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A Monte Carlo study of Pion Beta Decay in the RMC spectrometer Veillette, Sacha 1992

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A M O N T E C A R L O S T U D Y OF P I O N B E T A D E C A Y IN T H E R M C S P E C T R O M E T E R By Sacha Veillette B. Sp. (Physique) Université de Montreal, 1990 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S P H Y S I C S We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A October 1992 © Sacha Veillette, 1991 In p resen t i ng this thesis in partial fu l f i lment of the r e q u i r e m e n t s for an a d v a n c e d d e g r e e at the Univers i ty of Brit ish C o l u m b i a , I agree that t he Library shall m a k e it f reely avai lable for re fe rence and s tudy. I fur ther agree that pe rm iss i on for ex tens ive c o p y i n g of this thesis fo r scho lar ly p u r p o s e s may be g ran ted by the h e a d of m y d e p a r t m e n t o r by his o r her representa t ives . It is u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n of this thesis for f inancial gain shal l no t b e a l l o w e d w i thou t my wr i t ten p e r m i s s i o n . D e p a r t m e n t of P h y s i c s T h e Un ive rs i t y of Brit ish C o l u m b i a V a n c o u v e r , C a n a d a Da te 1 9 9 2 - 1 0 - 1 5 D E - 6 (2/88) Abstract Through Monte Carlo simulation, this thesis assesses the efficiency, strengths and weak-nesses of the T R I U M F Radiative Muon Capture pair-spectrometer for the purpose of performing a measurement of Pion Beta Decay. We discuss the importance of Pion Beta Decay in terms of current theories of particle physics, with a special emphasis on the Standard Model. Properties of this weak process are described and some past and ongoing experimental efforts are briefly reviewed. The actual Radiative Muon Capture facility is described since on its configuration, the signatures of the relevant processes, the Pion Beta Decay signal and the experimental backgrounds. The detailed manner by which the respective rates have to be evaluated is also explained. We concentrate on the work done to obtain a realistic simulation for processes with branching ratios of the order 1 0 - 8 or less. The basic Monte Carlo software used, CERN's G E A N T 3 program, is introduced before the major modifications made to the package are described in detail. The optimal analysis scheme for the present detector is assessed by studying a variety of energy and geometry cuts on the Monte Carlo data. The expected experimental rates are obtained from a complete analysis by combining various cuts. We discuss the results in terms of the present experimental setup. Some possible modifications to the R M C pair-spectrometer are discussed based on the simulated prop-erties of Pion Beta Decay. Other possible modifications as well as alternative detector designs are also discussed briefly. This study shows that, due to an overall low acceptance for two-photon events, the 11 present detector is not suitable for a Pion Beta Decay measurement. However, because of its unique features for the reconstruction of photons from e+e~ conversion pairs, the spectrometer does present great advantages for background reduction for a Pion Beta Decay signal if a factor of 10 increase in the pion flux (7r+) could be obtained. i i i Table of Contents Abstract ii List of Tables vii List of Figures viii Acknowledgement ix 1 Introduction 1 1.1 A brief history of Pion Beta Decay 1 1.1.1 Beta Decay 1 1.1.2 Pion Beta Decay 2 1.2 Theory of Pion Beta Decay 3 1.2.1 Pion Beta Decay in the Standard Model 3 1.2.2 Theoretical Predictions 6 1.3 Basic Kinematics 7 1.4 Previous Experiments 8 1.4.1 Depommier et al 8 1.4.2 McFarlane et al 10 1.4.3 Summary 12 1.5 Next Generation of Experiments 13 1.6 Purpose of this Thesis 13 2 The R M C Spectrometer 15 iv 2.1 Design Requirements 15 2.2 The Detector 16 3 Signal and Backgrounds 10 3.1 Signal 19 3.2 Backgrounds 20 3.3 Relative Rates 23 3.3.1 Analytical Factors 23 3.3.2 Simulation Factors 28 3.3.3 Analysis Factor 31 3.4 Absolute Rates 31 4 Simulation 32 4.1 Monte Carlo Package 32 4.1.1 Generalities of Monte Carlo Simulations 32 4.1.2 G E A N T 33 4.1.3 R M C G E A N T 34 4.2 Modifications for Pion Beta Decay 34 4.2.1 Particle Definitions and Decay Channels 35 4.2.2 Forced Cross-Sections 35 4.2.3 'Double-Loop' Tracking 36 4.2.4 Trigger Requirements 37 4.3 Simulation of Signal and Backgrounds 37 5 Analysis and Results 40 5.1 Analysis Software 40 5.2 General Tracking Analysis 41 v 5.2.1 Basic Tracking parameters 41 5.2.2 Stopping Rates and Decay Window parameters 43 5.2.3 Initial Rate Estimates 44 5.3 Pion Beta Decay Analysis 46 5.3.1 Single Photon Energy Cuts 46 5.3.2 Photon-Photon Angle Cuts 48 5.3.3 Photons Energy Sum Cuts 50 5.3.4 Neutral Pion Energy Cuts 51 5.4 Complete Analysis 53 5.5 Absolute Rates 53 6 Discussion and Conclusion 56 6.1 Possibility for an Experiment 56 6.2 General Monte Carlo Observations 58 6.3 Modifications to the R M C Pair-Spectrometer 59 6.4 Experimental Normalization 61 6.5 Other Detector Designs 62 6.6 Further Studies 64 Bibliography 65 vi List of Tables 1 Background Processes 22 2 Relative Rates 24 3 Branching Ratios of Main Decay Modes 25 4 Simulation Factors 29 5 Initial Rate Estimates 45 6 Complete Analysis Results 55 vii List of Figures 1 Neutron Beta Decay 2 2 Diagram of Pion Beta Decay 3 3 R M C Pair-Spectrometer 17 4 Monte Carlo Histogram 39 5 Signal After Loose Tracking Cuts 43 6 Energy Share Of Each Photon 47 7 Effect Of Individual Photon Energy Cuts 48 8 Photon-Photon Angle Distributions 49 9 Effect Of Photon-Photon Angle Cuts 50 10 Energy Share Of Each Photon Revisited 51 11 Effect Of Photons Energy Sum Cuts 52 12 Effect Of Successive Cuts 54 viii Acknowledgement The author wishes to express his gratitude to his supervisor, Dr. Mike Hasinoff, for the financial support and advice provided during the last two years. Many thanks also to Dr. Peter Gumplinger without whose help many aspects of this study could never have come into existence. The author is also grateful to Dr. Jean-Michel Poutissou and Dr. Pierre Depommier for their input on the project. Many smaller thanks to the friends and collègues (Paul, Jeff, Dr. Jennings, ...) who provided information, references and lATjjXinsight. Finally, all my thanks to Saskia for the sweetest of dreams a man can ever see come true... ix Chapter 1 Introduction 1.1 A brief history of Pion Beta Decay 1.1.1 Beta Decay Since its discovery, the process generally known as Beta Decay (/? decay) has literally revolutionized the world of particle physics. Few phenomena have had such an importance to the frontiers of physics for so many decades. Beta Decay and its diverse aspects are still being studied to this day. The first attempt at constructing a theory of the Weak Interaction, which was thought to control /? decay, is due to Fermi in 1934. At the time, a point-like interaction of vector form (see Figure la) was proposed to explain decay, which, in its elementary form is: n —> p + e~ + ve Developments of this Weak Interaction theory, to shape it into a form similar to the well established theory of Electrodynamics, led ultimately to the present unified model of the Electroweak Interaction, a cornerstone of the Standard Model. The principal steps of this evolution, from a point-like vector current interaction to the weak boson-mediated V — A interaction (see Figure lb) , will not be reviewed here. Most textbooks on Elementary Particles and Weak Interaction offer plenty of detail to the reader (see [1], [2] for instance). Instead, we shall direct our attention immediately to the main topic of this thesis; Pion Beta Decay (TT/?). 1 Chapter 1. Introduction 2 Figure 1: Diagrams of Neutron Beta Decay: a) the original point-like interaction used to describe the process; b) the lowest order diagram of the same process according to the Standard Model. 1.1.2 Pion Beta Decay A seminal work by Feynmann and Gell-Mann ([3]) set the form of the effective Weak Lagrangian, by introducing the Conserved Vector Current hypothesis (CVC) . At that point, the charge-changing weak vector currents and the electromagnetic vector current were brought together to form an isospin triplet of conserved vector currents. Some of the extra terms put into the Lagrangian to phenomenologically account for all aspects of Weak Interactions and preserve Lorentz invariance led naturally to the process of Pion Beta Decay: Even though there are other ways of explaining the existence of ir/3 decay, C V C allowed for the first time a clear and simple evaluation of the decay rate. The main diagram (without any corrections) responsible for ir(3 decay is shown in Figure 2. It is of prime importance to note that this is essentially the same reaction as the Superallowed Fermi Transition (SFT) responsible for nuclear /3 decay (compare Figure l b with Figure 2). Since the charges of the particles involved in the process make no difference when treating the problem from the standpoint of Field Theory, TT/3 decay is Chapter 1. Introduction 3 strictly equivalent to nuclear /3 decay. The striking feature of this process is that there are no nuclear effects entering the calculation of the irft decay. This offers a great theoretical advantage as we shall see in the next section. Figure 2: First order diagram responsible for ir/3 decay; note the similarity to Figure l b . 1.2 Theory of Pion Beta Decay 1.2.1 Pion Beta Decay in the Standard Model As was mentioned above, 7r/5 decay offers a rather unique way of testing our theoretical models. Being fundamentally dependent on the C V C hypothesis, it has already been used to verify and refine that part of the theory. It has a great potential for helping in the determination of the Vuct element of the Cabibbo-Kobayashi-Maskawa ( C K M ) matrix, thus yielding important information on the unitarity of the C K M matrix and on the existence of a fourth generation of quarks. Let us summarize how this comes about in the Standard Model. The C K M matrix relates the quark weak eigenstates, denoted as {d! s' b'}, to their mass eigenstates {d s b}. By convention, the +2/3 charged quarks are not mixed. If the Standard Model is correct, this matrix should be unitary. TV W Chapter 1. Introduction 4 s' = 1 vud vus \ I d 3 V v J \ vtd Vu vtb ) \ b ) The unitarity requires the following condition to be fulfilled for the first row: \Vud\2 + \Vu,\2+\Vub\2 = l Each of the elements can in principle be obtained from weak decays of the relevant quarks[4]. So far, kaon and hyperon decay experiments have yielded |K»|2 = 0.0488 ± 0.0007 while other types of decays indicate that |Kb|2 = 0.00002 ± 0.00002. The value found for |Krf|2, through means that we will review below, is currently 0.9512 ± 0.0006. Clearly, the most important term constraining the unitarity of the first row of the C K M matrix is Vud. The overall uncertainty on the unitarity test is due to Vud and Vua. To evaluate Vud, it is of primary importance to select processes where only that element plays a role. We are looking for reactions where an up quark turns into a down quark, or vice-versa. Three such processes particularly deserve our attention[5]; Superallowed Fermi Transitions, Pion Beta Decay and Neutron Beta Decay (neutron lifetime). These are basically /3 decays occurring in different contexts; SFT's within nuclei (transitions between nuclei of configurations I(JP) = 1(0 +) in the usual Isospin, Spin and Parity notation), 7T/3 decay for pions and /? decay of free neutrons. The principle is simple; quark and lepton decays are essentially analogous, after a renormalization of the coupling constants due to mixing in the quark sector. Purely lep-tonic decays have a vector coupling strength expressed as while for similar reactions involving quarks (semi-leptonic processes), the coupling is given by Gv- There is univer-sality such that the two coupling constants are simply related through the Vud element Chapter 1. Introduction 5 of the C K M matrix 1 ; Comparison of purely leptonic decays of the muon, such as fi+ —• e + + ue + v^, with 0 decay will immediately yield information on Vud and hence on the unitarity of the C K M matrix. It should be mentioned that in order to get to the level of extracting a value for Vud, and therefore to obtain bounds on the unitarity of the C K M matrix, we have to first verify fully the C V C hypothesis. That level of measurement precision, including the relevant corrections, has to be achieved before anything significant can be said about the quark mixing. Hence, careful attention has to be given to many effects in evaluating the theoretical decay rates. Specifically, precise knowledge of radiative and isospin breaking corrections, nuclear size effects and the importance of other currents involved in the processes must be obtained. For this reason, reactions that require simpler corrections or fewer corrections are preferred in general. The conventional way of determining Vu<i so far has been through the study of SFTs, since only the vector current û^^d contributes to such processes[5]. While 7T/9 decay is analogous to SFT's in the sense that it is also a transition between two spin zero members of an isospin triplet and the same vector current is the sole contributor, the rate of 7r/3 decay (0(1O~8)) has so far proven to be too low to provide a conclusive test of C V C . Although Neutron Beta Decay appears relatively free of nuclear effects, it involves both vector and axial currents2, and therefore introduces complications which have to do with the Partially Conserved Axial Currents (PCAC) hypothesis. This makes the task of extracting information on the Vua element through this process quite difficult. 