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B counting at BABAR McGregor, Grant D. 2008-09-02

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B Counting at BABARbyGrant D. McGregorB.Sc. (hons), University of Canterbury, 2005A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2008c Grant D. McGregor, 2008iiAbstractIn this thesis we examine the method of counting BB events produced in theBABAR experiment. The original method was proposed in 2000, but improve-ments to track reconstruction and our understanding of the detector since thatdate make it appropriate to revisit the B Counting method. We propose a newset of cuts designed to minimize the sensitivity to time-varying backgrounds.We  nd the new method counts BB events with an associated systematic un-certainty of  0:6%.iiiContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 CP Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Other Physics at BABAR . . . . . . . . . . . . . . . . . . . . . . . 42 The BABAR Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 The Silicon Vertex Tracker . . . . . . . . . . . . . . . . . . . . . 62.2 The Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 The DIRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 The Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . 102.5 The Muon Detection System . . . . . . . . . . . . . . . . . . . . 123 Particle Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.1 Lists Used in B Counting . . . . . . . . . . . . . . . . . . . . . . 143.2 Charged Candidates . . . . . . . . . . . . . . . . . . . . . . . . . 153.3 Neutral Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . 164 B Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1 Method for B Counting . . . . . . . . . . . . . . . . . . . . . . . 204.2 Derivation of the B Counting Formula . . . . . . . . . . . . . . . 214.3 B Counting Goals . . . . . . . . . . . . . . . . . . . . . . . . . . 224.4 TrkFixup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.5 Original B Counting Requirements . . . . . . . . . . . . . . . . . 255 Muon Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . 275.2 Cut on Muon Pair Invariant Mass . . . . . . . . . . . . . . . . . 285.3 Minimum EMC Energy Requirement . . . . . . . . . . . . . . . . 285.4 Optimization of Cuts . . . . . . . . . . . . . . . . . . . . . . . . . 33Contents iv5.5 Estimating Systematic Uncertainty . . . . . . . . . . . . . . . . . 365.6 Variation in    . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 Hadronic Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . 416.2 Cut on Total Energy . . . . . . . . . . . . . . . . . . . . . . . . . 426.3 Cut on Highest-Momentum Track . . . . . . . . . . . . . . . . . . 426.4 Optimization of Cuts . . . . . . . . . . . . . . . . . . . . . . . . . 436.5 Estimating Systematic Uncertainty . . . . . . . . . . . . . . . . . 456.6 Variation in  X . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 Cutset Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 537.1 B Counting Uncertainty . . . . . . . . . . . . . . . . . . . . . . . 537.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557.3 Choice of Muon-Pair Selection Cutset . . . . . . . . . . . . . . . 577.4 Choice of Hadronic Selection Cutset . . . . . . . . . . . . . . . . 587.4.1 ISR Production and Two-Photon Events . . . . . . . . . . 627.5 B Counting Results . . . . . . . . . . . . . . . . . . . . . . . . . 658 Sources of Contamination . . . . . . . . . . . . . . . . . . . . . . . 738.1 Bhabha Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 738.2 Continuum Fake-Rates . . . . . . . . . . . . . . . . . . . . . . . . 748.3 Tau Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759 Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . 789.1 BGFMultiHadron and Tracking E ciency . . . . . . . . . . . . . 789.2 Comparison of Data and MC . . . . . . . . . . . . . . . . . . . . 799.3 Summary of Systematic Uncertainties . . . . . . . . . . . . . . . 8210 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90A Uncertainties of a Multi-Variable Function . . . . . . . . . . . . 91B  (3S) Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93vList of Tables3.1 Criteria of some existing particle lists used in B Counting. . . . . 153.2 Criteria of the lists used in this thesis. . . . . . . . . . . . . . . . 184.1 Criteria of isBCMuMu and isBCMultiHadron. . . . . . . . . . . . 255.1 E ect of maxpEmcCandEnergy (Runs 1{3) . . . . . . . . . . . . 315.2 E ect of maxpEmcCandEnergy (Runs 4{6) . . . . . . . . . . . . 325.3 Cut optimization of isBCMuMu. . . . . . . . . . . . . . . . . . . 346.1 Continuum MC cross-sections. . . . . . . . . . . . . . . . . . . . 426.2 Cut optimization of isBCMultiHadron. . . . . . . . . . . . . . . . 457.1 Properties of the proposed and existing muon-pair selectors. . . . 587.2 Properties of the proposed and existing hadronic selectors. . . . . 717.3 Uncertainty and number of B meson events in Runs 1{6. . . . . 728.1 Fake-rates for Bhabha MC events. . . . . . . . . . . . . . . . . . 748.2 Fake-rates for hadronic continuum MC events. . . . . . . . . . . 758.3 Fake-rates for muon-pair MC events. . . . . . . . . . . . . . . . . 758.4 Fake-rates for  +   MC events. . . . . . . . . . . . . . . . . . . . 769.1 Revised e ciencies for hadronic cut quantities. . . . . . . . . . . 829.2 Summary of B Counting statistical and systematic uncertainties. 889.3 Number of B meson events in Runs 1{6 with revised uncertainty. 89viList of Figures1.1 Diagram of PEP-II linac and storage-rings. . . . . . . . . . . . . 11.2 The spectrum of hadron production near 10.58 GeV. . . . . . . . 22.1 Cross-section of the BABAR detector. . . . . . . . . . . . . . . . . 62.2 A schematic drawing of DCH drift cells. . . . . . . . . . . . . . . 82.3 Drift Chamber dE=dx as a function of particle momentum. . . . 92.4 A schematic drawing of the DIRC. . . . . . . . . . . . . . . . . . 102.5 A cross-section of the EMC (top half). . . . . . . . . . . . . . . . 112.6 The IFR barrel and forward and backward endcaps. . . . . . . . 123.1 High and low theta regions the GoodTracksLoose list. . . . . . . 163.2 High and low theta regions for the CalorNeutral list. . . . . . . . 173.3 BB data and MC for high and low neutral angles. . . . . . . . . 183.4 Neutral backgrounds in back-to-back mu-pair events. . . . . . . . 194.1 ETotal/eCM for events passing hadronic cuts. . . . . . . . . . . . 234.2 ETotal/eCM on- and o -peak subtraction, overlaid with MC. . . 235.1 Distribution of maxpEmcCandEnergy. . . . . . . . . . . . . . . . 295.2 Angular distribution of muons with maxpEmcCandEnergy = 0. . 305.3 On-peak mu-pair MC e ciency variation. . . . . . . . . . . . . . 355.4 O -peak mu-pair MC e ciency variation. . . . . . . . . . . . . . 355.5 Distribution of  2 statistic (on-peak). . . . . . . . . . . . . . . . 375.6 Distribution of  2 statistic (o -peak). . . . . . . . . . . . . . . . 375.7 Time-variation of   . . . . . . . . . . . . . . . . . . . . . . . . . . 395.8 Distribution of  2 statistic (  ). . . . . . . . . . . . . . . . . . . 406.1 Distribution of p1Mag for a sample of BB Monte Carlo. . . . . . 436.2 PrimVtxdr for a data sample from Run 6, overlaid with MC. . . 446.3 PrimVtxdz for a data sample from Run 6, overlaid with MC. . . 446.4 Time-variation of on-peak uds MC. . . . . . . . . . . . . . . . . . 466.5 Time-variation of o -peak uds MC. . . . . . . . . . . . . . . . . . 466.6 Time-variation of on-peak cc MC. . . . . . . . . . . . . . . . . . . 476.7 Time-variation of o -peak cc MC. . . . . . . . . . . . . . . . . . 476.8 Distribution of  2 statistic for uds MC. . . . . . . . . . . . . . . 506.9 Distribution of  2 statistic for cc MC. . . . . . . . . . . . . . . . 516.10 Time-variation of  X. . . . . . . . . . . . . . . . . . . . . . . . . 51List of Figures vii6.11 Distribution of  2 statistic ( X). . . . . . . . . . . . . . . . . . . 526.12 Distribution of  X d0 values. . . . . . . . . . . . . . . . . . . . . 527.1 On-peak muon-pair MC e ciency variation for the new cuts. . . 597.2 O -peak muon-pair MC e ciency variation for the new cuts. . . 597.3 On-peak muon-pair MC e ciency variation for isBCMuMu. . . . 607.4 O -peak muon-pair MC e ciency variation for isBCMuMu. . . . 607.5 Time-variation of    for the new cuts. . . . . . . . . . . . . . . . 617.6 Time-variation of    for isBCMuMu. . . . . . . . . . . . . . . . . 617.7 Comparison of ETotal for known MC types to o -peak data. . . 647.8 Di erence between known MC types and o -peak data. . . . . . 657.9 Time-variation of on-peak uds MC for the new cuts. . . . . . . . 667.10 Time-variation of o -peak uds MC for the new cuts. . . . . . . . 667.11 Time-variation of on-peak uds MC for isBCMultiHadron. . . . . 677.12 Time-variation of o -peak uds MC for isBCMultiHadron. . . . . 677.13 Time-variation of on-peak cc MC for the new cuts. . . . . . . . . 687.14 Time-variation of o -peak cc MC for the new cuts. . . . . . . . . 687.15 Time-variation of on-peak cc MC for isBCMultiHadron. . . . . . 697.16 Time-variation of o -peak cc MC for isBCMultiHadron. . . . . . 697.17 Time-variation of  X for the new cuts. . . . . . . . . . . . . . . . 707.18 Time-variation of  X for isBCMultiHadron. . . . . . . . . . . . . 708.1 On-peak tau lepton MC e ciency variation for the new cuts. . . 778.2 O -peak tau lepton MC e ciency variation for the new cuts. . . 779.1 Distribution of nTracks for BB data and MC. . . . . . . . . . . . 799.2 Distribution of nTracks for BB data and MC without `obvious' Bhabhas. 809.3 ETotal/eCM for BB data overlaid with original MC. . . . . . . . 839.4 Di erence between data and MC of Fig. 9.3. . . . . . . . . . . . . 839.5 ETotal/eCM for BB data overlaid with revised MC. . . . . . . . 849.6 Di erence between data and MC of Fig. 9.5. . . . . . . . . . . . . 849.7 R2 for BB data overlaid with revised MC. . . . . . . . . . . . . . 859.8 nTracks for BB data overlaid with revised MC. . . . . . . . . . . 859.9 p1Mag for BB data overlaid with revised MC. . . . . . . . . . . 869.10 PrimVtxdr for BB data overlaid with revised MC. . . . . . . . . 869.11 PrimVtxdz for BB data overlaid with revised MC. . . . . . . . . 87viiiAcknowledgementsThis work was only possible thanks to the guidance of my supervisor, ChrisHearty. Thanks also to the other members of the UBC BABAR group | DavidAsgeirsson, Bryan Fulsom, Janis McKenna and Tom Mattison | and to theTrigger/Filter/Luminosity Analysis Working Group, especially Al Eisner andRainer Bartoldus. Finally, thanks to the the Canadian Commonwealth Scholar-ship scheme and the Canadian Bureau of International Education (CBIE) whosefunding made this work possible.1Chapter 1IntroductionThe BABAR experiment is located at the Stanford Linear Accelerator Center(SLAC). Data from e+e  annihilations at a centre-of-mass (CM) energy ps  10:58 GeV are taken at the SLAC PEP-II storage-rings with the BABARdetector.This chapter provides a brief introduction to the experiment.PEP-II is a `B-Factory' | it is designed to produce a high number of Bmesons. This is achieved through the process e+e  ! (4S) !BB. Beams of9.0 GeV electrons and 3.1 GeV positrons collide with a CM energy of 10.58 GeV,which is the peak of the  (4S) resonance. Running at this energy is desirablebecause the  (4S) meson (a bound bb state) decays more than 96% of the timeto a BB state. The design luminosity of PEP-II (3 1033 cm2s 1) was exceededin 2001 and by 2006, peak luminosities above 12  1033 cm2s 1 were recorded.Figure 1.1: Diagram of PEP-II linac and storage-rings.Asymmetric beam energies cause the decay products to have a Lorentz boostof    = 0:56 relative to the laboratory. This is one of the most important designfeatures of the BABAR experiment.In the rest frame of each  (4S) particle, the B mesons are created almost atrest. By boosting along the z axis, the B mesons travel a measurable distanceinside the detector before decaying. The mean lifetime of a B meson is veryshort (around 1.5 ps), but by reconstructing the decay vertices of each B itpossible to calculate how far each travelled and hence the lifetimes.For some analyses (such as studies of CP violation in the BB system) therelative di erence in decay times is especially important. The BABAR detectoris speci cally designed to enable precise measurements of this quantity.Chapter 1. Introduction 2PEP-II is run at the  (4S) resonance most of the time, but it is importantto occasionally run `o -peak'. Typically just over 10% of the time, PEP-II isrun around 40 MeV below the resonance peak. This is achieved by lowering theenergy of the electron beam, which reduces the boost by less than one percent.Figure 1.2: The spectrum of hadron production near PEP-II's operational CMenergy. The curve shows the cross-section for inclusive productionof hadrons (vertical axis) as a function of CM energy. The peak atthe  (4S) resonance is clearly visible. The plot is originally fromUpsilon Spectroscopy by Besson and Skwarnicki [1].Continuum is the name used to describe all non-BB events produced inthe detector. The continuum contains many types of events, by far the mostcommon of which is e+e  !e+e  (Bhabha events) which have a cross-sectionclose to 40 nb. For each type of quark q (apart from t), events of the typee+e  ! qq have a cross-section of order 1 nb. The other leptons ( +   or +  ) are produced with cross-sections also close to 1 nb.These cross-sections all scale in a known way when PEP-II runs at the de-creased o -peak energy, while  (4S) (and hence BB) production is `switchedo '. The o -peak data can then be used to understand on-peak backgroundsand when scaled in the correct way can be used to count B events in on-peakdata. Any B physics analysis at BABAR will make use of the o -peak data, andit is an integral part of B Counting.Chapter 1. Introduction 31.1 CP ViolationThe BABAR experiment was designed to achieve a number of physics goals. Theprimary motivation for the experiment was to study CP violation in the decaysof B mesons [2]. A signi cant result [3] demonstrating the existence of CPviolation in this sector was published in 2001, two years after running began.CP is the product of two quantum mechanical operators. Charge conjuga-tion (C) interchanges particles with their anti-particles and parity (P) changesthe `handedness' of a co-ordinate system, i.e. P sends (t;x) !(t; x).Independently, C and P are not symmetries of nature and in particular,neither is a symmetry of the weak nuclear force. For example, left-handedneutrinos are transformed to right-handed neutrinos by the operation of P,and to left-handed anti-neutrinos by C. Neither of these states is observed toparticipate in the weak interaction.Cronin and Fitch were awarded the 1980 Nobel Prize in Physics for demon-strating the combination CP was also not a symmetry of nature [4]. Theyobserved this in the decay of neutral kaons, speci cally through the modeK0L !  +   which would not occur if CP were conserved. Following this,CP violation was also anticipated in B meson decays, and was expected to belarger and more varied than in the kaon system. Investigating this was one ofthe main reasons for running the BABAR experiment.There are several reasons for studying CP violation with an experimentlike BABAR. Measurements of CP violation are important to test the StandardModel (SM) of particle physics. Any results outside SM predictions by de -nition indicate new physics. A second reason relates to the matter-antimatterasymmetry of the universe. CP violation is one of the conditions proposed bySakharov [5] to explain how the observed asymmetry could occur.In the Standard Model, CP violation is governed by the weak quark mixingmatrix, known as the Cabibbo-Kobayashi-Maskawa (CKM) matrix [6, 7]. Thistakes the form:V =0@Vud Vus VubVcd Vcs VcbVtd Vts Vtb1A (1.1)where each Vij is complex, and the probability of a transition between two typesof quark i and j is proportional to jVijj2. Here u, d, s, c, t and b represent up,down, strange, charm, top and bottom quarks respectively.By studying a variety of di erent decay channels, BABAR can be used tomeasure or put limits on several components of the CKM matrix. In particular,many channels seen at BABAR allow the parameter  = Arg  VcdV cbVtdV  tb (1.2)to be measured. Other searches for CP-violation, such as in gluonic penguin de-cays allow the measurement of di erent CKM matrix elements (see for exampleChapter 1. Introduction 4[8]) including:  = Arg  VudV ubVcdV  cb : (1.3)1.2 Other Physics at BABARThe BABAR experiment has multiple uses apart from searching for CP violationin B decays. It is a high luminosity experiment, and as well as producing manyB mesons (enabling study of rare B processes), collisions create many otherspecies including charmonium states (such as J= ), other charmed mesons (suchas D),   leptons and two-photon states.Data from BABAR are used to study each of these to re ne and test theStandard Model. The cross-section for cc production in the BABAR detector isslightly larger than for bb, while the  +   cross-section is slightly smaller.The charm physics research at BABAR includes measuring D meson andcharm baryon lifetimes, rare D meson decay and D mixing. An importantresult demonstrating evidence for D0D0 mixing observed in D0 ! K  decayswas published in 2007 [9].An analysis group is speci cally devoted to studying charmonium (cc) states.This group studies several types of physics. This includes initial state radiation(ISR) production (such as e+e  ! ISR +  J= ), fully reconstructed B eventswith charmonium  nal states (for example B !J= X or B ! (2S)X where Xrepresents other unspeci ed particles) and studies of exotic states like Y(4260).Other groups study charmless hadronic decays of B mesons (e.g. B !  ),leptonic c and b decays (e.g. D;B ! ` `, where ` = e;  or  ) and radiativepenguins. The last of these describes processes involving radiative loops suchas b ! s . Radiative penguin events provide one way to test theories beyondthe Standard Model because new virtual particles could appear in the loop withdetectable e ects.Also, research at BABAR includes measurements of the properties of the  lepton produced through e+e  !  +  . An important area of research inthe   sector is the search for lepton  avour violation through decays such as + ! +  or  + !e+e e+.5Chapter 2The BABAR DetectorThis chapter provides a brief introduction to the hardware of the BABAR de-tector. Detailed descriptions of the detector [12] and also of PEP-II [13] areavailable elsewhere.It will be useful to brie y explain the (right-handed) co-ordinate system usedin the BABAR experiment.  The +z axis is the direction of the high-energy (electron) beam.  The +y axis is vertically upwards.  The azimuthal angle   lies in the xy plane. It is zero on the +x axis, andincreases towards the +y axis.  The polar angle   is measured from the z axis. It is zero on the +z axisand   on the  z axis.The beam energy asymmetry of PEP-II means the optimal detector shape isalso asymmetric. A schematic of the detector is shown in Fig. 2.1. Full detailsof the detector and its sub-systems can be found in [14] and [12]. The detectorwas designed to meet a large number of requirements which include:  performing tracking on particles with transverse momentum (pt) between  60 MeV/c and   4 GeV/c;  detecting photons and neutral pions with energies between   20 MeV and  5 GeV, and;  distinguishing electrons, muons, pions, kaons and protons over a widerange of momenta.To meet these requirements, the detector was constructed with  ve majorsubsystems. The innermost components are a  ve-layer double-sided siliconvertex tracker (SVT), which provides precision tracking information and a 40-layer drift chamber (DCH), which provides momentum information for chargedtracks. Outside these is a particle identi cation system, a detector of internally-re ected  Cerenkov light (DIRC). Surrounding all these is an electromagneticcalorimeter (EMC) built from more than six thousand CsI(Tl) crystals. TheEMC records energy deposited by electrically charged particles and photonsand also has some sensitivity to neutral hadrons such as neutrons and K0L. TheEMC is able to detect neutral pions by recording the photons from  0 !   .Chapter 2. The BABAR Detector 6Finally, outside the superconducting coil is the muon detection system, calledthe Instrumented Flux Return (IFR) consisting mostly of Limited StreamerTube (LST) modules.Figure 2.1: Cross-section of the BABAR detector.2.1 The Silicon Vertex TrackerThe silicon vertex tracker (SVT) is the component of the BABAR detector closestto the interaction point (IP). It provides the most precise angular measurementsof tracks because further from the IP, track precision is limited by multiplescattering. The SVT consists of  ve cylindrical layers of double-sided silicon-strip detectors.In total, there are 340 silicon detectors within the SVT, with around 150,000readout channels. The individual silicon detectors vary in size between 43  42mm2 (z    ) and 43   42 mm2. Each detector is double-sided, with strips tomeasure   running parallel to the beam axis (  strips) and strips to measure z(z strips) running orthogonally on the opposite side. The total area covered bythe  ve layers of silicon detectors is around one square metre.The ends of each strip are held at a potential di erence of around 35{45 V.When a charged particle passes through the silicon, it creates free electrons andelectron-hole pairs. This charge is collected by the applied voltage, and afterChapter 2. The BABAR Detector 7being ampli ed can be read out as a `hit' signal. The track position is calculatedby combining all the hits from individual silicon detectors.The resolution of the SVT depends on track angle and varies between layers.For tracks at normal incidence, the resolution of inner layers is approximately15  m in z and 10  m in  . For outer layers the resolutions are approximately35  m and 20  m respectively.Some very low momentum particles such as slow pions in D  decay have in-su cient energy to reach outer components of the detector. For these particles,the SVT provides the only tracking information.2.2 The Drift ChamberThe multi-wire drift chamber (DCH) provides precise tracking information andto a lesser extent is used to perform some particle identi cation (PID). It wasconstructed on the campus of the University of British Columbia at TRIUMF.The DCH is cylindrical and surrounds the SVT. It is  lled with a gas mixtureof helium and isobutane, which is kept 4 mb above atmospheric pressure.The DCH is strung with nearly thirty thousand wires arranged into 40 layers(and ten `superlayers') of hexagonal cells. The layout of these cells for 16 layersis shown in Fig. 2.2. A tungsten-rhenium `sense' wire in the centre of each cellis held at a positive high voltage, of around 1960 V. The surrounding gold-coated aluminium ` eld' wires are at ground potential. Cells on the boundaryof a superlayer have two gold-coated aluminium `guard' wires. These are held at340 V and improve the performance of the cells and ensure the gain of boundarycells is the same as that of inner ones.Of the ten superlayers, four are `stereo'. The wires of these layers are strungat a slight angle (between  45 and  76 mrad) relative to the z axis. This isimportant for tracking as it enables   co-ordinates to be measured.A charged particle moving through the drift chamber ionizes the gas. Theionized gas molecules within a cell move towards a ground wire and the electronsreleased from these molecules are accelerated towards the sense wire. In turnthese electrons collide with and ionize other gas molecules. This causes an`avalanche' of negative charge (up to a gain of 50,000) to arrive at the sensewire. For a particle energetic enough to exit the drift chamber, up to 40 DCH`hits' of this sort (one per cell) can be recorded.The drift chamber is contained within the 1.5 T  eld of the super-conductingcoil. Measurements of track curvature in the drift chamber allow momenta tobe determined. The momentum resolution of the drift chamber for a particle oftransverse momentum pt (i.e. the component of momentum perpendicular tothe z axis) in units of GeV/c is: pt = (0:13  0:01)%   pt + (0:45  0:03)%: (2.1)To be measured in the drift chamber (i.e. to travel past the inner radius of theDCH and trigger enough wires to provide a good measurement), a track musthave transverse momenta of at least 100 MeV/c.Chapter 2. The BABAR Detector 8     0Stereo 1    Layer     0Stereo 1    Layer     0     0     0    45    47    48    50   -52   -54   -55   -57     0     0     0     04 cmSense Field Guard Clearing1-2001 8583A14Figure 2.2: A schematic drawing of 16 layers of DCH drift cells. The lines con-necting wires are included for visualisation purposes only. Numbersin the `Stereo' column indicate the angle in mrad of the stereo layers.Di erent species of particles have a characteristic rate of energy loss withdistance (dE=dx), and the drift chamber can provide PID for low-momentumtracks by measuring this as a particle moves through the chamber. The dE=dxdistributions for di erent particles as a function of momentum are shown inFig. 2.3. Particle ID is achieved by recording the total charge deposited in eachcell. Corrections are made to account for several sources of bias including signalsaturation, variations in gas pressure and di erences in cell geometry.For low-momentum tracks (i.e. those below 1 GeV/c), the overall dE=dxresolution is around 7%. The  nal PID combines this information with thatgathered from the DIRC and other subsystems.Chapter 2. The BABAR Detector 910 310 410 -1 1 10Track momentum (GeV/c)80% truncated mean (arbitrary units)e ?piKp dFigure 2.3: Drift Chamber dE=dx as a function of particle momentum. Thescatter points are from beam scan data and the curves are appro-priately parameterized Bethe-Bloch curves. The letters have theirusual meanings, labelling the curves muon, electron, pion, kaon,proton and deuteron respectively.2.3 The DIRCThe function of the detector of internally-re ected  Cerenkov light (DIRC) is toperform particle identi cation. In particular, it especially separates kaons andpions of momenta between 2.0 and 4.0 GeV/c. It records the  Cerenkov radiationof charged particles passing through a ring of fused-silica bars located outsidethe drift chamber. This type of light is emitted whenever a charged particlepasses through a medium with a velocity greater than the speed of light in thatmedium.For a medium of refractive index n (for fused-silica, n   1:47), a particlemoving with velocity v =  c (where c denotes the speed of light in a vacuum)emits a characteristic cone of  Cerenkov light at an angle cos( c) = 1=( n).When the  Cerenkov angle  c of a particle is measured in the DIRC, momentuminformation from the drift chamber allows the mass (and hence type) of theparticle to be determined.Ring-imaging  Cerenkov counters have commonly been used in particle de-tectors since the 1980s, but the BABAR DIRC di ers from all previous ones byutilising total internal re ection. The DIRC radiator comprises 144 syntheticChapter 2. The BABAR Detector 10Mirror4.9 m4 x 1.225m Bars glued end-to-endPurified WaterWedgeTrack Trajectory17.25 mm Thickness (35.00 mm Width)Bar BoxPMT + Base 10,752 PMT'sLight CatcherPMT SurfaceWindowStandoff BoxBar{ {1.17 m8-2000 8524A6Figure 2.4: A schematic drawing of a DIRC radiator bar (left) and imagingregion.quartz bars of length 4.9m which function both as light guides and as a mediumfor  Cerenkov radiation. As shown in Fig. 2.4, light is carried towards DIRCelectronics in the imaging region | located at the backward-end of the detec-tor | by successive internal re ections. A mirror is placed at the forward-endof the radiator bars to ensure forward-travelling photons are re ected back toarrive at the DIRC electronics.At the DIRC imaging region, the light expands into the `Stando  Box' whichis  lled with six cubic metres of puri ed water of a similar refractive index tothe quartz. The photons are detected at the rear of this by almost 11,000photomultiplier tubes (PMTs), each of diameter 2.82 cm. The position andarrival-time of PMT signals are then used to calculate the  Cerenkov angle ofparticles passing through the DIRC radiator.At the high-momentum end of the DIRC's functional window (around 4.0GeV/c), the di erence in the  Cerenkov angle of pions and kaons is 3.5 mr. Atthis momentum, the DIRC is able to separate the two species to around 3 .This increases for lower momenta, up to a separation of as much as 10  at 2.0GeV/c.2.4 The Electromagnetic CalorimeterThe Electromagnetic Calorimeter (EMC) measures electromagnetic showers inthe energy range 20 MeV to 9 GeV. It comprises 6580 thallium-doped caesiumiodide (CsI(Tl)) crystals which sit in 56 rings in a cylindrical barrel and forwardend-cap which together cover a solid angle of  0:775   cos    0:962 in thelaboratory frame. This coverage region was chosen because few photons travelin the extreme backward direction. The barrel part of the EMC is locatedChapter 2. The BABAR Detector 11between the DCH and the magnet cryostat.Thallium-doped CsI is used because of its favourable properties. It has ahigh light yield, a small Moli ere radius and a short radiation length. Theseallow excellent resolution of both energy and angle within the compact designof the detector.112713759201555 229523591801558197922.7? 26.8? 15.8? Interaction Point 1-2001 8572A0338.2? External SupportFigure 2.5: A cross-section of the EMC (top half). The EMC is symmetric in . Dimensions are given in mm.Altogether, the EMC weighs more than 26 tonnes. The crystals are heldfrom the rear by an aluminium support system. Similarly, cooling equipmentand cables are also located at the rear. This con guration minimises the amountof material between the interaction point (IP) and the crystals. The supportstructure is in turn attached to the coil cryostat. The layout of the aluminiumsupport and the 56 crystal rings can be seen in Fig. 2.5.High-energy electrons and photons create electromagnetic showers whentravelling through the EMC crystals. The shower size depends on the prop-erties of the particle. The crystal absorbs the shower photons, and re-emitsthem as visible scintillation light. When tested with a source of 1.836 MeVphotons, the average light yield per crystal is 7300 emitted photons per MeV ofenergy. The scintillation photons are read out with a package consisting of twosilicon photodiodes and two preampli ers mounted on each crystal.There is a degradation in time due to radiation damage inside the EMC, andthe crystals are constantly monitored to gauge their individual performance.This is achieved by recording the EMC response both to known radioactivesources and to real events (i.e. from colliding beams). The latter involves cali-brating the system by measuring particles of a known type, energy and positionwith the EMC. A variety of events are used for this calibration, including e+e (Bhabhas),    and  +  .Chapter 2. The BABAR Detector 122.5 The Muon Detection SystemThe IFR consists of three sections | a central cylindrical barrel and two endcaps. When BABAR was commissioned, the IFR was  lled with Resistive PlateCounters (RPCs). Due to degradation and diminishing e ciency over the courseof running, it became necessary to replace the barrel RPCs between 2004 and2006 with a di erent technology (LSTs). RPCs are still used in the end caps.The IFR is designed to detect deeply penetrating particles such as muonsand neutral hadrons (mostly K0L and neutrons). The system covers a large solidangle and was designed to have high e ciency and high background rejection.The IFR structure, shown in Fig. 2.6, is made from large quantities of iron,segmented into 18 plates of thickness varying between 2cm (nearest the beam)and 10cm (the outermost layer). The total thickness of the barrel is 65 cm,and the end caps 60 cm. The iron (which also functions as the superconductingmagnet's  ux return) is optimized to be a muon  lter and neutral hadron ab-sorber allowing the best identi cation of muons and K0Ls. The iron layers areseparated by a 3.2 cm gap where up to 19 RPCs, LSTs, or layers of brass canbe housed.Figure 2.6: The IFR barrel and forward (FW) and backward (BW) endcaps.RPCs and LSTs are di erent designs which achieve the same goal | toprovide accurately timed, precise two-dimensional positions of charges passingthrough. An RPC is  lled with a gas mixture of argon, Freon and isobutane.Two graphite-coated surfaces located on either side of the gas are held at apotential di erence of 6700-7600 V. Ionising particles create a streamer betweenthese two surfaces and their presence is read-out by pairs of capacitive stripsrunning parallel and perpendicular to the beam.Linseed oil was used to coat inner surfaces, and degradation of this and theChapter 2. The BABAR Detector 13graphite surfaces contributed to e ciency losses as the experiment progressed.By 2002, the muon identi cation e ciency had dropped from 87% (at the startof running) to 78% at a pion misidenti cation rate of 4%. For this reason,LSTs were installed to replace all RPCs in the barrel. Two sextants were fullyreplaced in summer 2004, and the remaining four sextants in summer 2006. TheRPCs in the forward end cap were replaced with new, more robust RPCs in fall2000 [16].LSTs function slightly di erently from RPCs. An LST consists of eitherseven or eight gas- lled cells. Through the length of each cell runs a wire heldat high voltage (HV) of around 5500 V. To stop the wire sagging, several wire-holders are  tted along the cell's length. The gas mixture in the LST cells ispredominantly carbon dioxide, and also contains smaller amounts of isobutaneand argon.A charged particle passing through the cell ionizes the gas and creates astreamer which can be read out from the wire. This provides the   co-ordinate.The streamer also induces a charge on a plane below the wire. Running parallelto the wires are a series of conducting strips (z-planes) which detect this chargeand provide the z co-ordinate.For the upgrades in 2004 and 2005, the nineteen layers of RPCs in each barrelsextant were replaced by twelve layers of LSTs and six of brass. The outermostlayer of RPCs was inaccessible, so no LSTs could be installed there. The brasswas installed in every second layer starting with the  fth both to compensatefor the loss of absorption between the two outer layers and to increase the totalabsorption length.14Chapter 3Particle ListsThe BABAR database of events (including more than 400 million BB events) isvery large and several stages of processing exist to reduce the time and storagerequirements of analysts. The  nal selected data are stored in ntuples, andanalysts must make a number of decisions regarding the types of informationthat should be stored. For example, it is often desirable to store only events ofa certain type, and necessary to de ne what properties a track candidate shouldhave before it is considered relevant.As well as containing well-measured particles (charged tracks and neutrals)from genuine physics events, raw data includes a lot of other (`junk') informa-tion which must be  ltered as much as possible. This includes particles fromcosmic rays, and beam-gas and beam-wall interactions. The software used bythe BABAR Collaboration is  exible