UNIVERSITY OFf-IAWAI'1 LIBRARY AN ANALYSIS OF THE K+1l"+1l"- FINAL STATE IN A DISSERTATION SUBMITTED TO THE GRADUATE DMSION OF THE UNIVERSITY OF HAWAI'I IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS MAY 2008 By Hulya Guler Dissertation Committee: Stephen L. Olsen, Chairperson Thomas E. Browder Sandip Pakvasa John M. J. Madey Kathleen C. Ruttenberg We certify that we have read this dissertation and that, in our opinion, it is satisfactory in scope and quality 118 a dissertation for the degree of Doctor of Philosophy in Physics. DISSERTATION COMMI'ITEE ii © 2008, HuIya GuIer iii Anneanneciifime. Hatice Giir 1919-2007 iv Acknowledgements I thank Stephen Olsen, Thomas Browder, Sandip PakvaBa, John Madey, and Kathleen Ruttenberg for serving on my committee. I am especially indebted to my advisor Stephen Olsen for his support and for trusting me enough to let me work inde­ pendently. I also thank ThomaB Browder, Sookyung Choi, ThomaB Dombeck, Fang Fang, Alexei GarmaBh, Li Jin, Michael Jones, Kay Kinoshita, Alexander Kuzmin, Jimmy Macnaughton, Daniel Marlow, Kenkichi MiyabayaBhi, Shohei Nishida, Sandip PakvaBa, Michael Peters, Yoshihide Sakai, Karim Trabelsi, Gary Varner, and Hitoshi Yamamoto for helpful discussions. I thank my mother, Bema Giir, for the sacrifices she haB made to enable me to pursue my interest in physics. I thank Jamal Rorie for being the ideal officemate and for his patience and un­ derstanding aB I worked on this thesis. I am grateful to my friends who have supported and encouraged me; in particu­ lar: Gene Altman, Javier Ferrandis, Tamar Friedmann, Jeanne Hogan, Abidin Kaya, Elena Martin, Miifit Tecimer, and Melek Yal!tmt~. Finally, I thank the KEKB team and the Belle Collaboration for producing the beautiful data that have made this thesis possible. v Abstract Inclusive branching ratios have been measured for the decays B+ -+ J /1/JK+7r+7r­ and B+ -+ '1/1 K+7r+7r- using 492 fb-1 of data collected at the T(4S) resonance by the Belle detector at KEKB. Three-dimensional amplitude analyses have been performed to study the resonant structure of the K+7r+7r- final state in these decay modes. vi Contents Acknowledgements v Abstract . .. vi List of Tables xi List of Figures xiii 1 Introduction . 1 1.1 The Standard Model 1 1.2 Meson Spectroscopy 2 1.3 Production and Decay Rates . 3 1.4 Motivation.. 5 1.5 Synopsis... 6 2 Experimental Apparatus 7 2.1 KEKB ....... 7 2.2 The Belle Detector . 9 2.2.1 Silicon Vertex Detector . 9 vii 2.2.2 Central Drift Chamber . 12 2.2.3 Aerogel Cherenkov Counters . 14 2.2.4 Time-of-Flight Counters ... 17 2.2.5 Electromagnetic Calorimeter . 18 2.2.6 Extreme Forward Calorimeter 18 2.2.7 Kdp, Detector ....... 20 2.3 1i.igger, Data Acquisition, and Software . 21 2.3.1 Trigger ............... 21 2.3.2 Data Acquisition 25 2.3.3 Software.. 26 3 Particle Identification 27 3.1 Electron Identification 27 3.2 Muon Identification . 30 3.3 Hadron Identification . 31 4 Event Selection . 35 4.1 Multiply-Reconstructed Tracks 36 4.2 Selection of J N and 1/J' Candidates 38 4.2.1 Leptonic IN and 1/J' Decays .... 38 4.2.2 1/1 Decays to JN7r+7r- . 40 4.3 Selection of K± Candidates 41 4.4 Selection of 7r± Candida.tes . 41 4.5 B-Meson Reconstruction .... 42 viii 4.6 Signal and Sideband Regions. · · 45 4.7 Cut Optimization . · · 47 5 Coordinate Transformations 49 5.1 M(K7r7r). 49 5.2 M(K7r) 57 5.3 M(7r7r). · · 63 5.4 Peak Transformations. · · 69 6 Inclusive Branching Fractions 72 6.1 Measurement Technique .. 72 6.2 Systematic Errors . 73 6.2.1 Efficiency Errors .. 76 6.2.2 Binning .... 76 6.2.3 Correction for Over-Subtraction . 77 6.2.4 Background Shape . 77 6.2.5 Determination of Signal and Sideband Regions . 78 6.2.6 NB ••••••••••••••••• 78 6.2.7 J N and 'I/! Branching Fractions . 78 6.3 Results.... 78 6.4 Cross-Check. 79 7 Amplitude Analyses 82 7.1 Fitting Technique .. 82 7.2 Normalization Procedure .... 83 ix 7.3 Background Functions · · . 85 7.4 Efficiency Functions . · · 91 7.5 Phase-Space Functions · 91 7.6 Signal Functions · 92 7.7 Results . · 95 7.8 Statistical Errors . 101 7.9 Systematic Errors . · . 103 7.9.1 Background Parameterization 103 7.9.2 Efficiency .. 104 7.9.3 Integration Step Size .. 