1 Formerly, this element was the cosine of the Cabibbo Angle. However, generalization to three families of quarks has led to the actual C K M matrix where Vutj is the generic term. 2 A s opposed to the other two processes, neutron j3 decay allows both Fermi and Gamow-Teller transitions. Chapter 1. Introduction 6 Pion Beta Decay becomes extremely interesting when one considers the ability to make predictions. Strictly in the C V C framework, we can take the ft value from ir0 decay to be equal to the ft value from pure Fermi nuclear (3 decay. The differences in radiative corrections can be included before establishing the correspondence. Although there remains some hadronic effects, the total absence of nuclear effects in the evaluation of x/3 decay allows us to make a precise calculation, in which the corrections are limited to radiative and p-w mixing. This latter correction arises from isospin violation due to the mass difference between the up and down quarks. It has been often noted that, for the above reasons, a precise measurement of 7T/3 decay offers a uniquely sensitive test of C V C and ultimately of the quantum loop level of the Standard Model. Our actual results, based on SFTs, provide valuable information. Nevertheless, important corrections due to nuclear structure effects[6] force us to question the quality of our knowledge of Vud- A clean measurement, free of nuclear effects, is needed. 1.2.2 Theoretical Predictions The C V C hypothesis allows for a fairly precise estimate of the irfi decay rate (see for instance [3, 7]). Recently, a lot of effort has been put into refining the calculation to include the radiative corrections[8] and isospin breaking[9], such that the actual prediction for the rate of Pion Beta Decay is:[10] R^fi = 0.39973 ± 0.00061s -1 The uncertainty, 0.15%, appears mostly because of some experimental parameters in the calculation. Those parameters are the ff* — 7r° mass difference as well as the pions and electron masses. Also contributing are the corrections mentioned above. Chapter 1. Introduction 7 In order to fully test this theoretical estimate, it is necessary to perform a measure-ment at the 0.2% level or better. We will examine very shortly to what extent this prediction has been tested experimentally. 1.3 Basic Kinematics The 7r/3 reaction, ir+ —• ir° + ue + e + , is a fairly simple problem to treat kinematically. We will give the main features in the 7r+ rest frame and leave discussions of specific reference frames for the relevant sub-sections. From the 7r+ — 7r° mass difference, only 4.5937(±0.0005) MeV is available for the decay products[4]. The positron takes 0.511 MeV for its rest mass, leaving a maximum of about 4.1 MeV for the kinetic energies of the 7r°, e + and ve. In the centre of mass frame, the neutral pion recoils with an average momentum of 54 keV/c (with a maximum of 75.1 keV/c; see [11] for details). The positron energy spectrum can be explicitly calculated from the V — A theory and three-body phase space, but the critical point here is that the kinetic energy cannot exceed 4.1 MeV. At first glance, 7r/3 decay would appear to be a difficult process to observe; the neu-trinos interact too weakly and the positrons have very low energies. Fortunately, the neutral pion's main decay modes compensate in terms of detectability; TT° —• 7 + 7 (98.798%) TT° —• 7 + e + + e~ (1.198%) The first channel offers a fantastic advantage for detection. The two photons have obviously opposed momenta in the ir° rest frame, the sum of the energies being equal to the rest mass of the neutral pion. In more practical terms, going back to the ir+ frame, the recoil will cause the photon energies to be contained in the 'box' spectrum Chapter 1. Introduction 8 ranging from 65.61 to 69.43 MeV. The angle between the two photons then differs from collinearity by at most 3.8 degrees. These properties represent an ideal basis on which to base the observation of ir/3 decay. Moreover, they offer a great potential for background rejection. 1.4 Previous Experiments During the last 30 years, many experiments have been performed to measure the rate of 7r/3 decay. They attained a level of accuracy which was previously deemed impossible because of the very low branching ratio for this process. However, the current results do not test the models to their limits. We will briefly review two major efforts in the determination of the T/3 decay rate. 1.4.1 Depommier et al. From the outset, and after a quick detour to measure the radiative pion decay[12] 7r —• evy, Depommier et al. made the first accurate measurement of the 7r/? branching ratio[ll]. Extensive details of that experiment, carried out in the 1960's, may be found in their paper; we will mention here only the essential features. Method Positive pions of momentum 77 M e V / c , created with the C E R N synchro-cyclotron, were stopped in an instrumented target. The target was made of scintillating plastic of cylin-drical shape, with a radius of 10 cm and a thickness of 6 cm. The final identification of tr/3 events was based on the observation of prompt coinci-dence between the two photons from ir° decay and the decay e + observed in the target following the 7r+ stopping signal, as well as on the decay products total energy. Chapter 1. Introduction 9 The photon detector consisted of lead-glass counters spanning a 4ÎT solid angle. Only the energies were measured. Their detector was designed to be fast enough to handle the beam rate while giving medium quality resolution (~ 28% full width at half maximum) on the energies. Results Depommier et al. reported a total of 411 ±20 events which, after background subtraction gave 332 ± 23 TTJ3 events. The branching ratio was calculated to be r = (i.ooiS:?o) x io~8 for a decay rate of R = ( O . S S t ^ ) * - 1 The uncertainty, roughly 8%, was mainly due to statistics; an amount equivalent to a total uncertainty of 7%. This accounted for both the signal counts and the subtraction of backgrounds. Only 1% of the total error was due to the efficiency of the detector and trigger. The observed backgrounds were caused by the other decay channels of the 7r +. Of all background events, 65% came from the decay chain: 7 r + — > fi + + V,,, fi + —• e + + up + ue + 7 where the radiative decay gamma is in coincidence with a Bremsstrahlung gamma from the positron (e + —» e + + 7 ) . The energies and spatial distributions can sometimes appear like a 7r/3 event. Most of the other background events came from radiative pion decay; 7 T + —> e + + ue + 7 where again the photons (including the one from Bremsstrahlung) can look like a good event. Chapter 1. Introduction 10 Background estimates were established from monitor events kept during the data taking, so that the relevant rates could be determined. We will come back to the significance of these results, in Section 1.4.3. 1.4.2 McFarlane et al. In the early 1980's, McFarlane et al. attempted to increase the precision of the experimen-tal 7T/3 branching ratio[13]. Using modern techniques and a specifically designed in-flight experiment, they reduced the uncertainty by half compared to the earlier measurement. Method This group pursued a radically different approach from previous experiments. Using a high energy beam of pions at L A M P F , they built a detector with the particular geometry necessary to observe 7T/3 decays in-flight. A pion beam of momentum 522.1 ± 0.8 M e V / c , with an intensity of 2 x 1 0 8 7 r a _ 1 was used. The neutral pions from 7r/3 decays had a mean total energy of about 523 MeV, and approximately the same momentum as the beam in the lab frame. This made the detection of ir° photons easier, since their energies were between 175 and 350 MeV. This also provided some advantages for background reduction 3. The neutral pions and the beam pions had essentially the same momentum in the laboratory frame. This constrained the 7T° decay photon directions so accurately that it became unnecessary to verify the coincidence between the 7T° photons and the ir/3 positron. The detector was composed of interspersed arrays of scintillators and converters, with blocks of lead-glass at the rear to collect the total energy of the particles entering the 3 T h i s energy of the pion beam permits the reduction of backgrounds from exotic sources, as it is still below the kaon production threshold and it also occurs at a conveniently low point of the charge exchange cross-section. Chapter 1. Introduction 11 detection region. Good spatial and energy resolution allowed them to reconstruct the location and energy of the decaying pions, and thus to verify the identity of the responsible process. More details of this experimental setup can be found in [13]. Results McFarlane et al. reported a decay rate R = (0.394 ±0 .015>- 1 from the observation of 1223.9 ± 36.2 7r/3 events. This yields a branching ratio of T = (1.026 ±0.039) x 1 0 - 8 Of the 3.8% total uncertainty, only the equivalent of 1% was caused by detection efficiency. Background subtraction accounted only for the equivalent of 0.1% while the rest of the error was due to statistics on the number of observed events. For this experiment, the main source of background was the combination of radiative pion decay in coincidence with a Bremsstrahlung photon from the positron. Care was taken to account for other sources as well as for the possible loss of 7Tj3 events due to Dalitz decays of the neutral pion (the second most important channel for 7T° disintegration). This experiment relied extensively on simulation to establish the background event predictions. Let us now summarize the knowledge acquired through these experiments. Chapter 1. Introduction 12 1.4.3 Summary Based mainly on the results from the two experiments that we have just reviewed, the Particle Data Group lists the following value for the Pion Beta Decay branching ratio[4]: T = (1.025 ±0.034) x 10~8 or a rate of R = (0.394 ± 0.013)*-1 When this rate is compared with the most recent (corrected) C V C calculation, R = (0.39973 ± O.OOOôlJs-1, a good agreement is seen between experiment and theory. A l -though this is an important observation, the full extent of the theoretical prediction is still not being tested. The experimental error is still 3.4% while the theoretical estimate states a precision of 0.15%. From this result,4 G. Lopez Castro calculates[5]; IKdL = 0.968 ±0.016 This estimate has an uncertainty of roughly 1.7%, which is still an order of magnitude less precise than values obtained from Superallowed Fermi Transition experiments. This is mostly due to the fact that the TT/3 decay rate is not known to better than 3.3%. It is clear that in order to fully test the C V C hypothesis and the relevant correction factors, a great deal of improvement still has to be made in the experimental precision of the 7T/3 decay rate. If we want to push even further and use Pion Beta Decay to assess the unitarity of the C K M matrix, a level of precision of at least 0.2% on the TT/9 decay branching ratio must be achieved. 