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Measurement of the Radiative Muon Decay As a Test of the V − a Structure of the Weak Interactions

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Measurement of the Radiative Muon Decay As a Test of the V − a Structure of the Weak Interactions Measurement of the Radiative Muon Decay as a Test of the V − A Structure of the Weak Interactions Emmanuel Munyangabe Kigali, Rwanda B.S., National University of Rwanda, 2006 A Dissertation presented to the Graduate Faculty of the University of Virginia in Candidacy for the Degree of Doctor of Philosophy Department of Physics University of Virginia June, 2012 Abstract Measurements of the radiative muon decay can be used to test the validity of the V − A form of weak interactions. All the Michel parameters can be extracted from + + the analysis of the ordinary muon decay µ → e νeν¯µ, with the exception of the + + η¯ parameter which is measured by analyzing the radiative decay µ → e νeν¯µγ. This analysis is based on more than 5.1 × 105 radiative muon decays recorded by the PIBETA experiment at the Paul Scherrer Institute (PSI), Switzerland in 2004. Based on these events, the experimental branching fraction was measured to be B = [4.365 ± 0.009 (stat.) ± 0.042 (syst.)] × 10−3. Theη ¯ parameter was extracted using the least squares method and the experimental value was found to beη ¯ = 0.006 ± 0.017 (stat.) ± 0.018 (syst.). This result is to be compared to the V − A Standard Model valueη ¯SM = 0. Our experimental result ofη ¯ gives an upper limit of:η ¯ ≤ 0.028 (68.3 % confidence), a fourfold improvement in precision over the existing world average. Contents 1 Introduction 1 1.1 The Standard Model . 1 1.1.1 Weak Interactions . 3 1.1.2 V-A Theory . 6 1.2 Muon decay . 11 + + 1.2.1 Michel Decay: µ → e νeνµ(γ) . 13 + + 1.2.2 Radiative Michel Decay: µ → e νeνµγ . 15 1.2.3 Motivation . 20 2 PIBETA Detector 26 2.1 Introduction . 26 2.2 Experimental area . 27 2.3 Beam-defining elements . 28 2.3.1 Passive Collimator . 28 2.3.2 Active beam-defining elements . 29 2.4 Detector Tracking System . 31 2.5 Calorimeter . 33 2.6 Cosmic muon veto detectors . 34 2.7 PIBETA Triggering System . 34 2.7.1 Introduction . 34 2.7.2 Random Triggers . 35 2.7.3 Beam Triggers . 35 2.7.4 Calorimeter Triggers . 36 3 Event Reconstruction 40 3.1 Introduction . 40 3.2 Data Analysis Software . 41 3.2.1 Tracking System algorithm . 41 3.2.2 Clump Algorithm . 42 3.3 Particle Identification . 45 3.4 Monte Carlo Simulation . 49 i ii 3.5 Data Calibration . 51 3.5.1 Introduction . 51 3.5.2 Energy Calibration (ADC Calibration) . 51 3.5.3 Time Calibration (TDC Calibration) . 53 4 Data Analysis 56 4.1 Branching Fraction . 56 4.1.1 Introduction . 56 4.1.2 Muon decay time distribution . 58 4.1.3 Non-Radiative Muon Decay . 65 4.1.4 Radiative Michel decay . 67 4.1.5 Background Signal . 68 4.1.6 Kinematic cuts . 71 4.1.7 Systematic errors . 75 4.1.8 Results (branching fraction) . 76 4.2 Extraction ofη ¯ and ρ Parameters . 80 4.2.1 Systematic error . 87 4.3 Conclusions . 98 A The functions fi(x, y, θ) 100 B The Least Squares Method 103 List of Figures 1.1 Elementary particles and gauge bosons . 4 1.2 Beta decay . 5 ◦ 1.3 f1(x, y, θ ≥ 45 ).............................. 18 ◦ 1.4 f1(x, y, θ ≥ 90 ).............................. 18 ◦ 1.5 f1(x, y, θ ≥ 135 ) ............................. 19 ◦ 1.6 f1(x, y, θ ≥ 157 ) ............................. 19 ◦ 1.7 (f2/f1)(x, y, θ ≥ 45 )........................... 20 ◦ 1.8 (f2/f1)(x, y, θ ≥ 90 )........................... 21 ◦ 1.9 (f2/f1)(x, y, θ ≥ 135 )........................... 22 ◦ 1.10 (f2/f1)(x, y, θ ≥ 157 )........................... 23 ◦ 1.11 (f3/f1)(x, y, θ ≥ 45 )........................... 23 ◦ 1.12 (f3/f1)(x, y, θ ≥ 90 )........................... 24 ◦ 1.13 (f3/f1)(x, y, θ ≥ 135 )........................... 24 ◦ 1.14 (f3/f1)(x, y, θ ≥ 157 )........................... 25 2.1 Detector cross-section . 30 2.2 Decay chain signal . 32 2.3 The pion stop signal . 37 3.1 The primary vertex x0, y0, z0 ....................... 43 3.2 CsI-MWPC angle . 44 3.3 Positron (Michel) θ ............................ 45 3.4 Positron Michel) φ ............................ 46 3.5 Positron θ ................................. 46 3.6 Photon φ ................................. 47 3.7 Photon θ ................................. 47 3.8 Positron φ ................................ 48 3.9 Positron energy in CsI calorimeter for 1-arm low trigger events. 52 3.10 Positron energy in plastic veto (PV) for 1-arm low trigger events. 53 3.11 Walk-correction effect on the energy and time of PV. The straight horizontal line indicate the removal of energy-time dependence in the observed TDC values. 