct the energy of a photon produced in the spectrometer and to identify 74 Chapter 4. The Measured RMC Photon Spectrum it as a photon from RMC in hydrogen. This was accomplished in three stages: firstly by searching for the tracks of a positron and electron that intersect at the radius of the lead converter {indicating the conversion of a photon), secondly by applying kinematical and geometrical restrictions to remove poorly resolved photons, and thirdly to estimate the contribution from photon backgrounds . 4.2 Track Reconstruction , The reconstruction of charged particle tracks in the drift chamber was done us-ing RMCOFIA (Radiative Muon Capture OFfline Interactive Analysis) . RMCOFIA was adopted from the original program KOFIA (Kaon OFfline Interactive Analysis) which was developed at TRIUMF for the BNL 787 experiment at the Brookhaven National Laboratory. RMCOFIA was specifically designed to analyse data from a multi-layered drift chamber, calculate the momenta of the pair tracks and deter-mine the energy of the initial photon. RMCOFIA also contains a "PHOTO" pack-age allowing a graphical representation of events, as well a histogramming package FIOWA, which can be accessed via a user routine DPLOT. The DPLOT routine is called on an event-by-event basis after all track reconstruction and fitting has been performed, and permits user-defined cuts to be applied . RMCOFIA uses drift chamber information to reconstruct tra cks. In the case of a photon event, two tracks ( an C track and an e+ track from a photon conversion ; --+ e- e+ in the lead converter layer) are required. The tracks must have opposite curvature, and intersect at the lead converter. RMCOFIA calculates the momenta of each track and hence the initial photon energy, E,.,, given by: {4.1) where, and E2 --2 2 e+ = Pe+ + me+ · (4.2) 4.2. Track Reconstruction 75 me- and me+ are the electron and positron masses respectively, and Pe-and Pe+ are their momenta. RMCOFIA uses the relationship ... _ ... Tranaverae + --Longitudinal Pe- - Pe- Pe- , (4.3) (and similarly for the positron) determining the moment a transverse to the muon beam axis and the momenta along the beam axis for the positron and electron pair, from which the momenta are computed. Within the acceptance of the RMC spectrometer , 75- 100% of the particles' mo-mentum is transverse to the magnetic field in the detect or. This means that the precision of the measured curvature is dominated by the position resolution in the transverse plane . 4.2.1 Transverse Momentum of a Track The transverse momentum of a track in a uniform magnetic field B, can be expressed as: PTnnaverae = (0.3)BR (4.4) where B is in kilogauss, R is the radius (in cm) of the circle obtained by projecting the helical trajectory of the particle onto the plane transv erse to the magnetic field, and PTranaverae is in Me V / c. The radius R, is obtained from the fitted track in the drift chamber. The pattern recognition procedure is as follows. Each drift cell with wire hits is examined and the hits are assigned to 'line segments' according to the road method [91]. Although the hits of a track fall on a circular path, a straight line can be approximated over the small dimensions of the cell; this saves valuable compu ting time. Once the track algorithm has found all segments in all cells of the drift chamber, it then uses the position and directional cosines of each segment to link segments in the first, second and fourth layers [92]. The linked track segments are fitted to a circle using a least-76 Chapter 4. The Measured RMC Photon Spectrum : I ta. Magnetic Field -- e = 2.7 kG .. Longitudinal p zcirc A = Pitch angle R = Radius of Track in x-y R Beam Axis Figure 4.1: Determination of the longitudinal component of momentum for a charged particle in a uniform magnetic field. squares fit method to obtain the track centre ( Xe, Ye) and radius R. The transverse momentum of the particle can then be determined. 4.2.2 Longitudinal Momentum of a Track The longitudinal component of the particle momentum is given by, PLongitudinal = (0.3):BZcire, (4.5) where (4.6) and A is the pitch angle of the helical path of the charged particle, see Fig. 4.1. Because of the constant drift velocity of the particles in the uniform magnetic field, the pitch angle is constant. The z-coordinates are thus fitted to the simple equation 4.2. Track Reconstruction 77 of a line Eq.(4.6). To construct the line, at least two, well separated, z-coordinates are needed. The first is obtained from the IWC, located just outside the radius of the lead converter layer, the others are obtained from the six anode sense wires of the third stereo layer of the drift chamber. Because of the small separation in distance of the points from the stereo layer, they alone are not sufficient to define the gradient of the particle trajectory along the z-axis. To find points which lie along a line the road routine [91], starts with four points, the real point and its reflection from wire 1 in the cell and the real point and its reflection from wire 6. These four points determine the four possible lines along which any hits from wires 2 through 5 must fall if the hits are due to a track which is relatively straight when it passes through a cell. Figure 4.2 illustrates this procedure. Next all points in the cell are tested to see if they fall within a given distance (typically 0.2 cm) of any of the lines. If they do, they are assigned to that line. The two lines with the most points are passed on as candidate track segments. The next step is to rotate the segments of the stereo layer into the global coordinate system and assign them to a circular track that has already been found by the x - y tracking algorithm. The z-coordina.te of the stereo hits are found by finding the intersection of the track and the helical locus of points whose axis is a given stereo wire and whose radius is the drift distance. The z-coordinates are then fitted to Eq. ( 4.6), allowing the longitudinal component of the momentum to be determined. Once the momentum for each of the particles has been fully determined, the energy of the photon, E-r, can be deduced according to Eq. ( 4.1 ). The initial raw data set ( consisting of 350, 2.3 Gbyte data cartridges) was pro-cessed by the RMCOFIA tracking package. An 8mm data cartridge would typically contain,_ 106 events. This number was reduced by,_ 85% on a first pass search for valid e- e+ pairs. This completed the first stage of data reduction. Of the 15% of valid pairs identified by RMCOFIA only a small percent are photons from radiative muon capture in the hydrogen. The remainder are from 78 Chapter 4. The Measured RMC Photon Spectrum Direction of 6 .- drift • Anode Sense wires 1. to 6 Figure 4.2: The Road Method procedure for locating tracks in a drift cell. 4.3. 2D or NOT 2D 79 photons whose track reconstruction produces photon energies far from their true value, or are photons from other physical processes, such as radiative pion capture, electron bremsstrahlung and radiative muon decay. These photons are identified in the second and third stages of the data reduction, described below. 4.3 2D or NOT 2D The initial design of the drift chamber and trigger system was for a "2D trigger", i.e. both the electron and positron tracks traverse the full radial volume of the drift chamber and exit through the outer segmented scintillator "D ring". Inspection of the earliest test data revealed that a considerable number of valid photons were being rejected because only one D counter was hit. The second particle had lower energy and remained inside the volume of the drift chamber. It was realized that provided the "wrap around track" reached the radius of the third stereo layer (so that Z coordinate information could be collected), the photon energy could be reconstructed with only one of the particles exiting the drift chamber . The trigger logic was altered to accept both a "ID" and "2D" triggered events. Subsequently, a photon event could be identified as coming from a "nowrap event" corresponding to a 2D triggered event or a "wrap event" from a ID triggered event. The two event types are pictured in Fig 4.3. In general the wrap around events have poorer track reconstruction. The main reason for this is that the particle that wraps around has a longer path in the volume of gas in the drift chamber. Energy loss in the drift chamber gas, together with scattering from the anode and cathode wires, will result in a departure from the ideal helical path. The circular track fitting performe d by RMCOFIA does not accommodate these effects. The circular fit to the wrap around particle's path is therefore expected to be of poorer quality compared with the non-wrap around path. Consequently, a single set of cut parameters was found to be unsatisfactory. Cuts 80 (a) Outer D scintillator ring (b) Chapter 4. The Measured RMC Photon Spectrum I NOWRAP (2D Event) I - --- --- -Both e - and e + exit " the drift chamber WRAP ( 1D Event) Only one of the tracks , uits the drift chamber ) Figure 4.3: Figure (a) illustrates the characteristics of a nowrap event, (b) illustrates those of a wrap event . 4.4. Cuts 81 that were tuned to nowrap events were cutting too hard on the wrap events, while cuts tuned to wrap events could have been tighter on the much better fitted nowrap tracks. Two sets of cut conditions were developed. One set was applied if the event met the conditions of a wrap event, and the other which generally allowed for tighter cuts, was applied to nowrap events. Despite this effort to increase the experimental acceptance, it was later discovered that the Monte Carlo simulation could not successfully reproduce the experimental ratio of wrap to nowrap events. For the experimental data the ratio of wrap to nowrap events was 30%, after all cuts for photons above 58 MeV; this is in contrast to 15% for the Monte Carlo data. In addition wrap around tracks are more likely in the energy region where the RMC photon spectrum is most dominant. Hence the discrepancy is particularly worrisome. The determination of gp relies strongly on the reliability of the Monte Carlo simulation to reproduce experimental conditions. It was decided that wrap events would not be used in the analysis until the wrap around tracks could be well reproduced by the Monte Carlo simulation. The subsequent extraction of gp will rely only on the nowrap events. 4.4 Cuts The first stage of the track finding and reconstruction algorithms was optimized for maximum acceptance (95% of good photons generated by Monte Carlo are found by the track finding routines). This is not to say that of the 95% found, all were reconstructed with their originally generated energies. It was the objective of the offiine software analysis to select out the well resolved genuine photons. This was achieved by applying a number of user defined cuts on the data. A cut is the term used to describe a condition (or set of conditions) that removes non-genuine RMC photon events from the data sample. The cuts can be classified into two categories: 82 Chapter 4. The Measured RMC Photon Spectrum (i) Quality cuts, which discard photon events because the quality of the fit-ted track was unsatisfactory, and hence the reconstructed photon energy is not reliable. (ii) Physical cuts, which identify and remove photons from a specific physical process such as, pion capture, muon capture from non-target material, and cosmic-ray induced events. 4.4.1 Quality Cuts The first stage was to identify a good pair ; an e+ track and an C track that converge at the lead converter. The vector sum of each track's momentum at the vertex must project back to the target, indicating the initial photon had originated from the target . Cuts that identified these events are called Photon cuts. They included, the Axy cut; requiring that the distance between the e+ and e- tracks at the vertex in the x - y plane be less than a maximum value. The Az cut, similar to the Axy cut , but along the z-projection. Another cut was made on the opening angle 0, defined as the angle between the tangents of the two helices of each of the tracks, at their point of closest approach. For photons of energy greater than 58 MeV, the opening angle is small ( < 5°), but due to multiple scattering in the Pb converter can be measured to be considerably larger . Large opening angles are also indicative of poorly fitted tracks. The remaining Photon cuts were concerned with the origin of the photon. Parameters Zradmax and Zradmin set upper and lower limits on the z-position of the photon at the radius of the lead converter. Similar cuts, Zclosmax and Zclosmin, confined the z-position of the photon at the point of closest approach of the track to the target. Finally, the cut Radclos sets an upper limit on the distance the reconstructed photon path can be from the centre of the target. All good photons found by the Photon cuts was passed to the second stage of the Quality cuts, the Track cuts. In this stage the quality of the fitted e+ and e-4.4. Cuts 83 Cut Description Event Type Cut Description Event Type PHOTON Wrap Nowrap TRACK Wrap Nowrap XY converter 4.00 cm 3.3 cm Npts e+ 10 11 Z converter 6.25 cm 4.5 cm Npts e- 10 11 Opening Angle 56.0° 42.0° Xz11e + 0.0045 0.00245 Zrad max. 12.0 cm 12.0 cm Xz11e - 0.0034 0.0024 Zrad min. -10.0 cm -10.0 cm xze+ 0.18 0.05 Zclos max. 10. cm 10.0 cm xze - 0.18 0.075 Zclos min. -6.5 cm -6.5 cm Pz/Pe+ 0.72 0.72 Radclos 6.0 cm 5.95 cm Pz/Pe- 0.72 0.72 Table 4.1: Summary of the Photon and Track cut parameters used in the DPLOT routine. tracks was examined. These cuts were responsible for ensuring that the energy of a photon was in fact a reliable estimate of its true energy. Such cuts included the x2 of the circular fit to the e+ and e- track both in the x-y plane, x;11 and the z plane x;. The position resolution in the x - y projection was considerably more accurate than in the z projection. This is reflected in the maxim um assigned values of the x;11 and x~ parameters. Other cut variables tested were Nz 11, the number of xy points used in the fit of each track. The cut variables tha t were used to select good photons are shown in table 4.1. The distribution of these parameters are illustrated in histograms of Fig. 4.4. After both the Photon and Track cuts, all remaining photons in the spectrum are considered to be real photons that are close in energy to their true value ( there is one exception, this case is discussed under the section heading 'False' Photons in the following section). The cuts were tuned using two procedures. In the calibration 1r-p data, almost all of the event triggers were valid photons. This data could be used to identify the characteristics of good photon events . Additionally µ+p was also used to define the value of the cuts. In this case no physical muon induced process could result in a photon greater then 53 MeV (the end-point of the free muon decay spectrum). Any event above this energy was either not a real photon, a poorly resolved one, or some background (e.g. cosmic-ray induced). Using those events above the 53 MeV 84 Chapter 4. The Measured RMC Photon Spectrum 35000-+-- ....... -- ...... - ......... __ ........,.....,.~ 20000 ....... -~ ....... ~--~~~~---i-JOOOO 25000 20000 15000 llOOO 5000 11000 6000 4000 2000 ll000 IIOOO 4000 2000 56000 42000 28000 14000 j 2 4 II cm 20 40 IIO dell"NI 4 8 cm II 110 12 2 -X. e j .01 .02 .03 .04 .05 16000 12000 ll000 4000 I 10 4 II cm 16000 12000 ll000 4000 j o+-,.~.........-..-.-..-,;:::-1" 100 -40 -24 -II II 50000 40000 30000 20000 10000 16 0 .000 50000 40000 30000 20000 10000 cm .002 .004 0 +-,~........,--,.