by RAHMAT RAHMAT A DISSERTATION Presented to the Department of Physics and the Graduate School of the University of Oregon in partial fulfillment of the requirements for the degree of Doctor of Philosophy Septenlber 2008 11 University of Oregon Graduate School Confirmation of Approval and Acceptance of Dissertation prepared by: Ralunat Ralunat Title: "Hadronic Spectrum of tau -> pi- piO nu_tau Decays" This dissertation has been accepted and approved in partial fulfillment of the requirements for the degree in the Department of Physics by: James Brau, Chairperson, Physics Eric Torrence, Member, Physics Stephen Kevan, Member, Physics Nilendra Deshpande, Member, Physics James Isenberg, Outside Member, Mathematics and Richard Linton, Vice President for Research and Graduate Studies/Dean ofthe Graduate School for the University of Oregon. September 6, 2008 Original approval signatures are on file with the Graduate School and the University of Oregon Libraries. III An Abstract of the Dissertation of Rahmat Rahmat in the Department of Physics for the degree of to be taken Doctor of Philosophy September 2008 Approved: Dr. Eric Torrence, Advisor We report on a study of the invariant mass spectrum of the hadronic system in T- -----+ 1r-1r°VT decays. This study was performed using data obtained with the BABAR detector operating at the PEP-II e+e- coUider. We present fits to phe- nomenological models in which resonance parameters associated with the p(770), p'(1450) and p" (1700) mesons are determined. Vve also discuss the implications of our data with regard to estimates of the hadronic contribution to the muon anomalous magnetic moment. IV CURRICULUM VITAE NAME OF AUTHOR: Rahmat Rahmat PLACE OF BIRTH: Jakarta, Indonesia DATE OF BIRTH: September 18, 1974 GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED: University of Oregon, Eugene University of Indonesia, Indonesia DEGREES Doctor of Philosophy in Physics, 2008, University of Oregon, Eugene. Master of Science in Physics, 2004, University of Oregon, Eugene. Bachelor of Science in Physics, 1998, University of Indonesia, Jakarta. ACADEIvlIC INTERESTS Tau decays Muon g-2 Trigger and Data Acquisition PROFESSIONAL EXPERIENCE Research Assistant, Department of Physics, University of Oregon, Eugene, 2004-2008 Teaching Assistant, Department of Physics, University of Oregon, Eugene, 2002-2004 GRANTS, AWARDS AND HONORS Ghent Fellowship, University of Oregon vACKNOWLEDGMENTS Thanks to Prof. James Brau, who has accept me to join Oregon High Energy Physics and guided me to see the beauty of High Energy Physics. Thanks to Prof. Eric Torrence, who has worked very hard to guide me in this thesis. He has written comments and suggestions which are longer than than this thesis itself. For more than 4 years, he has dedicated tremendous efforts in this thesis. Thanks to Dr. Olga Igonkina and Dr. ]'vIinghui Lu, who has helped me a lot when I started this analysis. Thanks to Prof. Stephen Kevan, who accepted me to be an Oregon Graduate student. Thanks to Prof. Nilendra G.' Deshpande, who has guided me to see the beauty of Quantum Mechanics. In addition, Prof. Nilendra G. Deshpande had sponsored me to win one of the prestigious fellowships in University of Oregon, Ghent Fellowship. Thanks to Prof.James Isenberg for his advice and suggestions in this thesis. . I would like to thanks to Prof. David Strom, Prof. Ray Frey, Jan Strube, Jeff Kolb and Nick Blount for important discussions, advice and comments. Very special thanks to my wife Yam Sau Kuen, who has sacrificed her study in Ph.D. Accounting at University of Oregon to come with me to SLAC,California. She has given the best support to me to finish this thesis. Thanks to my daughters, Jasmine Jong and Jane Jong, who have given me joy and happiness while working on this thesis. TABLE OF CONTENTS Chapter VI Page I INTRODUCTION 1 1 2 3 4 Hadronic Tau Decay Spectral Function of ,- -----+ 7f-7fOVT Decays . Comparison to e+e- Data . Analysis Overview . . . . . . . . . . . . . . 2 3 4 7 II OVERVIEW OF MUON MAGNETIC ANOMALY III PHENOMENOLOGICAL MODELS .... 10 15 1 2 The Model of Kuhn and Santamaria The Model of Gounaris and Sakurai 16 16 IV THE BABAR EXPERIMENT 18 1 2 3 The PEP-II Collider .. The BABAR Detector . 2.1 Silicon Vertex Tracker . 2.2 Drift Chamber . . . 2.3 Cherenkov Detector .. 2.4 Magnet Coil . 2.5 Electromagnetic Calorimeter 2.6 Instrumented Flux Return 2.7 Trigger............ Offline Data Processing . . . . . . . 3.1 Prompt Data Reconstruction 3.2 Data Skimming . 18 21 24 24 27 29 29 39 41 44 44 46 Chapter Vll Page V DATA AND :MONTE CARLO(MC) 48 1 Data ........ 48 2 J\l1onte Carlo(MC) 50 VI EVENT PRESELECTION 52 1 KO Candidate Preselection .52 2 Charged Candidate Preselection 5:3 VII EVENT SELECTION .... 59 1 Event Reconstruction ,59 2 Selection Process . . 59 :3 Final Event Sample 67 VIII UNFOLDING ....... 70 1 Singular Value Decomposition. 71 2 Unfolding Procedure 72 IX FITTING RESULTS. 77 1 Form Factor 79 2 Integration Procedure 81 X UNCERTAINTIES. 82 1 Method ... 82 2 Efficiency . . 8:3 2.1 'Iracking 8:3 2.2 KO Efficiency 8:3 2.:3 KO R;econstruction 86 :3 Resolution ........ 94 :3.1 Tracking Resolution 94 3.2 Photon Resolution . 94 4 Backgrounds ...... 99 4.1 qq Background 99 4.2 T Background 101 5 Other Systematic. . . . 110 Chapter 6 7 5.1 Bin Size of 1f-1fo Invariant Mass 5.2 Unfolding............. 5.3 Stability Over Runs Period . . . Comparison between OS and KS Fitting . Statistical Uncertainty. Vlll Page 110 110 11:3 115 115 XI CONCLUSION . 118 1 2 3 Theoretical Correction . Summary . Comparison with Other Experiments . 3.1 M p 3.2 f p . 3.3 Mpl 3.4 f p l 3.5 Mpll 3.6 f pll 3.7 (3. 3.8 ¢/3 . 3.9 r' 3.10 ¢'Y' 3.11 a;7r 3.12 Comments on p" 119 121 122 122 122 122 123 123 123 124 124 124 125 125 12.5 APPENDICES. A PHOTON RESOLUTION PLOTS 128 128 1 2 3 Energy Resolution Plots . . Neutral Theta(e) Resolution Plots Neutral Phi(¢) Resolution Plots 128 130 132 B OTVL . 14~3 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 144 IX LIST OF FIGURES Figure Page 1.1 Comparison between JrJr spectral function from T experiments of CLEO, OPAL and ALEPH, taken from [7]. The two most precise results from ALEPH and CLEO are in agreement. The statistics are comparable in both cases, however due to fiat acceptance in ALEPH and an increasing one in CLEO, ALEPH result has better precision below p peak, while CLEO's has better precision above p peak. 5 1.2 Comparison between JrJr spectral function from T and e+c experiments, taken from [7]. The green bar shows the average T- -----+ Jr-Jr°vT from ALEPH, CLEO and OPAL. The e+e- data are taken from CMD-2 [8], DMI [9], DM2 [10], OLYA [11] OLYA-CMD [12], TOF [13]. All error bars shown contain statistical and systematic errors. Visually, the agreement appears to be satisfactory, however the large dynamical range involved does not permit an accurate test. To do so, the e+C data are plotted as a point-by-point ratio to the T spectral function. 8 1.3 Relative comparison of the T data(average) and Jr+Jr- spectral functions from e+e~ data taken from [7]. The shaded band is the uncertainty on the T spectral function. There are small discrepancies between e+e- and T data, particularly in p peak region. . . . . . . . . . . . . . . . . . . .. 9 xFigure Page 11.1 Representative diagrams contributing to aw First column: lowest-order diagram (upper) and first order QED correction (lower); second column: lowest-order hadronic contribution (upper) and hadronic light-by-light scattering (lower); third column: weak interaction diagrams; last column: possible contributions from lowest-order Supersymmetry. . . . . . . . .. 12 IV.1 PEP-II 19 IV.2 BABAR Detector.The detector is designed according to the boosted CM system. The interaction point is not at the geometrical center of the detector. It is shifted towards the backward direction which is defined by the outgoing low energy beam. 22 IV.3 BABAR detector end view. . . 23 IVA Transverse section of Silicon Vertex Tracker(SVT). 25 IV.5 The plot of longitudinal section of Drift Chamber(DCH). The chamber is offset by 370 mm from the interaction point(IP) . . . . . . . . . . . . .. 26 IV.6 The detector for internally reflected Cherenkov light(DIRC). The Cherenkov light is internally reflected until it gets detected in the water-filled readout reservoir. 28 IV.7 The longitudinal view of the Electromagnetic Calorimeter(only the top half is shown) indicating arrangement of the 56 crystal rings. The detector is axially symmetric around z-axis. All number are given in milimeter . 30 IV.8 The Electromagnetic Calorimeter(E1/IC) barrel support structure, with great details on the modules and electronic crates . . . . . . 32 IV.9 The plot of one wrapped CsI(Tl) Crystal and the front-end readout package mounted on the rear face. 33 Xl Figure Page IV.10 Overview of the IFR: Barrel sectors and forward (FW) and backward (BW) end doors; the shape of the RPC modules and their dimensions are indicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40 V.1 Integrated Luminosity of BABAR Detector 49 VI.1 Thrust Magnitude of MC and Data, all preselection cuts have been applied, except thrust magnitude cut. All MC samples are normalized to Data Luminosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .57 VI.2 The number of photon in signal hemisphere of MC and Data Distribution, all selection cuts have been applied, except number of cluster cut. All I\dC are normalized to Data Luminosity. . . . . . . . . . . . . . . . . . . . .. 58 VII. 1 Simplified picture of event reconstruction in this analysis. . . . . . .. 60 VII.2 The 7f- Momentum (in GeV/c) of the signal 7f-7fo, in the LAB frame. All Monte Carlo samples are generated using SP8 and normalized to collected Data Luminosity. DATA and Monte Carlo show good agreement, All cuts have been applied, except 7f- Momentum cut. . . . . . . . . .. 61 VII.3 The"( Candidate Energy (in GeV) on the signal side, in the LAB frame. All MC samples are normalized to the collected Data Luminosity. DATA and MC show good agreement, all cuts have been applied, except "( energy cut. 62 VIlA The 7fo Momentum (in GeVIc) of the signal 7f-7fo, in the LAB frame. All MC samples are normalized to the collected Data Luminosity. DATA and MC show good agreement, all cuts have been applied, except 7f- Momentum cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63 XlI Figure Page· VII. 5 The 7[0 invariant mass (in GeV) of the signal 7[-7[0. All MC samples are normalized to the collected Data Luminosity. DATA and MC show good agreement, all cuts have been applied, except 7[0 Mass cut. . . . . . . .. 6:3 VII.6 Polar Angle of Missing Momentum 8miss (rad) of the event in the LAB frame. A1l1!IC samples are normalized to the collected Data Luminosity. DATA and MC show good agreement, All cuts have been applied, except polar angle of missing momentum 8miss cut. The lower plot is the zoom for high polar angle region, where cut is applied to reduce the contributions from non-signal events. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 64 VII. 7 The Polar Angle of 7[- (rad) in the LAB frame. All MC samples are normalized to the collected Data Luminosity. DATA and MC show good agreement, all cuts have been applied, except the polar angle of 7[- cut. The lower plot is the zoom for high polar angle region, cuts are applied to non-signal events. . . . . . . . . . . . . . . . . . . . . . . . . . . 65 VII.8 The plot of the 7[-7[0 invariant mass of Data(black dots) and ]'viC samples, all Monte Carlo samples are normalized to data luminosity. The major backgrounds are the contributions from non signal T and continuum qq backgrounds 68 VII.9 The plot of 7[-7[0 invariant mass after MC backgrounds are subtracted from Data. The dip about 1.5 GeV shows a destructive inteference between p' and p". . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 VII.lO The efficiency plot, as defined by the number of selected 7[-7[0 events divided by the number of generated 7[-7[0 events, plotted as a a function of 7[-7[0 invariant mass. 69 Figure VIlLI Unfolding 1/Iatrix in 2D. The upper plot is the unfolding matrix for full MC with 0.3 GeV < M7r - 7r0 < 2.8 GeV. The lower plot is the unfolding matrix for lower mass region MC with 0.3 GeV < M 7r - 7r0 < 1.8 GeV. Xlll Page Efficiency is not included. . . . . . . . . . . . . . . . . . . . . . . . . .. 73 VIIl.2 Unfolding Ivlatrix in 3D. The upper plot is the unfolding matrix in box style for full MC with 0.3 GeV < M7r - 7r0 < 2.8 GeV. The lower plot is the unfolding matrix in box style for lower mass region MC with 0.3 GeV < l\I!7r-7r0 < 1.8 GeV. Efficiency is not included. . . . . . . . . . . . . .. 74 VIlL3 The Reconstruction Mass - The True Mass and fit it using Gaussian. The Os are the mean value of invariant mass of the specific truth bins .. 75 VIllA Comparison between background-subtracted DATA(black) and Unfolded DATA(red) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 76 IX.l Fitting to Unfolded Background Subtracted Data using Gounaris Sakurai Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78 IX.2 The pion Form factor 1F1 2 as derived from the spectral function of selected Data after background subtraction . . . . . . . . . . . . . . . . . . . .. 80 X.l The upper left plot is the comparison between Reconstructed(black) and Detected(red) E!;1C. The upper right plot is the comparison between Reconstructed(black) and Detected(red) E~ata. The lower right plot is the comparison between efficiency of Data(black) and MC(red). The lower left plot is the the ratio between efficiency Data and MC. 87 X.2 Comparison of Muon Momentum between Data(circle) and MC(square) from e+ e- --t p,+ p,-,,! samples. MC is normalized to Data Luminosity 88 Figure XIV Page X.3 Comparison of Cosine Theta(LAB) of 1\1uon between Data(circle) and MC(square) from e+e- -> /l+ IF/' samples. rvlC is normalized to Data Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88 X.4 Comparison between selected photon energy Data, .t\1C and Corrected- MC. Corrected MC is MC after photon efficiency correction applied which calculated using /l/l/' sample. Both MCs are normalized to Data Lumi- nosity. 89 X.5 Comparison between selected Af'rf of Data, MC and Corrected-MC. Both MCs are normalized to Data Luminosity. Corrected MC is MC after photon efficiency correction which calculated using /l/l/' sample. 90 X.6 The Cosine of Opening Angle between 2 photons of?fo in LAB frame after all selection cuts applied. From top to bottom, the plots are zoomed. Top plot ranges from 0.5-1, Mid plot ranges from 0.95-1 and Bottom plot ranges from 0.995-1. MC is normalized to Data Luminosity. . . . . . .. 91 X.7 The opening angle of selected 2 photons of ?fo decay(LAB frame) after all selection cuts applied. Corrected MC is MC after photon efficiency correction which calculated using /l1J/Y sample. 92 X.8 The total mass on the 3 Prong side(tag side), assuming the 3 tracks are pions after all cuts applied, X axis is in GeV. MC is normalized to Data Luminosity. 99 X.9 The total mass on the 3 Prong side above tau Mass, assuming the 3 tracks are pions after all cuts applied, X axis is in GeV . . . . . . . . . . . . .. 100 X.10 The Signal ?f-?fo invariant mass of some events which have total mass on 3 prong side bigger than 1.8 GeV (Log Scale). . . . . . . . . . . . . . .. 101 xv Figure Page X.ll The invariant 7f-7fo IvIass from major contributors to T background, after all cuts applied. The horizonatlline is in GeV . . . . . . . . . . . . . .. 103 X.12 The invariant 7f-7fo7fo mass, all IvICs all normalized to Data Luminosity. Vlfe see that there is no significance difference between Data and MC in 109 128 128 129 A.2 Energy Resolution :~/IC All Runs. . A.3 Energy Resolution Data(black line) and 1\1C(red line) All Runs. A.4 After Energy smearing: MC after smearing(blue line), initial MC(red line) and Data(black line) All Runs. . 129 A.1 Energy Resolution Data All Runs. A.5 Theta Resolution Data All Runs. 130 A.6 Theta Resolution MC All Runs. . 130 A.7 Theta(e) Resolution Data(black line) and IvIC(red line) All Runs. 131 A.S Neutral Theta(e) smearing result. After e smearing: MC after smear- ing(blue line), initial MC(red line) and Data(black line) All Runs. 131 A.9 Phi Resolution Data All Runs. 132 A.10 Phi Resolution MC All Runs. . 132 A.ll Phi(¢) Resolution Data(black line) and MC(red line) All Runs. 133 A.12 After ¢ smearing: IvIC after smearing(blue line), initial MC(red line) and Data(black line) All Runs. . . . . . . . . . . . . . . . . . . . . . . . .. 133 A.13 Linear fit (y = a + bx) to scale and resolution (smearing) parameters. 134 XVI LIST OF TABLES Table Page 1.1 Standard IVlodel . 2 V.l DATA and IvIC . 48 V.2 Generated Monte Carlo events for this analysis 51 V1.l Event PreSelection Table After Tau1N. Preselection efficiencies in percent for Data and Monte Carlo background samples. Cuts are applied sequentially and the marginal efficiencies are quoted 56 VI1.1 Event Selection Table in sequential percentage(%) of efficiency after each cut. MC is normalized to data luminosity 66 IX.l Fitting Result with Gounaris Sakurai Function.The statistical errors are shown in the table . . . . . . . . . . . . . 