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A study of B --> ccBAR γK in the BABAR experiment Fulsom, Bryan Gregory 2009

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A Study of B —> c7K in the BABAR Experiment by Bryan Gregory Fulsom B.Sc., Queen’s University at Kingston, 2000 M.Sc., Queen’s University at Kingston, 2003 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Physics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2009 © Bryan Gregory Fulsom 2009 Abstract The BABAR Collaboration is a high energy physics experiment located at the Stanford Linear Accelerator Center. The primary goal of the experiment is to study charge and parity violation in the B-meson sector, however the copious production of B mesons decaying to other final states allows for a wide-ranging physics program. In particular, one can access the charmonium system via colour-suppressed b — c decays of the type B — ciK. This thesis presents a study of B —f e’yK decays where c includes J/ and &(2S), and K includes K, K° and K*(892). The particular emphasis is on a search for the radiative decays X(3872) — J/i7 and X(3872) —* (2S)7. The X(3872) state is a recently-discovered resonance of undetermined quark composition, speculatively a conventional charmonium state or exotic four-quark di-meson molecule. This research is also sensitive to the well-known radiative charmonium decays B —* xcl,2K, which are used as verification for the analysis technique. This dissertation sets the best B —* xK branching fraction measure ments to date, and sees the first evidence for factorization-suppressed 0 — XC2K*O decay at a level of 3,6o. It also provides evidence for X(3872) J/b7 and X(3872) —* (2S)7 with 3.6u and 3.3o significance, respectively. The product of branching fractions B(B —* X(3872)Kj . B(X(3872) = (2.8 ± O.8(stat.) ± O.2(syst.)) x 106 and B(B — X(3872)K). t3(X(3872) —* (2S)7)= (9.5±2.7(stat.)±0.9(syst.)) x 106 are measured. These results improve upon previous X(3872) —* y measurements, and represent the first evidence for X(3872) —÷ b(2S)7. 11 Table of Contents Abstract ii Table of Contents iii List of Tables vii List of Figures ix Glossary xiv Acknowledgements Dedication xxii 1 Introduction 1 2 Background Information 4 2.1 The Charmonium Model 4 2.2 Charmonium Production 8 2.3 Charmonium Decay 10 2.4 Exotic Quarkonia 11 2.5 Recent Experimental Results 13 2.5.1 X(3872) 14 2.5.2 The X/Y/Z Family 16 2.5.3 States Produced in TSR 17 2.5.4 Charged Multiquark States 18 2.6 X(3872) Phenomenology 18 2.7 Analysis Outlook 20 ‘U Table of Contents 3 The BABAR Experiment 22 3.1 The Linear Accelerator and PEP-IT Storage Rings 22 3.2 Detector Overview 24 3.3 The Silicon Vertex Tracker (SVT) 28 3.4 The Drift Chamber (DCH) 29 3.5 The Detector of Internally-Reflected Cherenkov Light (DTRC) 30 3.6 The Electromagnetic Calorimeter (EMC) 34 3.7 The Instrumented Flux Return (IFR) 37 3.8 Triggering and Software 41 4 Analysis Preliminaries 44 4.1 Data Set 44 4.2 B Candidate Reconstruction 45 4.2.1 “JpsitollTight” Skim 45 4.2.2 J/ —* tt Reconstruction 47 4.2.3 &(2S) Reconstruction 47 4.2.4 X —* c&y Reconstruction 48 4.2.5 Kaon Reconstruction 48 4.2.6 B —p XK Reconstruction 48 4.3 Event Variables 49 4.3.1 B Meson Variables 49 4.3.2 Event Topology Variables 50 4.3.3 Photon Variables 51 4.3.4 Kaon Variables 53 4.4 Event Selection 53 4.4.1 Cut Optimization Procedure 53 4.4.2 Optimization Results 54 4.4.3 Multiple Candidate Selection 70 4.4.4 Event Selection Efficiency 70 5 Analysis Methodology 75 5.1 Signal Extraction Procedure 75 5.1.1 Probability Density Functions 75 iv 5.1.2 Choice of PDF shapes. 5.1.3 PDF Parametrization, mmjss 5.1.4 PDF Parametrization, mx 5.1.5 PDF Parametrization, mK* 5.1.6 PDF Correlations 5.1.7 The Plot Technique 5.2 X(3872) Signal Extraction on Monte Carlo 5.2.1 Monte Carlo Tests 5.2.2 Bias 5.2.3 Fit Efficiency 5.2.4 Total Efficiency 5.2.5 Cross-feed and Other Backgrounds 5.2.6 Null Signal Tests 5.3 The Xcl,2 Benchmark Modes 5.3.1 Xci PDF Parametrization 5.3.2 Xc2 PDF Parametrization 5.3.3 PDF Correlations for XcJ 5.3.4 ‘&tnt of B —* xciKir Non-Resonant grounds 5.3.5 .y,2 Cross-feed 5.3.6 Xci Signal Extraction Efficiency . . 5.3.7 Signal Extraction Efficiency . . 6 Signal Extraction from Data 6.1 Xci,2 Signal Extraction from Data 6.2 X(3872) Signal Extraction from Data . 6.2.1 B —÷ X(3872)K, X(3872) —* 6.2.2 B —* X(3872)K, X(3872) —* 6.2.3 B —* X(any)K, X(ariy) — cë-y . 6.3 Systematic Uncertainties and Corrections 6.3.1 B Counting 6.3.2 Branching Fraction Uncertainties 6.3.3 MC/Data Differences 138 138 150 150 161 172 173 173 173 176 Table of Contents (NR) Back- 76 77 80 88 88 100 101 101 102 104 112 112 113 114 115 116 121 127 129 133 135 V Table of Contents 6.3.4 6.3.5 6.3.6 6.3.7 6.3.8 6.3.9 6.3.10 PDF Fit Parameter Uncertainty True X Mass and Width Uncertainty Bias and Efficiency PID Correction and Systematics . Tracking Systematics Photon Corrections Total Systematic Error 176 177 180 181 181 181 182 185 185 187 Bibliography 194 7 Conclusions 7.1 Analysis Results 7.2 Discussion and Implications vi List of Tables 4.1 Number of events and luminosity weighting 46 4.2 Selection criteria optimization results 56 4.3 Average number of B candidates per event 70 4.4 Reconstruction and event selection efficiency 71 5.1 mmjss PDF fit results for X(3872) signal modes 80 5.2 mmjss PDF fit results for X(3872) background modes 83 5.3 mx PDF fit results for X(3872) signal modes 88 5.4 mx PDF fit results for X(3872) background modes 91 5.5 m PDF fit results for the X(3872) modes 91 5.6 Test of signal extraction for truth-matched signal MC events with PDF-generated background events 103 5.7 Test of signal extraction for all signal MC events with PDF generated background events 105 5.8 Total signal extraction efficiency for each signal mode based on MC samples 112 5.9 Expected B —* X(3872)(JiJnrrrjK background 114 5.10 Number of events returned by the signal extraction from a background-only toy data sample 115 5.11 mmjss PDF fit results for Xci. signal modes 121 5.12 mmjss PDF fit results for Xci background modes 121 5.13 mx PDF fit results for xci signal modes 127 5.14 mx PDF fit results for xci background modes 127 5.15 mK* PDF fit results for xci modes 128 5.16 mx PDF fit results for Xc2 signal modes 128 5.17 Cross-feed for the B —* XcjK modes 133 vii List of Tables 5.18 Reconstruction and event selection efficiency for B —> xiK MC events 134 5.19 Results of tests of signal extraction for B —i x1K 135 5.20 Signal extraction efficiency for B —+ xiK 135 5.21 Reconstruction and event selection efficiency for B —* xc2K MC events 136 5.22 Test of signal extraction for Xc2 with zero MC events 136 5.23 Results of tests of signal extraction for B —* x2K 137 5.24 Signal extraction efficiency for B —* x2K 137 6.1 Results of Z3(B — xCl,2K) signal extraction 146 6.2 Results of B(B —* X(3872)(J/7)K signal extraction 161 6.3 Results of 13(B —. X(3872)(&(2S)’y)K) signal extraction. . . . 172 6.4 Values and uncertainties for the relevant daughter branching fractions 173 6.5 Systematic uncertainties due to PDF parameter uncertainties for the X(3872) —* J/-y modes 177 6.6 Systematic uncertainties due to PDF parameter uncertainties for the X(3872) — (2S)7modes 178 6.7 Systematic uncertainties due to PDF parameter uncertainties for the Xcl,2 modes 179 6.8 Summary of the systematic uncertainties due to uncertainties in the properties of X(3872) 180 6.9 PID and tracking corrections and systematic uncertainties ap plied to the efficiency 182 6.10 Total systematic uncertainties for the X(3872) —* J/-y decay modes 183 6.11 Total systematic uncertainties for the X(3872) —* b(2S)’y decay modes 183 6.12 Total systematic uncertainties for the Xcl decay modes. . . . 184 6.13 Total systematic uncertainties for the Xc2 decay modes. . . . 184 7.1 Comparison of B — xcl,2K results with previous measurements. 191 viii List of Figures 2.1 Predicted and observed spectrum of the charmonium model. 7 2.2 Feynman diagram of B — cK 8 2.3 Cartoon depiction of exotic QCD states 12 2.4 Previous results of X(3872) — J/7 from Belle and BABAR. 15 3.1 Illustration of the linear accelerator and PEP-Il collider. , 23 3.2 Integrated luminosity of the BABAR experiment 25 3.3 Longitudinal view of the BABAR detector 26 3.4 End view of the BABAR detector 27 3.5 Transverse cross-sectional view of the SVT 28 3.6 Longitudinal cross-sectional view of the SVT 29 3.7 Longitudinal diagram of the DCII 31 3,8 Layout of the DCII drift cells 32 3.9 Diagram of the DIRC system 33 3.10 Layout of the EMC barrel and forward endcap 35 3.11 Diagram of a typical CsI(T1) crystal in the EMC 36 3.12 Layout of the IFR barrel and endcaps 38 3.13 Cross section of Resistive Plate Chamber construction 39 3.14 Diagram of a limited streamer tube 40 3.15 Z-plane read-out strip diagram 41 3.16 Muon identification efficiency by IFR region 42 4.1 Optimized B mass for the J/’t’7 modes 55 4.2 Optimized J/& mass for the J/’&’y modes 57 4.3 Optimized y LAT and 7A42 for the J/i-y modes 57 4.4 Optimized ir0 veto for the J/b7 modes 58 ix List of Figures 4.5 Optimized cos8thrust and cos0sphericity for the J/7 modes 58 4.6 Optimized R2 for the J/&-y modes 59 4.7 Optimized B x2 values for the J/’7 modes 60 4.8 Optimized K cuts for the J/y modes 61 4.9 Optimized K*± cuts for the J/7 modes 62 4.10 Optimized K*O cuts for the J/7 modes 62 4.11 Optimized B mass for the (2S)y modes 63 4.12 Optimized J/ mass for the (2S) — J/irir modes. . 63 4.13 Optimized (2S) mass for the (2S)7 modes 64 4.14 Optimized y LAT and 7A42 for the b(2S)7 modes 65 4.15 Optimized ir0 veto for the (2S)7modes 65 4.16 Optimized cos8thrust and cos8spherjcity for the (2S)7 modes 66 4.17 Optimized R2 for the Y(2S)7 modes 66 4.18 Optimized B x2 values for the (2S)7modes 67 4.19 Optimized K cuts for the i’(2S)7 modes 68 4.20 Optimized K*± cuts for the (2S)7 modes 69 4.21 Optimized K*o cuts for the (2S)7modes 69 4.22 mx distribution of MC background events for X(3872) —* J/i1b7. 72 4.23 mx distribution of MC background events for X(3872) —+ 73 4.24 mx distribution of MC background events for Xci J/’b . . 74 5.1 mmj3s PDF fits for the J/ signal modes 78 5.2 mmjss PDF fits for the (2S) signal modes 79 5.3 m3 PDF fits for the J/ background modes 81 5.4 PDF fits for the ‘(2S) background modes 82 5.5 mx PDF fits for the J/ signal modes 84 5.6 mx PDF fits for the (2S) signal modes 85 5.7 mx PDF fits for the J/ background modes 86 5.8 mx PDF fits for the ,b(2S) background modes 87 5.9 m< PDF fits for the J/ signal and background modes. 89 5.10 mK* PDF fits for the ‘i(2S) signal and background modes 90 x List of Figures 5.11 Plots of mmjss versus mx for the X(3872) —* J/&7 signal modes 92 5.12 Plots of mmjss versus mK* and mx versus mK* for the X(3872) —+ J/’h signal modes 93 5.13 Plots of mmjss versus mx for the X(3872) —* (2S)7 signal modes 94 5.14 Plots of mmjss versus mK* and mx versus mK* for the X(3872) —f (2S)7 signal modes 95 5.15 Plots of mmiss versus mx for the X(3872) —* J/’7 back ground modes 96 5.16 Plots of mmjsg versus mK* and mx versus mK* for the X(3872) —> J/b’y background modes 97 5.17 Plots of mmjss versus mx for the X(3872) —* ‘(2S)7 back ground modes 98 5.18 Plots of mmjss versus mjç and mx versus mK* for the X(3872) —p 4(2S)7 background modes 99 5.19 Comparison of truth-matched and non-truth-matched MC for B —* X(3872)(?,b(2S))K 106 5.20 Comparison of truth-matched and non-truth-matched MC for B° — X(3872)((2S)7)K 106 5.21 Comparison of truth-matched and non-truth-matched MC for mx, mmjss, and mK*± for B — X(3872)((2S)y)K*±. . . . 107 5.22 Comparison of truth-matched and non-truth-matched MC for mx, ‘Tflmiss, and mK*o for B° — X(3872)((2S))K*o 108 5.23 Comparison of truth-matched and non-truth-matched MC for B — X(3872)(J/&7)K 109 5.24 Comparison of truth-matched and non-truth-matched MC for B° —* X(3872)(J/’zb7)K 109 5.25 Comparison of truth-matched and non-truth-matched MC for mx, mmjss, and mK*± for B —> X(3872)(J/b7)K*+ 110 5.26 Comparison of truth-matched and non-truth-matched MC for mx, mmjss, and mK*o for B° —* X(3872)(J/b7)K*o 111 5.27 mmjgs PDF fits for the Xci signal modes 116 xi List of Figures 5.28 mmjss PDF fits for the Xci background 117 5.29 mx PDF fits for the Xci signal modes 118 5.30 mx PDF fits for the Xci background modes 119 5.31 mK* PDF fits for the Xci signal and background modes. . . . 120 5.32 mx PDF fits for the Xc2 signal modes 122 5.33 Plots of mmjss versus mx for the XcJ signal modes 123 5.34 Plots of mmjss versus mK* and mx versus mK* for the XcJ signal modes 124 5.35 Plots of mmjss versus mx for the XCJ background modes. . . 125 5.36 Plots of mmjss versus mK* and mx versus mK* for the XcJ background modes 126 5.37 mx and mK*± distributions for XciK*± background MC eventsl3O 5.38 mx and mK*o distributions for Xc1K*O background MC events 131 5.39 mx versus mK*o for Xc1K*O background MC events peaking in mmjss 132 6.1 Data/MC comparison for B —* XiK 139 6.2 Data/MC comparison for B —* XciK 139 6.3 Data/MC comparison for B — Xc1K*± 140 6.4 Data/MC comparison for B —+ Xc1K*O 141 6.5 Event type components for the fit to mmjss for B± XcJK. 142 6.6 Event type components for the fit to mmjss for B° —+ XcjK. 143 6.7 Event type components for the fit to mmjss and mK*± for B XcJK*± 144 6.8 Event type components for the fit to mmj8s and mK*o for B° XcJK*O 145 6.9 P1ots for B —* Xci,2K events from data 147 6.10 3Plots for B± Xci,2K*± events from data 148 6.11 3Plots for B° —f Xci,2K*O events from data 149 6.12 Data/MC comparison for B — X(J/i,b7)K 150 6.13 Data/MC comparison for B — X(J/&)K 151 6.14 Data/MC comparison for B —* X(J/b7)K*± 152 6.15 Data/MC comparison for B —> X(J/y)K*O 153 xi’ List of Figures 6.16 Event type components for the fit to mmjss for the B± , X(J/i’y)K decay mode 154 6.17 Event type components for the fit to mmjss for the B° X(J/’ç&y)K decay mode 155 6.18 Event type components for the fit to mmiss and mK*± for B —, X(J/by)K*± 156 6.19 Event type components for the fit to mmjss and mK*o for B°—*X(J/’by)K 157 6.20 3Plots for B —* X(3872)(J/i’y)K events from data 158 6.21 3Plots for B —* X(3872)(J/1,b)K*+ events from data 159 6.22 3Plots for B° —* X(3872)(J/,7)K*O events from data 160 6.23 Data/MC comparison for B — XQ(2S)7)K 162 6.24 Data/MC comparison for B — X(&(2S)-y)K 162 6.25 Data/MC comparison for B — XQ&(2S)7)K*+ 163 6.26 Data/MC comparison for B — XQ’(2S))K*o 164 6.27 Event type components for the fit to mmjss for the B+ X((2S))K decay mode 165 6.28 Event type components for the fit to mmjss for the B° —> X((2S)7)K decay mode 166 6.29 Event type components for the fit to mmjss and mK± for B — X((2S)7)K*± 167 6.30 Event type components for the fit to mmjss and mK*o for B° —p X((2S)7)K 168 6.31 3Plots for B — X(3872)((2S)7)Kevents from data 169 6.32 3PIots for B —* X(3872)((2S))K*+ events from data. . . 170 6.33 3Plots for B° —* X(3872)((2S))K*o events from data. . . . 171 6.34 3Plots for X —* J/’b’y in the range 3.6 < mx <5.0GeV/c2 . . 174 6.35 P1ots for X — (2S)y in the range 3.6 < mx <5.0GeV/c.. 175 7.1 Results for the Xcl,2 decay modes 188 7.2 Results for the X(3872) —+ J/by decay modes 189 7.3 Results for the X(3872) —* (2S)7 decay modes 190 xlii Glossary ARGUS - The name of a particle physics experiment conducted at the Deutsches Elektronen Synchrotron in Germany during the late l98Oies. B Factories - Collective name for the BABAR and Belle experiments. B meson - A particle consisting of a bottom quark (or anti-quark) and an anti-quark (quark), particularly of the up or down type. BA.BAR - A particle physics experiment located at SLAC, designed primarily to explore CP violation in the decays of B mesons. Belle - A particle physics experiment similar to BABAR, located in Japan. C++ - A computer programming language. c - Shorthand notation for a charmonium state. CDF - A particle physics experiment examining proton-antiproton colli sions at Fermilab. charmonium - The bound state of a charm and anti-charm quark. Cherenkov light - Photons emitted by a particle traveling faster than the speed of light in a given medium. XcO,1,2 - Symbolic name for a series of charmonium states with an orbital xiv Glossary angular momentum L = 1, and total angular momentum of J = 0, 1,2, re spectively. CKM matrix - Abbreviation for the Cabibbo-Kobayashi-Maskawa matrix. A 3 x 3 matrix describing the relationship between the weak and flavour eigenstates of the quarks. CLEO - A particle physics experiment examining ee collisions located at Cornell University in New York. CP violation - The concept that the laws of physics are not identical under the interchange of a particle to antiparticle and swapping the spatial definition of left and right. Crystal Ball - A particle physics detector originally used at SLAC in the late 1970ies and early l98Oies. D meson - A particle consisting of a charm quark (or anti-quark) and a light (up or down) anti-quark (quark). Dø - A particle physics experiment examining proton-antiproton collisions at Fermilab. Dalitz plot - The scatter plot of the invariant mass of a pair of parti cles versus that of another pair of particles in a three-body decay. DCH - Abbreviation for drift chamber. In BABAR, a detector component consisting of multiple wires in a gas chamber used to track the passage of charged particles. DOD*O molecule - A loosely-bound four-quark state consisting of a and meson. xv Glossary DIRC - Abbreviation for Detector of Internally-Reflected Cherenkov light. A unique detector component in BABAR that uses Cherenkov light emitted and reflected inside of quartz bars for particle identification. EMC - Abbreviation for electromagnetic calorimeter. In BABAR, a detector component composed of scintillating crystals used to detect electrons and photons. factorization - A theoretical assumption that decays of the form B —* cK can be simplified by considering only the interaction between the final state c and the vacuum. One implication is the prediction of a decay rate of zero for B — xo,2K Fermilab - A U.S. national laboratory for particle physics located near Chicago, IL. GEANT4 - A software package for simulating the interaction of particles with matter. gluon - According to the Standard Model, the particle responsible for the strong force between quarks. HER - Abbreviation for High Energy Ring. Refers to the ring used for circulating 9 GeV electrons in the PEP-TI collider. hybrid - Term used to describe a state consisting of a quark-antiquark pair (particularly a cc in this case) and a gluon. IFR - Abbreviation for Instrumented Flux Return. In BABAR, it refers to a detector region consisting of metal plates sandwiching gas-filled parti cle detection chambers used both for managing the magnetic field and for muon detection. xvi Glossary ISR - Abbreviation for Initial State Radiation. Describes events in which the initial e+e collision occurs at a reduced energy due to earlier emission of a photon. J/1’ - Symbolic name for the lowest charmonium state with orbital an gular momentum L = 0 and total angular momentum J = 1. The first experimentally-discovered c state. kaon - Short for “K meson”. A particle consisting of a strange quark (or anti-quark) and a light (up or down) anti-quark (quark). klystron - A vacuum tube used for microwave generation and particle ac celeration. LER - Abbreviation for Low Energy Ring. Refers to the ring used for circulating 3.1 GeV positrons in the PEP-TI collider. LST - Abbreviation for Limited Streamer Tubes. In BABAR, a detector component consisting of a gas-filled chamber with a sense wire, used for muon detection. Replaced failing resistive plate chambers in BABAR. MC - Abbreviation for Monte Carlo. Monte Carlo - A computational analysis method using many random ized detailed simulations of an experiment to understand and predict how it will perform in reality. mK* - The invariant mass of a K* candidate. mmjss - The difference between the four-momentum of the e+e system and that of the reconstructed B candidate with the mass constrained to the known value. xvii Glossary mx - The invariant mass of the X — e&y candidate. particle identification - Methods used to assign a particle type to an ob ject reconstructed from primary information collected by a particle detector. PDF - Abbreviation for Probability Density Function. A function describ ing the probability distribution of a given variable in an integral form. PEP-IT - A positron and electron particle accelerator located at SLAC. PID - Abbreviation for particle identification. PMT - Abbreviation for photomultiplier tube. Used to detect photons. ‘&(2S) - Symbolic name for the first excited charmonium state with orbital angular momentum L = 0 and total angular momentum J = 1. Analogous to the J/’. QCD - Abbreviation for quantum chromodynamics, the theoretical descrip tion of the strong force of particle physics. ROOT - A software package commonly used for particle physics analy ses. RPC - Abbreviation for Resistive Plate Chambers. In BABAR, a detector component consisting of a gas-filled gap under high voltage used for muon detection. SLAC - Abbreviation for the Stanford Linear Accierator Center, now known as the SLAC National Accelerator Center. A U.S. national particle physics laboratory located near Stanford University in California. Standard Model - The basic modern theoretical description of all of par xviii Glossary tide physics. P1ot - A statistical technique for unfolding the distribution of a sample in one variable based on its distribution in another uncorrelated variable. SVT - Abbreviation for Silicon Vertex Tracker. In BABAR, a detector com ponent consisting of silicon strips under an applied voltage used for precise tracking of a B meson decay at its decay vertex. tetraquark - Term used to describe a tightly-bound state of two quarks and two antiquarks. TRIUMF - Abbreviation for TEl-University Meson Facility, a particle physics laboratory located in Vancouver, Canada. X (3872) - A recently discovered particle with a mass of 3872 MeV/c and unknown internal quark content. T(4S) - Symbolic name for the bottomonium state produced at the B Factories that promptly decays to B mesons. xix Acknowledgements First and foremost, I wish to thank my supervisor, Chris Hearty. He has been incredibly supportive of my scientific pursuits, and I am very grateful for the many opportunities he has afforded me during my graduate work. He is an impressive physicist, and his advice and suggestions have been extremely valuable in advancing this analysis and my career. It has been a pleasure to work with him and have him as my academic mentor. I wish to thank all of the members of the BABAR Charmonium Work ing Group, past and present, especially Claudia Patrignani, Philippe Gre nier, Shuwei Ye, Tulay Cuhadar-Donszelmann, Arafat Gabareen Mokhtar, and Bill Dunwoodie. Their insight and help have been very important to me in my explorations of heavy quarkonium physics. I would also like to extend my thanks to the members of the BABAR review committees that oversaw the publications related to this work: Paul (Jack) Jackson, Nicolas Arnaud, Woochun Park, Georges Vasseur, Frank Winklmeier, and David Lopes Pegna. Many thanks to the members of the LST team: Charlie Young, Peter Kim, Mark Convery, Stew Smith, Changguo Lu, Sanjay Swain, Gabriele Benelli, Wolfgang Menges (Ehrenfeld), and Sasha Telnov, to name only a few, whose expertise, friendship, and teamwork made the LST upgrade project one of my most rewarding graduate school experiences. Thanks to professors Janis McKenna and Tom Mattison, and to Ph.D. committee members, Scott Oser, Javed Iqbal, and Vesna Sossi, for all of their helpful guidance and input over the course of my studies at UBC. To fellow graduate students, Dave Asgeirsson, Tae Mm Hong, Keith Ulmer, Dan Balick, Karsten Koeneke, Jim Hirschauer, Chris Schilling, Tim Piatenko, Andy Ruland, Grant MacGregor, Joe Tuggle, Jake Anderson, xx Acknowledgements and the many others I’ve worked with at SLAC: thank you for making my experience somewhat more intellectual and mostly a whole lot more fun. Finally, a special thank you to my wife Melissa, without whose love, support, and sacrifice, this would not have been possible. xxi Dedication For Mariposa Jane, with love. xxii Chapter 1 Introduction The development of particle physics over the past century has led to what is called the Standard Model (SM) of particle physics. This framework en compasses the fundamental particles of matter, leptons (electrons, muons, taus, and their associated neutrinos) and quarks (with “flavours” up, down, charm, strange, top, and bottom), and their interactions via the electro magnetic, strong, and weak forces (mediated by photons, gluons, and the W and Z bosons, respectively). Weak interactions are capable of changing quark flavour, with the coupling between flavours described by the Cabbibo Maskawa-Kobayashi (CKM) matrix. The Standard Model also predicts the existence of the Riggs boson, thought to be responsible for the masses of the other particles in the SM, and necessary to explain the symmetry breaking of the electromagnetic and weak forces. It is a highly successful theory, and represents our best description of how all known matter exists and interacts in the most fundamental way. The study of particle physics is the study of our universe at its deepest level. In the Standard Model, quarks are massive point-like particles that in teract with one another predominantly via the strong force. The strong force is mediated by gluons and acts between particles (i.e. quarks) that have colour, the strong force analogue of electromagnetic charge. The the ory describing these processes is called quantum chromodynamics (QCD), and it essentially explains how quarks bind together to form matter. This work focuses primarily on bound states of a charm and anticharm quark, known as charmonium (efl) mesons, whose interactions are described within the realm of QCD. By investigating particles in the charmonium system, one can indirectly test and improve the theory of quantum chromodynamics. Charmonium was first discovered experimentally in 1973 [1]. This was 1 Chapter 1. Introduction the first convincing evidence for the quark model. This system has been well described by a phenomenology analogous to that for hydrogen or positron ium states. The so-called “charmonium model” [2] has successfully predicted and characterized all of the charmonium states expected up to a mass of 3.72 0eV/c, above which the dominant decays are via the strong force to a pair of D mesons. The BABAR experiment, located at the PEP-TI ee collider at the Stan ford Linear Accelerator Center, was designed to explore the violation of charge conjugation and parity (CP) symmetry in the decays of B mesons. In addition, the decays of B mesons provide a fertile ground for studying a broad range of particle physics topics, including the charmonium system. B mesons decaying via the weak interaction quark decay b —b c produce char monium states via B —‘ cK. This can be used to test the predictions of the charmonium model, and to search for yet-to-be-discovered .exotic states. In 2003, the Belle experiment discovered a signal in the decay B XK, X —* J/ir7r [3]. Called the X(3872), it was found to have a mass of mx = 3872.0 ± 0.6(stat.) ± 0.5(syst.) MeV/c2 and a width of F < 2.3 MeV/c2 This discovery was verified by BABAR [4], as well as by Dø [5] and CDF [6] at Fermilab. Angular analyses suggest a quantum number assignment of jPC = l or 2 [7] The X(3872) displays some characteristics of a charmonium-like state, but its narrow width above the DD threshold and quantum numbers limit its possible assignment within the charmonium model. Its mass near mDo + mD—*o has led to speculation that the X(3872) may be the bound state of two D mesons. Other more exotic interpretations include a tetraquark (tightly bound state of four quarks) model, or charmonium-gluon hybrid bound states. If the X(3872) is not a conventional charmonium state, it pushes the boundaries of the well-known framework of QCD. A search for the radiative decays X(3872) —* J/7 and X(3872) — &(2S)7 provides a useful diagnostic for this particle. Decays of this type would confirm charge-parity to be positive (C = +). While some molecular theories can accommodate X(3872) — J/’zb7, the decay X(3872) —* is expected to be greatly suppressed. On the other hand, the charmonium 2 Chapter 1. Introduction model predicts that the ratio of the branching fraction for the decay to (2S)7 compared to J/b y could be substantial for the Xci (2P) charmo nium state, one of the few available charmonium options remaining for the X(3872). This thesis presents a study of B —p cë-yK decays where cë includes J/i& and (2S), and K includes K, K° and K*(±,o) (892), with an emphasis on a search for the radiative decays X(3872) — J/b7 and X(3872) —* This analysis is also sensitive to the well-known radiative charmonium de cays B —x1(1P)K and B — xc2(1P)K, which can be used as benchmark modes to confirm the analysis technique, as well as to make improved mea surements of their respective branching fractions in their own right. It aims to determine the internal structure of the X(3872) and improve the under standing of the known charmonium system, contributing to the wider base of knowledge describing the formation of quarks into matter. Chapter 2 provides background information relevant to this analysis, in cluding the theoretical description of the charmonium system, a review of the recent experimental results concerning the X(3872), and a summary of the theoretical proposals to describe the nature of this newly discov ered state. Chapter 3 gives a physical description of the PEP-TI collider, the BABAR detector, and its hardware and software. Chapter 4 describes the data set, its properties and the selection criteria used in this analysis. Chapter 5 explains the signal extraction methodology and its verification on simulated datasets. Chapter 6 contains the analysis of the actual data and the branching fraction measurements. Chapter 7 summarizes this research and presents its larger implications. 