-.,. .06 0 10 .006 20 12 115 24 40 2 ~e .008 .010 30 40 Figure .4.4: Histograms of the various parameters used to select well resolved photons . The histograms are 11'- p calibration data before and after (hatched region) all cuts were applied. The arrows indicate the location of the software cuts. The parameters are: (a) A2'r, (b) Az, (c) Oongle, the opening an-gle, (d) Z.-od, (e) Re1ou, (f) x~,, (g) X~, (h) N2'r· For a description of the parameters, see the text. 4.4. Cuts 85 threshold, both the Photon and Track cuts could be tuned to minimise the number of events in the high-energy-tail. After all data had been passed through the Photon and Track cuts only good, well-resolved photons remained. This is reflected in the photon spectrum for the µ+ data, before cuts and after cuts, shown in Fig. 4.5. 4.4.2 Physical Cuts In addition to the software cuts that define the quality of the tracks, there are a number of cuts that are applied to identify and eliminate the photons from processes other than RM C by hydrogen . The following sources of photons have been identifie d as the most significant between 58 and 100 Me V: 1. Radiative pion capture. 2. Muon decay bremsstrahlung. 3. Radiative muon capture from the gold container. 4. False photons. 5. Cosmic-ray induced photons. By examining the specific characteristics of the photon events from each of the above processes, cuts were developed to identify and reduce thei r number. The cuts were not 100% effective, consequently a small fraction of these background photon events was not rejected. The following sections discusses the specific cut conditions for . each background process .and gives estimates of the remaining contributions to the final photon spectrum. 86 Chapter 4. The Measured RMC Photon Spectrum 200000 3500 (a) 3000 + 160000 µ. Data 2500 Before cuts 2000 i> 120000 1500 Q) ::s rn i:: ::, 0 t.) .. I > Cl) ::s rn i:: ::, 0 t.) 1000 80000 500 60 80 100 120 140 40000 0 4-,,..........~-r-r.......-4.....-,,............~~ .................... ~ .....-~-r-r""T'"""T........,,............T"""T""°T'""'T".......,.........,r-+-o 20 40 60 80 100 120 140 160 Photon Energy {MeV) 25000 10 (b) + 20000 8 µ Data 6 After Cuts 15000 4 2 10000 0 40 60 80 100 120 140 5000 0 ~~T'""'T""T"""T"".,...,..T"T"'T""T-it-l--.-,.........+r-r-T"""T""-r-r-"T""T""'T""T"""T'""1~~,.........T"""T"""T""'T"-.-+-o 80 100 120 140 160 Photon Energy {MeV) Figu e 4.5: (a) Photon energy spectrum from the µ+•s stopping in liquid hy-drogen before cuts. The inset shows the extent of the high energy tail above 58 MeV. (b) The same data is shown after the Photon and Track cuts have been applied to the data. 4.4. Cuts 87 Radiative Pion Capture The muon beam at TRIUMF is prociuced from pion decay (1r--+ µv) in flight. It is expected that some pion content will remain in the beam when it arrives at the target. The branching ratio for radiative pion capture is eight orders of magnitude larger than the signal from RMC. Clearly, even a small pion contamination in the µ-beam will result in a potentially serious source of background photons. Radiative pion capture almost exclusively proceeds in two ways: 39.6% (4.7) emitting a mono-energetic 129 MeV photon, or 60.4% (4.8) 1r0--+ 11 98.8% (4.9) The produced ,r 0 's subsequently decay into two photons, each with an energy be-tween 55 and 83 Me V. Several steps were taken to eliminate this photon background. The first, was the use of a radio frequency (RF) separator ( the principle of operation has already been discussed in chapter 3). This reduced the ,r / µ ratio in the beam to 10-3 • Pions that passed the RF stage continued down the beam channel. However, most stopped in the assembly of four beam scintillator counters, before reaching the target. The primary purpose of the .beam counter package was to provide the time the last beam particle entered the target before the trigger, as well as to provide pulse height information for particle identification. However, because of the heavier mass of the pion, the beam counters also served to degrade and absorb many of the pions remaining in the beam after the RF separator. The level of pion contamination in the beam that reached the target was of the order 1 o-6 per muon. Figure 4.6 (a), displays the photon energy spectrum from µ-p. Even after con-( · 88 Chapter 4. The Measured RMC Photon Spectrum siderable pion rejection, the photon energy spectrum with no, cuts clearly displays the features indicative of pion capture; a large photon energy peak at 129 MeV together with the ('1T'0 T'Y) "box" between 53 and 85 MeV. The additional peak at 53 Me V is the photon spectrum from muon decay bremsstrahlung. The spectrum is also shown to drop off sharply after 45 MeV, a consequence of the limited acceptance of the spectrometer at low energies. Clearly, this level of pion contamination is still sufficient to overwhelm the signal from RMC. However, pion capture is a strong interaction and as such, it proceeds very quickly, typically within a few nanoseconds of the pion being stopped. An offiine software cut is employed to reject photon events that have occurred within 30 ns of an incident beam particle stopping in the target. In addition pion-induced photon events can be characterised by identifying large pulse heights from the beam counters at the time of the STROBE· EVENT signal. These cuts were extremely effective at eliminating the remaining pion-induced photon events. This is evident from Fig. 4.6 (b) which displays the photon spectrum after the pion cuts. The hatched region in Fig. 4.6 (a) are those events that were identified as being m prompt coincidence with a beam particle stopping in the target. In the event the beam counters fail, no beam TDC or ADC information is avail-able. Consequently, 7T'-induced photon events are indistinguishable from µ-induced events. To avoid such an eventuality a "Bit cut" was used. If no beam particle was present in any of the beam counters over a 10 µs period, a bit register was set. For each event this register is examined. If the bit was found ON, than the event was rejected. At a beam rate, typically greater than 500,000 s- 1 , one expects a beam particle, on average, every 2 µs. If no beam particle has been "seen" in 10 µs, this would indicate a possible problem. As it happened, in the early data taking pe-riod of August 1990, unreliable high voltage supplies resulted in the beam counters turning on and off for ~/ iort periods of time. If not for the Bit register test, all data collected over this running period would have had to be discarded, since there would have been no way to identify 7T'-from µ-induced events. Therefore, the Bit cut, was 4.4. Cuts 8 ,--..... II) 7 0 ..--X 6 '---"' ... 5 I > Cl) 4 {I.) .,J 3 s:: ;:J 0 u 2 1 0 ..--5 ... '> 4 Cl) ::a 1 0 0 ! ' I I ' ' ' I I ' ' I I I ' ' ' Photo1 ... spectrum NOCUTS (a) Bremastrahluna from muon decay ,.,, ..t v. v,. e' 7 / Radiative muon decay µ. .. e v. v,. 7 20 40 60 80 100 120 Photon Energy (MeV) Photon Spectrum after PION cu t (b) 25000 20000 15000 140 60 80 100 120 140 160 20 40 60 80 100 120 140 Photon energy (MeV)1 Figure 4.6: (a) The photon energy spectrum obtained by stopping aµ- beam in liquid hydrogen, with no cuts on the data. (b) The same photon spectrum after the 1r cuts have been applied . 89 160 160 90 Chapter 4. The Measured RMC Photon Spectrum an essential safety test, guaranteeing the integrity of the data. There will be a small number of good RMC 1H events cut ,that were in random coincidence with an incident beam particle; this correction will be examined later. Muon Decay Bremsstrahlung When a muon is stopped in material it may either be captured by a nucleus or it may simply decay. In heavy nuclei, Z~l3, capture dominates. In light nuclei the muon has considerably more chance to decay before it is captured by the smaller nucleus. In the case of hydrogen essentially all (99.9%) of the stopped muons will decay, with a lifetime very close to that of the free muon, 2.2 µs. These muon decay events can produce photons either via radiative muon decay,µ-. eveVµ"f, (internal bremsstrahlung), or the decay electron can emit bremsstrahlung radiation through interaction with the surrounding target material, µ -. evevµ; e -. e1, ( external bremsstrahlung) . The end-point of the photon energy spectrum for both of these processes is 53 MeV. Photons from these two processes are unavoidable and cannot be distinguished from the photons of RMC in hydrogen . The bremsstrahlung back-ground therefore limits detection of RMC photons to energies above the bremsstrahlung threshold of 53 MeV. A lower limit somewhat higher than this is usually preferable to allow for the finite energy resolution of the detector. With this in mind, a lower limit of 58 Me V was chosen for this experiment. In any case, it is clear that the bremsstrahlung photon background is formidable; eight orders of magnitude larger then the RMC signal from 1H. The energy resolution at the bremsstrahlung end-point must be minimised and the extent to which it extends into the high photon energy region well known. The task of minimising the energy resolution was achieved by the design of the pair spectrometer, providing up to 18 (x, y) coordinates per track for precise spatial resolution and ultimately energy resolution. Additionally, the choice o.1 gold-plated aluminium cathode wires instead of the more common, gold-plated tungsten wires improved the energy resolution of the spectrometer considerably through reduced particle scattering. 4.4. Cuts 91 To obtain a quantitative estimate of the high energy tail in the detector re-sponse, a µ+ beam was stopped in the target. A µ+ will not undergo nuclear capture, but it will decay in a similar way to a negative muon, via internal and external bremsstrahlung. This has the effect of turning off the muon capture prer cess while maintaining the muon decay bremsstrahlung process. It is then a matter of determining the number of reconstructed photons greater than 58 Me V after all cuts . This number, after being normalised to the number of stopped negative muons, should then be an estimate of the photon background from the high energy tail of the bremsstrahlung spectrum. This technique was first developed in the TRlUMF TPC exJ?eriments of nuclear RMC (95]. It requires no change to the experimental arrangement, except for the changing of the polarity of the beam line magnets to focus a µ+ beam rather then a µ- beam. It has the added advantage of avoiding lengthy Monte Carlo simulations, where one can never be certain all physical processes are being taken into account. The summed photon energy spectrum after all cuts of (µ+p) from all beam pe-riods (August 1990, December 1990 and January 1991} is displayed in Fig. 4.5 (b}. The acceptance of the pair spectrometer falls to zero at the lower energies, conse-quently, no photons are detected below about 40 MeV. This is an attribute of the trigger requirement, which demands that one track exit the chamber and the other extend at least as far as the third layer. Theµ+ tail was minimised by tuning the cuts described earlier (Section 4.4.1). If the cuts were chosen to be too restrictive, i.e. zero high energy ta.ii above 58 MeV, then a marked decrease was observed in the acceptance. A compromise between a small a.nrount of high energy tail and a reasonable acceptance was preferred. In this analysis, two assumptions have been made; 1. the µ- and µ+ decay bremsstrahlung spectrum shapes are the same, and 2. no additional process are available to the µ+ and not to the µ-. The question is, "are these assumptions valid ?", and if not, "what are appropriate 92 Chapter 4. The Measured RMC Photon Spectrum _ corrections?" Addressing the first assumption, the µ,+ does not become bound to the nucleus. It therefore decays with the free muon lifetime >.0 = 2.2µ,s. The µ,- on · the other hand is trapped in an orbit around a proton. It will decay from a bound state, with a lifetime slightly shorter than >.0 • The additional energy of the bound system can produce photons with energies greater than 53 MeV [96). Measurements of RMC on carbon, oxygen and calcium by Armstrong et al. [95), investigated the effect the bound muon system would have on the high-energy tail. For carbon and oxygen the contribution to the high energy tail from the muon being bound to these nuclei was negligible, < 0.1%. For calcium, a small effect {1.3%) was observed. In lighter nuclei the bound muon behaves more and more like a free µ.-. In hydrogen the assumption that t~e µ.- decay is free, holds true. The second assumption was that the same processes available to negative muon are also available to the positive muon and vice versa. This, of course, is not true. The e+ from µ,+ -decay has the additional process of annihilation. The annihila- · tion effect will .produce photons in the µ,+ bremsstrahlung spectrum, which are not present in theµ,- bremsstrahlung spectrum. The high energy tail in theµ.+ spectrum therefore overestimates the tail from µ.- bremsstrahlung. To obtain a quantitative estimate of this effect, one needs to consider a negative muon beam with the RMC process turned off. Possible sources of photons are from the following process: N~- = (µ,- e-ziev,,-y) + (µ,- ziev,,e-) Le'-.,, = "It' + "B". Similarly _for a·µ+ beam, ' N~+ = (µ.+ Zleii,,e+) + (µ.+ Zleii,,e+) + (µ,+ e+veii,,-y) L e'+-y L + e- -y-y = II B" + II A" + II It'. (4.10) (4.11) 4.4. Cuts Where 11 B" = Bremsstrahlung process, 11 R" = Radiative decay process, and 11 A11 = Annihilation process. The ratio B+A+R B+R A l+ B+ l+X 93 (4.12) permits the effect of the annihilation process to be quanti fied. If the annihilation process has no contribution then X = O; if X > 0, then this indicates the number of photons measured above 58 Me V for a µ+ beam will be an over estimate of the size of the background from the high energy tail of the bremsstrahlung spectrum for a µ- beam . A study using a Monte Carlo simulation [97, 98] of the annihilation process following positive muon decay indicates that X = 4.0 ± 0.5 for photon energies greater than 58 MeV. It is an extremely rare occurrence that a photon of energy less than 52 MeV will be reconstructed with energy greater than 58 MeV. This is reflected in the large uncertainty associated with the value X, and is entirely st.atistical in _nature. Figure 4.8 gives an indication of the value of X at different photon energies greater than 52 MeV. Clearly the effect is not small. The tail spectrum from µ+ decay overestimates the µ- tail by a factor of 5. This is in contrast to the investigation of RMC in carbon and oxygen by Armstrong et al. (95) which found the contribution · from annihilation to be negligible. The reason for this is that in hydrogen the decay spectrum · dominates considerably, therefore enhancing the effect of annihilation, while in carbon and oxygen, the capture process dominates, even at the lower photon energies. Figure 4. 7 shows the contribution to the photon spectrum from the three processes: radiatiy~ decay, bremsstrahlung and annihilation in hydrogen. Taking into account the contribution from the annihilation process and normalising to the - -=------ - -· .. - . - -- - ----- --- ---- -·-·' ·--- -94 Chapter 4. The Measured RMC Photon Spectrum 600~----1--__,i.--.L----'--.-J--_,_ _____ -r-500 400 300 200 100 40 42 44 46 48 50 52 54 Photon energy togged for force pair-prod. [MeV] Figure 4. 7: The contributions to the muon decay photon spectrum from the three processes (i) radiative decay, (ii) bremsstrahlung and (iii) annihilation. 5.0--_.___.___.___.___.___.___.___.___.___.___.___.___.___.___.___, -u ., 4.6 -~ -C .5! 0 't> ·- 0 - 0:: + 4.2 . E 2' < ::, :E 3.8 ., ., E ., CD 11- 3.4 X .. f ...... -~. ~. ~=~. 7. ~:~...... . . . . . . . . . .... . L I I I I I ................. I .............. -.... --3.0 ;--,----.