55 iii iv 3.12 Walk-correction effect on the energy and time of CsI calorimeter. The straight horizontal line indicate the removal of energy-time dependence in the observed TDC values in the energy range of 10-53 MeV. 55 4.1 Time coincidence of positron and photon in the CsI calorimeter. 62 4.2 The time distribution of Michel events . 63 4.3 The time distribution of radiative Michel events. This is measured as 1 e+ γ the time difference ( 2 (tCsI + tCsI) − tDeg). 64 4.4 The time ratio before selection . 64 4.5 The time ratio after selection . 65 4.6 The positron energy . 72 4.7 The photon energy . 73 4.8 The opening angle . 74 4.9 The positron energy cut stability . 76 4.10 The photon energy cut stability . 77 4.11 The signal window cut stability . 77 4.12 The opening angle cut stability . 78 4.13 The χ2 as a function of ρ from analysis of non-radiative Michel decays 82 ◦ ◦ 4.14 (f2/f1)(x, y, 150 < θ ≤ 160 ) ...................... 83 ◦ ◦ 4.15 (f2/f1)(x, y, 160 < θ ≤ 170 ) ...................... 84 ◦ ◦ 4.16 (f2/f1)(x, y, 170 < θ ≤ 180 ) ...................... 85 ◦ ◦ 4.17 (f2/f1)(x, y, 157 < θ ≤ 180 ) ...................... 86 4.18 The χ2 as a function of photon energy scale andη ¯ for 170◦ < θ ≤ 180◦ bin. 89 2 ◦ ◦ 4.19 The χ as a function ofη ¯ for 170 < θ ≤ 180 bin, with Cγ = 0.994. 89 4.20 The χ2 as a function of photon energy scale andη ¯ for 160◦ < θ ≤ 170◦ bin. 90 2 ◦ ◦ 4.21 The χ as a function ofη ¯ for 160 < θ ≤ 170 bin, with Cγ = 0.994. 90 4.22 The χ2 as a function of photon energy scale andη ¯ for 160◦ < θ ≤ 180◦ bin. 91 2 ◦ ◦ 4.23 The χ as a function ofη ¯ for 160 < θ ≤ 180 bin, with Cγ = 0.994. 91 4.24 The χ2 as a function of photon energy scale andη ¯ for 150◦ < θ ≤ 160◦ bin. 92 2 ◦ ◦ 4.25 The χ as a function ofη ¯ for 150 < θ ≤ 160 bin, with Cγ = 0.997. 92 4.26 The χ2 as a function of photon energy scale for 160◦ < θ ≤ 180◦ bin, withη ¯ = 0.006................................ 93 List of Tables 1.1 Range and lifetimes . 6 1.2 Weak isospin . 6 1.3 Muon decay modes . 12 2.1 Trigger pre-scaling factors . 39 4.1 Pibeta time scales . 59 4.2 Michel cuts . 66 4.3 Event generator level cuts. 71 4.4 Event reconstruction cuts . 72 4.5 Systematic errors (largest accessible phase space . 78 4.6 Experimental branching fraction . 79 4.7 Values ofη ¯ ................................. 88 4.8 Systematic errors of the region 0.5 < x ≤ 0.75, 0.28 < y ≤ 0.48 . 93 4.9 Systematic errors of the region 0.5 < x ≤ 0.75 and 0.5 < y ≤ 0.75 . 94 4.10 Systematic errors of the region 0.28 < x ≤ 0.48 and 0.5 < y ≤ 0.75 . 94 4.11 Systematic errors of the region 0.28 < x ≤ 0.48 and 0.28 < y ≤ 0.48 . 95 4.12 Statistics for bin 170◦ < θ ≤ 180◦ .................... 95 4.13 Statistics for bin 160◦ < θ ≤ 170◦ .................... 96 4.14 Statistics for bin 160◦ < θ ≤ 180◦ .................... 96 4.15 Statistics for bin 150◦ < θ ≤ 160◦ .................... 96 4.16 Systematic errorsη ¯ parameter . 97 v Chapter 1 Introduction 1.1 The Standard Model The Standard Model of particle physics [1] is a theory that describes the behavior of subatomic particles. This behavior is manifested by the interactions between these particles. So far, there are four known fundamental interactions; electromagnetic, strong, weak and gravity. The Standard Model theory was developed throughout the mid to late 20th century, the current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks and the intermediate bosons (W and Z). Because of its success in explaining a wide variety of experimental results, the theory is sometimes regarded as a theory of almost everything. Yet, the theory fails to incorporate the physics of general relativity, such as grav- itation and dark energy or dark matter particles that are deduced from cosmological 1 Chapter 1: Introduction 2 evidence. Nevertheless, the Standard Model theory is an important tool to explain particle physics. The Standard Model includes 12 elementary particles of spin-1/2 known as fermions and their corresponding anti-particles. The fermions of the Standard Model are clas- sified according to how they interact. Some interact strongly, weakly, and electro- magnetically (quarks), while others never interact via strong interactions (leptons). There are six quarks (up, down, charm, strange, top, and bottom) and six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino), grouped into three generations as shown in Fig 1.1. The main difference between quarks and leptons is that quarks carry strong color charge, therefore, only quarks can interact via strong interaction. Quarks bound to one another form color-neutral hadrons.
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