3 Chapter 2 Background Information This chapter outlines the theoretical and experimental background appro priate to this analysis. It specifically describes the charmonium system, including c binding, production, and decay. The recent experimental re suits of several newly discovered charmonium-like phenomena are presented along with their likely theoretical interpretation. The potential contribution of this analysis to the further understanding of these new states is explained. 2.1 The Charmonium Model The understanding of particle physics was revolutionized in 1974 with the discovery of the J/b [1] and (2S) [8], identified as c mesons. These dis coveries were the first evidence for the existence of the charm quark, and taken as confirmation of the quark model describing the underlying con stituents of baryons and mesons. In its simplest terms, the quark model for mesons describes them as a combination of a spin- quark and antiquark. The combined total spin is S = 0 or 1, the orbital angular momentum can be L = 0, 1,2, ..., and the principle quantum number is denoted by N. For charmonium, the parity1 of these states is p = (_l)L+l, and the charge conjugation2 C-parity is defined as C (_i)L+S. In standard spectro ‘The parity transformation is a spatial inversion operator, i.e.: PW(x, y, z) >—÷ IW(—x, —y, —z)>. (Anti)quarks have (negative)positive parity. Bound states with wave- functions described by spherical harmonics have the property P = (_1)L. The total parity is multiplicative. ‘The charge conjugation operator transforms a particle into its antiparticle. The total charge conjugation eigenvalue is multiplicative. Similar to parity, C = (_1)” for the spatial part of the wavefunction. Conjugation of the spin part is antisymmetric for S = 0 and symmetric for S = 1, thus C = (_1)’. A factor is introduced for the charge part of the wavefunction, its value defined by C = —1 for the photon. 4 2.1. The Charmonium Model scopic notation, a state is referred to as N24Lj (where L = 0, 1, 2, ... is represented by letter notation S, F, D, ...), with quantum numbers JPC• The earliest theoretical models describing the cë system are purely phe nomenological. Their assumption is that the bound charm and anticharm quarks are non-relativistic, and interact via a simple mechanism of one gluon exchange. This interaction reduces to the same form as the electromagnetic interaction and can be represented in a form similar to the Coulomb po tential with 1/7’ dependence (where r is the distance between quarks). One of the tenets of the quark model, known as quark confinement, stipulates that quarks are restricted to bound states and cannot be free. A term pro portional to r was added to the potential to model this behaviour. The cc interaction in this “Cornell model” [2] of charmonium was thus described by the potential V(r)=—+- (2.1) where k and a are parameters determined by fitting to experimental data. This basic description serves as the foundation of the charmonium model, upon which all subsequent developments were based. Necessary corrections can be made by including spin-spin and chromodynamic couplings, such that the potential is described as 4c 32ira —V(r)—_——-+br+ 9m 50.(r)S. S (2.2) where (r) = (a//)3e_0T2,is a Gaussian-smeared contact hyperfine in teraction, and the standard cc 1/r colour-Coloumb and cc r confinement terms are retained. The parameters a8, b, m, and a are determined from a fit to the experimental spectrum. Perturbation theory can be used to include the spiii-orbit interaction, Thomas precession, and the tensor inter action, resulting in an additional term for the potential 1 /2a3 b—’ —> 4cx8V57,(r) = — — L. S + —-T (2.3) where and are the orbital and spin angular momentum operators with 5 2.1. The Charmonium Model • >= [J(J + 1) — L(L + 1) — S(S + 1)1/2, and the tensor T has non-zero entries between L > 0 spin-triplet states, 6(2L+3)’ J=L+l (3LjTIj) = +, J = (2.4) (L+i) — 6(2L—1)’ — — These perturbations are applied to solutions of Schrödinger equation for the basic central potential. Values for the unknown parameters, o, b, m, and o, are determined by fitting the predicted spectrum to the data. This model is generally known as the “non-relativistic” model. One of the most important theoretical developments is the so-called “Godfrey-Isgur model” [9], which extended the basic model to include rela tivistic corrections and a variable (“running”) strong force coupling constant, and applied it to u, d, s, c and b quark systems. The power of this model is that it is valid for describing all quarkonia flavours, heavy and light, yet it reduces to the usual non-relativistic approximations of the original charmo nium model (to first order). These two theoretical descriptions are the most widely accepted basis for a complete description of the charmonium system. The charmonium spectrum predicted by the most up-to-date calculations [10] is presented in Figure 2.1. It is worth mentioning in passing that lattice QCD, a numerical method for calculating the strong force interaction between quarks and gluons on a tiny, discrete scale, can also be employed to study the charmonium system [11]. Unfortunately the accuracy and predictive power of these calculations does not yet approach that of the phenomenological models presented here; therefore they will not figure substantively into this discussion. 6 2.1. The Charmonium Model C1 0 > a) 0 0 Figure 2.1: Predicted and observed spectrum of the charmonium model. The blue points indicate the experimental results for well-established char monium states, the red points indicate newly discovered states and their likely jPC assignments, and the gray boxes indicate the range of theoreti cal predictions from the non-relativistic model and the Godfrey-Isgur model [10]. The DD threshold is also shown. (2S+1 ) I-J O- f 2 1- 2 f 2 ?‘ jPC 7 2.2. Charrnonium Production b U Figure 2.2: Feynman diagram of B —÷ ccK. 2.2 Charmonium Production There are four main production mechanisms for cë states in BABAR. The colour-suppressed3b —f c decay of B mesons (B —p cK, for example) is the dominant method of production, and the most important in this analysis. Charmonium states of any quantum numbers jPG are accessible from this decay. Charmonium can also be produced via an initial-state-radiation (TSR) process, i.e. e+ e —* where the incoming e± has lost some energy via photon emission. The third charmonium production method accessible in e+e collisions is the two-photon process e+e e+ec. Finally, double charmonium production, e+e c+c, was stumbled upon experimentally at the B Factories only recently. The decay of the B meson to cK, shown in Figure 2.2, is a hadronic decay. While it is a flavour-changing weak decay, it is greatly complicated by additional gluonic strong interactions between the particles. These in teractions are typically described by a phenomenological approach known as factorization [12j. When the c pair is produced, it is susceptible to ad ditional interactions with gluons and light quark-antiquark pairs. However, because it is a colour-singlet4bound state, the cZ will both move away from 31n Figure 2.2, the quark must be produced with the correct colour to match that of the “spectator” quark, u. This results is a suppression factor for the decay rate. 4For simplification, the colour-octet contribution is ignored and colour-singlet is con sidered to dominate. C w+ C S U 8 2.2. Charmonium Production the production vertex and interact as a single bound state rather than as individual quarks. As a result, the c pair hadronizes as a single meson. The benefit of the factorization assumption is that the decay amplitude can be broken down into the multiplication of two currents, for example, (KcI?-teff IB) is evaluated as the product of the matrix elements between the B and K, and between c and the vacuum. The matrix element for the B —* cK decay can be expressed as [13]: (Kcl (sc) V_A(Cb) V—A IB) cx (Kl (b)v_AIB) (cI (c)V_A 10) (2.5) where the notation (‘q)v—A represents y’(l — y’)q. Thus the amplitude for the decay is proportional to the matrix element (cal (cc) V—A 0). This analysis is particularly interested in the case c? includes the xci and Xc2 charmonium states. The axial-vector 1+ Xci couples to the V — A operator, resulting in a non-zero matrix element and a decay amplitude that can be predicted theoretically using further numerical inputs. Because Xc2 is a tensor (2+) particle, it does not couple to vector or axial-vector operators, hence the matrix element (Xc21(&) V—Al0 = 0. Similarly, (xol(c)v_Al0) = 0 because (0++1(c)v_Al0+j = 0 due to charge conjugation invariance. Thus according to this naïve factorization approach, decays of the type B ,- XcO,21 are forbidden while decays to Xc1K decays are allowed [14]. Experimental data from both BABAR [15, 16, 17] and Belle [18, 19] some what contradict these predictions. Decays B — xoK have been observed with branching fractions (9(10), while B —* Xc2K only has upper limits nearly an order of magnitude lower. Extensions to the factorization model (for example, rescattering effects [20], next-to-leading order corrections [21], etc.) allow for B —* XCO,2K decays with branching fractions similar to what has been observed for B(B —‘ xiK) 4x i0. Measurement and discovery of B decays to Xc2K are a crucial test for these theories. 9 2.3. Charmonium Decay 2.3 Charmonium Decay The decays of charmonium states can be broadly classified into three types: annihilation, radiative, and via the strong interaction. Annihilation decays (i.e. J/’/’ —+ are generally suppressed for bound states, but the final state of two leptons is an experimentally clean signal that is easily identified. Common radiative decays include electromagnetic radiative transitions of an excited c? state to a lower energy charmonium state by emitting a photon, or by the emission of gluons creating light quarks (i.e. (2S) —> J/rirj. Above the threshold for the production of a pair of D mesons, 3.72 GeV, decays via the strong interaction are entirely dominant. Below this energy, strong decays are OZI-suppressed5[22], leading to (relatively) long lifetimes and narrow widths. Radiative decays are often the most accessible transi tions. The principle charmonium decay modes of interest in this analysis are radiative decays of the form c’ —* The electromagnetic transition between two states is expected to be dominated by the electric dipole (El) transition6,for which the decay width can be calculated from [23]: FEl(fl2S+1LJ — n’28’’L ji +7) = (2.6) where e = 2/3 is the charge of the c quark, c is the fine structure constant, P27 is the photon energy, (?f IrIbj) is the matrix element between the initial and final radial wavefunctions describing the charmonium states in question, and the angular matrix element Cf is defined as: IL’ J’ Gf = max(L, L’)(2J’ + 1) (2.7) L lJ 5The “OZI rule” identifies the suppression of strong decays that occur between disjoint Feynman diagrams via multiple gluon exchange. In these decays, gluons must carry enough energy to hadronize into the final state products. As a result, they have a high energy and hence a smaller value for the strong coupling constant a8. 6Higher order multipole (so-called “forbidden”) transitions such as Ml are not consid ered here as their rates are expected to be relatively suppressed by orders of magnitude. 10 2.4. Exotic Quarkonia where the curly brackets indicate a 6— j symbol, which are a generalization of Clebsch-Gordon coefficients for the coupling of three angular momenta (in this case, the initial and final c states and photon). Equation 2.6 can be evaluated for any charmonium state given the ex pected masses and an expression for the wavefunctions and These inputs can be provided from the phenomenologicai models described in Sec tion 2.1 to produce estimates for the radiative transition widths. Of particu lar interest are the yet to be discovered charmonium modes for which decays to J/ and &(2S) are expected or favoured, namely the xj(2P) states. Al though the predictions are highly model-dependent for these states, they generally predict decay widths ranging 10 — 100 keV, with decays to (2S)7 tending to be favoured over decays to J/’by by a factor of ‘- 1 — 10. Thus a measurement of the relative branching fraction of a newly discovered state to these final states could help to identify it, given certain assumptions regarding the choice of model. Although they are not the subject of this study, it is important to men tion the role of open-flavour strong decays of charmonium. The general description is the creation of a light qq pair from the vacuum, with the cë splitting to form separate c and ?q mesons. The qq pair is assumed to be produced with quantum numbers 0++, hence the model describing these decays is called the “3P0 model” [24]. This model has been successfully ap plied to most meson and baryon systems. In terms of charmonium, it is used to describe the expected decays for cc states above the DD threshold. In general, calculations of the decay widths above this “open charm threshold” demonstrate that decays c —* are expected to entirely dominate [10]. 2.4 Exotic Quarkonia In addition to the well-known charmonium model, there have been other proposals describing the formation of exotic QCD states expected above the DD threshold. Three particular classes of models, diquark molecules, tetraquarks, and charmonium hybrids, illustrated in Figure 2.3, are poten 11 2.4. Exotic Quarkonia qZj-gluon”hybrid” Figure 2.3: Cartoon depiction of plausible exotic QCD states: diquark molecules, tetraquarks, and g hybrids. Figure from [25]. tially relevant to this analysis. Diquark molecules, also called densons, are a pair of loosely bound charmed mesons [26]. While predictions for states of this sort have existed for some time, it is only in light of recent evidence from the B Factory exper iments(described in Section 2.5) that they have been closely re-evaluated. The binding of these states is described as dominantly via pion exchange at large distance, with short-range contributions from quark interactions. Be cause of their weak binding and separation distance, the mesons are expected to decay as though they are free. Detailed theoretical treatments of a bound D°D° state [27] have produced specific and testable quantum number and decay branching fraction predictions, the implications of which will be dis cussed in detail in Section 2.6. In brief, a DOD*O molecular bound state is expected to violate isospin, decay dominantly to D0D°ir0 and DOD°7, and diquark-diantiquark D° — D*O “molecule” 12 2.5. Recent Experimental Results have quantum numbers of The tetraquark model [28] describes a closely bound four-quark state, [cq] [] in which scalar and vector triplets are formed and attract via spin- spin interactions. Decays are expected to occur by internal rearrangement of the tetraquark followed by dissociation into component mesons. This the ory predicts a rather ambitious multitude of states in the region above the open-charm threshold. Should they exist, tetraquark states are expected to exhibit a range of quantum numbers (0, 1, 1+—, and 2, with degen eracies), and include states with non-zero strangeness and non-zero charge. The final set of states worth considering in this analysis are charmonium gluon hybrids. These are c states with an excited gluonic degree of freedom. There are several models describing quarkonium-gluon hybrids [29]. As a general remark, these models predict many states with distinct and exotic quantum numbers (e.g. a doubly-degenerate octet [30]), and could possibly decay to ccgg and D(*,**)D(*,**). For charmonium-gluon hybrids, the lowest mass predictions are expected to be at least 4.2 GeV/c,well above the open- charm threshold. 2.5 Recent Experimental Results The past few years have seen a flurry of activity in the charmonium sector. The B Factories, BABAR and Belle, have thoroughly explored the charmo nium system below the DD threshold. In addition to measuring the well known (lS), J/’’, xj(lP), and (2S) states, they have also observed the (2S) [31]. Perhaps the most interesting of these results have been the dis covery of many new charmonium-like states above the DD threshold that do not fit into the standard charmonium model and possibly point to more exotic QCD discoveries. A concise review of these surprising new findings is given here. 7The only remaining below-threshold charmonium state yet to be observed in the B Factories, h, was discovered at CLEO [32] 13 2.5. Recent Experimental Results 2.5.1 X(3872) In 2003, Belle discovered a narrow peak in the invariant mass distribution of X —* J/rr in the exclusive decay B —* J/rrK [3]. Until its nature is fully understood, the placeholder name assigned to this particle is X(3872). This discovery was subsequently confirmed by the CDF [6] and Dø [5] experiments, as well as in BABAR [4]. The current world average mass of this new resonance is m(X) = 3872.2 ± 0.8 MeV/c2 with a width of F = 3.0t ±0.9MeV/c2 [33]. The decay has been seen in both neutral and charged B decays, although the latest updates from BABAR [34] and Belle [35] in the high-statistics X(3872) — J/irir mode agree only marginally regarding the ratio of X(3872) decays from charged and neutral B mesons. Both Belle (in an unpublished conference presentation [36]) and BABAR (as a precursor to this thesis, published by the author [37]) have found evi dence for the decay X (3872) —* . These results are shown in Figure 2.4. Because the charge conjugation (C) parity of the J/ and -y are both neg ative, this implies C = + for the X (3872). Combining charged and neutral B decays, the Belle measurement found B(B —f X(3872)K) . B(X(3872) J/-y = (1.8±0.6±0.1) x 10—6 with a significance of 4.Oa, while BABAR mea sured B(B —* X(3872)Kj . B(X(3872) — J/iy = (3.3 ± 1.0 ± 0.3) x 10—6 with a statistical significance of 3.4o. CDF [38] and Belle [39] analysed the dipion mass distribution from X(3872) —* J/1r7r decays and found them to favour a “p-like” shape, suggesting X(3872) —* J/’t’p°. Belle also found evidence for the decay X(3872) — irirr in B decays, where the X(3872) decay is thought to proceed via X (3872) —k J/ [36]. However, this claim has been disputed by BABAR [40]. CDF performed an analysis of the angular distributions of the daughters in the X(3872) —* J/rir decay, ruling out all JPC assign ments except for 1 and 2 [7]. In studies of the decay B — D0irK, both Belle [41] and BABAR [42] find a significant narrow enhancement slightly above threshold. Belle’s initial measurement of the mass was m(X) = 3875.2 ± 1.9MeV/c2,while BABARfoundm(X) = 3875.1±1.2MeV/c2,withawidthofF(X) = 3.0t± 14 2.5. Recent Experimental Results 3736 3928 4120 M(’yJ/) (MeV) 73’83’9 41 (GeV/c2) Figure 2.4: Previous results of X(3872) —* J/’b’)’ from Belle [36] (top) and BABAR [37] (bottom). 15 2.5. Recent Experimental Results 0.9 MeV/c2 and confirmation that the decay proceeds via X — DOD*O. This mass value is roughly 4.5 above the mass of the X(3872) as measured in X(3872) —* J/irir. A recent higher statistics update from Belle pre sented at conference [43] also favours the decay X —* DO.*O, although the mass value of 3872.6 ± 0.4 MeV/c2 is much closer to that of the X(3872). It is generally agreed [44, 45] that a mass shift at this level is still consistent with a single X(3872) state. The B Factories have conducted several other searches for the X(3872) decays, though all have returned null results and upper limits only. These include X(3872) —* J/’ [46], X(3872) —+ DD [47], X(3872) — Xcl,27 [3], and X(3872) — J/irr° [48]. Most of the experimental evidence at this time suggests that the X(3872) state is a DOD*O molecule, but the results are not entirely conclusive. Full details of the theoretical interpretations of the X(3872) are discussed in Section 2.6. 2.5.2 The X/Y/Z Family Following the discovery the X(3872), three more charmonium-like states were discovered by Belle in a similar mass region but via distinct produc tion methods and decay modes. All three states have possible conventional charmonium model interpretations. A resonance with a mass of m(X) = 3942±8 MeV/c2,called the X(3940), was discovered by the recoil of the J/’b in the double-charmonium pro duction of ee —* J/bX(3940) and confirmed in decays to DOD*O (but not DD) [49]. Observation of an additional state with a mass of m(X) = 4156 ± 29 MeV/c2 was also claimed by Belle [50]. Given the production mechanism and the decays to DOD*O, the most obvious quantum number assignment is jPC = o, implying 19O charmonium. However, the masses of both observations are inconsistent with charmonium model predictions. The X(3940) is at least 100MeV/c2below the (3S) expectation, while the X(4160) is similarly above this value yet 300 MeV/c2 below the predicted mass for the next excited state, ii(4S). 16 2.5. Recent Experimental Results The Y(3940) was first seen by Belle in the decay B —* KY(3940), Y(3940) — J/’bw. Belle measured a mass and width of m(Y) = 3943 + 11± 13 MeV/c2 and F(Y) = 87 ± 22 ± 26 MeV/c2 [51]. This state was recently confirmed by BABAR, measuring a mass and width of m(Y) = 3914.3t±1.6 MeV/c2 and F(Y) = 332 ± 1 MeV/c2 [40]. While the mass and width are generally consistent with predictions for the XcO (2P) or Xci (2P), the branch ing fraction to the observed decay mode is orders of magnitude higher than what would be expected for a charmonium state above the DD threshold. It is also still unclear if the X(3940) and Y(3940) are separate states. Finally, the Z (3930) was found by Belle in the two-photon process yy Z(3930) decaying to DD [521. They measured a mass and width of m(Z) = 3929 ± 6MeV/c2 and F(Z) = 29 ± 10MeV/c2,respectively. Belle also per formed an angular analysis of the D decay daughters that favours jFC = 2* Given charmonium model predictions of m(Xc2(2P)) 3970MeV/c2 and total (Xc2 (2P)) 30 MeV/c2, the combined experimental information strongly implies that the Z(3930) is the Xc2(2P) charmonium state. 2.5.3 States Produced in TSR Several new states have been discovered via initial-state-radiation produc tion. The first of these was BA.BAR’s discovery [53] of a broad structure in the decay ee —* Y(4260), Y(4260) — J/rir with a mass and width of m(Y) = 4259 ± 8t MeV/c2 and F(Y) = 88 ± 23t MeV/c2. Following this discovery, CLEO performed a centre-of-mass energy scan and also col lected data directly at the Y(4260) resonance, confirming BABAR’s discovery as well as finding evidence for the decay Y(4260) —* J/& irn0 [54]. Belle has recently also confirmed this state, and claims a second, much broader reso nance at m = 4008 ±401 MeV/c2 with a width of F = 226 ± 44 MeV/c2 [55]. BABAR’s search for an accompanying Y(4260) —* b(2S) ir decay turned up a structure at a higher mass incompatible with the Y (4260) [56]. This new state was found to have a mass of m(Y) = 4324±24 MeV/c2 and a width of F(Y) = 172 ± 33MeV/c2.Belle confirmed this discovery, while finding 17 2.6. X(3872) Phenomenology idence for a higher resonance with a mass of m(Y) = 4664 ± 11 ± 5MeV/c2 and width of F(Y) = 48 ± 15 ± 3 MeV/c2 [57]. Because these states are produced in the annihilation of e+e, they nec essarily have = 1——. However, all of the 1—— charmonium states have already been accounted for. This makes it difficult to accommodate even one, let alone all, of these new resonances within the charmonium model. Based on the masses (m(Y) > 4200 GeV/c2) and lattice QCD predictions, charmonium hybrid assignments appear to be an attractive explanation, al though tetraquark predictions, DD molecules, and threshold effects remain possibilities. At this time there are no definite conclusions. 2.5.4 Charged Multiquark States Belle recently announced the observation of a state in the decay B — /i(2S)irK [58]. Based on a Dalitz-plot analysis, they claim evidence for a charged state, Z, decaying via Z — (2S)7r with a mass of m(Z) = 4433 + 4 ± 1 MeV/c2 and a width of F(Z) = 44tt MeV/c2. In response, BABAR performed a search for the same state and found no significant evi dence to confirm Belle’s claim [59]. Provided this state actually exists, its non-zero charge implies that it could be the first evidence for a charged tetraquark. Belle also claims evidence for two additional features in the decay of B — xiirK that could be identified as charged tetraquarks decaying via Z+ —* Xc17r+ [60]. These results need further confirmation. 