---,---,r--~~-,--.----.---,---,-r---,----.----.---1-52 54 56 58 60 62 64 66 Photon Cut-off Energy (MeV) Figure 4.8: The magnitude of the ratio annihilation to bremsstrahlung plus radiative decay in positive muon decay at various photon energies. 68 4.4. Cuts 95 µ- stops, the magnitude of the background from the high energy tail in the µ- data is given by: ( µ+ Nµ+ ) N:i:r,11 l Nta.il = N'Y - CR • Nµ+ • (1 + X)' 11tops (4.13) where, · X : Accounts for the additional photons 58M e V due to µ+ annihilation N~+ : Number photons between 58-100 MeV after all cuts, from (µ+p) Nt~ : Number of photons from cosmic rays in theµ+ spectrum N;:Ops : l.2.3.4.RFµ-MV for (µ-p), (see below) N;:ps : l.2.3.4.RFwMV for (µ+p). Table 4.2 summarises the high energy tail contribution for each data collection period and data type. In all cases the contribution was negligible for the lower limit of 58 MeV. There were two cases where the subtraction of the expected cosmic-ray background from the photon spectrum above 58 Me V was negative. While a more formal analysis might be appropriate such an exercise was considered unnecessary. If one were to avoid the complication arising from the subtraction of the expected cosmic-ray component, one would obtain a contribution of "' 1 % from the high-energy tail for the sum of the December 1990 and Janua ry 1991 data . After the subtraction of the cosmic-ray background the contribution would be even smaller. Clearly there is little justification for a rigorous and exact determination of photon background from these two data taking periods. In these cases the background from the high-energy tail was considered negligible and simply neglected. Muon Capture in Gold The vessel confining the liquid hydrogen was construct ed of gold. The thickness of the walls was 250 µm. Muons from the beam may stop and subsequently undergo nuclear capture in the front face of the gold container . Photons produced from RMC in the gold will be a background to the photon signal from hydrogen . In addition, 96 Chapter 4. The Measured RMC Photon Spectrum Data Per iod N~+ (58 - 100) N,.,.~ CR N,.,.~ atoJ1a N~:pa Ntail Aug 90 3 ± 1.7 1.1 ± 0.2 5.10912 19.9729 1.5 ± 1.4 Dec 90 1 ± 1.0 1.6 ± 0.4 9.66849 39.1135 n/a Jan 91 0±0.0 1.6 ± 0.4 10.9023 83.4094 n/a Aug 91 7±2.6 2.6 ± 0.6 12.9733 38.5144 2.6 ± 1.6 Table 4.2: Contribution to the RMC photon spectrum from the high energy tail. In the cases were N.(( 5s-ioo) - N6; is less then zero with the limits of uncertainty, no high energy tail is assumed. the much higher RMC rate in the gold will dominate the photon spectrum between 58-100 MeV. This background had to be minimised, estimated , and subtracted from the final photon spectrum. The choice of gold as the containing vessel was carefully chosen. It is soft and relatively easy to machine to the required dimensions. More importan~Jy, it has a high atomic number. Consequently the muon disappearance time is relatively short, 73 ns, compared with 2195 ns for a muon in hydrogen. Because of the short disappearance time, a "blanking time", tb, could be used to reject all photon events that occur within a time tb of a muon stopping in the target. A blanking time of 365 ns (or 5 Au lifetimes) was found to eliminate most of the photons arising from capture in the gold. This was called the "Blank cut". Figure 4.9 show the time history of the remaining photon events after all cuts, except the Blank cut, for each of the data taking periods . The time history, is the lapsed time between a photon event detected in the spectrometer and the time a beam particle passed through the beam counters. A small fraction of gold RMC events will remain after the Blank cut. By fitting two exponentials, one corresponding to the 73 ns gold lifetime and the other to a 2.2 µs hydrogen lifetime, along with a constant background, the amplitudes for each component can be measured and the fraction of gold RMC events remaining can be estimated. This background was estimated using the following procedure. If 10 ns time binning is used in the histogram, then the number of counts in a 10 ns bin starting 4.4. Cuts U) 60 C 0 ..--F:t Y = Ae<-t1219n + Be<-t/73> + C A= 6.± 6. E 58 MeV 7 8= 122.± 9. C= 0 .± 4. x2 /N = 1.2159 0 --l--.---.---.--~~~----.-- ............. --..,..........----.-'2_~.....,.....=,--=.-......--.-----.--97 0 200 400 Time 600 (ns) 800 1000 50-------~-~--------r-40 en c§ 30 ..--L Q) 20 -+--' C :::J 0 u 10 Fit Y = AeH/ 2197> + 8eC-t/73) + C A= -4.± 3. E 58 MeV 7 8= 62.± 4 . C= 6.± 2 . x2/N = 0.97197 0 -+----r-..--.---.---.-.L....,--,-=-+-,1,=-=.r=,="T'~-,--....;::...i'r-.-L-r=,..=,=-r~-r-~ 0 200 400 600 Time (ns) 800 Figure 4.9: Decay curve for muons in Au for the data taking periods (a) January 1991, (b) December 1990. 1000 98 Chapter 4. The Measured RMC Photon Spectrum at time tis : N(t) - N(t + 10) -10 -t N0 (l - e""T )e7. (4.14) So, for a lifetime of T = 73 ns, the number of gold events surviving a time t, given 10 ns time bins is: -t N(t) =Au . e'"Au' where, A -10 Au= N 0 u • (1 - e73 ). (4.15) Similarly for the hydrogen lifetime of T = 2197 ns, we obtain -t N(t) = H · erii, where, H -10 H = N0 • (1 - effi1). (4.16) The amplitudes Au and H are determined by a fit to the exponential decay curve for photons with energies E,., 2: 58 MeV. The fits are displayed in Fig. 4.9.The fit has the form: -t -t N(t) = H · effi1 + Au· e 73 + C. ( 4.17) The constant C arises due to the fact that the times of all muons rather than just the time of the last muon passing through the beam counters are entered into the histogram. N;! and N1u are the true gold and hydrogen initial amplitudes. Hence the number of gold events remaining after a blank time of 365 ns is: N Au _ >365 - L00 dN -dt 365 dt N Au >365 TAu -385 - Au· - · e13 · PO 10 (4.18) The factor PO is a correction that takes into consideration the fraction of events 4.4. Cuts 99 Data Period Au Amplitude Beam Rate PO NAU >365 Gold from fit (kHz) fraction% Aug 90 25±3 616 ± 50 0.76 ± .02 1.0 ± 0.2 0.99 ± 0.06 Dec 90 62±5 596 ± 50 0.77 ± .02 2.3 ± 0.3 0.76 ± 0.03 Jan 91 122 ± 9 741 ± 50 0.72 ± .02 4.3±0.4 0.79 ± 0.03 Aug 91 45±4 607 ± 50 0.76 ± .02 1.6±0.3 0.80 ± 0.08 Table 4.3: The estimated contribution from photons arising from RMC in the gold and surviving longer then 365 ns . that would be blankecl. due to a later arriving beam particle . This correction will be sensitive to the beam rate and must be determined for each data taking period . A more complete description of this correction is given in Chapter 5. For now the results are simply given in table 4.3. In addition, it is also instructive to examine the gold fraction from each data taking period. This should be constant and any variatio ns might be indication of poor fits or bad time histograms . The gold fraction can be written in the following way: Gold Amplitude Total Amplitude NAu + NH 0 0 (4.19) Once again ~he amplitudes Au and H are determined by a fit of Eq . ( 4.17) to the time histogram for all muons for all energies. Result s of the gold background contribution for each data taking periods are shown in table 4.3. The August 1990 data shows a slightly higher fraction of gold events in th e data sample. This was attributed to the slightly lower beam tune U:sed during the taking of the August 1990 data, resulting in more muons stopping in the front face of the gold target vessel. The remaining data sets indicate a consistent fraction, 0.8%, of gold RMC events in the data sample . In addition to muons stopping in the front face of the gold vessel, there is the question of the muons diffusing ( due to their relatively long lifetime) into the gold walls. However, such an effect is negligible for the following reason. When a muon stops in the hydrogen it quickly forms a µp atom and subsequently a pµp+ molecular ion. This ion, because of its large size and positive charge , is immobile in the liquid 100 Chapter 4. The Measured RMC Photon Spectrum hydrogen. The software cuts Zrad, Zclos and Radclos discussed earlier also restrict the photons origin to a distribution around the centre of the target, thereby reducing any contribution from the target walls. Cosmic-Ray Induced Photon Events The inherent low rate of radiative muon absorption entails long periods of data taking ( several months) to acquire a statistically significant number of RM C events. Photons from cosmic ray induced reactions can therefore be an important back-ground contribution to the photon spectrum from RMC. To minimise this cosmic ray contribution , an assembly of large area multi-wire proportio nal chambers and scintillator panels was positioned around all four sides and top of the magnet hous-ing the central tracking detector . The assembly consisted of one layer of scintillator (CRSC) followed by two layers of planar wire chambers {CRDC). Their purpose was to veto events that occurred in prompt coincidence with signals in these outer detectors. To indentify the characteristics of cosmic-ray induced photon events data were collected with the cyclotron off. This had the advantage that only cosmic-ray in-duced photon triggers were present in the spectrometer. Software cuts were devel-oped to eliminate these photon events. Those events remaining after all cuts were an estimate ( after normalising to data taking time) of the photon background from caosmic-ray induced events. The trigger condition was set to be the same as for µ- data taking. Data was collected and analysed in the same way that the µ- data was analysed. Photon triggered events seen in the spectrometer were due to cosmic rays entering the drift chamber. The time of the signals in the outer cosmic ray detectors was compared to the time of the triggered event. This provided a time window in the CRDCs and CRSCs that was correlated with a photon trigger. The condition identifying the arrival of a charged cosmic particle was a signal in at least two of the three layers of veto counters. The hit layers had to be spatially overlapping, and the signals had 4.4. Cuts 101 to have been in the time window defined above. In the majority of cases the cosmic-ray induced event consisted of a single charged track passing into the drift chamber , hitting at least ID counter, and skimming one of the C counters, satisfying the trigger condition A · iJ · C· < ID. Generally these events did not satisfy the condition of a pair (two tracks converging at the lead con-verter) . Consequently, they were rejected in the first stage of the tracking . Another possibility is the charged cosmic particle traversing one half of the drift chamber, interacting with the material (target, lead or scintillator) in the central part of the detector, and producing a photon. The photon emerges in the opposite half of the chamber, converts in the lead and produces the characteristic e+ e- signature. These events were identified by looking for a single charged trac k in the opposite half of the chamber to the e+e- pair. A third and final possibility is that the charged cosmic particle can cause an electromagnetic shower in the iron of the magnet. A variety of charged particles and -y-rays can be produced and enter the chamber. As already mentioned, the charged particle tracks rarely resemble the e+ e- signa-ture, characteristic of a photon conversion in the lead. The photons, however, may traverse the chamber undetected a.nd convert in the lead producing a valid e+ C sig-nature . These photons, when reconstructed, tend not to originate from the target, but are distributed evenly along the z-axis . A software cut , demanding the photon originate from a distribution around the target centre, eliminates the majority of these cosmic-ray induced photons. After applying all cuts , the cosmic-ray rate was reduced to just 0.3 events/day, in the energy range 58-100 MeV. A smaller sample, 500 hours, of cosmic ray data was collected with beam on. That is, the cyclotron was on, but no beam was incident on the hydrogen target . Instead the µ- beam was directed down the adjoining M9B channel to another experiment. Analysis of this data gave a cosmic ray rate of 0.9 ± 0.2 events/day , after cuts; considerably higher than the beam-off rate. The explanation is that there is a beam related component to the "cosmic-ray" data which contributes to the higher photon rate. Since the beam is on during norm al data taking, the higher 102 Chapter 4. The Measured RMC Photon Spectrum Beam on Data days (livetime) N..,(58 -100) RcJR June 91 20.0439 18 ± 4.2 0.9 ± 0.2 Table 4.4: Summary of the cosmic-ray background data analysis. rate of 0.9 ± 0.2 events/day must be used to estimate the background contribution. The small but significant component of cosmic-ray photons remaining after all cuts was attributed to the neutral component in cosmic ray showers. These un-charged particles go undetected by the cosmic ray veto counters and leave no track in the drift chamber, but may interact in the target to produce photons. Under normal µ- data taking conditions, these events cannot be identified. Of all the backgrounds present this is the least well determined. In measurements of nuclear RMC, shorter data taking periods together with higher statistics in the RMC spectra, meant the cosmic-ray background was negli-gible (Alvaro (84) 1 %, Armstrong [93) 2%). However, for hydrogen it contributes as much as 20% of the RMC signal. Table 4.4 shows the results of the cosmic-ray background analysis. N..,(58 - 100) is the number of photons remaining between 58 and 100 Me V after all cuts were applied to the data. The cosmic ray rate after all cuts is then given by, ( 4.20) where, RcR = Rate (per 24 hrs) of cosmic-ray-induced events surviving all cuts between 58-100 Me V PO = Takes account of the fraction of events that would be blanked due to a later arriving beam particle, and LT = µ- livetime (24 hr units). For the calculated rate of cosmic-ray-induced photons after all cuts, the number of cosmic-ray-induced photon events in the µ- and µ+ data can be calculated. The results are given in Table 4.5 for the different data taking periods and the two different data types, µ- and µ+. 