4 The calculation also uses more up to date information on the pion masses and other decay rates. Chapter 1. Introduction 13 1.5 Next Generation of Experiments A new experiment has recently been approved at the Paul-Scherrer-Institut (PSI). This collaboration[10, 14, 15, 16] will try to bring the uncertainty on the decay rate to the 0.5% level in the first phase of the measurement, and possibly to 0.2% ultimately. They expect the experiment to run for about five months of beam time. The experiment will stop pions of momentum 100 M e V / c in an active target sur-rounded by a fast shower calorimeter made of Csl crystal blocks in a near-spherical geometry. A multi-wire proportional chamber and fast veto counters will be inserted between the target and the calorimeter. The rate will be kept to about 106 7 r + / s S O as not to saturate their detector. To identify the TT/3 events, the observation of two photons (from 7r° decay) in proper coincidence with a pion stopping in the target will be sufficient, given the energy reso-lution of their counters. The sectioning of the calorimeter along with the proportional chamber will give further information on the spatial distribution of the photons, though a full angular reconstruction will not be performed. Special care will be taken to avoid accidental coincidence due to pile-ups in the target. Some of the aspects treated by the collaboration responsible for this new experiment will surface again later in this thesis; their concerns being very similar to the ones this study will address. 1.6 Purpose of this Thesis Having now attained a good understanding of the theoretical importance and the ac-tual status of 7r/3 decay, we shall investigate the possibility of performing a significant measurement of ir/3 decay using the R M C Spectrometer at T R I U M F . To be significant, such a measurement should test fully the theory, to the extent of Chapter 1. Introduction 14 setting bounds on the unitarity of the C K M matrix through an evaluation of the Vud element. The detector currently used for Radiative Muon Capture experiments reconstructs photons with good energy and angular resolution, and therefore represents an asset for the detection of neutral pions. We shall assess with what precision, and in what timeframe, a measurement of 7r/3 decay might be achieved using the present R M C pair-spectrometer. Modifications to the R M C setup could be proposed if the need can be clearly demonstrated. The following chapters will describe the main features of the apparatus, the simulation package used for the study, the processes pertaining directly to the experiment, the parameters on which we based our analysis, the results of this analysis and finally the conclusions and suggestions for further studies on this topic. Chapter 2 The R M C Spectrometer Before tackling the subject of Pion Beta Decay and its related processes, a few comments should be made about the experimental setup used for this study. Several Radiative Muon Capture (RMC) experiments have been carried out at T R I U M F over the last few years[17]. Recently (1989), a new detector specifically designed to measure the R M C signal on the proton[18] was commissioned at T R I U M F . This pair-spectrometer will be described briefly here, since it is an excellent candidate for the detection of photons stemming from neutral pions in 7r/3 decay. The detector components assumed in this study of Pion Beta Decay are the same as those used in the R M C spectrometer. 2.1 Design Requirements The R M C signature is straightforward; a gamma ray of energy ranging from 0 to 100 MeV is emitted when a muon is radiatively captured by the target nucleus or proton. The clean measurement of a single R M C photon in the energy range of 56 to 100 MeV, along with criteria for supression of backgrounds from muon decays and Ordinary Muon Capture (high energy neutrons), dictated the design of this detector. The requirements are met by a large-solid-angle (~ 37r) photon pair-spectrometer and by the implementation of a sophisticated trigger to identify the conversion pairs (e+e~). Tracking algorithms and cuts on the geometry of the conversion pairs are found sufficient to reject almost all backgrounds. 15 Chapter 2. The RMC Spectrometer 16 The detector is calibrated with photons from 7T +p 7T° • 7 + 7 and 7T +p 7 + n (see [18] for more details). As noted in [18], the spectrometer is capable of measuring photon energies between 30 and 400 MeV with suitable changes in the magnetic field. Preliminary studies indicate that photons from x° decays can be reconstructed with a total energy resolution of 5.4%. However, from those same early analyses, the acceptance for two-photon events is much lower (~ 0.01%) than it could be in a carefully designed study. 2.2 The Detector The R M C spectrometer is shown in Figure 2. The beam is stopped in the target at the center of the spectrometer. Between the target and the inner radius of the tracking drift chamber are three layers of azimuthally segmented scintillation counters used to veto charged particles coming from the target, a lead photon converter, one layer of azimuthally segmented scintillation counters which trigger on (e+e~) conversion pairs from the lead, and a thin cylindrical inner wire proportional chamber (IWC) which is situated just inside the inner radius of the drift chamber. Outside the drift chamber is an outer set of azimuthally segmented trigger scintillation counters. A l l of these elements are enclosed within a magnet providing a uniform axial magnetic field for momenta analysis. The decision to include an IWC in the spectrometer was based on the need to minimize the high- and low-energy tails of the spectrometer response function. These tails arise from uncertainties in the radial projection resolution. The high energy tail is of particular Chapter 2. The RMC Spectrometer 17 Figure 3: Schematic of the pair-spectrometer currently used for Radiative Muon Capture at T R I U M F . concern since it can increase the apparent energy of photons from the very prolific lower energy backgrounds from radiative muon decay. The inner wire chamber is a dual-coordinate multiwire proportional chamber. It consists of structural cylinders supporting axial anode wires and cathode strips. The strips of the outer cathode layer form an angle of +45 deg with respect to the anode wire while those of the inner cathode layer are inclined at —45 deg. Charged particles passing through the chamber induce pulses on the two cathode planes as well as on the anode wires. The large volume drift chamber is the principal device of the R M C spectrometer. It consists of four superlayers of sense-wire drift cells. Chapter 2. The RMC Spectrometer 18 The sense wires are staggered alternately right and left of the cell midplane, by 250//m, to provide local resolution of the right/left drift ambiguity. Each cell has eight sense wires, the outer two of which are not currently instrumented. Each of the six central wires are read out independently. The wires of superlayers 1, 2 and 4 are axial and provide x and y track coordinates. The wires of superlayer 3 are at a stereo angle of 7.0 degrees with respect to the drift chamber axis in order to provide a z-coordinate. A typical track in the chamber will thus generate 18 xy hits and 6 z hits. The primary trigger definition for valid R M C events in the drift chamber is derived from five cylindrical layers of scintillation counters which select e+e~ pairs from pho-ton conversion and reject charged particles originating in the target. Each counter is independently read out at one end by a light guide and photomultiplier. The three innermost layers veto charged particles produced inside the radius of the lead converter. The first two layers (A and A' ) each have four-fold azimuthal segmen-tation with one layer rotated 45deg with respect to the other one in order to cover the seams between the counter segments. The third layer (B) has twelve segments. The converter is a cylindrical sheet of lead, 1.08 mm thick, sandwiched between the B and C layers of scintillation counters. This latter layer, which is also twelve-fold segmented, identifies charged particles produced in the converter before they enter the inner wire chamber. The outermost layer of counters (D) identifies charged particles exiting the outer cir-cumference of the drift chamber. The D layer has sixteen-fold azimuthal segmentation. Along with the C layer, the D counters provide a fast geometrical hit pattern character-istic of e+e~ pairs. The performance and characteristics of this photon spectrometer will be exploited throughout this study. Chapter 3 Signal and Backgrounds The process of Pion Beta Decay offers some unique properties for experimental observa-tion. However, its low branching ratio renders it difficult to measure with good accuracy. At the level of the TT/3 experimental signal, many processes1 which would otherwise be considered negligible become extremely important. This fact greatly increases the com-plexity of performing such an experiment. This chapter will describe in detail the features of our signal, why background pro-cesses occur in this experiment, and also how the expected rates of signal and backgrounds can be estimated. 3.1 Signal As was briefly discussed in Chapter 1, the kinematics of are fairly simple. For the purpose of this study, we chose to adopt the 'stopped pion' approach. This will allow us to concentrate on the anti-collinearity property for the ir° photons, as well as the particu-larly good resolution of the R M C spectrometer for individual photons. Furthermore, for stopped pions with the two photons at almost 180 degrees, the acceptance of the detector is also as high as possible for a two photon event. The signal, 7r/3 decay events, will therefore consist of two coincident photons (from 7T° decay) within a predefined decay window delayed by a certain time from the ir+ 1 Decays of pions and muons, random occurrences of rare combinations of strong, weak and electro-magnetic processes as we shall see in later sections. 19 Chapter 3. Signal and Backgrounds 20 stopping in the target. The delay is required to reject strong interaction events which are in prompt coincidence with the pion stop. The decay window must be long enough to maximize the probability of seeing a decay, yet short enough to account for successive beam pulses. The precise timing of the pion stop in comparison to the beam rate will be discussed in Section 3.4. The two photons are the basis for the detection; they have practically the same energy, which is within the box spectrum [65.61,69.43] MeV, and deviate from collinearity by no more than 3 degrees. Therefore, the signature we propose to look for is mainly made of the following "high level cuts": • the energies of individual photons (J5 7 l , El2 ), • the photon-photon angle (# 7 l 7 2), • the energy sum of two photons (.E7 l + Ey2) and • the total (reconstructed) energy of the neutral pion (£v>). With such specific requirements, added to stringent tracking cuts, we do not foresee the need to observe the 7r/3 positron. Section 3.3 will address the question of the Pion Beta Decay rate evaluation in the proposed detector. For now, we will assess what could be the principal processes respon-sible for background events. 3.2 Backgrounds For this experiment, any other process which gives two photons in very close coincidence (a scintillator trigger timing of 5ns) is considered a background. Specifically, the photons have to be physically well separated in the detector as well as energetic enough to fulfill Chapter 3. Signal and Backgrounds 21 the trigger requirement of 2C-2D, i.e., two hits in the C counters and two hits in the D counters. A certain number of processes, combined appropriately under the right conditions, can yield 7r/3-like events. Since no other reaction has the same signature as Pion Beta Decay, the photons will invariably come from the coincidence of two independent reactions such as; • radiative decay of a pion (7r+ —• fi+i/tf), • radiative decay of a muon —» e+uei>tif), • 'hard' Bremsstrahlung of a positron. Obviously, the photons created by these weak and electromagnetic interactions must have sufficient energies. This means that, at most, only a small part of each reaction's spectrum can give the right kind of photon; thus the specified requirement for a Bremsstrahlung to yield a high-energy photon. The major way we can have background reactions displaying the proper photon char-acteristics is to have two particles stop in the target and then decay within the same decay window. This is what we call a 'pile-up' mode event. In fact, we expect most of our back-grounds to arise because of such occurrences, although some important backgrounds can also be caused by single mode events. Before going into more details of the rate evaluations, Table 1 gives a qualitative assessment of the expected ir/3 backgrounds. The ordering of the backgrounds in Table 1 is not necessarily indicative of their importance. Table 1 : Table of all expected background processes for a two-photon signal from Pion Beta Decay. Shown here are the primary and secondary reactions, the maximum mo-mentum possible for any of the decay products (usually positron or photon), the mode (single or pile-up) as well as the number assigned to each process as a label for subsequent reference. The primary reactions involve particles that stopped in the target while the secondary reactions are processes which can occur to any of the products of the initial decay reactions. Chapter 3. Signal and Backgrounds Chapter 3. Signal and Backgrounds 23 Other processes, such as i r + —> fi + + + 7, were not even generated since the kinematical endpoint of the reaction (the energy of the photon) is much too low to be a problem. Moreover, essentially all events of this type are expected to fire the veto counters, either directly or after the decay of the muon. 3.3 Relative Rates It was decided early on that the yields of all backgrounds should be evaluated in a unique and systematic manner, after thorough analysis of the Monte Carlo data. Therefore, no preliminary estimate of rates has been made. But in order to perform the simulation and to prepare for the analysis, expressions for the relative yields of signal and backgrounds had to be worked out. Table 2 gives the expressions for the rate of each process, relative to a single beam particle stopping in the target. Details on the factors involved in the expressions will be given below. For practical reasons, as well as to reflect the reality of the techniques used in this study, the factors entering the expressions shown in Table 2 have been divided into three categories; the analytical factors, the simulation factors and the analysis factor. Each category is the subject of more discussions in the following sub-sections. 