enough to give analysts control over this ltering.The term particle list means a list of all charged or neutral candidates ina particular event which pass certain criteria. These criteria are varied anddepending on the type of list can include limits on track angle, momentum,distance of the track from the interaction point and many other quantities. Acandidate is a collection of hits within the detector (for neutral particles thistakes the form of energy deposits in certain detector components) which afterreconstruction have been identi ed as a likely particle. Candidates can be eithercharged or neutral, and there is no guarantee a candidate is in fact anythingother than background noise | it only has to appear to be a genuine particle.A charged candidate is a track associated with a particle moving inside thedetector which (because of its charge) curves in the magnetic  eld. A neutralcandidate is any EMC cluster which has no matching track.3.1 Lists Used in B CountingThe most basic lists, on which others are based are ChargedTracks and CalorNeu-tral. These contain every charged and neutral candidate after event reconstruc-tion.The lists used in the past for B Counting are ChargedTracksAcc (for chargedcandidates) and GoodNeutralLooseAcc (neutrals). There is also an additionalrequirement based on the number of charged candidates on the GoodTracksAc-cLoose list.The lists used in this analysis are slightly di erent to these and are in-Chapter 3. Particle Lists 15stead based on the established lists GoodTracksLoose (for charged candidates)and CalorNeutral with some customized additions. The requirements for Good-TracksLoose, ChargedTracksAcc and GoodNeutralLooseAcc are shown in Table3.1.Table 3.1: Criteria of some existing particle lists used in B Counting.GoodTracksLoose ChargedTracksAcc GoodNeutralLooseAccpT > 0:05 GeV/c 0:41 <   < 2:54 Raw energy > 0:03 GeVDOCA in xy < 1:5 cm 0:41 <   < 2:409DOCA along z < 2:5 cmjpj < 10 GeV/cV0 daughters excludedThe addition of `Acc' (within acceptance region) to a list name denotes angu-lar requirements which keep the track within the detector. The list GoodTrack-sAccLoose is the same as GoodTracksLoose with the additional requirement0:41 <   < 2:54 for each track.DOCA stands for the Distance of Closest Approach of the track to theinteraction point. By rejecting tracks which do not closely approach the IP, alarge number of background tracks can be removed from the event.Tracks clearly identi ed as V0 daughters are removed from the GoodTrack-sLoose list. These are tracks which originate at a vertex far from the IP, andare obviously secondary decay products.3.2 Charged CandidatesThe list of charged candidates used in this thesis is based on the standard Good-TracksLoose with V0 daughters included. For many analyses it is convenient notto include them in the main charged list so they can later be identi ed and addedonly if desired. For example, it is bene cial for some analyses to reconstruct 0 mesons in this way. For B Counting, this sort of  exibility is not necessary.The quantities of importance for labelling events hadronic or mu-like mostlyrely on information from the entire event such as the total event energy, the to-tal number of tracks, or the sphericity of the event. The sphericity is measuredby a quantity called R2, which is the ratio of the event's second and zerothFox-Wolfram moments [15].In addition to this, some angular requirements are imposed to keep trackswithin the detector's acceptance region. These are determined by comparingdata and Monte-Carlo simulated data. At very high or very low angles, MC isless able to simulate tracks, so the maximum and minimum angular values arechosen to ensure data and MC agree closely in the selected region.At very high or very low angles there are fewer layers of the detector (espe-cially the drift chamber) which particles can traverse. Tracks passing near theedges of detector will be more di cult to reconstruct than other tracks, andChapter 3. Particle Lists 16some may be lost. This is di cult to simulate accurately with Monte Carlo.The angular cuts chosen are almost identical to those used in 'Acc' charged lists.Theta of Each Charged Candidate0 0.1 0.2 0.3 0.4 0.5 0.6Tracks per 0.0030200040006000800010000120001400016000Theta of Each Charged Candidate2.2 2.3 2.4 2.5 2.6 2.7 2.8Tracks per 0.00305001000150020002500300035004000Figure 3.1: High and low theta regions for tracks on the GoodTracksLoose list.The solid line represents on-peak data, and the points (+) o -peakdata.Figure 3.1 shows the high and low   regions for tracks on the GoodTrack-sLoose list. The solid curve represents on-peak data, and the dotted curveo -peak data. In both regions the agreement between MC and data is goodeven beyond the cuts, but sharp drop in data events at just below 0.4 andabove 2.6 indicate the regions where the e ects of reaching the detector's edgesbecome apparent. The cuts are chosen on either side of these drops to ensurethe selected region is both modelled well by MC and doesn't include regionswhere edge e ects appear.For later convenience, this new list is given the name ChargedTracksBC.3.3 Neutral CandidatesThe list of neutral candidates used in this analysis is based on the standardCalorNeutral list. It has additional angular requirements (again to ensure theregion studied is well-described by Monte Carlo), and a minimum energy re-quirement of 100 MeV.The reasoning behind choosing these particular angular cuts (0:42 <   <2:40) is similar to that of the charged tracks list. The high and low theta regionsChapter 3. Particle Lists 17are shown in Fig. 3.2. The acceptance region for neutral particles depends on theangular range of the EMC (see Fig. 2.5), so is di erent than for charged tracks.The shape of Fig. 3.2 clearly shows the EMC construction | the highest peaksare at the centre of EMC crystals.Theta of Each Neutral Candidate0 0.1 0.2 0.3 0.4 0.5 0.6Tracks per 0.0030100002000030000400005000060000700008000090000Theta of Each Neutral Candidate2.2 2.3 2.4 2.5 2.6 2.7 2.8Tracks per 0.00305000100001500020000250003000035000Figure 3.2: High and low theta regions for candidates on the CalorNeutral list.The solid line represents on-peak data, and the points (+) o -peakdata.The angular cut for high theta values is made to exclude the two mostextreme crystals, ensuring neutrals are well within the detector. For the lowtheta region, the cut is based on the agreement between MC and data. AlthoughEMC crystals are in place for theta values as low as 0.3, the best agreementbetween MC and data occurs above 0.42. Within reasonable limits, the exactchoice of angular cut is arbitrary, but the range 0:42 <   < 2:40 is made for theneutral list for the above reasons.To reduce backgrounds, a minimum energy requirement of 100 MeV percluster is also imposed on the neutral list. Erroneous neutral clusters due tobeam gas or electronic noise have a random distribution throughout any event.The level of this background can be determined by examining muon-pair eventswhere the muons are back-to-back. These e+e  ! +   events are very clean| the back-to-back requirement implies the muons have not radiated photons,so within certain limits the muons are the only genuine physics tracks in theevent.Figure 3.4 shows the distribution of energy per neutral cluster for suchback-to-back muon events (solid curve) and compares this to mu-pair MonteChapter 3. Particle Lists 18Theta of Each Neutral Candidate0 0.1 0.2 0.3 0.4 0.5 0.6Tracks per 0.003020004000600080001000012000140001600018000Theta of Each Neutral Candidate2.2 2.3 2.4 2.5 2.6 2.7 2.8Tracks per 0.0030100020003000400050006000700080009000Figure 3.3: BB data and MC for high and low neutral angles. Candidates areon the CalorNeutral list. The solid line represents BB data thepoints (+) BB MC.Carlo. The events plotted pass isBCMuMu and additionally the two highest-momentum tracks are within 0.02 radians (1:1 ) of back-to-back. A cut at 0.1GeV removes the vast majority of neutral energy from this event at the expenseof little physics, so this requirement is included in the B Counting neutral list.This new list is given the name NeutralsBC.Table 3.2: Criteria of the lists used in this thesis.ChargedTracksBC NeutralsBCOn ChargedTracks list On CalorNeutral listpT > 0:05 GeV/c Cluster energy > 0:1 GeVDOCA in xy < 1:5 cm 0:42 <   < 2:40DOCA along z < 2:5 cmjpj < 10 GeV/c0:42 <   < 2:53Chapter 3. Particle Lists 19Energy of Each Neutral Candidate (Data)0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Clusters per 0.005050100150200250300350400450310?Figure 3.4: Neutral backgrounds in Run 6 back-to-back mu-pair events. Thesolid curve represents data, and the points (+) mu-pair MC. Theenergy of each neutral cluster in an event is plotted for mu-likeevents where the muons are within 0.02 radians of back-to-back.20Chapter 4B CountingAs its name suggests, B Counting involves determining the number of BB eventsin a particular data sample. It is necessary to know this to measure any B mesonbranching ratio for a particular  nal state. For example, B(B0 ! D  +) isapproximately 0.3%. This value is equal to the number of B0 !D  + decaysin a particular sample divided by the total number of B0 events in the sample.4.1 Method for B CountingThe B mesons produced at BABAR are from the decay of the  (4S) meson (a bbstate). Due to ine ciencies, the ratio of B0B0 production to B+B  productionfrom  (4S) decay is di cult to measure, but the currently accepted value isconsistent with 1. The BABAR Collaboration has published the result [10]:R+=0 = B( (4S) !B+B )=B( (4S) !B0B0)= 1:006  0:036 (stat.)  0:031 (syst.): (4.1)It is common to assume this number is exactly unity. Hence, to calculate aparticular B branching ratio in a sample, it is only necessary to count the totalnumber of BB events in the sample, regardless of charge.The current method used to count B mesons by the BABAR Collaborationhas been in place since 2000 [11]. In a sample of on-peak data, the number ofBB events is equal to the total number of hadronic events (N0H) less the numberof non-BB hadronic events (N0X).N0B = N0H  N0X (4.2)In this sense, hadronic means events which look like e+e  ! hadrons. Thesuperscript \0" in each case indicates these quantities are the actual numbersproduced of each event type. In reality, every quantity has an associated e -ciency since nothing can be counted perfectly. In the B Counting code, we canonly use the number of each quantity counted, and the number of B mesonsproduced is calculated from the number of B mesons counted by dividing bythe BB e ciency "B.The number of on-peak continuum events can be found by scaling (by lu-minosity) an o -peak sample where, without  (4S) production, all events arenon-BB. The small decrease in energy from on-peak to o -peak data-takingChapter 4. B Counting 21changes all continuum production rates slightly, but almost all of these eventsscale in the same way as muon-pair events (i.e. e+e  !  +  ). Hence, theratio of muon-pairs in the on- and o -peak samples is approximately equal tothe ratio of the luminosities of the two samples. B Counting relies on the factthat the ratio of muon-pair to continuum (i.e. non-BB) events in a sample isthe same (to an excellent approximation) regardless of the CM energy:N0XN0   N00XN00  : (4.3)In this thesis, unless stated otherwise, primed symbols represent o -peak values.4.2 Derivation of the B Counting FormulaSuppose we wish to calculate the number of B mesons in a sample of on-peakdata of luminosity L, using an o -peak data sample of luminosity L0. For sim-plicity, o -peak quantities are primed, and hadronic, mu-pair, BB and contin-uum quantities have the subscripts H,  , B and X respectively. The numbersproduced of each quantity (as opposed to those counted by the B Countingselectors) have the superscript \0".In a sample of on-peak data, the number of BB events is equal to the totalnumber of hadronic events (N0H) less the number of non-BB hadronic events(N0X).N0B = N0H  N0X (4.4)The number of on-peak continuum events can be found by scaling (by lu-minosity) an o -peak sample (in which all events are non-BB). The smalldecrease in energy from on-peak to o -peak data-taking changes all continuumproduction rates slightly, but almost all of these events scale in similar wayswith luminosity.For any particular type of event, the number counted is equal to the numberproduced multiplied by the e ciency ("). So for example,N  = " N0  = "   L (4.5)andN0  = "0 N00  = "0  0 L0: (4.6)For o -peak data, there is no  (4S) production, so we can assume that allhadrons are from continuum events (and hence the symbols N0H and N0X areequivalent):N0H = N0X = "0XN00X = "0X 0XL0: (4.7)We de ne:    "0  0 "     "X X"0X 0X (4.8)        X: (4.9)Chapter 4. B Counting 22We combine (4.6), (4.7) and (4.8) to give:N0XN0    ="0X 0XL0"0  0 L0   ="X X"    : (4.10)The hadronic events in the on-peak sample consist of continuum and BBevents:N0H = N0X + N0B (4.11)and the number of counted hadronic events isNH = "XN0X + "BN0B: (4.12)Hence from (4.10), we can write"BN0B = NH  "XN0X (4.13)= NH  "X XL (4.14)= NH   N0HN0        "     N "    (4.15)= NH  N    N0HN0     : (4.16)Hence, the number of BB mesons produced in the on-peak sample is givenby:N0B = 1"B(NH  N    Roff    ); (4.17)whereRoff   N0XN0  : (4.18)In general,   is close to unity. The exact values and uncertainties of    and  Xare discussed in detail later.4.3 B Counting GoalsFigure 4.1 demonstrates the scaling of on- and o -peak data by the number ofmuon-pairs in each sample. The  gure is a plot of total energy for events passingall hadronic cuts, except for one on ETotal itself (the existing B Counting cut isset at 4.5 GeV). Samples of on- and o -peak data from the same time period areplotted | in this case from `Run 4', which took place between September 2003and July 2004. The o -peak data is luminosity-scaled (by the ratio of muonpairs in each sample) to match the on-peak data.When correctly-scaled o -peak data is subtracted from on-peak data, theremaining events are those from  (4S) decay, the vast majority of which areBB events. This BB data is shown in Fig. 4.1 and again in Fig. 4.2 where it isoverlaid with BB Monte Carlo (MC) generated events. The agreement betweendata and MC is generally very good.Ideally the B Counting hadronic selection e ciency should be:Chapter 4. B Counting 23Total Event Energy Divided by CM Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4Events per 0.007 Units0100002000030000400005000060000700008000090000Figure 4.1: Total energy divided by CM energy (ETotal/eCM) for events passingall B Counting hadronic cuts apart from one on ETotal for a sampleof data from Runs 5 and 6. The bin width is 0.007. The solid (+)histogram represents on-peak (o -peak) data. The o -peak data isscaled by luminosity to the on-peak data, and the dotted histogramis the di erence between the two.Total Event Energy Divided by CM Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4Events per 0.007 Units0500010000150002000025000300003500040000Figure 4.2: ETotal/eCM on- and o -peak subtraction, overlaid with BB MonteCarlo. The solid histogram represents data (o -peak subtractedfrom on-peak in Fig. 4.1) and the dotted histogram is from MC.The histograms are normalised to have the same area from 0.0{1.0.Chapter 4. B Counting 24  high for B meson events,  insensitive to changing background conditions (i.e. stable in time), and  in good agreement with simulation BB Monte Carlo.Similarly the B Counting muon selection should also be insensitive to back-grounds and be in good agreement with MC. The speci c selection requirementsare described in later chapters.More than 400 million BB pairs have been created in BABAR during itsrunning, so B Counting is a very high statistics task and uncertainties arepredominantly systematic. The main aim of the work described in this thesis isto  nd selection criteria optimising these requirements and minimising the  nalsystematic error in the number of B pairs counted.4.4 TrkFixupThis thesis proposes the  rst major update to B Counting since the originalmethod was devised in 2000. Since then, many improvements have been madeto both hardware and software within BABAR which have improved the precisionof many analyses. One of the most signi cant for B Counting, named TrkFixupwas proposed in 2005 and fully implemented by mid-2007.A systematic uncertainty present in any BABAR analysis comes from thetracking precision. There are many reasons the tracking information of chargedparticles passing through the detector can be incorrect. For example, a collectionof drift chamber and SVT hits due to noise could be incorrectly reconstructed asa charged track. Similarly low-momentum particles which loop around withinthe detector can be misidenti ed as more than one track.TrkFixup improves the tracking precision through several methods. Firstly,it improves track resolution by modifying pattern recognition algorithms. It alsoincreases the track  nding probability and removes unwanted (`junk') trackssuch as duplicate (e.g. looping) tracks and backgrounds. This is achieved byre-examining `questionable' tracks with more sophisticated algorithms than pre-viously used.These improvements are important to B Counting for several reasons. Re-ducing sensitivity to beam backgrounds is a key part of this thesis and theaddition of TrkFixup to track reconstruction improves this even before any ad-justment to the B Counting cuts is made. Some other improvements are obvious,such as increased precision in measurements of track momentum and position.This is important for border-line events which narrowly pass or fail a particularcut.When