4.4. Cuts Data Period D iys (livetime) NcR (24 hrs) µ - Aug90 4.19982 2.9 ::I:: 0.8 Dec90 · 8.06458 5.6 ± 1.6 Jan91 13.5080 8.8 ± 2.7 Aug91 7.87855 5.1 ± 1.6 µ+ Aug90 1.18010 0.8 ± 0.2 Dec90 1.82532 1.2 ± 0.4 Jan91 1.73041 1.2 ± 0.4 Aug91 2.84426 1.9 ± 0.6 Table 4.5: Estimated background contribution from cosmic-ray induced events for each data period and data type . Random 'False' Photons 103 In addition to the photon backgrounds already discussed, a rather unusual back-ground was discovered in the early stages of the experiment. It is possible that a photon from the target, most likely from bremsstrahlung, could convert with very asymmetric energy sharing between the e- and e+, such that only the e+ particle has sufficient energy to pass into the drift chamber. Such an event would trigger the data acquisition. At an earlier or later time, an C from µ·-decay may pass near to the point of the photon conversion. A photon could then be reconstructed from the e+ track of the photon conversion and the C track of th e µ-decay electron. The reconstructed photon would have an energy greater than the original photon that caused the trigger. The time of emission of thee- track must be greater than ±30 ns so as to not be vetoed by the hardware condition requiring no signals in the A and B veto scintillators, but must be less than 250 ns, which is the effective memory time of the drift chamber. Events with scintillator times greater than 250 ns will not have drift chamber TDC drift times and hence no track can be reconstructed. In addition, the µ-decay electron must be spatially near to the C counter that caused the photon trigger. As such, random Michel electrons may occur elsewhere in the spectrometer at the time of an event, but only those that may be confused with a 104 Scintillator FBTDC timH \ Track 1 Track 2 (n•) (n•) At : -09 A'2 : -07 B2: -79 C2: -78 C2 : 0 D11 : -78 D1 : 0 Chapter 4. The Measured RMC Photon Spectrum - --RUN 1:595 EVENT 45451 Figure 4.10: An example of a Random photon event . photon event are rejected. Events that fall into this category were called Random or Charged in near coincidence events and were discarded from the photon spectrum by the Random cut. While these False photon events were undoubtedly present in the early RMC experiments on nuclear targets at TRI UMF [41, 40], the significantly higher rate of nuclear RMC masked these events. It was only in the low rate ex-periment using hydrogen that these rather rare events were noticed, Figure 4.10 displays the characteristics of a Random photon event. RMC on 3 He T e final source of background photons that needs to be considered is that from muon capture on 3He. The 3He is produced via muon catalyzed fusion of a proton and a deuterium impurity. Details of this process have been discussed previously in 4.4. Cuts 105 Data Period HJrr.c Aug 90 0.980 ± :).007 Dec 90 0.965 ± 0.009 Jan 91 0.967 ± 0.007 Table 4.6: Summary of the 3He contribution to the photon background. Chapter 2. The discussion here concentrates on the extent to which this affects the final photon spectrum. It was suggested [97], and subsequently shown [98], that for a wide range of muon chemistry parameters the ratio, R -r(I.4) - r(o) r(103) - r(I.4) 0.02 ± 0.0015 ( 4.21) is essentially constant. f(ppm) is the RMC branching rati o for a given ppm concen-tration of deuterium impurity. The hydrogen fraction is then given by: where, (r(103) ) H1rac = 1 - R f(I. 4) - 1 (N,.::; - Ne~ -Nrail - NAu) r(ppm) = --------µstops ( 4.22) ( 4.23) By introducing deuterium impurities into a second protiu m target, the level of deu-terium concentration was increased to 103 parts per million. Data were then col-lected in August 1991. The higher deuterium concentration permitted the muon-induced fusion process to proceed at a much higher rate . The observed increase in the photon rate was clear evidence for the production of 3He. Consequently, the extent of the photon background from RMC on 3He at lower concentrations could ;f' be deduced via the ratio, given in Eq. ( 4.21 ). The results of the hydrogen fraction are summarised in Table 4.6 for each data period. 106 Chapter 4. The Measured RMC Photon Spectrum 4.5 The Expertme_ntal PhotQn Spectrum The RM C photon spectrum from hydrogen with all photon backgrounds sub-tracted is given by: (4.24) where: N;- : Number of photons between 58-100 MeV, after all cuts on (µ-p) data. Nd; : Number of photons expected from cosmic-ray-induced events. Ntail : Number of photons expected from the high-energy tail above 58 MeV. NAu : Number of photons from the Au vessel surviving the 365ns blank time. HFRAC : Fraction of the spectrum that is from 1H and not 3He. Figures 4.11 and 4.12 illustrate the effect of the various cuts on the photon energy spectrum for (µ-p) data. Figure 4.11 (a) shows the energy spectrum of photons after the Photon cuts. The dominant feature is the peak below 50 MeV from muon decay bremsstrahlung. The inset depicts the energy region of interest, 58-100 MeV. At approximately 129 Me V there is a small peak, an indication of some pion contami-nation still remaining in the muon beam. Figure 4.11 (b) shows the energy spectrum after both the Photon and Track cuts have been applied. Clearly, the Track cuts have removed many of the poorly resolved photons, thereby improving the quality of energy resolution. The peak from radiative pion capture is still evident. The final diagram of Fig. 4.11 ( c) displays the photon spectrum after the Bit cut has been applied to the data. The most obvious effect is the removal of the events from radiative pion capt ire. Figure 4.12 (a) shows the photon spectrum after the Photon, Track, Bit, and Random cuts. There is a noticeable improvement in the extent of the high-energy tail. Following the Random cut is the Cosmic cut (Fig. 4.12 (b)). The 4.5. The Experimental Photon Spectrum "b 4 .... X 2 2 C: ::::, 0 u 1 (a) M00+--.......,.......,.~ ............... .......,.~~ ....... -1200 1000 1100 100 400 200 After Photon cut 04-~.......,::;:i.....-.i;;..~,......"T""'.....,.........+ 40 ISO ISO 100 120 MO 1150 '110 200 0 -+--.---.--,L--,--.,,...,--..--.---,,---,---r---r--r---r---,--,---,--,---.--+-•52 15 X ,-.. ' > CD 10 ::\? ......... (/) ..... C: g s u 0 50 (b) 100 150 Photon energy {MeV) 400 After Track cut 300 200 100 04..... ................ ~~m,...,...,, ........................ ... ..1-40 ISO 80 100 120 MO 160 '110 200 200 0 -+--.---.---,-,<---,---,,.....T--.--r--r---,,---,,---,---r---r--r--r---r---,--,---+-14 • 0 12 .... X 10 _,..... I 8 ::\? ......... 6 (I) -§ 4 0 u 2 0 50 100 150 200 Photon energy (MeV) (c) 400 After Bit cut 300 200 100 o4..... ................ :;:w....._.........,.__,.,. . ..... .,. .......,.........i-40 ISO 110 100 120 MO 160 1110 200 0 -+--.--.--,-L-,---~r-,r--,---r---r---r---r-r--r----r-~~-.---.-+ 0 50 100 150 200 Photon energy (MeV) Figure 4.11: Photon spectrum after (a) Photon, (b) Track and (c) Bit cuts have been applied. 107 108 14 .. $2 12 X ---10 I > 8 '-' !? 6 C: 5 4 u 2 Chapter 4. The Measured RMC Photon Spectrum (a) After Random cut 100 o+,-......,...........;~..,.,.,.....,........,.......,...-....... -+ 40 150 IIO 100 120 140 1150 190 200 0 -...-...,..... ........ ---....-,........, ....... ---.---.---.-----.-~--..---,---,-.....-""T"""-r • 15 0 .... X (I) ..., § 5 0 u 0 (b) 50 100 150 200 Photon energy (MeV) After Cosmic cut 100 • RMC on Au • RMC on H 80 80 100 120 140 1150 190 200 - 0--...-------------.--........ ---.---.---.-----.-~~--..---,--o 50 100 150 200 Photon energy (MeV) 10-......._...__.__.___.__..__..__.__.__..__.__.__.___.____.___.___._ ...... ...... .. ... 0 .... X 8 -- 6 ' > Q) '-' 4 (I) ..., C: ::, 8 2 (c) After Blank cut 10 • RMConH 150 IIO 100 120 140 1150 1110 200 0 -~-r-......... - --..--..--.--....--,---.---.---.----.-----.-~--..---,---,--0 50 100 150 200 Photon energy (MeV) Figure 4.12: Photon spectrum after (a) Random, (b) Cosmic and (c) Blank cuts have been applied. 4. 6. Counting the µ and 1r Stops. Data N,r NtR NAu NTail HFrac NRMC ( 58-100 Me\ ') Aug 90 24 ± 4.9 2.9 ± 0.8 1.0 ± 0.4 1.5 ± 1.4 0.980 18.2 ± 5.2 Dec 90 35 ± 5.9 5.6 ± 1.6 2.3 ± 0.3 n/a 0.965 26.2 ± 6.2 Jan 91 73 ± 8.5 8.8 ± 2.7 4.3 ± 1.4 n/a 0.967 57.9 ± 9.1 Aug 91 88 ± 9.4 5.1 ± 1.6 1.6 ± 0.3 2.6 ± 1.6 n/a 78.7 ± 9.7 Table 4.7: Summary ofµ- data, with the estimated contributions from the most significant sources of photon background. 109 most significant effect is a reduction in the fiat background of high-energy photons. The ha.shed region depicts those photon events greater than 58 Me V that occurred within 365 ns of a beam particle entering the target. The se events are most likely attributed to RMC in the front face of the gold vessel conta ining the liquid protium. Applying the Blank cut removes the majority of these event s. The remaining photon spectrum is attributed to the RMC photon spectrum from hydrogen between 58 and 100 MeV, Fig. 4.12 (c). The above software cuts were not 100% efficient in rejection of the various photon backgrounds . Table 4. 7 summarise s the contribution to the photon spectrum from photon backgrounds that were not rejected by the software cuts . 4.6 Counting the µ and 1r Stops. To determine the partial branching ratio it is essentia l to know the number of muons captured by the target nucleus. The number of muons captured is equal to the number of muons stopped multiplied by the fraction that capture. The latter will be discussed in chapter 5. The number of muons stopped was counted by four plastic scintillators, located 17 cm downstream of the targ et. The scaler that counted the stopped muons was incremented whenever all four beam counters fired in coincidence with an RFµ pulse. The RFµ pulse was a logic pulse set to correspond with the time of arrival of a muon at the RF separator. It was set by observing the time-of-flight characteristics of each beam particle relative 110 Chapter 4. - The Measured RMC Photon Spectrum to the cyclotron RF. A delay between the RF pulse from the separator and the cyclotron RF pulse was used to select a particular beam particle from the beam. Muons were typically 20 ns ahead of the pions. The scaler was inhibited whenever the computer acquisition was busy or off, consequently the muon stops were corrected for dead time. Therefore, the scaler counting the number of muons stopped in the target could be defined by the following logic condition, µatop• - 1.2.3.4.RFµ.MV, ( 4.25) where 1, 2, 3, 4 refer to the signals from the four beam counters. There is a number of corrections to the above scalar value; they are given by the following, N':t~. = (l.2.3.4.RFµ-MV) · (1 +Ip)· (1 +le)· (1 - 1.) · (1 - Iv) (1 + IP) = Correction for mult iple beam particles per beam burst (1 + le) = Correction for beam counter inefficiency (4.26) (1 - Is) = Correction for beam scattering and absorption in non-target material (1 - Iv) = Correction for random vetoing of an event 4.6.1 Pile-up correction The plastic scintillator~ had a short recovery time of approximately 3 ns. With a beam rate of approximately 650, 000 s- 1 , the chance of not counting a muon is negligible. However, it is possible that more than one muon may arrive in a single beam burst. As such, the µstops scaler will under count the true number of muons stopped. The probability of having n partiL les in a beam pulse, of width 6.t and ' rate r is, P(n) - (r6.tt r~t I e ' n. ( 4.27) 4.6. Counting theµ and 1r Stops. Data Beam Average beam (1 + fp) Period Tune rate (kHz) ± 4% Aug 90 µ - 608 1.013 µ+ 515 1.011 7r - 148 1.003 Dec 90 µ - 595 1.013 µ+ 637 1.013 7r - 112 1.002 Jan 91 µ - 742 1.016 µ+ 715 1.015 7r - 279 1.006 Table 4.8: Correction factors due to the effect of multiple beam particles per beam pulse . The correction due to beam pulse "pile-up" is then given by: {1 + fp) - R R - (Beam rate) · (Beam pulse width = 42 ns) 111 ( 4.28) Using the above expression the correction to the µstops can be calculated. The results are shown in Table 4.8 for the different beam rates of each data taking period as well as the type of beam tune. For the µ- and µ+ beams the correction for multiple beam particles per beam pulse was 1.3-1.6% . For pions the beam rate was considerably lower, consequently the correction was only 0.3-0.6%. 4.6.2 Beam counter efficiency correction A second correction to the number of counted muons stopped in the target arises from inefficiencies in the individual beam counters. The individual counter efficiency was typically better than 99%, so the probability that an incident µ- did not register in a beam counter was small. However, the efficiency of beam counter number three was measured to be poorer than the others, around 98%. It was suspected that the joint at the scintillator lightguide interface had either cracked or was poorly joined . All four beam counters were assembled as a package. To remove 112 Chapter 4. The Measured RMC Photon Spectrum Beam Data Period Beam 1 Beam2 Beam3 Beam4 {1 + fe) Scint. Scint. Scint. Scint . ±0.5% µ - Aug 90 99.67 100.02 98.54 99.46 1.023 Dec 90 99.73 100.00 97.91 99.53 1.029 Jan 91 99.73 100.04 98.61 99.56 1.021 µ+ Aug 90 99.69 100.02 99.28 99.52 1.015 Dec 90 99.72 100.03 99.02 99.57 1.017 Jan 91 99.71 100.04 98.96 99.57 1.017 7r - Aug 90 99.92 100.07 97.63 99.35 1.031 Dec 90 99.89 100.02 96.93 99.44 1.038 Jan 91 100.04 100.17 96.33 99.55 1.041 Table 4.9: Beam counter efficiencies and correction factors. and repair the possiblely damaged joint, was at the risk of damaging the remaining good counters. It was decided to continue with the counter at its lower efficiency and make a correction to the countered muon stops in the analysis . The correction for the beam counters inefficiency was calculated by taking the product of the inefficiency for each of the beam counters. Since the inefficiency in the beam counters under counts the number of true µStops, the scaler 1234RF,.,.MV should be mult iplied by 1 + (the product of the inefficiencies). The individual beam counter efficiencies were measured by the taking the ratio of two coincidences, 1·2·3·4 efficiency BEAM 1 = 2 3 . .. 4 {4.29) Similar expressions were used for beam counters two three and four. The results are shown in Table 4.9. For aµ- beam, the correction was "'2.5%; for theµ+ it was "' 1. 7% and 3.1 - 4.1 % for pions. 4.6.3 Random veto correction Another correction to the number of µ,topa is from random vetoing of a good RMC event. This occurs when a charged particle enters the inner veto counter A rmg. This also happens to some extent in the A' and B rings, but because of the 4.6. Counting theµ and 1r Stops. Data (1 - fv) ±0.4% Period µ - µ+ 7r -Aug 90 0.9556 0.9665 0.9927 Dec 90 0.9555 0.9575 0.9936 Jan 91 0.9563 0.9534 0.9890 Table 4.10: Correction factors arising from random vetoing of an event by the the inner veto counters . 113 high efficiency of the A ring the veto effects of A' and B ring have been ignored. The correction due to random vetoing is calculated by knowing the total amount of time the A counters are actually active and hence providing a veto pulse. This amount of time is given by the rate of the counters in the A ring firing multiplied by the width of the A counter plus strobe pulses. The effect of the random vetoing is to reduce the number of good photon events detected. To compensate, the number of counted muons stopped 1234RFµMV must be reduced by the following correction: (1 - fv) = (1::A rate) · ((A counter+ strobe pulse widths)=80 ns). (4.30) Table 4.10 summarises these results for each data taking period . For muons this correction was significant, typically 4.5%; for pions it was negligible, < 1 %. 4.6.4 Scattering and absorption correction The final significant correction to the number of counted µ.top• is from the scat-tering and absorption of the beam particle before it reaches the hydrogen target. The scattering or absorption can occur in the beam counters, silver collimators or gold vessel. The extent of these effects in the various mater ials is strongly dependent on the profile of the beam as it emerges from the series of 12 quadrupole magnets along the M9A beamline. To obtain some estimate of this profile, a beam optics simulation was carried out using the REVMOC Monte Carlo program [99]. Up to 5,000,000 rays were generated and traced through the beam optics of the M9A channel. Of the 5,000,000 generated, approximately 30,000 remained in the profile 114 Chapter 4. The Measured RMC Photon Spectrum Location % of all muon stops BM4 0.25 Mylar 0.05 Silver collimator 4.6 Outer heat shield 0.1 Inner heat shield 0.6 Gold flask 1.8 Liquid protium 92.6 Table 4.11: Fraction of muons stopping in the various material . surrounding and before the liquid protium target. after emerging from the last quadrupole. These rays were then read into the RM-CGEANT Monte Carlo and tracked through the RMC detector arrangement to the target. The results are displayed in the Table 4.11. To verify that the REVMOC was indeed well representing the behaviour of the beam, a test run in June 1993 was performed. This test run consisted of replacing the hydrogen target and gold vessel with a copper vessel of the same dimensions as the gold vessel. The thickness of the copper was chosen so that the fraction of muons stopping in the front face was the same as for the gold. The copper vessel was empty and a scintillator was positioned at the rear of the cylinder. The beam was tuned to 65.5 MeV /c muons. The ratio 1234.RFµ-{Target scintillator) to 1234.RFµ (that is the ratio of the number of particles entering the 'target scintillator with correct muon time-of-flight, to the number of particles passing all four beam counters with muon time-of-flight) was measured to be, 1234.RF.