3.3.1 Analytical Factors This first category of factors is comprised of the decay branching ratios of all primary reactions for the signal and the backgrounds, including the neutral pion decay branching ratio, as well as the decay probabilities for the first and the second (pile-up) particles in the target. Chapter 3. Signal and Backgrounds Table 2: Expressions giving the relative importance of each process, compared to a single pion stopping in the target. Refer to the text for details. Chapter 3. Signal and Backgrounds 25 The branching ratios are absolute factors known from experimental measurements of pion and muon decays. They are taken from the Particle Data Group's compilation^], and have the values listed in Table 3. Decay Branching Ratio (T) 7 T + • 7T° + e + + Ve 1.025 x 10" 8 7T° — • 7 + 7 0.98798 7 T + —• e + + ve 1.218 x 10" 4 7T+ — > e+ + ve + 7 5.6 x 10- 8 (Ee+ > 56MeV) fi+ — > e+ + ue + 0.986 (i+ —> e + + ve 4- up + 7 0.014 ( £ 7 > lOMeV) Table 3: List of the pion and muon main decay mode branching ratios. Included here are all those channels that are expected to play a role in the study of Pion Beta Decay. The fourth entry, the Radiative Pion Decay branching ratio, is a partial value only for total positron energies greater than 56 MeV. The Radiative Muon Decay branching ratio, the last entry, is also a partial value for photon energies greater than 10 MeV. Although the branching ratios have been included in the Monte Carlo program, they are not used when the events are generated. Instead, as will be explained in the next chapter, we force the interactions to proceed in the desired channels and simply keep the branching ratios as factors in the global event probability or weight2. Such 'forcing' of the reactions is done to improve the statistical accuracy of the Monte Carlo simulation. Then those factors are extracted from Monte Carlo data banks at the analysis level; they are included here because they fall naturally into the logical category of analytical factors. The other types of analytical factors are the decay probabilities for pions and muons in the target. These depend on our choices for the duration of the time delay after a stop, the length of the decay window, the trigger coincidence time, and also on the expected 2 At the simulation stage, each event comes with an attached weight. The weight essentially gives the probability of observing such an event in reality, relative to a pion stopping in the target. Chapter 3. Signa.! and Backgrounds 26 stopping rates for pions and muons. A l l these factors can be varied at the analysis level, so only the analytical expressions are given here; typical values will be listed in Chapter 5. In the case of a single pion decay, the probability is be evaluated using where tt is the charged pion half-life (2.603 x 10" 8s [4]), and t0 and A T are the time delay and length of the decay window, respectively. To consider the decay of a second pion during a trigger coincidence initiated by a first pion, we have to include contributions from many possibilities. The second pion, or pile-up pion, could come from the same beam pulse ('bucket') as the pion responsible for the trigger coincidence, or even from previous beam buckets3. To evaluate each of the contributions, we need first to establish how many pions are present in a given beam bucket. To do this, we assume that the number of pions in a beam bucket follows a Poisson distribution with average where 7Vs is the pion stopping rate, (8 x 1 0 7 a - 1 is used as the initial estimate), and ts is the beam pulse time spacing or macro-structure which at T R I U M F is 43 nanoseconds. So we ask for any previous beam bucket to have at least one pion; P{> 0) = 1 - P(0) = 1 - er"stB For the contribution of the same beam pulse, we require that there should be at least two pions present; P (> 1) = P(> 0) - P ( l ) = 1 - er'stB - rrStBer*stB 3 It is easy to show that contributions from more than two buckets previous to the trigger coincidence are too small to be included. Chapter 3. Signal and Backgrounds 27 Now to evaluate the probabilities that pile-up pions will decay so as to form a good coincidence, we average by integrating over a specific decay window delayed from the stop by the following times: t0 for the current bucket, to + tB for the bucket immediately preceeding and t0 + 2tB for the second previous bucket. This average can be written as (for a to delay for instance) I ft0+AT JWrage(*0, A T ) = — jf PrD(t,At)dt which, in this case, yield; / a -^.n 7V / Al \ / _ AT \ _tQ_ Pavera9e(to, A T ) = — ( l - e ** J ( l - e ^ J C ** Identical expressions are obtained for the other delays, where the only difference consists in replacing to by the proper delay. Putting all these terms together, we obtain the expression that includes the contri-butions of the given beam bucket and the previous two buckets: / V D ( A M „ , A T ) = [ ^ ( l - « - " ) ( l - e - " ) e _ ~ ] [ l - e r - " « - r . s « e « ' " ' » ] i . (1 - . - * ) (1 - . - * ) e-^} [1 -+ + The decay probabilities for muons are very simple in this context. Given a typical pion beam contamination of 10% muons, the long muon lifetime and considering that almost all of the pions decay into muons, we see that there are muons constantly ready to decay inside the target. Therefore, we can evaluate the decay probabilities as a simple time coincidence average as follows; PtlD(t0,AT) = rtlSAT Chapter 3. Signal and Backgrounds 28 for a muon to initiate a trigger coincidence within the decay window, and P „ ' D ( A M O , A T ) = r „ 5 At for a second muon to decay within the trigger coincidence initiated either by a decaying pion or another muon. Note that the muon stopping rate, r^s is a function of the pion stopping rate; r^s = 1.1 X 7V5 since we estimate the beam contamination at 10% and practically all the pions give muons in the target. The decay probabilities we just described can all be varied at the time of the anal-ysis by changing the parameters <0> A T and TVS, to optimize the relative rates. Thus, numerical values will be given when we discuss the analysis (Chapter 5). 3.3.2 Simulation Factors In Table 2, all simulation factors have been synthesized in the terms A Detect.{^-t e i w * ) t which then represents the overall acceptance of the detector for process " i " . This ac-ceptance is a function of the solid angle fi, the efficiency of the detector e (trigger and electronics) and also a series of weights introduced during the Monte Carlo sampling of sub-processes. So this "detection acceptance" includes both detector-specific information as well as some information on the underlying physics of an event. The detection acceptance can be broken down into a number of terms which will take on different values for each generated event. Table 4 gives the expressions of simulation factors explicitly for each different signal and background processes simulated in this study. More details on the individual terms of Table 4 are given below. Chapter 3. Signal and Backgrounds Table 4: Expressions giving the factors introduced by the Monte Carlo simulation. Ex-planations for each factor are given in the text. Chapter 3. Signal and Backgrounds 30 The factor Psrem., Anni. represents the probability for a positron to yield a photon in the most energetic part of the Bremsstrahlung or annihilation spectra. Special sampling techniques require us to enter this factor in our expressions as a probability weight for the event. The methods used to obtain this weight and all other similar weights will be explained in the next chapter. The factor / 7('process') is another such weight. It is due to a special sampling (high energy part) of the photon spectrum of a 'process', which is essentially a radiative decay. Of the factors which appear invariably in all the expressions of Table 4, only Pconv.(Pb, C Scint.) contains an additional sampling weight. This extra weight represents the probability for a photon to convert into an e + e _ pair as it passes through the lead converter or one of the C scintillators, evaluated at 11% for the present R M C detector. Basically, both ^ and e are extracted from the total number of trials necessary to obtain the Monte Carlo data, for each different signal and background processes. The first term represents the geometrical acceptance of the detector for pair-producing photons, as a fraction of the total solid angle. The overall efficiency of the special trigger and of the electronics, as programmed in the simulation package4, is represented by e. Most of the sampling weights are evaluated during the simulation and written to a data bank. The information contained in this bank is then read during the analysis and combined with the analytical information. Weights vary greatly from one event to another, and there are substantial differences between the signal and the different backgrounds as we can readily see from the expressions. It is therefore impossible to give all factors numerically. Hence we simply extract and combine all the different simulation factors at the time of the analysis to obtain the total probability that a given event will occur. 4 A discussion of the software used for the simulation of processes relevant to Pion Beta Decay will be presented in Chapter 4. Chapter 3. Signal and Backgrounds 31 3.3.3 Analysis Factor The final factor appearing in Table 2, PCVT represents the probability that a particular event will not be rejected by the tracking and Pion Beta Decay-specific cuts. This factor is evaluated and included during the analysis, when we determine the combined efficiency of our chosen set of cuts. 3.4 Absolute Rates What we have described so far only allows us to obtain relative rates, i.e. probabilities for a particular pion stop to yield a specific type of event. To evaluate the absolute rates, in terms of beam time, we need to include additional factors: R(i) = Rr(i) x TVs x fDW x T)live for process V (signal or background) where R(i) is the absolute rate of this particular process per second of beam. The factor fjjw is the fraction of useful decay windows, which depends on the beam rate, our pile-up incidence requirement as well as on the allowable total rate of events in the tracking chambers and trigger/veto scintillators. The last term in the expression, 7)nve, is the experimental live-time, determined by the data acquisition electronics, computer hardware and software. These factors all need to be adjusted in order to evaluate the feasibility of a mea-surement. They will be discussed more thoroughly and their values will be calculated in Chapter 5. For now, we will direct our attention to the Monte Carlo simulation package used for this study and to the method implemented to obtain a data sample. Chapter 4 Simulation We will now discuss the Monte Carlo simulation program used for this study. Because of the nature of the expected background processes, extensive modifications to the existing R M C simulation program were required to obtain a satisfactory simulation. 