counting muon-like events, a requirement of the B Counting code isthat the event have at least two `good' tracks. TrkFixup a ects B Countingdirectly through this cut, as events previously with only one good track couldnow be found to have two or more. Similarly, an event previously labelled asmu-like could be found after TrkFixup to have fewer than two good tracks andthus fail the selection.Chapter 4. B Counting 254.5 Original B Counting RequirementsThe original requirements (i.e. those in place before the research describedherein) for an event to be labelled as mu-like or hadronic for B Countingpurposes were proposed in 2000 [11]. An event passing these criteria duringprocessing receives a label (known as a `tag') isBCMuMu or isBCMultiHadronrespectively. The criteria are summarized in Table 4.1.During reconstruction, events can receive one or more BGF tag. They havevery simple criteria and are designed to quickly accept all possibly useful physicsevents. The BGF tags enable some time to be saved during reconstruction, asan event must have at least one of them to be fully processed. BGFMultiHadronand BGFMuMu are two of these which are used in B Counting.BGFMultiHadron has the very simple selection requirements of at least threecharged tracks, and R2 of less than 0.98 in the CM frame. R2 is the secondFox-Wolfram Moment divided by the zeroth Fox-Wolfram Moment and is ameasure of the event's sphericity [15]. A pair of back-to-back particles haveR2 approaching one, while very spherical events (i.e. ones with many tracksdistributed evenly around the event) have R2 approaching zero. Thus the eventswhich do not receive the BGFMultiHadron tag are mostly e+e  ! `+` . Thethree track requirement also  lters out several types of two-photon and InitialState Radiation (ISR) events.Table 4.1: Criteria of the isBCMuMu and isBCMultiHadron B Counting tags.The de nitions of each quantity are given in the text.isBCMuMu Tag isBCMultiHadron TagBGFMuMu BGFMultiHadronmasspair > 7:5 GeV/c2 R2All   0:5acolincm < 0:17453 (10 ) nGTL   3nTracks   2 ETotal   4:5 GeVmaxpCosTheta < 0:7485 PrimVtxdr < 0:5 cmmaxpEmcCandEnergy > 0 GeV jPrimVtxdzj < 6:0 cmmaxpEmcLab < 1 GeVThe criteria of BGFMuMu are also very broad, and are designed to quicklyreject events which cannot be mu-pair events. To be labelled BGFMuMu, thetwo tracks of highest momenta must have momenta above 4 GeV/c and 2 GeV/crespectively and be approximately back-to-back (2:8 <  1 + 2 < 3:5). Also, theenergy deposited in the EMC by the two highest-momentum tracks must addto less than 2 GeV.The isBCMuMu tag has many criteria which depend on the properties of thetwo highest-momenta tracks | if the event is a genuine mu-pair event, these willalmost certainly be the two muons. The quantity masspair is the invariant massChapter 4. B Counting 26of the pair and acolincm is the acolinearity (the angular departure from back-to-back) of the pair in the centre-of-mass (CM) frame. Also in the CM frame,both tracks must have j cos( )j < 0:7485. The maximum energy deposited in theEMC by one of these tracks must be less than 1 GeV in the laboratory frame,and at least one must leave some energy in the EMC. The former conditionrejects approximately 99.7% of all Bhabha events, which on average depositjust over 5 GeV of energy per electron track. The  nal isBCMuMu quantity isnTracks, the number of reconstructed charged tracks on the TaggingList list.The criteria of isBCMultiHadron mostly involve quantities related to theentire event. R2All is R2 calculated only using charged and neutral candidatesfrom within the detector acceptance region (i.e. from the ChargedTracksAccand GoodNeutralLooseAcc lists). There are also requirements on the number oftracks on the GoodTracksLoose list (nGTL) and the total event energy recordedin the laboratory frame (ETotal).A possible source of background events is beam-wall interactions. These areshowers caused by a particle from the beam interacting with the walls of thebeam pipe and can resemble genuine physics events. The primary vertex is thepoint calculated after reconstruction to be the most likely vertex for all tracks inthe event. To reject beam-gas interactions, isBCMultiHadron has requirementson the distance between the primary vertex and the beamspot in the xy plane(PrimVtxdr) and in z (PrimVtxdz).The number of B mesons in a particular on-peak sample can be calculatedusing these tags and (4.17) by equating the number of isBCMuMu events withN  and the number of isBCMultiHadron events with NH.The value of Roff depends on beam conditions and backgrounds and sochanges with time. O -peak running occurs only for short periods around largerblocks of on-peak running, so when calculating the number of B mesons in anyparticular on-peak sample, the value of Roff is based on the closest blocks ofo -peak running.Many e ects including changing background conditions cause long-term time-variations in selector (hadronic and muon-pair) e ciencies and this is discussedin the following chapters. The association of on-peak data with only the mostrecent o -peak running period ensures this variation has a minimal e ect on BCounting.27Chapter 5Muon SelectionThe motivation for the work in this thesis is to improve the understanding ofB Counting at BABAR and if possible to modify the method to reduce overalluncertainty. With more than 400 million BB pairs recorded, statistical e ectsare often negligible, so improvements must come through reducing systematicuncertainty. This chapter describes proposed modi cations to the mu-pair partof the B Counting code.5.1 Monte Carlo SimulationMuon-pair events are simulated with the KK2F MC generator [17]. Before anydetector simulation is applied, the physics cross-sections for the process e+e  ! +   within the detector can be calculated using a BABAR application calledGeneratorsQAApp. Based on 10 million generated on- and o -peak events, thecross-sections are (1:11853 0:00011) nb and (1:12647 0:00011) nb respectively.For detector simulation of all MC events, the BABAR Collaboration usesGEANT 4 [18]. After GEANT has been applied to the simulated events, they aremade to correspond to a particular time by adding background frames from data.These frames are random `snapshots' of detector occupancy and are recordedat a rate of 1 Hz. The events are then reconstructed in the same way as data.This background mixing increases the realism of the Monte Carlo simulationby more accurately re ecting the processes occurring simultaneously within thedetector.The detector conditions (such as the number of non-functioning EMC crys-tals), the levels of beam-background, luminosity and other e ects vary withtime and cause a time-dependence in the e ciency of the mu-pair selector. Thee ciency of isBCMuMu (and almost any other quantity) for a sample of MCdepends on the time at which it was `taken', i.e. on the time of the mixed-inbackgrounds. Here, e ciency means the proportion of generated mu-pair eventswhich pass the mu-pair B Counting selector. In this way MC simulates the samee ect in data.The e ciency of isBCMuMu for simulated mu-pair MC is approximately43%. As described in Chapter 4, the number of mu-pair events in a data sampleis used to scale the sample by luminosity. In modifying the muon selection, thegoal is to reduce the total uncertainty when counting B mesons, so the absolutevalue of the e ciency is not as important its variation in time.Chapter 5. Muon Selection 285.2 Cut on Muon Pair Invariant MassIdeally the muon selection will function identically on both on- and o -peakdata. The total change in energy between the two is small (around 40 MeV),but any cut which varies depending on CM energy should be altered to minimizethe e ect.Of the isBCMuMu cuts listed in Table 4.1, the one altered the most by thise ect is masspair | the invariant mass of the two highest momentum tracks.This cut is designed to reject tau pairs but accept almost all genuine muonevents. The tau pairs are very short-lived and decay into multiple particlesbefore reaching the beam-pipe walls. These events fail because the two highest-momentum tracks do not carry the majority of the energy and their invariantmass is comparatively low. For muon-pair events, masspair peaks near the beamenergy.A simple method of removing sensitivity to CM energy (eCM) is to de nea new quantity, masspair scaled by the total energy | masspair/eCM | andcut instead on this. If the cut value in Table 4.1 is scaled by the on-peak beamenergy of 10.58 GeV, the revised cut is:masspaireCM >7:5 GeV=c210:58 GeV   0:709: (5.1)In this thesis, we set c = 1 for convenience unless otherwise stated.5.3 Minimum EMC Energy RequirementAs described in Chapter 4, to receive the isBCMuMu tag an event must meetcertain EMC requirements. Of the two highest-momenta tracks, the maximumenergy deposited in the EMC by either one must be non-zero and less than 1GeV. It was found during this research that depending on the time-of-running,up to 2% of events failed muon selection because both tracks deposited no energyin the EMC, i.e. events which would otherwise pass the selection were rejectedbecause the quantity maxpEmcCandEnergy was zero.In the original B Counting code, the maximum EMC energy cut was calcu-lated in the lab frame, while the minimum was calculated in the CM. However,any zero measurement in the EMC is equivalent regardless of frame, so for sim-plicity in this thesis, the minimum and maximum allowed EMC deposits areboth calculated in the lab frame.This e ect was studied in samples of at least a million on-peak data eventswith the BGFMuMu tag from each of the six major running periods (Runs 1{6). Some of the quantities of interest for events passing all other muon selectionrequirements are shown in Tables 5.1 and 5.2. The value of p1EmcCandEnergyis the amount of energy left in the EMC by the highest momentum track, andp2EmcCandEnergy the amount for the second highest momentum track. Themaximum of the two is named maxpEmcCandEnergy. The distribution of thisChapter 5. Muon Selection 29maxpEmcCandEnergy (GeV)0 0.2 0.4 0.6 0.8 1 1.2Events per 12 MeV0100200300400500310?Figure 5.1: Distribution of maxpEmcCandEnergy for on-peak Run 6 data pass-ing all other muon-pair selection cuts.quantity for a sample of Run 6 on-peak data passing all other muon-selectioncuts is shown in Fig. 5.1.Any track has a non-zero chance of leaving no energy in the EMC. This couldbe due to any of several reasons including reconstruction errors or the particlehitting a gap between two EMC crystals. Assuming the individual probabilitiesare independent, the probability of both of the two highest momentum tracksleaving no EMC energy should be approximately the square of this number.However, as can be seen in Tables 5.1 and 5.2, the number of events with bothEMC clusters equal to zero (i.e. where maxpEmcCandEnergy=0) is much higherthan would be expected.This e ect does not appear to be due to EMC failures in a particular region.Figure 5.2 shows the angular distribution in cos( ) and   of the muons in asample of Run 6 data events which pass all other muon-selection cuts, butwhich have maxpEmcCandEnergy of zero. Note that the distribution is fairlyrandomly spread in   and  , although some broad bands are visible at constant  due to detector geometry.The high proportion of events with maxpEmcCandEnergy of zero indicatessome other e ect is present | it is especially noticeable in Runs 2 and 3 wherethe probability of both tracks leaving nothing in the EMC is greater than theprobability that the highest momentum track alone deposits nothing. This wasexamined by Rainer Bartoldus and the BABAR Trigger, Filter and LuminosityAnalysis Working Group (AWG). The predominant cause was found in eventswhere the DCH and EMC event times di ered.The Drift Chamber and EMC have di erent timing systems, so can occa-Chapter 5. Muon Selection 30cos(theta) of track-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Phi co-ordinate of track-3-2-10123Figure 5.2: Angular distribution of muons from Run 6 data with maxpEmc-CandEnergy of zero. The value of   and cos( ) in the CM frameare plotted for the two highest-momentum tracks in events whichpass all other muon-selection requirements. The number of eventsin each bin of this 100  100 grid is proportional to the area of thebox at the bin-centre.sionally disagree on the event time (t0). The EMC t0 is calculated in two stages.First, the average arrival-time of energy in a wide time-window around the eventis found. The window is then narrowed around this average to select the EMChits to be reconstructed. This method is susceptible to calculating incorrectt0 if background events such as stale Bhabhas arrive at an inopportune time.Stale Bhabhas are unwanted Bhabha events which happen to occur at almostthe same time as another physics event.Such an event passing through the EMC at either end of the event windowcould cause the average arrival time of energy to shift to a time when no energyis in the EMC. Through this process events that would otherwise pass muonselection can have no energy visible in the EMC and be rejected. The proportionof events with EMC information lost in this way is complicated to simulate, butTables 5.1 and 5.2 show reasonable agreement (usually within a factor of 2)between data and Monte Carlo.The majority of these events can be regained by changing the minimummaxpEmcCandEnergy to:  Either maxpEmcCandEnergy > 0,  or at least one of the two highest momentum tracks is identi ed as a muonin the IFR.Chapter 5. Muon Selection 31Table5.1:E ectoftheminimummaxpEmcCandEnergyrequirementonsamplesfromRuns1{3.Run1Run2Run3DataMCDataMCDataMC#BGFMuMuEvents1:001 1060:807 1061:542 1062:580 1064:622 1061:718 106Passallcutsbutminimum0:681 1060:576 1061:055 1061:837 1063:155 1061:223 106EMCenergy(y) %ofywith0.520.321.340.411.090.38p1EmcCandEnergy=0 andp2EmcCandEnergy6=0 %ofywith0.910.701.710.831.440.79p2EmcCandEnergy=0 andp1EmcCandEnergy6=0 %ofywith0.040.141.701.911.371.66maxpEmcCandEnergy=0(z) %ofzwithat23.385.483.393.480.691.3leastonetrackidenti ed asamuoninIFRChapter 5. Muon Selection 32Table5.2:E ectoftheminimummaxpEmcCandEnergyrequirementonsamplesfromRuns4{6.Run4Run5Run6DataMCDataMCDataMC#BGFMuMuEvents2:516 1063:556 1062:694 1063:045 1063:151 1061:003 106Passallcutsbutminimum1:724 1062:542 1061:874 1062:186 1062:154 1060:711 106EMCenergy(y) %ofywith0.660.450.650.430.630.36p1EmcCandEnergy=0 andp2EmcCandEnergy6=0 %ofywith1.070.841.080.831.040.76p2EmcCandEnergy=0 andp1EmcCandEnergy6=0 %ofywith0. %ofzwithat65.193.489.897.987.693.5leastonetrackidenti ed asamuoninIFRChapter 5. Muon Selection 33A requirement on the IFR has not been used previously in B Counting. Thisis because in general its muon identi cation e ciency is too low and variabilitywith time too large to provide stable identi cation. However, in this case theIFR is used only to recover genuine muon-pair events that would otherwise belost, so enables a net e ciency gain and improved stability in time.Muons are identi ed in the IFR by a Neutral Net muon selector [19], speci -cally by muNNVeryLoose. The e ciency of this selector varies with time, but inmuon-pair MC the probability that at least one of the two highest-momentumtracks passes is typically over 90%.The  nal row of Tables 5.1 and 5.2 shows the percentage of events recoveredby adding this IFR requirement. In Run 6 data for example, 87.6% of eventswhich pass all other isBCMuMu requirements but which have maxpEmcCan-dEnergy of zero are recovered.5.4 Optimization of CutsThe muons counted by isBCMuMu selection are used to measure the luminosityof a sample of events. Since on- and o -peak data are taken at di erent times,the two have di erent background conditions. Hence, to correctly perform theB Counting background subtraction it is important the muon-pair selection beas insensitive as possible to changing backgrounds. The variation is reducedto some extent by changing to the particle lists described in Chapter 3 and byaltering the masspair and maxpEmcCandEnergy cuts as described above.This sensitivity can be measured by the changes in muon-pair MC e ciencywith time. Ideally the e ciency should be identical regardless of run number |a sample of generated mu-pair events with Run 1 backgrounds should have thesame e ciency as the same events with Run 6 backgrounds. In practice this isnot the case, but by choosing di erent cut values for the requirements outlinedin Table 4.1 it can be reduced.The requirement of BGFMuMu is essential as it quickly  lters out largeamounts of events which cannot be muon-pairs. Likewise there is little  exibilityin the requirement of at least two well-identi ed charged tracks. The selectorshould identify events with well-tracked muons, and all events of this type willhave at least two tracks on the charged list. The modi cation of the minimummaxpEmcCandEnergy requirement described above helps veto Bhabha eventsand is not further adjusted.The four remaining isBCMuMu requirements have slightly more  exibilityin their cut values. The justi cation for the current cuts is given in [11], but theaddition of TrkFixup and the di erent particle lists (ChargedTracksBC and Neu-tralsBC) used in this thesis are reason enough that they should be re-evaluatedat this stage. Additionally, the method used in this thesis to  nd an optimalcut-set is improved and more robust.To optimise the isBCMuMu cutset, the month-by-month e ciency for muon-pair MC in both on- and o -peak running was calculated for di erent cutsetchoices. Up to and including Run 6, there are 63 months with on-peak muon-Chapter 5. Muon Selection 34pair MC and 27 months with o -peak MC. For convenience, each month fromthe time of running is given an integer label | from January 1999 (month 0)to December 2007 (month 107).The total number of cutsets trialled in the optimization procedure was 13 17 20 14 = 61880. The weighted mean e ciencies of these cutsets are between0.262 and 0.450.Table 5.3: Cut optimization of isBCMuMu.Quantity No. of increments Rangemasspair/eCM 13 (6:0 { 9:0)=10:58maxpCosTheta 17 0.650 { 0.765acolincm 20 0.01 { 0.20maxpEmcLab 14 0.7 { 2.0 GeVThe forward and backward ends of the detector have di erent acceptanceregions, and the di erent angular cuts on ChargedTracksBC and NeutralsBCre ect this. When varying maxpCosTheta (the maximum value of j cos CMj forthe two highest momentum tracks), some care must be taken to ensure the cutis not varied into a region excluded by the list's own angular cuts.To  nd the  CM angles corresponding to the angular cuts of ChargedTracksBCfor a typical muon we boost into the laboratory frame from the CM by    = 0:56 along z. The method for calculating the transformation of the angles ofa velocity can be found in many relativistic kinematics texts, for example [20].We  nd:tan  CM = v sin  (v cos  +  c) (5.2)where v is the velocity of a particle travelling at angle   relative to the z axisin the laboratory frame. Practically all muons from e+e  !  +   have CMmomenta between 5.0 and 5.5 GeV/c, which corresponds to having velocitiesof 0.9999c in the laboratory frame (the two are identical to four signi cant gures). Using (5.2) and this velocity, the minimum and maximum angles ofChargedTracksBC (0.42 and 2.53) boost to 0.698 (cos CM = 0:766) and 2.776(cos CM = 0:934) in the laboratory frame respectively.Hence, when varying maxpCosTheta, values above 0.766 should be ignoredto agree with the angular requirements of the charged list. In practice, cutvalues up to and including 0.765 are trialled.The on- and o -peak muon-pair MC e ciency variation is shown in Fig. 5.3and 5.4. The cutset shown has fairly typical time-variation. It has an acolincmcut of 0.07, masspair/eCM of (8:00=10:58), maxpCosTheta of 0.765 and amaximum maxpEmcCandEnergy cut of 1.0 GeV.In each month i, the statistical error  ("i) is assumed to be binomial with ("i) =p"i(1  "i)=Ni (5.3)Chapter 5. Muon Selection 35Month number20 40 60 80 100Efficiency0.410.4120.4140.4160.4180.420.422Figure 5.3: On-peak mu-pair MC e ciency variation. Details of cutset choiceand error bars are in text. The  2 value is 124.04 and M (thenumber of degrees of freedom) is 63. The dashed lines show  0:5%from the mean.Month number20 40 60 80 100Efficiency0.410.4120.4140.4160.4180.420.422Figure 5.4: O -peak mu-pair MC e ciency variation for the same cutset choiceas on-peak distribution. The  2 value is 47.94 and M (the numberof degrees of freedom) is 27. The dashed lines show  0:5% from themean.Chapter 5. Muon Selection 36where "i is the e ciency and Ni the total number of generated events for thatmonth. If we assume the e ciencies come from a statistical distribution whichis constant in time, the weighted mean ^ (the solid horizontal line on the plots)is given by^ = 1wMXi=1wi"i (5.4)where M is the number of months with MC events, wi = 1=( ("i))2 and w =Pwi. The statistical standard deviation (shown by dashed horizontal lines)of ^ is 1=pw [21]. The variation around the weighted mean is obviously notrandom, and this shows the presence of some non-statistical systematic e ects.The amount of systematic variation present can be measured by calculatingthe  2 statistic 2 =MXi=1("i   ^)2( ("i))2 (5.5)for each cutset. If the variation was entirely statistical, an average  2 value ofM  1 would be expected. The value of M  1 is 62 for on-peak MC and 26 foro -peak MC. For the cutsets trialled,  2 is much higher than this: for example124.04 and 47.94 in Fig. 5.3 and 5.4. The on- and o -peak distributions of  2values for the 61880 cutsets are shown in Fig. 5.5 and 5.6.All cutsets trialled have a lower  2 statistic than the existing B Countingmuon-pair selection. For the same samples of on- and o -peak MC, the  2statistics of the isBCMuMu tag were 1016.5 and 402.25 respectively.5.5 Estimating Systematic UncertaintyFrom Fig. 5.5 and 5.6 it is clear that all cutsets have  2 values indicating vari-ation beyond statistical  uctuations. There is however, a broad range of  2values | this indicates that some choices of cutset are objectively better (i.e.less sensitive to systematic e ects) than others.To gauge the size of the systematic uncertainty we look for d0 in a modi ed 2 statistic 02(d) =MXi=1("i   ^)2( ("i))2 + d2 (d   0) (5.6)such that 02(d0) = M  1: (5.7)Equation (5.6) is equivalent to a polynomial of order 2M in d. Clearly ford = 0,  02(0) =  2 > M   1 and for large d,  02(d) ! 0. So, since (5.6) iscontinuous, by the Intermediate Value Theorem there is at least one real d0satisfying (5.7).In practice, d0 is found numerically by incrementing d from zero in steps of1  10 6 until  02(d) < M  1. The value of d at this point is taken to be equalChapter 5. Muon Selection 37Chi-squared statistic90 95 100 105 110 115 120 125 130 135Cutsets per 0.4502004006008001000120014001600180020002200Figure 5.5: Distribution of  2 statistic for trialled cutsets with on-peak mu-pairMC. M (the number of degrees of freedom) is 63.Chi-squared statistic25 30 35 40 45 50 55 60 65 70Cutsets per 0.4502004006008001000120014001600180020002200Figure 5.6: Distribution of  2 statistic for trialled cutsets with o -peak mu-pairMC. M (the number of degrees of freedom) is 27.Chapter 5. Muon Selection 38to d0. The ranges of d0 values for di erent cutsets are (5:57 { 9:27)  10 4 inon-peak MC and (2:93 { 7:89)  10 4 in o -peak MC.The total uncertainty for a particular cut-set is then the sum in quadratureof statistical uncertainty (1=pw) and systematic uncertainty (d0). The `optimal'set of cuts is the one which causes the lowest uncertainty in the total numberof B mesons.It is important to note the di erence between the uncertainty used for thepurposes of optimization and the value of the systematic uncertainty in data.The optimization procedure seeks to  nd the cutsets (muon-pair and hadronic)which cause the lowest uncertainty in B Counting due to time-variation of MC.This amounts to  nding the cutsets which are most stable in time.The systematic uncertainty for MC does not correspond directly to the sameuncertainty in data. Steps are taken in data to reduce the e ect of varying e -ciencies, and the association of on-peak data with only the most recent Roff valuereduces this e ect to a large degree. The estimation of systematic uncertaintiesin data is discussed in Chapter 9.5.6 Variation in   The results above can be used to evaluate the value of    as de ned in (4.8). Inpast B Counting code,  , the product of    and  X has been set equal to unity.   is equal to the ratio of o - to on-peak muon-pair cross-sections, multipliedby the respective e ciencies.The theoretical cross-section for electron annihilation to a muon-pair e+e  ! +   at CM energy squared of s is approximately [22]:   = 4  23s  86:8 nbs (in GeV2): (5.8)So, since the muon-pair cross-section scales inversely with s, the expected valueof    is approximately:   =  0  0       10:58210:542   1:0076: (5.9)To  nd the time-variation in    some care needs to be taken when choosingtime bins. On- and o -peak running occur at di erent times, and often the gapbetween o -peak running periods is quite large. To manage this, the runningtime is divided into 24 unequal bins such that each contains periods of both o -and on-peak running. This makes it possible to calculate a value for    in eachtime bin.Variation in    is calculated using the same method used to calculate varia-tions in mu-pair e ciency. The statistical uncertainty in    includes the e ectsof the independent statistical uncertainties of on- and o -peak mu-pair MC ef- ciencies which are given by (5.3). There is also a small contribution from theuncertainty in the MC cross-sections,  (  ) and  ( 0 ).Chapter 5. Muon Selection 39Time bin number0 5 10 15 20 25K value per time bin11.0051.011.0151.02Figure 5.7: Time-variation of    for the cutset shown in Fig. 5.3 and 5.4. The 2 value is 21.01, M is 24 and the weighted average is 1.00854. Thedashed lines show  0:5% from the mean. ("i  ) = [( ("i)  )2 + ("i (  ))2]12 (5.10)and similarly for o -peak MC. The method used for calculating propagationof uncertainties is given in Appendix A. The statistical uncertainty in    fortime-period i is then given by (A.4): (  ;i) ="   ("0i 0 )"i   2+  "0i 0    ("i  )("i  )2 2 # 12: (5.11)The shape of the time distribution for the same cutset considered in Section5.4 is shown in Fig. 5.7. It is much closer to a constant than for either the on-or o -peak e ciencies, and the variation in time seems to be mostly consistentwith only statistical variation. This is an indication that much of the variationin mu-pair MC is due to systematic e ects which a ect on-peak and o -peakMC similarly.With 24 periods of time considered, the value of M  1 for    is 23. The  2statistic can again be calculated, and for the pictured cutset it has a value of21.01. The weighted mean value of    for this cutset is^  = 1:00854  0:00044 (5.12)Chapter 5. Muon Selection 40which within two (statistical) standard deviations of the theoretical expectation.The distribution of  2 values for all cutsets is shown in Fig. 5.8. Across allcutsets, the mean value of  2 is 24.88.Chi-squared statistic10 15 20 25 30 35 40 45 50 55Cutsets per 0.45050010001500200025003000Figure 5.8: Distribution of     2 statistic for all trialled cutsets. M (the numberof degrees of freedom) is 24.As before, the amount of systematic uncertainty present in each cutset's   variation can be estimated by  nding d0 satisfying a modi ed (5.7). We do notallow d2 to be negative, so for cutsets with  2 less than 23, d0 is set to zero.Following the same method as above, the range of d0 values is between zero and0.00172. This is added in quadrature with the statistical uncertainty to give thetotal uncertainty on each cutset's    value.41Chapter 6Hadronic SelectionThe criteria for good hadronic selection requirements were mentioned in Section4.1. This chapter describes proposed modi cations to the hadronic part of theB Counting code.The change to the NeutralsBC list with a minimum neutral energy require-ment reduces the sensitivity to backgrounds before any optimization is per-formed on the hadronic selection. Several of the other cut quantities are changedto match the new lists. Instead of requiring at least three tracks on the Good-TracksLoose list, the cut is instead based on ChargedTracksBC. Previously, thevalues of ETotal and R2All were based on the the GoodNeutralLooseAcc andChargedTracksAcc lists. Now, they are calculated by combining all candidateson the ChargedTracksBC and NeutralsBC lists.Similarly, PrimVtxdr and PrimVtxdz (the distance of the event's primaryvertex from the beamspot in r and z) were formerly calculated by  nding thevertex of all tracks on ChargedTracksAcc. In this thesis, these quantities arecalculated from tracks on an intermediate charged list, which is equivalent toChargedTracksBC before any cuts on DOCA (in either xy or z) are made.6.1 Monte Carlo SimulationThe method for optimizing hadronic selection is similar to the mu-pair selectionoptimization discussed in the previous chapter. Hadronic continuum eventsare simulated with e+e  ! uu=dd=ss and e+e  ! cc on-peak and o -peakMC using the JETSET MC generator [23]. As with muon-pair MC, once theMC events are generated, detector response is simulated with GEANT 4 andbackground frames are added.In data, there are additional sources of hadronic continuum events | InitialState Radiation (ISR) and two-photon events. These are small in comparisonto the other continuum events and their e ects are discussed in later chapters.The present optimization procedure seeks to minimize the time-sensitivity ofhadronic selection for uds and cc Monte Carlo only.The production cross-sections for the continuum MC used in the optimiza-tion procedure are given in Table 6.1. These values are based on 1 millionon- and o -peak events of each type simulated by the KK2F generator. BBevents are simulated in a similar way to continuum MC, but with the EvtGenMC generator [24]. The e ciency of the isBCMultiHadron tag for BB MC isapproximately 96%.Chapter 6. Hadronic Selection 42Table 6.1: Continuum MC cross-sections used in optimization.Continuum On-Peak   O -Peak  MC Typeuu 1:5735  0:0013 nb 1:5847  0:0013 nbdd 0:3931  0:0003 nb 0:3959  0:0003 nbss 0:3751  0:0003 nb 0:3778  0:0003 nbcc 1:2929  0:0004 nb 1:3021  0:0004 nb6.2 Cut on Total EnergyAs in Section 5.2, hadronic selection should function in the same way, regardlessof CM energy. Of the isBCMultiHadron cuts listed in Table 4.1, the one a ectedby this is the cut on total event energy in the laboratory frame. This dependenceis removed by scaling by eCM. If the cut value is scaled by the on-peak beamenergy, the adjusted requirement is:ETotaleCM >4:5 GeV10:58 GeV   0:4253: (6.1)The cut on total lab energy is primarily in place to reject beam-gas andtwo-photon events. The adjusted cut slightly increases the isBCMultiHadrone ciency for o -peak continuum events.6.3 Cut on Highest-Momentum TrackEvents of the type e+e  !`+`  where ` is either e or   typically have at leastone track with approximately half the beam energy in the CM frame. This doesnot happen for B decays, as the B mesons very quickly decay into other particleswell within the detector. Typically each B meson decays into two tracks, eachwith approximately a quarter of the beam energy. One possible way to increasethe Bhabha and mu-pair rejection in the hadronic selection without a ectingBB e ciency is to reject events where the highest momentum track has closeto half the beam energy.Some poorly-tracked particles have an arti cially high momentum (for ex-ample a momentum of 4  2 GeV/c), and SVT-only tracks are especially proneto this. At short distances chord and arc length are very similar, so to preciselymeasure a track's curvature (and thus momentum) it is usually necessary tomake measurements outside the SVT, some distance from the beamspot. Aminimum requirement for this is at least one hit in the drift chamber.In hadronic selection optimization, one variable is a new proposed cut onp1Mag, the CM momentum of the highest-momentum track. If the highest-momentum track has at least one hit in the drift chamber and its momentumis greater than the cut value, the event is rejected.Figure 6.1 shows the distribution of p1Mag for BB MC events where thehighest-momentum track has at least one drift chamber hit. The sample containsChapter 6. Hadronic Selection 431.8 million Run 6 MC events. Clearly, above 3.0 GeV/c the number of eventsis negligible.p1Mag (GeV/c) 0 1 2 3 4 5 6 7 8 9 10Events per 0.05 GeV/c 110210310410510Figure 6.1: Distribution of p1Mag for a sample of BB Monte Carlo events wherethe highest-momentum track has at least one DCH hit.In the optimization procedure, the cut on p1Mag (with the requirement onDCH hits) is varied between 3.0 and 5.0 GeV/c or is turned o  altogether.6.4 Optimization of CutsSimilarly to mu-pair selection, there are certain cuts necessary for isBCMul-tiHadron which allow little  exibility. These include the cuts on PrimVtxdrand PrimVtxdz. The reasons for the current cut values on these quantities aregiven in [11]. Both cuts are designed to reject backgrounds, while maintaininghigh BB e ciency. They especially reject events which have a vertex at thebeam-wall.Figures 6.2 and 6.3 show the distributions of these two quantities for a sampleof BB data (i.e. o -peak subtracted from on-peak) from Run 6 overlaid with BBMC. The data sample contains the BB events from a sample of 2.81 million on-peak events which pass all isBCMultiHadron requirements apart from those onPrimVtxdr and PrimVtxdz. The cuts used in hadronic selection (PrimVtxdr <0.5 cm, jPrimVtxdzj < 6.0 cm) are far from the sharp peaks of these distributionsand movements around these cut values have an almost negligible e ect on theMC time-variation or BB e ciency.To ensure the selected events are hadronic, the requirements of BGFMul-tiHadron and having at least three good tracks are necessary. There are twoChapter 6. Hadronic Selection 44PrimVtxdr (cm)0 0.5 1 1.5 2 2.5 3 3.5 4Events per 0.02 cm-110110210310410510Figure 6.2: PrimVtxdr for a data sample from Run 6 (solid line), overlaid withBB MC.PrimVtxdz (cm)-20 -15 -10 -5 0 5 10 15 20Events per 0.2 cm110210310410510Figure 6.3: PrimVtxdz for a data sample from Run 6 (solid line), overlaid withBB MC.Chapter 6. Hadronic Selection 45remaining cut quantities (in addition to p1Mag) which can be optimized: R2Alland ETotal. The total number of cutsets trialled during the optimization pro-cedure is 36  26  12 = 11232.Table 6.2: Cut optimization of isBCMultiHadron.Quantity No. of increments RangeR2All 36 0.45 { 0.80ETotal/eCM 26  (2:5 { 5:0)=10:58 p1Mag (  1 DCH hit) 12 3.0 { 5.0 GeV/c, or no cutThe optimization procedure is very similar to the mu-pair optimization.There are 66 months of uds and cc on-peak MC, 27 of uds o -peak MC and26 of cc o -peak MC. The statistical uncertainties are again treated binomiallyand are given by (5.3). The weighted mean e ciency and  2 statistic are givenby (5.4) and (5.5) respectively.The time variations of these four types of MC are shown in Fig. 6.4 { 6.7. Thecutset pictured has fairly typical time-variation: R2All < 0:50, (ETotal/eCM)> 0:42533 and p1Mag < 3:8 GeV/c. These plots all display obvious systematictime-variation. The shapes of the distributions are reasonably similar across allfour plots and they also resemble the muon-pair