2.6 X(3872) Phenomenology From the results presented in Section 2.5, it is known that the X(3872) has a mass of 3872.2±0.8MeV/c and a width of MeV/c2. Both BABAR and Belle have seen evidence for it decaying to the final states J/ ir DOD*O, and J/’& y. Belle also claims to have observed X(3872) — w, although this is not confirmed by BABAR. The decay to J/7 determines C = +, and the p-like shape of the dipion distribution in X(3872) —* J/irr is 18 2.6. X(3872) Phenomenology consistent with this finding. Based on the angular analysis from CDF, the jPG quantum numbers have been narrowed down to either 1 or 2*. If the X(3872) is a conventional charmonium state, then according to the quantum number assignments from CDF’s angular analysis, it could be either the Xci(23P1) or the 71c2(1 D2). In the case of the xi(2P) assignment, the mass does not match predictions given the assumption that Belle’s Z(3930), discovered in two-photon production, is the xc2(2P). The charmonium model predicts a splitting of < 50 MeV/c2 between the xc(2P) states, thus the mass of the X(3872) is too low. Regarding the 7c2 possibility, higher multipole (Ml and E2) radiative decays of the type ‘7c2 —f J/’*y should be strongly suppressed. The decay cë —* J/p0 vi olates isospin and is unexpected for either charmonium assignment (i.e.: ‘—O’J/ =0+Io=l). Of the exotic QCD models, the tetraquark explanation predicts the pres ence of a second neutral X(3872) with a mass splitting of 8MeV/c2, and allows for charged partners. Both Belle and BABAR’s measurements of the X(3872) in neutral and charged B decays find an X(3872) mass consistent with one another. The BABAR search for a charged partner to the X(3872) found no result. Furthermore, no indications for the predicted rich spec trum of charged and neutral accompanying states has been found. Given the experimental evidence to date, the tetraquark explanation is highly dis favoured. Regarding charmonium-gluon hybrids, the experimental results seem ingly do not match any predictions. The lightest charmonium-gluon hybrids have predicted masses more than 300 MeV/c2 above the current X(3872) mass. The expected dominant decay is to DD (no results to date) over DD (ruled out by BABAR), with little expected contribution to DD (the opposite has been observed by both BABAR and Belle). The mass of the X(3872) is very nearly equal to the mass of the D° and mesons, mDo +m,o = 3871.81 ±0.36MeV/c2 [33], leading many to be lieve that the X (3872) may be a DOD*O diquark molecular state. Molecular models predict the decay of the X(3872) toD07r and D°D°7 as the con stituent D mesons decay separately. These models can accommodate mixing 19 2.7. Analysis Outlook of the DoDo wavefunction with J/’b w and J/ p, which may explain the ap parent isospin violating decays observed in experiment. The 1 quantum number assignment is also consistent with the molecular model picture. It is worth noting that not all of the molecular model predictions have been confirmed by experiment. The large decay rate of X(3872) seen in BABAR and Belle is inconsistent with the molecular model, as is the relatively large B —* X(3872)K production rate. The radiative X(3872) J/’zb7 decay is allowed by the molecular model, but the predicted rate is again, smaller than experimentally observed. Finally, the production rate of the X(3872) in p and B decays is strikingly similar to that of b(2S) charmonium. A possible simple interpretation is that the X(3872) contains some c component, and is thus an admixture of a weakly-bound DO*O state and xi(2P) charmonium. The current status of the X(3872) remains an open question requiring further theoretical and experimental input. 2.7 Analysis Outlook The goal of this analysis is to use the full BABAR dataset to search for radiative decays of the X(3872), namely X(3872) — J/7 and X(3872) — (2S)7,produced in the decays B —* X(3872)K. This search includes both charged and neutral B meson decays to excited kaon and charmonium states. Because the general form of the decay is B —* (J/ ‘y)K, a measurement of B —* xi,2(J/’h)K can be performed in conjunction with the X(3872) search. The B —* x1K modes are well-established and can be used to validate the signal extraction method, while the factorization-suppressed B —* XC2K decay modes have never been observed. This analysis uses the largest data sample to date for such a search. To preserve signal efficiency, only charged final states of the kaons are reconstructed, and the c candidates are reconstructed decaying to lepton pairs. The b(2S) —* J/rir decay mode is also included to increase statis tics. Based on the B — X(3872)K, X(3872) —f J/’&y branching fraction measured by BABAR [37], this analysis could expect in the range of 20 — 35 20 2.7. Analysis Outlook events with -.- 4o statistical significance, given a similar analysis efficiency. The decay process to K* should follow the same Feynman diagram, and if the standard charmonium system is any guide, the branching fraction for decays of this type could be of similar order (with some reduction due to kaon daughter branching fractions). The expected number of &(2S) events is completely unknown. Within the framework of the charmonium model, Barnes and Godfrey [61] calcu lated that the branching fraction for the decay of xi(2P) —* b(2S)-y could be several factors higher than xi(2P) —÷ J/y. Radiative decays of a 2 charmonium state to J/ib and t’(2S)y should be highly suppressed. Re garding the molecular model for the X (3872), radiative decays to J/& -y are allowed in a vector-meson dominance scenario (where the p° or in the J/ p° and J/’& components of the X (3872) couple to a photon), whereas decays to b(2S)y proceed via annihilation of uuZ quarks (from the DO*O components of the X(3872)) and the branching fraction is expected to be very small [62]. If the X(3872) is the xi(2P) charmonium state, the de cay X(3872) —* (2S)’y may be observed. If X(3872) is a molecular or tetraquark state, decays to (2S)-y are unexpected. As stated in [27], “Per haps the most robust diagnostic is the b(2S) decay mode.. .Clearly a mea surement of the J/ and i42S) decay modes of the X(3872) will provide compelling clues to its internal structure.” 21 Chapter 3 The BABAR Experiment This chapter summarizes the detector hardware components and operation of the BABAR Experiment, including the design specifications, and the recon struction and simulation software. A full description of the technical aspects of the detector can be found in [63] and [64]. 3.1 The Linear Accelerator and PEP-Il Storage Rings The PEP-IT B-Factory is an asymmetric ee collider located at the Stan ford Linear Accelerator (SLAC) in Menlo Park, California. The electrons and positrons are first generated and accelerated in the 2-mile long linear accelerator (linac), and then circulated in opposite directions and focussed to collide by the PEP-TI storage rings. A diagram illustrating the layout of the linac and PEP-IT is shown in Figure 3.1. Electrons are first produced by an “electron gun”, where a filament is heated by an electrical current within a strong applied electric field. This generates free electrons which are accelerated away by the field toward the linear accelerator structure. The electrons are injected into the linac and accelerated to an energy of approximately 10eV, where they are then chan neled into damping rings. These are circular storage rings where the elec trons are maintained at a constant energy by accelerating them only to compensate for synchrotron radiation losses. This has the effect of “damp ing” the electrons, that is, tuning the spread and energy of the electrons in the beam to a desired constant. The damped electrons are then returned to the linac where they are accelerated to 9 GeV. Half of these electrons are 22 3.1. The Linear Accelerator and PEP-lI Storage Rings Figure 3.1: Illustration of the linear accelerator and PEP-IT collider. SLAC/LBL/LLNL B FACTORY 23 3.2. Detector Overview diverted from the linac and accelerated onto a tungsten target to produce electron-positron pairs. The positrons are collected and returned back to the start of the linac by a separate beam line, then redirected, damped, and accelerated to an energy of 3.1 GeV. The acceleration in the injector, damping rings, and the linac is pro duced by microwave pulses generated by klystrons adjacent to the beam line. Klystrons consist of an electron gun whose electrons are accelerated into a resonant cavity to produce microwaves, which are transmitted to the linac cavities via a waveguide. The microwave pulses from the klystrons cre ate electromagnetic fields in the copper linac cavities. The pulses are timed to provide the maximum acceleration to the particle bunches, and the field varies for electrons and positrons. Once accelerated to the desired energies, the electrons and positrons are split off from the end of the linac into the High Energy Ring (HER) and Low Energy Ring (LER), respectively. They travel around the rings in opposite directions, receiving additional acceleration to match synchrotron radiation losses. The beams are steered and focused using a series of magnets to coffide at an interaction point (IP) located at the centre of the BABAR detector. The initial PEP-IT coffider design aimed to deliver an instantaneous lu minosity of 3 x i0 cm2 Upgrades during the BABAR running period allowed the collider to reach up to a peak luminosity of of - 12x i0 cm2 The machine operated from 1999 through 2008, delivering a total lu minosity of 553 th of which more than —‘ 95% was recorded by BABAR. This included 433 th’ taken at the Y(4S) resonance resulting in approx imately 476 million BB pairs. The integrated luminosity over the course of the BABAR experiment is shown in Figure 3.2. 3.2 Detector Overview The BABAR detector is located at the collision point of the PEP-IT B Fac tory. It is designed primarily for the study of CP violation in the B meson sector, but also supports a robust secondary physics program for the study of bottom and charm mesons and T leptons. To meet these goals, it requires 24 3.2. Detector Overview Figure 3.2: Integrated luminosity delivered by PEP-TI to the BABAR exper iment. > 500 As of 2008/04/11 00:00 25 3.2. Detector Overview a large acceptance, good vertexing, reconstruction, energy and momentum resolution, high lepton (particularly e and ) and hadron particle identifi cation efficiency, and radiation hardness. Moving outwards from the centre, the detector consists of a silicon ver tex tracker (SVT) responsible for measuring the decay vertices close to the interaction point (IP), a drift chamber (DCH) for charged particle tracking and momentum measurement, a ring-imaging Cherenkov detector for parti cle identification, and an electromagnetic calorimeter (EMC) for measuring electromagnetic showers from electrons and photons. These detector subsys tems are contained within a large solenoidal magnet capable of generating a 1.5 T magnetic field, and for which the steel flux return is instrumented with a muon detection system. The BABAR detector is illustrated in Figures 3.3 and 3.4. Figure 3.3: Longitudinal view of the BABAR detector. Magnetic Shield for DIRC Bucking Coil 26 3.2. Detector Overview Figure 3.4: End view of the BABAR detector. I 0 3-2001 8583A51 27 3.3. The Silicon Vertex Tracker (SVT) 3.3 The Silicon Vertex Tracker (SVT) The purpose of the SVT is to provide precise tracking and reconstruction of charged particles close to the interaction point. The design specifications aim for a resolution of better than 80j.tm and ‘—‘ lOOJLm in the x and yz planes, respectively, driven by the requirements for time-dependent CF—violation in B meson decays. As well, the SVT is responsible for providing tracking information for low momentum particles (pt < 120 MeV/c) that may not reach the DCH. To accomplish these goals, the SVT is made of five layers of double-sided silicon strip sensors, with the inner three layers responsible for accurate vertex resolution, and the outer two for low Pt tracking. The strips on opposite sides of the silicon sensors run orthogonal to one another, and the layers are arranged to cover the largest angular coverage possible. Figures 3.5 and 3.6 show transverse and longitudinal cross-sectional views of the SVT, respectively. Figure 3.5: Transverse cross-sectional view of the SVT. The silicon sensors in the SVT are 300zm thick, composed of high resistivity n-type bulk silicon with n+ and p+ strips on either side. When a charged particle passes through the silicon, it ionizes the material, pro ducing electron-hole pairs. Under an applied depletion voltage of 25 — 35 V, the electrons drift to the n+ strips, and the “holes” to the p+ strips. 28 3.4. The Drift Chamber (DCH) Seam Pipe 27 Sewn radus Lym5a Se /: H * iH\\\ Leye,2 Figure 3.6: Longitudinal cross-sectional view of the SVT. This results in an electrical signal that is read-out via capacitative coupling between the strips and the electronics. Due to its proximity to the interaction point, one of the primary concerns for SVT operation is radiation hardness. The lifetime radiation budget for the SVT is an integrated dose of 2 Mrad. To limit the exposure, the SVT includes a radiation protection system consisting of PIN8 and diamond diode sensors located in close proximity to the beam. These monitors can abort the colliding beams in the event of sudden high instantaneous or prolonged background levels that could be damaging to the hardware components. To ensure continued successful SVT operation, other operating conditions including temperature, humidity, and alignment are closely monitored, and the SVT system undergoes frequent electronics calibration. 3.4 The Drift Chamber (DCH) The DCH is used for charged particle tracking and momentum measurement. It provides particle identification information based on the measurement of the ionization energy loss (dE/dx) for low momentum (< 700 MeV/c) particles, and those in the extreme forward and backward directions. It is also necessary to reconstruct longer-lived particles (such as K) that decay away from the interaction region outside of the SVT. It was designed to 8PIN diodes consist of doped p-type and n-type semiconductor regions separated by an intrinsic semiconducting region, hence the name “p-i-n”. 29 3.5. The Detector of Internally-Reflected Cherenkov Light (DIRO) provide a position resolution of l40im and a dE/dx resolution of 7%. The DCII was constructed at TRIUMF on the UBC campus. The DCII is a cylindrical gaseous multi-wire chamber detector; its di mensions are illustrated in Figure 3.7. It is approximately 3m in length, and consists of over 7000 hexagonally-shaped drift cells arranged in 40 cylindri cal layers. Each cell consists of a tungsten-rhenium sense wire surrounded by six aluminum field wires. In 24 of the layers, the sense wire (or “stereo wire” in this instance) is strung at a slight angle with respect to the z di rection to provide longitudinal position information (i.e.: for a given sense wire detection of a track, which adjacent stereo wire that detects the same track will depend on the track’s z co-ordinate position). A schematic of the typical cell layout is shown in Figure 3.8. The sense wire is operated at a potential difference of 1900V compared to the grounded field wires, and the chamber is filled with a mixture of 80% helium and 20% isobutane. The gas is continually flushed and the system closely monitored to control tem perature, pressure, mixture proportion, and to maintain a relatively high level of water vapour to prevent electrical discharge. Charged particles ionize the gas, producing free electrons that are accel erated towards the sense wires by the applied electromagnetic field. This results in further ionization, resulting in an avalanche of electric charge close to the wire. The avalanche accumulates at the sense wire producing a mea surable electrical signal that is amplified and read-out to the electronics. The integrated charge and drift time (time required for the ionized electrons to arrive at the wire) provide ionization energy-loss and position information of the particle track, respectively. 3.5 The Detector of Internally-Reflected Cherenkov Light (DIRC) The DIRC is primarily responsible for the particle identification (PID) in BABAR. It is a novel device that uses internally-reflected Cherenkov light ring images to provide better than 4cr separation of ir and K for the momentum 30 Q C, CM z a q - 1 CM I — . CD ? C D _ • ; C D CD - Ci ) + C D O 0 c o C M :+ + - O 0 - C D ) — 3 0 - CD C — . E o - a -, c D E C — . CM Ci ) 0 CD )- 0 - C D C M CD , <1 C M C D C D C, C D C - t• - C - . o C) Ci ) CM ç ,c C ç , o CD — ÷ 0 C -C D C M 0 C D CM 1 h 0 ‘ C D O ‘ - II CM c I C + CD 0 CD - I - O çD - : : CD ; p — f C ) i- E • I _ 0 C — CD CD I T j C D C 1 . C + q CD E - O . CD I- C C t , C + C + C + C D CM Ci ) 0 C t CD CD C D C D CD CD C t CD CD CD 0 CD C + CD CD C , — C t C) - - , . C - 4 CD C , - C D 0 0 C M CD - _ o c i i CD , I- 1 - I - q 0 C D C M ) CD — C t C + C t - CD C+ — . C + C ) C , 0 0 CM CD I CD ) CD 1 j CD -.4 0 C+ CD C— CD C, CI 3.5. The Detector of Internally-Reflected Gherenkov Light (DIRC) 16 0 15 0 14 0 13 0 12 -57 11 -55 10 -54 9 -52 8 50 7 48 6 47 5 45 4XX 0 2 0 Layer Stereo 4 cm + Sense o Field • Guard x Clearing 1-200 1 8583A14 Figure 3.8: Layout of the DCH drift cells, with lines illustrating the cell boundaries, and the sense wire stereo angle (in mrad) for each layer. 32 3.5. The Detector of Internally-Reflected Cherenkov Light (DIRC) Cherenkov light, and as such, can trap the Cherenkov light within the bar. The light propagates the length of the bar, reflecting at the boundaries and off a mirror at the forward end, to be emitted at the backward end. At the backward end, they pass into the “standoff box”, a water-filled expansion region9. The standoff box contains approximately 6000 litres of ultra-pure, de-ionized water, and houses 12 sectors of 896 photomultiplier tubes (PMTs) located - 1.2m from the end of the DIRC bar. The PMTs are outfitted with light-catcher cones to increase their effectiveness and, since they are located outside of the magnetic field region, the “traditional” photomultiplication method of photon-electron conversion and multiplication using photocath odes and dynodes is employed. Figure 3.9: Diagram of the DIRC system. 9The index of refraction for water is n 1.346, chosen in an attempt to match that of fused silica in order to minimize the amount of reflection and dispersion at the backward end of the bar. Purified Water 17.25 mm Thickness 135.00 mm Width) Standoff Track 4.9 m H 1.17 m4 x 1 .225m Bars j glued end-to-end 8-2000 8524A6 33 3.6. The Electromagnetic Calorimeter (EMC) Based on the position and timing of the PMT signals from the DIRC, coupled with the particle position and angle from the tracking system, the Cherenkov angle can be over-constrained and measured with a resolution of 3 mrad. 3.6 The Electromagnetic Calorimeter (EMC) The EMC is used to measure electromagnetic showers produced by electrons and photons. It is designed to be a hermetic total-absorption calorimeter, ca pable of measuring the position and energy of showers ranging from 20 MeV up to 9 GeV. For the BABAR experiment at large, the EMC is crucial for reconstructing r0 —p yy and ?J —* 77 decays. In this analysis, it is used for measuring the photon in X(3872) —* cy, and identifying the electrons in —+ ee. The absorptive material of the EMC consists of thallium-doped cesium iodide (CsI(Tl)) crystals, chosen for their high scintillation light yield, small Moliere radius’0 (to minimize transverse shower size), and short radiation length. Photons and electrons interact with the crystal to produce electro magnetic showers that result in scintillation light. This light is captured and used to measure the shower properties. The EMC consists of a cylindrical barrel with a conical forward endcap, each containing 5760 and 820 crystals, respectively. Figure 3.10 illustrates the this layout. Each crystal has typical dimensions of 4.7 x 4.7 cm2 at the front face, a size on the order of the Moliere radius of the material, increasing to approximately 6.1 x 6.0 cm2 at the rear. The scintillation light is contained in each crystal by internal reflection at the polished surface and by white reflective wrapping. The accumulated light is read out by silicon PIN diodes (suitable for operation within a magnetic field) glued to the rear face of the crystal. The crystals are held into place by a large carbon-fibre support structure. A schematic of the crystal structure is found in Figure 3.11. The temperature of the system is closely monitored and controlled by ‘°The Moliere radius for a material is the radius of a cylinder in which, on average, 90% of the energy of an electromagnetic shower is deposited. 34 3.6. The Electromagnetic Calorimeter (EMC) water and Fluorinert cooling to prevent leakage currents in the photodiodes, and to protect the diode-crystal epoxy interface from temperature variation. Figure 3.10: Layout of the EMC barrel and forward endcap. Units in mm. The EMC crystals are calibrated individually to ensure reliable energy response. The low energy threshold is calibrated by irradiating the Flu orinert coolant with neutrons to produce radioactive ‘6F, which emits a 6.13 MeV gamma ray. At high energy, the calibration is performed using Bhabha scattering events (e+e_ e+e) from the colliding beams, and by comparing the energy response of the detector with that from Monte Carlo (MC) simulation. The light response of the crystals is also tested using a light-pulser system that can transmit light from a xenon-flash lamp via fibre optics to each crystal. The radiation dosage and its effect on crystal light yield is also monitored over time. Typical electromagnetic showers tend to spread over more than one crys tal, forming a cluster of adjacent energy deposits. A reconstruction aigo rithm analyzes the shower shape and projects tracks from the inner detectors to the EMC to determine if a cluster can be associated with a charged par ticle. Otherwise, the EMC cluster is assumed to originate from a neutral particle. The energy resolution, based on the calibrations described as well 38.2 22.7-.---’ 15.8 Iflra:tionPot 121I 1 979 35 3.6. The Electromagnetic Calorimeter (EMC) Output Cable Preamplifier Fiber Optical Cable \\\\\\\\\ Board to Light Pulsar Diode - -- Carrier Plate Aluminum —. Frame Silicon Photo-diodes TVyE K (Reflector) Alumnium CsIffl) Crystal (RE Shield) Mylar (Electrical Insulation) CFC Compartments (Mechanical lls000Support) u572A02 Figure 3.11: Diagram of a typical CsI(Tl) crystal in the EMC. 36 3.7. The Instrumented Flux Return (IFR) as other well known decays, is measured to be: = (2.32 ± 0.30)% (1.85 ± 0.12)% (3.2)E ./E(GéV) where signifies addition in quadrature. Analyzing decays of ‘ir0 and to two photons of equal energy produces an angular resolution parametrization of: (3.87 ± 0.07) = = _______ (0.00 + 0.04)mrad (3.3) /E( GeV) The first (energy-dependent) term is due to statistical fluctuation in the number of photons and noise, while the second term arises due to non uniformity in light collection and light absorption in the detector materials. Both results are close to design specification. 3.7 The Instrumented Flux Return (IFR) The purpose of the IFR is twofold: it directs the field lines for the return of the solenoidal magnetic field, and acts as a particle identification system for muons and neutral hadrons (primarily Ks and neutrons). It consists of alternating layers of steel plates and particle detection instrumentation, ar ranged into a hexagonal barrel region, and a forward and backward endcap. Figure 3.12 illustrates the layout of the IFR. The IFR was originally equipped with 19 layers of resistive plate chambers (RPCs) between the 18 layers of steel, in addition to two layers of cylindrical RPCs close to the EMC. Resistive plate chambers are two highly-resistive planes closely separated by a gap filled with a gas mixture, held at a large potential voltage. Particles passing through the chamber ionize the gas, and the applied high voltage accelerates the resulting electrons into a controlled gas-discharge avalanche called a “streamer”. The streamer signal is collected by inducing a charge in capacitatively-coupled read-out strips outside of the RPC. The gas gain in streamer mode is sufficient to produce a large signal independent of initial ionization, greatly simplifying the electronics read-out. The advantage of using RPCs lies in their relative simplicity, and ability to achieve a large 37 3.7. The Instrumented Flux Return (IFR) active area at a financially reasonable cost. The BABAR RPCs were constructed of bakelite sheets coated with lin seed oil (to provide a uniformly smooth surface) separated by a 2mm gap containing 56.7% argon, 38.8% Freon 134a, and 4.5% isobutane. The RPCs were operated at approximately 8000V, and the streamer signals read-out by aluminum strips on the exterior of the plates. A cross-sectional diagram of a planar RPC is shown in Figure 3.13. Unfortunately, the RPCs did not perform well in BABAR. During the first summer of operation, many of the chambers began drawing very high dark currents and their efficiency dropped severely. It is suspected that high operating temperatures (> 37°C) coupled with insufficient care and curing in the application of the linseed oil coating led to localized accumulation of the oil. These accumulating droplets, under the high electric field, could “bridge the gap” between plates, leading to discharge and large detector dead areas. As a result, the muon identification performance suffered. Ex trapolation of the RPC failure rate indicated that BABAR would be without muon identification capability unless efforts were made to repair the system. Figure 3.12: Layout of the IFR barrel and endcaps. Units in mm. 38 3.7. The Instrumented Flux Return (IFR) In 2002, new RPCs constructed under much stricter tolerances were in stalled into the forward endcap, and although their performance met expec tations, it was decided to replace the entirety of the IFR barrel RPCs with Limited Streamer Thbes (LSTs)” [65]. LSTs consist of a gas-filled cell with grounded walls and a central wire at high voltage. Similar to RPCs, the gas operates in streamer mode when ionized, with the charge collected on the high voltage wire while simultaneously inducing a charge in the external read-out strips. Figure 3.14 illustrates the BABAR limited streamer tubes. The LSTs consist of groupings of seven or eight 15 x 17mm graphite-coated PVC- walled cells approximately 3m in length. Each cell consists of a gold-plated beryllium-copper wire running its entire length, and is filled with a non flammable mixture of 3.5% argon, 8% isobutane, and 88.5% carbon dioxide. The LSTs are operated at a voltage of 5500V. In order to avoid a repeat of the RPC debacle, the LSTs were subjected to a battery of strict quality assurance tests, which included high voltage conditioning, gas leak testing, examining sense wire quality with a radioactive source scan, and characteri 11No action was taken to repair the deteriorating cylindrical and backward endcap RPCs, as their impact on muon identification is limited. Figure 3.13: Cross section of Resistive Plate Chamber construction. 39 3.7. The Instrumented Flux Return (IFR) zation of tube performance by measuring the counting rate “plateau” versus applied voltage12. The phi-direction signals are read off of the high voltage wire using AC- coupled electronics. The z-signal is picked up by capacitatively-coupled read out strips oriented in a plane orthogonal to the LSTs [66]. These “z-strips” were constructed’3out of 35mm-wide conducting copper tape, grouped in a large Mylar-laminated sheet approximately 3 x 3.5m in size (dependent on the size of IFR layer). Figure 3.15 demonstrates the composition of the “z-planes”, the accumulation of all of the z-strips of a single layer. Figure 3.14: Diagram of a prototypical limited streamer tube. Twelve layers of LSTs and six layers of brass (to preserve absorption length) were installed in the place of 18 layers of RPCs’4. The first phase ‘2The author was personally involved in all of these tests for the IFR upgrade, and provided an important contribution to this effort with the authorship of software for the performance and automation of the rate plateau versus voltage scan ‘3The “z-planes” were built at SLAC, also with contribution from the author. ‘4The outermost layer of RPCs was inaccessible in the upgrade, but was disconnected Profile Bridge & Cover High End 5-94 5996A6 Gas 40 3.8. Triggering and Software 0.0127 cm Mylar Cu StiiPS With _____________ Solder Joints j 0.0254 cm Mylar i L1 0.0254cm Mylar —. =— + Cables I 0.0254 cm Mylar 0.0018cm CU Foil 0.0762 cm Mylar i---.. --S-. Stflp El --. Strip E . . rweh-n,rc-’.- .