4.1 Monte Carlo Package 4.1.1 Generalities of Monte Carlo Simulations A Monte Carlo method is essentially a means of integrating functions over all possible paths by randomly selecting a large number of them. The number of selected paths determines the accuracy of the result. The method can be applied to many different processes. In the present context, a Monte Carlo simulation performs the integral of a detector response function, or of detector acceptance, over all possible types of events, by randomly choosing a large sample of possibilities. The expected rates for the signal and background processes in most Particle Physics experiments are influenced by the geometrical acceptance of the apparatus, the finite resolution of the various counters and by the detailed physics of particle propagation in the setup1. This influence is too complicated to be folded into the theoretical spectrum analytically. Therefore, one often resorts to the technique of Monte Carlo simulation to 1 For instance; decays, annihilations, Bremsstrahlung, pair-productions, energy loss in matter, multi-ple scattering, etc. 32 Chapter 4. Simulation 33 simulate the response of the apparatus. 4.1.2 G E A N T A Monte Carlo program was written to fully test and understand the R M C pair-spectro-meter. It is based on G E A N T 3 , a general Monte Carlo simulation program developed at C E R N for high energy physics experiments. G E A N T is meant to help with the design and optimization of detectors, to develop and test the reconstruction and analysis programs and to interpret the experimental data (see [19]). To achieve this, it allows physicists to describe an experimental setup by volumes and materials, to indicate the presence of electric or magnetic fields, to generate simulated events from standard generators, to simulate all possible interactions and physical effects of the particles and to record the elements of the particle trajectories and the response from the sensitive detector. Such a Monte Carlo package is still very general. As noted above, the user has to provide all the information relevant to the particular simulation. Moreover, the way the simulation information is to be translated (digitized) into a format that can be analyzed like 'real' data also has to be specified by the user. The user is responsible for controlling the flow of the program. After initialization of the simulation conditions, G E A N T proceeds to generate a user-specified number of events. For each event, an initial reaction is sampled, and particles stemming from this initial process are tracked one by one through the experimental setup. Possible interactions of these particles are taken into consideration during propagation, in a way that accounts for all known properties of the particles and the materials they traverse2. After all particles forming an event have been processed, information stored by the user 2 New particles may be created as the result of such interactions; they are in turn tracked as part of the same event. Chapter 4. Simulation 34 along the trajectories may be digitized. This last step requires a detailed knowledge of detector properties such as inefficiencies and electronic noise. The complete event is then written out, in a format completely analogous to the real data, and a new event may be sampled. 4.1.3 R M C G E A N T The R M C G E A N T program, developed using the G E A N T framework, reproduces nearly all aspects of the R M C pair-spectrometer; its geometry, resolution in position, momentum and energy, as well as the specific kinematical processes relevant to Radiative Muon Capture. This program has been used extensively already. As noted in [18], the Monte Carlo simulations agree well enough with the experimental data that they may be used to predict the spectrometer performance under a broader range of conditions. Assuming that proper care is taken in modifying the relevant aspects of the Monte Carlo, this package becomes an ideal tool for studying the feasibility of future experiments. 4.2 Modifications for Pion Beta Decay In order to perform a study of Pion Beta Decay in the R M C facility, several modifications had to be made to the R M C G E A N T program. The initial kinematics had to be changed completely for the new processes under scrutiny, while other changes to the basic R M -C G E A N T program were required simply to reduce the time necessary for the computer simulation. The following items of the R M C G E A N T Monte Carlo were modified for this study: • particle definitions and decay channels, • 'forced' or enhanced cross-sections for particle interactions in the detector, Chapter 4. Simulation 35 • 'double-loop' tracking for 'pile-up' events, • trigger requirements. Explanations for each modification will be given below. 4.2.1 Particle Definitions and Decay Channels G E A N T comes with a data bank of particles, each defined by its mass, charge, half-life and a set of numbers used for identification and decay mode definition. It also allows for 'user-defined' particles so that other processes in which the user might be more interested can be studied. A l l decay channels are not included in the original G E A N T data bank; only the main (large branching ratios) processes are present. Thus, for this specific application, we had to explicitly define the decays which constitute the main features of a 7r/3 experiment. For that purpose, it proved better to define a set of new particles, each with a unique decay mode, so that we could streamline the reactions in an efficient manner. Special muons and pions were denned and given the usual decay channels, plus all processes up to the order of the Pion Beta Decay branching ratio. The kinematics of some of the decay channels thus included had to be generated outside the normal G E A N T routines. The R M C experiment had already necessitated the precise simulation, beyond the phase-space generators included in G E A N T , of / i + —• e+t/eù~n and fi + — • e +veù~fi'y. We had to write an adequate generator for 7 T + —• e+i>e7 based on cross-section calculations by Bryman et al.[20] 4.2.2 Forced Cross-Sections The interactions that occur while particles travel through the detector, e.g. Bremsstrah-lung, annihilation, and pair-production, were simulated with increased probability in the Chapter 4. Simulation 36 Monte Carlo. This was necessary to reduce the amount of computer time needed to obtain processes of the order 1 0 - 8 and lower for most backgrounds events. Specifics of the locations and energies of the processes were modelled amd sampled proportionally to the known cross-sections and media properties. Studies conducted for the R M C experiment provided information on the probabil-ities for Bremsstrahlung of a certain energy to occur in the various component of the detector through which positrons travel. In our 7r/3 Monte Carlo, we required that any Bremsstrahlung yield a photon of at least 80% of the positron energy. We then weighted the events by a factor < T ( r u e / (T a a r n p i e d where <rtrue is the true cross-section for the process, which depends on the surrounding media, and <rsampiec[ is the cross-section which was used for the sampling. The pair-production probability for any photon that reaches the lead converter-C scintillator package was forced to be 100%. The normal probability for a particular photon, as stated in chapter 3, is 11%, and therefore we have another weight for all two-photon events; 0.112 = 0.0121. Although we do not expect many events to arise from the coincidence of positron an-nihilation with other processes, we nevertheless increased the probability of annihilation by a factor of 10. Hence, we have another weight of 0.1 whenever an annihilation yields a "useful" photon. A l l weights, integral parts of the global probabilities of each event, were recorded in a special data bank to be extracted at the time of analysis. 4.2.3 'Double-Loop' Tracking The G E A N T program does not allow for simultaneous tracking of many particles stop-ping in a target. Since an important part of the background is expected to come from coincidences of multiple particle decays within a decay window, it was necessary to change Chapter 4. Simulation 37 the way the tracking of particles in the detector was done by G E A N T . Events were re-defined, to include 'pile-up' modes, so that G E A N T could proceed with the tracking the way it normally does while actually 'looping' fully over two initial particles as part of a same event. As explained in chapter 3, the probabilities of such pile-ups actually arising in an experiment will be evaluated as part of the analysis. 4.2.4 Trigger Requirements Finally, the basic trigger pattern had to be changed to optimize the yield of 7r° events from 7r/3. The RMC-specific trigger routine, which looks for the coincidence of at least one C and one D counter3 to define a candidate photon event, was modified so that it identifies two photon events through a 2C-2D coincidence requirement4. Other parts of the R M C G E A N T program remained unchanged. Ideally, pions are stopped in a plastic scintillator for the purpose of a Pion Beta Decay experiment. How-ever, in the framework of a first investigation into the feasibility of such an experiment inside the R M C spectrometer, it was felt sufficient to keep the existing liquid hydrogen target. The reason for this is simple; the most important target information pertaining to this study, the stopping distribution of pions, is very well known experimentally for this target. 4.3 Simulation of Signal and Backgrounds The simulation of 7r/3 and its related processes, the signal and the possible backgrounds, proved to be extremely time consuming. Some processes took literally months of com-puter time to produce statistically reasonable data sets. The machines used for this study 3 T h i s allows for one of the charged tracks in the drift chamber to be wrapped around; i.e. not exiting the chamber. Further analysis specifies the minimum curvature radius allowed for such a track while maintaining a reasonable resolution. 4 T h i s in turn allows for a maximum of two 'wraparound' tracks per neutral pion detected. Chapter 4. Simulation 38 were DECstations 2100, 3100 and 5000. Most of the simulation was performed on the 3100 model (16.7 M H z , 14 MIPS, 1.6 Mflops). We aimed at getting good statistics on the signal, since it is the main feature to decide whether the yield of TT/3 in the R M C detector would be sufficient to justify an experiment. The diverse backgrounds were generated so that rates, energies and geometrical properties in the detector could be assessed. Unfortunately, because of the sheer time demand of some of the backgrounds, it was impossible to obtain very good statistics in all cases. After the special treatment given to interactions in the detector, only the overall (weighted) rates remain significant. Spectral shapes are sometimes distorted because of the increased weight given to processes that occur without the need of 'forced' interac-tions. There are basically three points on which we concentrated for the simulation: • We generated a data sample of the signal without forced processes to obtain a fundamental evaluation of the rate. • Data samples of signal and backgrounds were generated separately with all forced interactions to produce relatively good statistics of "signal to background" ratio. • To enhance the interactions, we used the same increases in cross-section system-atically throughout the simulation, for all backgrounds. This ensured our under-standing of the simulation results. To verify that the generation was proceeding correctly, a set of histograms from the G E A N T program were scrutinized. They give indications of the types of processes responsible for the Monte Carlo event generated, the media where particular interactions occurred during tracking, the initial energies of the converted photons and other relevant information. A sample of those histograms is shown for the TT/3 signal (see Figure 4). Chapter 4. Simulation 39 ^ 12 + 0 20 40 60 80 Energy of pair-producing photon in MeV 100 Figure 4: Monte Carlo histogram for the simulated TT/3 signal. Shown here is the his-togram of pre-conversion photons; the peak on the right is the 7T° photon 'box' while the rest of the signal is due to Bremsstrahlung, annihilation and other 'random' photons. The simulation of the signal and associated backgrounds was an important step in this study. The information contained in the various G E A N T simulated data sets had to be analyzed thoroughly by the same analysis package which would be used to determine the signal and background for real data. This analysis yields the final rates and probabilities for each process as they would be observed in an experiment. Chapter 5 Analysis and Results We will now summarize how the analysis was performed and present the various results obtained. 