78 IX.2 Correlation Matrix between fit parameters 79 X.l Parameters after Track Efficiency correction. The number in parentheses are only statistical errors. . . . . . . . . . . . . . . . . . . . . . . . 84 X.2 Fitting parameters before and after linear nO efficiency correction. Vve also include the uncertainties of a(O'a) and b(O'b), by varying their 10' up and down. The number in parentheses are only statistical errors. 93 xvii Table Page X.3 GS Fitting Parameters after Btrack resolution correction. The number in parentheses are only the statistical errors. . . . . . . . . . . . . . . . .. 95 X.4 GS Fitting Parameters after Ptrack resolution correction. The number in parentheses are only statistical errors. 96 X.5 Photon Resolution Uncertainties. The numbers in parentheses are only statistical errors. . . . . . .. 98 X.6 We estimate the contribution of uds background uncertainty using the ratio of Data and IVIC above tau mass ( 1.8 GeV). After varying the uds background contribution by its uncertainty ±a, we refit the spectrum using GS function. This table shows the parameters before(default values) and after uds background variation. The numbers in parentheses are only statistical errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 100 X.7 After cuts applied, the T backgrounds are reduced significantly. This table shows the main T decays that contributes to T Backgrounds after all cuts applied. . . . . . .. 102 X.8 Parameters after T- ----7 e-vevr background variation. The number in parentheses are only statistical errors. 104 X.9 Parameters after T- ----7 Jr-vr background variation(MC Mode 3). The number in parentheses are only statistical errors. . . . . . 105 X.lO Parameters after T- --+ al ----7 Jr-Jr°Jr°vr background variation. The number in parentheses are only statistical errors. . . . . . . . . . .. 105 X.ll We vary the contribution of T- ----7 al ----7 Jr-Jr°Jr°vr due to possibility that 1 missing Jr0 of a1 can be mis-identified as signal. The number in parentheses are only statistical errors. 106 XVlll Table Page X.12 Parameters after T- -----+ K- K°7[°vT background variation. The number in parentheses are only statistical errors. 106 X.13 Parameters after T- -----+ 7[- K°7[°vT background variation. The number in parentheses are only statistical errors. . . . . .. 107 X.14 Parameters after T- -----+ K*- -----+ K-7[°vT background variation. The number in parentheses are only statistical errors. . . ... " 107 X.15 We also vary the track efficiency correction to T- -----+ K*- -----+ K-7[°vT background. The number in parentheses are only statistical errors. 108 X.16 GS Fitting Parameters with 5, 10 and 50 MeV Bins. The number in parentheses are only statistical errors. 111 X.17 Fitting parameters with and without unfolding. 'vVe also compare it with unbinned fitting. The number in parentheses are statistical errors. 112 X.18 The Branching Fraction T- -----+ 7[-7[°VT for 5 different Runs. 113 X.19 Fitting parameters for 5 different runs. The number in parentheses are only statistical errors. 114 X.20 The errors are only statistical and we find that the fitting parameters for both KS and GS models are consistent within the statistical errrors. . 115 X.21 Summary of fitting parameters and their experimental uncertainties 116 X.22 Final fitting parameters and their experimental uncertainties . 117 XLI External Parameters and their uncertainties . . . . . . . . . . . . . . .. 121. XL2 The results of fitting to the Jl,17[7ro distribution using Gounaris-Sakurai function from some experiments. . 126 .XL3 The results of a;7r from some experiments 127 Table XIX Page A.l Energy Resolution Data Run 1-5 135 A.2 Energy Resolution Run MC 1-5 . 136 A.3 Energy Resolution Run MC 1-5 After Smearing 137 A.4 Energy Smearing ....... 138 A.5 Theta(8) Resolution Run 1-5 139 A.6 Theta(8) Smearing .... 140 A.7 Theta(8) After Smearing . 140 A.8 Phi(¢) Resolution Run 1-5 . 141 A.9 Phi(¢) Smearing ... 142 A.I0 Phi(8) After Smearing 142 A.ll Fit to photon scale and resolution parameters 142 B.l Good Track Candidate . . . . . . . . . . . . . 143 1CHAPTER I INTRODUCTION The Standard Model(SM) of particle physics predicts all matter is made of six leptons and six quarks. In addition, for every matter particle there is an antiparticle with exactly the same mass but opposite-signed additive quantum numbers (e.g. electric charge). Leptons are divided into three families: the first family consists of electron(e) and electron neutrino(ve ), the second family consists of muon(p) and muon neutrino(vp ), the third family consists of tau(T) and tau neutrino(vT ). The electron(e) , muon(p) and tau(T) have a negative charge, while the neutrinos(v) are electrically neutral. Each of the leptons carries its own family lepton number. In the Standard Model, lepton number is always conserved. For instance, the lepton decay is always accompanied with a neutrino to conserve the lepton number. There are six quarks with six different "flavors" (see Table 1.1). The up(u), charm(c) and top(t) quarks have a positive charge +2/3e(in units of electron charge), while the down(d), strange(s) and bottom(b) quarks have a negative charge -1/3e. Both leptons and quarks are spin-1/2 particles, or fermions. Unlike leptons, quarks are never found alone. They are confined to groups with other quarks, forming baryons (bound state of three quarks) and mesons (bound state of a quark-antiquark pair). There are four known forces responsible for interactions between the fundamental particles: strong, electromagnetic, weak and gravitational. Each force is mediated 2Quark Lepton up(u) down(d) electron(e) neutrino electron(ve ) charm(c) strange(s) muon(fL) neutrino muon(vJ1) top(t) bottom(b) tau(T) neutrino tau(vT ) Tab. 1.1: Standard rvlodel by one or more interaction-specific particle(s), gauge boson(s) (integer-spin parti- cle). Particles interact by exchanging gauge bosons. These force-carrier particles are fundamental, but are not considered as matter particles. 1 Radronic Tau Decay Martin Perl et. al. discovered the T lepton in 1975 using MARK I detector at the Stanford Linear Accelerator Center [1]. The mass of T lepton is 1776.90 ± 0.20 MeV[2] and its lifetime is (290.6 ± 1.0) x 10-15 s[2]. The T lepton is the only lepton heavy enough to decay into hadrons, and as this decay involves a pure charged-current interaction it makes an excellent system for studying the coupling of hadrons to weak current. This analysis will measure the hadronic decay spectrum of T- decays 1. The invariant amplitude for semileptonic(ha.dronic) T decays can be written in the form (1.1 ) where HJ1 represents a specific hadronic system, VCKM is the corresponding element of the Cabibbo-Kobayashi-Maskawa matrix (Vud for non-strange and Vus for strange) and GF denotes the Fermi coupling constant. The leptonic current is given by lCharge conjugation is implied throughout this analysis 3(1.2) which can be called charged weak current. The hadronic final states in tau decays can be classified as either vector or axial vector based on the isotopic parity (G-parity); the operation of isospin rotation fol- lowed by charge conjugation. The conservation of G-parity implies that, in the case of the decay of a T lepton to pions, decay modes with an even number of pions will proceed via the vector current, while those with an odd number of pions will proceed via the axial-vector current. The measurement of non-strange T vector current prop- erties requires the measurement of T decay modes with a parity G=+1. Similarly, the measurement of T axial-vector current properties requires decay modes with G=-1. The differential decay rate of T- ----+ 1r-1r°VT decays normalized to the total decay width is related to the spectral function V_(8) as [3]: 61rIVud ISHv Be (1 __8_)2(1 28)2 () AJ2 B 11112 + A12 V_ 8 , T ITIT T T (1.3) where 8 = q2 is the invariant mass squared of the 1r-1r0 system, Vud is the Cabbibo- Kobayashi-Maskawa matrix element, Be is the branching fraction of T- ----+ e-vevn B ITIT is the branching fraction of T- ----+ 1r-1r°Vn AIT is the T lepton mass, and SIF');v denotes electroweak radiative corrections. The data from T- ----+ 1r-1r°VT decays is expected to be dominated by production ofthe lowest lying vector meson, the p(770), while radial excitations, such as the p(1450) and p(1700), may also contribute. The interference of these mesons in T decays are of significant interest and new data are important. 4The T spectral function is related to the charged pion form factor(see Chapter III for phenomenological models of form factor) as f3~ (s) _ 2 v_(s) = 121r IFOT (s)1 , The threshold functions f3o,~ are defined by where (1.4) (1.5) Spectral function measurements for the two pion final state T- -----+ 1r-1r°VT are available from ALEPH [4], CLEO [5] and OPAL [6]. They are compared in Figure 1.1 and the two most precise results from ALEPH and CLEO are in agreement. The statistics are comparable in both cases, however due to flat acceptance in ALEPH and an increasing one in CLEO, the ALEPH result has better precision below p peak, while the CLEO result has better precision above p peak. 3 Comparison to e+e- Data The Conserved Yector Current (CYC) relates the spectral function from the T decay to the 1r+1r~ spectral function produced in the reaction e+C -----+ 1r+1r- in the limit of exact isospin symmetry. The e+C -----+ 1r+1r- data is used to determine the hadronic vacuum polarization correction to the photon propagator, which is needed to understand many precision electroweak meaurements. In particular, this data is needed to understand the SM prediction for the anomalous magnetic moment of muon af.L = (gfJ.-2)/2, where gf.L is the gyromagnetic ratio ofmuon(see Chapter II for Fig. 1.1: Comparison between 7fIT spectral function from T experiments of CLEO. OPAL and ALEPH, taken from [7]. The two most precise results from ALEPH and CLEO are in agreement. The statistics are comparable in both cases: hmvever due to flat acceptance in ALEPH and an increasing one in CLEO, ALEPH result. has better precision below p peak. while CLEO's has better precision 8.bove p peak. ~'1 0,70,65 • ALEPH CLEO OPAL 0,6 s (GeV2) 0.550.5 0.3~-~ 02 r --- L ---- ,....., ~ 0,1 ro I I- Q) -~ 0 1- - - , _ I f-' L......J '" ALEPH CLEO OPAL s (GeV2) 0.3 If' I I j I I --,-r I ' <: lJ.. 0.2 --- -i lJ..~ -0 1 f01 I'J!f ~ ,~ -02l 1~ -0.2 ~ _ lJ.. _ N ~~ I', J -OJ' ILl. I, I 12 '-' 'J 08 1 . -0.3 0,2 0.4 0.6 . ,....., f-' '--i N ---- r-I Q) OJ 0,1 hadrons) 47[a2 , 38 (II. 7) (II. 8) 14 where K(s) is the QED kernel [28], x 2 1 [ x 2 ] 1 + xK(8) = x 2 (1 - -) + (1 + x?(1 + ?) In(1 + x) - x + - + --, x2ln x (11.9)2 x~ 2 1 - x where with 1-13x= J.ll+pJ.l' (11.10) (11.11 ) Using equations, [11.7], [11.8], [1.7] and [I.8](the equation that relates T and e+ e- spectral function), we get: 2 7r7r = ( amJ.l)21mr 3V_(8)K( )daJ.l 2 8 8 + .... 31f 4m2 8 " (11.12) The tau decay only covers a range up to 8 = M;. Since the kernel K (s) is a smooth function with 1/82 dependence, hadronic final states at low energy dominate the contribution to (a~ad,LO) and "..." represents the integral above 1" mass. The dominant uncertainty on the evaluation of a;7r comes from the low energy range above 0.5 GeV, below which improved e+e- data are available from Cl ' vfD-2[8] and SND[29] have a better precision than the T data. The range of integration used in this analysis is from VS = 0.5 to 1.8 GeV of invariant 1f-1fo mass, where the T data is more useful than e+e- data. The a;7r calculation in this range(0.5-1.8 GeV) from T data has (about 2 times) better precision than e+ e- data. 15 CHAPTER III PHENOMENOLOGICAL MODELS There are 2 phenomenological models commonly used to parameterize the spectrum in T- -----+ 1f-1fOVy, Kuhn & SantaMaria(KS, see [30]) and Gounaris & Sakurai(GS, see [31]). The main difference between these models is a more sophisticated treatment of the Breit-Wigner(BW) function in GS. Both models are expanded to include not only the dominant p resonance, but also incorporates the contribution from p' and p". The form factor is written as a sum of BW terms: _ 1 pI-l (q2) = (BlIV + 13 eirPf3 BVVp' + rv eirP, BW II) 1r 1+13+1 PIP' (IlL 1) The real parameters 13 and 1 specify the relative coupling to pI and pI!, while the parameters 4/3 and 4>"1 specify the complex phase of each resonance with respect to p. The factor 1/(1+13+1) ensures the proper normalization of F. One can perform X2 fits to the measured 1f-1fo mass spectrum to extract resonance parameters using these models. In addition, having analytic function for the form factor allows a straightforward numerical integration procedure to be used to evaluate a;1r. The X2 minimization and parameter error determination is carried out using the l\lINUIT program[32] via RooFit[33]. We present results from both GS and KS, and the systematic errors on a;1r include the difference between either. 16 1 The Model of Kuhn and Santamaria One model of pion form factor was proposed by Kuhn and SantaMaria[30], where: (III.2) represents the Breit-wigner function associated with the p resonance lineshape, with 111p and r p(q2) denoting the p meson mass and q2 dependent total decay width. The assumed form for the latter is described below, where 1 P = _Jq2 - 4m2w 2 w' with 2 The 1v1odel of Gounaris and Sakurai (IIL3) (IlIA) (III.5) Many authors and analysis have been using Gounaris and Sakurai[31] to parame- terize e+e- ----t 1f+1f~ spectrum. This model is using the form for Fw which is derived from an effective range formula for the P-wave 1f -1f scattering phase shift, assuming p(770) meson dominance (III.6) d is defined as d = 3m; In Mp+ 2po + l\1p _ m;l\;p. 1rp6 2m1r 21rpo 1rPo' f(q2) is defined as with h(q2) is defined as and 17 (III. 7) (IlL8) (III.9) (III. 10) 18 CHAPTER IV THE BABAR EXPERIMENT The PEP-II used to collide high energy electron(e-) and positron(e+), described in the first section of this chapter, is an asymmetric e+e- collider operating at the 1(4S) resonance. Together with the BABAR. detector, described in the second part of this chapter, it is also called a B-meson factory since the 1(4S) decays to more than 96% into B-mesons. But the multi functional design of the detector allows a large number of measurement in T physics. The experimental facilities are located within the Stanford Linear Accelerator Cen- ter (SLAC) at Menlo Park near San Francisco, CA, USA. 1 The PEP-II Collider The PEP-II collider operates at energies about 10.58 GeV in the center-of-momentum (CM) frame. The main feature of PEP-II compared to other e+e- colliders is the asymmetry. Electrons are accelerated in the High Energy Ring (HER.) to energies of rv 9 GeV, positrons in the Low Energy Ring (LER.) to energies of rv3.1 GeV. This results in a CM system with a boost of ,8,=0.56. Fig. IV.1 shows a schematic view ofthe facility. The typical branching ratios are of the order of 10-4 to 10-6 • Thus, the collider needs to provide a very high luminosity. - -,oa: == ~g '\(f) cg 'en "-00.. ---- ""\ \ I J >>-< ,- IT o Z rr ~'\ .'=0\ IT /\ ~ .~ . ",--Ot: '"o , 20 The bunches collide head-on at the interaction point(IP). For each machine run, the event vertices are averaged to determine the averaged beam position, the beam spot. The uncertainties in the beam spot are of the order of a few 11m in the transverse plane and 100 11m along the collision axis. The high beam currents and the large number of closely-spaced bunches required to produce the high luminosity of PEP-II tightly couple the issues of detector de- sign(see Figure IV.2), interaction region layout, and remediation of machine-induced background. The bunches collide head-on and are separated magnetically in the hor- izontal plane by a pair of dipole magnets (B1), located at ± 21 on either side of the IP, followed by a series of offset quadrupoles. separate the beams to avoid parasitic collisions. The low energy beam (LEB) is further deflected horizontally by passing ofl-axis through the first quadrupole pair (Q1). Beyond Q1 the beams have separate beam pipes and focussing magnets with a field-free slots for the other beam. The Q2 quadupoles focus the LER horizontally, while Q4/Q5 focus the high energy beam (HER). The tapered B1 dipoles, located at ± 21 em on either side of the IP, and the Q1 quadrupoles are permanent magnets made of samarium-cobalt placed inside the field of the BABAR solenoid, while the Q2, Q4, and Q5 quadrupoles, located outside or in the fringe field of the solenoid, are standard iron magnets. The collision axis is off-set from the z-axis of the BABAR detector by about 20 mrad in the horizontal plane to minimize the perturbation of the beams by the solenoid field. The interaction region is enclosed by a water-cooled beam pipe of 27.9 mm outer radius, composed of two layers of beryllium (0.83 mm and 0.53 mm thick) with a 1.48 mm water channel between them. To attenuate synchrotron radiation, the inner surface of the pipe is coated with a 4 11m thin layer of gold. In addition, the beam pipe is wrapped with 150 11m of tantalum foil on either side of the IP, beyond z = 21 +10.1 cm and z = -7.9 cm. The total thickness of the central beam pipe section at normal incidence corresponds to 1.06 % of a radiation length. The beam pipe, the permanent magnets, and the SVT(see subsection 2.1 in this Chapter) were assembled and aligned, and then enclosed in a 4.5 m-long support tube which spans the IP. The central section of this tube was fabricated from a carbon-fiber epoxy composite with a thickness of 0.79 % of a radiati<;m length. 