-r -. - Strip E • - .5 Li Li Cables Figure 3.15: Diagram of the z-plane read-out strips constructed for the IFR LST upgrade. The figure on the left illustrates a cross-sectional view of a single z-strip. The figure on the right is shows a top-down view of a plane (not all strips shown). of the installation replaced the top and bottom sextants of the barrel in the Summer of 2004. Replacement of the remaining four side sextants was completed in the Fall of 2006. In total, 1200 LSTs were installed in the detector. Their performance through the end of operations was exemplary, with an operating efficiency approaching the geometric limit of 90%. The total failure rate of LSTs and z-strips is less than 0.5%. Figure 3.16 demon strates the improvement in muon detection efficiency in BABAR. The LST upgrade restored the muon detection efficiency to a level greater than that achieved from the RPCs even at the outset of the operations. 3.8 Triggering and Software To select events of physical interest with high efficiency and adequate back ground rejection, BABAR relies on a two-tier trigger system. The Level 1 (Li) trigger is a hardware-based trigger that uses the raw information di- nonetheless. Stric Stnp Strio 17 33 49 65 81 96 41 3.8. Triggering and Software Muon eff and u-as-p misiD x5,: (red/magenta) Run 6, (blue/green) Run 4 0.9 backward . LST barrel + endcapG) 0.8 :forward muon efficiency0 .endcap • -÷... RPC barrel 1 +++0.7: G) + + +0.6— * + ,.÷+ .- + +++ 0.5 — + +++ O.4E ++++ 0.3. + + 0.2E pion-as-muon mis-ID x5 (tuned to be -constant) + +0.1 LST RPC I I 0.5 1 1.5 2 2.5 [muNNTightFakeRate, 1.5 <p_CM <3.0 GeV/c] 8_LAB Figure 3.16: Comparison of the muon identification efficiency for various regions of the IFR. [67] The red and blue points represent a comparison of the LST and RPC muon identification efficiencies, while the magenta and green points represent a comparison of the pion-as-muon misidentification rate for the two subsystems scaled up by 5 times. 42 3.8. Triggering and Software rectly from the DCH, EMC, and IFR’5 electronics, while the Level 3 (L3) trigger uses software to analyze data from the event to further refine the selection. The Li trigger decision is based on tracks in the DCH exceeding a given transverse momentum, and showers in the EMC. It has a selection efficiency for BB events of greater than 99.9%, and a total rate of ‘- 1kHz under normal beam operation and background conditions. The L3 trigger rapidly identifies DCH tracks and EMC clusters, and makes a decision based on reconstructed DCH track momentum and distance of closest approach to the interaction point, and the EMC cluster multiplicity and deposited en ergy. The combined Li and L3 triggers maintain a BB selection efficiency > 99.9% and reduce the rate to 100 — 200 Hz for all event types. Once an event passes the Li and L3 triggers, it is processed by the reconstruction software to form charged tracks using the SVT and DCH information. Particle identification hypotheses are generated with this in formation combined with the information from the DIRC, EMC and IFR. These fundamental particles are formed into composite particle candidates, such as J/& — e+e or I(0 —* and this information as well as the other event properties (e.g. vertexing, track momenta, cluster energy) is stored to disk for more detailed analysis. Offline analysis is performed using a variety of software simulation tools and packages. Simulated events, known as Monte Carlo (MC), are produced using the EvtGen [68] generator for user-defined physics events, with the detector response modeled in GEANT4 [69], a toolkit for the simulation of the passage of particles through matter. User-defined programs for the analysis of data and MC events are based in C++ using the ROOT [70] software package, an object-oriented data analysis framework. ‘5The IFR trigger information consists of tracks detected from cosmic rays and Ci events, and is only used for diagnostic purposes. 43 Chapter 4 Analysis Preliminaries This chapter describes the data sets used in this analysis, and the recon struction of B-meson candidates. It defines the variables used to describe each event, and the procedure used to optimally define the event selection criteria and the results. 4.1 Data Set This analysis uses the full BABAR dataset collected from the start of oper ations in 1999 to the conclusion of Y(4S) running in 2007, for a total of 424.4 th’ or 465 ± 5M BB decays. BABAR defines data collection periods as “Runs”, with the full BB data set referred to as Run 1—6. Separate signal Monte Carlo modes have been generated for each of the X(3872) decays to be studied in this analysis. The X(3872) is generated as a zero-width particle, decaying by two-body phase space. Monte Carlo for modeling the background is taken from generic B+B, B0, cc, ui, dd, s and r+r samples, as defined with EvtGen. Inclusive J/ib, Xcl,2, and, b(2S) samples (i.e. generic BB decays filtered to include a J/’b, Xcl,2 or 2S) in their decay chain) are also used to supplement the background sample and to provide B —* xCl,2K events. A summary of the number of events generated for each mode and the appropriate cross-sections and weighting is given in Table 4.1. The inte grated luminosity is calculated from L = N/a, where a is the cross-section for a given decay mode in units of nb. The Weight column of the Table is the fraction by which this mode’s events were weighted in order for the MC sample to be equivalent to the Run 1-6 dataset size. For the signal MC modes, the weighting was based upon the branching fraction (BF) values 44 4.2. B Candidate Reconstruction for B —* X(3872)K from [37]. 4.2 B Candidate Reconstruction The B-meson candidates are reconstructed using BABAR software packages designed to create composite particle candidates and store event informa tion. To streamline this process, the data and MC are filtered or “skimmed” to reduce the number of events according to a set of well-defined criteria. Composite particles are constructed from daughters drawn from PID “lists” of particle candidates. The B-meson candidates are built up from a final state of charged parti cles. A J/’ or (2S) (hereafter referred to a “ca”) candidate is reconstructed from decays to two oppositely charged leptons (e+e_ or or the de cay (2S) —* J/irir. This c candidate is combined with a photon to make an “X” candidate, where X represents any possible physical combina tion, including the X(3872) and the XcJ. K° candidates are reconstructed from decays to two charged pions (K —b ir+irj, while excited kaons are composed from the decays K*± —* KSIr± and K*O KrF. Neutral final states are not considered to maintain a higher reconstruction efficiency. The B candidate is formed by pairing the X candidate with a kaon candidate. This analysis considers 24 final states decaying to B — XK where: B includes charged and neutral B mesons; K represents kaons K±, K — Tr1r, K*± K1r±, and K*O Kr; and X —f J/iI’7 and X —* where J/ — £t, i’(2S) —* t’t, and (2S) —p J/rr with £ = e and I-I. 4.2.1 “JpsitollTight” Skim The JpsitollTight skim used to restrict the dataset requires events to include decays identified as J/b —* £t or ‘(2S) —* £.t. The definition of these decays matches our J/’b and ‘(2S) reconstruction as defined in the following sections. The decay b(2S) —÷ J/(ttjnr is automatically included because of the decay of the daughter J/ into a lepton pair. The event must 45 4.2. B Candidate Reconstruction Table 4.1: Number of events, equivalent luminosity, and weighting for the Run 1—6 MC modes and data sample. Decay Mode Total Events Lumi (pb1) Weight q(q = u, d, s) 904, 082, 000 432, 575 0.967 c 1,088,218,000 837,091 0.500 BB 702,558,000 1,277,378 0.327 B°B° 702,788,000 1,277,796 0.327 rr 382, 614, 000 429, 903 0.973 J/’b Inclusive 15, 307, 903 5, 358, 275 0.078 ‘(2S) Inclusive 2, 393, 121 6, 762, 395 0.062 Xcl,2 Inclusive 1, 658, 371 8, 748, 312 0.048 X(3872) Decay Modes J/ —+ K 195, 000 9.241 x i0 K(irirj 391, 202 3.187 x iO K*+(K307r ) 394, 183 2.109 x iO K*O(K±irF) 396,000 3.029 x (2S) —* K 363, 324 0.612 x i0 50rir) 378, 160 0.406 x i0 K*±(K3Oir±) 379,050 0.270 x iO K*O(K±irF) 406,486 0.364 x iO &(2S) — K 750, 676 0.763 x iO K50(irrj 780, 317 0.508 x i0 K*±(Kir±) 782,425 0.337 x K*O(K±irF) 838, 514 0.454 x iO Run 1—6 Data 465,035,698 424,353 1.000 46 4.2. B Candidate Reconstruction also contain more than one particle identified as a hadron, or have R2 < 0.5 (this variable is described in Section 4.3.2). The skim selection rate from all events in the dataset is 1.1%. Skimming is not applied to signal MC modes as it is unnecessary. 4.2.2 J//, — tt Reconstruction The J/& candidates are reconstructed in two decay modes. The e+e decay uses a pair of bremsstrahlung-recovered’6electron candidates reconstructed with a geometric constraint (i.e. both electrons are forced to originate from the same vertex) and requires 2.5 < m(e+ej < 3.3 0eV/c2. The electron candidates are chosen from a standard BA.BAR list that calculates the likeli hood of the electron particle ID hypothesis based on calorimeter, DIRC and energy loss information [73]. The r mode uses muon candidates with a geometric constraint ap plied and requires 2.8 < m(r) <3.3 0eV/c2. The muon candidates are chosen from a list defined using a neural net-based identification algorithm [74]. 4.2.3 b(2S) Reconstruction The (2S) candidates are reconstructed in three decay modes: (2S) —* J/irrr and b(2S) —* t, where £ = e or i. For the former decay, J//i candidates use the same reconstruction as described in the previous section, and are constrained to the nominal J/’b mass. The pion candidates are drawn from the list of all charged tracks identified in the event. The three decay particles are constrained to the same vertex and pass the requirements 3.586 < m((2S)) < 3.786 0eV/c2 and 0.4 < m(1rr) < 0.6 0eV/c2. For the leptonic (2S) decays, the reconstruction uses electron and muon candidates selected in the exact same manner as for J/1’ —* £t decays except that the invariant mass of the lepton pairs is restricted to 3.3 < m(tt) <4.0 0eV/c2. ‘6Bremsstrahlung energy losses are recovered by an algorithm that associates low energy photons with the charged track and includes this into the electron candidate reconstruc tion. 47 4.2. B Candidate Reconstruction 4.2.4 X —* c&y Reconstruction The X candidates are reconstructed using J/ib and b (2S) candidates as defined above and refit with their masses constrained to the nominal value, combined with a photon candidate. The photon candidates are chosen from a list comprised of single EMC bumps unmatched with a track, requiring a minimum energy of 30 MeV and a maximum lateral moment of 0.8 (see Section 4.3.3 for a definition of this quantity). There are no restrictions on the X mass range to allow for the possibility of discovering new states up to the kinematic limit, and to include xi — J/’b 7 decays as a benchmark mode. 4.2.5 Kaon Reconstruction Four kaons are considered in this analysis: K±, K30, K*±, and K*O. Qf these kaons, the K are selected from a standard BABAR PID list, while the remainder are composite particles. The K± candidates require a likelihood of the kaon particle hypothesis versus pion to be > 0.5 and kaon versus proton > 0.018. The particle must have a momentum p < 0.4 GeV/c or else not be defined as an electron by other PID algorithms. The K3° candidates are reconstructed from the decay to oppositely charged pions drawn from the list of all charged tracks and are subject to a geometric constraint, and must be within ±200 MeV/c2 of the nominal I(0 mass. The charged excited kaons, K*±, are reconstructed from their decay to K307r± using pion candidates that are charged tracks with a kaon and proton likelihood < 0.98, and K8° as defined here. The K*± mass is required to be within ±200 MeV/c2 of the nominal K* (892) mass. The neutral excited kaons are formed from the decay K*O Kr+, drawing K± candidates as defined above and pions identified using the same definition for the K *+ selection. For K*O, a geometric constraint is applied and 0.7 < mK*o < 1.1 GeV/c2 required. 4.2.6 B —* XK Reconstruction The final B candidate is reconstructed from an X candidate and a kaon. The daughters are constrained to come from the same vertex, and loose 48 4.3. Event Variables selection cuts of 5.0 < mB < 5.5 GeV/c2, 5.2 < mmjss < 5.3 GeV/c2 (see Section 4.3.1 for a description of this variable), and the probability of the B vertex x2 > 0.001 are applied. Once a B candidate has been established, it and its daughter decays are refit with the B mass constrained to the known value. 4.3 Event Variables This section describes some of the variables used to characterize the recon structed events used in this analysis. These variables are used for event selection and signal extraction. Final selection cuts and the optimization procedure for these variables is described in Section 4.4. 4.3.1 B Meson Variables Kinematic Variables: mmjss and mB To select true B candidates from background events, two kinematic variables are used in this analysis: the mass of the reconstructed B candidate mB, and the missing mass mmjss. m = IPBI (4.1) mmj8s = IPe+e PBI (4.2) where m is the unconstrained B-candidate mass from the four-momentum PB of the reconstructed B meson, and the missing mass mmjss where Pe+e is the four-momentum of the e+e system and B is the four-momentum of the B candidate after applying a B mass constraint. Correct values of mB and mmjss for true B mesons should peak at the nominal B mass of 5.279 MeV/c2 [33]. B Vertex x2 Probability The probability x2 for the vertex reconstruction of the B meson is another variable to separate real B candidates from background events. It is a 49 4.3. Event Variables measure of the probability that the decay daughters from the B candidate originated from the same initial vertex. This variable is used to remove very poorly reconstructed background events with low x2 values from the data sample. 4.3.2 Event Topology Variables Fox-Wolfram Moment and R2 The Fox-Wolfram Moments are defined as [75]: H1 = IPiIIPip(9) (4.3) tot where p, p3 are the momenta of the particle candidates, Oij is the angle between them, E0 is the total visible energy of the system, and P1 are the Legendre polynomials. The quantity R2 is defined as: R2 = (4.4) which can range from 0 to 1. This quantity is a measure of the isotropy of an event. Highly directional continuum events have higher R2 values, whereas B events tend to be more isotropic and have lower R2 values. B Thrust and Sphericity Angles The thrust angle, 8thrust, and sphericity angle, esphere, are a measure of the correlation between the direction of the B candidate compared to the other particles in the event. The thrust axis () is the direction which maximizes the sum of the longitudinal momenta of the particles (also called thrust, T), while the sphericity axis is the direction maximizing the sum of the transverse momenta (called sphericity, S). The thrust is defined as [76]: (4.5) 50 4.3. Event Variables The sphericity tensor is: s=z a,b=x,y,z (4.6) and the sphericity is defined as the 3/2 times the sum of the largest two eigenvalues of this tensor [77]: S=CX2+)3) (4.7) The thrust and sphericity angle is the angle between the thrust or sphericity axis of the reconstructed B meson (based on its decay particles), and the equivalent axis for the rest of the event (all other particles). For highly directional continuum events, the absolute value of the cosine of these angles peaks at 1 (i.e. the axes for the B candidate and all other particles point in the same or opposite direction). True B decays tend to be isotropic, hence cos9thrust and cos °sphere tend to be uiiiformly distributed. 4.3.3 Photon Variables Photon LAT The lateral energy distribution [78] of a photon candidate in the electromag netic calorimeter (LAT) is defined as: .ç-N E 2 LAT = j3 (4.8) E,r + Eirg + E2r where N is the number of crystals in the shower, E is the energy deposited in the ith crystal, r is the polar radius in the plane perpendicular to the line pointing from the interaction point to the shower centre, and r0 = 5cm is the average distance between two crystals. The energies are ordered E1 > E2 > ... > EN so that the sum in the numerator excludes the contribution from the two highest-energy crystals. The LAT quantity is used to differentiate electromagnetic showers from hadronic showers, where most of the energy from an electromagnetic shower 51 4.3. Event Variables is typically deposited in the first few crystals. This leads to a lower value of LAT, which can be used to distinguish photons shower from fake showers produced by hadrons. Photon A42 The Zernike moment is defined as [79]: Anm = (E/E) fnm(pi)e_im (4.9) where E is the energy and (p, are the locations of the hit crystals in the EMC with respect to the centre of the shower. The location is defined in cylindrical coordinates with the z axis running from the beam spot to the centroid, with p = r/Ro where R0 = 15 cm. fnm represents the Zernike functions, (n—m)/2 — (_l)s(n_s)!pn_2s 410 s!((n+m)/2-s)!((n-m)/2-s)! with m < n and (n — m) even. The Zernike moment A42 is a measurement of the azimuthal asymmetry of a photon’s EMC cluster about its peak, an other variable that can be used to distinguish hadronic and electromagnetic showers. .O Veto A possible source of misreconstruction is photons originating from the decay of a neutral particle such as —* ‘y’y. To ensure that the photon selected in the reconstruction of X — cy has not originated from a r0 decay, it is combined iteratively with each other photon candidate and the invariant mass of the four-momentum of the pair, m77 = (pi +p7j)2 (4.11) 52 4.4. Event Selection is determined. If the invariant mass from the pair of photons falls within a specified range of the ir0 mass, the event is rejected. 4.3.4 Kaon Variables K3° Flight Significance Because K8° have a measurable lifetime, they travel a finite distance in the detector before decaying into charged pions. The distance from the inter action point to the reconstructed vertex of the charged pions is defined as the kaon flight length, and the flight significance is this length divided by its uncertainty. K, K*±, K*O Vertex The term “K vertex” is a shorthand notion used to describe the probability x2 for the vertex reconstruction of the kaon in question. It is a measure of the probability that the charged-track decay daughters from the kaon candidate originated from the same initial vertex. 4.4 Event Selection This section describes the method used to establish values for the “cuts” applied to select signal events. The goal is to maximize the number of signal events versus background. In order to avoid bias, this exercise is first conducted independently from the experimental data using the signal and background Monte Carlo samples described in Section 4.1. 4.4.1 Cut Optimization Procedure To best separate the signal from the background, selection cuts were imposed on several discriminating event variables. The selection criteria were found by maximizing a figure of merit defined as: F (4.12) VS + B 53 4.4. Event Selection where ns and B are the number of signal and background events, respec tively. The number of events are subject to the weighting described in Table 4.1. To avoid double-counting in cases with multiple B candidates passing the reconstruction and selection cuts, the candidate with the value of m closest to the true B mass is used. The optimization begins with a reasonable17 choice of values for the possible discriminating variables. For each variable, all cuts are applied except those on the variable in question. The cut range on this variable is then chosen to maximize Equation 4.12. This is repeated for every variable, determining each optimized values independently. These values are then used as the input for the next iteration of the optimization procedure. The process continues until the cuts for each variable converge to stable values. The event selection cuts for all of the X —p J/b7 modes were optimized simultaneously, and the X —÷ (2S)7 modes simultaneously as well, but separately from each other (i.e. a single cut on variable x is applied to all J/7 events, and a different cut on x is applied to all i’(2S)7 events). The B vertex x2 probability cuts were optimized individually for each decay channel. The final values for some of the selection criteria were rounded off to provide agreement between signal modes and for ease of description and use. Note that the exact optimized values are not so much the priority as is selecting them in a manner uninfluenced by knowledge of what is in the experimental dataset. 4.4.2 Optimization Results The results of the optimization procedure are given in this section. The final selection cuts for the B — X(c7)K modes are listed in Table 4.2. “No optimal cut” signifies that the optimization procedure found that this variable offers no discriminating power between signal and background. Loose, non-optimized cuts of mmjss = mB(pDG) ± 100 MeV/c2 and mx = mx(3872) ± 100 MeV/c2were chosen to limit the size of the data sample to our 17The initial values were roughly estimated based on the previous analysis [37]. Other starting points were found to converge to similar optimal results. 54 4.4. Event Selection region of interest. Because the photon energy for the (2S) decay modes is relatively low, a non-optimized cut of E7 > 100 MeV was applied to reduce the large combinatoric background contribution from misreconstruction due to selecting a random low-energy photon. For the J/ modes, no cut on was required because the resulting mx from low-energy photons is well below the X(3872) region of interest. Cuts were applied to mK*+ and mK0* during the optimization procedure to better isolate signal events, but cuts on these variables were not applied in the final selection. Figures 4.1 through 4.10 show the distributions of the event variables for the J/& decay modes. Figures 4.11 through 4.21 are the corresponding plots for the &(2S) modes. For each plot, the optimized cut values have been applied to all other event variables except for the one being plotted. In all cases, the red line indicates the distribution for the signal MC, the blue line indicates background MC, and the two black arrows indicate the optimal cut range. Although the distributions have been normalized to have the same area in the plots for visualization purposes, the optimization was conducted using the proper weights as given in Table 4.1. I B Candidate Mass Figure 4.1: Optimized B mass for the X(3872) —* J/b7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. Q 0. C 0. 0. 0. 55 4.4. Event Selection Table 4.2: Results of optimization of the selection criteria. The centre column lists the optimized values for the c = J/ modes, and the right hand column gives the values for the .cc = (2S) modes. Variable J/b Range (2S) Range Bx2(Ki > 0 > 0.01 B2(K) > 0 > 0.002 Bx(K*i > 0 > 0.05 B X2(K*o) > 0 P(2) > 0.05 mB (MeV/c2) mB(PDG) mB(PDG) ± 20 mmjss (GeV/c (5.2 < 5.3) ( MeV/c2) mx(3872 ± 100 mj1+6— (GeV/c (2.96,3.15) (3.01,3.15) mj+— (GeV/c2) (3.06,3.13) m,1,(2s)e+e— ( GeV/c2) - (3.61, 3.73) m,(2s)÷,+— ( GeV/c2) - (3.65, 3.72) m(2s)J/,r+— ( GeV/c2) - (3.68, 3.69) R2 R2 < 0.45 cos No optimal cut cos No optimal cut E7 ( MeV) No cut applied E7> 100 “yLAT 0.001 < LAT < 0.5 ‘yA42 A42 < 0.1 ir0 veto ( MeV/c2) 124 < m77 < 146 No optimal cut mKo (MeV/c mKo(PDG) ± 17 K8° flight K° flight> 3.7 K° vertex P(2) > 0 P(2) > 0.001 mK*+ (MeV/c2) mK*+(PDG) ± 50 K*+ vertex P(2) > 0 P(2) > 0.02 m* ( MeV/c2) m (PDG) ±35 K vertex P(2) > 0 P(2) > 0.002 56 4.4. Event Selection JpsiMassee I Jpsi Mass mumu modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. I Photon LAT 0 0 Figure 4.3: Optimized 7 LAT and 7A42 for the X(3872) — J/7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. Figure 4.2: Optimized J/ mass for the X(3872) — J/’t’7 modes. Signal Photon A42 57 4.4. Event Selection PlO Veto Figure 4.4: Optimized ir0 veto for the X(3872) —k J/7 modes. The invari ant mass m7 closest to mo is plotted. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. I Cos Thrust Angle r-m- C 0.02 O.01 8 0.016 0.014 0.012 0.01 0.008 0.006 0.004 - 0.002 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 cOs(0th,t) Figure 4.5: Optimized cos9thru8t and cos sphericity for the X(3872) —* J/7 modes. Signal modes are represented in red; background modes are rep resented in blue. Arrows represent the optimized values of the selection cuts. Cos Sphericity Angle 58 4.4. Event Selection Figure 4.6: Optimized R2 for the X(3872) —* J/b7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. I Fox-Wolfram Moment R2 C 0 R2 59 4.4. Event Selection IBchi”2 BchiA2I 0.06 0.0 ‘ 2 2 2 0.05 - 2 0.04 <0.04 - EE 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 P(2), B(X K) Vertex PCi2), B(X K3) Vertex BchiA2 BchiA2I O.08 0.O7 0.O7 - 006 0.06 0.05 0.05 0.04 - 0.04 0.03 - 0.03 :______________ :______________ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 G0 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 P(x9, B(X K) Vertex P(2), B(X K°) Vertex Figure 4.7: Optimized B vertex probability x2 values for the X(3872) — J/’tb7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. 60 4.4. Event Selection I Ks Mass Ks Flight Significance 03.IIhhIhhII z n .0.16- W - 0.25 0.14- - 0.12 - - 0.2 0.1 - - 0.15 0.08- - 0.06 - - 0.1 0.04- - 0.05 0.02- - . JLnA—Pf . I. L __________________________ O47 0.48 0.49 0.5 0.51 0.52 0.53 0 10 20 30 40 50 60 70 80 90 100 rn (GeV/c2) K5 Flight Significance I Ks chiA2 0.0t >0.07 - 0.06 - 0.05 - 0.04 - 0.03 - ::: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P(2), K5 Vertex Figure 4.8: Optimized K cuts for the X(3872) —* J/&7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. 61 4.4. Event Selection I Kstar Mass I Kstar chtA2 2 0.14 2 0.12 [1 - 0.1 - :: 0.02 0.7 0.8 0.9 1 1.1 1.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mv-. (z2), K Vertex Figure 4.9: Optimized K*+ cuts for the X(3872) —* J/’y modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. In the final selection, the full mK*+ range shown here is used. Kstaro Mass I Kstaro chiA2 0.14 - - 0.06 - 0.12- n - o.os - 3 3 a 01 I a 0.04 - 0.08- 1 0.03 - 0.06- H H - 0.02 - o.o 0.7 0.8 0.9 1 1.1 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mK. P(x’), K° Vertex Figure 4.10: Optimized K*o cuts for the X(3872) —* J/7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. In the final selection, the full mK0* range shown here is used. 62 4.4. Event Selection B Candidate Mass I 0.3- I 0.25- L 0.2- - 0.15- - 0.1- - 0.05 - - 05 5.1 5.2 5.3 5.4 5.5 m8 (GeV/c2) Figure 4.11: Optimized B mass for the X(3872) —* &(2S)7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. I Jpsi Mass ee Jpsi Mass mumu 0.2 0.3- ri 1::: .1 2.9 3 3.1 3.2 3.3 3.4 .8 2.9 3 3.1 3.2 3.3(GeV/c) (GeV/c) Figure 4.12: Optimized J/ mass for the (2S) —‘ J/irir modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. 63 4.4. Event Selection EPiFMiss ee to, C z n 4 Psi Mass jpsi I 0 0.14 0.12 4 0.1 0.0€ 0.0€ 0.04 0.02 3.6 3.64 3.68 3.72 3.76 m(2,)(Jfl, (GeV/c2) Figure 4.13: Optimized b(2S) mass for the X(3872) —* b(2S)’y modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. ill” 64 4.4. Event Selection 0.18 / 0.16 - J & - 0.14j/1 :: Figure 4.14: Optimized ‘y LAT and7A42 for the X(3872) —> (2S)7modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. Figure 4.15: Optimized r0 veto for the X(3872) — b(2S)’-y modes. The invariant mass m77 closest to mo is plotted. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. 65 I Photon LAT I Photon A42 0.04 C 0.035 0.0:3 0.025 0.02 0.015 0.01 0.005 E11 0.08 ‘0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 y LAT ‘0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 yA I PiO Veto 1111 0.05 0.1 0.15 mGevic2) 4.4. Event Selection I Cos Thrust Angle I Cos Sphericity Angle I Figure 4,16: Optimized cos8thrust and cos0sphericity for the X(3872) b(2S)7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. I Fox-Wolfram Moment R2 I 0 0.045 0.04 0.035 0.02 0.025 0.05 0.015 0.0 0.005 ‘0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 R2 Figure 4.17: Optimized R2 for the X(3872) —* (2S)7modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. 