5.1 Analysis Software The software used for the Monte Carlo data analysis is based on R M C O F I A (Radiative Muon Capture OFfline Interactive Analysis), which was written to analyze the data taken with the R M C detector facility[21]. The program performs essentially three functions; • it constructs graphical representations of the detector information banks for each event, • it stores, and presents in histogram form, the primary physical quantities calculated from the hit patterns in the detector and • it allows the user to apply specific offline analysis cuts on any stored or calculated quantity. Track reconstruction starts with the recognition of good drift chamber points and their connection into vectors. These are then linked to form arcs in the XY plane (per-pendicular to the direction of the beam). The program determines the center and radius of each circle thus defined, and uses information from the proportional chamber and the drift chamber stereo layer to obtain a momentum vector on the Z axis. These parameters 40 Chapter 5. Analysis and Results 41 are finally fitted to a helical curve; the knowledge of the solenoidal magnetic field allows us to extract values from the momentum components (p±,pz) of each trajectory. This analysis is done for each charged particle tracked in the spectrometer. These are then paired (a positron with an electron) to give a converted photon. Hence the program is able to reconstruct the direction and momentum of each photon which in turn allows us to trace back to the origin of two-photon events in the detector volume. This latter part of the analysis was introduced specifically for the reconstruction of 7r° events and uses simple geometrical and kinematical calculations to evaluate the opening angle between the photons as well as the pion's total energy. 5.2 General Tracking Analysis As described above, most of the tracking, or event reconstruction, is fairly general. We will briefly describe the parameters used for the basic analysis and how they influence the observed rates and physical properties of events in the detector. 5.2.1 Basic Tracking parameters During the initial stage of the analysis, we observe the distributions of each of the param-eters listed below, for both signal and background events. We then proceed to implement a set of loose tracking cuts on these parameters as listed below. This basic set of cuts is simply meant to eliminate poorly defined events in terms of tracking and geometry; it has practically no effect on the overall acceptance or rate of good events, but it may be sufficient to eliminate some of the backgrounds. • Maximum X Y distance at the Converter; 6 cm • Maximum Z distance at the Converter; 15 cm Chapter 5. Analysis and Results 42 • Maximum e+e~ pair opening angle; 50 degrees • Minimum, maximum Z at closest approach to target center; —10, 10 cm • Minimum number of points in electron or positron track; 10 • Maximum Chi-square for electron's or positron's X Y track; 0.01 • Maximum Chi-square for electron's or positron's Z track; 0.2 • Minimum curvature radius for wrap-around tracks; 45 cm • Minimum, maximum number of OR boards fired; 10, 40 • Minimum, maximum number of drift chamber wires fired; 80, 160 • Minimum, maximum number of drift chamber cells fired; 15, 45 • Maximum number of IWC hits; 20 A second set of cuts is also applied on the TT/3 specific information calculated by the analysis program. These other cuts, listed hereafter, do not affect the signal rate either; they are simply for primary background reduction. • Minimum, maximum ir° reconstructed total energy (E^); 50, 250 MeV • Minimum photon-photon angle (# 7 l 7 2); 90 degrees • Minimum, maximum photon energy sum (E7l + Ey,); 50, 250 MeV • Minimum, maximum individual photon energy (Eyi and E^); 25, 80 MeV After this stage, the signal is very clear and well defined. Figure 5 shows the four pertinent histograms for TT/3 events after the basic analysis. In the rest of the analysis, we will concentrate on cuts specific to the parameters illustrated in these histograms. Chapter 5. Analysis and Results 43 50 60 70 80 90 Individual photon energies in MeV 50 100 150 200 Photon—photon angle in degrees Energy sum of photon pairs in MeV 250 100 120 140 160 180 Reconstructed neutral pion total energy in MeV Figure 5: Energy and geometry information on Pion Beta Decay events after the basic set of tracking cuts given in the text. Only poorly denned events have been discarded from the data at this stage of the analysis. 5.2.2 Stopping Rates and Decay Window parameters Because most of our expected backgrounds are due to pile-up events, the time structure of the beam and the rate used in the experiment affect the specific probabilities for the different processes. As we saw in chapter 3, we want to have the longest possible decay window, to increase the occurrance of 'good' pion decays, while we want to keep the pile-up probability within a range that allows the extraction of the signal from the backgrounds. Since the level of the signal is expected to be low (less than 1 0 - 8 7r/3 events /TT+ once the detector's response has been accounted for), we aim for the Chapter 5. Analysis and Results 44 maximum beam rate available and the most efficient time structure. Only the basic 43 ns beam macro-structure, at a rate of 2.6 x 108 ff+/s, suits our needs. It is possible to get a beam rate of up to 5.3 x 107 ir+/s with a 217 ns time structure, and thus increase the pion decay probability during each decay window. However, this reduces the experimental event rate considerably and also seems an unnecessary measure because of our ability to reject pile-up events through analysis, as we shall see in the sections below 1. Hence, the values we will use for the study are as follows: • Stopping Rate, TVs; 2.6 x 108 ir+/s • Beam macro-structure, 43 ns • Decay window length, A T ; 38 ns • Decay window delay, to', 5 ns 5.2.3 Initial Rate Estimates After the initial photon analysis, which uses the parameters described in the previous two sections, we can assess the initial rate for the signal, with respect to a beam particle stopping in the target, as well as the relative importance of each type of background process compared to a irfi event. We will give the information consistently in this fashion throughout this chapter and the next, since it provides us with what we need at a glance: the expected level of signal observed and the fraction of observed events which might be caused by backgrounds during an experiment. Table 5 summarizes the initial rate estimates. x N o attempt will yet be made to deal with problems which arise from the chosen high beam rate; a more complete discussion of this can be found in chapter 6. Chapter 5. Analysis and Results Table 5: Initial rate estimates for Pion Beta Decay. The rate for the 7r/9 signal is given per beam particle stopping in the target while all identified backgrounds are given relative to the occurrance of a izfi event. The parameters used for this first analysis are detailed in Sections 5.2.1 and 5.2.2. Chapter 5. Analysis and Results 46 From Table 5 we notice that some backgrounds can already be considered negligible while others are of the order of the expected signal, or even greater. For the rest of the analysis, we choose to try to eliminate the backgrounds which appear at the level of 1 0 - 5 or greater compared to the signal. The reason for this is simple; an ideal measurement, at a precision of 0.2%, would require approximately 106 7r/? events. Hence, only events which have a relative importance greater than a few parts in a million would become significant for such a measurement. Therefore, the following sections will concentrate on reducing the level of backgrounds 5, 6, 7, 8 and 11, by applying further cuts on the data. These backgrounds will be referred to hereafter as 'problematic'. Other signal simulations were made with different magnetic fields to evaluate the acceptance of the detector. Decreasing the field from 2.4 kGauss (value set for R M C experiments) to as low as 1.5 kGauss increases the initial rate to 2.69 x 1 0 - 1 2 TT(3/TT+. This represents a factor of three gain on the rate, without a dramatic loss in energy resolution or variation of the backgrounds. 5.3 Pion Beta Decay Analysis The purpose of the following analyses is to devise a scheme which offers the best features for background rejection while maximizing the 'signal to noise' ratio. 5.3.1 Single Photon Energy Cuts The primary quantity on which we can rely for background reduction in a 7r/3 experiment is the energy of the individual photons. Because the 7r/? signal gives two photons of about 67 MeV each while some of the pile-up modes involve a muon decay (endpoint at 53 MeV), we expect this type of energy cut to be particularly efficient in the rejection of backgrounds due to muons. We also Chapter 5. Analysis and Results 47 80 > 5 - 70 H a> o -C <n S!60 v c 750 o x: 40 I 1 Signal : : : : : : : : : : ! : t s : : : ; ; : : : ' : - . ' 1 1 40 80 > 2 - 70 a> o CO &60 V c 0> 7 50 o Q-40 40 50 60 70 Photon 2 energy share in MeV 60 80 - . 1 1 Background 11 I 1 50 60 70 Photon 2 energy shore in MeV 80 > à 5 0 c o o 0. 40 Background 6 a o B B B B B D D B D D . - jo: B D 40 60 > 2 o -C Q_ 40 40 50 60 Photon 2 energy shore in MeV Background 5 D 50 60 Photon 2 energy share in MeV Figure 6: Distribution of energy between the two photons of each event. Included here are scatterplots of the signal and backgrounds 5, 6 and 11. Note that a minimal cut at 50 MeV (as illustrated here) is quite efficient at rejecting the backgrounds. expect to be able to reject most of the backgrounds where a muon is in coincidence with a pion since photons in the detector are paired by the analysis software. Hence if one of them has very little energy, the entire event will be rejected. Figure 6 shows the way the signal and some of the problematic backgrounds appear to share the energy between the two observed photons; we use that information to set our cut at 50 MeV minimum per photon, as can be seen on the graphs. We examined how an increase in the minimum individual photon energy affects the signal and remaining backgrounds (mainly background 11, the radiative pion decay). Chapter 5. Analysis and Results 48 49 50 51 52 53 54 55 56 Position of cut on individual photon energy (MeV) .0002 T 1 1 1 1 r 49 50 51 52 53 54 55 56 Position of cut on individual photon energy (MeV) Figure 7: Individual photon energy cuts effect on the signal and the remaining prob-lematic background; background 11. Note that all other backgrounds vanish after the minimal cut of 50 MeV. We must be careful not to be too stringent on this particular cut since the detector's finite resolution causes some good events to be reconstructed at lower energies. Hence information such as is plotted in Figure 7 is essential to select the final cuts which are to be applied to the data. 5.3.2 Photon-Photon Angle Cuts Figure 8 shows the photon-photon angle distributions for the signal and some of the problematic backgrounds. We can see clearly that cutting on 0 7 l 7 2 to reject any event Chapter 5. Analysis and Results 49 200 200 Photon-photon angle in degrees Photon—photon angle in degrees Figure 8: Histograms of the 0 7 l 7 2 distributions for the signal and backgrounds 5, 6 and 11. Note the distribution for background 11, the radiative pion decay, which mimics the 7T/3 signal quite well. for which the angle is smaller than 150 degrees does not affect the signal. Although it does not appear so on the histograms, the distributions for all backgrounds (except for background 11) are essentially flat2 Furthermore, we have already put a cut at 90 degrees during the initial phase of the analysis, which amounts to what an intelligent trigger would allow us to do at the hardware level. Once again, as was done for the previous type of cut, we vary the value of 0 7 l 7 2 below 2 Because of the poor statistics and all the forced processes, the spectrum shapes are somewhat distorted. Nevertheless, the random nature of pile-up events insures that the distributions of such backgrounds has to be flat. Chapter 5. Analysis and Results 50 .75 .65 .55 g. .45 150 152 154 156 158 160 Position of cut on photon-photon ongle (degrees) .25 .15 A * \ \ 10x(Background 6) \ ^ Background 5 150 152 154 156 158 160 Position of cut on photon—photon angle (degrees) .0020 150 -\52 154 156 158 160 Position of cut on photon-photon angle (degrees) _i i i_ N - s 10x(Background 8) \ Background 7 ' ^ - ^ 150 152 154 156 158 160~ Position of cut on photon—photon angle (degrees) Figure 9: Photon-photon angle cuts effect on the signal and the problematic backgrounds. Note that backgrounds 6 and 8 have been scaled up by a factor of 10 to fit the graphs. Background 5 remains very important and seems unaffected by the variation in cut, but this is due to the poor statistics on the spectrum shape; only the order of magnitude of the rate is really meaningful. which an event is rejected. The effects can be seen schematically in Figure 9. 