e ciency variation of Fig. 5.3and 5.4.The distributions of  2 for all 11232 cutsets are shown in Fig. 6.8 and 6.9.These are all clearly well above the M  1 values for each type of MC.A comparison between the new cutsets and the existing B Counting selector,isBCMultiHadron can be made. The on-peak (o -peak)  2 statistic for thistag is 1081.82 (527.27) for uds MC and 2669.32 (1304.13) for cc MC. Almostall cutsets for each MC type have  2 values below these which indicates animprovement on average.6.5 Estimating Systematic UncertaintyTo estimate the systematic uncertainties in continuum MC time-variation, weuse the procedure outlined in Section 5.5. We look for d0 in the modi ed  2statistic of (5.6) such that 02(d0) = M  1: (6.2)Again, d0 is found numerically by incrementing d from zero in steps of 10 6until  02(d) < M   1. The ranges of d0 values for di erent cutsets are (1:07 {1:69) 10 3 in on-peak uds MC, (0:67 { 1:59) 10 3 in o -peak uds MC, (1:60{ 2:13)  10 3 in on-peak cc MC and (1:29 { 2:16)  10 3 in o -peak cc MC.As with muon-pairs, the total uncertainty for a particular cutset is then thesum in quadrature of statistical uncertainty (1=pw) and systematic uncertainty(d0). The `optimal' set of hadronic cuts is determined at the same time as the`optimal' set of muon-pair cuts by  nding the combination which causes thelowest uncertainty in the total number of B mesons.Chapter 6. Hadronic Selection 46Month number20 40 60 80 100Efficiency0.5180.520.5220.5240.5260.5280.53Figure 6.4: Time-variation of on-peak uds MC e ciency. Details of cutsetchoice are in text. The  2 value is 372.46 and M (the num-ber of degrees of freedom) is 66. The weighted mean e ciency is0:52376  0:00008. The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.5180.520.5220.5240.5260.5280.53Figure 6.5: Time-variation of o -peak uds MC e ciency. Details of cutsetchoice are in text. The  2 value is 160.71 and M (the num-ber of degrees of freedom) is 27. The weighted mean e ciency is0:52557  0:00010. The dashed lines show  0:5% from the mean.Chapter 6. Hadronic Selection 47Month number20 40 60 80 100Efficiency0.6220.6240.6260.6280.630.6320.634Figure 6.6: Time-variation of on-peak cc MC e ciency. Details of cutset choiceare in text. The  2 value is 842.20 and M (the number of degrees offreedom) is 66. The weighted mean e ciency is 0:62686  0:00007.The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.6220.6240.6260.6280.630.6320.634Figure 6.7: Time-variation of o -peak cc MC e ciency. Details of cutset choiceare in text. The  2 value is 319.67 and M (the number of degrees offreedom) is 26. The weighted mean e ciency is 0:62941  0:000010.The dashed lines show  0:5% from the mean.Chapter 6. Hadronic Selection 486.6 Variation in  XUsing the e ciencies and cross-sections found above, we can evaluate the con-tinuum part of  , de ned in (4.8). The cross-sections of e+e  ! uu=dd=ss=ccall scale inversely with s (the CM energy squared): X = "X X"0X 0X  10:54210:582   0:9925: (6.3)Note that in this approximation, the product of  X and    (de ned in (5.9)) isexactly unity.There are other processes in data which can pass the hadronic selectionand can a ect  X but are not included in this approximation. These includetwo photon events, Initial State Radiation, cosmic rays, Bhabhas and beam gasevents. The hadronic selection is designed to minimize many of these (especiallycosmic rays and beam gas events) and the e ects of these sorts of contaminationare discussed in Chapter 8.To ensure there is on- and o -peak uds and cc MC in every time bin, thetime-variation of  X is divided into 23 unequal time periods. As with   , thestatistical uncertainty of  X in each time bin includes the statistical uncertain-ties of each type of MC given by (5.3) (e.g.  ("uds;i)) and a contribution fromthe uncertainty in the MC cross-sections (e.g.  ( uds)).To an excellent approximation, X = "uds uds + "cc cc"0uds 0uds + "0cc 0cc(6.4)and the statistical uncertainty in  X for each time period is given by (A.6): ( X;i) ="   ("uds;i uds)"0uds;i 0uds + "0cc;i 0cc!2+  ("cc;i cc)"0uds;i 0uds + "0cc;i 0cc!2++  ("0uds;i 0uds)   ("uds;i uds + "cc;i cc)("0uds;i 0uds + "0cc;i 0cc))2!2++   ("0cc;i 0cc)   ("uds;i uds + "cc;i cc)("0uds;i 0uds + "0cc;i 0cc))2!2 # 12(6.5)where, following (5.10), ("uds;i uds) = [( ("uds;i) uds)2 + ("uds;i ( uds))2]12 (6.6)and similarly for other MC types.The time-variation of  X for the same cutset shown in Fig. 6.4 { 6.7 is shownin Fig. 6.10. The variation appears to be largely (though not entirely) statisticaland systematic e ects are not as obviously apparent as they are in the individualChapter 6. Hadronic Selection 49MC e ciencies. The  2 statistic of  X can be calculated, and for every cutsettrialled it is above M 1, so there is a small amount of variation which cannot beexplained by statistical uncertainties alone. For the cutset pictured in Fig. 6.10,the  2 statistic is 93.82, and the weighted mean value of  X is^X = 0:98909  0:00019; (6.7)where the uncertainty quoted is statistical only. The distribution of  2 valuesfor all cutsets is shown in Fig. 6.11. Across all cutsets, the mean value of  2is 86.53. The weighted mean values of  X are in the range (0:98751 { 0:99238)with a typical statistical uncertainty of 0.00020 or less.To estimate the systematic uncertainty in each cutset's  X, again we  nd d0satisfying 02(d0) = M  1; (6.8)where 02(d) =MXi=1( X;i   ^X)2( ( X;i))2 + d2 : (6.9)In this case, M  1 = 22. The d0 values found are between 0.00066 and 0.00144and the distribution of these values is shown in Fig. 6.12. The systematicuncertainty in each cutset is added in quadrature with the statistical uncertaintyto give the total uncertainty on each cutset's  X value.Chapter 6. Hadronic Selection 50Chi-squared statistic300 400 500 600 700 800Cutsets per 6.0050100150200250300350Chi-squared statistic0 100 200 300 400 500 600Cutsets per 6.0050100150200250300350400450Figure 6.8: Distribution of  2 statistic for trialled cutsets (left) for uds on-peakMC and (right) for uds o -peak MC. The mean values of thesedistributions are 479.86 and 232.47 respectively. M is 66 and 27respectively.Chapter 6. Hadronic Selection 51Chi-squared statistic800 1000 1200 1400 1600 1800 2000 2200 2400 2600Cutsets per 16.5050100150200250300350400450Chi-squared statistic0 200 400 600 800 1000 1200 1400 1600 1800Cutsets per 16.5020040060080010001200Figure 6.9: Distribution of  2 statistic for trialled cutsets (left) for cc on-peakMC and (right) for cc o -peak (right) MC. The mean values of thesedistributions are 1292.82 and 441.28 respectively. M is 66 and 26respectively.Time bin number0 2 4 6 8 10 12 14 16 18 20 22Value per time bin0.9840.9860.9880.990.9920.9940.996Figure 6.10: Time-variation of  X for the cutset shown in Fig. 6.4 { 6.7. The  2value is 93.82, M is 23 and the weighted average is 0.98909. Thedashed lines show  0:5% from the mean.Chapter 6. Hadronic Selection 52Chi-squared statistic40 50 60 70 80 90 100 110 120Cutsets per 1.2050100150200250300350400450Figure 6.11: Distribution of  X  2 statistic for all trialled cutsets. M is 23.Value of d00 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002Cutsets per 2E-50100200300400500Figure 6.12: Distribution of  X d0 values for all trialled cutsets.53Chapter 7Cutset OptimizationThe main purpose of the research described in this thesis is to recommend anoptimal set of cuts which count B meson events with a minimal systematicuncertainty. This uncertainty has contributions from the uncertainties in thecounting of both muon-pairs and hadronic events. The number of B mesonevents counted with the optimal cutsets should also agree with the original BCounting code, which has been in place since 2000 and has a total uncertaintyof  1:1%.As was mentioned in Chapter 5, the B Counting uncertainty for optimizationpurposes found in this chapter is di erent to the  nal estimate of systematicuncertainty in data (given in Chapter 9). In this chapter we  nd the B Countingcutsets which give the lowest sensitivity to the time-variation of uds, cc and mu-pair Monte Carlo e ciencies. We also include the statistical uncertainty of theMC cross-sections (included in   uncertainties),The method used to calculate the propagation of uncertainties is outlined inAppendix A.7.1 B Counting UncertaintyThe B Counting formula of (4.17) is:N0B = 1"B(NH  N    Roff    ) (7.1)= 1"B(NH        X   R    N0H) (7.2)whereR    N N0 ; (7.3)N0H is the number of o -peak hadronic events counted and    and  X are de nedin (4.8). The subscripts \H" and \X" in an o -peak sample are interchangeablesince the o -peak hadronic data contains no BB events from  (4S) decays.The uncertainty in the number of B meson events,  (N0B) is given by: (N0B)2 =Xi  @N0B@xi  xi 2: (7.4)Here, xi represents each quantity with associated uncertainty (such as "uds or  ). To estimate the uncertainty in the number of B meson events in a sample ofChapter 7. Cutset Optimization 54on-peak data of luminosity L with continuum subtracted by an o -peak sampleof luminosity L0, we can rewrite (7.1) as:N0B = 1"B  (H + HO)     XR  (H0 + H0 )  (7.5)whereH   L("uds uds + "cc cc + "B B) (7.6)andH0   L0("0uds 0uds + "0cc 0cc): (7.7)HO and H0O (the subscript \O" represents \other" event-types) are the numbersof on- and o -peak events which are not BB, uds or cc but pass the hadroniccuts. These terms are discussed in detail in Chapter 8, but are neglected duringthis optimization procedure. We can also writeR    N N0 = L"    + MOL0"0  0 + M0(7.8)where MO (M0O) is the number of on-peak (o -peak) events which are note+e  ! +   but still pass the muon-pair cuts. We again neglect these duringthe optimization.In calculating the uncertainty in the number of B mesons, we omit theuncertainties in e ciency of o -peak MC. The time-variations of on- and o -peak MC are correlated, and it is important not to double-count the uncertainty.O -peak data (and hence also MC) is taken only for short periods of time aroundlonger periods of on-peak running. For this reason, o -peak running can beviewed as a `snapshot' of the non-BB continuum at a particular time.It is clear the two are not independent, since    and  X both have  2statistics much lower than any MC type has alone. The time-variation visiblein o -peak MC is to a large degree the same as that displayed in on-peak MC.For these reasons, the o -peak MC e ciencies are treated as constants in (7.4).Hence, we have: (N0B)2 =  @N0B@"uds  "uds 2+  @N0B@"cc  "cc 2++  @N0B@"B  "B 2+  @N0B@"   "  2++  @N0B@ X   X 2+  @N0B@       2(7.9)where( "uds)2 = ( ("uds)stat)2 + (d0;uds)2 (7.10)and similarly for "cc, " ,  X and   . Equation (7.10) gives the combined sta-tistical and systematic uncertainty found during the previous optimization pro-cedure and has the same form as the denominator of the  02 statistic in (5.6).Chapter 7. Cutset Optimization 55Once an optimal cutset is found, a value for  "B can be estimated by com-paring BB MC to data. During the optimization procedure, we estimate itsvalue by setting: "B = 0:2(1   ^B): (7.11)This is chosen to favour cutsets with higher BB e ciency. For a cutset with ^Bof 0.96, (7.11) gives an uncertainty in ^B of around 0.83%.The di erential quantities of (7.9) are:@N0B@"uds =1"B L uds (7.12)@N0B@"cc =1"B L cc (7.13)@N0B@"  =  1"B    XL  L0"0  0  H0 (7.14)@N0B@ X =  1"B   R H0 (7.15)@N0B@   =  1"B  XR H0 (7.16)and@N0B@"B =  1"2B L("uds uds + "cc cc)   R L0 ("0uds 0uds + "0cc 0cc)  : (7.17)This last term is very small (and would be exactly zero if B Counting wereperfect) so is negligible in comparison to the other terms.As was mentioned above, the expression (7.9) is useful for  nding an optimalset of B Counting cuts, but it will not be used to estimate the systematicuncertainty of data.7.2 OptimizationThe optimal mu-pair and hadronic B Counting cutsets are those which minimize( N0B)=N0B (the relative uncertainty in N0B) while meeting the selection goalsoutlined in Section 4.1. As a cross-check, the number of B mesons counted in asample by any pair of cutsets can be compared to that given by the existing BCounting code.The total uncertainty of (7.10) can be divided into two parts: one depen-dent only on uncertainties related to muon-pair selection and the other only onhadronic uncertainties. The muon-pair part (N0B)2  =  @N0B@"   "  2+  @N0B@       2(7.18)Chapter 7. Cutset Optimization 56includes terms dependent on  "  and    . The hadronic part  (N0B)2H con-tains all other terms. The two are not entirely independent | for example the    term, (7.16) depends speci cally on the number of o -peak hadronic eventscounted by a chosen set of hadronic cuts.The only quantities in (7.9) which are constant independent of cutset choiceare L, L0 and the cross-sections. The variable quantities of (7.12 { 7.16) | thenumber of hadronic and muon-pair data events, e ciencies,  X and    | arespeci c to each cutset trialled during the procedure.The  rst stage of the optimization procedure calculates the number of Bmesons in a sample of on-peak data and the value of  (N0B)2  for each muon-pair cutset. Continuum subtraction is provided by a corresponding o -peakdata sample.To calculate these values, the number of hadronic events in the two samplesmust be input. Initially these are taken to be the number of isBCMultiHadronevents in each sample, i.e. the number counted by the existing B Counting code.It is also necessary to input the value of "B for isBCMultiHadron (approximately0.96) and a value of  X, which is initially taken to be the theoretical estimateof (6.3). The 61880 muon-pair cutsets are then sorted by  (N0B) =N0B.Assuming it meets the B Counting selection goals, the `optimal' muon-paircutset is the one with the lowest relative uncertainty in N0B. The numbers ofmuon-pair on- and o -peak data events counted by this cutset, along with thevalue of    are then used as inputs to optimize the hadronic selection.Following the same procedure, the values of N0B and  (N0B)2H are calculatedfor the 11232 hadronic cutsets, which are then sorted by  (N0B)2H=N0B. Thevalues of "B,  X and the number of on- and o -peak hadronic events countedby the optimal hadronic cutset are used as inputs to re-optimize the muon-paircutsets. This procedure continues until the optimal cutset choice stabilizes.This procedure was performed on each major running period (Runs 1{6).There is typically less than 5% variation in the value of  (N0B) =N0B acrossthe  rst  ve hundred muon-pair cutsets (this number is around 10% for thesame number of hadronic cutsets). With so many nearly-identical cutsets, theoptimal choice for each Run varies and statistical  uctuations can change eachcutset's rank.Due mainly to these statistical  uctuations, no single cutset is consistentlythe optimal choice, but some trends emerge. Muon-pair selection cutsets tendto have a low values of  (N0B) =N0B if:  the masspair/eCM cut is high, typically in the range (0.756 { 0.827),  the maxpCosTheta cut is high, typically above 0.735,  the acolincm cut is high, typically above 0.11.No trend is obvious for the maxpEmcLab cut. For the hadronic selection, cutsetstend to have low values of  (N0B)H=N0B if:  the ETotal/eCM cut is high, typically above 0.378,Chapter 7. Cutset Optimization 57  the p1Mag cut is low, typically less than 4 GeV/c.No trend is obvious for the R2 cut, and cutsets without a p1Mag cut do notgenerally perform near the top.7.3 Choice of Muon-Pair Selection CutsetAs mentioned above, many cutsets have almost identical values of  (N0B) =N0Bor  (N0B)H=N0B. The change to the new B Counting particle lists (Charged-TracksBC and NeutralsBC) has increased stability (in comparison to isBC-MuMu and isBCMultiHadron) even before any cuts were varied. Deciding onone cutset to recommend for B Counting is to some degree an arbitrary choice.The cutset we recommend to select muon-pairs is:  BGFMuMu,  masspair/eCM > 8:25=10:58,  acolincm < 0:13,  nTracks   2,  maxpCosTheta < 0:745,  either maxpEmcCandEnergy > 0 GeV, or at least one of the two highest-momentum tracks is identi ed as a muon in the IFR,  maxpEmcLab < 1:1 GeV.This can be compared to the isBCMuMu requirements listed in Table 4.1. Notethat the meaning of nTracks is slightly changed, as it now refers to the numberof tracks on the ChargedTracksBC list.Some properties of this cutset and isBCMuMu for muon-pair MC are givenin Table 7.1.This new cutset clearly displays less systematic variation than isBCMuMu.For example, the di erence in d 0 values shows an order of magnitude stabilityimprovement in   . The time-variation of on- and o -peak MC for these newcuts is shown in Fig. 7.1 and 7.2. The equivalent plot for the isBCMuMu tag(with a vertical axis of the same scale) is shown in Fig. 7.3 and 7.4 and the timevariations of    are shown in Fig. 7.5 and 7.6.We use one other method to estimate the systematic uncertainty on    | wevary the mu-pair selection cuts on maxpCosTheta and measure how the changea ects the quantity     N N0 =   R : (7.19)This quantity appears explicitly in the B Counting formula (4.17). Any changesto it as the selection cuts vary show the combined e ects of the altered cuts onboth data and MC. This allows us to estimate the systematic uncertainty on   Chapter 7. Cutset Optimization 58as the number of mu-pair events counted should be almost constant regardlessof the arbitrary choice of mu-pair selection cuts.Speci cally we allow the cuts on maxpCosTheta to vary between 0.60 and0.77 (in increments of 0.005) while the value of   R  is recalculated for each cutchoice. The value of   R  for the original cuts is 9.7126. The largest (positiveor negative) variation from the original value occurs when maxpCosTheta isequal to 0.635 | this