66 4.4. Event Selection I Bchi2 I I Bchi2 I 0.07 - > it it - 0.04 - .0 .0 <0.05 - 0.03 - 0.04 - 0.52 o.o2ff0.OL ‘fl 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9(x2), B(X IC) Vertex P(x9, B(X K) Vertex IBchIA2I IBChIA2I 0.09 0.09 to.08 - 20.08 - it 0.07 4. 4 0.06 0.06 0.05 - 0.05 0.04 0.04 0.03 1 - o.os . - tIX, 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 PC12), B(X K ) Vertex SW), B(X K 0) Vertex Figure 4.18: Optimized B vertex probability x2 values for the X(3872) —, b(2S)-y modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. 67 4.4. Event Selection 0.03 0.02 0.01 I Ks Flight Significance 0.05 60 70 80 90 1U0 K Flight Significance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P(2), K Vertex Figure 4.19: Optimized K8 cuts for the X(3872) — (2S)7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. Ks Mass I 0 C 0 .0 0 C 0.35 0.3 0.25 0.2 0.15 0.1 0 10 20 30 40 50 Ks chiA2 0 C > 0.05 0 .0 0.04 68 4.4. Event Selection Kstar Mass Kstar chiA2 10.14- - 0.12 - I - 0.07i < 0.1 - r - < 0.06 0.7 0.8 0.9 1 1.1 1.2 00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mx.. P(X2), K • Vertex Figure 4.20: Optimized K*+ cuts for the X(3872) — (2S)7 modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. In the final selection, the full mK*÷ range shown here is used. I Kstaro Mass I Kstaro chiA2 Ij 0.7 0.8 0.9 1 1.1 1.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mK. P(2), K° Vertex Figure 4.21: Optimized K*o cuts for the X(3872) —* ‘(2S)y modes. Signal modes are represented in red; background modes are represented in blue. Arrows represent the optimized values of the selection cuts. In the final selection, the full mK*o range shown here is used. 69 4.4. Event Selection 4.4.3 Multiple Candidate Selection In some events there is more than one way to reconstruct the desired final state (due to reconstruction uncertainties and particle misidentification, for example). As in the optimization procedure, only the candidate with the value of mB closest to the true B mass is retained. Table 4.3 lists the average number of B candidates per event versus decay mode, determined from signal Monte Carlo. This is the number of candidates per event that pass all of the optimized cuts described in Section 4.4.2. Table 4.3: Average number of B candidates per event. Decay Mode Cand./Evt. (MC) X(J/b7)K 1.006 X(J/)K° 1.010 X(J/7)K*± 1.170 X(J/c/ry)K*O 1.098 X(ib(2S)7)K 1.428 X(’b(2S))K° 1.426 X(b(2S)y)K*± 1.781 X((2S)7)K*o 1.621 xi(J/’,b)K 1.023 xi(J/’/7)K° 1.023 xci(J/y)K*+ 1.143 Xci(J/b7)1<*o 1.087 4.4.4 Event Selection Efficiency The efficiency of event selection is the number of signal events reconstructed and passing the optimized cuts, divided by the total number of events gen erated in Monte Carlo. For the purposes of this analysis, two sets of Monte Carlo events are considered: those with truth-matching (i.e.: all recon structed charged particles in the final state correspond to those generated in the MC), and those that do not require this condition. The efficiency for each signal mode based on the MC is summarized in Table 4.4. As 70 4.4. Event Selection a general comment, the efficiency decreases as the number of final state particles increases. Furthermore, the noticeable drop in the efficiency for truth-matching seen for the (2S)7 signal modes is due to the fact that it is common to misidentify a pion in ‘(2S) — J/irir decay or the low-energy photon or by selecting an incorrect r or ‘y from the rest of the event. Table 4.4: Summary of the reconstruction and event selection efficiency () for signal MC, without and with requirements on truth matchin X(3872) Events Pass E(%) Pass cuts/ f(%) Decay Generated duts/reco reco/truth JA& K 195000 28469 14,6 24274 12.4 K 391202 43554 11.1 37051 9.5 K*+ 394183 31280 7.9 25118 6.4 K*O 396000 45629 11.5 37541 9.5 /(2S) — K 363324 83870 23.1 60194 16.6 K 378160 67303 17.8 49605 13.1 K*± 379050 42277 11.2 29249 7.7 K*o 406486 70216 17.3 50945 12.5 ‘(2S) — J/irir K 750676 87656 11.7 48019 6.4 K 780317 69471 8.9 42935 5.5 K*± 782425 42508 5.4 25204 3.2 K*o 838514 71874 8.6 44668 5.3 ‘(2S) —*all K 1114000 171526 15.4 108213 9.7 K 1158477 136774 11.8 92540 8.0 K*± 1161475 84785 7.3 54453 4.7 K*o 1245000 142090 11.4 95613 7.7 The expected number and composition of background events can be seen in Figure 4.22 and Figure 4.23 for X(3872) — J/i,b(2S)’y and X(3872) ?j’(2S)7 events, respectively, and for Xci — J/-y events in Figure 4.24. These plots represent the weighted MC background events remaining after the selection cuts have been applied. They are overwhelmingly from B+B 71 4.4. Event Selection — and B B decays; there is little to no contribution from the qq and rr MC modes. Distribution of Background MC Types I Distribution of Background MC Types — ______ N ______ 14 (a) .s (b) 12 : . 4 : C 3.8 3.85 3.9 3.95 3.8 3.85 3.9 3.95 mx (GeV/c2) n (GeV/c2) Distribution of Background MC Types j Distribution of Background MC Typea I N 2( °1u ;i8 (c) (d) [1, Eli 71—i--r-n,rr .-m-,--I-,, i—a 7Th-,,C 3.8 3.85 3.9 3.95 3.8 3.85 3.9 3.95 m2 (GeV/c2) m2 (GeV/c2) Figure 4.22: mx distribution for MC background events passing all of the selection cuts for X(3872) —> J/’t/vy decays for (a) B —‘ X(3872)K, (b) B° — X(3872)K, (c) B —* X(3872)K*+, and (d) B° —+ X(3872)K*o. 72 E ve nt s/ S M eV /c 2 E ve nt s/ 5 M eV /c 2 4- C CD CO 0 0 !- — 1 C, ) C O Q S — c - I- - I- • c . 00 00 - - Io DC C 0 3 0 w DC C, 0 C 3 C, CD 6, 0• C 0 3 0 w DC C, 0 C 3 C, CD DC E ve nt s/ 5 M eV /c 2 DC C 0 3 0 a’ DC C, 0 C 3 C, DC DC 0• C 0 3 0 a’ DC C, CD 0 C 3 C’ CD DC E ve nt s/ 5 M eV /c ’ el i I CD C C, CO 4.4. Event Selection Distribution of Bsckground MC Types I V to at C Si [pribution of Bsckground MC Types I V at a, at C at Distribution of BsckgroundMC Types I V e to at C at Si [p!ibution of Bsckground MC Types I a, e to at C at Si Figure 4.24: mx distribution for MC background events passing all of the selection cuts for Xci —, J/&7 decays for (a) B± —‘ Xc1K±, (b) B° —* xciKs°, (c) B —, XC1K*+, and (d) B° —÷ Xc1K*O. The peaks evident in (c) and (d) are from background events due to non-resonant B —* xciKir decays (ie: events where the Krr final state does not come from a K*). mx (GeV/c’) 74 Chapter 5 Analysis Methodology This chapter contains a detailed description of the analysis technique. It includes tests of this procedure on simulated data sets for the extraction of X(3872) events, as well as the method for extracting the Xcl,2 signal modes to be used as further verification of the signal extraction strategy. 5.1 Signal Extraction Procedure This section describes how the analysis of B — c7K (*) will be performed. The signal extraction is based on an unbinned extended maximum likelihood (UML) fit to the kinematic variables mmjss and mK* (if applicable), followed by a fit to the 3Plot [80] projection of mx. The P1ot method, described in Section 5.1.7, is chosen over a conventional 2(3)-D UML fit to improve the visual presentation of the fit, and for the separation of signal types and the search for new bumps. The parametrization of the probability density functions (PDFs) of the relevant variables, mmjss, mK* and mx, for each of the expected event types (signal, peaking background, non-peaking background) is performed by fitting the PDF shape to MC samples. 5.1.1 Probability Density Functions From a signal extraction standpoint, each event is characterized by two important observables: mmjss and mK* (if applicable). For mmjss and mK*, the characteristic PDFs are derived for signal and background separately. The probability of observing a total of N events, some of which are signal 75 5.1. Signal Extraction Procedure and the others background, is = ñ [sig(mmiss,mK) +abkdkd(mmiss,mK*)] (5.1) where F represents the PDFs, and Oj and cxbkd are the number of events for signal and background, respectively. For ease of computation, rather than maximizing Equation 5.1, it is customary to minimize the negative log likelihood: ln() = —2 in (sjgF8Z9 + bkdFbkd) (5.2) In practice, the minimization is performed on the extended likelihood func tion, defined as exp N = N! (5.3) which includes a Poisson statistics factor to account for the probability of measuring N events from a distribution of mean q. This additional factor does not change the values of c, but it converts the uncertainty on the fit parameters to include an uncertainty from the Poisson distribution. The extended maximum likelihood equation is now ln(E) = 2 [siY + bkd + ln(N!) — ln (asigF8 + bkdFd)] (5.4) This is the equation which is minimized to determine the number of events of each type in the dataset. 5.1.2 Choice of PDF shapes The PDFs were selected for a balance of ease of use and based on some physical relation to the variable being plotted18. To obtain a clean definition for the signal modes, truth-matching was required for all of the final state charged particles used to reconstruct the event, and the range of the fits ‘8This is a simplification from an initial attempt to determine the shape of the PDFs by comparing the x2 probabilities of fits to several different functional forms. 76 5.1. Signal Extraction Procedure were truncated to mmjss + 25 MeV/c2 and mx ± 25 MeV/c2 to improve the x2 and the convergence of the fits. Note that the signal MC reconstruction is very clean, so that there are essentially no events faffing outside of this range. For background shape PDFs, the cuts were applied as defined in Section 4.2. 5.1.3 PDF Parametrization, mmjss For the signal modes, the mmiss PDF is described by the Crystal Ball func tion [81], defined as: ( —(x--mp)2 I e 22 form>crf(x; , n, m0, o) = N. ‘ (5.5) 1A.(B—), for-—c where A = ()2 exp (_) (5.6) B=-IoI This function can be thought of as a Gaussian core with a power-law low- end tail. The parameters m0 and u can be thought of as the Gaussian mean and width, with n representing the power of the exponential tail, and c the number of Gaussian standard deviations from the mean where the low-side exponential tail begins. N is a normalization factor. All of the parameters are determined by fitting to MC samples. In order for the fit to converge, an iterative approach was used by finding an initial value for n, fixing it while refitting the other parameters, then fixing all other parameters and refitting for n. The fits to signal MC for X(3872) —* and X(3872) —÷ b(2S)7 are shown in Figures 5.1 and 5.2, respectively, with the numerical results summarized in Table 5.1. For the background, the peaking component was represented by using the Crystal Ball shape with parameters fixed to values from the signal fit, plus an ARGUS function [82] used to model the non-peaking background component. The ARGUS function, used widely in BB physics analyses, is slightly curved over a large range of data points and terminates smoothly 77 5.1. Signal Extraction Procedure 900 u, 800 q1200 700 600 ‘U UI800 500 758529 1400 I I I I 5.275.59 400 600 300 400 200 200100 m,, (GeV/c2) m,,, (GeV/c2) 0 800 1200S. 700 1000 600 UI 800500 75.595.3 900 752852953 1400 (d) 400 600 300 400 200 200100 m (GeV/c2) m (GeV/c2) Figure 5.1: mmjss PDF fits for the J/ signal modes, (a) B — X(3872)K, (b) B° —* X(3872)K0,(c) B —* X(3872)K*±, and (d) B° —* X(3872)K*o. 78 5.1. Signal Extraction Procedure — 4000 a) (b) 3500 ‘°.3000 3000 2500 2500 1u2000 J28529 3500 2000 V 1500 1500 V 10001000 V V 500 V V 500 C’ m, (0eV/c’) m,, (GeV/c’ 0 0 4, 1800 V ‘1600 3000 4, Cl400 V V E2500 4, a, ‘1200 V V 2000 2000 75285 3500 (d) 1000 V V 800 V 1500 600 V V 400 V V 500200 V V C rn,, (GeV/c’) m,, (GeV/c’) Figure 5.2: mmjss PDF fits for the (2S) signal modes, (a) B —* X(3872)K, (b) B° —* X(3872)K, (c) B —i X(3872)K*±, and (d) B° — X(3872)K*o. 79 5.1. Signal Extraction Procedure Table 5.1: Summary of the mmjss PDF parameter fit results for the signal uodes. Crystal Ball Parameters Decay Mode a mo (GeV/c2) n o (MeV/c2) J/7K 1.54 ± 0.04 5.27919 ± 0.00004 145 ± 36 4.96 + 0.03 J/’,LryK° 1.54 ± 0.03 5.27956 ± 0.00003 146 ± 29 4.92 + 0.03 J/b7K*± 1.50 ± 0.04 5.27923 + 0.00004 140 ± 29 4.99 + 0.03 J//yyK*O 1.55 ± 0.03 5.27959 ± 0.00003 142 ± 38 4.98 ± 0.03 (2S)7K 1.68 ± 0.02 5.27925 ± 0.00001 155 ± 42 4.94 ± 0.01 J(2S) 1.72 ± 0.03 5.27951 + 0.00002 141 + 46 4.93 ± 0.02 &(2S)yK*+ 1.64 ± 0.03 5.27929 ± 0.00002 154 ± 19 4.94 ± 0.02 (2S)7K*o 1.64 ± 0.02 5.27953 + 0.00002 154 + 21 4.91 ± 0.02 at an endpoint. It is defined as: f(x;c,x) =x ()2exp{_X. (i_ (X)2)} (5.7) where x represents the curvature of the function and c is the endpoint. The fraction of peaking to non-peaking events was fitted to the MC at this stage, but the value is allowed to float in the final fit to data. The results of the PDF fit for the background modes is shown in Figures 5.3 and 5.4, with a summary of the numerical results given in Table 5.2. Based on the examination of BB generic MC events with 5.27 < mmjss < 5.29 GeV/c2, the peaking backgrounds for the X(3872) —> J/’’y modes are predominantly of the type B — J/K, where the K is some excited kaon (K*(890), but also any higher resonance, K1,2 K*(1430), etc.), as well as B —* J/Krr. Similarly for the X(3872) —* &(2S)7 decays, the primary backgrounds come from B — i,(2S)K* and B —* (2S)K7r non-resonant. 5.1.4 PDF Parametrization, mx To parametrize mx for the signal modes, a double Gaussian shape was chosen for ease of use. The background parametrization for mx uses a first-order polynomial for all modes except B/°) — 2S)yK(/°). In 80 5.1. Signal Extraction Procedure :: ‘ 2 5.22 5.24 5.26 5.28 5.3 2 5.22 5.24 5.26 5.28 5 mmI (GeV/c) m (GeV/c2) 5.22 5.24 5.26 5.28 5.3 .2 5.22 5.24 5.26 5.28 D.3 (GeV/c) ni (GeV/c2) Figure 5.3: mmjss PDF fits for the J/ background modes, (a) B X(3872)K, (b) B° —* X(3872)K, (c) B —* X(3872)K*±, and (d) B° X(3872)K*o. 81 Figure 5.4: mmjss PDF fits for the (2S) background modes, (a) B X(3872)K, (b) B° —> X(3872)K50,(c) B —+ X(3872)K*±, and (d) B° X(3872)K*o. 5.1. Signal Extraction Procedure 0 C’, 6, a, U U, C., 6, C a, 0 C., C a’ U > a, U, 6, C a’ U 82 5.1. Signal Extraction Procedure Table 5.2: Summary of the mmjss PDF parameter fit results for the back ground modes. ARGUS Parameters Decay Mode x c ( GeV/c2) Peaking Fraction J/’/,7K —12.86 5.299 ± 0.001 0.263 ± 0.057 J/&’yK° —17.98 + 9.33 5.294 ± 0.003 0.220j J/&yK*± —24.36’ 5.2989 ± 0.0005 0.109 ± 0.050 J/ryK*O —19.841 5.2988 ± 0.0003 0.153 + 0.030 ‘4’(2S)7K —67.51t 5.2991 ± 0.0003 0.07l ‘/)(2S)7Ks° 5.2990 ± 0.0005 0.061 ± 0.078 b(2S)7K*± —28.941 5.2991 ± 0.0005 0.029 ± 0.038 ?/(2S)K*O 5.2990 ± 0.0003 0.038tX these two decay channels, the mx distribution for background events is not represented by a simple linear shape. There is a fall-off of the number of events for mx < 3.84 MeV/c2,related to the cut applied to E7. To describe this background, a linear function multiplied by a Fermi Dirac (F-D) function was used. The function is described by: m• (mx — 3.772) + 1N(mx) = (5.8) 1+e where m represents the slope of the linear part, b represents the point of inflection of the Fermi-Dirac function, and c represents the “steepness” of the Fermi-Dirac function. The results of the fit for the signal modes are shown in Figures 5.5 and 5.6 for the J/& and (2S) signal modes, respectively, and summarized in Table 5.3. The results of the fits for the background modes are found in Figures 5.7 and 5.8 and Table 5.4. 83 5.1. Signal Extraction Procedure 0 800 1200700 0 600 1000 uJ 500 800 900 1400 (b) 400 600 300 400 200 100 200 G ..S5 3.86 3.87 3.88 3.89 m2 (GeV/c2) m2 (GeV/c2) r180(.i U, .1400 800 1200E 0 0 I1000600A 1600800400 600400200 200 3.65 3.86 3.87 3.88 3.89 m, (GeV/c2) m2 (GeV/c2) Figure 5.5: mx PDF fits for the J/ signal modes, (a) B —* X(3872)K, (b) B° —* X(3872)K80,(c) B —* X(3872)K*±, and (d) B° — X(3872)K*o. 84 ‘o 2400 2200 Lq2000 e 1800 0 1600 1400 1200 1000 800 600 400 200 5.1. Signal Extraction Procedure > 3500 U, 3000 0 2500 LU 2000 1500 1000 500 c 4000 3500 3000 I2500 2000 1500 1000 500 Figure 5.6: mx PDF fits for the ‘4’(2S) signal modes, (a) B —* X(3872)K, (b) B° —f X(3872)K, (c) B — X(3872)K*±, and (d) B° — X(3872)K*o. 85 c4000 > 3500 C 3000 0 C 2500 2000 1500 1000 500 . 3.86 3.87 3.88 3. . 3.86 3.87 3.88 3. rn, (GeV/c2) m (GeV/c2) mx (GeV/c’) m2 (GeV/c2) 5.1. Signal Extraction Procedure Figure 5.7: mx PDF fits for the J/ background modes, (a) B X(3872)K, (b) B° —* X(3872)K0, (c) B —* X(3872)K*+, and (d) B° —+ X(3872)K*o. >8 w 4 3 2 C 0 > 7 . 6 4 3 2 (a) >2(b) I 3.8 3.85 3.9 3.95 3.8 3.85 3.9 3.95 m,A (GeV/c2) m. (GeVIc’) +14+ii 3.8 3.85 3.9 3.95 3.8 3.85 3.9 3.95 m2 (GeV/c2) m (GeV/c2) 86 5.1. Signal Extraction Procedure > U, C C uJ G 3.8 3.85 3.9 3.95 0 3.8 3.85 3.9 3.95 m (GeV/c’) m, (GeV/c’) j 14 (c) (d) I. 0 >35 30 6, C 25 2C 15 5 3.8 3.85 3.9 3.95 m, (GeV/c’) Figure 5.8: mx PDF fits for the (2S) X(3872)K, (b) B° —* X(3872)K, (c) B° —* X(3872)K*o. 3.8 3.85 3.9 3.95 n(GeV/c2) background modes, (a) B+ B — X(3872)K*±, and (d) 87 5.1. Signal Extraction Procedure Table 5.3: Summary of the mx PDF parameter fit results for the signal modes. Fit Parameter Decay o’2 Core Mode (MeV/c2) (MeV/c2) (MeV/c2) Fraction J/7K 3871.74 ± 0.04 4.93 ± 0.09 10.48 0.70 ± 0.03 J/’çb7K8° 3871.63 ± 0.03 4.32 + 0.06 10.121 0.71 ± 0.02 J/yK*± 3871.78 ± 0.03 3.78 ± 0.06 10.281 0.64 ± 0.01 J/,byK*O 3871.82 ± 0.03 3.70 ± 0.04 10.59 0.68 ± 0.01 (2S)7K 3871.25 ± 0.02 4.44 ± 0.04 8.10 0.72 ± 0.02 (2S)’yK 3871.30 ± 0.04 3.89 ± 0.04 7.56 ± 0.09 0.70 + 0.01 (2S)7K*± 3871.36 ± 0,02 3.66 ± 0.04 7.93 ± 0.11 0.71 ± 0.01 &(2S)K*o 3871.47 ± 0.01 3.58 ± 0.03 8.14X 0.73 ± 0.01 5.1.5 PDF Parametrization, mK* For the signal modes, a Breit-Wigner function convoluted with a Gaussian19 was chosen for the mK* PDF. For background, the same peaking shape was used with the addition of a first-order polynomial. This represents a peaking component (real K* in the event) plus a combinatoric component. Like the mmjss case, the fraction of peaking background was fitted at this stage but allowed to float in the final signal extraction fit. The results of the fits for both the J/ signal and background modes are shown in Figure 5.9, and similarly for (2S) in Figure 5.10. The values for the parameters for all of the modes are summarized in Table 5.5. 5.1.6 PDF Correlations The likelihood fit and PDFs defined in the previous sections rely on the assumption that the variables chosen for the fitting procedure are indepen dent from one another. To investigate the presence of any dependencies, 2-D plots are produced between mx, mmjss, and mK*, which are shown in Fig ures 5.11 — 5.14 for the X(3872) signal modes, and Figures 5.15— 5.18 for the ‘9This total convolved function is referred to here as a Voigtian function. 88 5.1. Signal Extraction Procedure S. S.2200 14O0 (a) oo (b) 1200 - 11 - !.1800 16OO 1O00 i I l400 coo- J I - 1200 1000 600 800 40o- - 600 400 200 - - 200 b .75 0.80.850.90.951 1.05 1.1 . 0.75 0.80.850.90.951 1.05 1.1 mK.. (GeV/c2) mK (GeV/c2) Eu 075 08 085 09 095 1 105 11 075 08 085 09 095 1 105 11 ni.., (GeVIc2) (GeV/c2) Figure 5.9: mK* PDF fits for the J/ signal and background modes, (a) B —* X(3872)K*± signal events, (b) B° —* X(3872)K*o signal events, (c) B — X(3872)K*± background events, and (d) B° — X(3872)K*o background events. 89 5.1. Signal Extraction Procedure >3000 -(a) A 5000 (b) 250O - - £8 c4000 a, 200O - - 3000 1500 - - 2000 -1000 - - 500 - - 1000 - 0.750.80.850.90.9511.05 .75 0.8 0.85 0.9 0.9511.05 1.1 m.(.. (GeV/c’) inK. (GeV/c2) 97 075 08 085 09 095 1 105 11 87 075 08 085 09 095 1 105 11 111K, (GeV/c2) mK. (GeV/c2) Figure 5.10: m1<. PDF fits for the (2S) signal and background modes, (a) B — X(3872)K*± signal events, (b) B° —÷ X(3872)K*o signal events, (c) B —÷ X(3872)K*± background events, and (d) B° —* X(3872)K*o background events. 90 5.1. Signal Extraction Procedure Table 5.4: Summary of the mx PDF parameter fit results for the background mn,l oo Table 5.5: Summary of the mK* PDF parameter fit results. Fit Parameter Decay width Slope Peak Mode (MeV/c2) (MeV/c2) (GeV/c2) (GeV/c2)’ (91) J/ryK*± 891.8 ± 0.2 10.4 ± 0.7 42.3 ± 0.8 0.5 ± 1.5 11 ± 6 J/7K*o 895.8 ± 0.2 9.5 ± 0.6 43.3 ± 0.6 8.2 ± 3.8 15 ± 4 1J(2S)K*± 891.9 ± 0.2 10.2 ± 0.5 42.9 ± 0.5 60 ± 20 9 ± 4 (2S)7K*o 896.0 ± 0.1 9.1 ± 0.4 43.7 ± 0.4 4.9 ± 2.8 8 ± 2 background. For the signal modes, the absence of a linear relationship in the plots clearly demonstrates no correlation between the variables used in the fit. This statement applies equally to the background modes. This was also investigated numerically by calculating the correlation coefficient between each set of variables, which was found to be very small (generally <<0.1). The lack of events in the low mx region is due to the E7 > 100 MeV/c2 cut applied to reduce the level of background due to random low-energy photons, but this is an isolated effect that has a minor overall impact. The calculated correlation factor is found to be negligible (< 0.04) between all of the PDF fit variables. Decay Mode J/’çb7K J/’i,b7K y-intercept ( GeV/c2) 47.1±6.7 6.9 ± 2.7 slope ( GeV/c2)’ —11.2 ± 1.2 —1.6±0.7 F-Db ( GeV/c) F-Dc ( GeV/c2)’ Fit Parameter J/yK*± 27.0 ± 7.6 —5.9 ± 2.0 - - J/7K*o 82.1 ± 12.1 —18.2 ± 3.0 - - b(2S) - —3.3 ± 1.0 3.8 ± 0.03 0.037 ± 0.016 (2S)’yK - —1.4 ± 3.7 3.8 ± 0.06 0.023 ± 0.011 (2S)7K*± 40.0 ± 10.8 —8.1 ± 2.8 - - J.(2S)K*o 76.1 ± 20.4 —12.5 ± 5.3 - - 91 5.1. Signal Extraction Procedure Figure 5.11: Plots of mmjss versus mx for the X(3872) —+ J/’i7 signal modes. I X(3872) (JIy) K Signal X(387 Signal I o 5.3 0 5.28 E 5.26 [(72) (JIiiy) K*o SigjJ 5.3 5.24 5.22 _.. I I I I I I 11H. ____ m(GeV/c2) 1200 000 5.28 E 00 5.26 300 5.24 100 5.22 00 5.2 0 5.2 3.82 3.84 3.86 3.88 92 5.1. Signal Extraction Procedure I X(3872) (J/,y) K° Signal I 7 0.75 0.5 0.55 0.9 0.95 1 1.05 1.1 mK (GeV/c2) I X(3872) (J1i4 y) K Signal I X(3872) (JI y) K*o Signal I 0.7 0.75 0.8 0.85 0.9 0.95 1 1 “ m( _a) I I I 5 0.8 0.85 0.9 0.95 1 n. Figure 5.12: Plots of mm/ss versus mK* and mx versus mK* for the X(3872) — J/7 signal modes. 93 5.1. Signal Extraction Procedure II UJJ6S 4 _i_J_L_ 1- 3.9 3.92 11¼ (GeV/c2) Figure 5.13: Plots of mmjss versus mx for the X(3872) —‘ ‘(2S)’y signal modes. [x(3872) (w(2S) y) IC Signal I I 5.3j_I 5.28 6 [i3872) (w(2S) 7) K: Signal 5.26 5.24 5.22 5.2 C .9 5.3 5000 5.28 woo 5.26 5000 000 1000 I I 5.24 5.22 3.82 3.84 3.86 3.88 3.9 3.92 m,(GeV/c2) I X(3872) (w(2S)y) K Signal 5.2 rr¼(GeV/c2) L72 (p(2S) y) K° Signal 6.26 5.24 5000 4000 3000 2000 1000 5.22 5.2 3.84 3.86 3.88 94 5.1. Signal Extraction Procedure X(3872) (‘(2S) ‘) K Signal X(3872) (i(2S) y) K0 Signal I Figure 5.14: Plots of mmjss versus X(3872) —f &(2S-y signal modes. .0.750.80.850.90.95 1. ,.1 ‘‘ m. (GeV/c2) X(3872) ((2S) y) Signal X(3872) ((2S) .y) K° Signal I 3L2Ii 0.7 0.75 0.8 0.85 0.9 0.95 1 1. 1.1 mK (GeV/c2) mK* and mx versus mK* for the 95 5.1. Signal Extraction Procedure 1.6 1.4 1.2 0.8 0.6 0.4 0.2 0 Figure 5.15: Plots of mmjss versus mx for the X(3872) —* J/7 background modes. X(3872) (J/i ‘) K Backgroun4j ..II X(3872) (JIr ‘) K Background 1.4 1.2 I 0.6 0.5 0.8 0.6 0.4 0.2 0.3 3.95 m2 (Gev/c2) 0.2 0.1 X(3872) (J/t ‘) K° Background IX(3872) (J/iy) K Background . - 5.3i 0 0 E 5.28j 5.24 10.6 5.265.26 > S 5.24k10.45.22 10.2 5.22[5.2 1 5.2[ 3.8 3.85 3.9 3.95 n (GeV/c2) 96 5.1. Signal Extraction Procedure I X(3872) (Jhi -y) K Background Figure 5.16: Plots of mmiss versus X(3872) — J/7 background modes. L3872 (J/4iy) K Background I 03.98 — 3.96 3.94 0.7 0.75 0.8 0.85 0.9 0.95 1 1J5 1.1 mK (GeV/c2) 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK (GeV/c2) 0.7 0.75 0.8 0.85 0.9 0.95 1 . . mK (GeV/c2) mK* and mx versus mK* for the 97 5.1. Signal Extraction Procedure C2 5.3 > aC, 5.28 a 5.26 5.24 5.22 5.2 cl 5.2 > C C, 5.28 a 5.26 5.24 5.22 5.2 I X(3872) (w(2S) y) W Background 3.8 3.85 3.9 3.95 m,(GeV/c2) n (GeV/c2) I X(3872) (w(2S) y) Background I !!!!! 1.4 Ii 1.2 15.28[ a 0.8 0.6 0.4 0.2 3.9 3.95 m, (GeV/c2) Figure 5.17: Plots of mm/ss versus ground modes. • — — • • • • • • • I _i._i_ ai__r_.’ [72) (w(2S) y) K*o Background I 2.5 2 1.5 0.5 — 3.85 3.9 3S5 0 m,(GeV/c2) for the X(3872) —* ‘z,b(2S)’y back- 3.8 mx 98 5.1. Signal Extraction Procedure Figure 5.18: Plots of mmjss versus X(3872) — (2S)7 background modes. mK (GeV/c2) 1 1.1 mK (GeV/c2) 1 1.1 (GeV/c2) mK* and mx versus mK* for the 99 5.1. Signal Extraction Procedure 5.1.7 The 5Plot Technique The 3Plot statistical technique [80] is used to display the results of the PDF fits to mmjss and mK*. This technique is effectively a sophisticated background-subtraction method that assigns weights to each event describ ing how “signal-like” the event is. These weights, represented here by the symbol w, are calculated for each event i in the data sample according to: — 59Wai (N.F))2 (.) where a represents the event type or species (i.e.: signal, background, peak ing background, etc.), (y) is the set of observables used in the fit (mmjss and mK*), F is the corresponding PDF as defined in Section 5.1.1, N is the total number of events of type returned from a maximum likelihood fit to the data, and o and /3 are indices to indicate the summation over all possible event types. V in this equation is the covariance matrix between a and o, defined as: v—’_v’ Fa()FaQ) 510a The sum of the weights over all species for a given event will be equal to 1 (i.e.: L’awa = 1). The result is that each event in the dataset has a weight which describes how much like a given species that event is. This weight is based on the known PDFs and event yield from the fit to a given variable. In practice, the weight for signal events will typically be 1 for true signal events, while background events will be weighted 0. The power of this technique arises from the ability to examine the distribution of the data in another, uncorre lated variable, using the event-species categorization information given by w. For example, in this analysis, one fits the data for B± XK± decays using the mmjgs variable and its associated PDFs for signal and background events. The resulting information is used to calculate for each event. When the mx distribution of the data is then plotted using the signal-species weights, 100 5.2. X(3872) Signal Extraction on Monte Carlo it gives a clear picture of X invariant mass for the signal-like content of the data. This resulting distribution can subsequently be fit to get a signal-event yield versus mx, possibly indicating the presence of new resonances. 5.2 X(3872) Signal Extraction on Monte Carlo To reiterate, the signal extraction is based on an unbinned extended maxi mum likelihood fit to the kinematic variables mmjss and mK* (if applicable), followed by a fit to the 8Plot projection of mx for signal events. For the simplest modes, B —> XK±,O there are three species of events: signal events that peak in both mmjss and mx, combinatoric background events that are parameterized with an ARGUS function in mmjss and are linear in mx, and peaking background events that peak in mmjss but have a linear mx distribution. The first fit (defining two event types and using two PDFs in mmjss) separates out the combinatoric background, and the second fit (in mx) separates out the peaking background events. For the excited kaon modes, B —‘ XK*, there are three relevant kine matic distributions: mmjs8, mK*, and mx. For these modes, four types of events are defined (hence four PDFs in the mmiss x mK* fit): signal events that peak in all three distributions; combinatoric background events that have an ARGUS shape in mmjss and are fiat in the other variables; peaking background events that peak in mmjss but are fiat in mjç* (i.e.: B —* XKir non-resonant events, which also peak in mx), and combinatoric background events that have a real K* (ie: B — J/&K*) that may peak in mK* but are flat in mmjss. 