2 The BABAR Detector The components of the BABAR detector are arranged radially. The tracking con- sists of a silicon vertex detector (SVT) and a drift chamber (DCH). The SVT is located close to the beam pipe surrounded by the second tracking device, the DCH. The next component is the Detector of Internally Reflected Cherenkov Light (DIRC) which is mainly used to identify pions and kaons. Its photon detection system is lo- cated at the backward end of the BaBar detector. The Electromagnetic Calorimeter (EMC) is a crystal calorimeter with a forward endcap. It is the last sub-detector within the super-conducting magnet coil which provides a 1.5 T magnetic field. The Instrumented Flux Return (IFR) is the outermost component. Figure IV.2 shows a longitudinal section through the detector center, and Figure IV.3 shows an end view with the principal dimensions. e+ ELECTROMAGNETIC CALORIMETER IEMC) DRIFT CHAMBER (DCH) SILICON VERTEX TRACKER ISVTI SUPERCONDUCTING COIL IFR ENDCAP _"__.J~ ~~§~1~G .. 3045 /- .- ... t--~ 1375 r I I Ir}J 8iOJ I ,Cb:; INSTRUMENTED FLUX RETURN IIFRJ BARREL ~1 detector t. I I.P. I I , 1015 ---,--1- 1749 ___~--.L. 4050 r370 I - 1149 ~ I I I Scale 4 m BABAR Coordinate System y ~ 02 I o 01 BI~ 1IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIl1fH .... ·····~I-- ..~-··. -'-.. ~IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII I",~ 35 1 00 FLOOR ~--------o::==.~---===-~J~ .lJi_ 'J I'-~----_·_-_·_--"··"--- I L BUCKING COIL CRYOGENIC -- CHIMNEY MAGNETIC SHIELD FOR DIRC CHERENKOV DETECTOR IDIRC) Fig. IV.2: BABAR Detector.The detector is designed according to the boosted eM system. The interaction point is not at the geometrical center of the detector. It is shifted towards the backward direction which is defined by the outgoing low energy beam. t-.,;) t-.,;) CORNER PLATES --DIRC DCH -SVT 1----+-----~--------j--____1 o Scale 4 m BABAR Coordinate System y)-, z ,-------",-,---cutawaylsection ---------., IFR BARREL EMC SUPERCONDUCTING-- COIL EARTH QUAKE TIE-DOWN -GAP-FILLJ PLATES 'I 3500 EARTH QUAKE LISOLATOR FLOOR ~::=3r~~~~~~~~~~::5~~~~~~~~E==!~=k____ ___ IFR CYLINDRICAL RPCs Fig. IV.3: BABAR detector end view. tv W 24 2.1 Silicon Vertex Tracker The silicon vertex tracker (SVT), as shown in Figure IVA, is a part of the tracking devices of the detector. It is built from cylindrical layers of double sided silicon micro strip detectors. The SVT covers the polar angle region from 20° to 150°. The three inner layers are critical for the measurement of the secondary vertices for the B-meson decays. The two outer layers are important for the pattern recognition and the low Pt tracking. The arrangement of the strip sensors along the beam direction as well as perpendicular to it allows the spatial measurement of the track directions and angles with a high resolution. The SVT is especially optimized for excellent vertex resolution and reaches a pre- cision of approximately 70 Mm for a fully reconstructed B-meson decay. 2.2 Drift Chanlber The drift chamber (DCH) measures the tracks of charged particles and their mo- menta. Additionally, the specific energy loss by ionization can be determined and contributes up to momenta of 700 MeV/ c to the particle identificatioIl. The DCH complements the measurement of impact parameter and the directions of charged particles provided by the SVT near Interaction Point (IP). A side view is shown in Figure IV.5 The DCH is a multi-wire chamber with an inner radius of 26.6 cm and an outer radius of 80.9 cm and a length of 280 cm. It is composed of 40 layers with small hexagonal cells. In 24 of the layers, the wires are placed at small angles with respect to the z-axis. This provides longitudinal position information. The drift gas is a mixture of helium and iso-butane in a ratio of 80:20. ;- Beam Pipe 27.8mm radius / :--------___+___ ,/' Layer Sa/ ~'«/ LayerSb /; / ~/ Layer4b . / ""/ \ J ~ , \ 0/ } ~ . Layer 1 ~~/ Fig. IVA: Transverse section of Silicon Vertex Tracker(SVT). 25 26 A 1618 u Fig. IV.5: The plot of longitudinal section of Drift Chamber(DCH). The chamber is offset by 370 mm from the interaction point(IP) - . . - ._--------- 27 The reconstruction of tracks is done with a Kalman filter which considers data from the SVT and the DCH as well as the detector material and magnetic field. The average resolution for single tracks is given as 125 J-Lm. Schematic view of the drift chamber. The center of the chamber has an off"set of 370 mm from the IP. The pattern of axial (A) and stereo (U,V) layers is shown in the right hand side of Figure IV.5. 2.3 Cherenkov Detector The detector for internally reflected Cherenkov light (DIRC), shown in Figure IV.6 is the most important particle identification device of the BABAR detector. It is used to separate pions and lcaons from T and B decays. The 7r/K separation is possible up to momenta of 4 GeV with a significance of 2.50". The active detector material of the DIRC is constructed of 144 bars of fused silica arranged in bar boxes in a polygonal barrel. The DIRC bars are used both as radiators and as light pipes. Charged particles which traverse the DIRC-bars emit Cherenkov light in the angle ec with respect to the direction of the particle track, 1 Jl + (m/p)2 cosec = - = -'-------'------'----(3n n (IV.l) where m and p are mass and momentum of the particle respectively and n=1.4,5:3 is the refractive index of the synthetic quartz medium. The photons are reflected many times until they reach the stand off box, a tank of purified water. 10572 photo- multiplier tubes(PMT) cover the inside of the surface of the standoff" box, where fractions of the Cherenkov rings are projected. BUGKING COIL 36.5 64.5° 1- 1755. 1.4 10495 IRON GUSSET e - --- STRONG SUPPORT TUB~ ) .,- 2095.5 ...,~~ ----------------------------------- MAGNETIC SHIELD Fig. IV.6: The detector for internally reflected Cherenkov light(DIRC). The Cherenkov light is internally reflected until it gets detected in the water-filled readout reservoir. tV (f) 29 2.4 Magnet Coil All sub detector components are inside a toroidal super conducting magnet coil to allow momentum measurement from track curvature. The BABAR magnet creates a 1.5 T magnetic field parallel to the beam axis. 2.5 Electromagnetic Calorinleter Purpose and Layout The electromagnetic calorimeter (ElVIC) is designed to measure the energy, the position and the transverse shape of showers with excellent efficiency. It is designed to detect electrons and photons over the energy range of 20 MeV to 9 GeV with high resolution. This allows the detection of photons from 7fo and TJ decays as well as from QED and radiative processes. Besides that, the EJVIC contributes via E /p measurements to the electron identification for flavor tagging of neutral B-mesons and via the shower shape analysis to the identification of neutral hadrons. Furthermore, the EMC has to be compatible with the 1.5 T field of the solenoid and operate reliably over the anticipated lO-year lifetime of the experiment. The longitudinal cross section is shown in Figure IV. 7. To achieve these goals, a hermetic, total absorption calorimeter composed of thal- lium doped cesium iodite crystals (CsI(Tl)) was chosen. The main advantages are a very high light yield and good radiation hardness. This permits the use of silicon photodiodes which operate reliably in magnetic fields for the readout of the scintil- lation light. Another advantage of CsI(Tl) crystals is the small Moliere Radius (R 1VI = 3.8 cm) and the short radiation length (Xo = 1.8.5 cm) which allows a compact detector design for the measurement of fully contained showers. I- 2359 -I 1-2001 8572A03 External Support ~1127 .'. 1801 ., r1555 + 2295 38.2° II ,1 _ __ __ __ __ ! 558 1\ _____) L 22.7' .--A 15i8' Interaction Point~ ! - - -1- --- J , I-e------ 1979 • 1 920 1375 Fig. IV.7: The longitudinal view of the Electromagnetic Calorimeter (only the top half is shown) indicating arrangement of the 56 crystal rings. The detector is axially symmetric around z-axis. All number are given in milimeter eN o :31 The energy resolution of a calorimeter as a function of energy can be parameter- ized to consist of two parts which are added quadratically: A constant part to which electronics nonlinearities and non-uniformities are contributing as well as calibration errors. The second, energy dependent part has a statistical nature since the basic pro- cesses in an electromagnetic shower are statistical processes as fluctuations in photon statistics, electronic noise and beam generated background. In crystal calorimeters, the energy dependent part of the resolution is assumed to be proportional to 1/ \IE due to photon statistics. The target energy resolution of the BABAR ElvIC was O"E E 1% . ---:-;:::=::=;=::;:===::=c= E9 1.2%\!E(GeV) , (IV.2) where both terms are added in quadrature. The angular resolution is determined by the transverse crystal size and the average distance to the interaction point. The target was to achieve O"() = O"q:, = ( 3 + 2) mrad JE(GeV) at 90° incident angle to the beam direction. Geometry (IV.3) The EMC consists of a cylindrical barrel and a conical forward endcap. It has full coverage in azimuth and extends in polar angle from 15.8° to 141.8° corresponding to a solid angle coverage of 90% in the CM system. The barrel part consists of 5760 crystals which are ordered cylindrical around the beam axis. The radial distance from the interaction point to the crystal front face is 92 cm. Along the polar angle, the barrel is divided in 48 crystal rings. A longitudinal view along the polar angle is Detail of Mini-Crate Fan Out Board Electronic Mini-Crates Fig. IV.8: The Electromagnetic Calorimeter(EMC) barrel support structure, with great details on the modules and electronic crates Detail of Module Aluminum RF Shield 3-2001 8572A06 W tv Diode\---'--- Carrier Plate output Cable Aluminum~Frame SiHcon :-,Ttr====t=~.llIlul-li r-""rPhoto-diodes Fiber Optical Cableto Light pulser TYVEK~~(Renector) A\uminum _ ........,Foil(R.E Shield) cs\(T\) Crystal Mylar--....(ElectricalInsulation) 11-2000 8572A02 CFC--....... 'Compartments(MechanicalSupport) Fig. lV.9o The plot of one wrapped CsJ(TI) Crystal and the front-end rewiont package mounted on the rear face. 34 shown in Figure IV. 7 along the azimuthal angle, 120 crystals are segmented. Each crystal is wrapped in aluminum and mylar foils. Thus, between two crystals is about 130 f-tm of dead material. The crystals are ordered into modules of 7 . 3 (e· ¢) crystals. Those modules are wrapped with carbon fiber tubes, in-between two modules is on average 1.3 mm of material. The modules are bonded to an aluminum strong-back that is mounted on the external support. By supporting the modules at the back, the material in front of the ElVIC is kept to a minimum. A schematic view of the cylindrical barrel and the assembly of a module is shown in FigureIV.8. The endcap covers the forward area of the calorimeter. It consists of 820 crystals which are ordered circularly. The eight rings in the polar angle consist of 80 (the innermost two rings), 100 (the next three rings) and 120 (outer three rings) crystals respectively. All crystals point with their front face to the interaction point. In order to minimize losses in-between the crystals, a small non-projectivity is added in the polar angle. The average size of this non-projectivity is 1.4 mrad. The crystals are numbered with an index Ie which in the polar angle, 1 :::; Ie :::; 56, (IVA) where Ie = 1 is the very forward part of the endcap, the barrel part begins with Ie = 9 and the very backward part of the barrel is Ie = 56. In the azimuthal angle, 0:::; I¢:::; 79/99/119 depending on Ie. (IV.5) The material in-front of the ElVIC was minimized, depending on the polar angle 0.3-0.6 Xo of dead material are between the interaction point and the ElVIC. In front of the first 3 rings in the endcap are about 3 Xo of support structure. Reconstruction of Clusters and Bumps A particle which enters the ElVIC deposits, in general, energy in several crystals. Such a group of crystals is called a cluster. The following algorithm is used to recon- struct clusters from the information of individual crystals: 1. The crystal with the highest energy of the cluster is called the seed. It is required to have more than 5 MeV. 2. All adjacent crystals with energies above 1 MeV are added to the cluster. 3. The neighbors of each crystal with more than 3 MeV are added to the duster if their energy exceeds 1 1,1eV 4. The cluster energy is defined as the sum of the energy of all associated crystals. The' cluster energy is required to be more than 20 MeV in total for the cluster to be accepted. If two particles enter the calorimeter close to each other, it is possible that the energy deposition takes place in one cluster with two local maxima. In this case the cluster is splitted according to the weights of its single crystal information into b'umps with only one maximum each. The energy and the position of the bump is associated to one single particle. Energy Calibration of the Calorimeter The calibration of the BABAR calorimeter is performed in three steps: 1. Electronics Calibration The electronics calibration corrects the pedestal offsets, determines the overall gain and removes non-linearities. 36 2. Single Crystal Calibration In this calibration step, the measured pulse height in a single crystal is assigned to an energy. It also corrects variations in the light yield from crystal to crystal and over time. The time dependence is mainly due to radiation damage. 3. Cluster Calibration In the cluster energy calibration, energy losses which are not due to the features of a single crystal are corrected. These energy losses are due to interactions in front of the EMC, leakage behind the EMC and energy loss in dead material in-between the crystals. The three steps of the energy calibration of the EMC are discussed in more detail in the following: Electronics Calibration The electronics calibration is performed by precision charge injection into the preamplifier input. Initially up to 12% non-linearity were observed. These non- linearities were traced to oscillations on the ADC cards that have since been corrected. Remaining non-linearities are of the order of 2%. Single Crystal Calibration The single crystal calibration is performed for two energies at opposite ends of the dynamic range, the two measurements are combined by a logarithmic interpolation (line calibrator). For low energies, a radiative source spectrum is used (E, = 6.13 MeV) whereas for high energies, electrons from Bhabha scattering are used (E = 3-9 GeV). 37 For the radioactive source calibration, irradiated Fluorinert gets pumped through thin walled aluminum pipes which are mounted right in front of the crystals of the EMC. The Fluorinert decays via a radioactive decay chain, 19F+n -----+ 16 N -+- (x, 16N -----+ 160* + e-- + De 160* -----+ 160 +,' (IV.6) (IV.7) (IV.8) under emission of a monoenergetic photon with the energy of 6.13 :MeV. The high energy single crystal calibration factors are determined from electrons from Bhabha scattering (IV.9) The deposited energy E~ep of a final state electron k is purely determined by the angle fJ1ab between e+ and e-, 2 --+2 E k (fJ) = Etot - Ptot . dep 2(Etot - IPtot Icos fJ1ab ) , (IV. 10) where E tot , Ptat are the total energy and momentum in the laboratory system, respec- tively. The energy deposited in each individual crystal is compared to a prediction derived in a MC simulation. This means that not only the single crystal calibration factor can be determined, but also slight differences between data and simulation of the crystals are taken out. A more detailed description of the sophisticated algorithm can be found in The crystal response with electronics calibration and single crystal calibration ap- plied is called ei' The raw cluster energy, Eraw , is defined as the sum of the single 38 crystal calibrated energies ei, (IV.11) where i is enumerating all crystals in the respective cluster. Cluster Calibration The cluster energy calibration corrects for energy loss due to shower leakage, dead material in front of the calorimeter and in-between the crystals. The true energy of a photon can be expressed as photon energy = deposited energy + energy losses. (IV.12) The cluster calibration is obtained as a correction function c(E,8) which depends all the polar angle 8 and the energy, Ecal = Eraw . c(E, 8), (IV.13) where E cal is the cluster calibrated energy, Eraw the raw energy as defined in Eq. and c(E,8) is the calibration function. On Simulation The processes of energy loss in dead material are included in the simulation. The generated energy describes therefore the single crystal energy ei. The raw cluster energy is obtained from the generated single crystal energies. In order to have the cluster energy in the simulation at the right scale, the raw energy has to be corrected for these simulated energy losses. This is called Me calibration. Since Etrue is known 39 from the generator, cMc(E,8) can easily be determined (IV.14) On Data For data, the situation is more complicated. It is necessary to find a physics process which provides photons with known energies. Currently, the only mechanism which is exploited is the decay. The reconstructed two photon mass is known to be (IV.15) where E[ is the photon energy and 0: the opening angle between the two photons. This process produces clusters with an energy up to 1.5 GeV in the laboratory frame. At higher energies, the two photons are merged to one cluster and the reconstruction of neutral pions becomes difficult. 