104 7.9.4 Modeling of the Signal . 104 7.10 Discussion ........... 105 7.10.1 Interference Effects . 105 7.10.2 The L-Region ..... 109 7.10.3 Deficiencies of the Fits 110 8 Conclusions ..................... 112 x List of Tables 1.1 Quarks and Leptons . 2 2.1 SVDl and SVD2 parameters . 11 2.2 Physical processes of interest and their cross sections 23 4.1 Leptonic J /1/J and 'if! yields . 39 4.2 1/J' -> J/'Ijnr+7r- yields ... 41 4.3 Selection criteria for ~ -> 7r+7r- decays . 42 4.4 Fractions of events with multiple B candidates 44 4.5 Mean of the signal peak, width of the main Gaussian, and background fraction in the signal region, according to I~EI fits for data . .. 47 4.6 Background rejection factors and signal efficiencies for kaon and pion cuts 48 6.1 Measured inclusive branching fractions for B+ -> J/1/JK+7r+7r- and B+-> 1/J' K+7r+7r- . • . • • . 79 6.2 Measured inclusive branching fractions for B+ -> 1/J'K+ 81 7.1 Fitted values of background-function parameters for B+ -> J/1/JK+7r+7r- and B+ -> 1/J' K+7r+7r- . • . • . .. 87 7.2 Angular distribution of the K+7r+7r- final state for various combinations of initial and intermediate-state spin parities . 94 7.3 Fitted values of signal-function parameters for B+ -> J/1/JK+7r+7r- 96 xi 7.5 Decay fractions for B+ -+ JNK+w+w- submodes . 102 7.6 Decay fractions for B+ -+ 1/J'K+w+w- submodes. 103 7.7 Masses, widths, and spin-parity values of the resonances included in the fits 105 xii List of Figures 1.1 Masses and widths of observed kaon states. 4 2.1 A conceptual diagram of KEKB ..... 8 2.2 A three-dimensional depiction of the Belle detector 10 2.3 Side-view of the Belle detector . 10 2.4 Impact-parameter resolution of SVDl and SVD2 in the r-t/> and z directions 12 2.5 The structure of the CDC . 13 2.6 Spatial resolution and transverse-momentum resolution of the CDC . 14 2.7 Configuration of the cathode layers of the CDC 15 2.8 The configuration of the ACC . 16 2.9 Barrel and endcap ACC modules. 16 2.10 The layout of a TOF module. 17 2.11 The layout of the ECL . 19 2.12 The structure of an ECL counter. 19 2.13 A three-dimensional view of the EFC's crystal structure . 20 2.14 Cross-section of a KLM detector layer; barrel and endcap RPC's 22 2.15 The Belle Level-l trigger system 24 2.16 The Belle DAQ system . 25 xiii 3.1 dE!d:c as a function of momentum for electrons and pions 29 3.2 Leld distributions for electrons and pions. • 29 3.3 Muon likelihood distributions, and efficiencies of various muon-likelihood cuts, for simulated muons and pions 31 3.4 Muon efficiency and pion fake rate . 32 3.5 CDC measurements of dE!d:c as a function of momentum for charged tracks in collision data . 34 3.6 Charged-hadron meffles, calculated using TOF and CDC information, for data and MC ..............................•. 34 4.1 Interpretation of a single track as multiple tracks by the tracking software 37 4.2 Cosine of the opening angle between track pairs in data . 37 4.3 Measured invariant maS!!e8 of electron and muon pairs. 39 4.4 Measured invariant maffles of '1/1 -+ J Nnr+ 1r- candidates 40 4.5 dE versus MBC for J!'l/JK+1r+1r- and'l/lK+1r+1r- 43 4.6 dE versus M BC after best-candidate selection . 44 4.7 l!;.E distributions for MC . 45 4.8 l!;.E distributions for data 46 5.1 M (K1r1r) distributions for data in the signal and sideband regions . 50 5.2 dE versus M (K1r1r) for data . 52 5.3 dE versus M' (K1r1r) for data 52 5.4 M'(K1r1r) distributions for data in the signal and sideband regions 53 5.5 dE versus M(K1r1r) for generic MC . 54 5.6 dE versus M'(K1r1r) for generic MC . 54 5.7 M(K'lr1r) distributions for generic MC 55 xiv 5.8 M'(K1r1r) distributions for generic Me . 56 5.9 t:.E versus M(K1r) for data 58 5.10 t:.E versus M'(K1r) for data 58 5.11 t:.E versus M(K1r) for generic Me . 59 5.12 t:.E versus M'(K1r) for generic Me 59 5.13 M(K1r) distributions for data in the signa.! and sideband regions 60 5.14 M' (K1r) distributions for data in the signal and sideband regions 60 5.15 M(K1r) distributions for generic Me . 61 5.16 M'(K1r) distributions for generic Me 62 5.17 t:.E versus M (1r1r) for data . 64 5.18 t:.E versus M'(1r1r) for data 64 5.19 t:.E versus M(1r1r) for generic Me 65 5.20 t:.E versus M'(n) for generic Me .