5.2.1 Monte Carlo Tests The signal extraction was tested by inputting a given number of signal events drawn from the Monte Carlo sample while generating a specified number of background events based on the PDFs for the background shape. While the amount of generated signal MC is large, the available sample of background events passing all cuts is much lower, hence the choice to generate the back 101 5.2. X(3872) Signal Extraction on Monte Carlo ground events from the PDF distribution. This allows many repeated trials of the signal extraction in order to test the robustness, define any biases, and calculate the expected efficiency for measuring our signal from the data. In the case of the X(3872) — &(2S)7 decay modes, it was necessary to trim the number of (2S) —* tt events in the MC sample. The ratio of (2S) decays to tt- compared with Jnrir was incorrectly defined in the generation of the MC events and does not match the physical value reported by the PDG [33]. In order to compensate, 20% of the (2S) —> events were removed at this stage of the analysis. This was done in a uniform fashion across lepton type and over the chronological running period to avoid introducing any further bias into the MC sample. The expected number of signal events was estimated by multiplying the “Total Events” column by the “Weight” column in Table 4.1 and by the “Efficiency” column in Table 4.4 for truth-matched events. The expected number of background events was estimated by counting the total number passing the reconstruction and selection cuts, while applying the correct weighting based on the MC background type. These values were used as inputs for testing the signal extraction and are included in the “Signal Input” and “Background Input” columns of Table 5.6. For the case of X(3872) —k (2S)7 decays, using the assumption that it has the same branching fraction as B± X(3872)K± leads to a very small number of expected events in the data. In order to test the robustness of the signal extraction technique, the X(3872) —* ‘(2S)7 trials were also run using 6 times the number of signal events (roughly following the branching fraction assumption for a x(2P) assignment for the X(3872) from [61]). 5.2.2 Bias To test for a possible bias, repeated signal extraction trials using truth matched signal events were performed. The PDF parametrization was based on this sample of events, so one would expect the signal extraction procedure to correctly handle events of this type. The results of the trials can be found in Table 5.6. 102 5.2. X(3872) Signal Extraction on Monte Carlo Table 5.6: Test of signal extraction for truth-matched signal MC events with PDF-generated background events. While these results show the procedure to be robust, it also points to some small systematic bias present in nearly all of the modes, as indicated by the difference between the number of input signal events compared with the number extracted. This shift will be applied to the number of events found from the signal extraction to correct for these biases arising from possible correlations between the PDFs and mechanics of the fit. Note that these tests are the culmination of hundreds of independent trials using different input signal and background events, thus the error is essentially equal to In practice, it was found by fitting the results of the N trials with a Gaussian. Furthermore, in a small fraction (dependent on the signal mode but generally < 0.2% for X(3872) —* ,b(2S)y decays) of the trials, the fitting procedure failed to properly converge. These trials were eliminated from the study without any loss of generality. Decay Mode Trials Signal Background Mean Signal Standard X(3872) Input Input Output Deviation J/’,b7K 900 27 164 27.8 ± 0.2 4.79 ± 0.12 J/?JyK8° 2500 7 38 6.6 ± 0.1 2.43 ± 0.04 J/b7K*+ 2500 3 217 2.4 ± 0.1 3.02 + 0.05 J/,K*o 2500 14 599 15.5 ± 0.1 6.26 ± 0.10 /(2S)7 1000 12 501 13.4 + 0.2 6.29 + 0.14 b(2S)K° 1000 3 123 2.7 ± 0.1 3.16 ± 0.07 (2S)yK*± 1000 1 501 1.1 ± 0.1 2.93 ± 0.08 (2S)yK*O 1000 6 1417 7.1 ± 0.2 6.43 ± 0.14 (2S)7K 1000 71 501 71.7 ± 0.3 8.68 ± 0.21 ‘z.’(2S) 1000 19 123 19.2 ± 0.1 3.98 ± 0.11 (2S)yK*± 1000 8 501 8.0 ± 0.2 4.77 ± 0.10 (2S)7K*o 1000 35 1417 38.8 ± 0.3 9.29 ± 0.24 103 5.2. X(3872) Signal Extraction on Monte Carlo 5.2.3 Fit Efficiency To calculate the signal extraction efficiency of the fit method, the same procedure as described in the previous section is adopted for non-truth- matched MC events. These events are most like those one expects when analyzing the data. After extracting the number of signal events, the result is shifted by the bias defined in Table 5.6 and divided by the number of input events to determine the fit efficiency. The results of this series of trials are summarized in Table 5.7. Repeating the X(3872) — ‘(2S)’y signal extraction tests with a greater number of input events for the signal mode shows that the technique is consistent, producing a fit efficiency that matches the small number of events within uncertainty. Because the values for the efficiency were shown to be the same, the results using the greater number of signal events will be taken as the fit efficiency since they have a smaller uncertainty. While the signal extraction efficiency for the B — X(3872)(J/&’y)K(’°) modes is very high, there is a noticeable drop from the K(’°) modes to the K*(+,o) modes. There is an even greater difference seen when comparing the J/ and (2S) modes. This is due to much larger effects of misre construction in the latter case (for instance, incorrect pions in the decay to J/rir, or the greater probability of substituting a random low en ergy photon in place of the correct signal photon). Indeed, if one compares the cut and reconstruction efficiency between truth-matched and non-truth- matched events in Table 4.4, there is a notable difference in the case of the (2S) decay channels. This can also be seen by comparing the shapes of the distributions between truth-matched and non-truth-matched events (Figures 5.19 - 5.22). The PDFs for the fit are defined using truth-matched events, but the reconstructed events in data should look more like non-truth matched events. In the latter case, there are tails in both mmjss and mx which lead to the drop in efficiency. For the X(3872) — Jy modes, there is a much closer agreement between truth- and non-truth-matched events, as shown in Figures 5.23 - 5.26, hence a better fit efficiency. 104 Table 5.7: Test of signal extraction for all signal MC events with PDF-generatedbackground events. Decay Mode Trials Sig. Bkgd. Mean Sig. Standard Bias Corrected Fit X(3872) In In Out Deviation Correction Output Eff. (%) J//7K 1000 27 164 27.8 + 0.2 5.01 + 0.13 —0.8 ± 0.2 27.0 ± 0.2 100.1 ± 0.8 J/’b7K° 3000 7 38 6.6 ± 0.1 2.50 + 0.04 +0.4 ± 0.1 6.9 ± 0.1 99.3 ± 1.0 J/z,bK*± 2500 3 217 2.0 ± 0.1 2.83 ± 0.05 +0.6 ± 0.1 2.6 ± 0.1 87.4 ± 3.6 J/yK*O 3000 14 599 14.0 ± 0.1 6.38 ± 0.08 —1.5 ± 0.1 12.6 ± 0.2 89.9 ± 1.3 &(2S)7 1000 12 501 9.5 ± 0.2 6.40 ± 0.14 —1.4 ± 0.2 8.2 + 0.3 68.0 ± 2.4 ‘&(2S)K 1000 3 123 1.8 ± 0.1 3.15 ± 0.07 +0.3 ± 0.1 2.1 ± 0.2 71.0 ± 5.0 ,b(2S)7K*± 1000 1 501 0.8 ± 0.1 2.75 ± 0.08 —0.1 ± 0.1 0.7 + 0.2 69.1 ± 16.3 1/(2S)yK*O 1000 6 1417 4.6 + 0.2 6.29 ± 0.16 —1.1 ± 0.2 3.5 + 0.3 58.4 + 4.8 ‘,b(2S)7K 1000 71 501 48.9 ± 0.3 9.22 ± 0.19 —0.7 ± 0.3 48.2 ± 0.4 67.8 ± 0.6 /‘(2S)7K° 1000 19 123 13.1 + 0.2 4.58 + 0.12 —0.2 ± 0.1 12.8 ± 0.2 67.5 + 1.0 z,h(2S)7K*± 1000 Th 501 4.7 ± 0.2 4.32 + 0.09 —0.0 ± 0.1 4.7 ± 0.2 58.2 ± 2.7 ?/(2S)K*O 1000 35 1417 23.7 ± 0.3 8.58 ± 0.19 —3.8 ± 0.3 19.9 ± 0.4 56.7 ± 1.2 Co Cl) o. 0 0 Cl’ 5.2. X(3872) Signal Extraction on Monte Carlo Distribution, True vs. Untrue Q45OOU > 40000 - 35000 - I30000 - 25000 - 20000 - 15000 - 10000 5000 I. Figure 5.19: Comparison of truth-matched (blue) and non-truth-matched (red) MC for B —* X(3872)Q&(2S))K. Lmx Distribution, True vs. UnJ 35000 U)30000 25000 20000 15000 10000 5000 Figure 5.20: Comparison of truth-matched (blue) and non-truth-matched (red) MC for B° — X(3872)Q(2S)-y)K.. x Distribution, True vs. Untrue F-H 5.2 5.22 5.24 5.26 5.28 5.3 m (GeV/c2) 40000 -, ,35OO0 - 0 30000• uJ 25000 - 20000 - 15000 _j_ - 10000 - 5000 LII:0 3.8 3.85 3.9 3.95 mx (GeV/c2) Lmm Distribution, True vs. Untrue I III 3.8 3.85 3.9 3.95 m2 (GeV/c2) 106 5.2. X(3872) Signal Extraction on Monte Carlo m1.. DIStribUtIOfl, True vs. Untrue I C, > 0 C w Figure 5.21: Comparison of truth-matched (blue) and non-truth-matched (red) and MC for mx, mmjss, and mK*± for B —* X(3872)((2S)7)K*±. L!! Distribution, True vs. Untrue I I mx Distribution, True vs. Untrue C, 18000 160O0 14O00 12000 10000 8000 6000 4000 2000 - 2000O H— - 18000- H- 16000- - - - ,14000- - - 12000- - - F - 10000- - - H — - 8000- - 6000- - F H 4000- - - j—— 2000- - —rjfEi, I E11 GL2 5.22 524 5.26 5.28 5.3 3.8 3.85 3.9 3.95 m,,1 (GeV/c’) m2 (GeV/c2) 107 5.2. X (3872) Signal Extraction on Monte Carlo m Distribution, True vs. Untrue m1 Distribution, True vs. Untrue ;:16000 14000 12000 w 10000 8000 6000 4000 2000 0.75 0.9 0.95 0.9 0.95 1 1.05 1.1 mK (GeV/c2) Figure 5.22: Comparison of truth-matched (blue) and non-truth-matched (red) and MC for mx, mmjss, and mK*o for B° — X(3872)(b(2S)7)K*o. 108 I m,,1, Distribution, True vs. Untrue t 35000 3000O 25000 25000 ::: - - 5.28 5.3 m (GeV/c2) 52 5.22 524 5.26 3.8 3.85 3.9 3.95 m (GeV/c2) 5.2. X(3872) Signal Extraction on Monte Carlo I m,, Distribution, True vs. Untrue mx Distribution, True vs. Untrue Figure 5.23: Comparison of truth-matched (blue) and non-truth-matched (red) MC for B — X(3872)(J/7)K. 5.22 5.24 5.26 5.28 5.3 3.8 m,(GeV/c) Figure 5.24: Comparison of truth-matched (blue) (red) MC for B° — X(3872)(J/b7)K. 0 LU m2 (GeV/c2) m,, Distribution, True vs. UnJ I mx Distribution, True vs. Untrue 016O0U > 14000 U, 12O0O 10000 8000 6000 4000 2000 “0 14000 - rL - 12000 - -I_ - I10000- - 8000- - 6000- - 4000- - 2000- - t I . 3.85 3.9 3.95 m (GeV/c2) and non-truth-matched 109 5.2. X(3872) Signal Extraction on Monte Carlo m<.. Distribution, True vs. untrue 4000 3500 3000 w2500 2000 1500 1000 500 C Figure 5.25: Comparison of truth-matched (blue) and non-truth-matched (red) MC for mx, mmjss, and m<± for B —* X(3872)(J/1y)K*±. mx Distribution, True vs. Untrue Immjgs Distribution, True vs. Untrue ‘10000 - - 8000- - w 6000- - 4000- - 2000 5.22 5.24 5.26 5.28 5.3 m,,1, (GeV/c2) m (GeV/c2) ZL ti.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 m<.. (GeV/c’) 110 0 > 140O0 12000 I10000 8000 6000 4000 2000 5.2. X(3872) Signal Extraction on Monte Carlo Figure 5.26: Comparison of truth-matched (blue) and non-truth-matched (red) MC for mx, mmjss, and mK*o for B° —* X(3872)(J/&7)K*o. Distribution, True vs. Untrue I m Distribution, True vs. Untrue 114000 12000 I10000 8000 6000 4000 2000 - -I .2 5.22 5.24 5.26 5.28 5.3 3.8 3.85 3.9 3.95 m, (GeV/c2) m2 (GeV/c2) m uistrioution, True vs. Untrue 0 6000 - 0 5000- ‘4000 - 3000- :Jç 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 m(GeV/c2) 111 5.2. X(3872) Signal Extraction on Monte Carlo 5.2.4 Total Efficiency The total efficiency for each signal mode is found by multiplying the cut, reconstruction, and fit efficiencies together. These values are compiled in Table 5.8. Table 5.8: Total signal extraction efficiency for each signal mode based on MC samples. Decay Mode Cut/Reco Fit Total X(3872) Efficiency (%) Efficiency (%) Efficiency (%) J/?,b’yK 14.6 100.1 ± 0.8 14.6 ± 0.1 J/&-yK8° 11.1 99.3 ± 1.0 11.1 ± 0.1 J/7K*± 7.9 87.4 ± 3.6 6.9 ± 0.3 J/iyK*O 11.5 89.9 ± 1.3 10.4 ± 0.1 (2S)7K 15.4 67.8 ± 0.6 10.4 ± 0.1 i,b(2S)’yK 11.8 67.5 ± 1.0 8.0 + 0.1 (2S)7K*± 7.3 58.2 ± 2.7 4.3 ± 0.2 (2S)K*o 11.4 56.7 ± 1.2 6.5 + 0.1 5.2.5 Cross-feed and Other Backgrounds Cross-feed is defined as one signal mode being misreconstructed as another. A priori, the main type of cross-feed that might be expected is the case of a K* incorrectly being formed as a combination of a signal K plus a r, or vice versa with a ir being missed in the reconstruction. This is tested by attempting to extract a number of events of type j from a MC sample of signal type i. This effect was found to be tiny. Based solely on the number of events passing reconstruction and cuts, the largest amount of cross-feed ex pected was in the case of B° — X(3872)K*O events being misreconstructed as B± X(3872)K*± events. The “efficiency” for this misreconstruction was measured to be 0.4% of all B° — X(3872)K*o events (for both X(3872) —> J/ry and X(3872) —* &(2S)7), and this is before even attempt ing to fit these events using our PDFs and discriminating variables (which look completely different for signal events). Thus this background is ignored. 112 5.2. X (3872) Signal Extraction on Monte Carlo Another source of background could be from other known X(3872) de cays, in particular B —* X(3872)(J/ir+irjK. This is not included in our background MC sample, so the signal MC for these types of events (and the neutral B decay) was used. In general, the number of events of this type passing our reconstruction and selection cuts is small. To deter mine the expected number of events before fitting, one divides the number of events passing the reconstruction and selection cuts by the total num ber generated in the MC, and multiply it by the branching fractions for B —* X(3872)(JiJnrrjK and subsequent daughter decays from the re cent BABAR result [34]. As shown in Table 5.9, very little contamination is expected from this decay mode for all of the event types except possibly B —* X(3872)(?,b(2S))K. This background comes from picking up a low energy photon to create the same final state, ie: J/ +,ryK±. Note that the same background exists for the K mode, and the raw number of events from the MC sample confirms this, but the small branching fraction mea surement for B° —p X(3872)K° makes this background relatively negligible in this analysis. it is important to note that even though these events may pass the se lection cuts, it does not mean their distribution is signal-like. To test the effect of these events, signal extraction trials are conducted using the nomi nal number of signal events from MC, toy-generated background events, and inserting cross-feed events from the MC. Two hundred trials are performed for the B —* X(3872)(J/ rjK mode, where the largest effect po tentially exists, and find that an addition of 4 cross-feed events causes an average of change in the number of signal events extracted of less than 0.002. This check makes it clear that these cross-feed events are correctly separated from signal events and that they are not a source of background. 5.2.6 Null Signal Tests The signal extraction was also tested for the null signal case. For each mode, 1000 toy trials were conducted with zero signal events and the expected num ber of background events, to determine if a fluctuation from the background 113 5.3. The Xcl,2 Benchmark Modes Table 5.9: Number of MC background events from B —* X(3872)(J’birirjK passing reconstruction and selection cuts and the resulting number expected in the data based on known branching fractions. The total number of events generated in each MC mode was 175000. ____________________ ____________________ Decay Mode X(J/Øir )K X(J/Ør )K° X(3872) Pass Cuts Expected Pass Cuts Expected J/’JryK 133 0.4 1 0.0 J/?,b7Ks° 0 0 98 0.0 J/bK*± 5 0.0 52 0.0 J/b7K*o 40 0.1 10 0.0 /(2S) 1311 3.5 18 0.0 ‘?/)(2S)7Ks° 4 0.0 1145 0.4 b(2S)7K*± 23 0.1 247 0.1 b(2S)yK*O 215 0.6 87 0.0 could produce a significant signal. The results are summarized in Table 5.10. For each trial, the significance of the result is defined as the number of events divided by the uncertainty. A histogram of the significances for each trial was fitted with a Gaussian and the probability of a trial having > 3cr result was determined from the integral of the Gaussian. This shows that while a small bias may be present in the signal extraction, none of the modes are expected to have a particularly strong bias that would generate a significant signal. 5.3 The Xcl,2 Benchmark Modes The decays B — xcj=o,1,2K, XcJ=O,1,2 — J/’y have the same form as the X(3872) decay searched for in this analysis. Using the same method for extracting the X (3872) signal, a measurement of the Xci mode can be at tempted. The branching fractions for the B —* x1K decay channels are ap proximately 30 times greater than those to XcO (which is also much wider), and decays to XC2K have never been observed. Thus a measurement for B —* XC1K will be used as a validation of our signal extraction method. The 114 5.3. The Xcl,2 Benchmark Modes Table 5.10: Number of events returned by the signal extraction from a background-only toy data sample. Decay Mode Signal Background Mean Signal P(> 3u) X(3872) Input Input Output Fluctuation J/b7K 0 164 1.6 ± 0.1 3.2% J/7K 0 38 1.1 ± 0.1 0.5% J/K*± 0 217 1.0 + 0.1 2.4% J/b7K*o 0 599 0.0+0.0 0.9% (2S) 0 501 1.4 ± 0.2 0.5% ‘(2S)7K 0 123 0.1 ± 0.1 1.3% z(2S)7K*± 0 501 0.1 + 0.1 0.8% ?47(2S)K*O 0 1417 0.9 ± 0.2 0.4% XcO region is effectively removed by the cut of mx = m1 ± 100 MeV/c2,but any Xc2 signal should remain in our selection window. 5.3.1 Xci PDF Parametrization For purposes of defining the PDFs, the Xcl sample was drawn from the + - .B B and B B generic and J/& Inclusive MC collections. A mass cut of 3.411 < mx < 3.611 GeV/c2 was applied to restrict our range to the Xcl region, and truth-matching was required. The PDF functional forms used were the same as those from the X(3872) decay modes. Figures 5.29 — 5.31 show the results of the PDF fit for signal and background in mx, mmjss and mK*, with the numerical results summarized in Tables 5.11 — 5.15. The fits to the mx distribution for xclK* background events in Figure 5.30 show that there is a considerable B —* XiKir non-resonant component. Examining a sample of the Monte Carlo background events falling in a tight mmjss, mx and my-. signal range shows that B —b xiKir events comprise the majority (‘ 65%) of the events. Other decay modes include B —* J/bK*+something events (where the K* is any excited kaon), B —* (2S)K, and B —* xclK* events with the K* decaying to a mode not considered in this analysis (e.g.: Kr, K±irO). However, no other single decay mode was comparable to the B —f XiKir decay. The handling of this 115 5.3. The Xcl,2 Benchmark Modes non-resonant background will be described separately in Section 5.3.4. 0 U.’ 0 U, Figure 5.27: mmjss PDF fits for the Xci signal modes, (a) B —÷ XC1K events, (b) B° —* xiK8° events, (c) B± xclK*± events, and (d) B° XciK*O events. 5.3.2 x PDF Parametrization For the XC2 modes, the same mmjss and mK. parameters as derived for the Xci decays are used. The only difference comes in the mx distribution, which is centred at approximately m2 = 3.55 GeV/c2. Due to the lack 0 U, U’ C U’ w 0 U, c4 U, C U’ 116 5.3. The Xcl,2 Benchmark Modes 9+’’• F;’•’’’ç• 2 5.22 5.24 5.26 5.28 5 .2 5.22 5.24 5.26 5.28 5 m (GeV/c2) m (GeV/c 5.22 524 5.26 5.28 5.3 .2 5.22 5.24 5.26 5.28 5.3 m, (GeV/c2) m (GeV/c2) Figure 5.28: mmjs3 PDF fits for the backgrounds to the Xci modes, (a) B+ Xi1< events, (b) B° — xiK° events, (c) B± Xc1K*± events, and (d) B° —* XciK* events. 117 5.3. The Xcl,2 Benchmark Modes 400 > 350 300 “ 250 200 150 100 50 Q 450 . 400 350 300 250 200 150 100 50 Figure 5.29: mx PDF fits for the Xci signal modes, (a) B± xciK± events, (b) B° —* xiK5° events, (c) B± xclK*± events, and (d) B° —* XC1K*O events. 118 > 1400 1200 1000 800 600 400 200 12( > 100 80 60 40 20 345- 3.5 355 3.6 n (GeV/c2) , . I3.45 3.5 3.55 3.6 n (GeV/c’) 3.45 3.5 355 3.6 m (GeV/c2) 5.3. The Xcl,2 Benchmark Modes I . 12 1(a) (b)e T ‘) . 3.5 - I 101 1 = 3 i 2.5: 2 0.5 3.45 3.5 3.55 3.6 3.45 3.5 3.55 3.6 mA (GeV/c2) mA (GeV/c2) 80 20 7Q 25c) I I I W UJ 10 5• 20 10 C C3.45 3.5 3.55 3.6 3.45 3.5 3.55 3.6 m2 (GeV/c2) mA (GeV/c2) Figure 5.30: mx PDF fits for the backgrounds to the Xci modes, (a) B± xclK+ events, (b) B° — xiK8° events, (c) B± Xc1K*± events, and (d) B° . XclK* events. Figures (c) and (d) show clear evidence of B — xiKir non-resonant background events. 119 5.3. The Xcl,2 Benchmark Modes (b) 41 •180 40 _______ 20 b.7 0.75 0.8 0.85 0.9 0.95 1 1.05 11 U, G750.8 0.85 0.9 0.95 1 1.05 11 m.. (GeV/c2) m,,.. (GeV/c2) b.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 d.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK.. (GeV/c2) mK (GeV/c2) Figure 5.31: mK* PDF fits for the Xci signal and background modes, (a) B± , Xc1K*± signal events, (b) B° —* XciK*o signal events, (c) back grounds to B± Xc1K*± events, and (d) backgrounds to B° — Xc1K*O events. V 120 5.3. The Xcl,2 Benchmark Modes Table 5.11: Summary of the mmjss PDF parameter fit results for the Xcl m nd ___________ Crystal Ball Parameter Decay Mode a m0 (GeV/e2) n a (MeV/c2) J/’zJryK 1.57 5.27880 ± 0.00005 144 ± 35 5.09 ± 0.04 J/&7K° 1.60 + 0.10 5.27907 ± 0.00011 25 ± 12 5.11 ± 0.09 J/cbK*± 1.34 5.27923 ± 0.00022 18 ± 13 4.69 ± 0.18 J/i47K*O 1.52 5.27907 ± 0.00011 149 ± 35 5.04 ± 0.09 Table 5.12: Summary of the mmjss PDF parameter fit results for the Xci of MC statistics for this mode, the mx PDF could not be fit to the same precision as for the other modes (i.e. X(3872) and Xci), so a single Gaussian is used rather than a double Gaussian. The results of the fit to mx for truth-matched Xc2 MC are shown in Figure 5.32, with the numerical values summarized in Table 5.16. 5.3.3 PDF Correlations for x As in Section 5.1.6, the 2-D plots of mx, mmjgs, and mi<* are useful for identifying correlation between fit variables. In the X(3872) modes, no significant correlations were found. This process is repeated for the XcJ modes in Figures 5.33 — 5.36. As expected, no significant correlations are found. 121 45 > 40 (.4 35 20 15 10 5 5.3. The Xcl,2 Benchmark Modes Q 4c Cl3 30 ‘ 25 20 15 10 5 40 35 30 20 15 10 5 Figure 5.32: mx PDF fits for the Xc2 background modes, (a) B± Xc2K± events, (b) B° —* x2K8° events, (c) B± —* xc2K*± events, and (d) B° XC2K*O events. 122 (a)} .JI. 3.52 3.54 3.56 3.58 3.6 m (GeV/c2) C 3.52 3.54 3.56 3.58 3.6 mx (GeV/c2) 12 10 C 8(LI 363.52 3.54 3.56 mx (GeVc’) A3.52 3.54 3.56 m(GeVIc2) 5.3. The Xcl,2 Benchmark Modes ni,, (GeV/c2) Figure 5.33: Plots of mmjss versus mx for the XCJ signal modes. 123 5.3. The Xcl,2 Benchmark Modes Figure 5.34: Plots of mm/ss versus mK* and mx versus mi for the signal modes. 1 1.1 mK (GeV/c2) 124 5.3. The Xcl,2 Benchmark Modes 25 20 15 10 5 Figure 5.35: Plots of mm/ss versus mx for the XcJ background modes. 1.4 12 0.6 0.6 0.4 02 52 3.4 3.45 3.5 3.55 3.6 rr (GeV/c2) n (GeV/c2) K° Background (3 5.28k I “U 35 30 3.55 3.6 ni, (GeV/c2) 125 5.3. The Xcl,2 Benchmark Modes Figure 5.36: Plots of mmjss versus mK. and mx versus mK* for the XCJ background modes. 126 K Background U C, xc, ((° Background H-.-L. - — 5.28I E K Background 3.98 > 3.96 0.7 0.8 0.9 1 1.1 (GeV/c2) K*o Background - 3.98L > I 3.96 3.94 1 1.1 1 1.1 mK (GeV/c2) mK (GeV/c2) 5.3. The Xcl,2 Benchmark Modes Table 5.13: Summary of the mx PDF parameter fit results for the Xci signal modes. Fit Parameter Decay /1 01 Core Mode ( MeV/c2) ( MeV/c2) ( MeV/c) Fraction J/’/i7K 3509.53 + 0.07 6.95 ± 0.11 15.731 0.84 ± 0.02 J//-yK° 3509.65 ± 0.14 5.98ii 13.43 0.781 J//,,7K*± 3509.79 ± 0.24 5.17 ± 0.32 13.08 0.76j J/K*o 3509.97 ± 0.12 5.91 ± 0.15 17.04X 0.851 Table 5.14: Summary of the mx PDF parameter fit results for the Xci background modes. Fit Parameter Decay Mode y-intercept slope ( GeV/c2) J/ib7K 47.13 ± 6.65 —11.20 ± 1.17 J/’z4vyK 6.94 + 2.66 —1.61 ± 0.69 J/i4’7K*± 26.95 ± 7.59 —5.92 ± 1.96 J/K*o 82.11 ± 12.05 —18.17 ± 3.11 5.3.4 Treatment of B —* xiKir Non-Resonant (NR) Backgrounds Fits to two kinematics variables, mmjss and mK*, are used to produce the 3Plot versus mx for signal extraction. Based on these two variables, four types of events are defined (with their names in parentheses): those that have a peaking distribution in both mmjss and mK* (“signal”), those that peak in only mmjss (“KTr non-resonant”) or mK* (K* combinatoric”), and those that do not peak in either variable (“combiiiatoric”). SigrIal events were modeled with a Crystal Ball function in mmjss and Voigtian function in mK*. Kir non-resonant events use the same m38 parametrization as signal events, but are linear in mK*. Combinatoric events of both types are modeled with the ARGUS background function in mmjss, and with the signal Voigtian or first-order polynomial in mK* for K* and other combinatoric events, respectively. The parameters for the PDFs are fixed based on the 127 5.3. The Xcl,2 Benchmark Modes Table 5.15: Summary of the modes. Table 5.16: modes. Summary of the mx PDF parameter fit results for the Xc2 signal Fit Parameter Decay Mode i (GeV/c2) cr (GeV/c2) J/7K 3.5556 ± 0.0004 0.0092 ± 0.0003 J/’l/)7K5° 3.5556 ± 0.0004 0.0078 ± 0.0003 J//YyK*± 3.5559 ± 0.0008 0.O085t J/7K*o 3.5562 ± 0.0005 0.0091 fits to the Monte Carlo in the previous section, and allow the yield for each of these four event types to float in the final fit. Note that in mx, both signal events and Krr non-resonant events peak at the Xci mass: this is because there is a real Xci properly reconstructed in the event, while for the combinatoric backgrounds of both types, the mx distribution is predominantly flat. One can get an indication of the distributions in the kinematic vari ables for the different background types by putting a cut requiring mmjss < 5.26 GeV/c2. This roughly selects the combinatoric background events, whose distributions from Monte Carlo in mx (linear) and mjç (linear plus a peaking part for events containing a real K*) for events reconstructed as B± .S XciK*± can be found in Figure 5.37. The Kir non-resonant events are sampled by requiring 5.27 < mmjss < 5.29 GeV/c2. The distribution of these events in mx (peaking at mx = m1 and including a fiat component mi<. PDF parameter fit results for the Xci Decay Mode Parameter J/b7K*± J/b7K*o Mean ( GeV/c2) 0.8945 ± 0.0013 0.8986 ± 0.0006 Sigma ( GeV/c2) 0.000 ± 0.005 0.0066t Width ( GeV/c2) 0.053 ± 0.003 0.048 + 0.002 Bkgd Slope ( GeV/c2) —28.1 ± 131.2 986 ± 818 Peaking Fraction 0.102j 0.125 ± 0.029 128 5.3. The Xcl,2 Benchmark Modes from combinatoric events under the mmjss peak) and mK* (flat) are also found in Figure 5.37. The fits to the data shown in Figure 5.37 are used for the purpose of generating toy MC events to simulate the background in signal extraction tests. For the combinatoric events, the mK* distribution is fit with a linear plus Voigtian part, with the Voigtian parameters fixed to those determined from the signal MC, and only the relative fraction allowed to float. For the Kir non-resonant events, the mx fit is modeled with a linear term plus a double Gaussian with the mean and core width fixed to the values determined from signal MC, and the secondary width and relative fractions allowed to float. The same exercise can be performed for the background events for B° —* xclK*o, shown in Figure 5.38. The combinatoric background events, selected using mmjss < 5.26 GeV/c2, show a distribution similar to that seen for the K*+ mode. For the non-resonant events, the mx distribution is fit in the same manner as for the K* non-resonant case, but the mK*o distribution includes some K*O component, as fit with the Voigtian shape determined from signal MC. By plotting the mx distribution versus mK*o in Figure 5.39, one sees that the events peaking in mK*o are due to events with a XcOK*O part (based on the their collection at low mx near m0). Indeed, this is also seen as a deviation from the fitted line at the low end of the mx distribution for the mmjss peaking component in Figure 5.38. Figure 5.39 also shows there is no significant K*O peak in the mx = m12 regions. That is, there is no indication from the MC of any signal-like background that peaks in mmjss, mK*o and mx = m12. 5.3.5 Xci Cross-feed Cross-feed for the Xci modes is slightly more substantial than for the X(3872) modes. To estimate the contribution of each signal type i to each signal type j, dedicated B —f XciK MC samples were used. To estimate the number of cross-feed events entering our samples, the number of events of type i passing the reconstruction and cuts as signal type j is divided by the total number of MC events generated, and multiplied by the expected BF for the 129 5.3. The Xcl,2 Benchmark Modes I;3c n (GeVIc2) m... (GeVIc2 m, (GeV/c2) m.. (GeV/c2) Figure 5.37: mx and mK*± distributions from MC for backgrounds to XC1K*+ events that are peaking (Kit non-resonant, a and b) or non-peaking (combinatoric, c and d) in mmjss. 