2.6 Instrumented Flux Return The Instrumented Flux Return (IFR) was designed to identify muons with high efficiency and good purity, and to detect neutral hadrons (primarily J(L and neutrons) over a wide range of momenta and angles. IFR is very important for studying the decays of e+e- ---+ p+p-, that will be llsed to assign some systematic uncertainties in this analysis. The principal requirements for IFR are large solid angle coverage, good efficiency, and high background rejection for muons down to momenta below 1 GeVIe. For neutral hadrons, high efficiency and good angular resolution are most important. 40 Barrel 342 RPC Modules 4-2001 8583A3 BW 432 RPC Modules End Doors Fig. IV.10: Overview of the IFR: Barrel sectors and forward (FW) and backward (Bv\!) end doors; the shape of the RPC modules and their dimensions are indicated. Because this system is very large and difficult to access, high reliability and extensive monitoring of the detector performance and the associated electronics plus the voltage distribution are required. The IFR uses the steel flux return of the magnet as muon filter and hadron absorber. Single gap resistive plate chambers with two-coordinate readout have been chosen as detectors. The RPCs are installed in the gaps of the finely segmented steel of the barrel and the end doors of the flux return, as illustrated in Figure IV.10 The steel segmentation has been optimized on the basis of Monte Carlo studies of muon penetration and charged and neutral hadron interactions. The steel is segmented into 18 plates, increasing in thickness from 2 em of the inner nine plates to 10 cm of the outermost plate. The RPCs are inserted into the gaps between these plates in the six barrel sector and the two end doors, as illustrated in Figure IV.10. The nominal gap between the 41 steel plates is 3.5 cm in the inner layers of the barrel and 3.2 cm elsewhere. There are 19 RPC layers in the barrel and 18 in the endcaps. In addition, two layers of cylindrical RPCs are installed between the EJVIC and the magnet cryostat to detect particles exiting the EMC. RPCs detect streamers from ionizing particles via capacitive readout strips. They offer several advantages: simple, low cost construction and the possibility of covering odd shapes with minimum dead space. .Further benefits are large signals and fast response allowing for simple and robust front-end electronics and good time resolution, typically 1-2 ns. The position resolution depends on the segmentation ofthe readout: a few mm are achievable. 2.7 Trigger The BABAR trigger is useful for selecting interesting physics events, which will subsequently be processed and written to the datastore. If competitive physics mea- surements are to be made, it is essential that a high efficiency is achieved and that this efficiency is well understood. The BABAR trigger consists of two levels. The Levell/Ll (hardware) trigger is designed to select candidate physics events at a rate of no more than 2 kHz, the maximum rate allowed by the data acquisition system. The Level3/L:3 (software) trigger uses more complex algorithms (after event construction) to reduce the event rate to about 200 Hz, the maximum rate that the event processing farm and mass storage facility can tolerate. L1 The Level-l trigger consists of the drift chamber trigger (DCT), calorimeter trigger (EMT) and global trigger (GLT). The DCT and EMT construct 'primitive objects' 42 which are then combined by the GLT to produce a whole range of 'trigger lines'. A L1 accept is generated if a GLT trigger line is active for a particular beam crossing. This accept signal must be distributed to the sub-system data acquisition systems with a latency of no more than 12 s. The main DCT primitive objects are short and long tracks, corresponding to tracks with a transverse momentum, 120 MeVIc and 180 MeVIc respectively. In the case of the EMT, the basic trigger object is a tower, corresponding to three adjacent rows of crystals along the length of the calorimeter. To allow cross-calibration of efficiencies for the EMT and DCT, the L1 trigger system is designed to be able to trigger independently from pure DCT and EJVIT triggers fo1' most physics channels. Tau and two-photon events are the exception, and rely mainly on DCT triggers. In order to keep the L1 trigger rate at a practical level, it is necessary to prescale some of the GLT trigger lines. The pre-scale factor determines what fraction of the accepts for a particular trigger line are logged, ensuring that processes with large cross sections, such as Bhabhas, do not dominate the data. L3 The L3 trigger consists of a set of software algorithms designed to reduce back- grounds while retaining physics events. In order to achieve the reduction in rate, the Level 3 algorithms use complete events rather than the elementary trigger objects constructed at the hardware level (Levell) of the trigger. The rates of all other physics process amount to only about 200 Hz. The L3 trigger software comprises event reconstruction and classification, a set of event selection filters, and monitoring. This software runs on the online computer farm. The filters have access to the complete event data for making their decision, including the output of the L1 trigger processors and Fast Control and Timing Sys- 43 tem(FCTS) trigger scalers. L3 operates by refining and augmenting the selection methods used in L1. For example, better DClI tracking (vertex resolution) and El\1C clustering filters allow for greater rejection of beam backgrounds and Bhabha events. The L3 system runs within the Online Event Processing (OEP) framework. OEP delivers events to L3, then prescales and logs those which pass the L3 selection criteria. To provide optimum flexibility under different running conditions, L3 is designed according to a general logic model that can be configured to support an unlimited variety of event selection mechanisms. This provides for a number of different, inde- pendent classification tests, called scripts, that are executed independently, together with a mechanism for combining these tests into the final set ofclassification decisions .. The L3 trigger has three phases. In the first phase, events are classified by defining L3 input lines, which are based on a logical OR of any number of the 32 FCTS output lines. Any number of L3 input lines may be defined. The second phase comprises a number of scripts. Each script executes if its single L3 input line is true and subsequently produces a single pass-fail output flag. Internally, a script may execute one or both of the DClI or ElVIC algorithms, followed by one or more filters. The algorithms construct quantities of interest, while the filters determine whether or not those quantities satisfy the specific selection criteria. In the final phase, the L3 output lines are formed. Each output line is defined as the logical OR of selected script flags. L3 can treat script flags as vetoes, thereby rejecting, for example, carefully selected Bhabha events which might otherwise satisfy the selection criteria. L3 utilizes the standard event data analysis framework and depends crucially on several of its aspects. Any code in the form of modules can be included and configured at run time. A sequence of these software modules compose a script. The same instance of a module may be included in multiple scripts yet it is executed only once, thus avoiding significant additional CPU overhead. 44 3 Offline Data Processing Events which are selected by the L3 trigger are stored for further processing. These events are grouped into Tuns. The full set of detector signals for a run of events is written to a single data file, usually referred to as an extended tagged container (XTC) file. The raw size of each event in the XTC is about 30 KB, and XTC files are typically a few tens of GB in size. 3.1 Pron1pt Data Reconstruction In recent years, the full processing of the event data has been conducted offline, meaning that the data are not fully processed in real-time (i.e. as the signals are recorded by the detector). Instead, all subsequent processing operates groups of events corresponding to one run (and one XTC file). These data are processed in a two-pass system. First, calibration conditions are calculated from a subset of the events in the run and written to the conditions database. This step is referred to as Prompt Calibration (PC). Secondly, all the events are reconstructed based on the conditions in the database, and are written out to event collections. This step is referred to as Event Reconstruction (ER). The PC step of the data processing makes use of only a subset of the events in a run. For technical reasons, these events are also stored in a secondary data file called a calib-XTG. The calib-XTC file for each run is filled with events passing a particular set of L3 trigger output lines, all of which are designed to provide a constant output rate of 1 or 2 Hz, depending on the trigger line. These output lines select Bhabha events, di-muon events, cosmic muons, and low-multiplicity hadronic events. The PC processing software runs on these events and writes out a set of calibrations which give a picture of the detector conditions at the moment the events were recorded. 45 To better account for changing detector conditions, the PC processing software makes use of roWng calibrations. In this method, the calibration constants from previous runs are stored and used as additional input information for the calculation of the current run's calibrations. This method also effectively provides for larger statistics without actually increasing the sampling rate for the calibration events. When all the calibration events in a run have been processed, the results are collected and passed to a final processing module. This module calculates the final calibration constants for that run and writes them to a temporary database where they are made available for the next run. The calibration constants are also written to the main conditions database, and assigned a validity interval corresponding to the time interval over which the run was recorded. During a period of high luminosity typical of the later years of BABAR running, the PC processing step was performed on computers at SLAC, utilizing around 30 CPUs. The Event Reconstruction step processes the full set of events in the XTC file. Because the detector has already been calibrated for the run period, the event recon- struction can process the events in any order. This task is accomplished by a farm of a few hundred multi-CPU computers at Padova, Italy, along with (more recently) a similar farm at SLAG The actual reconstruction of an event. (both PC and ER) is done by a software application called Elf. In contrast to the trigger algorithms, this software uses the full event data to reconstruct tracks in the DCH and SVT and clusters in the EMC and IFR. Elf also creates lists of different particles by running particle identification (PID) algorithms on the reconstructed tracks for a full description of the algorithms using in the analysis). Finally, Elf fills a set of Boolean variables called tags which provide a way of quickly classifying events based on very general characteristics. Background filter and trigger information are also stored as tags. The charged-track 46 lists, neutral particle lists, PID lists, and tag variables are written out to files called event collections, which are made available for further processing and analysts' use. Simulated data are also reconstructed with Elf, but are not run through the prompt reconstruction system. The event generator software is bundled with the detector simulation software and with Elf to form one integrated production package which directly outputs events collections. 3.2 Data Skimming Most physics measurements made with the BABAR data involve only a specific type of event. Often these events constitute only a small fraction of the total data set. To facilitate the many BABAR analysts, one final step of centralized data processing takes place before the typical user sees the data. Once a run is processed by the prompt reconstruction system, the output collections are skimmed. A skim refers to a subset of reconstructed events which fulfill some basic criteria. Groups of physicists working with similar analyses define a skim by choosing a simple set of criteria that selects an acceptably large fraction of the events of interest. BABAR analysts have defined hundreds of skims over the years, and some number of these skims are chosen to be calculated for the data and MC events. Using a large farm of computers at SLAC, each event in an event collection is processed and assigned a true or false value for each skim being run. A deep-copy skim is a physical copy of the reconstructed data for each event that passes a particular skim. A pointer skim is a collection of pointers to the data for event that passes the skim. Pointer skims are much smaller, but the redundant data of deep-copy skims provides better computing performance with large numbers of users. 47 This analysis only uses data and MC events which pass the TaulN skim. This skim selects events for which the following criteria are true • Event passes either DCH L3 trigger or EMC L3 trigger (always true for data, not necessarily true for tiC). • Event passes one or more ofthe following background filters: BGFMultihadron, BGFNeutralHadron, BGFTau, BGF11uMU, BGFTwoProng. • The number of entries in the ChargedTracks list is less than eleven. • The thrust is defined as the vector which minimizes the transverse momentum for all entries in the ChargedTracks and CalorClusterNeutral lists. The thrust axis is used to divide the event into hemispheres in the eM frame. The number of EMC clusters with energy greater that 50 MeV in each hemisphere must be less than or equal to six. • Using tmcks from the GoodTracksVeryLoose list, one hemisphere must contain one track, while the other must contain at least three. 48 CHAPTER V DATA AND ]VIONTE CARLO(MC) 1 Data The number of tau pairs recorded in BABAR detector is proportional to the in- tegrated BABAR Luminosity. We use about 297 tb-1 DATA taken by BABAR de- tector from Run 1-5 (see Table V.1), which consists of 274 fb- 1 taken at a center-of- momentum energy of m')'(4S) = 10.58 GeV (On-Peak DATA, because at energy 10.58 GeV, the rate of BE is at maximum) and 22.9 fb- 1 taken at a center-of-momentum energy of m')'(4S) = 10.54 GeV (Off-Peak DATA). The integrated luminosity of the data recorded by BABAR detector as a function of time can be seen in Figure V.I. Run On-Peak Data Off-Peak Data Total Per Run Begin End 1 19908 (pb 1) 2307 (pb 1) 22216 (pb-c1 ) Feb 2000 Oct 2000 2 58692 (pb-1) 5401 (pb-1) 64093 (pb-1) Feb 2001 Jun 2002 3 31865 (pb 1) 2440 (pb 1) 34305 (pb 1) Dec 2002 Jun 2003 4 96423 (pb-1) 8790 (pb-1) 105213 (pb-1) Sep 2003 Jul2004 5 67120 (pb 1) 3954 (pb 1) 71074 (pb-1) May 2005 Mar 2006 TOTAL 274008 (pb 1) 22892 (pb 1) 296900 (pb-1) Tab. V.1: DATA and MC 4~) As of 2000/04/11 0000 ~ :c :=. >- -"(j) 5000 c: 'E :s -I "C 400Q) -nl ... Ol Q) -£: 300 200 100 ~~?r PEP I( Delivered Luminosify: 553.4fJ/fb BaBar Recorded Luminosity: 531.43/fb BaBar Recorded Y(4s): 432.89/lb BaBar Recorded Y(3s) 30.23/fb BaBar Recorded Y(2s): 14.45/fb Off Peak Luminosity: 53.85/fb __ Delivered lumil1o...~ly __ AccOlded lum:no~ly __ ACWfded lllrrllnosilY Y(4S) __ AOC()(ded lumnoSlly Y(3,s) RecOlded lunllroSlly Y(2s) __ OUPeak Fig. V.1: Integrated LUlllillosity of DADAR Detector 50 2 Monte Carlo(T\1C) These simulations are very important to understand the detector response. Sim- ulation of signal properties help one to study signal efficiency, while simulation of non-signal helps the analyst to reject and reduce backgrouud significantly. After background properties can be well simulated, they can be used to make predictions of some specific background contributions. Some backgrounds in this analyis for examples are Bhabhas, quark-antiquark and non-signal T decays. To have better understanding of background, we generate significant number of Monte Carlo ntuples. Background estimations ean be grouped into six classes: uds(uu, dd, 88), bb,cc (these 3 can called qq continuum background), Bhabha, f.