causes a decrease in   R  of 0.047%. We attributethis percentage di erence to an additional systematic uncertainty in    as anestimate.Table 7.1: Properties of the recommended muon-pair cutset and isBCMuMu.Cutset property New Cutset isBCMuMuOn-peak: ^  0.41558 0.42566Stat. uncert. in ^  0.00010 0.00010 2 statistic of "  118.11 1016.58Syst. uncert. in ^  (d0; ) 0.00082 0.00311O -peak: ^0  0.41598 0.42627Stat. uncert. in ^0  0.00014 0.00014 2 statistic of "0  51.71 402.25Syst. uncert. in ^0  (d00; ) 0.00060 0.00353  : ^  1.00791 1.00769Stat. uncert. in ^  0.00044 0.00043 2 statistic of    23.82 62.11Syst. uncert. in ^  (d 0; ) 0.00032 0.00306Syst. uncert. in ^  (  R ) 0.00047 N.A.7.4 Choice of Hadronic Selection CutsetThe cutset we recommend to select hadronic events is:  BGFMultiHadron,  R2All   0:65,  nTracks   3,  ETotal/eCM   4:60=10:58,  PrimVtxdr < 0:5 cm,  jPrimVtxdzj < 6:0 cm,  p1Mag < 3:0 GeV/c (  1 DCH hit).Chapter 7. Cutset Optimization 59Month number20 40 60 80 100Efficiency0.4060.4080.410.4120.4140.4160.4180.420.4220.424Figure 7.1: On-peak muon-pair MC e ciency variation for the new proposedmuon-selection cuts. The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.4060.4080.410.4120.4140.4160.4180.420.4220.424Figure 7.2: O -peak muon-pair MC e ciency variation for the new proposedmuon-selection cuts. The dashed lines show  0:5% from the mean.Chapter 7. Cutset Optimization 60Month number20 40 60 80 100Efficiency0.4160.4180.420.4220.4240.4260.4280.430.4320.434Figure 7.3: On-peak muon-pair MC e ciency variation for isBCMuMu. Thedashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.4160.4180.420.4220.4240.4260.4280.430.4320.434Figure 7.4: O -peak muon-pair MC e ciency variation for isBCMuMu. Thedashed lines show  0:5% from the mean.Chapter 7. Cutset Optimization 61Time bin number0 5 10 15 20 25K value per time bin11.0051.011.0151.02Figure 7.5: Time-variation of    for the new cutset. The dashed lines show 0:5% from the mean.Time bin number0 5 10 15 20 25K value per time bin11.0051.011.0151.02Figure 7.6: Time-variation of    for isBCMuMu. The dashed lines show  0:5%from the mean.Chapter 7. Cutset Optimization 62Some properties of this cutset and isBCMultiHadron are shown in Table7.2. The proposed cutset is more stable in time than isBCMultiHadron, butthe improvement from the existing tag is not as large as it was for the muon-pair selector. Nevertheless the new hadronic cutset has a lower  2 statistic forall types of MC, and consequently the estimated systematic uncertainty (d0) islower in each case. The  2 statistics of each MC type decrease to between 26%and 36% of their isBCMultiHadron values.The time-variation of  X and the e ciency of each type of continuum MCfor the proposed cutset and isBCMultiHadron are shown in Fig. 7.9 { 7.18. Thetime-variation of uds MC e ciency for the new cuts and isBCMultiHadron areshown in Fig. 7.9 { 7.12. The equivalent plots for cc MC e ciency (with verticalaxes of the same scale) are shown in Fig. 7.13 { 7.16. Finally,  X for the newcutset and isBCMultiHadron is shown in Fig. 7.17 { 7.18.The weighted mean BB e ciency (^B) for this cutset is 0:94046   0:00003(where the uncertainty is statistical only), which is slightly lower than the is-BCMultiHadron value of 0.9613. The main reasons for this decrease are theaddition of a p1Mag cut and the slightly higher cut on ETotal.7.4.1 ISR Production and Two-Photon EventsWe have not yet considered the e ect on  X from events which are di cult tosimulate with Monte Carlo; in particular Initial State Radiation (ISR) and two-photon events. Our limited knowledge of these events introduces an additionalsystematic uncertainty to the value of  X.ISR events are those in which one of the incoming beam particles emits aphoton before interacting. The theoretical ISR cross-section used in this analysisis based on that described by Benayoun et al. [25]. For ISR production of anystate (labelled \V"), the ISR cross-section is taken to be: VISR   12 2 eemV   s   W(s;1  m2Vs ); (7.20)where W is a function de ned in [25], and mV and  ee are the resonance massand partial width of V !e+e  respectively. The total cross-section is estimatedto be the sum of each possible JPC = 1   resonance. The dominant terms inthis sum are to the  0 (by an order-of-magnitude), J=  and  (3S) resonances.Two-photon events are those where the two colliding particles emit virtualphotons which in turn interact to produce some system of particles. A reviewof two-photon particle production can be read in [26]. For high energies (suchas those provided by PEP-II), the cross-section for two-photon production of alepton pair is given approximately by: e+e !e+e `+`  = 28 427 m2l ln sm2e 2ln 2m2l; (7.21)where l can be either e or   and ps is the CM energy.Chapter 7. Cutset Optimization 63The (high-energy limit) cross-section for hadron production (h) is given ap-proximately by: e+e !e+e h =  418 2m2  lnsm2 m2em2  lnsm6 m6em2  ln sm2  2; (7.22)where m  and m  are the masses of the   and   mesons.Since these two processes are not known especially well, we attempt to quan-tify their e ect on systematic uncertainty. We do this by using cc, uds,  +  and high-angle Bhabha MC to estimate the e ective cross-section for other (i.e.not of these four types) events in o -peak data of passing the hadronic selection,and the corresponding systematic uncertainty on  .The hadronic part of   takes the form: X = "X X"0X 0X(7.23)=Pknown "i i +Punknown "j jPknown "0i 0 +Punknown "0j 0: (7.24)Here, by known we mean events for which BABAR has a reliable MC modeland well-known cross-sections. The e ects of the unknown types can be esti-mated by comparing o -peak data and the known MC. We assume that the un-known component is comprised solely of two-photon, ISR and low-angle Bhabhaevents.We compare the known MC types to o -peak data. The cross-sections foreach MC type are used to combine them in the correct proportions to modeldata as accurately as possible. Normalization is achieved by forcing the MC tohave the same value as data at 0.9 on the plot of total event energy. The MCdistributions of total energy are shown in the left plot of Fig. 7.7 and the sumoverlaid with data on the right.The excess in data over the cut range (above 0.4348 on the ETotal=p(s)plot) is found to be equivalent to an e ective cross-section of approximately0.10 nb. The value of  X for the optimal cuts for only the known types ofMC has the value 0:98979  0:00016 (where the uncertainty is statistical only).To estimate  X including two-photon and ISR events we estimate the e ec-tive on-peak cross-sections by scaling by the theoretical cross-sections. Theseconsiderations increase the value of  X and introduce an additional systematicuncertainty on its value. We combine this new uncertainty in quadrature withthat due to MC time-variation.Note that we do not use the (fairly old) theoretical models to predict theabsolute cross-section, but use the ratio of theoretical on- and o -peak cross-sections for the processes to estimate the total e ective on-peak cross-section.The proportions of two-photon and ISR events in the data are unknown, sofor a range of   values from 0.01 to 0.99 we letunknownX"0j 0j =     "0ISR 0ISR + (1   )   "02  02 : (7.25)Chapter 7. Cutset Optimization 64and use the ratios of  ISR= 0ISR and  2 = 02  from theory to estimate the on-peak unknown e ective cross-section (assuming the on- and o -peak e cienciesare identical).The value of  X including the unknown component can be estimated. Wetake its value to be the   = 0:5 value, and equate the di erence as   varies tobe systematic uncertainty. Performing the identical analysis for the theoreticalBhabha cross-section does not change the solution | for 100% Bhabhas or a1:1:1 mixture of two-photon, ISR and Bhabha events, the value of  X stayswithin the range found using two-photon and ISR events alone.Total Event Energy/sqrt(s)0 0.2 0.4 0.6 0.8 1 1.20100200300400500600700310?Total Event Energy/sqrt(s)0 0.2 0.4 0.6 0.8 1 1.2020406080100120140160180310?Figure 7.7: Comparison of ETotal=ps for known MC types to o -peak data forevents passing all other hadronic selection cuts: (left) in decreasingorder distributions of sum of all MC types, uds, cc,  +  , low-angleBhabha MC; (right) the sum (points) is shown overlaid with data {the plots are normalized to have the same value at 0.9.Fig. 7.8 shows the ETotal/eCM distribution of the \unknown" events (i.e.the di erence between the MC and o -peak data distributions).The result is:  X = 0:9901  0:0002. Note that the addition of two-photonand ISR events give a central value of  X higher than that calculated for theknown types only (although they agree within uncertainties). We assume thisuncertainty is independent of that calculated in Section 6.6.Combining the two uncertainties (from the MC time-variation and this two-photon, ISR and low-angle Bhabha analysis) in quadrature, the value for theoptimal cutset is:  X = 0:9901  0:0010.Chapter 7. Cutset Optimization 65Total Event Energy/sqrt(s)0 0.2 0.4 0.6 0.8 1 1.20100002000030000400005000060000700008000090000Figure 7.8: Di erence in ETotal between known MC types and o -peak data.The cut at 0.4348 is marked with a dashed line.7.5 B Counting ResultsThe numbers of B meson events counted in data by this pair of new proposedcutsets for each major running period are given in Table 7.3. The two uncer-tainty terms,  (N0B) =N0B and  (N0B)H=N0B are added in quadrature to givethe total uncertainty in the number of B mesons. For comparison, the numbercounted by the existing code (with a total uncertainty of 1:1% in each case) isalso provided.For every Run, the number of B meson events counted by the new cutsetsagrees with the existing value within uncertainty. The total uncertainty rangesbetween 0:615% and 0:634%. Note that these values are calculated only to  ndthe optimal pair of cutsets. The  nal estimate of systematic uncertainty in datausing the optimal cutset is discussed in Chapter 9.Chapter 7. Cutset Optimization 66Month number20 40 60 80 100Efficiency0.6240.6260.6280.630.6320.6340.6360.6380.64Figure 7.9: On-peak uds MC e ciency time-variation for the new proposedhadronic cuts. The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.6240.6260.6280.630.6320.6340.6360.6380.64Figure 7.10: O -peak uds MC e ciency time-variation for the new proposedhadronic cuts. The dashed lines show  0:5% from the mean.Chapter 7. Cutset Optimization 67Month number20 40 60 80 100Efficiency0.610.6120.6140.6160.6180.620.6220.6240.626Figure 7.11: On-peak uds MC e ciency time-variation for isBCMultiHadron.The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.610.6120.6140.6160.6180.620.6220.6240.626Figure 7.12: O -peak uds MC e ciency time-variation for isBCMultiHadron.The dashed lines show  0:5% from the mean.Chapter 7. Cutset Optimization 68Month number20 40 60 80 100Efficiency0.7480.750.7520.7540.7560.7580.760.762Figure 7.13: On-peak cc MC e ciency time-variation for the new proposedhadronic cuts. The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.7480.750.7520.7540.7560.7580.760.762Figure 7.14: O -peak cc MC e ciency time-variation for the new proposedhadronic cuts. The dashed lines show  0:5% from the mean.Chapter 7. Cutset Optimization 69Month number20 40 60 80 100Efficiency0.7280.730.7320.7340.7360.7380.740.7420.744Figure 7.15: On-peak cc MC e ciency time-variation for isBCMultiHadron.The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.7280.730.7320.7340.7360.7380.740.7420.744Figure 7.16: O -peak cc MC e ciency time-variation for isBCMultiHadron.The dashed lines show  0:5% from the mean.Chapter 7. Cutset Optimization 70Time bin number0 2 4 6 8 10 12 14 16 18 20 22Value per time bin0.9840.9860.9880.990.9920.9940.996Figure 7.17: Time-variation of  X for the new cutset. The dashed lines show 0:5% from the mean.Time bin number0 2 4 6 8 10 12 14 16 18 20 22Value per time bin0.9860.9880.990.9920.9940.9960.998Figure 7.18: Time-variation of  X for isBCMultiHadron. The dashed lines show 0:5% from the mean.Chapter 7. Cutset Optimization 71Table 7.2: Properties of the recommended hadronic cutset and isBCMulti-Hadron.Cutset property New Cutset isBC-MultiHadronOn-peak: ^uds 0.62998 0.61708Stat. uncert. in ^uds 0.00007 0.00007 2 statistic of "uds 344.93 1081.82Syst. uncert. in ^uds (d0;uds) 0.00121 0.00227^cc 0.75364 0.73431Stat. uncert. in ^cc 0.00006 0.00006 2 statistic of "cc 939.95 2669.32Syst. uncert. in ^cc (d0;cc) 0.00175 0.00278O -peak: ^0uds 0.63200 0.61752Stat. uncert. in ^0uds 0.00009 0.00009 2 statistic of "0uds 164.46 527.27Syst. uncert. in ^0uds (d00;uds) 0.00094 0.00216^0cc 0.75568 0.73580Stat. uncert. in ^0cc 0.00009 0.00009 2 statistic of "0cc 349.56 1304.13Syst. uncert. in ^0cc (d00;cc) 0.00167 0.00274 X: ^X (known MC only) 0.98979 0.99198Stat. uncert. in ^X 0.00016 0.00017 2 statistic of  X 80.19 101.19Syst. uncert. in ^X (d 0;cont) 0.00095 0.00122Syst. uncert. in ^X (ISR/2 ) 0.0002 0.0002^X (incl. ISR/2 ) 0.9901 0.9918Combined uncert. in ^X 0.0010 0.0012Chapter 7. Cutset Optimization 72Table 7.3: Uncertainty terms and number of B meson events with overall un-certainty found during optimization procedure in Runs 1{6.Run 1 Run 2 (N0B) =N0B 0.461% 0.456% (N0B)H=N0B 0.416% 0.412%N0B (new cutsets) (22:39  0:14)  106 (67:61  0:42)  106N0B (existing code) (22:40  0:26)  106 (67:39  0:74)  106Run 3 Run 4 (N0B) =N0B 0.463% 0.460% (N0B)H=N0B 0.417% 0.414%N0B (new cutsets) (35:75  0:22)  106 (110:70  0:69)  106N0B (existing code) (35:57  0:39)  106 (110:45  1:21)  106Run 5 Run 6 (N0B) =N0B 0.462% 0.471% (N0B)H=N0B 0.416% 0.424%N0B (new cutsets) (146:19  0:91)  106 (82:19  0:52)  106N0B (existing code) (147:19  1:62)  106 (82:04  0:90)  10673Chapter 8Sources of ContaminationAs mentioned in previous Chapters, there are several possible contaminatione ects which are considered negligible for B Counting. This includes e+e  ! +   decays incorrectly passing hadronic selection and Bhabha events incor-rectly passing muon-pair selection among others. In this Chapter we quantifythese e ects.8.1 Bhabha EventsThe process with by far the highest cross-section in PEP-II is Bhabha scattering.Most processes, like e+e  !  +   or e+e  ! qq have cross-sections propor-tional to 1=E2CM, where ECM is the event's CM energy. The cross-section forBhabha scattering is more complicated, and at PEP-II's on-peak CM energy of10.58 GeV is around 40 times larger than most other processes. The di erentialcross-section takes the form:d d cos  =  2s"u2  1s +1t 2+  ts 2+  st 2#(8.1)where s, t and u are the Mandelstam variables, which relate the four-momentaof the incoming and outgoing particles [22].The majority of Bhabha events scatter at low angles (i.e. continue down thebeam-pipe), but the cross-section for large-angle Bhabha scattering (i.e. withinthe angular limits of ChargedTracksBC) is still substantial. Based on samplesof one million generated Monte Carlo Bhabha scattering events, the values foron- and o -peak running are (13:8910   0:0040) nb and (14:0918   0:0041) nbrespectively. These are more than ten times the BB cross-section of 1.1 nb.Ideally, the B Counting muon-pair and hadronic selectors should reject allBhabha events, but due to many imperfections a small number incorrectly pass.To estimate the size of this e ect, we apply the selectors to 7.725 million high-angle Bhabha MC events. The numbers of Bhabha MC events passing theselectors are given in Table 8.1. For the new cuts, the Bhabha hadronic fake-rateis approximately 0.006%, and the Bhabha muon-pair fake-rate is approximately0.002%.We can estimate the ratio of Bhabha events to B meson events passing thehadronic cuts in an on-peak sample of luminosity L:NBha (pass had. cuts)NB (pass had. cuts) ="had:Bha BhaL"had:B  BL (8.2)Chapter 8. Sources of Contamination 74Table 8.1: Fake-rates for Bhabha MC events passing hadronic and mu-pairselectors. The sample contained 7.725 million large-angle on-peakBhabha MC events.Number passing selector Percent of totalNew hadronic selector 449 0.0058%isBCMultiHadron 1559 0.0202%New mu-pair selector 149 0.0019%isBCMuMu 22 0.0003%NBha (pass had. cuts)NB (pass had. cuts)  0:00006  13:9 nb0:941  1:1 nb (8.3)  0:08%: (8.4)Thus, even though the cross-section for high-angle Bhabha events is more thanten times the other continuum cross-sections, the Bhabha hadronic fake-rate isvery much smaller than the selector's systematic uncertainty. The equivalentnumber for the muon selector (of fake Bhabhas to genuine muon-pairs) is factorof three smaller.The  nal possible source of Bhabha contamination relates to the energy-dependence of the Bhabha cross-section. One of the most important assump-tions for B Counting is that background events scale in the same way with CMenergy as muon-pair events. This assumption enables backgrounds to be sub-tracted by using the ratio of on-peak to o -peak muon-pair events. For Bhabhaevents however, this assumption is not true. The ratio of on-peak to o -peakmuon-pair MC events from Section 5.1 is:   0  =1:11853 nb1:12647 nb = 0:99295 (5 sig.  g.) (8.5)and for Bhabhas, this ratio is Bha 0Bha =13:8910 nb14:0918 nb = 0:98575 (5 sig.  g.): (8.6)This di erence means that when subtracting continuum events, the numberof on-peak Bhabha events passing the hadronic cuts will be over-estimated by afactor of approximately 0.7%. The total e ect is 0.7% of the 0.006% of Bhabhaevents passing hadronic selection. Since this number is negligibly small it canbe ignored safely.8.2 Continuum Fake-RatesThere is a small probability of hadronic continuum events passing muon-pairselection. These events scale with energy in the same way as muon-pairs. WhenChapter 8. Sources of Contamination 75counting B meson events, the ratio of muon-pairs (R ) is used, so if the per-centage of on- and o -peak fake muons from hadronic continuum events are thesame, any hadronic continuum fakes will have no e ect on B Counting.Table 8.2 shows the percentage of hadronic continuum MC events which passthe new muon-pair selector and isBCMuMu. Clearly uds events have a higherfake-rate, but the overall e ect is too small (in both the number of fakes andon-/o -peak di erence) to have any consequences for B Counting.Table 8.2: Fake-rates for hadronic continuum MC events passing the mu-pairselector. The sample contained 5.20 million on-peak cc, 4.20 milliono -peak cc, 6.40 million on-peak uds and 4.20 million o -peak udsMC events.