130 53. The Xcl,2 Benchmark Modes I mx (GeV/c2) m (GeV/c2) C35353 ______________ m (GeV/c2) (GeV/c2) Figure 5.38: mx and mK*o distributions from MC for backgrounds to xclK*o events that are peaking (KTr non-resonant, a and b) or non-peaking (combinatoric, c and d) in mm/ss. 131 5.3. The Xcl,2 Benchmark Modes (3 > G)03.6 3.55 3.5 3.45 3.4 Figure 5.39: mx versus mK*o for XC1K*O background MC events in the range 5.27 < mmjss < 5.29 GeV/e2. The small excess of events near mK*o = mK*o in Figure 5.38 is from events in a low mass region near mx = m0 (‘-. 3.414GeV/c2). I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I. I I I I I 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 m1 132 5.3. The Xcl,2 Benchmark Modes decay mode of type i. Although these events pass reconstruction and selec tion cuts, their distributions are not necessarily signal-like. For the cases where the number of cross-feed events of type i is greater than 1% of the total expected number of events of type j20, the expected number of cross- feed events are passed into a fit with the expected number of signal and background MC events to determine by what amount the cross-feed affects the signal extraction. The results for this study are summarized in Table 5.17. The cross-feed from the K* modes was not calculated due to lack of MC production. However, based on the results from the other event types, it is believed to be a tiny effect. The amount of cross-feed was simultaneously calculated for the Xc2 decay modes, and this was also found to be negligible. Table 5.17: The number of cross-feed events and their expected fraction of the total signal for the B —* xjK modes. “N/A” modes cannot cross-feed to themselves. “(<< 1%)” indicates that the number of cross-feed events passing selection cuts is below 1%, and the resulting number of cross-feed events returned from a fit to the distribution is expected to essentially be zero. All results are negligible. Decay Mode Expected Contribution per Mode XC1K± xiK Xc1K*± XclK*O xiK N/A (<< 1%) (<< 1%) 0.27(< 0.1%) xiK (<< 1%) N/A 0.06(< 0.1%) 0.01( 0%) 5.3.6 Xci Signal Extraction Efficiency The total signal extraction efficiency for the Xci decay modes was calculated using a similar procedure to that used for the X(3872) modes. First, the efficiency of the reconstruction and applied cuts was found using only the B generic MC sample. The total number of events generated in the MC was calculated from the branching fractions as defined in the MC generator decay file, which differ slightly from the most recent PDG values. The efficiency values are given in Table 5.18. 20Cases where the maximum amount of cross-feed is expected to be less than 1% of the total number of events are ignored. 133 5.3. The Xcl,2 Benchmark Modes Table 5.18: Summary of the reconstruction and event selection efficiency for B —* x1K MC events. Decay Mode Events Pass Efficiency Generated cuts/reco (%) x1K 29890 ± 173 3478 11.6 ± 0.1 xciK° 8278 ±91 753 9.1±0.1 XciK*± 3474±59 219 6.3±0.1 XclK*o 10491 ± 102 908 8.7 ± 0.1 The fit bias and efficiency were estimated with xiK events drawn from the BB generic and J/ Inclusive MC samples. Using the same proce dure as defined for the X(3872), a number of signal and background events roughly equal to that expected in data was input and then extracted using signal MC events and generated toy MC background events. At this stage, a Xc2 component is included in the mx fit but zero Xc2 events were actually included in the test MC samples. For the K* modes, an additional and sep arate non-resonant background component is generated and added to the signal extraction trials. The expected number of non-resonant-like events in data was estimated by imposing a cut of 5.27 < mmjss < 5.29 GeV/c2 and counting the number of surviving events in the MC background sam ple. While the non-resonant event PDF in the fit assumes a linear shape in mK*, in the tests of the signal extraction efficiency, the shapes of the mK* and mx distributions were refit to the MC using the linear plus Voigtian parametrization discussed in Section 5.3.4 and generated with those distri butions. The results are summarized in Table 5.19. The total efficiency is a combination of the reconstruction and cut effi ciency multiplied by the fit efficiency corrected for bias effects. The results for the Xci modes are given in Table 5.20. The efficiency of the B± xciK± decay mode found here (-.. 11%) is comparable to that from the previous version of this analysis ( 13%) [37j. 134 5.3. The Xcl,2 Benchmark Modes Table 5.19: Results of tests of signal extraction for B —+ xiK MC events with PDF-generated background events. Decay Trials Sig. Bkgd. NR Bias Corrected Fit Mode In In In Output Eff. (9o) xiK 24 1118 323 0 —2±7 1072± 10 95.9±0.9 xiK 16 241 75 0 +7 ± 4 231 ± 6 95.9 ± 2.3 XciK*± 15 103 270 130 +10± 5 94±6 91.1± 5.7 XciK*O 12 362 749 435 —14±8 332±11 91.7±3.1 Table 5.20: Total signal extraction efficiency for based on MC samples. 5.3.7 Signal Extraction Efficiency Although no signal is expected for Xc2, the efficiency for its detection can calculated based on our MC. The cut and reconstruction efficiency is defined identically to that used for the other decay modes. The number of events surviving the reconstruction and selection cuts is summarized in Table 5.21. The number of generated events is not an absolute value: it is calculated from the branching fractions as defined in the EvtGen decay definition file for BB generic events supplemented with events from the dedicated Xci,2 Inclusive MC sample. In the previous section, the Xci signal extraction was tested including a fit for a Xc2 component even though no events of that type were added to the MC sample. The results of the XC2 portion of this fit are summarized in Table 5.22. These tests indicate that there is no significant interference or bias from the adjacent large Xci peak in mx that would affect a Xc2 signal. B —÷ xiK signal modes Decay Cut/Reco Fit Total Efficiency (%) Efficiency (%) Efficiency (%) xiK 11.6 ± 0.1 95.9 ± 0.9 11.2 ± 0.1 x1K 9.1 ± 0.1 95.9 ± 2.3 8.7 + 0.2 Xc1K*± 6.3 ± 0.1 91.1 ± 5.7 5.7 ± 0.4 XciK*O 8.7 ± 0.1 91.7 ± 3.1 7.9 ± 0.3 135 5.3. The Xcl,2 Benchmark Modes Table 5.21: Summary of the reconstruction and event selection efficiency for B —p x2K MC events. Decay Mode Events Pass Efficiency Generated duts/reco (%) x2K 5481 ± 26 692 12.6 ± 0.1 x2K° 2433 ± 26 266 10.9 ± 0.1 XcK*± 1919 ± 18 125 6.5 ± 0.1 Xc2K*O 2243 ± 26 201 9.0 + 0.1 This is in contrast to the results obtained in the previous analysis [37]. Table 5.22: Test of signal extraction for Xc2 with zero Xc2 MC events included in the sample. Decay Trials Xci Bkgd. NR Xci Xc2 Xc2 Mode In In In In Out x2K 24 1118 323 0 0 —2.7±1.1 x2K5° 16 241 75 0 0 1.2 ±0.6 Xc2K*± 15 103 270 130 0 —0.4 ± 0.9 Xc2K*O 12 362 749 435 0 —2.2±3.3 To estimate the efficiency of the fit for the Xc2 modes, the signal extrac tion trials are repeated while including a number of Xc2 MC events based upon the expected efficiency, the available number of events in MC, and branching fraction upper limit as given in the PDG [71]. The number of Xci, background, and Kir non-resonant events remains the same as given in Table 5.19. The number of Xc2KTr non-resonant events is assumed to be zero. The results and the total signal efficiency are summarized in Tables 5.23 and 5.24. 136 5.3. The Xcl,2 Benchmark Modes Table 5.23: Results of tests of signal extraction for B —* x2K MC events with PDF-generated background events. The Total Efficiency is derived using the cut and reconstruction efficiency from Table 5.22. Decay Trials Sig. - Bias Corrected Fit Mode In Output Eff. (%) x2K 24 34 +0.7 ± 1.7 33.6 ± 2.4 99 ± 7 x2K° 16 17 +4.3 ± 1.1 17.3 ± 1.6 102 + 10 XC2K*+ 15 9 +0.5 ± 1.5 5.8 ± 2.0 65 ± 22 XC2K*O 12 30 +1.2 ± 0.3 27.8 ± 0.5 93 ± 2 Table 5.24: Total signal extraction based on MC samples. efficiency for B — xc2K signal modes Decay Cut/Reco Fit Total Efficiency (%) Efficiency (%) Efficiency (%) x2K 12.6 ± 0.1 99 ± 7 12.5 ± 0.8 x2K 10.9 ± 0.1 102 ± 9 11.1 ± 1.0 XC2K*± 6.5 ± 0.1 65 ± 22 4.2 ± 1.4 XC2K*O 9.0 ± 0.1 93 ± 2 8.3 ± 0.2 137 Chapter 6 Signal Extraction from Data This chapter presents the results of the signal extraction for B —* xci,2K, and B —÷ X(3872)K for X(3872) — J/&7 and X(3872) —* (2S)7, from the full BABAR dataset. The final measurements of the branching fractions or their upper limits are calculated here. The results exploring the c-y invariant mass range up to the kinematic limit are also shown. 6.1 Xcl,2 Signal Extraction from Data A useful verification of the signal extraction method is to measure B(B —* xiK) from data, and to compare it with other previous experimental re sults. As a cross-check, the raw data distributions and their comparison with the generic MC sample (includes both signal and background) for the variables of interest are examined. The results for Xc1K+, XciK, Xc1K*±, and XciK*O are shown in Figures 6.1, 6.2, 6.3, and 6.4, respectively. There is fair agreement in the peaking regions. Note that the branching fractions for B —p xiK in MC are only approximately equal to the current PDG values, so a difference in the peak height is expected. While the relative normalization between the peaking and the background events in MC does not exactly match the data (as evidenced by the lacking “sideband” regions), the features of the distributions are the same; hence the chosen parametriza tions are good. These differences in the MC event yield are accounted for by allowing the event yields to vary in the final fit. Using the PDFs defined from MC with the mmjss ARGUS parameters allowed to float (see Section 6.2.2), the number B —* J/7K events in the Xci mass region is found by fitting the 3Plot result with the mx double Gaussian plus linear background shape, allowing the number of signal and 138 Figure 6.1: B± XC1K±. 6.1. Xcl,2 Signal Extraction from Data 5.28 5.3 mmi (GeV/c) 0 U, ‘2 2. I0 3.6 m(GeV/c’) Figure 6.2: Comparison of data (blue) and MC (red) for mx and mmjss for B° — xiK. I m,, Distribution, Data vs. MC c 4c > 400 U, 350 300 250 200 150 100 50LI I m, Distribution, Data vs. MC I 5.2 5.22 5.24 5.26 3.45 3.5 3.55 Comparison of data (blue) and MC (red) for mx and mmjss for uistrioution, uata vs. M0. 120- 100 - I 80- 40 - 20 5.22 5.24 5.26 5.28 5.3 m, (GeV/c2) 70 60 50 40 30 20 10 m Distribution, Data vs. MC I 3.45 3.5 3.55 3.6 m2 (GeV/c2) 139 6.1. Xcl,2 Signal Extraction from Data I Distribution, Data vs. MC m Distribution, Data vs. MC C C 4: 60 50• W W 5.22 5.24 5.26 5.28 5.3 C 3.5 3.55 3.6 mmig, (GeV/c) m (GeV/c2) mK Distribution, Data vs. MC 11 1111111 > 30 25- - Li 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK (GeV1) Figure 6.3: Comparison of data (blue) and MC (red) for mx, mmjsg and mK*± for B± —, XC1K*±. 140 6.1. Xcl,2 Signal Extraction from Data I m,,1 Distribution, Data vs. MC m, Distribution, Data vs. MC Io 24 !€ 180 6O4\ 5.22 5.24 5.26 5.28 5.3 3.45 3.6 3.55 3.6 m,,1 (GeV/c2) mx (GeV/c2> m< Distribution, Data vs. MC I I E 30 L.I !t U LIU - 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mx- (GeV/c2) Figure 6.4: Comparison of data (blue) and MC (red) for mx, mm/ss and mK*o for B° — XC1K*O. 141 6.1. Xcl,2 Signal Extraction from Data Figure 6.5: Projection of the peaking (dashed red) and background (dashed blue) event components for the fit to mmjss for B+ XcJK±. The solid line represents the sum. The points are from data. peaking background events and the linear background parameters to float. The number of signal events in the Xc2 region is found by adding a single Gaussian component to the fit, as determined in Section 5.3.2. The event yields are unrestricted in the fit, and are permitted to fluctuate statistically to negative values. The results of the UML fit to generate the Plot weights, with projections of the various event type components, are shown in Fig ures 6.5 — 6.8. These plots demonstrate that the choice of parametrization was generally adequate, as described previously in this Section. The signal extraction results using this method and the corresponding 8Plots for each event type are shown in Figures 6.9 — 6.11. 5.3 mm (GeV/c2) 142 6.1. Xcl,2 Signal Extraction from Data If 1 111 11 If11 1I1II II1 IIIIIjII 11f II.. >120 — 10 ioo — C > w80 — 60 — 40 — 20 — _ I 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mmjss (‘1,’c) Figure 6.6: Projection of the peaking (dashed red) and background (dashed blue) event components for the fit to mmjss for B° —* xjK°. The solid line represents the sum. The points are from data. 143 6.1. Xcl,2 Signal Extraction from Data a)80 U) - ;70 C - UJ - L :-g.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mmjss (‘3eWc) c I “iii 60 C - 50 — 8.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mx.. (GeV/c2) Figure 6.7: Projection of the signal (dashed red), combinatoric background with (dashed blue) and without (dashed green) a K*+, and non-resonant background (dashed magenta) event components for the fit to mmjss and mK*± for B± —, XCJK*±. The solid line represents the sum. The points are from data. 144 6.1. Xci ,2 Signal Extraction from Data 250- - 200— C - 0) 150— loo— H 2Y”%,..% - 3.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mmjss (GeV/c) :::h1/hh1: I i. U.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK (GeV/c2) Figure 6.8: Projection of the signal (dashed red), combinatoric background with (dashed blue) and without (dashed green) a K*O, and non-resonant background (dashed magenta) event components for the fit to mmjss and mK*o for B° —> XcJK*O. The solid line represents the sum. The points are from data. 145 6.1. Xci ,2 Signal Extraction from Data The number of events measured in each mode can be related back to a branching fraction measurement of B —÷ xi,2K via Nft — N Xcl,2K) = NB tot B(Xci,2 J/7) x) (6.1) where Nfit is the number of extracted events, Nbj is the bias correction from Table 5.19, NB is the number of B mesons in the data21, 6tot is the signal extraction efficiency (see Tables 5.20 and 5.23, and the PID correction factor given in Section 6.3.7), and the remaining terms represent branching fractions of particle decays (where the decay K — x represents the decay chain of a composite kaon to the daughters specified in this analysis). Using the PDG values for these branching fractions [33] and calculating NB from the number of events in Run 1—6 data as given in Table 4.1, the branching fractions for B —* XciK are derived and given in Table 6.1. The significance is defined as the square root of the difference in the x2 values of the fit with and without a signal component included. The uncertainty on these results is statistical only; systematic uncertainties are included in Section 6.3. Table 6.1: Results of B —f Xci,2K signal extraction from data. Error is statistical only. Decay Events u Total Daughter Derived (Corrected) Eff. BFs [33] 13(B — XCi,2K) xiK 1018±34 31o- 11.0% 2.21% (4.50±0.15)x10 XciK 242 ± 16 14a 8.7% 0.72% (4.18 + 0.28)x Xc1K*± 71 ± 13 4.9a 5.7% 0.51% (2.63 ± 0.47) x iO Xc1K*O 255 ± 25 11 8.0% 1.4% (2.50 ± 0.24) X Xc2K 14.0±7.9 1.8u 12.3% 1.22% (1.00±0.56)x10 Xc2K 6.1 ± 3.9 0.6g 11.1% 0.40% (1.48 ± 0.95)x 10 Xc2K*± 1.2 ± 4.7 0.2a 4.2% 0.28% (1.09 ± 4.27) X iO Xc2K*O 38.8 ± 10.5 3.7cr 8.3% 0.76% (6.60 + 1.78)x 10 21The ratio of Y(4S) decays to BB and B° is not assumed to be equal to 1. NB is derived from the total number of BB pairs multiplied by a factor of 2 and 13F(Y — BB ) or 13.F(Y — B B ), as appropriate. 146 0 7c 6C 5c UI 4c Co 2C ic 6.1. Xcl,2 Signal Extraction from Data 0 8 4 C, Cl, 0 Figure 6.9: 8Plots for the number of events versus mx for B —* xl,2K from data: (a) B± xci,2K+ signal events, (b) B± Xci,2K± background events, (c) B° —+ xcl,2Ks° signal events, and (d) B° — xc1,2K background events. 25C 20C 15C Co bC 5C ‘ 3.45 3.5 3.55 3.6 3.45 3.5 3.55 3.6 m2 (GeV/c’) m2 (GoVIc’) I I (C) (d) I____ 4 . . 3.45 . 3.55 3.45 3.55 3:6 m (GeV/c2) m2 (GeV/c2) 147 40 > 35 30 25 20 C, co 15 10 5 0 .5 6.1. Xcl,2 Signal Extraction from Data 20 ‘0 0 c 15 10 C, Co Figure 6.10: 3Plots for the number of events versus mx for B± Xcl,2K*± from data: (a) signal events, (b) B± xcl,2K1r+ non-resonant events, (c) combinatoric background events, and (d) K*± combinatoric background events. 148 (a) I ffN•?• 3.45 3.5 3.55 3.6 mx (GeV/c2) . . 3.45 3.5 3.55 3.6 3.45 3.5 3.55 3.b m, (GeV/c2) m2 (GeV/c’) 3.45 3.5 3.55 3.6 m(GeV/c2) ‘2 ‘0 15 1c C, 0) 5 0 -5 V 15 ‘0 (d) I > 100 U, 80 U) 60 U) a) 40 6.1. Xcl,2 Signal Extraction from Data > 60 U) . 50 40 Ui 30 a (I, Figure 6.11: 3Plots for the number of events versus mx for B° —* xcl,2K*O from data: (a) signal events, (b) B° —p xc1,2K±7r+ non-resonant events, (c) combinatoric background events, and (d) K*O combinatoric background events. 149 3.45 3.5 3.55 3.6 mx (GeV/c2) 50(c) Lt +, I 1. t+ 20 0 0 U, 40 I :: 10 0 (b) 3.45 3.5 3.55 3.6 m (GeV/c’) (d) ++t• 10 0 -in ç26 20 U, 0 15 I 3.4 3.5 3.55 3.6 in,, (GeV/c’) 3.45 3.5 3.55 3.6 mx (GeV/c2) 6.2. X(3872) Signal Extraction from Data 6.2 X(3872) Signal Extraction from Data 6.2.1 B —÷ X(3872)K, X(3872) —* J/b7 A comparison between MC and the raw distributions for our variables of interest is shown for each of our modes in Figures 6.12 — 6.15. In these plots, there is fairly good agreement between the MC and data. The MC consists entirely of background events; no signal events have been added to these samples. There are some hints of a signal based naively on the data/MC difference in some key regions (mmjss peak and mx = mx(3872)). To discriminate signal from background, the fits are performed as described and tested in Section 5.2, with the additional step of allowing the mmjss background ARGUS parameters to float (see Section 6.2.2). The resulting event type projections and 8Plots of these fits are shown in Figures 6.16 — 6.22. Figure 6.12: Comparison of data (blue) and MC (red) for mx and mmjss for B —* X(3872)K, X(3872) — J/çb7. 150 I m,,, Distribution, Data vs. MC mx Distribution, Data vs. MC I 0 10• U, a 6 5.2 5.22 5.24 5.26 5.2a 5.3 - 3.8 3.85 3.9 3.95 (GeV/c) m2 (GeV/c2) 6.2. X(3872) Signal Extraction from Data u 1.5 0.5 3.9 3.95 m,< (GeV/c2) Figure 6.13: Comparison of data (blue) and MC (red) for mx and mmjgs for B —, X(3872)K, X(3872) —* J/4-y. 5 I mmjss Distribution, Date vs. MC I 0 0 U) U C 0 m Distribution, Data vs. MC I 0 toj 2.5 C 0 uI, 52 5.22 5.24 5.26 528 5.3 - 3.6 3.85 m (Gay/c) 151 6.2. X(3872) Signal Extraction from Data Distribution, Data vs. MCi 0 C 0 5 4 3 2 6.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK (GeV/c2) Figure 6.14: Comparison of data (blue) and MC (red) for mK*± for B —* X(3872)K*+, X(3872) —* J/7. mx, mmjss and 152 I m,, Distribution, Data vs. MC ‘— , m Distribution, Data vs. MC7 0 . 7 C 6 5 4 3 2 5.2 5.22 5.24 5.26 5.28 5.3 - 3.8 3.85 3.9 3.95 m,, (GeV/c2) mx (GeV/c2) U 6.2. X(3872) Signal Extraction from Data I Distribution, Data vs. MC I mx Distribution, Data vs. MC :5r. 5.22 5.24 5.26 5.28 5.3 3.8 3.85 3.9 3.95 mmi (GeV/c) mx (GeV/c2) I mK Distribution, Data vs. MC 0 25 nRJ20 C 15 -!rF I r.rj- — lOr j j IL7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK (GeV/c2) Figure 6.15: Comparison of data (blue) and MC (red) for mx, mmjss and mK*o for B —* X(3872)K*o, X(3872) —* J/y. 153 6.2. X(3872) Signal Extraction from Data 35 > U) 0 = uJ Figure 6.16: Projection of the peaking (dashed red) and background (dashed blue) event components for the fit to mmjss for B± —* X(3872)K±, X(3872) — J/’7. The solid line represents the sum. The points are from data. 154 6.2. X(3872) Signal Extraction from Data II IlI II I 1111111 IlIJI I 11111 I 111111111 111111 10 H1 I .g.2 121 5.22 5.23 5.21 125 26 5.27 5.28 .2 5.3 mmjss (Ge’’,) Figure 6.17: Projection of the peaking (dashed red) and background (dashed blue) event components for the fit to mmjss for B° —* X(3872)K, X(3872) —* J/’&7. The solid line represents the sum. The points are from data. 155 6.2. X(3872) Signal Extraction from Data I — 115 _ 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mmjss (GeV/c) 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK.. (GeV/c2) Figure 6.18: Projection of the signal (dashed red), combinatoric background with (dashed blue) and without (dashed green) a K*+, and non-resonant background (dashed magenta) event components for the fit to mmjss and mK*± for B —* X(3872)K*±, X(3872) —* J/’y. The solid line represents the sum. The points are from data. 156 6.2. X(3872) Signal Extraction from Data > Lt) 40L 2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mmss (GeV/c) I ---.. I8.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 mK (GeV/c2) Figure 6.19: Projection of the signal (dashed red), combinatoric background with (dashed blue) and without (dashed green) a K*O, and non-resonant background (dashed magenta) event components for the fit to mmjss and mK.o for B° —* X(3872)K*o, X(3872) —+ J/’i4’-y. The solid line represents the sum. The points are from data. 157 6.2. X(3872) Signal Extraction from Data 0 10(a) 14’ (b) 8 12’ 6 cl0• o W 8 • 6 (0 _____ 2 +k++v.+12 420 3.8 3.85 3.9 3.95 3.8 3.85 3.9 3.95 m2 (GeV/c2) m (GeV/c2) 1(c) i (d) I I 4i C I I. 3 I 0 LI 3I TI 4 ft1 ft 3.8 3.85 3.9 3.95 - — 3.85 3.9 3.95 m,, (GeV/c2) m2 (GeV/c2) Figure 6.20: 3Plots for the number of events versus mx for B —* X(3872)K from data for X(3872) —* J/’&’y: (a) B —p X(3872)K signal events, (b) B —* X(3872)K background events, (c) B° —* X(3872)K° signal events, and (d) B° —* X(3872)K background events. 158 C) 0 uJ C ci, 16 . 14 C C 0) 6.2. X(3872) Signal Extraction from Data E 2 ci) 1 C l 0 0 —1 -2 -3 -4 Figure 6.21: 5Plots for the number of events versus mx for B± X(3872)K*+ from data for X(3872) —* J/7: (a) signal events, (b) B± X(3872)Kir± non-resonant events, (c) combinatoric background events, and (d) K*± combinatoric background events. 4 2 , . (a) 3 I —1 tt, )i 3.8 3.85 3.9 3.95 m (GeV/c’) (C) (b) 3.8 3.85 • 3.9 ‘x (GeV;c) •4_ 1 I1 I ++ $++% a 4. .1.... • 39 3.953.8 3.85 mx (0ev/c2) 4 2 C —4 3.9 3.95 3.9 3.95 mx (GeV/c2) 159 6.2. X(3872) Signal Extraction from Data Figure 6.22: 8Plots for the number of events versus mx for B° X(3872)K*o from data for X(3872) — J/1vy: (a) signal events, (b) B° —* X(3872)KrF non-resonant events, (c) combinatoric background events, and (d) K*o combinatoric background events. 160 U, I: > 25 20 C 15 10 5 0 1o.(b) k : 3.6 3.85 3.9 mx (GeV/c’) .20(d)(c) 15 I - 38 3.85 m (GeV/c) I 2 3.8 • 3.85 3. m (GeV/c) 6.2. X(3872) Signal Extraction from Data Defining the significance as the square root of the difference in the x2 values of the fit with and without a signal component included, evidence of a signal for the decay mode B —* X(3872)(J/b7)Kis found with a level of significance greater than 3 standard deviations. Nothing significant is found in the other decay modes. Using Equation 6.1, substituting X (3872) for XcJ, one derives the product of branching fractions, B(B —* X(3872)K). (X(3872) —* J/’’7). The results for X(3872) —* J/vy signal extraction are summarized in Table 6.2. Table 6.2: Results of B — X(3872)K signal extraction from data for X(3872) —* J/i’v. Error is statistical only. Decay Events a Total Daughter Derived BF (Corrected) Eff. BFs [33] x106 X(3872)K 23.0 ± 6.4 3.7a 14.5% 6.12% (2.78 ± 0.77) X(3872)K° 5.3 ± 3.6 1.4a 11.0% 1.99% (2.62 ± 1.76) X(3872)K*± 0.6 ± 2.3 0.Oa 6.9% 1.41% (0.71 ± 2.56) X(3872)K*o 2.8 + 5.2 O.8a 10.4% 3.82% (0.74 ± 1.41) 6.2.2 B —+ X(3872)K, X(3872) —* The procedure of the previous Section is repeated for the X(3872) — decay modes. A comparison between MC and the raw distributions for the variables of interest is shown for each of our modes in Figures 6.23 — 6.26. Again, in these plots, no signal MC has been added. The agreement between MC and data is somewhat adequate for the mx and mK* distributions, though the mmjss distributions in MC show a clear difference from the data for mmjss < 5.25 GeV/c2. In order to account for the inability of the MC to accurately model the mmjss background distribution, the parameters for the ARGUS function (endpoint and shape) are allowed to vary in the final fit. This improves the quality of the fit to the data and effectively removes a large systematic effect due to MC/data difference. The results of these fits for each X(3872) — (2S)7 decay mode are shown in Figures 6.27 — 6.33. 161 56.2. X(3872) Signal Extraction from Data 2 20 16 16 Ui 14 1 10 S 6 4 5.2 5.22 5.24 5.26 5.28 5.3 3.8 3.85 3.9 3.95 m1 (GeV/c2) m2 (GeV/c2) Figure 6.23: Comparison of data (blue) and MC (red) for mx and mmjss for B —* X(3872)K, X(3872) —* ,b(2S)7. Figure 6.24: Comparison of data (blue) and MC (red) for mx and mj55 for B —* X(3872)K, X(3872) —> b(2S)-y. 162 I uistrbution, uata vs. MC I I m Distnbution, Data vs. MC C, > e U, 0 UJ 45 40 35 30 25 20 15 10 2 C, > U, 0 mmlss Distribution, Data vs. MC 5.22 5.24 5.26 I mx Distribution, Data vs. MC 8 7 6 5 4 3 2 5.28 5.3 2.8 S.Ub 3.9 3.95 m (GeV/c’) m, (GeV/c’) 6.2. X(3872) Signal Extraction from Data mmjss Distribution, Data vs. MC I mx Distribution, Data vs. MC __ 5.22 5.24 5.26 5.28 5.3 C 3.8 3.85 3.9 3.95 (GeV/c9 mx (GevIc2) Distribution, Data vs. MC :*4 mK (GeV1©) Figure 6.25: Comparison of data (blue) and MC (red) for mx, mmjss and mK*± for Bth —* X(3872)K*±, X(3872) —* (2S). 163 3 c (I, 0 C 0 0 5) 5) C ) 0 (I) 0 C 0 z 0 5) 5) 0 C, 0 0 0• C 0 0 5) 5) 0 C, E ve nt s? (5 M eV ?c 2) 3 a E ve nt s? (1 0 M B V /c 2) - t C— fo CD H -” C ) II CD CD CO CO — 1 L’ .) o . 6.2. X(3872) Signal Extraction from Data C.) > U, 0 C 0) LLi Figure 6.27: Projection of the peaking (dashed red) and background (dashed blue) event components for the fit to mmjss for B+ —* X(3872)K±, X(3872) —* (2S)-y. The solid line represents the sum. The points are from data. 165 6.2. X(3872) Signal Extraction from Data > C) Lf) U) C) U.’ Figure 6.28: Projection of the peaking (dashed red) and background (dashed blue) event components for the fit to mmjss for B° —* X(3872)K, X(3872) —* (2S)7. The solid line represents the sum. The points are from data. 166 6.2. X(3872) Signal Extraction from Data oZ’ 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 mmjss (G11) ° - 35 H 0.8 0.85 0.9 0.95 .05 1.1 (GeV/c2) Figure 6.29: Projection of the signal (dashed red), combinatoric background with (dashed blue) and without (dashed green) a K*+, and non-resonant background (dashed magenta) event components for the fit to mmjss and mK*± for B — X(3872)K*+, X(3872) —p &(2S)’y. The solid line represents the sum. The points are from data. 167 6.2. X(3872) Signal Extraction from Data > 0) e (I, LU Figure 6.30: Projection of the signal (dashed red), combinatoric background with (dashed blue) and without (dashed green) a K*O, and non-resonant background (dashed magenta) event components for the fit to mmjss and mK*o for B° —* X(3872)K*U, X(3872) — b(2S)-y. The solid line represents the sum. The points are from data. ç9o 0) 0) C LU 1.05 1.1 m)(. (GeV/c2) 168 6.2. X(3872) Signal Extraction from Data ;3. 3.b mx (GeV/c2) 3.8 3. -- I g - -- m(GeV/c2) c25 > 0 !2. 20 0 15 10 5 0 14 0 , 12 5 10 0 0 c 6 C’, 4 2 0 -2 3.8 3.85 3.9 3.95 m (GeV/c2) :(d) J.e J C0 S.C’b 3. 3.9 m (GeV/c2) Figure 6.31: P1ots for the number of events versus mx for B —* X(3872)K from data for X(3872) — b(2S)7: (a) B —> X(3872)K signal events, (b) — X(3872)K background events, (c) B° —* X(3872)K° signal events, and (d) B° —* X(3872)K background events. 169 6.2. X(3872) Signal Extraction from Data Figure 6.32: 8Plots for the number of events versus mx for B± X(3872)K*± from data for X(3872) — (2S)7: (a) signal events, (b) B± X(3872)K1r± non-resonant events, (c) combinatoric background events, and (d) K*± combinatoric background events. 