5.3.3 Photons Energy Sum Cuts Looking again at the energy share of each photon, we can devise a cut on the sum of photon energies. We begin at £J7l + E17 = 100 MeV, as shown in Figure 10. This cut is more 'intelligent' than the simple individual photon energy cut, since it keeps events where one of the photons might have been poorly reconstructed while the other is in the Chapter 5. Analysis and Results 51 80 80 Photon 2 energy share in MeV Photon 2 energy share in MeV Figure 10: Distribution of energy sharing between the two photons of each event. Illus-trated here is the energy sum cut at 100 MeV for the signal and backgrounds 7, 8 and 11. proper range of energies. On the other hand, it is not as efficient at rejecting pile-up modes of a pion and a muon, as we shall see in a moment. We then proceed to vary this cut slowly and observe the signal and background rates in Figure 11. 5.3.4 Neutral Pion Energy Cuts One final cut can be applied on the data; the minimum 7r° total energy reconstructed from the photon energies and the photon-photon angle. This is highly dependent on the Chapter 5. Analysis and Results 52 100 102 104 106 108 110 Position of cut on photon energy sum (MeV) .012 .010 0 1 .008 I .006 -\ S .004 o z .002 .000 Background 7 100 102 104 106 108 110 Position of cut on photon energy sum (MeV) .0030 100 102 104 106 108 110 Position of cut on photon energy sum (MeV) .0016-1 .0014-o .0012 -"o ce .0010-~B c CT» .0008 -(/> \ Q> .0006 -CO 'o z .0004 -.0002 -.0000 -Background 8 100 t T ~r 102 104 lo6~ 108 110 Position of cut on photon energy sum (MeV) Figure 11: Photon energy sum cuts effect on the signal and the problematic backgrounds. Note that backgrounds 7 and 8, which are of the same order as background 11, do not vanish when applying this cut. Backgrounds 5 and 6 are eliminated by this cut, as can be expected from Figure 6. quality of the reconstruction in both energy and angle, and hence should only be applied as a last stage of the analysis. Typically, when we reject events for which Evo < 110 MeV (with no other cut than the loose tracking) we reduce the signal rate by 9% while getting rid completely of most problematic backgrounds, leaving only background 11 at 14.7% of its initial rate. The same cut applied after other cuts on 2£7 and # 7 l 7 2 has practically no effect on the signal. A complete analysis scheme will be presented in the next section; results in terms of initial and final rates will be given at that time. Chapter 5. Analysis and Results 53 5.4 Complete Analysis After consideration of the various types of cuts that can be applied on the data, we proceeded to implement what we consider to be the optimal combination for the present study. The next chapter will present a discussion of this analysis as well as some problems of the present study. In particular, we will then address some experimental aspects not treated in the present Monte Carlo simulation. The complete analysis scheme we selected is outlined below. Each cut is applied on top of the previous one, as a gradually more stringent event selection. • General loose tracking cuts; • Minimum individual photon energy of 50 MeV (Ey > 50 MeV); • Minimum photon-photon angle of 150 degrees (# 7 l 7 2 > 150 degrees); • Minimum reconstructed neutral pion total energy of 110 MeV (.E o^ > 110 MeV). As we can readily see in Figure 12, background 11 falls only slightly faster than the signal. The analysis allows us to reduce the background level to ~ 5 x 1 0 - 4 while keeping the signal at a 'reasonable' rate. A l l other backgrounds are either eliminated or can safely be considered negligible. It is useful to summarize this analysis with the initial and final rates, as given in Table 6, in the form introduced at the beginning of this chapter. 5.5 Absolute Rates As mentioned in chapter 3, in order to get an absolute rate for the experimental signal, we have to consider the data acquisition live-time as well as the fraction of decay windows that can be considered usable. Essentially, these quantities are well known from the Chapter 5. Analysis and Results 54 J 1 i i r • Signal T 1 1 1 L 0 1 2 3 Number of cuts implemented in analysis J i i i Background 11 T 1 1 1 L 3 1 2 3 Number of cuts implemented in analysis Figure 12: Schematic representation of the complete analysis. Shown here are the effects of the implementation of successive cuts on the data: 1) E1 > 50 MeV; 2) t 9 7 l 7 2 > 150 degrees; 3) EKo > 110 MeV. Backgrounds 5 thru 8 vanish after the first cut. present R M C setup, from the assumed beam time structure and from our efficiency at rejecting pile-up events at the analysis level. We can take the live-time to be approximately 90% while the analysis has so far shown a 100% efficiency at rejecting events which arise because of multiple particle decay in accidental coincidence. This allows us to say that all decay windows can be used and that our only limitation is actually the absolute stopping rate, rTs- Hence, we can use the expression of Section 3.4 and evaluate R*p = 8.58 x 1 0 - 1 3 x 2.6 x 108 x 1.0 x 0.90 88 9 8 6 -- c 8 4 o E 8 2 o <u " 8 0 , 7 8 -76 .0040 -i .0035 -o .0030 -"o cr .0025 -"5 c o> .0020 -to \ 0) .0015-CO "5 z .0010-.0005 -.0000 -Chapter 5. Analysis and Results 55 Rv0 = 2.0 x 10~4 T T / 3 / S for the initial (loose tracking cuts) analysis. A l l other rates can be simply determined relative to this one from the text, tables and figures of previous sections. Type of 'Initial Rate' 'Final Rate' Process (per beam particle) (per beam particle) Signal 8.55 x 10" 1 3 7.67 x 10" 1 3 Backgrounds (relative to signal) (relative to signal) 1 2.33 x 10- 6 4.78 x 10- 7 2 4.93 x 10~9 1.99 x l u ' 9 3 5.46 x 10" 1 2 0 4 0 0 5 5.70 0 6 3.40 x 10" 1 0 7 1.50 x 10- 2 0 8 2.02 x 10" 3 0 9 6.70 x 10" 7 0 10 2.68 x 10~6 3.81 x 10 - 1 2 11 3.65 x 10- 3 5.21 x 10- 4 12 0 0 Table 6: Initial and final rate estimates for Pion Beta Decay. The signal is given per beam particle stopping in the target while all identified backgrounds are given relative to the occurrance of a ?r/3 event. Note that all pile-up backgrounds either vanish (no simulated event survived the analysis, represented by a '0' in the table) or become negligible (rates < 1 0 - 6 relative to the signal) while only background 11, the radiative pion decay, remains a potentially important source of 7r/3-like events. The parameters used for this complete analysis are detailed in the text. Chapter 6 Discussion and Conclusion 6.1 Possibility for an Experiment We began this study of Pion Beta Decay in the R M C pair-spectrometer while other proposals for 7r/3 decay experiments were under review and the R M C experiment on hydrogen was nearing the completion of its data taking phase. The intent was to assess the R M C detector's strengths and weaknesses for a ir(3 decay measurement and to obtain some indications of the experimental feasibility in the present spectrometer or a slightly modified setup. As we draw to the end of this study, the conclusion we face is simple; it is impossible, without major modification to the apparatus, to perform a significant1 measurement of Pion Beta Decay. The reasons for this negative statement are outlined below. First and most important is the fact that even at the highest possible beam rate available, approximately 2.6 x 108 7 T + / s , the expected yield of signal in the detector is still only 2 x 1 0 - 4 7r/?/s. This implies that to get a 0.5% statistical measurement, which requires 4 x 104 events, an experiment would take 2 x 108 seconds of beam (or ten years)2. A slightly less stringent requirement on the accuracy of the experimental rate, say 1% or 104 events, would still require 2.5 years of beam time. For a lower field, as noted in Chapter 5, these figures become3 3.17 years for a 0.5% measurement and 0.8 year (just ' B y 'signifieant', we mean a result which fully tests our most up to date predictions as well as the models on which such theoretical estimates are based. See chapter 1 for more details. 2 B y convention, a 'useful' year of beam is taken to be 2 x 10 7 seconds or approximately eight months. 3It can be readily calculated from Chapter 5 that in this case RTp = 6.3 x 10~ 4 T / 3 / S . 56 Chapter 6. Discussion and Conclusion 57 under 10 months) for a 1% measurement. Second, some of the detector's properties appear inadequate for such an experiment. In particular, the necessarily high 7r + beam rate causes a high flux of Michel positrons into the chambers (IWC and drift chamber). This activity has three major consequences; • large current drain in the Internal Wire Chamber, which leads to problems in point identifications and in the extreme cases to physical failure of the chamber, • track saturation of the drift chamber which prevents the offline analysis software from successfully identifying and reconstructing e+e~ pairs, • constant rejection of good events by charged particles (positrons or muons) which trigger a veto gate (of length 40 ns in the present setup) when they fire the veto scintillators. We did not mention these problems earlier in the study because, given a certain set of modifications to the R M C setup, they can be successfully overcome. See Section 6.3 where an additional magnetic field in the interior of the drift chamber is discussed. However, in its present form, the detector imposes a limit of ~ 107 7r/s on the stopping rate. Finally, the beam counters system currently used for the R M C experiment does not have the necessary systematic precision for such a high quality measurement, even at a beam rate of 107 7 r + / s . Much thought has to be put into the design of the beam counters and a target system to obtain an absolute precision better than 1% on the number of pion stops. On the other hand, this type of detector offers an excellent method for background rejection, even at high pile-up probabilities. Hence, it minimizes the errors due to back-ground subtractions from the ir/3 signal. The energy resolution for the two photons as Chapter 6. Discussion and Conclusion 58 well as the reconstruction of the photon-photon angle and the neutral pion mass provide an excellent technique for 7r/3 signal identification, as expected. However the rather low conversion efficiency (10% for 1 mm Pb) means that it is only really feasible to convert one photon from the emitted ir°. The possibility of increasing the Pb thickness to 2 or 3 mm on one side of the drift chamber was considered but not simulated due to computer time limitations. In conclusion it seems that the observation of two-photon events in the R M C detector cannot be effectively performed with the present configuration unless the intrinsic event rate is relatively large (branching ratio > 10~4). 