-L+p- and generic T+T-. The signal events are generated using KK2f generator[59], whieh simulates inital state radiation(ISR) and final state photon production more precisely than KORALB[60], while the generic T decays are simulated using TAUOLA[61] and radiation from final state leptons has been simulated with PHOTOS[62]. Exact process names, MC statistics used and cross sections for each process are given in Table V.2. Special note, pI! was not included in the simulation, so that Data and MC are not perfect match in invariant 1f-1fG mass plot around pI! peak region(1.6-1.8 GeV). The path of simulated particles through the detector in the presence of magnetic field, their interaction with the detector material, and the response signal of the active detector. GEANT4 provides tools to construct the detector geometry, simulate the interactions and decays of each particle species and to display detector components, particle trajectories and track hits. Sample name MC Process name (J (nb) Nsample (106 ) LMC£Oa.ta TT e+e- ----;. T+T-(KK2F) 0.89 253.6 0.96 uds e+e ----;. uu/dd/ss 2.09 604.3 0.97 cc e+e- ----;. cc 1.30 547.3 1.42 bb e+e- ----;. bb(half B+ BO and half BOBO) 1.05 950 3.05 Bhabha e+e- ----;. e+e 28 5.3 0.02 ~lp, e+e ----;. p,+P, 1.16 151.1 0.44 Tab. V.2: Generated Monte Carlo events for this analysis 0'""1 f--' 52 CHAPTER VI EVENT PRESELECTION We will study the spectral function that we get from T- ---t 1f-1foz.JT decays using 300 fb -1 data recorded on the BABAR detector. The analysis was done using 1- 3 Topology, which means there is 1 track in signal(T-- ---t 1f-1fovT ) hemisphere and 3 tracks on the other hemisphere in every event. To do the analysis effectively, we need to remove background as much possible and it can be done in 2 steps: preselection(mainly to remove non-T events, discussed in this chapter) and event selection(mainly to remove non-signal events, next chapter). The main goal of preselection is reduce the size of the data significantly from unwanted events. After preselection, preselected events will be saved in "ntuples" (organized package data). 1 nO Candidate Preselection nO decays to 2 photons almost 100%, and we only need 11f0, so that we can remove all events which have more than 4 photons in 1 track hemisphere. Then, every pair of energy deposits in the ElVIe, which are isolated from any charged tracks, is considered as nO candidate if both the energy deposits exceed 100 1VleV and the associated invariant mass of the pair is between 90 MeV/ c2 and 160 1\leV/ c2 . 53 2 Charged Candidate Preselection Tracks are found independently in the two tracking devices, the silicon vertex de- teetor and the drift chamber; different algorithms are used in each. The silicon, vertex detector algorithm first combines r - ¢ and z hits in the same silicon wafer to form space points, and then does an exhaustive search for good helical tracks, requiring hits in at least four out of the five layers of silicon. The analysis is started by selecting events with a 1-3 topology and rejecting most of the high multiplicity qq and low multiplicit.y QED backgrounds. The TaulN skim is used in event selection. The crit.eria for the TaulN selection are described in [58]. The further preselection requirements are listed below. Efficiencies for ea.ch cut are shown in Table VI.I. The preselection requirements are listed below. The tag event store (nano-Ievel) cuts are applied for convenience to reduce the size of data sample and remove back- ground l . • The following cuts are applied to speed up the processing of data: - Event has either L30utDch or L30utEmc trigger bit set - Event has BGFMultiHadron filter bit set. BGFMultiHadron is a special filter that requires an event to have number of tracks bigger than 2 and R2 is bigger than 0.92. R2 is the ratio of the second and zeroth Fox-Wolfram moments. Its value ranges from (0, I). This quantity is indicative of the collimation (jettiness) of an event topology (closer to I); values of R2 closer to 0 indicate a more spherical event. The Fox \iVolfram moment is defined in [57]. IThe nano information derived from the OEP is stored separately from the much larger fully reconstructed events, and as such cuts applied at the nano level are much more efficient in terms of computing resources. 54 - Event has TaulN tag bit set. The TaulN skim was designed for a common use by the Tau Analysis Working Group at BABAR. The skim is designed to select T-pair events dassied as I-N(N2:.:3) topology. The events are required to have more than 2 tracks but less than 11 tracks • Exactly 4 'good tracks' are required in the event. For this analysis we select good tracks from the GoodTracksVeryLoose(see Appendix B) list of the micro level. The tracks are required in addition to point to the default primary vertex (docaXY < 1 em, docaZ < 5 em) and have a momentum in the range PT > 0.1 GeVIe, P < 10 GeVIe in the Lab frame2 • The tracks identified as a part of a converted photon candidate (found in gammaConversionDefault list) are not counted as good tracks. No attempt has been made to reconstruct J(s decays. • The event is divided on two hemispheres using the plane perpendicular to the thrust of the event. The sign of scalar product of the given track momentuIll with thrust direction determines which hemisphere this track belongs to. The thrust is defined by (Vr.1) where n is a unit vector. By denition, the thrust axis is chosen to minimize the sum of transverse momenta of all particles in an event, where momenta is taken with respect to this axis. The thrust axis of the event is calculated using charged and neutral (with energy greater than 50 MeV) particle candidates in the center-of-mass frame (eM). One 2The Lab frame is the rest frame of the detector, as opposed to the rest frame of the e+e··· collisions. 55 hemisphere must have exactly one good track, while other 3 tracks must belong to the second hemisphere. Each hemisphere must have total charge either -1 or +1. The total charge of the good tracks is equal to O. This defines a Confirmed topology. • 0.8 :::; Thrust:::; 0.985. Thrust I?agnitude varies from 0.5 for isotropic events to 1.0 for back to back events. Since e+e- ---+ qq events are more isotropic than e+e- ---+ T+T- events, one can differentiate T events from gq events. Bhabha events have Thrust about 1, and this upper cut is effective to remove Bhabhas. \Vhile the lower cut is effective to remove qq-background events. • Number of clusters:::; 4 in one track hemisphere We select photon candidates from CalorNeutral list [63], which are single EMC bumps not matched with any track and have lateral moment < 0.8 and energy> 100 MeV. Vve reject all events which have more than 4 clusters in one track hemisphere. We select good neutrals from CalorNeutrals, which are single El\lC bumps not matched with any track. • 0.09 < M 1r 0 < 0.16 GeV We recontruct KO from 2 photon candidates, we pair all cluster to reconstruct all posiible KO, we save only events with at least 1Ko whose mass 0.(l9 < ~A11ro < 0.16 GeV. Cuts are applied sequentially and quoted in the table. The trigger cut means DCB or EMC trigger standard cuts(technically, one can say L30utDch or L30utEmc tagbit is set). I T Generic I uds I CC I EO EO I E+ E- I Bhabha I DATA Trigger 84.45 95.46 98.89 99.74 99.76 20.08 100.00 Passed BGFMultiHadron or BGFTau 99.73 99;25 99.38 99.45 99.61 2.24 98.84 Total Charge = 0 90.10 54.86 46.22 35.69 35.89 83.93 60.21 Confirmed 1-3 Topology 76.75 60.94 55.89 52.54 20.45 32.98 61.49 0.8 < ThTust < 0.995 98.25 79.87 70.51 20.80 4.70 4.84 73.54 nCluster <= 4 98.02 70.83 57.12 70.77 3.01 56.80 87.66 Tab. VLl: Event PreSelection Table After TaulN. Preselection efficiencies in percent for Data and Monte Carlo background samples. Cuts are applied sequentially and the marginal efficiencies are quoted CJ1 C) 57 (f) 400 X103 ---- ~Q) > 350 cr.:J •300 250 200 150 100 50 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 Thrust Magnitude Fig. VI.l: 'Thrust ~'1agllitllde of lvIC and Ddta, all preselection cuts have been a.pplied, except thrust Jll<-lgnitude Cllt. All IvIC samples arc nonnaliy,cd to Data Lu- minosity. if! ..... c: ~ 3000 IJJ 2500 2000 1500 1000 500 x103 • DATA r I Signal r t=:J Tau Bgr r UDS I-- [=:=J CCBARr r ~ BBBAR r r - I-- - r - r - r - r - I-- - r - r ... - r - r- - I-- - r - r- - r- - r- - I-- - r- - r- I - r- - r- - - I-- - r- - r- - r- - '- 1-- - 1 2 3 456 Nunlber of photon(s) Fig. VI.2: The number of photon in signal lWlllisplwlC of MC and Data Distrihu- tion, all sclec:tioll cuts have been applied. (~x('ep1' 11\1l111)(~r of cluster (:111'. All J'dC arc nonna.1iy.ed to Data. Ll11I1inosity. 59 CHAPTER VII EVENT SELECTION In this analysis, the T- ---+ 1["-1["°VT decay is called signal(see Figure VII. 1) and all other decays are called as background. To be able to understand the signal, one should try to remove background as much as possible. The events that survived event selection are called selected events. 1 Event Reconstruction A pair of energy deposits in the EJVIC, which are isolated from any charged tracks, is considered as 1["0 candidate if both the energy deposits exceed 100 MeV and the associated invariant mass of the pair is between 115 MeVjc2 and 155 MeVjc2 with EnD bigger than 450 MeV(LAB). The p meson candidates are made by combining a selected 1["0 candidate with a charged track on the signal side. ~ ~ 2 Selection Process After preselection cuts applied to Data and IVIonte Carlo, all events are saved in ntuples, occupy about 100 GB and from J\;lonte Carlo study we estimate that we still have significant number of backgrounds. To increase the purity, we apply event selection cut 3 charged tracks + neutrino 't+ 60 Fig. VII.l: Simplified picture of event reconstruction in this analysis. • All tracks are required to fall in the fiducial range of detectors that we under- stand well. In this analysis we require -0.82 S Cos Otrack ::; 0.98 is the polar angle of the charged track candidates. • Figure VII.6 shows the polar angle of missing momentum. In this analysis, the polar angle of missing momentum in the LAB frame is required to be -0.82 ::; Cos Omiss ::; 0.92. • From Figure VI. 2 we can see that most of our signal has 2 photons on one track hemisphere, so that we eequire only 2 photons on signal hemisphere, and both photons have energy bigger than 100 JVleV in the LAB frame. From LorentzVector, we reconstruct 7[0 and asking 7[0 mass fall in the window 11.5 TvleV to 155 MeV. Using these requirements we reduce tau backgrounds significantly, especially from T _7[-7[07[0. (j] • In Figure V1.1 we can sec that we reclllce non-tau hackground if W(~ llSC cvents which have 0.0 :::; Thmst :::; (U)BG, the 11pper thms1. C11t effective to relllO\f(' Dha.bhaswhile the lower thrns1. cut effective to redllce hadronic ],ackgrollll<1. • \1I/e reject 7fo v"hieh ]HlVe energy below ackgrollnd fmther, we reqllirc that the toted lllass 01J :~ prong side is less than l.ts GeV. rr;- Momentum (GeV) 300 X103 250 7 10 GeV Fig. VII.2: The 7f- r-dollH~ntUJn (in GeV Ic) of tlJe SigW1J 7f--rr0 , ill the LAD frame All Montc Carlo s,unples me gelHTated uSillg SPB a.nd nonualized to collectecJ Data. LUlllinosity. DATA (l,nd i\Iontc Carlo show good agreclllcllt, All CllI,s have been applied, cxcept 7f- l'donJClltulll Cllt. Thl' table of event scllx:t,ioll dhciency(sce Tethlc VII.I) JS in scqllentia] I)Crccllt- ag(~(%) of efficiency after cadI clIt. 62 Phot n Candidate Energy 3 "1 800 pX+1~0r-r-.-.--r-..-r--r-.---,-.--.--,-,----,--.----.--.----.-.-.--r-l.;--"""i')A:TA-----~ 1600 1400 1200 1000 400 200 3 4 5 6 7 8 GeV Fig. VII.3: The roy Candida.te Energy (in GeV) on 1'.1)(' signal side, in tIl<' LAD fra.me All Me sa.mpl(~s arc nonnillizecl to the <:olkcted Data LllIninosity. DATA alld f\'IC show good agrecmcllt, all cuts lwve been ct] )plicd, ('xccpt, )' energy cut. In addition; by choosing 1-3 Topology, we get much smaller Bha1>llHs .. umpail'; t\VO- photon ba.ckgrounds comrMl'ed to 1-.l Topology. \V(~ would like to emphasize that. the cha.nce that Dlmbha and I\fupctir mimic the dm.lllwl is vel')' small, due t.o t]w fact that DllHbha; lllupair(rnostly they decay to 1-1 Topology) etnd two-photoll h;lcl<- ground have totally different t.opology. In additioll; 1>y l'<'qniring exactly two photons in signal hemisphere would rna,kc Dlw.hhcL,lLll1pair ,wd t'vvo-photon contl'ilmt.ions very small, due t.o the fact that thcse hackgrol1lj(]s produce two photons on I-track bcmi- spher very nerdy. From the previous study done in T -----. III [Gli] and T -) lhh[G51, which used the scune prcslection; frolll the tables in those analysis .. we can aSSlllnc that, the contribution froIll Dlwbha; lllll-pair al'<~ negligible'. 9 10 GeV 876 MonteCarlo DATA Signal Tau Bgr UDS c=J CCSAR SBBAR , , , I I , , I I ' I , , I I , , , 60 40 20 80 100 nO Momentum LAB (GeV) I x103 Fig. VII.4: The 1f0 "Momentum (in GcVIc) of the signal ?T-1fo, in UJ(' LAB frame. All j\tfC samples a,re nonnali~cd to thc collected Data Luminosity. DA1'A and l\lC show good agrc(mwnt, all cut::; have hecn applied, except ?T- 1'vlolllcnt11ln cut. TeO Mass I 3 200 F-'x,..".1-"qc---.'-'-'----'-I----.------.-----o-----.----.--.-----,---.--.--.--.--r--'--'--'-1-----0,-.---,---,---.---.--.---.--.-..,..---,--,---~ 180 160 140 120 100 80 60- 40 20~.........-- 0.16 GeV Fig. VII.5: The 1fo invariant mas::; (in GeV) of the signal ?T-1fo. All ]\IC si\Jnplcs are nonnalized to the collected Data LUIllinosiLy. DATA and l\lC show good c\grcclllcn1, all cuts have hecn applied, except ?To Mass cut. G4 Cosine of Polar Angle Missing Momentum ( Cos El miss ) 0.8 1 Cos El miss 0.40.2-0-0.4 -0.2 DATA Signal Tau Sgr UDS ~ CCSAR c=::J BBBAR -0.8 -0.6-1 50 350 200 250 300 150 100 3 400 p-x+1 .,.,0"--,-,--,,,--,-,--,,,--,-,--,,,--,-,--,,,----.--,--,-,----.---,---,-,----.---,---,-,----.---,---,-,----,---,---,-----.-_, Cosine of Polar Angle Missing Momentum ( Cos El miss ) -1 -0.95 -0.9 -0.85 -0.8 -0.75 -0.7 Cos Elmiss Fig VII.6: Polar Angl(' of :r'\lissing l\'IolllCntmn amiss (ra,d) of thc ('\!CuI" iu the LAD frame. All MC samples are normalized to thc collC'cted Data Lmnillosity. DATA and I\/IC show good agrecmcnt; All cnt8 have heen applied. cxccpt polar cUlglc of missing IllOllleutum amiss cnt. The lower plot is the zoom for high polar angle regioll; where cut is applied to rcdncc the contributions from llOll-signaJ cvents. G'r:.J osine of Polar Angle of rc- ( Cos err - ) 3 1 20 rX~1-,,0T-----,----,---,--,----.---,--,--.-.----r----'---'--'----'---'-----'--r-r-,-,----.---,--,--,---r-r----,---,--,----.---,----,,---,---,----,-----,----, 100 80 60 40 20 1 -1 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 Cos err - Cosin of Polar Angle of n;- ( Cos e1C ) I 12000 ,----. 10000 8000 ! 6000 4000 - 2000 0_1 -0.95 -0.9 -0.85 -0.8 -0.75 Cos err- Fig. VII.7: The Polar Angle of 7f-- (rad) in the LAD frame. All [\Ie sa.lIlplcs an~ 1l0l1llalizccl to the collected D(1,ta LUlllinosit.y. DATA and }\·,[C Sl1O\\! good agreement, all cuts have been applied, except the polar a.ngle of 7f- cut. The lO'Ncl' plot is the zoom for high polar angle region, Cllts arc npplied to non-signal events. I Signal I T Bgr I UDS I CC I BOBo I B+B- I DATA Preselection 100.00 100.00 100.00 100.00 100.00 100.00 100.00 0.9 ~ Thrust ~ 0.985 88.58 89.08 47.08 26.16 4.11 4.12 67.40 -0.82 ~ Cos e miss ~ 0.92 68.42 62.94 65.06 56.73 49.15 54.12 66.88 -0.82 ~ Cos etrack ~ 0.98 93.12 78.21 92.98 93.32 92.57 94.62 41.83 Exactly 2 100-MeV clusters 65.94 19.36 23.81 15.95 26.74 21.38 44.97 115 ~ 1\1r,0 ~ 155 MeV 94.56 54.88 72.86 66.50 78.00 76.74 86.34 Er,o > 450 MeV 93.81 72.21 88.25 78.91 76.92 80.82 91.94 Mass 3 prong < 1.8 MeV 99.88 96.73 85.78 88.79 83.33 86.88 98.93 Expected Events 2183168 60164 42059 12518 108 98 2318974 Percentage(%) 95.00 2.62 1.84 0.54 0.00 0.00 Tab. VIL1: Event Selection Table in sequential percentage(%) of efficiency after each cut. MC is normalized to data luminosity 0) 0) 67 3 Final Event Sample Vve normalize all Monte Carlo to the Data Luminosity from RUN 1-5, using Bbk- Lumi(standard BABAR package to calculate luminosity), no additional luminosity correction applied. After passing event selection, there are 2318974 events of data and 2298565 ]VIC events(normalized to Data Luminosity) remain which dominated by signal events(2,183,168 events). \iVe define the efficiency(.s) as the the number of selected 7f--7fo events (N:;f:C~~d) d· 'd d b th b . t -d - ° t (7\Tsignal -) Th ffi' 1 t 1IVI eye num er genel a ,C 7f 7f even S l' gene7'ated . e e Clency po- can )e seen in Figure VIL10 Nsignal E = selected Nsignal ' generated (VIL1) The overall efficiency in this analysis is about 1.5 %, which understandable because we are using 1-3 Topology (only about 14% of T decays to 3 tracks). VVe define the purity(P) as the percentage of number of selected 7f-7fo events (N:;.re:~~d) divided by the total number of selected MC events (N~":z~cted) events(signal + backgrounds). Nsignal P = selected NAlC . selected (VIL2) Total number of events from MC background is very small (less than 5%). We have a high purity sample because about 95% signal events survive. 12.5 GeV Fig. VII.8: The plot of the n-no invariallt mass of Data(black dots) r)11d I'dC samples, all MOllte Carlo sampl(~s arc nonnalized to (btCl Illlninositv. The nwjor backgronnds arc the contributions from non sigml,] T and contilllllllll qq hackgrounds l\lC Dc),ckgnmncls mc simply suhtntctcd from final data sc\.lIlple, no rtdclitional cor- rection applied at this strtge. (j<) 10° - 105 ••• • • - • •• •• • •••104 .