(Target veto scintillator) = 0 925 ± 0 002 1234.RF . . . {4.31) The muon rays from REVMOC were passed into a Monte Carlo simulation of the copper cylinder and target scintillator geometry. The ratio, (µ entries· 0.98) _ (22477 · 0.98) _ 0 9 1234.RF - 24099 - . 14 ( 4.32) 4; 7. Summary 115 Data Period l234RFµMV (1 + lp) (1 + le) (1 - lv) (1 + la) N;topa x10 10 ±4% ±0.5% ±0.4% ±1.6% ±4.4% µ- Aug 90 19.97 1.013 1.023 0.959 0.926 18.36 Dec 90 39.11 1.013 1.029 0.960 0.926 36.07 Jan 91 83.41 1.016 1.021 0.950 0.926 76.62 Table 4.12: Summary of the corrected number of µ,top,. was obtained, where 0.98 is the measured efficiency of the target scintillator for muons andµ entries is the number of muons REVMOC calculates will enter the tar-get scintillator given that there were originally 1234.RF rays. The excellent agree-ment is justification of the results in Table 4.11. The most significant source of absorption is in the silver collimator, positioned at the front of the target. The pur-pose of the collimator was to reduce scattering of the beam particles into the low-Z material ( such as the target veto scintillators) surrounding the target. These results indicate the collimator was behaving as expected. The correction due to scattering and absorption of the muons by non-target material was (1 - fa) = 0.926. 4.7 Summary The photon spectrum from radiative muon capture on hydrogen has been mea -sured . All significant sources of photon background have been identified, estimated and subtracted from the measured photon spectrum, refer to Table 4 . 7. In addition, the number of muons stopped in the liquid protium has been determined for each data taking period. Inefficiency in the beam counters, random vetoing of valid pho-ton triggers, multiple beam particles, and beam scattering and absorption have all been considered. Table 4.12 summarises these corrections to the number of muons stopped in the liquid protium . I 117 Chapter 5 Determining 9p 5.1 Introduction In the preceding chapter the measured RMC photon energy spectrum was deter-mined. In this chapter a description is given of how the photon spectrum for RMC on hydrogen for a particular value of gp is calculated. Th e value that gives agree-ment between the calculated spectrum and the spectrum obtained experimentally determines 9p· While the above recipe for determining 9p appears simple, there are many backgrounds to contend with in the experimental spectrum, and many nor-malisations and corrections to apply to the theoretical spectrum before they can be compared directly. 5.2 The Theoretical Photon Spectrum A more complete description of the various calculation s was given in Chapter 2. We use the expected photon rate for radiative muon capt ure by a proton as inves-tigated by Fearing and Beder (60, 61]. The results of the calculation are shown in Figs. 5.1, 5.2 and 5.3. These diagrams illustrate the variation in shape and mag-nitude of the RMC rate versus photon energy for values of gp ranging from 0.1 up to 2.0, (in PCAC units, gp = 1.0 when gp = 6.6ga). The calculations of the pho-ton rate are performed separately for initial singlet and t riplet atomic spin states. The photon rates for the ortho- and para-molecular state s are obtained by combin-118 Chapter 5. Determining gp 30 Atomic singlet ,r . state I 25 > Q) :::s ... 20 I f/l -IO I 0 15 ..... X '0 10 ' '0 u 5 gp=0.1 0 0 20 40 60 80 100 Photon Energy (MeV) Figure 5.1: Shape of the photon spectrum from the singlet state for different values of g,,. ing the appropiate linear combinations of the singlet and triplet case, see Eqs . 2.4 and 2.5. The ortho to para transition rate was taken to be the measu red value of 4.1 ± 1.4 x 104s- 1 [39). The photon rate from the atomic triplet spin state has not been shown. While its amplitude is larger than the singlet, the probability of a muon being captured from the triplet state is negligible and its contribution to the total rate can be neglected. Figure 5.4 illustrates the shape and magn itude of the photon spectra, df / dE, from the atomic singlet and the ortho- and para-molecular states for gp = 1.0. Figure 5.5 illustrates the partial rate r for all photons greater than 58 MeV. To determine the partial branching ratio for this process, the probability of a muon being captured by the proton must be known. This will vary for different experimental conditions. The following section calculates this probability for the conditions present during this experiment. 5.2. The Theoretical Photon Spectrum -... I ~.0006 ::s ... I rn -.0004 r:i::I 'C / t.. 'C ~ .0002 Ortho-molecular state . 0 0 0 0 -+-.---r--r---,.---r--r---,....-r--r---,....-r-........--,.---r-........--,.---r--r-.---r--.--.---r-0 20 40 60 80 Photon Energy {MeV) 100 Figure 5.2: Shape of the photon spectrum from the ortho state for different values of Yp· ... I rn -.0010 r:,:::i 'C / t.. 'C t.)0005 ::s Par a -molecular state . 0 00 0 -t-r--r--,---r-,----r--,---........,..-,---r--,----r-~..----,.--.---.--.---.-----.--"T""""""T~-+-0 20 40 60 80 100 Photon Energy {MeV) Figure 5.3: Shape of the photon spectrum from the para state for different values of gp. 119 120 -.. 1>.0015 a, :::s .. I Ill -.0010 ril 't:I ' i:.. 't:I u.0005 :::s o:= Chapter 5. Determining 9p para singlet .0000 ~.=:;:::::;:::::::;:::::::;:=:;::::::;:::::::=::::;::::::;::::;:::::;::::::::;:::::;:=:;::::;::::::::=::::;:::::;::::::;:=-,;iiii~ 0 20 40 60 80 100 Photon Energy (MeV) Figure 5.4: Shown are the photon contribution of the singlet , ortho and para states to the total photon spectrum for 9p = 1. Partial RMC rate in Liquid Hydrogen . 0 5 __ __.__.___.___._.__..__....____.___.___.___.___.___._.__..__....____.___.__.,__ -I I'll _, .04 .03 .02 t.) ::a P::: .01 . 0 0 --+--.;:::::::;:==;:::=,--,--,p==;:==;::=:;::::::;:::::.,............,----.----..--,--.,............,----.---,--..,L_ 0.0 0.5 1.5 2.0 Figure 5.5: Partial photon rate (Emin = 58 MeV) versus 9p · 5.3. Muon Chemistry Considerations 121 5.3 Muon Chemistry Considerations The number of photons radiated by the RM C process from a state k with energy greater than 58 Me V is given by, /105 df' rtss Mev = Jss dE d;. (5.1) The summation variable k indicates the initial state of the nuclear system when the photon is radiated. It takes the values k = s, o, p, corresponding to the, s = µp singlet, o = ortho pµp and p = para pµp spin states . The dI'k/dE are the photon spectra calculated in Section 5.2. The partial branching ratio is then given by the sum of the photo n spectrum from the three states, each weighted according to the probability of being occupied by a muon, fk, which may be time dependent. a~ss Mev = L !k r:ss Mev. (5.2) k=11,o,p The unavoidable photon background from bremsstrahlung permits only a portion (the upper one third) of the photon spectrum to be measur ed. The integration over photon ener~;y is therefore confined between 58 and 105 Me V. 5.3.1 The Atomic Singlet, Ortho and Para Molecular States The probability of a muon occupying the atomic singlet, ortho-molecular or para-molecular state is determined by solving the time differential equations de-scribing the occupation of the state . The state's occupation is determined by its decay rate and its probability of being populated by othe r states. The decay and transfer rates between the various atomic and molecular states of liquid hydrogen are given in Table 5.1. Assuming the de-population from the triplet state to the singlet state occurs almost immediately [63], the population of the atomic singlet state can be described 122 Chapter 5. Determining gp I Parameter I Description r. - 670 s- 1 OMC rate from the singlet state ft - 14.82 s- 1 OMC rate from the triplet state fo - 531 s-1 OMC rate from the ortho state rp - 212.4 s- 1 OMC rate from the para state -f µ-deca11 - 4.55 x 105 s- 1 Radiative muon decay rate ..\.,o - 2.36 X 106 S-l Transition rate from singlet to ortho state ..\op - 4.1 X 104 s-1 Transition rate from ortho to para state IP - 1.15 Overlap factor for the para fraction /0 - 1.01 Overlap factor for the ortho fraction Table 5.1: The decay and transfer between the various atomic and molecular states of liquid hydrogen. solely by its total decay rate, A.,: dN. = -A.,N, dt, where A., = f 1-1-deca11 + f, + ..X.o, and A;; is the transfer rate from state i to state j. (5.3) (5.4) The population of the ortho-molecule is given by its total decay rate A0 plus the transfer from the atomic singlet state: (5.5) where Ao = f µ-deca 11 + f o + ..\op. (5.6) Finally the population of the para-molecule is given by its total decay rate Ap plus the transfer rate from the ortho molecule. Population from the atomic singlet state is also possible but is strongly suppressed [63] and has been neglected (,\,p :::::: 0). Thus, (5.7) 5.3. Muon Chemistry Considerations 123 with Ap = r µ-deca 11 + rP. (5.8) By integrating each of these equations over time, the fracti ons la, lo, and lP for the probability of a muon undergoing capture from the singlet, ortho, and para states are obtained. (5.9) (5.10) where tb is the blanking time used in the Blank cut. The factors multiplying lo and lP are due to the differences in muon density at the proton between the atomic and molecular cases. Values for these parameters have been investigated by several authors and was discussed in Chapter 2. The photon rate is strongest from the para state; 3 times greater than the ortho state and more than 100 times greater than the singlet. However the pµp-para occupation is very low, see Fig. 5.6. Consequently, radiative muon capture from the ortho-molecular state is the most dominant, see Fig. 5.7. The atomic-singlet state, although it has a high occupation, has a decay time which is very short. Its contribution is subsequently strongly suppressed by the 365 ns blanking time. The blank time is necessary in order to remove RMC events resulting from muons stopping in the gold vessel containing the liquid hydrogen target. 124 Chapter 5. Determining gp i::::: 1.0 0 •.-t +J ro 0.8 singlet 0-t ::J CJ CJ 0 0.6 ::t '+-4 0 >. 0.4 +J •.-t ...... •.-t ,.c 0.2 ro ,.c 0 f-1 para 0.. 0 .0 0 2 4 6 8 10 Time µsec Figure 5.6: The population of the various atomic and molecular states in liquid hydrogen over time . . 0 0 7 -+---..._______,J.________._ _ __._ _ _,___.........__,.._____., _ ___.__--+-.006 .005 .004 .003 .002 .001 Probability of RMC in Liquid Hydrogen per Muon Capture singlet µp ' ' ' ....... . . . . . . . . . . . . ....... ······ ....... , .-·· para pµp___.r ·· ····· ·-:":':.--:-: __ ,. ....._ . 000 --,-.·a...'" ·-'-r· ----r----r---.--~--..---~---,------ ·.....,--·-..;;;;;..;;· ...... =+-0 2 4 6 8 10 Time µsec Figure 5.7: The probabilty of RMC in liquid hydrogen per muon capture as a function of time. 5.3. Muon Chemistry Considerations 125 gp Singlet Ortho Para Total ( x 1 o-is) PCAC units ( X IQ- 8 ) ( xl0- 8) ( X IQ- 8 ) TBlank = 365ns TBlank = 0 0.1 0.020 0.780 0.220 0.957 1.020 0.2 0.013 0.778 0.227 0.959 1.017 0.3 0.008 0.786 0.234 0.972 1.028 0.4 0.008 0.786 0.234 0.972 1.028 0.5 0.005 0.836 0.252 1.036 1.094 0.6 0.008 0.878 0.262 1.086 1.148 0.7 0.012 0.930 0.274 1.148 1.216 0.8 0.020 0.992 0.286 1.221 1.298 0.9 0.029 1.066 0.299 1.307 1.395 1.0 0.041 1.150 0.313 1.404 1.505 1.1 0.056 1.246 0.328 1.514 1.630 1.2 0.073 1.352 0.344 1.635 1.769 1.3 0.092 1.469 0.361 1.768 1.923 1.4 0.114 1.597 0.379 1.914 2.090 1.5 0.138 1.736 0.398 2.071 2.272 1.6 0.165 1.885 0.417 2.240 2.468 1.7 0.194 2.045 0.438 2.421 2.678 1.8 0.226 2.217 0.460 2.614 2.902 1.9 0.260 2.399 0.482 2.819 3.141 2.0 0.296 2.591 0.555 3.306 3.393 Table 5.2: Partial branching ratio, Emin = 58MeV, for RMC on hydrogen for various values of 9p with contributions from the singlet ortho and para states . The rates given reflect the effect of blanking the first 365 ns following muon capture. The last column is what the rate would be for no blanking time . The estimated uncertainty on the total branching ratio is 4%. 5.3.2 The Partial Branching Ratio From the above results for the occupation of the atomic and molecular states, and Eq. (5.2), the partial branching ratio for radiative muon capture was determined. Table 5.2 and Fig. 5.8 illustrate the increase in the partial branching ratio as gp is increased. The contribution from the atomic singlet state is negligible, as expected. In addition, the effect of introducing a blanking time of 365 ns is shown. The effect is to reduce the observed partial branching ratio by at most a few percent. This was considered acceptable in light of the photon background it removed from the experimental photon spectrum. 126 Chapter 5. Determining gp ,-.... 4-4-----'--'---'----'--'---'--L-~--'--L-~--'--'--_.__.__._ _ _.__.__.__~ co 1 Photon Energies 58 MeV 0 X ?'-- 3 0 0 ...... 2 t:lO ...... ,.q CJ ro So-4 o:l 1 ---- ------------------------total Tmau=O / / / / ,,/ total T81au=365ns / ,' / ,' / ,' ---.. .. .. .. .. -----/ ,' / .,,.' / .,,. . / ,, .... ,... ""Ortho -----------Para .... Sing let .. .. . . ... .. -· · · · · · · · · · · · 0 -+---,...~___,,--.,.----,--~......,............,. ...... =--=,· ·r=-=· ·....:...· T"". _. • ..... • ._. ·_,· r--. ·---.------.----,,----r---r--ir----r--+-0 . 0 0.5 1.5 2.0 Figure 5.8: Partial branching ratio (Emin = 58 MeV) versus g,. 5.4. Predicting the Experimental Photon Spectrum 127 5.4 Predicting the Experimental Photon Spectrum The spectrum and rate of RM C photons produced have been measured by the detector. The number of photons detected per muon stop can be determined by convolving the physical photon energy spectrum 1;: with the detector response function and detector acceptance, and then integrating over the available energy, E. where E (5.12) : Measured photon energy. : Real photon energy. : Experimentally measured number of RMC photons in the range E, E+dE . : The number of muon stops after all corrections . : The fraction of muons that undergo capture from state k : The fractional difference between the acceptan ce determined by Monte Carlo and the measured acceptance for the ('11·-p) process. Ne : Normalisation constant, this includes the efficiencies of the Bit, Random, and Cosmic cuts and the C counter efficiency. D(E, E...,) : Detector response function, this includes the geometrical acceptance of the spectrometer , the efficiency of the tracki ng software (RMCOFIA V3.0), and the efficiencies of the Photon and Track cuts. dI'Th(E ) ~E..,.., : Theoretical RMC photon spectrum. The value of the pseudoscalar coupling, gp, was determined by finding the theoretical spectrum ( defined by gp) that predicts the measured numb er of photons from RM C 128 Chapter 5. Determining gp in hydrogen. Restricting the i ntegration of _the photon energy to between 58 and 105 Me V, the predicted number of photons to be observed above 58 Me V is (rE:rp)~58 k predicted (5.13) 5.4.1 Detector Response The goal is to find a theoretical photon spectrum which, when convolved with the experimental response function and acceptance, reproduces the measured pho-ton spectrum . This is the technique that will be used to extract the value of the pseudoscalar coupling constant. But first, the acceptance and response function of the RMC spectrometer must be determined. That is, what is the probability of the experimental facility detecting a photon of energy E,.,, and with what energy is it likely to be reconstructed. The former is the detectors' acceptance, the latter is the response function, denoted by D(E, E,.,). The response function was determined by simulating mono-energetic photons between 50 and 100 Me V in 5 Me V increments. The photons' energy and momentum distribution were input into a GEANT [100] Monte Carlo simulation of the RMC spectrometer. The photons were tracked throughout the spectrometer , those that under went pair conversion in the lead foil and satisfied a valid photon trigger were written to an output device. These events were examined by the tracking package (RMCOFIA V3.0) and the trajectories of the e+ and e- pair were reconstructed. After all track reconstruction, the remaining events were analysed by the Photon and Track cuts in the same way as the experimental data, as discussed in Chapter 4. The resulting photon spectrum N(E, E,.,) is then related to the function D(E, E,.,) by the following, D(E, E.,) = N(E, E,.,) NE., Ebin (5.14) where NE., is the number of photons generated with energy E,.,, Ebin is the bin size, in this case 1 Me V and E is the energy of reconstructed photon. Figure 5.9 illustrates 5.4. Predicting the Experimental Photon Spectrum =.0020 0 .... ..., 0 § .0015 Cl) Ill = g_ .0010 fll Q) 0:: .0005 .0000 30 40 50 60 70 80 90 100 ·Photon energy E7 (MeV) Figure 5.9: The response function for various photon energies E-,. 