SLAC-R-645 A Measurement of the Lifetime and Mixing Frequency of Neutral B Mesons with Semileptonic Decays in the BABAR Detector* Chih-Hsiang Cheng Stanford Linear Accelerator Center Stanford University Stanford, CA 94309 SLAC-Report-645 Prepared for the Department of Energy under contract number DE-AC03-76SF00515 Printed in the United States of America. Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, VA 22161. * Ph.D. thesis, Stanford University, Stanford, CA 94305. A MEASUREMENT OF THE LIFETIME AND MIXING FREQUENCY OF NEUTRAL B MESONS WITH SEMILEPTONIC DECAYS IN THE BABAR DETECTOR a dissertation submitted to the department of physics and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy Chih-Hsiang Cheng August 2002 I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Patricia Burchat (Principal Adviser) I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Aaron Roodman I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Lance Dixon Approved for the University Committee on Graduate Studies: iii iv Abstract The neutral B meson, consisting of a b quark and an anti-d quark, can mix (oscillate) to its own anti-particle through second-order weak interactions. The measurement of the mixing frequency can constrain the quark mixing matrix in the Standard Model of particle physics. The PEP-II B-factory at the Stanford Linear Accelerator Center provides a very large data sample that enables us to make measurements with much higher precisions than previous measurements, and to probe physics beyond the Standard Model. 0 0 The lifetime of the neutral B meson τB0 and the B -B mixing frequency ∆md are measured with a sample of approximately 14,000 exclusively reconstructed B0 → ∗− + D ν signal events, selected from 23 million BB pairs recorded at the Υ(4S) reso- nance with the BABAR detector at the asymmetric-energy e+e− collider, PEP-II. The decay position of the exclusively reconstructed B is determined by the charged tracks in the final state, and its b-quark flavor at the time of decay is known unambiguously from the charge of the lepton. The decay position of the other B is determined inclusively, and its b-quark flavor at the time of decay is determined (tagged) with the charge of tracks in the final state, where identified leptons or kaons give the most information. The decay time difference of two B mesons in the event is calculated from the distance between their decay vertices and the Lorentz boost of the center of mass. Additional samples of approximately 50,000 events are selected for studies of background events. v The lifetime and mixing frequency, along with wrong-tag probabilities and the time-difference resolution function, are measured simultaneously with an unbinned maximum-likelihood fit that uses, for each event, the measured difference in B decay times (∆t), the calculated uncertainty on ∆t, the signal and background probabilities, and b-quark tagging for the other B meson. The results are +0.024 ± τB0 =(1.523 −0.023 0.022) ps and −1 ∆md =(0.492 ± 0.018 ± 0.013) ps , where the first error is statistical and the second is systematic. The statistical cor- relation coefficient between τB0 and ∆md is −0.22. This result is consistent with the current world average values, the the total errors are comparable with other most-precise measurements. vi Acknowledgement As I put a period to my journey through graduate school, I would like to acknowledge the guidance and support of my adviser Pat Burchat. I would also like to thank David Kirkby for his always-ingenious suggestions and insight, Tim Meyer, and Chris Roat for their camaraderie in finishing this ambitious analysis and making my graduate life so enjoyable, and Chris LeClerc at U. C. Berkeley, who, with David and Tim, has contributed a great deal to this analysis. I would also like to thank Wouter Verkerke for providing an amazing fitting package and answering numerous questions. This work cannot be accomplished without the dedication of all BABAR and PEP-II members. I appreciate the careful reading and comments by Pat Burchat and Lance Dixon in preparing this manuscript. Finally, I would like to thank my family for the support and encouragement, especially my wife, Joyce, who has added the pleasure to my life. Without her, this thesis would not have been possible. vii Contents Abstract v Acknowledgement vii 1 Introduction and Overview 1 2 Theory and Phenomenology Overview 8 2.1StandardModelPhysics......................... 9 2.2 A Few Words on C, P and T Symmetry................ 16 2.3 Neutral B MesonSystem......................... 