- •••• • -·0 • 103 • • • 102 ••• 10 ... 0.4 0.8 1.2 1.4 1.6 GeV Fig. VII.9: The plot of 7["-7["0 invariant lIlass aftc1' j\JC hackgn)\111ds arc subtracted hom Data. The dip about 1.5 GcV shows a destllletive illtcfcH'ncc betwccn p' alld p" . 0.0168 0.0166 0.0164 0.0162 0.016 0.0158 0.0156 ... 0.0154 o· • 0 .. .. ... .... ... .... ..... .... ...... ... ...... 1.8 GeV Fig. VII.lO: The dIiciency plot, as ddined by the number of selected 7["-7["0 events divided by the Illunher of gencratcd 71-7["0 events, plotted as a a bmctioll of 7f-IfO invariant mass. 70 CHAPTER VIII UNFOLDING The measured spectrum of a physical observable, like the invariant mass or the lepton energy, is distorted by detector effects. A comparison of the spectrum with theoretical predictions and with the spectra measured by other experiments, affected by different detector effects, is therefore difficult. Thus, the removal of the distortions to obtain the true, underlying physical spectrum is desirable. In order to extract the physical mass distribution (and hence the fully corrected partial width as a function of invariant 7r-1r° mass for the signal decay) it is necessary to unfold the measured spectrum from the effeCts of measurement distortion. The RooUnfHistoSvd package [70] software package contains routines which perform the relevant procedure, a description of which is contained in the following sections. The effects of finite resolution on an invariant mass distribution during the mea- surement process can be written as: (VIlLI) where x = Xl, ... , Xj is the binned true mass distribution to be determined and b = bl , ... , bi is the measured distribution. A = All, ... , A ij is the detector response matrix which can be produced by simulating the measurement process using NrC techniques. The matrix element Aij gives the probability that an event with a true 71 mass in bin j is reconstructed in bin i. If we generate the distribution and perform our detector simulation, every entry in a measured bin can be traced back to its origin, giving us a set of relations between the generated and measured distributions, as in Equation VIlLI. In the unfolding procedure, matrix A incorporates the efficiency and resolution matrix. Because the matrix A is usually singular, the direct inversion leads to unstable and therefore useless results. The following sections outline the steps in solving Equations VIlLI. The method, based the singulaT value decomposition of the response matrix A. 1 Singular Value Decomposition A Singular Value Decomposition (SVD) of a real m x n matrix A is its factorization of the form (VIIl.2) where U is an m x m orthogonal matrix, V is an n x n orthogonal matrix, while S is an m x n diagonal matrix (VIlL:)) (VIllA) (VIlL5) The quantities Si are called s'ingulaT values of the matrix A. and columns of U and V are called the left and right singulaT vectoTS. 72 The singular values contain very valuable information about the properties of the matrix. If, for example, A is itself orthogonal, all of its singular values are equal to 1. On the contrary, a degenate matrix will have at least one zero among its singular values. In fact the rank, the rank of a matrix is the number of its non-zero singular values. Once the matrix is decomposed into the form written is Equation VIlL2, its properties can be analyzed and it becomes very easy to manipulate. This technique is extremely useful for ill-defined linear systems with almost (or even exactly) degenerate matrices. Comprehensive description of SVD with many technical details can be found in [71] and [72] Once the matrix is decomposed into the form VIlL2, progress can be made. The factorization in this way means that its properties can be analyzed and calculation is made less difficult. 2 Unfolding Procedure \Ve study about the reconstruction of generated 7[-7[0 using Me. The inputs for Unfolding are Background-subtracted Data plot, 2D MC Truth-Reco matrix and ef- ficiency plot. Some useful plots are shown in Figure VIlLI (2 dimensional plot) and VIlL2 (3 dimensional plot to clarify 2 dimensional plot). The output of unfolding is the unfolded plot. At the end of unfolding procedure, the final result of unfolding of Background subtracted data is compared to the one without unfolding(see Figure VIllA). 73 I Rho Mass Truth xReeo I . . ...........................•..... : ,""'- . . ...~~~~.~ ; . 2.521.5 .' 2.5 1.5 ....- ..............., ..... . ' • • _ -. 104 • ·u.. ·· .. .........................~ . '. 1.6 0.4 1.4 1.2 > > I Rho Mass Truth xReeo I -iJl.8h=;=;:=;=;:=;=;=;=;::::;:::;~"--,,-,,---,-,,,--,-,-,-,--,,--,-,_ 105 Fig. VIILl: UufoJdillg IVlatrix ill 2D. The upper plot is the unfolding matrix [or fnlllVIC with 0.3 GeV < Ain-no < 2.8 GeV. The Im.ver plot is the Ullfolding matrix for lower mass region l\,fC with 0.:3 GeV < Af"'-'!r1J < .1.8 CeV. Efficiency is not included. J~~~8060- 4020o 0.5 x 120-····· 100 80 60- 40 20 120 100 80 60 40 20 I Rho Mass Truth xReeo I I Rho Mass Truth xReeo I Fig. VIII.2: Unfolding JVlatrix in 3D. The upper plot is the unfolding matrix in box style for full JVIC with 0.3 GeV < 1\1rr-/l" < 2.8 GeV. 'I'lw lower plot is tlle unfolding matrix in box style for lower nmss region TvIC witlt 0.3 GeV < Alrr - rro < 1.8 Ge\!. Efficiency is not included. 75 I Mr.'" (GeV) Reco from M" .. 0.3G-0.55 GeV True I I M•.r.' (GeV) Reco from M,,;/, 0.55-0.80 GeV True I 0.40.2o-0.2-0.4 450- 400C:- X'/ndf 7.1420+04/34 Prob 0 3501- Constant 4.4470+05 ± 652 300f- Mean 0.00806± 0.00002 Sigma 0.01961± 0.00002 2501- 2001- 1501- 1001- 50 F- J \"'L 0 X10- I f- x2/ndf 2.565e+04 /36 Prob 0 Constant 9.65e+04:t 311 Mea. O.002496± 0.000046 Sigma O,01976± 0.00004 - - I- - ~ \. -0.4 -0.2 0 0.2 0.4 20 40 60 80 100 -l/ndf 5304/35 Prob 0 Constant 3.4e+04± 163 Mean 0.004102± 0.000085 Sigma 0.02297 ± 0.00007 J l -U.4 -U.2 0 U.2 U.4o 5000 25000 20000 30000 35000 15000 10000 1 M... (GeV) Reco from Mr.;/' 1.05-1.30 GeV True I X2 / ndf 2.706e+04 J37 I- Prob 0 Constant 2.659e+05 ± 491 I- Mea. 0.001786± 0,000028 Sigma 0.02054 ± 0.00003 f- - f- - r- - l -U.4 -U.2 0 U.2 U.4 150 100 250 200 o 50 I Mr.'''' (GeV) Reco from Mr." 0.8G-l.05 GeV True 300 X10' Mr.,,' (GeV) Reco from M.... 1.30-1.55 GeV True M••, (GeV) Reco from M." 1.55-1.80 GeV True 4500 4000 3500 3000 2500 2000 1500 1000 500 o f- ~ x2 / ndf 553.1/28 f- 0Prob c- Constant 40S7± 55.8 Mea. 0.001484± 0.000248 Sigma 0.0242± 0.0002 - - c:- f- j t -0.4 -U.2 0 U.2 U.4 100 80 60 40 20 o ~ x2 / ndf 31.69/17 Prob 0.01645 Constant 111.5±8.2 Mean -0.003675 ± 0.001616 Sigma 0.02868± 0.00138 f- - f- - ~r1 .I""'n r) \. -U.4 -U.2 0 0.2 0.4 Fig. VIII.3: The Reconstruction I\·1ass - The True Mass and fit it using Gaussian. The as are the mean value of invariant mass of the specific truth bins 7G /lenDMass I 106 •••• I', 103 •, • " t. I " , • 102 "" •, ., •.. 10 i II I' .t I 1 I 0,4 0,6 0,8 1 1.2 1.4 1.6 Mass (GeV) Fig. VIllA: Comparison hetwcnl hac:kgrolllHl-subtrnct.cd DATA(hLlc:k) (Lnd Un- folded DATA(red) 77 CHAPTER IX FITTING RESULTS To obtain the important parameters in this analysis, a x2 fit using Gounaris-Sakurai function (see Section 2) is performed to the unfolded invariant 1T--1TO mass spectrum. The Gounaris-Sakurai function is used in this thesis, because it is used in many T experiments such as OPAL [6],CLEO[5], ALEPH[4] and Belle, to fit invariant 1T-1TO mass. The off-diagonal components of the covariance matrix of bin-by-bin invariant mass in this analysis are small(about 0.1%), and not included in X2 evaluation. The reason the smallness of off-diagonal components of the covariance matrix is because the bin size(25 MeV) is bigger than resolution(about 20 MeV). The fit utilizes a calculation software, RooFit[33]' with 10 free parameters, we obtain the result of Fitting parameters using Gounaris-Sakurai and their statistical errors. We found the value of X2 / d.o.f(degree of freedom) of default is around 48/50. The dip about 1.6 GeV in invariant 1T--1TO mass is predicted from destructive inter- ference of pI and pI! The value of 1F-rr1 2 at s = 0, is expected to be 1, and in this analysis we didn't fix the value 1F7r(s = 0)1 2 = 1. Using the parameter values in Table IX we can interpolate the value of IF-rr(0)12 and we get 1F7r(0) 12 = 1.008 ± 0.09, very close to unity. The 1F-rr(0)1 2 uncertainty is calculated by varying the input parameters that go into 1F7r(0)1 2 , using 7)) 1.4 1.6 Mass (GeV) 1.210.80.60.4 1 10 ]10tO Mass 106 =--------------------- Fig. IX.I: Fittillg to Ullfoldcc1 Da.ckgrOlllld Sl1 btractcd Data using GOlluaris Sakurai Function G&S Pmanl<'tcrs 1\11 p 774.4 ± 0.2 MeV fp 1499 ± 0.:3 iV[eV M' 12~m.~l ± 24./1 .I"lcV. p fp' 501.2 ± 12 l\lcV 1\11 p" W'::;2A ± U.!) MeV f " 24G.:3 ± j0.2 1\leVp /3 o.m.;t3 ± 0.012 ')' 0.05t3 ± o.oo~ Ipeniing Angle) 1 0000 ~:.... ----------------~- 30000 20000 40000 Fig;. X.G: The Cosillc of Openillg Angle ])('1"veen 2 pllOtollS of 11° ill LAD frame ann all selection cnts applied. Frolll top to hottom, thc plots arc ZOOlllCd. Top plot ranges from O.5-I., J'did plot ranges from 0.9.5-1 and Dottolll plot rallges from O.!J9G-l. l\dC is normalized to Data, Lnminosity. 92 5000 4000 3000 2000 1000 DATA MC -- After Carr ctian ~ "I, ,., I"" I"" I"" t" •• I"" I '~bJ 0.9955 0.996 0.9965 0.997 0.9975 0.998 0.9985 0.999 0.9995 Cos 'II (Opening Angle) C»-996 C»-9965 C»-997 Fig. X. 7: Thc opening angle of selected 2 pllOtons of nO (lC(;i-1.Y (LAD fnunc) after all selection cuts applied. Corn~cted j\:rc is MC aller photon efficicncy corrcction which calculat.ed using PWY sample. Default KG Eff Correction a - O"a, b - O"b a - O"a, b + O"b a+O"a,b-O"b a + O"a, b+ O"b M p(GeV) 0.7744 ± 0.0002 0.7745(0.0001) 0.7745(0.0001) 0.7745(0.0001) 0.7745(0.0001) 0.7745(-0.0001) fp(GeV) 0.1499 ± 0.0003 0.1493(-0.0006 ) 0.1494(-0.005) 0.1495(-0.0005) 0.1492(-0.0007) 0.1493(0.0006) M p'(GeV) 1.2983 ± 0.0024 1.2993(0.0010) 1.2992(0.0009) 1.2991(0.0008) 1.2995(0.0012) 1.2994(0.0011) fp'(GeV) 0.5012 ± 0.012 0.4990(-0.0022) 0.4999(-0.0013) 0.4996(-0.0016) 0.4985(-0.0027) 0.4988(-0.0024) M p"(GeV) 1.6524 ± 0.0068 1.6614(0.0090) 1.6610(0.0086) 1.6605(0.0081) 1.6623(0.0099) 1.6617(0.0093) fp"(GeV) 0.2453 ± 0.0362 0.2433(-0.0020) 0.2436(-0.0019) 0.2435(-0.0018) 0.2431(-0.0022) 0.2432(-0.0021) (3 0.088 ± 0.012 0.090(0.002) 0.090(0.002) 0.090(0.002) 0.090(0.002) 0.090(0.002) "( 0.058 ± 0.008 0.060(0.002) 0.060(0.002) 0.060(0.002) 0.060(0.002) 0.060(0.002) I IcPpl(degree) 118.3 ± 8.2 118.9(0.6) 118.8(0.5) 118.8(0.5) 118.9(0.6) 118.9(0.6) IcP"( I(degree) 58.9 ± 8.2 59.4(0..5) 59.4(0.5) 59.4(0.5) 59.4(0.5) 59.4(0.5) a~71"(10 10) 458.80 458.45 458.47 458.48 458.42 459.43 ~a~71" (10- 10 ) 0.35 0.33 0.32 0.38 0.37 Tab. X.2: Fitting parameters before and after linear KO efficiency correction. We also include the uncertainties of a(0"a) and b(O"b), by varying their 10" up and down. The number in parentheses are only statistical errors. '.D W 94 3 Resolution 3.1 Tracking Resolution One can use e+e- -7 /-L+ p-, to study charge track resolution. To estimate the tracking resolution uncertainty, we vary our 1/IC samples using the correction factors derived from e+e- -7 /-L+/-L-, study [75]. Taking the difference hetween initial and after resolution correction values as our systematic uncertainties, we found that only P(momentum) and B(theta) resolutions are quite significant sources of uncertainties, while ¢(phi) resolution contrihutes negligihle uncertainty. The result of this study is in Table X.3 and X.4. 3.2 Photon Resolution The control sample of e+ e- -7 {l+ {l-, ntuples are taken to study neutral resolution. This analysis takes the ratio of E~xpected(reconstructed from p+ and /-L- information) and E~etected variables(energy and angles). The measurement a.re done in the LAB frame for both Data and MonteCarlo samples. We divide the samples based on their Runs periods(Run 1- Run 5). Using this information we can get mean ratio(RMEAN ) and width(asmearing) of Data and MonteCarlo, which we define as: and EcccpectedD AT' A AiEAN( E~cteGtcdDATA ) RMEAN = 'YE"xpccte: The total mass Oll the :3 Prong sidc(tag side), ass1Hllillg tJ](~ :3 !.]'i\.cks arc pious after all cuts cl,ppJieel, x axis is ill GcV. i\JC is llol'llmlii,ed to Delta Lmnillositv. 4 Backgrounds 4.1 qCj Background OllC type of major backgroullels from gij is nels (jcts froIll 11, , (I.lld cOllservativcly we el,Ssigll 5% ll11certaillties frolll nOIl-tclll be\.ckg\'O\lnd. vVe add(rcducc) by this llmllhc]' the contributioll of lHls to the im'aria.llt 7f'-7fo mass and UWll I'd-it the illVMiaut 7f-7f0 mass using GOllllMis-Saklll'ai fUlH:tion. Tel.killg tll(' UlCtXilIllllll differcnce bdvveen of initial awl aJLer-colTection values as the 11lH;ertainty' The rcsult of this study IS nl Table X.G. 100 MonlcCnrlo • DATASignul TflU Bgf UOS c=J ceSAR BBBAR 3000 2500 2000 1500 1000 500 • 0 1.8 2 2.2 2.4 2.6 2.8 I Mass on 3 Prong ide I 4500r=---------------;::;:;:~::==.:========il Fig. X.9: Thc totallIlass on tIl<' 3 Prong side ,cbow tilll fllass, ass1Ullillg thc ~~ ITacks arc pions aftcr all Cllts applied, x axis is in CcV Defalllt +(}tuls -(}uds rv! p( GeV) 0.7744 ± O.OU02 O. 774G(O.0()()J) O. 77'J4( -O.lJOO l) I'p(G('V) ._-~-~1--O.140~) ± 0.0003 0.l49t5(-0. OOOl) 0.l500(O.OO()] ) I'd p:(G(~V) 1.29t5Ci (0.0003) 1.29t50(-(J.()OO3) -1.2083 ± 0.0024 rp'(GcV) 0.5012 ± 0.012 O. SO10(-0. O()()2) O. G0l4(0.00(2) M p"(GcV) l.G524 ± O.OO(ji) l.G52tS( (J.()004) l.GG20(-(J.()O(H) l'p" (GeV) 0.24G3 ± 0.0362 0.2538(-0. OOOG) O. 2548( O. ()()( lS ) (3 0.088 ± 0.012 O.087(-O.OOl) 0.089((J.()0l) ,. 0.()G8 ± O.OU8 O.OS7(-(l.(lOl) O.UG9(U.OOl) I 1.8eV I 2000r----------------r.M:;=o==.=n'o:;;:c==cor1c=o======11 • DATA Siunal Tau Bgr UDS c=:::J "CBAR £lBBAR 1.2 1.4 1.6 1.8 MTCTt° GeV Fig. X.lO: T'hc Signa,} 'if-'ifG invariant nmss of somc CVCll(,S \vhich havc total mass 011 3 prong side bigger than 1.8 GeV (Log Scale). 4.2 T Background T hackground is background constructcd frOnJ othcr t;tu decay chmlTlds, not hom 102 The overall estimated BF systematic uncertainty due to the errors in the branching fraction of the T background events surviving all the cuts is given by: (X.7) where Wi is the weight of the tau background mode i, that is the fraction of the selected events of mode i in the total number of selected events. BFtDG is the branching fraction and (J,fDG is the uncertainty of decay mode i from PDG 2007. In the table below, we quote some significant T backgrounds, the left column shows the T modes (charge conjugate is implied) and the right column is its contribution to the total T background (in percentage). The results of this study are in Tables [X.8], [X.9], [X.I0], [X. 1:L] ,[X. 11], [X.12], [X.13], [X. 14] and [X.15]. Decay Mode IContribution to T Background (o/c,) [wi(jl0-4 ) ;~;~~~ (%) T - -----+e - VTVe 1.71 4.91 0.34 T - -----+fJ, - VTV jt 0.24 0.69 0.34 T -----+ 1r - VT 2.83 8.12 0.99 T- -----+ 1r-1ru1r°V 55.22 158.48 1.53T T -----+K VT 0.22 0.63 3.35 T~ -----+ 21r-1r+vT 0.05 0.54 1.10 T- -----+ 21r-1r+1r°VT 0.,58 1.66 2.06 T- -----+ 1r-31r°vT 0.71 2.04 9.26 T- -----+ KOK-vT 0.31 0.89 10.39 T- -----+ K- K°1r°v 1.81 5.19 12.90T T- -----+ K-21r°vT 0.39 1.12 39.66 T -----+ 1r-K°1r°vT 6.00 17.22 4.49 T- -----+ fj1r-1r0 VT 0.08 0.23 13.79 T- -----+ K*-vT 28.77 82.57 3.88 Tab. X.7: After cuts applied, the T backgrounds are reduced significantly. This table shows the main T decays that contributes to T Backgrounds after all cuts applied. 0.18 0.09 0.16 0.08 0.11 0.07 0.11 It" -i e" Ve Vtl 0.06 0.1 0.05 11" -11t"V1 ! 0.08 0.01 \0.06- 0.030.01 0.01 .om 0.01 1.5 1.\ 0.5 1.5 1.5 0.08 0,07 0,06 0,06 0,01 0.03 r' 0,01 0,81 0,\ 0,5 1.5 15 O.1~ 0.09 0.11 0.08 0.07 0.1 It --'J n" nO KO vJ 0.06 Ir --1 K" -) K" nO V; I0.08 0.05 0.05 O.al 0.01 \, 0.81 0.5 1.5 1.5 °o~· 1.5 1.5 Fig. X.ll: The invariant 7f-'1I0 ]\'1,,1:--::--: hom major coui-rilmtms to T b,,"\.ckg;r011lld, ann itll cuts applied. The lJOrizoncltl linc is ill GeV II] t.his analysis, we study the 1ll]C8rtn,iJJ1:y by varying the specific T deci"\.Y ulOdc by ±lcr(Branching FrsctiolJ ulJccrtaiuty takcn from PDG 20(7). For ...\11 these lJJo(ks, 104 we refit the invariant 7[-7[0 mass spectrum using Gounaris-Sakurai function, all of the fitting results are written in the tables below. The maximum difference between + and - values is taken as the uncertainty of a parameter, in a conservative way. Another method to assign uncertainty is taking the average of the absolute values of both differences (from + and - uncertainty variation), but we didn't use because this method gives lower uncertainty. Default ..- +0-T-·· ---,;.e-·l-Jel/T - 0"T- -----+e-vr:1/T' M p(GeV) 0.7744 ± 0.0002 0.7744(0.0000) 0.7744(0.0000) fp (GeV) 0.1499 ± 0.0003 0.1499(0.0000) 0.1499(0.0000) M p'(GeV) 1.2983 ± 0.0244 1.2983(0.0000) 1.2983(0.0000) fp'(GeV) 0..5012(0.0000) -.;-0.5012 ± 0.012 0.5012(0.0000) M p'(GeV)' 1.6524 ± 0.0068 1.6524(0.0000) 1.6524(0.0000) fp" (GeV) 0.2453 ± 0.0362 0.2543(0.0000) 0.2543(0.0000) f3 0.088 ± 0.012 0.088(0.000) 0.088(0.000) I 0.058 ± 0.008 0.058(0.000) 0.058(0.000) 11>131 (degree) 118.3 ± 8.2 118.3(0.0) 118.3(0.0) 11>11 (degree) 58.9 ± 8.2 58.9(0.0) 58.9(0.0) a:7r (10- 1O ) 458.80 458.80 458.80 .6.a:7r (10- 1°) 0.00 ().OO ...