129 110 the response function at various photon energies E,.,. The number of mono-energetic photons generated at each energy E-r was chosen so that each photon spectrum had a similar number of events. This ranged from 3,000,000 photons generated at 50 MeV upto 800,000 at 95 MeV. 5.4.2 Detector Acceptance ' The response function determines the probability of detecting a photon of mea-sured energy E with photon energy E-r· To obtain the acceptance of a photon with energy E-r, it is necessary to integrate the response functio n at E-r over all available photon energies, Acceptance(E-r) = j D(E,E-r) dE (5.15) This acceptance is not the total acceptance of the spectrometer, it includes only the geometrical acceptance of the spectrometer, the efficiency of the track finding software (RMCOFIA V3.0) and the efficiencies of the Photon and Track cuts. The 130 Chapter 5. Determining gp 2.5-+-.L......L--'--'-.L......L--'--'-.L......L---'-....L-'--'----'--'--'--'----'-...,__,.____.__._-'---+-After Photon and Track cuts 2.0 Q) 1.5 CJ Q ro ., 1.0 Q) CJ CJ <C 0.5 Line = Nowrap only events Dots = Nowrap and Wrap events 0.0--1---~~~-~~-~~~~~~--~~~-~.---+-50 60 70 80 90 100 Photon energy, E7 (MeV) Figure 5.10: Acceptance curve for mono-energetic photons . remaining factors that affect the acceptance, such as the Bit, Random and Cosmic cuts and the C counter efficiency were not incorporated into the Monte Carlo sim-ulation. Hence the effects of these cuts are considered separately, in the following section. The acceptance curve in Fig. 5.10 is for mono-energetic photons originating from a distribution at the target center . The distribution was selected to represent the distribution for stopped muons in the experiment. The measured RMC photon spectrum extends from 58 up to 100 MeV. Therefore, the important quantity is the integrated acceptance between these limits. The integrated acceptance between 58 and 100 MeV can be written : 1100 100 Acceptance= I: AE., · WE.,, 58 E-,=58 (5.16) where the spectrometer acceptance, AE.,, has been weighted by the shape,WE.,, of the RMC photon spectrum between 58 and 100 MeV. The weighting has been 5.4. Predicting the Experimental Photon Spectrum 131 16 - gp=l. 0 ... I > Q) ::a 12 ... I I'll -'T 8 8 X singlet 0 _t:::;:::;::::::;:::::::;::::;:::;:::;:::::;:::;::::::;:::;:::;:::;:::::;::::;~;::::::;:::::;:::::;::=r::;:=?~iiji..;,.-,.....,+ 58 65 72 79 86 93 100 Photon Energy (MeV) Figure 5.11: Shape of RMC spectrum between 58-100 MeV. normalised such that 100 E WE-y = 1. (5.17) E-r=58 WE-r was calculated by summing the contributions to the photon energy spectrum from the singlet, ortho and para states. The photon spectrum corresponding to gp = 1.0 was chosen to be the representative shape. The change in shape between 58 and 100 MeV for gP between 0.1 and 2.0 is negligible for the ortho and para states (see Figs. 5.2 and 5.3). In the case of the singlet state the change in shape is significant (Fig. 5.1), but its contribution to the total photon spectrum is typically two orders of magnitude smaller then the ortho and para contributions, as displayed in Fig. 5.4. The shape of the RMC photon spectrum between 58 and 100 MeV is shown in Fig. 5.11. Folding this shape with the acceptance curve yields the integrated acceptance over the RM C region measured, /100 Acceptance - 0.905 %. lss (5.18) 132 Chapter 5. Determining gp -The value of the integrated acceptance incorporates the track finding efficiency of the RMCOFIA V3.0 software. It also takes account of the Photon and Track cut efficiencies. It does not reflect the effects of the remaining software cuts; the Bit, Cosmic, Random, and Blank. The affects of these cuts on the data must be known for the determination of the absolute acceptance for photons from RMC by hydrogen. 5.4.3 BCR Cut Efficiencies Described earlier were three types of cuts, called the Bit, Cosmic and Random. These cuts served to reject photon events that were not associated with photons from the RMC on hydrogen process. However, the type of events they were de-signed to reject are not reproduced in the Monte Carlo simulation that generates the theoretical RMC photon spectrum. Consequently there is no need for these cuts in analysing Monte Carlo data. However, it is possible that these cuts may be indiscriminately rejecting good RMC photon events from the experimental data. It is necessary to determine the effect these cuts have on the real data and scale the Monte Carlo data accordingly. The likelihood of these cuts rejecting a good photon was determined using the following procedure. When an event is passed into the user routine that applies the cuts, it is identified as being either in prompt coincidence with a beam particle passing through the beam counters, or non-prompt (no beam counter coincidence). If it is in prompt coincidence then it is highly probable that the event was a photon from pion capture. In this case a high proportion of the photons are real photons and are reconstructed accurately. By the time they have been passed through the Photon and Track cuts all remaining photons can be considered real photons. The likelihood of having photons from c ,smics rays and random type events in this prompt data set is negligible. Therefore, the probability of the Bit, Cosmic and Random cut rejecting a good photon can be determined simply by looking at the 5.4. Predicting the Experimental Photon Spectrum 133 number of photon events before and after each of these cuts on the prompt photon events . The advantage of using these pion events in the muon beam is there is nv rate effect due to different beam tunes. To investigate if th ese cuts were sensitive to the type and energy of the photon event, they were broken into four categories: (1) events with energy less then 52 MeV, i.e mostly bremsstrahlung photons, (2) events with energy between 55-85 MeV, (mostly ,r 0 events), (3) events with energy greater then 85 MeV, (mostly radiative pion capture events), and finally, (4) the sum of ,r 0 decay events and radiative pion capture events. Tables 5.3, 5.4 and 5.5 display the results. For the Bit cut there appears to be no energy dependence of the cut. For the Random cut, the cut efficiency is slightly less by 2-3% for the higher energy photons . This is because of the nature of Random events. Random events result when an e-from µ decay is tracked rather then an C from a photon conversion. The e- from µ decay is restricted to the low photon energies, subseque ntly the Random cut will be reject more events at the lower energies. For the Bit and Random cuts the cut efficiency was determined from photons in the ,r 0 region . In the case of the Cosmic cut , the cut efficiency is considerably higher in the ,r 0 region. This arises because ,r 0 decay produces two photons separated by "' 180°. The nature of the Cosmic cut is to identify tracks in the opposite hemisphere of the drift chamber that tracked the e-e+ pair. The Cosmic cut will therefore reject more ,r 0 events then single photon events . Consequently the cut efficiency was determined by taking the average of the cut efficiency at the lower photon energy below the ,r 0 region and above the ,r 0 region from the 129 MeV photons. In addition, the BCR cut efficiencies were looked at for both wrap and nowrap as well as nowrap only events. No differences outside of the quoted uncertainties were found for the BCR efficiencies. This was also found to be true when cut values in the Photon cut were tightened. This indicates that the B, C and R cut efficiencies are not sensitive to the type of events that pass the earlier Photon and Track cuts . 134 Chapter 5. Determining gp Period 1r - bremsstrahlung 1'129 'fro 55 < E,., < 140 E,., < 55 85 < E,., < 140 55 < E,., < 85 Aug 90 99.502 ± .004 98.500 ± .008 99.520 ± .006 99.480 ± .006 Dec 90 99.585 ± .002 99.990 ± .004 99.576 ± .002 99.590 ± .002 Jan 91 99.860 ± .002 99.995 ± .003 99.858 ± .002 99.855 ± .002 Table 5.3: Summary of the Bit cut Efficiency. Period 1r - bremsstrahlung ')'129 'fro 55 < E,., < 140 E,., < 55 85 < E,., < 140 55 < E,., < 85 Aug 90 93.126 ± .004 91.730 ± .008 94.676 ± .006 91.762 ± .006 Dec 90 89.809 ± .002 90.409 ± .004 91.838 ± .002 88.119 ± .002 Jan 91 88.789 ± .002 88.902 ± .003 90. 786 ± .002 87.158 ± .002 Table 5.4: Summary of the Random cut Efficiency. Period 1r - bremsstrahlung 1'129 'fro 55 < E,., < 140 E,., < 55 85 < E,., < 140 55 < E,., < 85 Aug 90 90.368 ± .004 95. 797 ± .008 93.192 ± .006 87.614 ± .006 Dec 90 87.477 ± .002 92.433 ± .004 90.399 ± .002 84.900 ± .002 Jan 91 89.285 ± .002 . 94.153 ± .003 92.216 ± .002 86.528 ± .002 Table 5.5: Summary of the Cosmic cut Efficiency. 5.4. Predicting the Experimental Photon Spectrum 135 Data Period BL Aug 90 0.77 ± .02 Dec 90 0.76 ± .02 Jan 91 0.72 ± .02 Aug 91 0.76 ± .02 Table 5.6: BL correction, due to vetoing from a second beam particle. 5.4 .4 Blanking Correction This is a correction that accounts for an incident µ- beam particle passing through the beam counters at a time between the arrival of an earlier µ- beam particle and the blank time of 365 ns. In such an event the second arriving beam particle will veto the previous event, which may have been a valid RMC event. This correction is sensitive to the beam rate and the timing cuts used in the Prompt and Blank cuts. To determine this factor a Monte Carlo program [101] was used. Muons were generated in the liquid hydrogen and then allowed to decay with the hydrogen lifetime. By varying the rate at which the muons were stopped, the vetoing affect of later arriving muons was estimated for a particular set of t iming cuts. The timing cuts included the Prompt cut and Blank cut . The Blank cut rejected any event that registered a beam particle coincidence within 365 ns of a photon trigger. A coincidence was defined as either a two three or four fold coincidence of the beam counters . Typically 96% of the coincidences were four fold and 3.5% 3 fold. The result of the vetoing effect for the appropriate beam rate is illustrated in table 5.6. 5.4.5 Checking the Monte Carlo Simulation In the determination of the response function and acceptance, one crucial as-sumption has been made, namely, that the RMCGEANT V5.207 Monte Carlo sim-ulation is a good description of the actual experimental conditions. It will be shown that the Monte Carlo methods used are a good representation of the detector re-sponse and the small variation that is present can be estimated. This section investigates the reliability of the Monte Carlo and establishes the r 136 Chapter 5. Determining 9p 10 Jl. 1r-p Monte Carlo Data ,......,_ 0 ,r-p Experimental Data "It 0 8 ...... X a, ..__ 0 ... 6 I > Q) r/l 4 +.> ::::1 0 u 2 o--~~~m-.--.-m--rT"T'"T"""l---r-r"T"T""1~~~...,. ..... ..-t-20 40 60 80 100 120 140 160 180 Photon Energy (MeV) Figure 5.12: The (1r-p) Monte Carlo spectrum generated using the Monte Carlo simulation RMCGEANT v5.207 together with the measured (1r-p) pho-ton spectrum. justification for using it to model the detectors' response and acceptance functions . To do this the well known ( 11'-p) process is utilised. Using RMCGEANT V5.207, with the (11'-p) process turned on, 3 x 106 trials were generated and normalised to a measured (11'-p) photon spectrum, (see Fig. 5.12). The normalisation of the Monte Carlo data to the real data consisted of de-termining the number of pions stopped in the target. Corrections similar to those calculated for the muon beam are shown in Table 5. 7 The beam optics simulation program REVMOC [99] was used to obtain the fraction of pions that stop in the target. The pion rays were generated by REVMOC and entered into the RMCGEANT geometry . The results are shown in Table 5.7. The fraction of pions that stop ir. the various materials around the target were similar to the muon distributions observed in Section 4.6. The important difference is that the the pion may decay to a muon and muon neutrino. Consequently a pion may register as a pion as it passes through the four beam counters, but may 5.4. Predicting the Experimental Photon Spectrum 137 subsequently decay into a muon before it reaches the target. In such a case the scaler 1234RF1rMV counting the number of pions stopping in the target will be an overestimate, and as such will need to be corrected. Calculations indicate - 7% of the pions will decay into muons after exiting the last beam counter, before entering the liquid protium. To verify the fraction of pions stopping in the various materials shown in Ta-ble 5. 7, the Monte Carlo simulation program REVM OC must be shown to be reliable. A procedure similar to the one described in Section 4.6 for counting stopped muons was used. The only difference was the delay between the RF cyclotron pulse and the pulse of the RF separator was set to correspond to the time-of-flight for pions. With the copper vessel and target scintillator in place the ratio was measured to be 1234.RF1r.(Target veto scintillator) = 0_926 ± 0_003 1234.RF1r (5.19) The pion rays from REVMOC were passed into a Monte Carlo simulation of the copper cylinder and target scintillator geometry. The ratio ((Pion entries· 0.99) + (Muon entries· 0.98) = 0_926 ± 0_004 1234.RF1r was obtained. (5.20) The sea.ling factors 0.98 and 0.99 are the measured efficiencies of the target scintillator for muons and pions respectively. "Muon entries" is the number of muons REVMOC calculates will enter the target after decaying from pions given that there were 1234.RF1r rays. The agreement is again impressive, clearly justifying the Monte Carlo results in Table 5. 7. The muons created from pion decay after the beam counter will penetrate farther into the target, with ,..., 67% stopping towards the upstream end and in the rear wall, while - 20% stop in the silver collimator and heat shields. The remaining fraction typically stop in the front of the gold vessel. The detector resolution was poorer for photons with energies as large as 129 MeV, at these energies the tracks in the chamber have very large radii of curvature , and 138 Chapter 5. Determining g11 Location % of all particle stops BM4 0.3 Mylar 0.06 Silver collimator 5.4 Outer heat shield 0.38 Inner heat shield 0.75 Gold flask 1.46 7r-+ µvµ, 7.65 liquid protium 84.0 . Table 5.7: Fraction of pions stopping in the various material surrounding and before the liquid protium target. so, very small changes in the fitted tracks cause large changes in the calculated momentum. Thus, it is perhaps not surprising that the Monte Carlo does not reproduce the exact details of the resolution at these energies. It should be noted that the RMC spectrum has an endpoint well below these energies. At the lower energies where one has more confidence in the accuracy of the Monte Carlo, the data are well reproduced by GEANT. 