18 2.3.1 Two-statephenomenology.................... 18 2.3.2 Neutral B decaytimeevolution................. 24 2.3.3 Standard Model calculation of ∆M ............... 27 2.3.4 Coherent BB state........................ 29 2.4Lifetime.................................. 31 2.4.1 Naiveexpectation......................... 31 2.4.2 OPEandspectatormodel.................... 32 2.5 B SemileptonicDecays.......................... 33 3 Current Experimental Status 39 3.1MixingMeasurements.......................... 39 viii 3.1.1 Time-integratedmeasurements................. 40 3.1.2 Time-dependentmeasurements................. 42 3.2LifetimeMeasurements.......................... 44 4TheBABAR Experiment 46 4.1Introduction................................ 46 4.2 The PEP-II Storage Rings ........................ 48 4.3 Silicon Vertex Tracker .......................... 54 4.4DriftChamber.............................. 56 4.5CherenkovLightDetector........................ 60 4.6ElectromagneticCalorimeter....................... 63 4.7InstrumentedFluxReturn........................ 66 4.8SolenoidandMagnets.......................... 69 4.9Trigger................................... 70 4.10DataAcquisition............................. 71 5 Reconstruction and Particle Identification 73 5.1ChargedTrackReconstruction...................... 73 5.1.1 Algorithm............................. 73 5.1.2 Trackingefficiency........................ 74 5.1.3 Trackparameterresolution.................... 75 5.2ParticleIdentification........................... 77 5.2.1 Electronidentification...................... 77 5.2.2 Muonidentification........................ 80 5.2.3 Kaonidentification........................ 81 6 Vertex and Decay Time Difference 83 6.1DecayVerticesMeasurement....................... 83 ix 6.2DecayTimeDifference.......................... 86 6.2.1 Conversion from ∆z to ∆t .................... 86 6.2.2 Calculation of error on ∆t .................... 89 6.3Decay-TimeDifferenceResolution.................... 90 6.4BeamSpotDetermination........................ 95 7 Flavor Tagging 103 7.1Algorithm................................. 104 7.1.1 Single variable-based tagging — lepton tag and kaon tag . 104 7.1.2 Neural network tagging ...................... 105 7.2MistagandVertexingCorrelation.................... 106 7.2.1 Transversemomentaofusedtracks............... 107 8 Event Selection 117 8.1Introduction................................ 117 8.2TrackSelection.............................. 119 8.3EventShape................................ 119 8.4 π0 Reconstruction............................. 120 8.5 KS Reconstruction............................ 121 8.6 D0 Reconstruction............................ 122 8.7 D∗ Reconstruction............................ 124 8.8 D∗ Vertex and Tag-side B Requirement................ 126 8.9BackgroundControlSamples....................... 126 9 Background Characterization 133 9.1LeptonIdentification........................... 133 9.2AngularVariables............................. 140 9.3 D∗-D0 MassDifference.......................... 142 x 9.4CombinatoricBackground........................ 148 9.5ContinuumBackground......................... 149 9.6FakeLeptonBackground......................... 149 9.7UncorrelatedLeptonBackground.................... 150 9.8SampleComposition........................... 152 10 Analysis of B0 Decay Time Evolution 163 10.1ResolutionModels............................ 164 10.1.1Functionforms.......................... 164 10.1.2Modeltestonlifetime...................... 168 10.2FitMethod................................ 172 10.2.1 Signal ∆t model.......................... 174 10.2.2 Background ∆t model...................... 178 10.2.3 Charged B model......................... 183 10.3FitResult................................. 185 11 Validation and Systematic Study 193 11.1ValidationandConsistencyChecks................... 193 11.1.1TestsoffittingprocedurewithMonteCarlosimulations....194 11.1.2Dataconsistencychecks..................... 197 11.1.3Changeinkaonmistagslope................... 198 11.1.4 Sensitivity to NT3 tagging information ............. 198 11.2SystematicUncertainties......................... 201 12 Conclusion and Outlook 212 A Sample Composition 220 B Additional ∆t-Projection Plots 225 xi C Dalitz Plot Calculation 228 Bibliography 231 xii List of Tables 2.1StandardModelelectroweakquantumnumbers............ 12 2.2Simulationdecaymodesandtheirbranchingfractions......... 34 4.1 PEP-II beam parameters ......................... 51 4.2Eventcrosssections,productionandtriggerrates..........