6.2 General Monte Carlo Observations Some interesting information on the Pion Beta Decay signal and backgrounds can be extracted directly from the Monte Carlo data banks and simulation histograms. This does not require any analysis, so we will simply present our observations here; they are highly relevant to any discussion of detector modifications or other possible designs. We note that the bremsstrahlung physical origins, the detector volumes where these photons are generally created, are (in order of importance): • the drift chamber • the target walls and container (mainly mylar) • the beam scintillators and collimators The first location indicates that there is a non-negligible inefficiency of the veto sys-tem, since the Monte Carlo package automatically stops the trajectory simulation when a veto counter is fired. On the other hand, since the drift chamber tracks from such photons are not reconstructed close to the converter, it is likely that events of this type are rejected at the analysis level. Chapter 6. Discussion and Conclusion 59 The other two locations can be considered parts of the same situation; a charged particle exits the target medium only to undergo a bremsstrahlung in one of the ma-terials surrounding the target, within the veto scintillator radius. This indicates that the choices made for those components in the experimental setup are of the utmost importance to reduce the type of background. Particularly affected are processes by which a bremsstrahlung occurs in coincidence with a radiative decay photon or another bremsstralung. This includes all pile-up modes as well as the most problematic back-ground (due to the pion radiative decay-positron bremsstrahlung combination). Note that some of these events could potentially be rejected by a stringent cut on the distance of closest approach of the photon-photon intersection point (the supposed origin of a 7r° decay) to the center of the target. However as the angle between the two photons becomes large, this point cannot be accurately determined. Although the bremsstrahlung volumes, and hence the bremsstrahlung occurances that follow, are specific properties of the actual detector used for this study, the information clearly indicates that care has to be taken in the overall design of the target, beam counters and collimators. 6.3 Modifications to the R M C Pair-Spectrometer The results presented in chapter 5 imply that a number of modifications have to be made to the existing setup before we can consider a measurement of Pion Beta Decay in the R M C detector. It follows clearly from Section 6.1 that we have to get rid of most of the charged particles that exit the target. One way to achieve this is to use a strong magnetic field to 'wrap' the muons and positrons around the beam axis. This can be done by the addition of a superconducting solenoid, in the volume which immediately surrounds the target, Chapter 6. Discussion and Conclusion 60 to produce a field strong enough to trap particles of energies up to 70 MeV. This extra magnet could be the photon converter. Its effect on the detector's energy resolution would have to be assessed carefully. However it is essential for any consideration of icfi decay in the R M C pair-spectrometer. To render possible even an intermediate (1% or 0.5%) measurement, the conversion efficiency of the detector has to be increased. Studies have already been performed to investigate various possibilities to achieve this[21]. Among the potential solutions, we note the following: • a lead converter of greater thickness; • a B G O 4 converter package replacing the actual lead converter and C scintillators; • a layered drift chamber-converter package. The resolution changes due to each different system have been calculated; it is possible to obtain an increase of 60% in conversion efficiency without any significant reduction in energy resolution. Another necessary change to the present detector consists in the replacement of the liquid hydrogen target by an active plastic scintillator target. This minimizes the charge exchange process and since it can be instrumented with a light guide and photomulti-plier, it can yield useful information on the 7r + stops and decays. A properly designed target could potentially lead to a change in detection philosophy; instead of the two-photon signature, we could look for a one-photon and positron signature. This would probably require the target to be made of scintillating libers individually instrumented with photomultipliers. Such a target already exists for a kaon rare decay experiment at Brookhaven National Laboratory, USA, and another one has just been approved for a 4 Bismuth Germanate scintillator; B i ^ G e s O ^ Chapter 6. Discussion and Conclusion 61 similar experiment at K E K in Japan. Rough estimates indicate that this new approach could gain a factor of 10 in the absolute rate because of the single photon detection re-quirement. Unfortunately, the pile-up backgrounds might become far too large; further studies in this direction are necessary before any conclusions can be made. 6.4 Experimental Normalization One very important aspect of any experiment, and particularly of a TT/3 measurement, is the experimental normalization. In addition to the identification and counting of the ir(3 events, the experiment must be able to compare the signal to either the absolute number of particles stopped or to some other known process. The two approaches differ greatly and deserve a few words of explanation. A n absolute normalization experiment requires a precise evaluation of the number of particles that stop in the decay region. It is the most direct method for evaluating an experimental rate since essentially only the number of signal events and the total number of 'good' beam particles contribute uncertainties to the calculation. The detec-tor needs to be optimized for only one type of process, the signal, and thus it can be designed to maximize background rejection. On the other hand, intense beams render the exact counting of beam particles extremely difficult; elaborate techniques have to be implemented to obtain the accuracy sought for a irfi decay experiment. A relative measurement is based on the observation of a precisely known reaction (or decay process) in addition to the signal. The experimental rate is then established from the ratio of the signal to the reference process. This can be done, in principle, at any stopping rate as long as the detector's live-time allows it . However, in order to obtain a high measurement accuracy, the reference process has to be known to a better precision than the ultimate precision for which the experiment aims. Also, the detector system Chapter 6. Discussion and Conclusion 62 must be tailored so that the acceptance and efficiency for both processes are very well understood. In the case of Pion Beta Decay, since all other processes which involve pion decays are quite different, this latter part can pose a few technical problems. Each of these two philosophies has been used or is about to be used for other decay experiments. The next section will review in general the experimental techniques as a summary for potential detector designs. 6.5 Other Detector Designs To our knowledge, no other study has ever considered a pair-spectrometer such as the R M C detector for a TV/3 decay experiment. After analysis, it would appear that the usual total energy scintillator detector designs are more suitable for such measurement because of the very low rates involved in this rare process. However, some of the insight gained through the present study should lead to some improvements over previously used techniques. Most detectors consist of calorimeters as the major components, both in stopped and in-flight decay approaches, to efficiently collect the photons[ll, 13]. They are usu-ally built of chemically grown crystals (Csl, N a l , B G O , etc.) which cause charged and neutral particles to produce showers of charged particles. This ultimately results in the transformation of particle momentum into scintillation light whose intensity is directly proportional to the particle's kinetic energy. The decay in-flight method used in one previous experiment[13] necessitated extensive Monte Carlo studies in order to understand the systematics introduced by the special geometry and decay region. This causes such an approach to be limited, in terms of accuracy, by those parameters. Therefore, it is unlikely to produce the kind of precision a significant test requires. On the other hand, there are no stringent constraints on the Chapter 6. Discussion and Conclusion 63 beam rate and, in principle at least, a relative measurement is also possible. For stopped pions, the rate has to be limited[10] since backgrounds arising from pile-up of beam particles in the target cannot be easily separated from the signal. There are also limits imposed by the size of the showers in the calorimeter elements and the decay time of the scintillation light, which means that measurements invariably require a certain minimum amount of time (due to the limitation on the incident beam flux). One way to reduce the activity in the calorimeter, to increase the rate and decrease the time necessary to perform the measurement, would be to keep all charged particles from reaching the calorimeter elements. Since these are usually in a cylindrical or almost-spherical geometry, this could be achieved as stated in Section 6.3 by the use of a high magnetic field to trap all positrons and muons inside a non-instrumented part of the detector volume. Although this kind of setup would allow for higher rates, the effects on pile-up backgrounds, particularly those where bremsstrahlung coincidences play a role, have to be studied in detail. It appears to us that the ideal setup is one where the following caracteristics are present; • a near-4ir solid angle is covered by the detector, • a calorimeter is used to collect the photons with a maximum resolution in energy and geometry, • a very high beam stopping rate is achieved in the target, • all charged particles are trapped inside or near the target, • the incidence of two-photon events from pile-up backgrounds is negligible, • the beam rate is known to ~ 0.1%. Chapter 6. Discussion and Conclusion 64 This last requirement is technically the most difficult to fulfill while most of the others have already been attained, either as part of other experiments or through various special-ized techniques. The present study has indicated a sure method of background rejection which may still be implemented to an extent in a sufficiently segmented calorimeter. 6.6 Further Studies If the interest in the R M C pair-spectrometer as a Pion Beta Decay detector remains, a certain number of aspects will have to be the subjects of further investigations. First of al l , the possibility of such a high intensity beam as the one used in the present thesis should be assessed. Beam counters and a target would have to be designed and modeled with the specific aim of attaining an accuracy of ~ 0.1%. A relative measurement technique could also be devised, although we do not feel such an approach would be efficient in the present spectrometer. Simulations should be performed to assess the effects of an extra solenoid inside the detector to trap the charged particles. The energy resolution and the conversion probability have to be modeled precisely. At the same time, modifications to the converter could be effectively included as part of the new design. This could be done quite rapidly with the help of the Monte Carlo package used for this study, after proper changes to the simulated detector within the program. Finally, the one-photon and positron detection scheme appears to be the most promis-ing approach in terms of 7r/? event rate. However, it requires extensive design modifi-cations for the target, a precise assessment of the tolerable activity in such a target (including the tracks 'wrapped' inside it by the high magnetic field discussed earlier) as well as a complete background evaluation equivalent to the work presented in this thesis. Bibliography [1] P. Renton, Electroweak Interactions, Cambridge University Press, Cambridge, 1990, 596 p. [2] E.D. Commins, Weak Interactions, McGraw-Hill , New York, 1973, 378 p. [3] R.P. Feynman and M . Gell-Mann, Physical Review 109 (1958) 193 [4] Particle Data Group, J . J . Hernandez et al . , Physics Letters B 239 (1990) [5] G. Lopez Castro, International Journal of Modern Physics A 6 (1991) 3293 [6] D .H. Wilkinson, Paper presented at the Int. Conf. on Spin and Isospin in Nuclear Interactions, Telluride, C O , March 11-15, 1991 [7] G. Kâllén, Elementary Particle Physics, Addison-Wesley, Reading (Mass.), 1964, 546 p. [8] A . Sirlin, Reviews of Modern Physics 50 (1978) 573 [9] G. Lopez Castro and J . Pestieau, Physics Letters B 203 (1988) 315 [10] D. Pocanic, PSI Proposal R89-01.0 December 1988 [11] P. Depommier et al . , Nuclear Physics B 4 (1968) 189 [12] P. Depommier et al . , Physics Letters 7(1963) 285 [13] W . K . McFarlane et al . , Physical Review D 32 (1985) 547 [14] D. Pocanic, R89-01.1 Progress Report March 1990 [15] D. Pocanic, PSI Proposal R89-01.1 May 1991 [16] D. Pocanic, PSI Proposal R89-01.2 December 1991 [17] D.S. Armstrong et al . , Physical Review C 43 (1991) 1425 [18] D .H. Wright et al . , Nuclear Instruments and Methods A 320 (1992) 249 19] G E A N T 3 User's Guide, C E R N DD/EE/84-1 20] D.A. Bryman et al . , Physics Reports 88, no. 3 (1982) 151 21] G. Jonkmans, Master's Thesis, Université de Montréal, 1991 65 


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