FIRST OBSERVATION OF THE ηb MESON AND STUDY OF THE DECAYS Υ (3S) γηb AND Υ (2S) γηb ! ! A DISSERTATION SUBMITTED TO THE DEPARTMENT OF PHYSICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Christopher West May 2010 © 2010 by Christopher Alan West. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/nv861zm8623 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Rafe Schindler, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Patricia Burchat I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Jonathan Dorfan I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Michael Peskin Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract This dissertation presents the results of an analysis of data samples consisting of 122 million Υ (3S) decays and 90 million Υ (2S) decays collected with the BABAR detector operating at the PEP-II asymmetric-energy storage rings at SLAC National Accelera- tor Laboratory. The η meson is observed for the first time in the decay Υ (3S) γη b ! b and its existence is confirmed in the decay Υ (2S) γη . The η mass extracted ! b b from the Υ (3S) γη sample is 9388:9+3:1(stat) 2:7(syst) MeV=c2, correspond- ! b −2:3 ing to a hyperfine mass splitting m m = 71:4+2:3(stat) 2:7(syst) MeV=c2. Υ (1S) − ηb −3:1 The branching fraction for the decay Υ (3S) γη is determined to be [4:8 ! b 0:5(stat) 0:6(syst)] 10−4. An analysis of the decay Υ (2S) γη confirms the × ! b observation of the ηb meson and provides an additional measurement of the ηb mass: 9394:2+4:8(stat) 2:0(syst) MeV=c2. The branching fraction for the decay Υ (2S) γη −4:9 ! b is determined to be [3:9 1:1(stat)+1:1(syst)] 10−4. As the measurements in the −0:9 × two samples are consistent, the masses are averaged to provide a combined value of m = 9390:9 3:2 MeV=c2. After canceling common systematic errors, the following ηb branching fraction ratio is determined: [Υ (2S) γη (1S)]= [Υ (3S) γη (1S)] = B ! b B ! b 0:82 0:24(stat)+0:20(syst). −0:19 iv Acknowledgments A Ph.D. dissertation is never completed without the help of many other people, and mine is no exception. First of all, I would like to thank my adviser, Rafe Schindler, for his guidance throughout the years and giving me the freedom to discover my interests in physics at BABAR. A great deal of my knowledge of physics analysis comes directly from those with whom I have worked: Philippe Grenier, Peter Kim, Peter Lewis, Silke Nelson and Veronique Ziegler. In particular, I would like to thank Peter Kim for spurring my interest in searches for undiscovered states, and the ηb in particular. My analysis of radiative decays benefits from the knowledge I gained in electromagnetic calorimetry from Martin Kocian and Bill Wisniewski. The support of my Group E colleagues Walt Innes, Peter Lewis, Selina Li, Martin Perl and Stephen Sun made the task of completing my dissertation a pleasant experience. Finally, I would like to thank my parents, Bill and Claudia West, for always believing in me and encouraging me to pursue my dreams. v Contents Abstract iv Acknowledgments v 1 Introduction 1 1.1 The Standard Model . 2 1.2 Quantum Chromodynamics . 3 1.2.1 Historical Overview . 3 1.2.2 Asymptotic Freedom . 4 1.3 Theoretical Approaches to QCD . 5 1.3.1 Quark Potential Models . 5 1.3.2 Lattice QCD . 6 1.3.3 Non-relativistic quantum chromodynamics . 10 1.3.4 Potential non-relativistic quantum chromodynamics . 12 1.4 Bottomonium . 13 1.5 Electromagnetic transitions . 13 1.6 The ground state of bottomonium, the ηb meson . 15 1.7 Conclusion . 22 vi 2 The BABAR Detector 24 2.1 Physics Motivation . 24 2.1.1 CP violation . 24 2.1.2 Bottomonium Physics . 26 2.2 PEP-II . 