- Tab. X.8: Parameters after T- ---+ e-vevT background va.riation. The number in parentheses are only statistical errors. This analysis study the possibility that missing 17[° from the T ---+ 7[-7[°7[°VT decays can fake our signals. Starting from equation: f(b, e) = 2be(1 ~ e) b = branching fraction of 301 e = efficiency of 7[0 2 because of 27[° involved in the process Default -+(}T-----,>1r-Vr -O"T---...+7r-Vr M p(GeV) 0.7744 ± 0.0002 0.7744(0.0000) 0.7744(0.0000) fp(GeV) 0.1499 ± 0.0003 0.1499 (0.0000) 0.1499(0.0000) M p'(GeV) 1.2983 ± 0.0024 1.2983(0.0000) 1.2983(0.0000) fp'(GeV) 0.5012 ± 0.012 0..5012(0.0000) 0.5012(0.0000) ]\II p" (GeV) 1.6524 ± 0.0068 1.6524(0.0000) 1.6524(0.0000) fp" (GeV) 0.2453 ± 0.0362 0.2543(0.0000) 0.2543(0.0000) f3 0.088 ± 0.012 0.088(0.000) 0.088(0.000) I 0.058 ± 0.008 0.058(0.000) 0.058(0.000) IcPf31 (degree) 118.3 ± 8.2 118.3(0.0) 118.3(0.0) IcP'Y I(degree) 58.9 ± 8.2 [18.9(0.0) 58.9(0.0) a~1r(10-1O) 458.80 458.79 458.81 ~a~1r(lO-lO) -0.01 0.01 Tab. X.9: Parameters after T- -----7 1r-VT background variation(lVIC lVIode 3). The number in parentheses are only statistical errors. Default +()T- ->al---+1r-1r°1r°Vr -()T- ->al ->1r-1r°1r°Vr M p(GeV) 0.7744 ± 0.0002 0.7744(0.0000) 0.7744(0.0000) fp(GeV) 0.1499 ± 0.0003 0.1499(0.0000) 0.1499(0.0000) M p'(GeV) 1.2983 ± 0.0024 1.2982(-O.00ei1) 1.2984(0.(001) fp'(GeV) 0.5012 ± 0.012 0.5011 (-0.0001) 0.5013(0.0001) M p" (GeV) 1.6524 ± 0.0068 1.6522(-0.00(2) 1.6526(0.0002) fp"(GeV) 0.2453 ± 0.0362 0.2542(-0.0(01) 0.2544(0.(001) f3 0.088 ± 0.012 0.088(0.000) 0.088(0.000) I 0.058 ± 0.008 0.058(0.000) 0.058(0.000) IcPf3\ (degree) 118.3 ± 8.2 118.3(0.0) 118.3(0.0) IcP'Y I(degree) 58.9 ± 8.2 58.9(0.0) 58.9(0.0) a: 1r (10- 10 ) 458.80 458.73 458.87 ~a~1r(10-1U) -0.07 0.07 Tab. X.IO: Parameters after T- -----7 al --} 1r-1r°1r°VT background variation. The number in parentheses are only statistical errors. 105 106 Default +2c1r0(1 - c1r0) -2c1r0(1 - c1r0) M p (GeV) 0.7744 ± 0.0002 0.7745(0.0001) 0.7743(-0.0001) fp (GeV) 0.1499 ± 0.0003 0.1498(-0.0001) 0.1500(0.0001) M p' (GeV) 1.2983 ± 0.0024 1.2989(0.0006) 1.2977(-0.0006) fp' (GeV) 0.5012 ± 0.012 0.5009(-0.0(03) 0.5015(0.0003) 1\1 p" (GeV) 1.6524 ± 0.0068 1.6530(0.0006) 1.6518(-0.0006) fp" (GeV) 0.2453 ± 0.0362 0.24.51 (-0'()002) 0.24.55(0.0002) (3 0.088 ± 0.012 0.088(0.000) 0.088(0.000) 'Y 0.058 ± 0.008 0.0.58(0.000) 0.0.58(0.000)I IrPfJ I(degree) 118.3 ± 8.2 118.2(-0.1) 118.4(0.1) IrP"( I(degree) .58.9 ± 8.2 58.9(0.0) 58.9(0.0) a:1r (10- 10 ) 4.58.80 458.66 4.58.94 6.a:1r(10 10) -0.14 0.14 Tab. X.11: \Ve vary the contribution of T-- ~ al ~ 1r-1r°1r°VT due to possibility that 1 missing 1r0 of a1 can be mis-identified as signal. The number in parentheses are only statistical errors. Default -'hTT -.....,]{- K°1r°ll, -CfT -.....,]{- ]{°1r°V, M p(GeV) 0.7744 ± 0.0002 0.7744(0.0000) 0.7744(0.0000) fp (GeV) 0.1499 ± o.oom~ 0.1499(0.0000) 0.1499(0.0000) M p'(GeV) 1.2983 ± 0.0024 1.2983(0.0000) 1.2983(0.0000) fp'(GeV) 0..5012 ± 0.012 0..5012(0.0000) 0.5012(0.0000) M p" (GeV) 1.6.524 ± 0.0068 1.6524(0.0000) 1.6524(0.0000) fp" (GeV) 0.2543(0.0000) -~0.24.53 ± 0.0362 0.2543(0.0000) (3 0.088 ± 0.012 0.088(0.000) 0.088(0.000) 'Y 0.058 ± 0.008 0.0.58(0.000) 0.058(0.000) IrPfJl(degree) 118.3 ± 8.2 118.3(0.0) 118.3(0.0) IrP, I(degree) .58.9 ± 8.2 .58.9(0.0) 58.9(0.0) a:1r (10- 10 ) 4.58.80 458.78 458.82 6.a:1r (10- 10 ) -0.02 0.02 Tab. X.12: Parameters after T- ~ K- K°1r°vT background variation. The number in parentheses are only statistical errors. 107 Default -~ +iJT- ->1r- KOy,,- -iJT -->1r- KOy,,- M p(GeV) 0.7744 ± 0.0002 0.7744(0.0000) 0.7744(0.0000) fp(GeV) 0.1499 ± 0.0003 0.1499(0.0000) Cl.1499(0.0000) M p'(GeV) 1.2983 ± Cl.0024 1.2983(0.00ClO) 1.2983(0.0000) fp'(GeV) 0.5012 ± 0.012 0..5012(Cl.0000) Cl.5012(0.0000) M p"(GeV) 1.6524 ± 0.0068 1.6524(0.0000) 1.6.524(0.0000) fp" (GeV) 0.2453 ± 0.0362 0.2543(0.0000) 0.2543(0.000Cl) f3 0.088 ± 0.012 Cl.088(0.000) 0.088(0.00Cl) I 0.058 ± 0.008 (1.058(0.000) 0.058( O.OClCl) 14>(31 (degree) 118.3 ± 8.2 118.3(0.0) 118.:3(0.Cl) 14>"11 (degree) 58.9 ± 8.2 58.9(0.0) 58.9(0.Cl) a:1r (10-1O) 458.80 458.84 458.76 6a~1r(10 10) Cl.Cl4 -0.04 Tab. X.13: Parameters after T-- ---7 7r- K°7r°vT background variation. The number in parentheses are only statistical errors. Default +iJT- ->K*-->K-1r0 y,,- -iJT -->K*---'[{-1r0//,,- I M p(GeV) 0.7744 ± 0.0002 0.7745(Cl.0001) 0.7743(-O.ClOO1) fp(GeV) 0.1499 ± 0.0003 0.1498(-0.(001) 0.1500(0.0001 ) 1.2990(0.0007) -~Iv1 p'(GeV) 1.2983 ± 0.OCl24 1.2976(-0.00(7) fp'(GeV) 0.5012 ± 0.012 0.5008(-0.0004) Cl.5016(0.0004) M p" (GeV) 1.6524 ± 0.0068 i.6535(0.0011) 1.6514(-0.0010) fp" (GeV) Cl.2453 ± 0.0362 0.2540(-0.0003) 0.2546(0.0003) f3 0.088 ± 0.012 0.087(-0.001) 0.089(0.001) I 0.058 ± 0.008 0.Cl57(-0.0(1) 0.059(0.001) 14>(3 I(degree) 118.3 ± 8.2 118.4(Cl.1) 118.2(-Cl.1) 14>"11 (degree) 58.9 ± 8.2 60.0(0.1) 58.8(-0.1) a:1r (10-1O) 458.80 458.64 458.96 6a:1r (10- 1O ) -0.16 0.16 Tab. X.14: Parameters after T~ ---7 K*- ---7 K-7r°vT background variation. The number in parentheses are only statistical errors. 108 Default 2etrack(1 - etrack) correction 1,1 p(GeV) 0.7744 ± 0.0002 0.7744(0.0000) rp(GeV) 0.1499 ± 0.0003 0.1499(0.00(0) 1,1 p'(GeV) 1.2983 ± 0.0024 1.2983(0.0000) rp'(GeV) 0.5012 ± 0.012 0.5012(0.0000) 1\1 p" (GeV) 1.6524 ± 0.0068 1.6524(0.0000) rp" (GeV) 0.2453 ± 0.0362 0.2553(0.0000) f3 0.088 ± 0.012 0.088(0.000) 'Y 0.058 ± 0.008 0.058(0.000) I¢f3[ (degree) 118.3 ± 8.2 118.3(0.0) I¢'Y I(degree) 58.9 ± 8.2 58.9(0.0) a:1C (10- 10 ) 458.80 458.80 L}.a:1C (10- 10) 0.00 Tab. X.15: We also vary the track efficiency correction to T~ --7 K*- -, K~7r°VT background. The number in parentheses are only statistical errors. If ae = 3% and e = 0.60 and using the equation below: ( df(b' e)) ~ 2(0.6) - 1 3o/c ~ 2.5 lJ'( f(b, e) 0.6(1 _ 0.6) (J o. (X.8) We can vary the contribution of a1 by 2.5% up and down and takes the biggest difference from the default values as our systematic uncertainty.The result of this study is in Table 26. Vie also check the shape of reconstructed T- --7 7r-7r°7r°VT to check whether Mon- teCarlo can simulate Data. Using the same selection procedures we can plot both Data and Me. From the plot in X.12, we see that there is no significance difference 3000 2500 2000 1500 1000 500 o~~~======-~~!!!!!!!II ........."""~0,5 1 1,,5 2 2,5 GeV Fig. X.12: The invariant 7f-7fo7fo mass, all I\lCs all11OUllalil':cd to Data Llllninosit..v. \Ne see that there is 110 significance dif-fcn:llce l)('t\v('('11 Dn,l,a and MC ill sirnulati11g T- ~ 1["--7fo7fol/y 110 5 Other Systematic 5.1 Bin Size of 7f-7fo Invariant Mass The Bin Size of 7f-7fo invariant mass may change the extracted values. This analysis studies the uncertainty that comes from bin Size of 7f-7fo invariant mass, by varying its size to 5, 10, 50 MeV. This analysis takes the biggest difference from default(25 MeV) values as the systematic uncertainty of bin size. This analysis assign 0.3. 10-10 as the bin size systematic uncertainty of a~7r. The result of this study is in Table X.16. 5.2 Unfolding The unfolding procedure may change the shape 7f-7fo invariant mass spectrum, so that we need to understand the effect of unfolding. Unfolding procedure is discussed in Chapter VIn page 70. One way to assign unfolding systematic uncertainties con- servatively is by comparing the extracted values with and without unfolding. This analysis extracts the results directly without unfolding and takes the difference be- tween unfolding and without unfolding values as the unfolding systematic uncertainty. Without unfolding we can perform unbinned analysis and compare its results to de- fault values. The result of this study is in Table X.17. Default 5 MeV Bin 10 MeV Bin 50 MeV Bin M p(GeV) 0.7744 ± 0.0002 0.7746(0.0002) 0.7744(0.0000) 0.7743(-0.0001) fp(GeV) 0.1499 ± 0.0003 0.1496(-0.0003) 0.1497(-0.0002) 0.1502(0.0003) M p'(GeV) 1.2983 ± 0.0024 1.2988(0.0005) 1.2985(0.0002) 1.2980(-0.0003) fp'(GeV) 0.5012 ± 0.012 0.5003(-0.0009) 0.5008(-0.0004) 0.5017(0.0005) M p"(GeV) 1.6524 ± 0.0068 1.6535(0.0011) 1.6529(0.0005) 1.6531(0.0007) fp" (GeV) 0.2453 ± 0.0362 0.2523(-0.0020) 0.2528(-0.0015) 0.2564(0.0021) ,0 0.088 ± 0.012 0.090(0.002) 0.089(0.001) 0.086(-0.002) I 0.058 ± 0.008 0.061(0.003) 0.060(0.002) 0.055(-0.003) I 10p[(degree) 118.3 ± 8.2 118.6(0.3) 118.5(0.2) 118.0(-0.3) i 1 0"! I ( degree) 58.9 ± 8.2 59.1(0.2) 59.0(0.1) 58.7(-0.2) aZ1f (10-1O) I 458.80 458.51 45~ 459. 04 1i ,6,aZ1f (10- 10 ) -0.29 -0.14 0.24 Tab. X.16: GS Fitting Parameters with 5, 10 and 50 MeV Bins. The number inparentheses are only statistical errors. ....... ....... ....... Default Without Unfolding Unbinned and Without Unfolding M p(GeV) 0.7744 ± 0.0002 0.7740(-0.0004) 0.7747(0.0003) fp(GeV) 0.1499 ± 0.0003 0.1501(0.0002) 0.1496(-0.0003) 1\1 p~(GeV) 1.2983 ± 0.0024 1.2995(0.0012) 1.2991(0.0008) fp'(GeV) 0.5012 ± 0.012 0.5008(-0.0004) 0.5004(-0.0010) M p"(GeV) 1.6524 ± 0.0068 1.6497(-0.0027) 1.6540(0.0016) fp" (GeV) 0.2453 ± 0.0362 0.2602(0.0149) I 0.2519(-0.0034) (3 0.088 ± 0.012 0.086(-0.002) 0.090(0.002) r 0.058 ± 0.008 0.056(-0.002) 0.062(0.004) I¢f31 (degree) 118.3 ± 8.2 118.6(0.3) 118.8(0.5) I¢-y I(degree) 58.9 ± 8.2 58.7(-0.2) 59.1(0.2) aZ1r (10- 1O ) 458.80 459.04 458.44 .6.a:1r (10- 1O ) 0.24 -0.36 Tab. X.17: Fitting parameters with and without unfolding. "\iVe also compare it with unbinned fitting. The number in parentheses are statistical errors. I----' I----' tv 113 5.3 Stability Over Runs Period The stability over Runs period is very important. The Data and MonteCarlo consist of data from 5 RUNs period. All Data and 110nteCarlo are classified into their Run periods, then we recalculate the Branching fraction of the T- -----+ 7r-7r°VT for each different RUN using the information of efficiency, number of selected events and number of generated events. Run 1 has very low number of events and it contributes the biggest deviation from default values. After careful calculation, this analysis find that the variations between all RUNs are within their statistical uncertainties. The result of this study is in Table X.lS. In addition to stability of branching for different Runs, we also refit the invariant 7r-7r0 for 5 different Runs. using Gounaris-Sakurai function and the same procedure. At the end of fitting, the analyst extract the value of a;1r. Taking the biggest differ- ences between default(all Runs) values and single Run values. Run 1 has the smallest number of events, so that the parameter values from Run 1 are slightly different from the default of all-Runs values. The result of this study is in Table X.19. I RUN Begin I End I 1 25.33% Feb 2000 Oct 2000 2 25.42% Feb 2001 Jun 2002 3 25.35% Dec 2002 JUl1 2003 4 25.42% Sep 2003 Ju12004 5 25.39% May 2005 Apr 2006 I TOTAL I 25.40% I Feb 200JD Apr 2006 I . Tab. X.lS: The Branching Fraction T- -----+ 7r-7r°VT for 5 different Runs. ALL RUNS Run 1 Run 2 Run 3 Run 4 Run 5 M p(GeV) 0.7744 ± 0.0002 0.7743(-0.0001) 0.7743(-0.0001) 0.7745(0.0001) 0.7744(0.0000) 0.7745(0.0001) fp(GeV) 0.1499 ± 0.0003 0.1497(-0.0002) 0.1500(0.0001) 0.1501(0.0002) 0.1498(-0.0001) 0.1499 (0.0000) M p'(GeV) 1.2983 ± 0.0024 1.2980(-0.0003) 1.2981 (-0.0002) 1.2982(-0.0001) 1.2984(0.0001) 1.2984(0.0001) fp'(GeV) 0.5012 ± 0.012 0.5008(-0.0004) 0.5009(-0.0003) 0.5013(0.0001) 0.5013(0.0001) 0.5012(0.0000) M p"(GeV) 1.6524 ± 0.0068 1.6532(0.0008) 1.6529(0.0005) 1.6531(0.0007) 1.6522(-0.0002) 1.6521(-0.0003) fp" (GeV) 0.2453 ± 0.0362 0.2562(0.0009) 0.2548(-0.0005) 0.2564(0.0011) 0.2452(-0.0001) 0.2454(0.0001) /3 0.088 ± 0.012 0.084(-0.004) 0.085(-0.003) 0.086(-0.002) 0.089(0.001) 0.089(0.001 ) "y 0.058 ± 0.008 O. 056(-0.002) 0.057(-0.001) 0.055(-0.003) 0.060(0.002) 0.058(0.000) 1. 115 6 Comparison between GS and KS Fitting Besides the default of fitting function, Gounaris-Sakurai, there is another fitting function, Kuhn-SantaMaria that has been used by many analysts to study spectral function of T- -----+ 7[-7[°I/T' We refit the spectrum using the same procedure, instead of using the default(GS), we fit using the Kuhn-SantaMaria fitting function. We take the difference between the results of two fitting as our systematic uncertainties. The results can be seen in Table X.20. Gounaris-Sakurai Kuhn-SantaJ\i1aria M p(GeV) 0.7744 ± 0.0002 0.7740± 0.0002 fp(GeV) 0.1499 ± 0.0003 0.1494± 0.0003 --- M p'(GeV) 1.2983 ± 0.0024 1.2998± 0.0026 fp'(GeV) - 0.5012 ± 0.0120 0.5105 ± 0.01~~2 M p"(GeV) 1.6524 ± 0.0068 1.6606 ± 0.0070 fp" (GeV) 0.2453 ± 0.0362 0.2480 ± 0.0356 ...__.__.- (3 0.088 ± 0.012 0.090 ± 0.015 r 0.058 ± 0.008 0.059 ± 0.009 I¢,el (degree) 118.3 ± 8.2 125.5 ± 11.5 I¢~f I(degree) 58.9 ± 8.2 63.4 ± 7.5Ia1r1f (lO-lO) E 458.8(E_ 458.56 £a;1r(lO 10) . -0.24 Tab. X.20: The errors are only statistical and we find that the fitting parameters for both KS and GS models are consistent within the statistical errrors. 7 Statistical Uncertainty This analysis asseses the overall statistical uncertainty by generating a large number of G&S parameter sets, with the parameter determined randomly about the central values returned by our nominal fit, assuming Gaussian uncertainties. This analysis determines a;1r separately for each parameter set. The r.m.s. of the distribution of values was found to be 0.4 x 10-10 . ~a1m ~J\;lp ~rp ~J\;lpl ~rpl ~J\;lpll ~rpll ~f3 ~r ~1¢,61 ~I¢'YI/-L 10-10 (GeV) (GeV) (GeV) (GeV) (GeV) (GeV) (deg) (deg) T- ~ e-vevT 0.00 0.00001 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 T- ~ 1I-V T 0.01 0.00002 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 T ~ a1 ~ 1T 1T01l0VT 0.07 0.00004 0.0000 0.0001 0.0001 0.0002 0.0001 0.000 0.000 0.0 0.0 T- ~ al ~ 1T-7iO"Cl v ,,(m,i,s - id) 0.14 0.00009 0.001 0.0006 0.0003 0.0006 0.0002 0.000 0.000 0.1 0.0 T- ~ K- K01l0V T 0.02 0.00003 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 T ~ 11- K01l0VT 0.04 0.00004 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 T- ~ K*'--- ~ !{---:1TOV T 0.16 0.00012 0.0001 0.0007 0.0004 0.0010 0.0003 0.001 0.001 0.1 0.1 uds bgr 0.23 0.00014 0.0001 0.0003 0.0002 0.0004 0.0005 0.001 0.001 0.2 0.1 trk eff 0.18 0.00012 0.0001 0.0002 0.0003 0.0003 0.0002 0.000 0.001 0.1 0.1 etrack smearing 0.07 0.00004 0.0001 0.0001 0.0001 0.0002 0.0002 ' 0.001 0.001 0.2 0.1 Ptrack smearing 0.18 0.00019 0.0002 0.0003 0.0002 0.0004 0.0005 0.001 0.001 0.2 0.1 E'Y smearing 0.46 0.00036 0.0008 0.0016 0.0050 0.0102 0.0039 0.002 0.002 0.7 0.6 e'Y smearing 0.15 0.00016 0.0004 0.0008 0.0006 0.0060 0.0019 0.001 0.001 0.5 Cl.6 ¢'Y smearing 0.08 0.00006 0.0001 0.0002 0.0003 0.0005 0.0005 0.001 0.001 0.3 0.5 11° efficiency 0.35 0.00003 0.0001 0.0002 0.0009 0,()009 0.0002 0.000 0.000 0.1 0.0 IVIodel dependencies 0.24 0.00040 0.0005 0.0015 0.0093 0.0082 0.0027 0.002 0.001 7.2 4.5 Bin Size 0.29 0.00022 0.0003 0.0005 0.0009 0.0011 0.0020 0.002 0.003 0.3 0.2 Different Run 0.11 0.00008 0.0002 0.0003 0.0004 0.0008 0.0011 0.004 0.002 0.3 0.4 Total Systematic 0.83 0.00069 0.0013 0.0029 0.0110 0.0176 0.0061 0.005 0.005 7.3 4.7 Statistical 0.40 0.00020 0.0003 0.0024 0.0120 0.0068 0.0362 0.012 0.008 8.2 8.2 Total Uncertainties 0.92 0.00072 0.0013 0.0038 0.0163 0.0189 0.0367 0.013 0.009 11.0 9..5 PDG 2007 0.775.5 0.1494 1.46.50 0.4000 1.7200 0.2500 ~ PDG 2007 0.0003 0.0010 0.0025 0.0060 0.0200 0.1000 Tab. X.21: Summary of fitting parameters and their experimental uncertainties f-' f-' OJ .6.. 7f7f .6..lv1p .6..fp .6..A1p l .6..fpi .6..Mp l! .6..fpI! .6../3 .6..,' .6.. 1¢f3 I .6.. I¢-r Iall 10-10 (GeV) (GeV) (GeV) (GeV) (GeV) (GeV) (deg) (deg) Background 0.32 0.00022 0.0002 0.0010 0.0005 0.0012 0.0006 0.001 0.001 0.2 0.1 Track Reconstruction 0.26 0.00023 0.0002 0.0004 0.0004 0.0005 0.0006 0.001 0.002 0.3 0.2 7[0 Reconstruction 0.60 0.00040 0.0009 0.0018 0.0051 0.0119 0.0044 0.002 0.002 0.9 1.0 Fitting Procedure 0.38 0.00046 0.0006 0.0016 0.0093 0.0083 0.0034 0.003 0.003 7.2 4.5 Statistical 0.40 0.00020 0.0003 0.0024 0.0120 0.0068 0.0362 0.012 0.008 8.2 8.2 Total Uncertainties 0.92 0.00072 0.0013 0.0038 0.0163 0.0189 0.0367 0.013 0.009 11.0 9.5 Tab. X.22: Final fitting parameters and their experimental uncertainties f-' f-' -J 118 CHAPTER XI CONCLUSION Using the BABAR Detector, we have studied the physics of hadronic T ----+ 7f-7fOJ/T decays. Hadronic T decays provide one of the most powerful testing grounds for QeD and this situation results from a number of favorable conditions: • T leptons are copiously produced in pairs at e+e- colliders, leading to simple event topologies with small number of backgrounds. The purity in this analysis about 95%, the percentage of backgrounds after all selection cuts is about 5%. • The experimental study of T decays could be done with large data samples and this analysis used about 250 millions T pairs. The T decay rates into hadrons are expressed through spectral functions of differ- ent final states. The spectral functions are the basic ingredients to the theoretical description of these decays, since they represent the probability to produce a given hadronic system from the vacuum, as a function of its invariant mass. From the T- ----+ 7f-7fOVT decays in BABAR Detector, we can measure p, pi and pI! resonance parameters an<;l extract the value of a;7r. The results of this analysis are comparable with other experiments and due to higher statistics the a;7r value has lower uncertainties compared to other experiments. 