170 to 2 C 2 Dt 0) 0 -2 c 20 to , 15 C’ 10 Co 5 0 (a) - (b) I 3.8 3.85 3.9 3.95 -- 3.8 3.85 3.9 3.95 mx (GeV/c2) mx (GeV/c2) 1 • (C) o. (d) ::____ 3.8 3.85 3.9 3.95 in2 (GeV/c’) 3.8 mx (GeV/c2) 6.2. X(3872) Signal Extraction from Data Figure 6.33: 8Plots for the number of events versus mx for B° X(3872)K*o from data for X(3872) — ,b(2S)-y: (a) signal events, (b) B° —* X(3872)Kr+ non-resonant events, (c) combinatoric background events, and (d) K*O combinatoric background events. 171 ! : (a) ;s. •J. •J. S.b m (GeV/c2) 16 8 2 6 6 15 10 0 0 0 00 -5 -10 3.8 3.85 3.9 3.95 mx (GeV/c’) (d) bi. 0 > 0 U) 50 0 C o 40 0 C a 30 0 20 10 3.8 3.85 3.9 3.95 m, (GeV/c2) 3.8 3.85 3.9 3.95 rT (GeV/c2) 6.2. X(3872) Signal Extraction from Data Like the X(3872) —* J/-y mode, significant evidence (> 3cr) of a sig nal for the decay mode B —p X(3872) (ry)K is discovered, but noth ing significant is seen in the remaining modes. The number of events ex tracted from the data and the corresponding product of branching fractions BF(B — X(3872)K)(X(3872) — b(2S)7) are summarized for these decay modes in Table 6.3. Table 6.3: Results of B —* X (3872)K signal extraction from data for X(3872) —* (2S)7. Error is statistical only. Decay Events a Total Daughter Derived BF (Corrected) Eff. BFs [33] x 10—6 X(3872)K 25.4 ± 7.3 3.7cr 11.0% 2.77% (9.50 ± 2.74) X(3872)K° 8.0 ± 3.9 2.0cr 8.4% 0.90% (11.36 ± 5.50) X(3872)K*± 1.9 ± 2.9 0.7cr 5.0% 0.64% (6.38 ± 9.77) X(3872)K*o —1.4 ± 3.3 - 6.7% 1.73% (—1.31 ± 3.10) As a crosscheck for X(3872) —k (2S-y in the K decay mode, the signal extraction was repeated treating the &(2S) —* £t and (2S) —* J/rir decay modes separately. The raw number of signal events measured is 12.4 ± 5.1 and 11.1 ± 5.4, respectively. To translate this into a rough branch ing fraction measurement, the total efficiency used in Table 6.3 is rescaled according to the cut and reconstruction efficiencies listed in Table 4.4, and the correct daughter branching fractions are applied. The resulting products of branching fractions are 9.7±4.0(stat.) x 10—6 for the (2S) —* tt mode, and 8.7 ± 4.2(stat.) x 10—6 for the (2S) — J/rir mode, results that are consistent with one another (albeit with large statistical uncertainty). 6.2.3 B —* X(any)K, X(any) —* cy For the sake of interest, the range of the mx invariant mass window can be opened beyond the X(3872) region to search for other higher mass radiative decays to the J/’b’y and ‘(2S)7 final states. Figures 6.34 and 6.35 span from 3.6GeV/c2,just above mx = to 5.0GeV/c2 While the B —* X(3872)K± signals are clearly visible in these plots, there are no other 172 6.3. Systematic Uncertainties and Corrections significant features of interest. 6.3 Systematic Uncertainties and Corrections 6.3.1 B Counting The number of BB events counted from the data sample is assigned a sys tematic error of 1.1%. This is based on a number of factors detailed in [72], with the largest contributions from uncertainty in the number of i pairs in the on and off resonance data samples, and uncertainty in the efficiency of hadron selection for defining BB events. 6.3.2 Branching Fraction Uncertainties To calculate the final branching fractions, the known values for the branch ing fractions of the daughter particles are required. The values and their uncertainties are taken from the PDG [33]. The branching fractions for the decays of interest are listed in Table 6.4. Table 6.4: fractions. Values and uncertainties for the relevant daughter branching Decay Mode BF Value B(Y(4S) —* BBj (51.6 ± 0.6)% 13(Y(4S) B°) (48.4 + 0.6)% B(J/ — ee) (5.94 + 0.06)% Z3(J/b —* (5.93 ± 0.06)% B(xi —* J/ry) (36.0 ± 1.9)% B(xc2 — J/7) (20.0 ± 1.0)% l3(b(2S) —f J/Ø+-) (32.6 ± 0.5)% B(ib(2S) —* eej (0.752 + 0.017)% B((2S) —* (0.75 ± 0.08)% Z3(K°—K) 50% B(K — (69.20 ± 0.05)% B(K*+ —f K°Tr) 4 x (99.901 ± 0.009)% B(K*o Kr) x (99.769 ± 0.020)% 173 6.3. Systematic Uncertainties and Corrections (a) mx (GeV/c2) (b) 48 - 5 mx (0eV/c2) —.10 I (C) mx (GeV/c2) (d) 4’6 • 48 • mx (0eV/c2) Figure 6.34: 3Plots for X — J/o-y signal—like events in the range 3.6 <mx < 5.0GeV/c2,(a) B —* J/yK, (b) B° —* J/7K, (c) B —* J/?hK*+, and (d) B° —* J/b7K*o. 174 6.3. Systematic Uncertainties and Corrections 2O- (a) — C • 38L4’2444’64’8 . mx (GeVIc2) (b)1. 44’8 1 mx (GeVIc2) (C) 38 .44446 48 mx (GeV/c2) I (d): 010— — :6 38424446 mx (0eV/c2) Figure 6.35: 3Plots for X —o &(2S)-y signal-like events in the range 3.6 < mx <5.0GeV/c2,(a) B —o ‘b(2S)7K, (b) B° —> (2S)7K, (c) B /,(2SyK*±, and (d) B° —* (2S)K*o. 175 6.3. Systematic Uncertainties and Corrections 6.3.3 MC/Data Differences The signal extraction uses PDFs based on Monte Carlo. If the Monte Carlo distributions or the choice of parametrization do not match the data, it can lead to a systematic effect. Due to a discrepancy in the MC description of mmjss for X(3872) (2S)7 decays from B —* X(3872)K/° in the low mmjss region, the AR GUS parameters were allowed to float to eliminate these systematic effects. The mmjss mean was also allowed to float for the signal PDFs, and the difference in signal yield taken as a systematic uncertainty. Uncertainty due to lack of knowledge regarding the shape of the mx background for these modes was also evaluated. Fits were performed us ing the complicated mx background model derived from MC and compared with similar fits performed with the seemingly more accurate (in data) and straightforward linear background model used for all other signal modes in this analysis. Because the correct background model is uncertain, the av erage number of events extracted by the two methods was taken for the signal yield and assigned a systematic uncertainty equal to half the differ ence between the two results. For other decay modes, the signal yield was recalculated fitting the mx background with a second-order polynomial (in place of linear), with half the difference between the two results taken as the systematic uncertainty. For the mx signal parametrization, the choice of peaking PDFs was robust and these uncertainties were considered to be negligible. The value for these systematic uncertainties are included in Tables 6.10 — 6.13 under the heading “Signal mmjss” and “mx Background”, respectively. 6.3.4 PDF Fit Parameter Uncertainty The uncertainties on the fit parameters determined from the Monte Carlo samples are translated into a systematic uncertainty on the signal extrac tion by repeating the signal extraction on data while varying the parameter values by ±1o, as fitted in Chapter 5. The effect is quantified as the frac tional change in the number of signal events, and the totals are added in 176 6.3. Systematic Uncertainties and Corrections quadrature. Effects due to correlations between variables are assumed to be negligible, and in any case, the size of this systematic effect is relatively small. The results for each decay mode are summarized in Tables 6.5 — 6.7. Table 6.5: Summary of the systematic uncertainties due to PDF parameter uncertainties for the X(3872) —, J/b7 decay modes. Values are given in (%). B —_X(3872)(J/)K_Decay K K° K*± K*o Signal mmjss a (tail transition) 0.17 0.02 0.15 0.07 m0 (GB mean) 0.17 0.04 0.28 0.17 n (CB exponent) 0.02 0.00 0.04 0.02 u (GB width) 0.09 0.00 0.12 0.09 my Parameters Mean - - 0.44 0.32 Gaussian Sigma - - 0.39 0.69 Breit-Wigner Width - - 1.11 0.12 Bkgd Slope - - 0.53 0.17 mx Parameters i (mean) 0.15 0.05 0.14 0.27 o (core width) 0.03 0.35 0.71 0.48 2 (non-core width) 0.83 0.58 0.03 0.35 Core fraction 1.15 0.60 0.92 0.72 Total 1.45% 0.90% 1.60% 1.27% 6.3.5 True X Mass and Width Uncertainty The mx fit requires an assumption on the mass and width of the X(3872) for the centre of the double-Gaussian peak. The data is refit using the PDG [71] value of 3871.4 ± 0.6 MeV/c2 for the mass and the fit parameters are varied within these errors to assign a systematic error on the number of events extracted from the fit. The width was determined from MC, with the X(3872) being generated as a zero-width particle. The X(3872) is known to be narrow, and the PDG limit is f’ < 2.3 177 6.3. Systematic Uncertainties and Corrections Table 6.6: Summary of the systematic uncertainties due to PDF parameter uncertainties for the X(3872) —* i(2S)’y decay modes. Values are given in (%). B —* X(3872)((2S)7)KDecay K K° K*± K*O Signal mmjss a (tail transition) 0.11 0.16 1.21 0.11 mo (CB mean) 0.08 0.19 0.21 0.00 n (CB exponent) 0.01 0.03 0.05 0.01 o• (CB width) 0.07 0.25 0.26 0.07, Background mx F-D b (inflection point) 0.00 0.00 - - F-D c (slope) 0.00 0.00 - - mK* Parameters Mean - - 1.35 0.93 Gaussian Sigma - - 1.49 0.38 Breit-Wigner Width - - 0.41 0.03 Bkgd Slope - - 0.02 0.93 mx Parameters u (mean) 0.13 0.10 5.07 0.11 o, (core width) 0.07 0.49 3.77 0.69 a2 (non-core.width) 0.31 0.31 1.13 0.36 Core fraction 0.44 0.21 0.92 0.18 Total 0.58% 0.72% 6.92% 1.59% MeV. This uncertainty is accounted for by increasing the width of the core Gaussian by adding this value in quadrature and repeating the fit. The values of these systematic uncertainties are given in Table 6.8. To determine the systematic uncertainty due lack of knowledge of the true mx mass distribution for the Xcl,2, the Gaussian peak position was allowed to float for the Xcl,2 modes and the difference in the event yield taken as the systematic uncertainty. The quantitative values for this uncertainty for Xcl,2 are listed in Tables 6.12 and 6.13, respectively. 178 Table 6.7: Summary of the systematic uncertainties due to PDF parameter uncertainties for the Xcl,2 decay modes. I Values are given in (%). xiK Xci1<s° I Xc2KS° Xci1t Xc2K*± Xi1c*O Signal mmjss a (tail transition) 0.08 0.69 0.06 0.55 0.56 114 0.32 1.03 m0 (CB mean) 0.00 0.41 0.00 0.77 0.14 57 0.07 0.11 n (CB exponent) 0.01 0.03 0.13 0.08 1.66 94 0.01 0.04 o (CB width) 0.07 0.05 0.08 0.08 0.30 61 0.18 0.89 mK* Parameters Mean - - - - 0.12 14 0.06 0.38 Gaussian Sigma - - - - 0.23 3.76 0.90 0.35 Breit-Wigner Width - - - - 1.89 4.75 1.72 0.96 Bkgd Slope - - - - 0.03 0.36 0.00 0.00 mx Parameters /(Xci) (mean) 0.20 0.19 0.33 0.02 2.78 3.64 0.44 0.03 i(Xci) (core width) 0.31 0.91 0.41 2.16 2.26 8.68 0.87 0.34 2(Xc1) (non-core width) 0.16 1.72 0.84 1.49 1.21 51 0.05 0.06 Core fraction 0.35 0.50 1.11 2.14 3.31 4.6 1.21 0.10 iU(Xc2) (mean) 0.01 0.91 0.03 4.27 0.03 100 0.03 1.55 0(Xc2) (width) 0.00 3.22 0.01 2.27 0.00 11.8 0.01 1.38 Total 0.55% 3.98% 1.49% 5.98% 5.66% 205% 2.52% 2.73% 6.3. Systematic Uncertainties and Corrections Table 6.8: Summary of the systematic uncertainties due to uncertainties in the properties of X(3872). Decay X(3872) mass X(3872) width X(Jb7)K 1.1% 0.8% X(J’b’y)K 3.2% 1.6% X(Jb7)K*± 7.2% 5.0% X(Ji,b)K*O 12.3% 5.6% X(’,b(2S)’y)K 3.0% 0.2% XQ’(2S)7)K 3.9% 4.6% XQb(2S))K*± 144% 44% XQi(2S)7)K*O 6.4% 9.8% 6.3.6 Bias and Efficiency The bias on the signal extraction was measured by conducting repeated signal extraction trials using truth-matched MC events. It was defined as the difference between the number of events input and the average number found by the fit. This quantity has a statistical error associated to it based on the number of MC trials conducted. The values of the bias corrections can be found in Tables 5.7, 5.19, and 5.23. In the summary tables to follow, uncertainty in the bias is expressed as a percentage of the total corrected number of events extracted. There is an uncertainty on the signal extraction efficiency related to two systematic quantities. The cut and reconstruction efficiency was calculated by dividing the number of events passing reconstruction and selection cuts by the number of events generated in MC. In the case where the exact number of generated events was unknown (Xc1,2), it was estimated using the BF from the EvtGen decay parameter definitions file, and is assigned an error of The fit efficiency was calculated by dividing the number of events returned from repeated MC signal extraction trials by the number of events input. The uncertainty on this quantity was given by the statistical uncertainty of the MC trials. The values are found in Tables 5.8, 5.20, and 5.23. 180 6.3. Systematic Uncertainties and Corrections 6.3.7 PID Correction and Systematics The BABAR PID Working Group generates correction tables to assign each reconstructed particle a weight in order improve the correspondence of MC and data. The total PID correction for an event is the product of the individual particle PID weights, and the total correction to the MC sample is the average of all of the event weights in the sample. The systematic uncertainty on the particle identification is assigned in BABAR as 0.7% per electron, 1.8% per muon, 0.2% per pion, and 1.2% per kaon [83]. The total PID systematic for each decay mode is found by sum ming the systematic uncertainties, and in the case of more than one possible decay chain (i.e. Ji/ — can have £ = e, ), is weighted by the number of events for each decay found in the data. The PID corrections and systematics uncertainties for each mode are listed in Table 6.9. 6.3.8 Tracking Systematics The BABAR Tracking Efficiency Task Force has a recipe for calculating the systematic uncertainty due to tracking [84]. The systematic uncertainty per track is combined in quadrature with a correction factor and the total is taken as the systematic error. The particles in this analysis derive from the ChargedTracks list, for which the tracking correction factor is 0.312% with a systematic uncertainty of 0.142% per track. For the decay channels with a (2S), the total tracking correction is the sum of the corrections for the £t and J/Øir modes weighted by their branching fractions and cut/reconstruction efficiency from Table 4.4. Table 6.9 lists the tracking systematic for each mode. 6.3.9 Photon Corrections The BABAR Neutrals Working Group recipe for correcting MC photons to match data involves a small smearing and shifting correction applied to the energy [85]. There is no additional correction required to the single photon 181 6.3. Systematic Uncertainties and Corrections Table 6.9: Summary of the PID and tracking (TRK) corrections and sys tematic uncertainties applied to the efficiency for each decay mode. Mode -- PID PID TRK Correct. Syst. (%) Syst. (%) xiK 0.9880 3.68 1.03 xiK° 0.9966 4.05 1.37 Xc1K*± 0.9961 4.26 1.71 Xc1K*O 1.003 3.85 1.37 x2K 0.9861 3.68 1.03 Xc2Ks° 0.9956 4.05 1.37 XC2K*± 0.9984 4.26 1.71 Xc2K*O 0.9970 3.85 1.37 X(J/i7)K 0.9917 3.63 1.03 X(J/b)K 0.9972 4.04 1.37 X(J/c/ry)K*± 0.9968 4.24 1.71 X(J/7)K*o 1.007 3.83 1.37 X(i/’(2S))K 0.9905 4.01 1.45 X(/(2S)7)K° 0.9989 4.46 1.79 X(,,(2S)7)K*± 0.9980 4.55 2.12 X(i4’(2S)y)K*O 1.008 4.16 1.78 efficiency, but there is a systematic uncertainty of 1.8% per photon (i.e. per event) [861. 6.3.10 Total Systematic Error The total systematic errors derived in this section are summarized in Tables 6.10 — 6.13. 182 6.3. Systematic Uncertainties and Corrections Table 6.10: Summary of total systematic uncertainties for the X (3872) —* J/y decay modes. Systematic B —* X(3872)(J/’z,b7)KDecay Table 6.11: Summary of total (2S)7 decay modes. K K*± K*o BB count 1.1% 1.1% 1.1% 1.1% Branching Fractions 1.9% 1.9% 2.2% 2.8% Fit Parameters 1.4% 0.9% 1.6% 1.3% Signal mmjsg 3.0% 2.5% 139% 10.4% X(3872) Mass 1.8% 3.2% 7.2% 12.4% X(3872) Width 0.2% 1.6% 5.0% 5.6% mx Background 0.0% 10.0% 0.4% 9.2% Bias 0.7% 0.9% 11.3% 4.7% Efficiency 0.8% 1.0% 4.1% 1.4% PID 3.6% 4.0% 4.2% 3.8% TRK 1.0% 1.4% 1.7% 1.4% Photons 1.8% 1.8% 1.8% 1.8% Total 6.2% 12.1% 140% 20.8% systematic uncertainties for the X(3872) Systematic B —+ X(3872)((2S)7)KDecay K ‘ K K*± K*o BB count 1.1% 1.1% 1.1% 1.1% Branching Fractions 2.7% 2.7% 3.0% 3.4% Fit Parameters 0.6% 0.7% 6.9% 1.6% Signal mmjss 5.8% 2.1% 22.2% 119% X(3872) Mass 1.2% 3.9% 144% 6.4% X(3872) Width 1.2% 4.6% 44% 9.8% mx Background 4.9% 4.9% 0.0% 146% Bias 0.7% 1.3% 5.8% 14.5% Efficiency 0.8% 1.5% 4.6% 2.1% PID 4.0% 4.5% 4.6% 4.2% TRK 1.4% 1.8% 2.1% 1.8% Photons 1.8% 1.8% 1.8% 1.8% r Total 10.0% 10.0% 153% 190% 183 6.3. Systematic Uncertainties and Corrections Table 6.12: Summary of total systematic uncertainties for the Xci decay modes. Systematic xiK x1K° XciK*± XciK* BB count 1.1% 1.1% 1.1% 1.1% Branching Fractions 5.6% 5.6% 5.7% 6.0% Fit Parameters 0.6% 1.5% 5.7% 2.5% Signal mmjss 0.0% 0.0% 0.1% 0.0% Xci Mass 1.0% 0.1% 8.0% 0.3% mx Background 0.1% 0.8% 1.3% 1.0% Bias 0.7% 1.7% 5.7% 3.3% Efficiency 1.1% 2.6% 6.1% 3.5% PID 3.7% 4.0% 4.3% 3.9% TRK 1.0% 1.4% 1.7% 1.4% Photons 1.8% 1.8% 1.8% 1.8% Total 7.3% 8.2% 15.1% 9.4% Table 6.13: Summary of total systematic uncertainties for the Xc2 decay modes. ___________________ _______ _______ ________ _______ Systematic XC2K Xc2K Xc2K* Xc2K*J BB count 1.1% 1.1% 1.1% 1.1% Branching Fractions 5.3% 5.3% 5.4% 5.7% Fit Parameters 4.3% 6.2% 217% 2.8% Signal mmjss 2.5% 2.5% 54.0% 0.0% Xc2 Mass 1.7% 0.2% 13.1% 0.1% mx Background 15.9% 43.0% 52.0% 5.1% Bias 6.2% 16% 455% 0.8% Efficiency 7.1% 9.1% 33.2% 2.0% PID 3.6% 4.0% 4.3% 3.9% TRK 1.0% 1.4% 1.7% 1.4% Photons 1.8% 1.8% 1.8% 1.8% Total 20.4% 47.9% 511% 9.6% 184 Chapter 7 Conclusions This chapter states the final results obtained from this analysis, includ ing statistical and systematic uncertainties. The B —* x1,2K results are compared with previous experimental measurements. The confirmation of X(3872) —* J/b’y, discovery of evidence for X(3872) —* ‘i&(2S)’y, and the broader implications for the further understanding of the X(3872) are dis cussed in detail. 7.1 Analysis Results The signal extraction method was successfully verified on the Xcl charmo nium modes to measure the branching fractions B(B — xciK) = (4.5 ± O.1(stat.) ± O.3(syst.)) X iO, xiK°) = (4.2 ± O.3(stat.) + O.3(syst.)) x iO, B(B _+ Xc1K*±) = (2.6 ± O.5(stat.) ± O.4(syst.)) x iO, Xc1K*O) = (2.5 ± O.2(stat.) ± O.2(syst.)) x iO. For the Xc2 decay modes, the following branching fractions were mea sured: B(B —*x2K) = (1.0 ± 0.6(stat.) + 0.2(syst.)) x i0, 13(B° — xC2K°) = (1.5 ± 1.0(stat.) ± 0.7(syst.)) x i0, B(B Xc2K*±) = (1.1 + 4.3(stat.) ± 5.6(syst.)) x i0, 185 7.1. Anaiysis Results 13(B° — xc2K 0) = (6.6 + 1.8(stat.) ± 0.6(syst.)) x i0. The upper limit on the branching fractions is defined by assuming a Gaus sian distribution for the number of signal events and its uncertainty, and integrating over the physically-allowed region from 0 to 90% of the total area around the mean. The total uncertainty is taken as the statistical and systematic uncertainties added in quadrature. These results are: B(B —* xC2K) < 1.7 x i0 B(B° —*x2K°) <2.8 x iü— B(B _4 Xc2K*±) <10.0 X 13(B° — XC2K*O) <9.0 x i0. For X(3872) — J/ry, this analysis finds: B(B —÷ X(3872)K). (X(3872) —. J/-y) = (2.8 ± 0.8(stat.) ± 0.2(syst.)) x 106, 13(B° —+ X(3872)K°) . (X(3872) —+ J/’7) = (2.6 ± 1.8(stat.) ± 0.3(syst.)) x 106, Z3(B — X(3872)K*±) . (X(3872) —* J/7) = (0.7 ± 2.6(stat.) ± 1.0(syst.)) x 106, 13(B° —÷ X(3872)K*o). (X(3872) —* = (0.7 ± 1.4(stat.) ± 0.2(syst.)) x 106. There is 3.5o evidence for X(3872) —p J/7 in B —k X(3872)K. Finding no significant signal in the other modes, 90% confidence level upper limits are calculated as described above: 13(B° —+ X(3872)K°) . (X(3872) —* J/iry) <4.9 x 10_6, X(3872)K*±). (X(3872) —f J/7) <4.8 x 10—6, 186 7.2. Discussion and Implications 13(B° —* X(3872)K*O) (X(3872) —÷ J/’7) =< 2.8 x 10. In the search for X(3872) —* &(2S)’y, this analysis finds: B(B — X(3872)K) (X(3872) — (2S)7) = (9.5 ± 2.7(stat.) ± 0.9(syst.)) x 10—6, 13(B° —> X(3872)K°) (X(3872) —* (2S)y) = (11.4 ± 5.5(stat.) ± l.2(syst.)) x 10_6, B(B — X(3872)K*±) . (X(3872) — = (6.4 ± 9.8(stat.) + 9.7(syst.)) x 10—6, 13(B° —* X(3872)K*O) . (X(3872) — &(2S)-y) = (—1.3 ± 3.1(stat.) ± 2.5(syst.)) x 10_6. This analysis measures 3.3u significance for X(3872) —* b(2S)y in B — X(3872)K. This is the first evidence for this decay channel. The 90% confidence level upper limits for the other decay modes are measured to be: X(3872)K°) . (X(3872) — (2S)7)< 1.9 x 10, B(B —÷ X(3872)K*±) . (X(3872) — (2S)7)<2.8 x 13(B° —÷ X(3872)K*O) . (X(3872) — /‘(2S)7)<0.4 x i0. These results for the Xcl,2, X(3872) ‘ J/7, and X(3872) ,‘ decay modes are displayed concisely in Figures 7.1, 7.2, and 7.3, respectively. 7.2 Discussion and Implications The Xcl,2 results and their comparison with previous BABAR and Belle mea surements are summarized in Table 7.1. It is important to note that the BABAR data set used in this analysis overlaps somewhat with previous BABAR results while the Belle measurements are entirely independent. Furthermore, 187 7.2. Discussion and Implications if 60 40 20 100 In cu 50 Figure 7.1: 8Plot of the uumber of signal events versus mx for (a) B+ Xci,2K± (b) B° —+ Xc1,2KTh (c) B± Xc1,21<*±, and (d) B° —> xci,2K*o. The solid curve is the fit to the data. o300 I) tn200 rID C (b) c2 .4 - GS.t+rrJPItrSl.Ø 3.45 3.5 3.55 3.6 m (GeV/c2) 30 I L )Cc2 04 sI&e cc’ In -. 2C cu C a) 3.45 3.5 3.55 3.6 m (GeVIc2) (c) 2CC2 •aA .•ai/ 3.45 3.5 3.55 3.6 3.45 3.5 3.55 3.6 m (GeV/c2) m (GeV/c2) 188 7.2. Discussion and Implications 3.8 3.85 3.9 3.95 m (GeVIc2) G’, TTT 1,1 ‘tit’ It’ I 3.8 3.85 3.9 3.95 m (GeVIc2) 10 3.8 3.85 3.9 3.95 m (GeV/c2) Figure 7.2: P1ot of the number of extracted signal events versus mx for (a) B — X(3872)K, (b) B° —* X(3872)K, (c) B —* X(3872)K*±, and (d) B° — X(3872)K*o, where X(3872) — J/7. The solid curve is the fit to the data. 10 5 (b) I_ I II I I __________________ 10 X(3’872)—,J4y I:., 3.8 3.85 3.9 3.95 m (GeVIc2) c’10. (C) In 0 Wf1 I.... I.... . . . .1 In C () C ID - 189 7.2. Discussion and Implications 15 (a) X(3872) -. y(2S) 10 > (b) 10• tr1 - I, _____________________ 5 I I I I j5 _________ II ‘I 6 3.8 3.85 3.9 3.95 3.8 3.85 3.9 3.95 m (GeVIc2) m (GeV/c2) 10 (‘ 1J - QI > (C) (d)’ U I I I - I ii - II .1 5. I 4- 1II I1ItI I 3.8 3.85 3.9 3.95 3.8 3.85 3.9 3.95 m (GeV/c2) mx (GeVIc2) Figure 7.3: P1ot of the number of extracted signal events versus mx for (a) B — X(3872)K, (b) B° — X(3872)K, (c) B — X(3872)K*±, and (d) B° —* X(3872)K*o, where X(3872) —÷ (2S)7. The solid curve is the fit to the data. 190 7.2. Discussion and Implications the previous measurements used daughter branching fractions taken from older versions of the PDG [71, 88], which have been resealed22 here to allow direct comparison to the results of this analysis. Table 7.1: Comparison of the present B —* xcl,2K signal extraction results with previous measurements. Previous BABAR and Belle results have been resealed to use the most up-to-date daughter BFs. Such corrections have apparently not been applied to the Xci results appearing in the latest version of the PDG. Decay Belle BABAR Old PDG [33] Present x x iO x x i0 x1K (3.8 + 0.5) [19] (4.7 ± 0.4) [37] (4.9 + 0.5) (4.5 + 0.4) xiK° (3.2 ± 0.5) [19] (4.1 ± 0.6) [87] (3.9 ± 0.4) (4.2 ± 0.4) XclK*± (3.0 + 1.0) [19] (2.5 ± 1.2) [87] (3.6 + 0.9) (2.6 ± 0.6) XciK*O (1.8X) [60] (3.0 ± 0.7) [87] (3.2 ± 0.6) (2.5 ± 0.3) xC2K < 0.28 [19] < 0.29 [16] < 0.29 < 0.17 x2K < 0.27 [19] < 0.42 [16] < 0.26 < 0.28 XC2K*± < 1.23 [19] < 0.12 [16] < 0.12 < 1.0 Xc2K*O < 0.74 [19] < 0.37 [16] < 0.36 (0.66 ± 0.19) The Xci measurements are in excellent agreement with and supercede all previous BABAR results. These measurements generally agree with Belle results. This analysis provides the single best measurements of all B —* xiK decay modes except for Belle’s very recently published measurement of B° —* xciK*O [60]. This analysis also provides a substantial statistical improvement over previous PDG xciK* world average results. Regarding the Xc2 decay modes, this analysis is in agreement with pre vious xC2K results, and provides the best B± —* xc2K± measurement to date. These results for B —+ Xc2K* are somewhat of a departure from previous measurements. The measurement of B± xc2K*± does not im prove over the previous BABAR result but it is at least in agreement with Belle’s measurement for B —*xc2K*±(K7ri. In the case of B° — Xc2K*O, 221n particular, improvements in the measurement of B(x1 —÷ J/b7) and B(J/i,b tt) and correcting for the assumption of an equal ratio of charged and neutral B pair production in Y(4S) decays. 191 7.2. Discussion and Implications the branching fraction is surprisingly larger than previous upper limits, and somewhat in disagreement with the former BABAR measurement of (1.4 ± 1.1 ± 1.4) x i0 [16]. The previous result was based upon 124 x 106 B events with a similar efficiency for the K*O K+7r decay mode (7.1 ± 0.1%), and measured 2.0 ± 1.6 events. As a cross-check, a fit was performed to the Run 1-3 dataset (the previous BABAR sample) using the analysis technique described herein, and found 5.4 + 5.7 events correspond ing to 13(B° —* xc2K*o) = (6.9 ± 7.3) x iO—. This result is consistent with the previously measured branching fraction. The only Belle measurement of this decay mode set a limit of < 1.27 x i0’ [19], which is also consistent with this result. Theoretical studies of the branching fractions for the B — x2K de cay modes have contradictory predictions, ranging from zero to O(10). Based on the most recent theoretical treatments, one could possibly expect B(B — x2K) ranging from -S.’ (0.2 — 4.0) x i0 [12, 20, 21]. Given this uncertainty, the first evidence for the factorization-suppressed B° — xc2K*O decay presented here is perhaps consistent. However, there is no plausible explanation for the lack of observation of decays to B —p X2K in the K±, K, and K*O modes; thus this result may not represent more than a statistical fluctuation. The value of B(B —* X(3872)Kj (X(3872) —* J/’y) = (2.8 ± 0.8) x 106, with a total significance of 3.6u, confirms and supercedes the pre vious BABAR value of (3.3 ± 1.0) x 10—6 [37], and represents the ultimate measurement of this quantity in BABAR. The only Belle measurement23 to date finds (1.8 ± 0.6 ± 0.1) x 10—6 by assuming = 1 and combining the neutral and charged decay modes [36]. The measurement of B(B —* X(3872)Kj. (X(3872) —* ‘(2S)7) = (9.5 ± 2.9) x 106 is the first discovery of evidence (3.3u) for this decay. The ratio of the branching frac B(X(3872)—(2S)7)tions for the two decay modes is B(x(3872)—J/ = 3.5± 1.4. Comparing to B(B — X(38’72)Kj 13(X(3872) — J/irr) [34] with the errors again in quadrature, one calculates the ratio = 1.1 + 0.4. For the kaon decay modes with smaller branching fractions and lower efficiency, 23Unpublished. 192 7.2. Discussion and Implications the lack of evidence is not unusual given the the size of the data sample. Radiative decays to J/7 and çb(2S)’y of standard higher-mass states in the charmonium model are likewise unexpected and unobserved. This discovery of evidence for the radiative decays to J/’7 and &(2S)7 is an important contribution towards the understanding of the X(3872) mys tery. The C-parity of the X(3872) is almost certainly determined to be positive. Regarding the DOD*O molecular interpretations of the X(3872), the presence of a X(3872) —* ‘(2S)’y decay is difficult to explain. Few the oretical DOD*O molecular models make explicit predictions for the existence of this decay, and it is expected to be suppressed in those that do. If the X(3872) is a charmonium state, observing c? —+ J/’&-y and c — (2S)’y dis favour the 2 assignment, since these would represent suppressed higher- order multipole transitions. Based on these radiative decays, 1 ++ is the most likely charmonium assignment. The large branching fraction of (2S)7com pared to J/&7 is consistent with charmonium model predictions for the 1 ++ Xci (2P) state. However, several outstanding problems exist for this conclu sion, namely that the Xci (2P) state is expected to be very broad, have a mass 100MeV/c2 above that of the X(3872), and decay far more domi nantly (orders of magnitude greater) to other final states. The results of this analysis are generally inconsistent with both a purely DOD*O molecular or purely charmonium model interpretation of the X(3872), and may indicate a state containing an admixture of both components, and that an improved theoretical treatment or perhaps even a new interpretation is required. 193 Bibliography [1] J.J. 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