26 2.3 The BABAR Detector . 26 2.4 Silicon Vertex Tracker . 27 2.5 Drift Chamber . 30 2.6 Detector of Internally Reflected Light . 34 2.7 Electromagnetic Calorimeter . 36 2.7.1 Design . 37 2.7.2 Calibration and Performance . 38 2.8 Superconducting Coil . 41 2.9 Instrumented Flux Return . 42 2.10 Trigger . 43 2.10.1 Level 1 Trigger . 44 2.10.2 Level 3 Trigger . 45 2.11 Datasets . 45 3 Analysis Overview 47 3.1 Introduction . 47 3.2 Backgrounds . 48 3.2.1 Non-peaking . 48 3.2.2 Υ (nS) γχ (mS); χ γΥ (1S) . 49 ! b b ! 3.2.3 e+e− γΥ (1S) . 49 ! vii 3.3 Selection Criteria . 50 4 Study of the Decay Υ (3S) γη 52 ! b 4.1 Selection Criteria . 52 4.1.1 Data set . 52 4.1.2 Event selection . 53 4.1.3 π0 veto optimization . 55 4.1.4 Investigation of a possible η veto . 62 4.1.5 N-1 cut plots . 64 4.2 Background to the Eγ spectrum . 66 4.2.1 Introduction . 66 4.2.2 Non-peaking Background . 67 4.2.3 Peaking Background from χbJ (2P ) ! γΥ (1S) . 69 + − 4.2.4 Peaking Background from e e ! γISRΥ (1S) . 73 4.3 Fitting procedure . 81 4.3.1 Fit and Unblinding strategies . 81 4.3.2 Minimization Details . 82 4.4 Toy Studies . 84 4.4.1 Conclusions . 86 4.5 Fit on the 2.5 fb−1 Optimization Sample . 93 4.6 Fit to the inclusive photon spectrum . 93 4.7 Systematic Uncertainties . 96 5 Study of the Decay Υ (2S) γη 98 ! b 5.1 Selection . 98 viii 5.2 Background Modeling . 102 5.2.1 Introduction . 102 5.2.2 Non-peaking Background . 102 5.2.3 e+e− γ Υ (1S) . 103 ! ISR 5.2.4 Υ (2S) γχ (1P ); χ (1P ) γΥ (1S) . 114 ! bJ bJ ! 5.2.5 Υ (2S) Υ (1S)(η; π0) . 117 ! 5.2.6 Υ (2S) Υ (1S)π0π0 . 119 ! 5.3 Control Sample Studies . 122 5.3.1 Selection . 122 5.3.2 Monte Carlo . 123 5.4 Fit Procedure for Υ (2S) γη Sample . 129 ! b 5.4.1 Introduction . 129 5.4.2 Fixed and floating parameters . 130 5.4.3 Fit to test sample, ISR yield fixed . 131 5.4.4 Fit to test sample, ISR yield floating . 134 5.4.5 Fit to full sample with signal region blinded, ISR yield fixed . 139 5.4.6 Fit to full sample with signal region blinded, ISR yield floating 139 5.5 Toy studies . 146 5.5.1 Introduction . 146 5.5.2 Toys with ISR yield fixed to incorrect yield . 147 5.5.3 Conclusion . 148 5.6 Fit results . 149 5.7 Systematic Errors . 155 5.7.1 Sources of Systematic Errors . 155 ix 5.7.2 Significance of Signal (Including Systematic Errors) . 156 5.7.3 Additional Fit Variations . 157 5.7.4 Branching Fraction Uncertainties . 160 5.8 Combination with Υ (3S) result . 164 5.8.1 Ratio of branching fractions . 164 5.8.2 New Υ (3S) γη branching fraction . 167 ! b 5.8.3 Mass of the ηb . 168 6 Summary and Outlook 169 Appendices A Use of EMC Timing to Improve π0 Veto 171 B Spurious Feature at 680 MeV 176 B.1 Description of problem . 176 B.2 Other investigations of spike . 177 Bibliography 183 x List of Tables 1.1 Predictions for the hyperfine splitting m m from lattice QCD Υ (1S) − ηb and perturbative QCD calculations. 17 1.2 Predictions for the two-photon partial decay width, taken from [41], and the total width determined by scaling the two-photon decay width using Eq. 1.12. 20 1.3 Limits (95% confidence level) on ηb two photon partial width times branching fraction from LEP. 23 4.1 On-resonance datasets used in the selection optimization . 53 4.2 Selection efficiencies () for truth-matched signal MC and on-peak data in the energy range 0:85 < Eγ < 0:95, in percent. The reconstruction efficiency on data is normalized to 100%. 56 4.3 Comparison of single cut efficiencies and S=pB from fitted χb yields and truth-matched signal MC. The background contribution is found by integrating the background function from E 2σ to E + 2σ. 59 g,χb1 − g,χb2 xi 0 4.4 Signal to background study for the π veto.