119 1 Theoretical Correction SU(2) can be broken by some sources • Electroweak radiative corrections to T decays are contained in the SEW factor (see [79] and [80]), which is dominated by short-distance effects. It is expected to be weakly dependent on the specific hadronic final state, as verified for the T ---> (71--, K-)lIT decays [81]. Detailed calculations have been performed for the Jr-Jro channel (see [82]), which also confirm the relative smallness of the long-distance contributions. The total correction is SEW = S~l£S~a;j / S~~1 , where S~\f. is the leading-log short-distance electroweak factor(which vanishes for leptons) and s~l1lep are the nonleading electromagnetic corrections. The latter corrections have been calculated at the quark level [79], at the hadron level for the Jr-Jro decay mode (see [82]), and for leptons [79],[80]. The total correction amounts to [83] 81;$ = 1.0198 ± 0.()006 for the inclusive hadron decay rate and 8E~ = (1.0232±O.0006)GE~(S) for the JrJro decay mode, where GE~(s) is an s-dependent long-distance radiative correct.ion [82]. This factor has been included in the a;1r calculation given in Section 2 Chapter IX. • The pion mass splitting breaks isospin symmetry in the spectral functions [44] 1 [84] since /L(s) # 130 (s). • Isospin symmetry is also broken in the pion form factor due to the Jr mass splitting [44],[82]. • A similar effect is expected from the p mass splitting. The theoretical expecta- tion [49], gives a limit « 0.7 MeV), but this is only a rough estimate. Hence the question must be investigated experimentally, the best approach being the explicit comparison of T and e+e- in 2Jr spectral functions, after correction for 120 the other isospin-breaking effects. No correction for p mass splitting is applied initially. • Explicit electromagnetic decays introduce small differences between the widths of the charged and neutral p's. • Isospin violation in the strong amplitude through the ma..ss difference between u and d quarks is expected to be negligible. • vVhen comparing T with e+e-- data, an obvious and locally large correction must be applied to the T spectral function to introduce the effect of p - w mixing, only present in the neutral channel. This correction is computed using the parameters determined by the e+e- experiments in their form factor fits to the 7f+7f- lineshape modeling p - w interference [8]. To incorporate the missing p - w interference in T data, we modify the GS function to include it, introducing the parameter 0: (following the notation of Ref. [30], 0: is 0 if there is no w) to quantify the w admixture, analogous to the parameters j3 and I which quantify the p' and p". From the CLEO, we use 0: = (1.71 ± 0.06 ± 0.20) x 10-3 . Ivlodifying our fit function in this way leads to an increase in a;Jr by 3.4 x 10-10 . The total correction from known SU(2)-violating effects which include all correc- tions above is predicted to be (-1.8 ± 2.3) x 10-10 , where the central values taken from [5] and we enlarge the error by interpolating the values in Table 5 of reference [83]. 121 2 Summary The result for a;1r integrated over the mass range VS = 0.50-1.8 GeV/ c2 after correction(see previous section) is: a;1r(0.50, 1.80) = 456.65±0.40(stat)±0.83(intsys)±2.61(ext sys)±2.3su (2)' (XLI) • stat. is the statitical uncertainty that has been calculated previously in the special section of Statitical Uncertainty[see section 7]. It has lower value, due to the fact that we use bigger number of data compared to all previous experiments. It should be noted that that the total uncertainty in this analyis is dominated by internal systematic error, so that adding more data samples will have no significant improvement to the precision of this analysis. • int.sys. is the total internal systematic uncertainty that comes from this analysis and explained in Chapter X. The internal systematic uncertainty is dominated by neutral resolution and efficiency uncertainties. • ex:t.sys. is the total external systematic uncertainty is are calculated from other experiments The sources of external systematic uncertainties are: Tab. XLI: External Parameters and their uncertainties [ Value ~r(%) ] 6 a~1r(10 10) I Source SHV/SEW 1.0233 ± 0.0006 0.06 ± 0.32 [83] [82] Vud 0.97418 ± 0.00027 0.027 ± 0.15 [2] Be (17.84 ± 0.05)% 0.28 ± 1.52 [2] B1r1r0 (25.50 ± 0.10)% 0.39 ± 2.09 Total ± 2.61 ------------ -- 122 To calculate a:7r , we use the branching fraction of T- --7 J[-J[°vT decays from PDG 2007 [2], which has very low uncertainty. This analysis only calculate the branching fraction for consistency check, due to its big systematic uncertainty(see Table X.18). 3 Cmnparison with Other Experiments The results of this analysis are compared to the results from other major experi- ments. 3.1 NIp The measured .Mp is 0.7745 ± 0.00072 GeV, the total uncertainty includes system- atic and statistical uncertainties. The central value closer to the result from e+ e-- experiment(CMD-2) than other T experiments(ALEPH and CLEO), except the the result from Belle(see Table XI.2). The measured f p is 0.1493 ± 0.0013 GeV, the result is consisent (within uncertain- ties) with other T experiments (Belle, ALEPH and CLEO) and not consistent 'with e+e-(CMD-2) experiment(see Table XI.2). One possible explanation is there is no LV interference in T decay, especially in p mass peak. For M p" the central value that we measured is 1.2993 ± 0.0038 GeV much lower than other experiments, but it has lower uncertainty compared to other experiments 123 in the table(see Table XI.2). The discrepancy in central value maybe related to the correlation with other resonaIlces(p and p"). 3.4 rpl For fpl, the central value that we measured is 0.4990 ± 0.0163 GeV consistent with Belle and CJ'VID-2; and within 20- with CLEO and ALEPH(see Table XI.2). The central value has lower uncertainty compared to other experiments in the table. 3.5 Mpll Measurement of Mpll is one of most significant results in this analysis, because our knowledge about Alpll was very limited, even in PDG 2007[2], the quoted value was only an educated guess(quoted 1.720 ± 0.020 GeV, but it is written "OUR ESTI- MATE", based on observed range of data. Not from a formal statistical procedure). In fact, this analysis confirmed the existence p". This analysis has seen that p" is peaking at 1.6614 ± 0.0189 GeV and its value and precision comparable to the values from CMD-2 and Belle experiments(see Table XI.2). Previous experiments, such as CLEO and ALEPH, couldn't measure }}fpll due to limited number of events at high invariant mass, so that their values are limited statistically. Our analysis has much higher number of events so that we can measure it. 3.6 r p" Measurement of the width of pI! (simplified as f pll resonance is also one of most significant results in this analysis, because our knowledge about f p" was very limited, 124 even in PDG 2007 [2], the quoted value was still an educated guess (quoted 0.250 ± 0.100 GeV, but it is written "OUR ESTIMATE", based on observed range of data. Not from a formal statistical procedure). This analysis has measured that r> is 0.2433 ± 0.0366 GeV and its value and precision comparable to the values from CMD-2 and Belle experiments(see Table XI.2). Our analysis has much higher number of events than previous experiments, so that we can measure it . 3.7 f3 f3 is the coeficient of p' in Gounaris-Sakurai function and the precision measurement of this value is very important to study the characterics of p'(see Table XI.2). We found its value is 0.090 ± 0.013. 3.8 ¢/3 cPj3 is the phase of p' in Gounaris-Sakurai function and the precision measurement of this value is very important to study the characterics of p', we found that cPj3 = 118.9 ± 11.0 deg(see Table XI.2). 3.9 "'( "y is the coeficient of p" -in Gounaris-Sakurai function and the precision measurement of this value is very important to study the characterics of p" (see Table XI.2). vVe found its value is 0.060 ± 0.009, about 60" significance. 125 3.10 cP, ¢/ is the phase of p" in Gounaris-Sakurai function and the precision measurement of this value is very important to study the characterics of p". "y"le found that ¢/ = 59.4 ± 9.5 deg, consistent with Belle(44.2 ± 17) but ours has smaller uncertainty(see Table XI.2). 3.11 From Table XI.3 we can see that the value of a:1r from this analysis is lower than the other T experiment results, but higher than the result form CMD-2(e+e- experi- ments). Interestingly, the result of this analysis is statistically consistent with both T and e+ e- experiments, so that it may solve one of the debated topics in High Energy Phyiscs about discrepancy result of T and e+e- experiments. This analysis may improve the precision of Standard Model prediction of muon g-2, becauae our result has lower uncertainty than all previous Q,:1r measurement. In the light of precision measurement muon g-2 result from BNL,a:1r that is derived from T not consistent with the result of BNL g-2 (previously, it wa.s claimed tha.t the result of BNL is consistent with the result derived from T experiment, but not e+e- experiments) . 3.12 Comnlents on p" In addition, in this analysis we confirm the existence of p". We have measured its coupling and phase with more than 5eT. p" was observed non significantly by ALEPH,CLEO and OPAL. BaBar Belle ALEPH(T) CLEO CMD-2(e+e-) M p(GeV) 0.7745 ± 0.0007 0.7735 ± 0.0002 0.7755 ± 0.0007 0.7753 ± 0.0005 0.7733 ± 0.0006 fp(GeV) 0.1493 ± 0.0013 0.1492 ± 0.0004 0.1490 ± 0.0012 0.1505 ± 0.0011 0.1452 ± 0.0013 M p'(GeV) 1.2993 ± 0.0038 1.4530 ± 0.0070 1.3280 ± 0.0150 1.365 ± 0.007 1.3370 ± 0.0350 fp'(GeV) 0.4990 ± 0.0163 0.4376 ± 0.0199 0.468 ± 0.0410 0.356 ± 0.026 0.5690 ± 0.0810 M p"(GeV) 1.6614 ± 0.0189 1.7300 ± 0.0220 1. 7130(fixed) 1.700(fixed) 1. 7130 ± 0.0150 fp"(GeV) 0.2433 ± 0.0367 0.1379 ± 0.0500 O. 2350(fixed) O. 2350(fixed) 0.2350(fixed) (J 0.090 ± 0.013 0.167 ± 0.005 0.210 ± 0.008 0.121 ± 0.009 0.123 ± 0.011 '"Y 0.060 ± 0.009 0.031 ± 0.011 0.023 ± 0.008 0.032 ± 0.009 0.048 ± 0.008 IePf3! (degree) 118.9 ± 11.0 210.3 ± 6.3 15:3.0 ± 7.0 139.4 ± 6.5 IeP"f I(degree) 59.4 ± 9.5 44.2 ± 17 o(fixed) o(fixed) Tab. XI. 2: The results of fitting to the 1'VITr7r 0 distribution using Gounaris-Sakurai function from some experiments f--' t'V 0:. 127 a~7r (10-10 ) BaBar 456.65 ± 0.40(stat) ± 0.83(int sys) ± 2.61(ext sys) ± 2.30su(2) Belle 459.80 ± 0.50(stat) ± 1.00(int sys) ± 3.00(ext sys) ± 2.30SU (2) ALEPH(T) 464.0 ± 3.2 ± 2.3su(2) CI\iID-2(e+e ) 450.2 ± 4.9 ± 1.6SU (2) Tab. XI.3: The results of a~7r from some experiments 120 APPENDIX A PHOTON RESOLUTION PLOTS 1 Energy Resolution Plots 1 :"7' """u•.••"n·..··'LS·······<_vo..~] T:"~"-._ "~.n..".~~_.,_.~~ _.._ ] .. ,[ :: ..:.:~ - -= ... -. - -. .- ~~ , _. ~ :: n --'-"_.._ .. .. 'L =r ..".... .. ... ;) ~'~""'7\~. ,i: 1I·~~.· c •..•._'h~~ ~.-J' ::.~I -/~~ Ii ; .::.~ L~ ~ ,······'K, i Fi.g. A.l: Enc:'l'I-';:Y n.cSO]utloll Data AJJ RUllS. Fig. A.2: En8rg.y n(~solutiOll iVIC All RIms. Fig. A.3: Encrgy Rcsolution Data(black hllC) ,_ ..-~'V) Fig. A.7: Theta(e) Resolution DHt,n.(bla,ck line) all(1 lVI C( red line) All Rnns . ._;:.:'~,';.'~.",. Fig. A.8: Nelltml Theta(e) smearing result. AiJ,(T e smearing: ]\J(; ,tYter Slllem· ing(bluc line), initial ~JC(red line) and Datrl.(black linc) AJI Rl111S. 132 3 Neutral Phi(¢) Resolution Plots The ratio of expecteel all( I detected photon energy (cjJe:cpected / ¢detected) from _Ie- -;. •...... 1'- ....•. 1'- .,..... fi-. ..... 1'- G:'~"'" - ..• ~~ -~ "A a o.v> I :~i uA. . , ..... - ... _., ...~-.__.. 0 .. , ... "' ....... ... ~ ...... (~.... _ '" 0.") I Fig. A.9: Phi HCso]llt1on Data All Runs. Fig. A.10: PIti Resolution Me All 1l1l1lS. 1"---" -------<-<--... ,::: ~- J.~,.." .. ".- , ... ~. ... I ';~'-----'''d), ·c_· .=t. ~ , (~ _. _.# •• V~Jl .--.._.._..,."-'='-" ~" ~~..• '" .. .... ~. I .... ~'l ...A ..... ''''''0 .9. -:-;-...-7:'",.....!'"~. .... r.-.......---r:--r...----.~-.-..... ....,.- k-. 11~1 "," {.... ~·rL,~~~::e'1:---~~,. Fig. A.Il: Phi( ....11: _ " ...."J 1 J Fig. A.I2: After cp smearing: rvIC aftcr slIw;\rillg(lJlnc Jille), initial J\JC(rcd linc) c11lC1 Datcl'( black line) All Huns. 134 Fig. A.13: Linear fit (y = a -+ bx) to scale and resolubon (smearing) parameters. I __ I Dat~ I ! I I - I I , 0.1 < E"f < 0.5 GeV 1.01901±0.002604 0.054155±0.00179 -0.5637±0.04000 111.685±53.388 0.5 < E')! < 1.0 GeV 1.01263±0.000472 0.047603±0.00006 -0.9775±0.03674 5.984± 1.415 1.0 < E"f < 2.0 GeV 1.01044±0.000204 0.030754±0.00016 -1.0711±0.01874 4.229± 0.246 2.0 < E"f < 3.0 GeV 1.00823±0.000178 0.022178±0.00013 -0.9999±0.01942 3.856± 0.173 3.0 < E"f < 5.0 GeV 1.00560±0.000080 0.016001±0.00000 -0.8680±0.00921 3.332± 0.076 E"f> 5.0 GeV 1.00216±0.000079 0.015556±0.00000 -0.8867±0.00829 3.454± 0.075 Tab. A.l: Energy Resolution Data Run 1-5 f--' W v'l I I __ I Me;; I I I I - I I I 0.1 < E{ < 0.5 GeV 1.01647±0.01062 0.046618±0.00778 -0.8738±0.35555 129.010±65.088 0.5 < E~f < 1.0 GeV 1.01635±0.00138 0.047603±0.00102 -1.0240±0.11152 11.676±10.969 1.0 < E y < 2.0 GeV 1.01083±0.00036 0.026466±0.00027 -0.8529±0.02672 7.176± 0.989 2.0 < E"Y < 3.0 GeV 1.00694±0.00031 0.017367±0.00022 -0.7369±0.02389 5.203± 0.412 3.0 < E"Y < 5.0 GeV 1.00087±0.00014 0.013653±0.00()10 -0.6567±0.01123 3.736± 0.132 E"Y> 5.0 GeV 1.00088±0.00020 0.011618±0.00013 -0.5497±0.01386 4.295± 0.179 Tab. A.2: Energy Resolution Run Me 1-5 f-' W G c= I __ __ M~ I I I I - I I I 0.1 < E"f < 0.5 GeV 1.01940±0.005701 0.0557008±0.000844 -0.887176±0.287465 104.9965±60.256 0.5 < E'Y < 1.0 GeV 1.01255±0.000984 0.0476891±0.000485 -1.000432±0.090988 5.3746± 4.826 1.0 < R( < 2.0 GeV 1.01046±0.000389 0.0309906±0.000289 -0.970635±0.036589 5.6045± 0.747 2.0 < E'Y < 3.0 GeV 1.00827±0.000258 0.0221550±0.000191 -0.920639±0.029759 4.3695± 0.296 3.0 < E"( < 5.0 GeV 1.00453±0.000150 0.0158453±0.000109 -0.886355±0.017002 3.6162± 0.122 E"( > 5.0 GeV 1.00147±0.000148 0.0149698±0.000103 . -0.820265±0.014780 3.8359± 0.152 Tab. A.3: Energy Resolution Run Me 1-5 After Smearing f--' W --0 Mean Ratio asmearing AleanData J 2 2 IV'PrmMr a Data - a MC 0.1 < E"( < 0.5 GeV 1.0025 0.02756 0.5 < E"( < 1.0 GeV 0.996;j 0.0 1.0 < E"( < 2.0 GeV 0.9996 0.01566 2.0 < E"( < 3.0 GeV 1.0013 0.01379 3.0 < E"( < 5.0 GeV 0.9969 0.00834 E"( > 5.0 GeV 0.9935 0.01034 Tab. A.4: Energy Smearing 138 ___I Data I Me I Mean I Sigma Mean I Sigma I , I I I I 0.1 < E~( < 0.5 GeV 1.016±0.00l O. 02404±0.00057 1.015± 0.001 0.02271± 0.00065 0.5 < E"'( < 1.0 GeV 1.010±0.000 0.01761±0.00017 1.011± 0.000 0.01682± 0.00018 1.0 < E"'( < 2.0 GeV 1.005±0.000 0.01160±0.00010 1.004± 0.000 0.0112± 0.00010 2.0 < E"'( < 3.0 GeV 1.003±0.000 0.00827±0.00009 1.002± 0.000 0.008248± 0.00008 3.0 < E"y < 5.0 GeV 1.002±0.000 0.00661±0.00005 0.9982±0.0001 0.006588±0.000052 E~( > 5.0 GeV 1.000±0.000 0.00688±0.00007 0.9966±0.0001 0.006752±0.000068 Tab. A.5: Theta(e) Resolution Run 1-5 f-' eN CD Mean Ratio± ersmear'ing MeanData± Ver'bata 2 erMC 0.1 < E", < 0.5 GeV 1.00099± 0.007885 0.5 < E", < 1.0 GeV 0.99901± 0.000.521 1.0 < E", < 2.0 GeV 1.00096± 0.003020 2.0 < E", < 3.0 GeV 1.00099± 0.000589 3.0 < E", < 5.0 GeV 1.00381± 0.000514 E'Y> 5.0 GeV 1.00341± 0.001316 Tab. A.6: Theta(8) Smearing 140 I Mean Ratio] ersmearing 0.1 < E'Y < 0.5 GeV 1.016± 0.0 0.02414± 0.00057 0.5 < E'Y < 1.0 GeV 1.01O± n.o 0.01742± 0.00017 1.0 < E", < 2.0 GeV 1.005± 0.0 0.01162± 0.00010 2.0 < E'Y < 3.0 GeV . 1.003± 0.0 0.00837±0.000086 3.0 < E'Y < 5.0 GeV 1.002± 0.0 0.00661 ±O.000053 E'Y> 5.0 GeV 1.00± 0.0 0.00689±0.000074 Tab. A.7: Theta(8) After Smearing --------1 Mean IData Sigma I Mean I Me Sigma I I L I I I I 0.1 < E" < 0.5 GeV 1.001±0.001 0.019± 0.001 1.001±0.0 0.0l898± 0.00141 0.5 < E" < 1.0 GeV 1.000± 0.0 0.01514± 0.00024 LOOO±O.O 0.01499± 0.00023 1.0 < E" < 2.0 GeV 1.000± 0.0 Cl.008395±0.000123 1.000±0.0 0.008315±0.000134 2.0 < E" < 3.0 GeV 1.000± 0.0 0.005991±0.000104 1.000±0.0 O. 005505±0.000085 3.0 < E" < 5.0 GeV 1.000± 0.0 0.003407±O.000048 1.000±0.0 0.003275±0.000042 E.,)' > 5.0 GeV 1.000± 0.0 0.002493±0.000045 1.000±0.0 0.002581±0.000041 Tab. A.8: Phi(¢) Resolution Run 1-5 f---' ~ f---' Mean Ratio (Jsmearing MeanData V 2 2 """AIr. -~---;r;=; (JData - (JMe 0.1 < E"j < 0.5 GeV 1. 0.0000 0.5 < E"j < 1.0 GeV 1. 0.002126 1.0 < E"j < 2.0 GeV 1. 0.001156 2.0 < E"j < 3.0 GeV 1. 0.002363 3.0 < E"j < 5.0 GeV 1. 0.000939 E"j> 5.0 GeV 1. 0.000141 Tab. A.9: Phi(¢) Smearing 142 I Mean Ratio I (Jsmearing~ 0.1 < E"j < 0.5 GeV 1.000± 0.0 0.0191±0.000647 0.5 < E"j < 1.0 GeV 1.000± 0.0 0.01504±OJlO0180 1.0 < E"j < 2.0 GeV 1.000± 0.0 OJ)0840±0.000132 2.0 < E"j < 3.0 GeV 1.000± 0.0 0.00598±0.000084 3.0 < E"j < 5.0 GeV 1.000± 0.0 0.00336±0.000042 E"j> 5.0 GeV 1.000± 0.0 0.00251±0.000040 Tab. A.lO: Phi(8) After Smearing [] a b E Mean 1.001583±0.005786 -0.OO1218±0.000167 E Width 0.018874±0.000850 -0.002125±0.000218 8 rvlean 0.999819±OJ)57911 0.000781±0.000016 8 Vlidth 0.(lO1116±0.000200 -0.OOO103±0.000055 ¢ rvlean 1.000± 0.0 Cl.OO± 0.00 ¢ Width 0.002204±0.000235 -0.000363±0.000048 Tab. 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