5.5 Determining F(E) Despite the impressive agreement between the experimental and Monte Carlo acceptance at low photon energies, there was a small discrepancy. The discrepancy can be measured and will be described by the function F(E). To measure this dis-crepancy, a physical process that emits photons over the relevant range of energies, namely 58-100 Me V, is required. A process that meets this requirement is pion capture on the proton. Given this fortuitous situation, it is possible to measure the function F(E) using the following procedure: Step 1: Run the (1r-p) process through the RMCGEANT V5.20'{ Monte Carlo program writing out all events that produce a valid photon trigger. 5.5. Determining F(E) 139 Step 2: Step 3: Step 4: Step 5: Pass the above data set through the RM CO FIA V3.0 tracking pack-age and obtain the photon spectrum after applying the Photon and Track cuts. Turn now to the experimental (1r"-p) data: (i) For each (1r"-p) run plot the relative acceptance [=(total photon counts)/1234RF,rMV] after the Photo n and Track cuts. (ii) Sum up all (1r"-p) runs for each period (Aug90, Dec90 and Jan91) Normalize the Monte Carlo photon spectrum to the number of 7r"-stops for each data taking period. Finally, take the ratio between the (1r"-p) photon spectrum ob-tained experimentally and the ( 'lr"-p) photon spectrum obtained from Monte Carlo. The ratio which can vary with photon energy will define the function F(E). A function F(E) has been obtained that describes the difference in acceptance be-tween Monte Carlo and experiment as a function of energy and is shown in Fig. 5.13. However, for the (1r"-p) process between 55-85 MeV, two photons are released. Be-fore using F(E) for absolute normalization of the Monte Carlo RMC photon spec-trum, it must be shown that the difference in acceptance between Monte Carlo and experiment is identical for the ( 'lr"-p) and (µ-p) processes. To do this let, (5.21) be the probability of the detector arrangement detecting a photon, given that there was only ~me photon generated, and also let, (5.22) 140 Chapter 5. Determining 9p be the probability that the Monte Carlo simulation gives for the detection of the photon. Ll thus identifies the difference in acceptance between the Monte Carlo · simulation and the true, experimental conditions . Consider now the (1r-p--+ n1r0 --+ ')")') channel where two photons are emitted. In this case the event will be triggered if both photons are detected. The probability of this occurring is f • f. The event will also be detected if only one of the photons is detected. The probability of detecting only one of the photons is given by 2 · f{l - f ). The total probability a detecting a 1r0 decay event is given by the sum, i.e., (5.23) Since f is small ( about 1 % ) the €2 term has been ignored . A similar expression can be written for the Monte Carlo probability of detecting a 1r0 decay event, pMC (,l1ro) = 2(f + Ll) - (f + Ll)2 = 2(f + Ll) - f.2 - Ll2 - 2fLl 2(f + Ll). (5.24) Since both f and Ll are small, the squared and product terms can be ignored. The function, F(E), for radiative muon capture is obtained by taking the ratio between the experimental acceptance (Eq. (5.21)) and the Monte Carlo acceptance, (Eq. (5.22)), FRMC(E) = pEXP(,I,) = _f __ pMC (,I,) f + Ll (5.25) Using Eq. (5.23) and Eq .(5.24) a similar ratio can be obtained for the 1r0 production process, namely F1f0 (E) - (5.26) 5.6. Normalisation 0 '"i: 1.0 aj u O.O--+-....---.......,."""'T""...,......,......,."""'T"-.-....---.......,."""'T""...,......,......,."""'T"-,-....---l""""T---.--.-T-i-.-""T""...,.....r-t-58 65 72 79 86 93 100 Photon Energy (MeV) Figure 5.13: The Function F(E) for January 1991. This represents the differ-ence between the acceptance determined by a Monte Carlo calculation and the measured acceptance for the 11'-p process. 141 The ratios, Eq. (5.25) and Eq . (5.26) are equivalent if the squared and product terms of f and are ignored, (5.27) This suggests that the measured function F(E) is also applicable to the (µ-p) process, with a variation of order E2• The above description provides a procedure that will allow the absolute normalization of the Monte Carlo generated RMC photon spectrum so that a direct comparison with the measured photon spectrum can be made. 5.6 Normalisation The data for this experiment were collected over a number of data taking pe-riods . During these periods, trigger counter efficiencies, beam counter efficiencies , electronic timing conditions, and beam tunes varied. Consequently, the photon ac-142 Chapter 5. Determining 9p After Photon and Track cuts .7 a> 0 i::: Id .6 i:l.. a> 0 0 < Ausust. '90 December '90 lanuary '91 .5 .4-+-...,.....-.--.-..--....--,--.--.-----r-~---r-~...,.....-.--.-..--....--,----.--.-----r-~---r-~--t-o 20 80 100 Figure 5 .14: ( 11"- p) acceptance data. ceptance for each period may have been different. The changes in acceptance were accommodated by normalising the acceptance to one particular data taking period. The January 1991 period contained the highest proportion of the data and had a stable acceptance, (see Fig. 5.14). For this reason all other data periods were nor-malised to the January 1991 data. The function F(E) obtained from (1r-p) data in January 1991 provided the absolute normalisation for the Monte Carlo simulation. The data were normalised by scaling the number of muons stopped for each data period. To do this, one has to first determine the change in acceptance for the three data periods. This was achieved by measuring the relative acceptance Acen,o, of the (1r-p) process between 55 and 100 MeV. The relative acceptance was taken as the ratio of good photons remaining after Photon and Track cuts, to the number of counted pions 1234RF1rMV. Figure 5.14 illustrates the variation of thi:, ratio for the (1r-p) data taken throughout the experiment. The three distinct data taking periods are obvious. As with the counting of the muon stops (section 4.6), the pion stops for each data period also had to be corrected for the effects of pile-up, 5. 6. Normalisation 143 Data 1 + 1: 1 + I: 1-J: Ae<:,ro BCR BL Norm Aug90 1.031 1.003 0.993 0.6392 0.866 0.77 1.02 Dec90 1.038 1.002 0.994 0.6622 0.802 0.76 0.97 Jan91 1.041 1.006 0.989 0.7120 0.811 0.72 1.00 Table 5.8: Normalised acceptances for the ,r-p data . Data 1 + ft 1 + J: 1-ft Norm 1234RFµMV X 101u NS tops x 101u Aug90 1.023 1.013 0.959 1.02 19.97 20.24 Dec90 1.029 1.013 0.960 0.97 39.11 37.97 Jan91 1.021 1.016 0.950 1.00 83.41 82.20 Table 5.9: Normalised stops for the µ-p data . The last column needs to be further scaled by the scattering correction (1 - /,)=0 .926. This was obtained using REVMOC and a,~counts for the fraction of muons that stop in non-target material, mostly the front face of the gold vessel and the silver collimators. beam counter efficiencies and random vetoing. The corrections to the number of counted pion-stops for each data taking period are given in table 5.8. Quantities such as the Bit, Cosmic and Random cut efficiency as well as the Blank correction have the effect of reducing the number of detected photons. For the purpose of comparing the data from different data taking periods, the number of pion stops for each period was scaled by the corresponding correction factors . These are also presented in Table 5.8. The value Norm is the product of all the correction factors for each (11'-p) data taking period normalised to the value for January 1991. It is the normalisation factor that brings all data periods to equal acceptance. A normalisation greater than unity implies the acceptance for that data taking period was determined to be greater than the January 1991 perio d. The corrected number of muons stopped for that period then needs to be scaled up by the corresponding normalisation value, Norm . Table 5.9 displays the quantiti es that affect the number of muon-stops for each µ- data taking period . Using th ese values the number of counted muons stops, 1234.RFµ-MV, can be scaled to give the corrected number of muon stops normalised to the January 1991 acceptance. 144 Chapter 5. Determining gp 5.7 The RMC on H Partial Branching Ratio and 9p All quantit ies necessary to extract the pseudoscalar coupling from the partial branching ratio have been calculated. Using the theoretical calculation of Fearing and Beder, values of gp ranging from 0.1 up to 2.0 in 0.1 increments of 6.6ga were used to obtain theoretical photon spectra for RMC in hydrogen (see Figs. 5.1, 5.3, 5.2). The resulting photon spectra were folded with the RMC spectrometer response function {see Fig. 5.9) and sea.led by the cut efficiencies BCR and BL which are not intrinsic to the Monte Carlo simulation. The photon rate was also corrected for the effect of capture from the different atomic and molecular species pertain ing to liquid hydrogen. Figure 5.15 illustrates the change in the rate of radiated photons per muon capture as a function of the pseudoscalar coupling constant. The number of stopped muons was calculated by summing the corrected number of muon stops from each data period with the appropriate normalisation. Two values of gp are obtained . The first value is obtained by using the measured transition rate between the ortho and para molecular states . The experiment by Bardin et al. [38] quotes a measured ~alue of Aop = 4.1 x 104 • This result gives a value of gp which is 1.34 times higher than the value predicted by the PCAC and Goldberger-Treiman hypothesis, i.e. gp = 11.2±2.5. The second value of gp is obtained by using the theoretica l calculation [ 64] for the ortho to para transi tiori rate, Aop = 7 .1 x 104 • This gives a value of gp 1.26 times higher than the PCAC hypothesis and Goldberger-Treiman prediction for 9p, i.e. gp = 10.5 ± 2.2 (see figure 5.15). A summary of the results is displayed in Tables 5.10 and 5.11. 5. 7. The RMC on H Partial Branching Ratio and gp 0 :;:; 0 a::: .2 ...., lo.. 0 Cl. 14 12 Acceptance folded in 4 ........... ----4 A0 p=4.1X10 145 2 L---.---.--.-~~~~~~L.---.-J 0.0 0.5 1.5 2.0 Figure 5.15: Determination of Up· The dashed curve was obtained using the cal-culated ortho to para transition rate of Aop = 7 .6 x 104 • The solid curve uses the experimentally determined rate of Aop = 4.1 x 104 . 100 Data Taking I: NE:r:p flrMC µ11top11 X 1010 Aop = 4.1 X 104 58MeV period a~:.is x 1 o-is 9p (PCAC) Aug90, Dec90, Jan91 102.3 ± 12.2 130.0 1.80 ± 0.34 1.34 ± 0.22 Dec90, Jan91 84.1 ± 11.0 111.3 1.75 ± 0.37 1.30 ± 0.27 Jan91 57.9 ± 9.1 76.1 1.76 ± 0.39 1.31 ± 0.30 Table 5.10: Values for G~5s and Up using Aop = 4.1 x 104 . Est imated uncertainty on the µStops is 9% (this includes the absolute normalisation of the acceptance). 100 Data Taking I: NE:r:p RMC µ11topa X 1010 A0 p = 7.1 X 104 58MeV period G~:,is X 10-is gp (PCAC) Aug90, Dec90, Jan91 102.3 ± 12.2 130.0 1.82 ± 0.34 1.26 ± 0.22 Dec90, Jan91 84.1 ± 11.0 111.3 1.76 ± 0.37 1.21 ± 0.27 Jan91 57.9 ± 9.1 76.1 1.77 ± 0.39 1.22 ± 0.30 Table 5.11: Values for G>ss and Up using Aop = 7.1 x 104 • Est imated uncertainty on the µStops is 9% (this includes the absolute normalisation of the acceptance). 147 Chapter 6 Conclusions 6.1 Summary of Results This work has reported the first measurement of the radiative muon capture photon spectrum from hydrogen. From the measured photon spectrum a partial branching ratio for the RM C process was determined. In addition, the strength of the pseudoscalar coupling constant was obtained. This is one of only a handful of measurements of 9p attempted for the bare nucleon, and the only measurement using the rare RMC process . This process is unique in that it is considerably more sensitive to the pseudoscalar coupling, and consequently capable of providing a more accurate determination of its strength . The measurement consisted of comparing the number of photons measured above 58 Me V with the number of photons predicted by a fully relativistic calculation (60, 61] of the RMC process. The intermediate il(1232) resonance between nucleons was included in this calculation. This had the effect of increasing the expected RMC rate by 7-8% . In addition, the dependence of the orientation of the proton and muon spins was investigated as well as the effect of the transfer rates between the various atomic and molecular species on the total muon capture rate. Two values of gp were obtained . One, using the measured ortho to para trans ition rate, >.0p = 4.1 x 104 giving a value of gp = 11.2 ± 2.5, approximately 34 % higher than the PCAC prediction. The corresponding partial br anching ratio for photons greater than 58 MeV was measured to be 1.80 ± 0.3 x 10- 8 • The second value was 148 Chapter 6. Conclusions obtained using the theoretical prediction [64] for the transfer rate to the ground para state, Aop = 7.1 x 104 • This gives a value of gp = 10.5 ± 2.2 with the equivalent partial branching ratio of 1.82 ± 0.3 x 10-s, 26% larger than the PCAC prediction. The data presented in this thesis are a subset of the RMC program at TRIUMF. Presented were data taken up to the end of February 1991, consisting of three data taking periods, August 1990, December 1990 and January 1991. The RMC experiment continues at this time, expecting to be completed in February 1994. The total number of photons detected from RMC by hydrogen is expected to be four times the number presented here. This work has also contributed to the construction, development and testing of the RMC spectrometer facility. In particular, extensive work was done in the testing and performance of the trigger system. This work has identified and described the main contributing photon backgrounds and aided in the development of techniques to estimate their magnitude. These techniques establish a procedure for examining the remaini~g data on radiative muon capture on hydrogen and the subsequent extraction of the pseudoscalar coupling strength. 6.2 Further Work The determination of the pseudoscalar coupling constant for radiative muon cap-ture relied on the accuracy of the Monte Carlo simulation of the RMC experimental facility. It was also reliant on the accuracy to which GEANT could reproduce the physical processes that were present under the experimental conditions. With due regard to these limitations justification of the use of the Monte Carlo simulations was sought whenever they were used. In the case of REVMOC and GEANT, used in the simulation of the muon and pion beam stopping distributions, this was achieved by experimental verification. The acceptance of photons from RMC was also determined through a Monte Carlo procedure. It was justified by showing that the Monte Carlo simulation 6.2. Further Work 15 12 9 -a:, a:, = a:, s-. s-. Q) GS .c ::s • • 0 0 x x .... .... • .,i ,.,: .... n II PCAC - - -- - - -~ - - - .0: 6 II 3 bO bO 0 -3 -a:, Q) s-. Q) ll'l Q) -Q:l ..... 0 t1D 1::: Q) .0 -< s-. .... a:, = ::s Q:l :! :::, s-.-::s 0:: u e-, 1962 1963 1969 1974 198 1 1993 Year Figure 6.1: All measurements of 9p· 149 could reproduce the acceptance of a well known and measurable process, namely (11"-p). The agreement was found to be better than 8% bet ween the energies 58 and 100 Me V. The Monte Carlo slightly overestimated the measured acceptance from 11"-p ___. n11"0 • This is to be expected for Monte Carlo data were the majority of event triggers are free from noise. However, by having available a measurable process with photons of similar energy to the photons radiated in RMC, the discrepancy could be measured. Using the (11"-p) process, the discrepancy was measured and is described by the function F(E). It was further shown that F(E) was applicable to the (µ-p) process. It was this function that normalised the Monte Carlo data to obtain the predicted experimental spectrum of photons from RMC. Admittedly this function was introduced to conceal the lack of understanding towards the discrepancy between the Monte Carlo calculations and the real data. Obviously a complete understanding would be more satisfying. While it is unlikely any one solution is likely to account for the entire discrepancy, further investigation may reveal a single, significant contribution. 150 Chapter 6. Conclusions One such investigation has already begun. During this work, an investigation into the small discrepancy between the Monte Carlo calculated 1r-p acceptance and the measured (1r-p) acceptance revealed the following. The measured (1r-p) acceptance between 85-140 MeV was 2.4±.12%. The Monte Carlo simulation of the (1r-p) process gave a calculated acceptance for 2.53 ± .15%. When mono-energetic photons at 129 MeV were generated (using the same initial distribution of photons as in the above), the acceptance was 2.75 ± .03%. To better understand the discrepancy bet~een the two Monte Carlo results the reaction ( 1r-p -+ n1r0 ) was "turned off". The remaining channel { 1r-p -+ n1129 ) could then be compared directly with the simulation of the mono-energetic 129 MeV photon spectrum without confusion. The result was an acceptance for the (1r-p)-+ wr129 process of 2.45 ± .03%, ,..., 11 % lower than in the case of just mon~nergetic photons. This was most puzzling; in both cases a single 129 MeV photon is emitted. The one difference being that in the case of the ( 1r-p) process, a neutron is also released. A summary of the above investigation is shown in Table 6.1. Prior to this result it was believed that the RMC spectrometer was insensitive to neutrons, in fact it had been designed specifically with this as a requirement. Earlier measurements of the OMC rate detected the outgoing neutron with Nal detectors. Consequently the discrimination of background neutrons in these experiments was difficult. The construction of a pair spectrometer for detecting the photon from RMC removed the inherent difficulty of neutron discrimination. However, as the present result suggests, the spectrometer is not entirely insensitive to the effects of the neutron. On the assumption that the neutron is responsible for the decreased acceptance, what possible process could be responsible? The neutron released in ( 1r-p -+ n,129 ) has 8.4 MeV of energy. It is thus possible for the neutron to enter one of the inner A, A' 'l" B scintillators surrounding the target. If this occurs, and a nuclear interaction takes place, the inner scintillators may veto the event and consequently reduce the photon acceptance. The Monte Carlo results given above for the (1r-p -+ n1129 ) 6.2. Further Work 151 channel suggests this is as large as 11 %. The µ-p --+ n-yvµ process also liberates ant; , tron. The response function and acceptance used to determine gp were calculated by generating mono-energetic pho-tons between 50 and 100 Me V. Consequently, a similar reduction in the calculated acceptance might be expected for the (µ-p) process. The neutron released in (µ-p) has less energy than in the ( 1r-p) process, only about 4 Me V in this case. Conse-quently the neutron is less likely to reach the inner counters and veto the event . The difference is therefore expected to be less than 11 % found in the case of the 1r-p process. It is suggested that the effect of the neutro n on the veto counters is responsible for some of the 8% discrepancy between the Monte Carlo results and real data in the region 55-100 Me V. The extent of the vetoing by neutrons in the inner counters will be determined by the thresholds on these counters. To incorporate the full effects of the neutron into the RMCGEANT Monte Carlo is not a trivial task. To do so requires the introduction of a hadronic package. This will enable the propagation of the neutron through the spectrometer to be accurately simulated. The incorporation of the hadronic package, FLUKA into the RMCGEANT Monte Carlo is currently underway [102]. In addition, experimental investigation of the effect of the veto threshold on the acceptance is being studied [103]. It is hoped that these investigations will provide a more quantitative understanding of the dis-crepancy between the Monte Carlo acceptance and the measured (1r-p) acceptance, and thus eliminate the need for the function F(E) . Preliminary results from these studies [103, 104] suggest the effect of the neutron is about a 6 - 7% reduction in the acceptance. This almost entirely accounts for the function F(E). Further, there is the discrepancy between the measured and calculated Aop rate. The measured rate, Aop = 4.1 ± 1 .4 x 104, and the calculated, Aop = 7 .1 ± 1 .4 x 104, are clearly in disagreement. This affects the determination of gp by as much as 10%. This discrepancy must be resolved. Currently only one measurement [39) exists; a second would be most welcome. 152 Process Mono energetic E-r=129 MeV Mono energetic E-y=129 MeV 1r-p-+ n-r129 1r-p Experiment 1'129 1r-p Montecarlo 1'129 Chapter 6. Conclusions Stopping distribution Acceptance 2.81 ± .04 2.75 ± .03 2.45 ± .03 2.4 ± .12 2.53 ± .15 Table 6.1: Summary of the investigation into the acceptance. In summary, this thesis work has presented, for the first time, a measurement of the rare radiative muon capture process in hydrogen. The partial branching ratio for photons greater than 58 Me V was measured to be 1.80 ± 0.3 x 10-s for ..\ 0p = 4.1 x 104 and 1.82 ± 0.3 x 10-s for Aop = 7.1 x 104 • From the measured branching ratio the magnitude of the weak pseudoscalar coupling constant, gp was determined. The values of gp are gp = 11.3±2.5 and gp = 10.5±2.2 for >.0P = 4.1 x 104 and Aop = 7.1 x 104 respectively. These values are respectively, 34% and 26% larger than the value of gp predicted by the PCAC hypothesis and the Goldberger-Treiman relation. Bibliography [1) H.P.C. Rood and H.A. Tolhoek. Nucl. Phys., 70:658 , (1965). [2) S. Glashow. Nucl. Phys., 22:579, (1961). [3) S. Wejnberg. Phys. Rev. Lett., 19:1264, (1967). 153 [4) A. Salam. Elementary Particle Physics (Nobel Symp. No. 8}, page 367. Almqvist and Wilsell, Stockholm, (1968). [5] E. Fermi. Z. Physik, 88:161, (1934). [6) E. Fermi. Nuov. Cim., 11:1, (1934). [7) R.P. Feynman and M. Gell-Mann. Phys. Rev., 109:193, (1958). [8) H.P.C. Rood J.R.Luyten and H.A.Tolhek. Nucl. Phys., 41:236, (1963). [9] N.Cabbibo. Phys. Rev. Lett., 10:531, (1963). [10] S. Weinberg. Phys. Rev., 112:1375, (1958). [11) P.Langacker. Phys. Rev., D14:2340, (1976). [12] A.Halprin, B.W.Leen, and P.Sorba. Phys. Rev., D1 4 :2343, (1976). [13] P.Lebrun. Phys. Rev. Lett., 40:302, (1978). [14] H.Stremnitzer. Phys. Rev., D1O:1327, (1974). [15] C.Leroy and J.Pestieau. Phys. Lett., B72:398, (1978). 154 BIBLIOGRAPHY [16) R.E. Marshak, Riazuddin, and C.P. Ryan. Theory of Weak Interactions in Pa~icle Physics. New York: Wiley, (1969). [17) L.B. Okun. Weak interactions of elementary Particles. Int. Ser. Monger. in Natural Philosophy, Vol 5, Oxford: Pergamon, (1965). [18] Particle Data Group. Phys. Lett., B239:l, (1992). [19] W.K. McFarlane, L.B. Auerbach, F.C. Gaille, V.L. Highland, E. Jastrzembski, R.J. Macek, F.H. Cverna, C.M. Hoffmann, G.E. Hogan, R.E . Morgado, J.C. Pratt, and R.D. Werbeck. Phys. Rev., D32:547, (1985) . [20] J.M .Gaillard and G.Sauvage. Ann. Rev. Nucl. Part. Sci., 34:351_, (1984). [21] B.R.Holstein. Phys. Lett ., B244 :83, (1990). [22) M.Derrick et al. Phys. Lett., B189:260, (1987). [23) M. Gell-Mann and M. Levy. Nuov. Cim., 16:705, (1960). [24] Y. Nambu. Phys. Rev. Lett., 4:380, (1960). [25) S.A.Coon and M.D.Scaldron. Phys. Rev., D42:2256, (1990). [26] M.L. Goldberger and S.B. Treiman . Phys. Rev., 110:1178, (1958). [27] A.Thomas and K.Holinde. Phys. Rev. Lett., 63:1025, (1989) . [28] C.A.Dominguez. Phys. Rev., D25:1937, (1982). [29] C.P. Bhalla and M.E. Rose. Phys. Rev., 120:1415, (1960). [30] H. Schopper. Weak interactions and nuclear beta decay. North-Holland, (1966). [31) M. Rho. Ann. Rev. Nucl. Part. Sci., 34:532, (1984). [32] J.J. Aubert et al. (EMC collaboration). Phys. Lett ., B123:275, (1983) . BIBLIOGRAPHY 155 [33] B. Buck and S.L. Perez. Phys. Rev. Lett., 50:1975, (1983). [34] E.J. Bleser, L.M. Lederman, J. Rosen, J. Rothberg, and E. Zavattini. Phys. Rev. Lett., 8:288, (1962). [35] J.E. Rothberg, E.W. Anderson, E.J. Bleser, L.M. Lederman, S.L. Meyer, J.L.Rosen, and LT. Wang. Phys. Rev., 132:2664, (1963). [36] A. Alberigi Quaranta, A. Bertin, G. Matone, F. Palmonari, G. Torelli, P. Dalpiaz, A. Placci, and E. Zavattini. Phys. Rev., 177:2118, (1969) . [37] V.M. Bystritskii, V.P. Dzhelepov, G. Chemnitz, V.V. Filchenkov, B.A. Khomenko, N.N Khovansky, A.I. Rudenko, and V.M. Suvorov. Sov. Phys. JETP, 39:19, (1974). [38] G. Bardin, J. Duclos, A. Magnon, J. Martino, A. Richter, E. Zavattini, A. Bertin, M. Piccinini, A. Vitale, and D. Measday. Nucl. Phys., A352:365, (1981). [39] G. Bardin, J. Duclos, A. Magnon, J. Martino, A. Richter, E. Zavattini, A. Bertin, M. Piccinini, and A. Vitale. Phys. Lett., 104B:320, (1981 ). (40] D.S.Armstrong et al. Phys. Rev., C43:1425, (1991). [41] D.S.Armstrong et al. Phys. Rev., C46:1094, (1992). (42] M. Dobeli, M. Doser, L. van Elmbt, M.W. Schaad, P. Truol, A. Bay, J.P. Perroud, and J. lmazato. Czech. J. Phys., B36:386, (1986). (43] A. Frischknecht, W. Stehling, G. Strassner, P. Truol, J.C. Alder, C. Joseph, J .F. Loude, J.P. Perroud, M.T. Tran, W. Dahme, and H. Panke. Czech. J. Phys., B32:270, (1982). (44] M. Dobeli. Radiative Muon Capture Yield in Nuclei. PhD thesis, University of Zurich, (1987). unpublished. 156 BIBLIOGRAPHY [45] T. Suzuki, D.F. Measday, and J.P . Roalsvig. Phys . Rev., 35C :2212, (1987). [46) K.Huang, C.N.Yang, and T.D.Lee . Phys. Rev., 108:1340, (1957) . [4 7] G.Conforto, M.Conversi, and L.di Lella. Phys. Rev. Lett., 9:22, (1962). [48) M. Gmitro and P. Truol. Radiative muon capture and the weak pseudoscalar coupling in nuclei. Adv. Nucl. Phys ., 18:241, (1987). [49] J. Bernstein. Radiative muon capture. Phys. Rev., 115:694, (1959). [50] Geoffrey I. Opat. Radiat ive muon capture on hydrogen . Phys. Rev., B134:428, (1964). [51] S.L. Adler and Y. Dothan. Low energy theorem for the axial weak force. Phys. Rev., 151:1267, (1966). [52] F.E. Low. Bremsstrahlung of very low-energy quanta. Phys. Rev., 110:974, (1958). [53] P. Christ illin and S. Servadio. About low energy expansio:qs of two current anplitudes . Nouvo Cim., 42:165, (1977). [54] G.K.Manacher and L.Wolfenstein. Phys. Rev., 116:782, (1959). [55] W-Y. P. Hwang. Radiat ive muon capture. Phys. Rev., C22:233, (1980). [56] W-Y. P. Hwang. Theory of radiative muon capture with applications to nuclear spin and isospin doublets. Phys. Rev., C18:414, (1978). [57] W-Y. P. Hwang and H. Primakoff. Phys. Rev., C18:445, (1978). [58] M. Gmitro and A.A. Ovchinnikova. Current divergences, pion photoproduc-tion and radiative muon capture. N id. Phys., A356:323, (1981 ). [59] J.D . Bjorken and S.D. Drell. Relativistic Quantum Mechanics. McGraw-Hill, (1974). BIBLIOGRAPHY 157 [60] Harold W. Fearing. A relativistic calculation of radiat ive muon capture in hydrogen and 3he. Phys. Rev., C21:1951, (1980). [61] Douglas S. Beder and Harold W. Fearing. Contribution of the delta(1232) to rmc on the proton. Phys. Rev., D35:2130, (1987). [62] J. Bernstein, T.D. Lee, C.N. Yang, and H. Primakoff. Effects of the hyperfine splitting of a µ-mesonic atom and its lifetime. Phys. Rev., 1111:313, (1958). [63] M. Morita . Beta Decay and Muon Capture. W.A. Benjamin Inc., (1973). [64] D.D. Bakalov, M.P. Faifman, L.I. Ponomarev, and S.I. Vinitsky. Nucl. Phys ., A384:302, (1982). [65] S.S.Gershtein. Soviet Phys. JETP, 34(7):318,685, (1958). [66) S.Cohen, D.L.Judd, and R.J .Riddell. Phys . Rev., 110:1471, (1958). [67] S. Weinberg. Phys. Rev. Lett., 4:575, (1960). [68] S. Cohen, D.L.Judd, and R.J.Riddell. Phys. Rev., 119:384, (1960). [69] A.Halpern. Phys. Rev . Lett ., 13:660, (1964). [70] P.K.Kabir. Phys. Lett.!! 14:257, (1965). [71] W.R.Wessel and P.Phillipson. Phys. Rev . Lett., 13:23, (1964). [72] A.Halpern. Phys. Rev., A34:135, (1964). [73] C. Rubbia. High Energy Physics, page 304. Academic Press, New York, eds. E.H.S. Burhop, (1969). [74] W. Berti, (1987). RMC on Hydrogen, second workshop, November 4-5. [75] TRIUMF Users Executive Committee. Triumf users handbook. Technical report, TRIUMF, (1988). 158 BIBLIOGRAPHY [76] E.W. Blackmore, D.A. Bryman, J.V. Cresswell, J . Doornbos, K.L. Erdman, J .A. Macdonald, R.M. Pearce, R.L. Poirier, J.M. Poutissou, J . Spuller, and G. Waters. An rf separator for cloud muons at triumf. Nucl. lnstrum . Methods, 234:235, (1985). [77] RS .Henderson, R.J .Dawson, M.D.Hasinoff, G.Azuelos, S.Ahmad, A.Serna-Angel, M.Blecher, T.P.Goringe, B.C.Robertson, and D.H. Wright. A cylin-drical drift chamber for radiative muon capture experiments at triumf. IEEE Transactions on Nuclear Science, 37:1116, (1990). [78] D. Wright et al. Triumf radiative muon capture facility. Nuclear Instruments and Methods, A32O:249, {1992). [79] J.V. Cresswell et al. IEEE Transactions on Nuclear Science ., NS-35:460, (1988). [80] LeCroy Corporation, Model 1879 FASTBUS Pipeline TDC, 96 Input Multi-hit Time to Digital Converter , Chestnut Ridge, and NY 10977-6499. [81] P.Bennet , M.Blecher, R.Chan, S.Davial, M.Hasinoff, S.Ko, R.Poutissou, D.Sample, and D. Wright. IEEE Transactions on Nuclear Science, 37:1200, (1990). (82] S.Bird R.G.Findlay and A.A.Raffier. Nuclear Instruments and Methods, 166:155, (1979). [83] S.Ahmad et al. Nuclear Instruments and Methods, A286:76, {1989). [84] A. Serna-Angel. Radiative Muon . Capture on Al, Si, Ca, Mom Sn, and Pb. PhD thesis, Virginia Polytechnic Institute and State University, (1991 ). un-published . _ [85] E. Zavattini. Muon Physics II, Weak Interactions, page 227. Academic Press, New York, eds. V.W. Hughes and C.S. Wu, (1975). BIBLIOGRAPHY 159 [86] G. Bardin et al. Nucl. Phys ., A352:365, (1981). [87] P. Bennett, 1991. TRIUMF Internal Technical Note. (88] H. Brafman, T. Glanzman, A.J. Lankford, J. Olsen, and L. Paffrath. IEEE Trans. Nucl. Sci., NS-32:336, (1985). [89] B. Struck, Model 320 Branch Driver, Hauptatrasse 95, D-200 Tangstedt, and Germany. [90] B. Struck, Model 300 CFI, Hauptatrasse 95, D-200 Tangstedt, and Germany. [91] Y.Nakagawa, T.Hirose, and J.Kanzaki . Jpn. J. Appl . Phys., 25:1049, (1986). [92] W.B. Atwood, (1985). SLD Detector Note 135. [93] D.S. Armstrong. Radiative Muon Capture on Carbon, Oxygen and Calcium. PhD thesis, University of British Columbia, (1988). unpublished. [94] R.E . Behrends, R.J. Finkelstein, and A. Sirlin. Phys. Rev., 101:866, {1956). [95] P. Gumplinger (RMC Collaborator). Group Minutes, 20 November, 1991. [96] P. Gumplinger (RMC Collaborator). Group Minutes, 1 May, 1992. [97] D. Armstrong (RMC Collaborator), 1992. private communication. [98] M. Blecher (RMC Collaborator). Group Minutes, 17 November, 1992. [99] TRIUMF. REVMOC ., (1993). REVMOC, A Monte Carlo Beam transport program. [100] R. Brun, F. Bruyant, M. Maire, A.C. McPherson, and P. Zanarini. GEANT3., (1992). GEANT, a general purpose Monte Carlo programme developed at CERN. [101] P. Gumplinger (RMC Collaborator), 1993. private communication. 160 BIBLIOGRAPHY (102] B. Doyle and P. Gumplinger (RMC Collaborators). Group Minutes, 18 May, 1993. (103] B. Doyle (RMC Collaborator). Group Minutes, 29 June, 1993. (104] P. Depornrnier (RMC Collaborator). Group Minutes, 29 June, 1993.
Thesis/Dissertation
eng
Unreviewed
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
A Measurement of the Weak Pseudosclar Coupling by Radiative Muon Capture in Hydrogen
Text