% passing new muon-pair selector % passing isBCMuMucc (on-peak) 0.00014% 0.00036%cc (o -peak) 0.00002% 0.00021%uds (on-peak) 0.009% 0.024%uds (o -peak) 0.010% 0.026%There is also a small chance that muon-pair events can pass the hadronicselector. The probabilities for this are shown in Table 8.3. The e ect is negligiblysmall.Table 8.3: Fake-rates for muon-pair MC events passing the hadronic selector.The sample contained 4.05 million on-peak and 4.08 million o -peak +   MC events.% passing new % passing isBCMulti-hadronic selector Hadron +   (on-peak) 0.0078% 0.0359% +   (o -peak) 0.0082% 0.0377%8.3 Tau ProductionAnother process with a cross-section close to 1 nb is e+e  !  +  . The  leptons are short-lived and decay within the beam pipe. These events have onlya small probability of passing the muon-pair selector, but the probability ofpassing the hadronic selector is much larger.Similarly to mu-pair events, tau-pair events are simulated with the KK2FMC generator, GEANT 4 and background addition. The production cross-sections for the process e+e  !  +   based on 10 million generated on- ando -peak events are (0:918797   0:000066) nb and (0:925180   0:000066) nb re-spectively.The hadronic and mu-pair selector e ciencies are shown in Table 8.4. Thehadronic e ciency for   pairs is approximately 4% of the uds and cc hadronicChapter 8. Sources of Contamination 76e ciencies.Table 8.4: Fake-rates for  +   MC events passing hadronic and mu-pair se-lectors. The sample contained 4.55 million on-peak and 4.26 milliono -peak e+e  ! +   MC events.% passing new % passing isBCMulti-hadronic selector Hadron +   (on-peak) 2.67% 1.37% +   (o -peak) 2.68% 1.37%% passing new % passing isBCMuMumuon-pair selector +   (on-peak) 0.052% 0.126% +   (o -peak) 0.051% 0.117%The rate at which   leptons pass the hadronic cuts is a factor of two higherthan for isBCMultiHadron, but this largely does not a ect B Counting. Theincrease in e ciency is mainly due to the increased R2 cut (which changed from0.5 to 0.65). The cross-section for   production changes with energy identi-cally to muon-pairs, and since the on-peak and o -peak e ciencies are almostidentical, the overall e ect on B Counting is small.As for other MC types, we can calculate the  2 statistic for the time-variationof  +   MC. Again, we  nd the d0 value of (5.6) such that 02(d0) = M  1: (8.7)This value provides an estimate of the systematic uncertainty in the   leptone ciency.The time-variation of on- and o -peak  +   MC is shown are Fig. 8.1 and8.2. The overall uncertainties (combining systematic and statistical uncertain-ties in quadrature) are  1:5% for on-peak and  0:99% for o -peak   leptonMC. When combined with the e ciency for passing the hadronic cuts of around2:7%, the contribution to B Counting uncertainty from variations in   leptone ciency is an order of magnitude lower than the uds and cc contribution.Chapter 8. Sources of Contamination 77Month number20 40 60 80 100Efficiency0.02350.0240.02450.0250.02550.0260.02650.0270.02750.0280.0285Figure 8.1: On-peak tau lepton MC e ciency variation for the new proposedhadronic cuts. The dashed lines show  0:5% from the mean.Month number20 40 60 80 100Efficiency0.02350.0240.02450.0250.02550.0260.02650.0270.02750.0280.0285Figure 8.2: O -peak tau lepton MC e ciency variation for the new proposedhadronic cuts. The dashed lines show  0:5% from the mean.78Chapter 9Systematic UncertaintyIn this chapter we estimate the total systematic uncertainty on B Counting.We consider the uncertainties on BB e ciency,  X and    and estimate thecombined uncertainty.9.1 BGFMultiHadron and Tracking E ciencyOne contributor to systematic uncertainty in "B is the e ciency of the BGFMul-tiHadron tag. To examine this, we studied samples of random on- and o -peakevents which pass the Level Three trigger (the stage at which BGF tags areassigned). This dataset has the name DigiFL3Open and consists of 0.5% ofall Level Three events. The samples contained 17.57 million on-peak and 1.67million o -peak data events from Run 4.BGFMultiHadron requires at least three charged tracks and R2 of less than0.98 in the CM frame. For events with a low number of charged tracks, thequantities BGFMultiHadron and nTracks are closely correlated. Events whichfail hadronic selection because nTracks is too low (less than three) also usuallyfail because they do not have the BGFMultiHadron tag. In the on-peak sample,1.89 million events passed all hadronic cuts except those on BGFMultiHadronand nTracks. The combination of BGFMultiHadron and nTracks cuts rejecteda further 0.19 million events; of these, 86% failed both cuts. This number was87% in the o -peak data.To  nd the component of systematic uncertainty due to the combination ofthe BGFMultiHadron and nTracks cuts in hadronic selection, we compare thelow-end tail of the nTracks distribution in BB data and MC for events passingall hadronic cuts except those two. The distribution for data (luminosity-scaledo -peak subtracted from on-peak) overlaid with BB MC is shown in Fig. 9.1.The BB MC sample contained 12.43 million events.After scaling, the o -peak data has more zero- and one-track events than theon-peak data. This causes the equivalent data bins in Fig. 9.1 to be negative.This is due in a large part to contamination by Bhabha events. The proportionof on-peak (o -peak) data events in this plot with exactly one charged track,where that track is identi ed as an electron is 83.7% (83.8%). This comparesto 12.1% for BB MC. Similarly the proportion of two-track events where bothare identi ed as electrons is signi cantly higher in data (26.2% and 28.3% inon-peak and o -peak respectively) than in MC (3.6%).Events with one or two charged tracks where the number of charged tracksChapter 9. Systematic Uncertainty 79Number of Charged Tracks in Event0 2 4 6 8 10 12 14 16 18 20Events020040060080010001200140016001800310?Figure 9.1: Distribution of nTracks for BB data (solid) and MC (points). Allhadronic cuts except those on BGFMultiHadron and nTracks areapplied. The two are normalized to have the same area from 3{20.is equal to the number of electrons in the event are likely to be Bhabhas. Whentracks of this type are removed, the agreement between data and MC improves,especially in the bin of data events with exactly one track. The revised distri-bution is shown in Fig. 9.2. The MC distribution is largely unchanged.To estimate the contribution to systematic uncertainty by these two cutswe can compare the proportion of events in Fig. 9.2 with nTracks less thanthree for BB data and MC. For data we sum the absolute value of the bincontents (since they are negative for the  rst two bins) and  nd 0.56% of allevents in the plot are in the  rst three bins. For BB MC, this number is 0.20%.The di erence (0.36%) is attributed to systematic uncertainty in "B from theBGFMultiHadron and nTracks cuts.9.2 Comparison of Data and MCNext we estimate the systematic uncertainty in "B for the optimal cutset choicedue to the di erence between BB MC and data. We assumed in Chapter 4 thatthe proportions of charged and neutral BB decays of the  (4S) are the same,i.e. thatR+=0 = B( (4S) !B+B )B( (4S) !B0B0) = 1: (9.1)Since the decays of charged B mesons are slightly di erent to those of neutralones, a source of uncertainty arises if this assumption is false.Chapter 9. Systematic Uncertainty 80Number of Charged Tracks in Event0 2 4 6 8 10 12 14 16 18 20Events020040060080010001200140016001800310?Figure 9.2: Distribution of nTracks for BB data (solid) and MC (points) with`obvious' Bhabha events removed. All hadronic cuts except thoseon BGFMultiHadron and nTracks are applied. In addition eventsare not plotted if the number of electrons is non-zero and equal tothe number of charged tracks. The two are normalized to have thesame area from 3{20.Two of the most precise measurements of f00   B( (4S) ! B0B0) andf+    B( (4S) ! B+B ) are described in [27]. That analysis uses a partialreconstruction of the decay B0 !D +`   to obtain:f00 = 0:487  0:010(stat)  0:008(syst) (9.2)and infer:f+  = 0:490  0:023: (9.3)Since f00 and f+  agree within experimental uncertainty, in this thesis we as-sume that they are equal and that the e ects of any variation from (9.1) arenegligibly small.To  nally estimate  "B, we compare the cut-quantity distributions of BBdata and MC. We shift the MC distributions by small increments (the nature ofwhich depend on the original distributions) to determine whether any variationfrom the original value improves the agreement between data and MC. To pro-vide maximum statistics, we examine all Runs simultaneously (approximately464 million BB events).If a better agreement is found, the BB e ciency of the shifted MC is cal-culated and the di erence between this and the original value is attributed toChapter 9. Systematic Uncertainty 81systematic uncertainty. To measure goodness-of- t between data and MC his-tograms of n bins, we use again use a  2 statistic of the form: 2 =nXi=1 Ndatai  NMC 2  datai 2 +   MCi 2 (9.4)where Ndatai (NMCi ) is the number of data (MC) events in bin i, and for esti-mation purposes we make the approximations datai = 1Ndataiand  MCi = 1NMCi: (9.5)The increments made to each relevant quantity are listed below. Here,   isan integer, varied between 0 and 200.  ETotal is shifted by an increment, up to 0.2 GeV:{ ETotal/eCM ! (ETotal + 0:001 )/eCM.  R2 is multiplied by a constant between 0.96 and 1.04:{ R2 ! (0:96 + 0:0004 ) R2.  To simulate the e ect of tracks being lost due to tracking ine ciencies(when a genuine track is not correctly reconstructed as such), the trackinge ciency of each track (ptrack) is varied between 90% and 100%. Eachtrack is given a random number between 0 and 1, and it is kept if thevalue is less than (0:9 + 0:0005 ). Any rejected track reduces the value ofnTracks for the event:{ ptrack = (0:9 + 0:0005 ).  The value of p1Mag is shifted by an increment, positive if p1Mag is belowthe peak of the distribution and negative if it is above the peak. This hasthe e ect of narrowing the distribution:{ p1Mag !(1:0 + 0:0005 ) p1Mag if p1Mag < 0:97 GeV/c,{ p1Mag !(1:0  0:0005 ) p1Mag if p1Mag > 0:97 GeV/c.  PrimVtxdr is multiplied by a constant between 0.8 and 1.0:{ PrimVtxdr ! (1:0  0:001 ) PrimVtxdr.  PrimVtxdz is multiplied by a constant between 0.6 and 1.0:{ PrimVtxdz ! (1:0  0:002 ) PrimVtxdz.Chapter 9. Systematic Uncertainty 82In each case, once the value of   resulting in the lowest  2 is found ( opt:),the BB MC e ciency is recalculated for the new quantity while all other cutsremain unchanged (^1B). For some quantities like PrimVtxdz, even though theinitial MC and BB distributions do not agree perfectly, the revised e ciencyis almost identical to the original. This is because the cut value is so far fromthe distribution's peak that only a small number of events in the tail movefrom failing to passing the cut. The results are shown in Table 9.1. Before anyincrements are made, the original value of ^B is^B = 0:940456  0:000033 (9.6)where the uncertainty stated is statistical only.Table 9.1: Revised e ciencies for hadronic cut quantities after shifting BBMC. The statistical uncertainty on each "1B value is  0:000033 (or 0:003%)Quantity  opt: ^1B ^"1B  ^"B^"BETotal 87 0.944242 +0:403%R2 110 0.940378  0:008%ptrack 191 0.940308  0:016%p1Mag 8 0.940408  0:005%PrimVtxdr 105 0.940644 +0:020%PrimVtxdz 59 0.940408  0:005%The quantity with the largest change in e ciency is ETotal. The value of opt: in this case implies that adding 87 MeV to each MC event improves the  tto data the most. The e ciency increases by 0.403% because events up to 87MeV below the cut now pass selection. The original and revised distributionsare shown in Fig. 9.3 and 9.5, and the di erences between data and MC for thetwo plots are shown in Fig. 9.4 and 9.6.The change in R2, p1Mag and PrimVtxdz are negligible in comparison toETotal, and the variation is comparable to the statistical uncertainty. The plotsof data and revised MC for these variables are shown in Fig. 9.7 { 9.11.To estimate  "B we treat each e ciency di erence as an independent sys-tematic uncertainty and add them in quadrature. The result is: "B = 0:404%: (9.7)9.3 Summary of Systematic UncertaintiesWe can now summarize by estimating the total B Counting systematic uncer-tainty for the new proposed cuts by combining the independent uncertaintiesChapter 9. Systematic Uncertainty 83Total Event Energy Divided by CM Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4Events per 0.0070100200300400500600700800900310?Figure 9.3: ETotal/eCM for BB data overlaid with BB Monte Carlo for theoriginal MC ETotal cut. The solid histogram represents data (o -peak subtracted from on-peak) and the dotted (+) histogram isfrom MC. The histograms are normalised to have the same areafrom 0.45{1.0.Total Event Energy Divided by CM Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4Events per 0.007-30000-20000-10000010000200003000040000Figure 9.4: The di erence between the data and MC histograms of Fig. 9.3.Chapter 9. Systematic Uncertainty 84Total Event Energy Divided by CM Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4Events per 0.0070100200300400500600700800900310?Figure 9.5: ETotal/eCM for BB data overlaid with BB Monte Carlo for therevised MC ETotal cut. The solid histogram represents data (o -peak subtracted from on-peak) and the dotted (+) histogram isfrom MC. The histograms are normalised to have the same areafrom 0.45{1.0.Total Event Energy Divided by CM Energy0 0.2 0.4 0.6 0.8 1 1.2 1.4Events per 0.007-20000-10000010000200003000040000Figure 9.6: The di erence between the data and MC histograms of Fig. 9.5.Chapter 9. Systematic Uncertainty 85Total Event R20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Events per 0.005020040060080010001200310?Figure 9.7: R2 for BB data overlaid with BB Monte Carlo for the revised MCR2 cut. The solid histogram represents data (o -peak subtractedfrom on-peak) and the dotted (+) histogram is from MC. The his-tograms are normalised to have the same area from 0.0{0.5.Number of Charged Tracks in Event0 2 4 6 8 10 12 14 16 18 20Events010002000300040005000600070008000310?Figure 9.8: nTracks for BB data overlaid with BB Monte Carlo for the MC withrevised tracking probability. The solid histogram represents data(o -peak subtracted from on-peak) and the dotted (+) histogram isfrom MC. The histograms are normalised to have the same area.Chapter 9. Systematic Uncertainty 86p1Mag (GeV/c)0 1 2 3 4 5 6 7 8 9 10Events per 0.05 GeV/c020040060080010001200140016001800200022002400310?Figure 9.9: p1Mag for BB data overlaid with BB Monte Carlo for the revisedMC p1Mag cut. The solid histogram represents data (o -peak sub-tracted from on-peak) and the dotted (+) histogram is from MC.The histograms are normalised to have the same area from 0.0{5.0.PrimVtxdr (cm)0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Events per 0.0025 cm050010001500200025003000350040004500310?Figure 9.10: PrimVtxdr for BB data overlaid with BB Monte Carlo for therevised MC PrimVtxdr cut. The solid histogram represents data(o -peak subtracted from on-peak) and the dotted (+) histogramis from MC. The histograms are normalised to have the same area.Chapter 9. Systematic Uncertainty 87PrimVtxdz (cm)-8 -6 -4 -2 0 2 4 6 8Events per 0.08 cm02004006008001000120014001600180020002200310?Figure 9.11: PrimVtxdz for BB data overlaid with BB Monte Carlo for therevised MC PrimVtxdz cut. The solid histogram represents data(o -peak subtracted from on-peak) and the dotted (+) histogramis from MC. The histograms are normalised to have the same area.in "B and  . Note that in Chapter 7 an optimal cutset was found by minimiz-ing the time-variation, measured by the expression (7.9). This cannot be usedwhen estimating the actual systematic uncertainty in the number of B mesons,since by treating all MC variation as independent, it double-counts much of thetime-variation. For the true estimate of the systematic uncertainty, we insteadonly consider the uncertainties of those quantities explicitly appearing in the BCounting formula, i.e.   and "B. The statistical and systematic uncertaintieson these quantities are summarized in Table 9.2.Combining the uncertainties (systematic and statistical) on "B in quadra-ture, we have: "B = 0:9405   0:0051. Similarly, we have the value of   =0:9979 0:0012. The total uncertainty on the number of B mesons in a samplecan now be found by the standard method of error propagation. From the BCounting formula (4.17) we can write:  N0B 2 =   @N0B@  2(  )2 +  @N0B@"B 2( "B)2 : (9.8)We have@N0B@  = 1"B (N    Roff); (9.9)and@N0B@"B = 1"B N0B: (9.10)With this, we are able to make an estimate on the total systematic uncer-tainty on the number of BB events,  N0B. By considering the two terms ofChapter 9. Systematic Uncertainty 88Table 9.2: Summary of B Counting statistical and systematic uncertainty com-ponents of   ,  X and "B.Uncert. Value Contrib. to  N0B    Statistical 0.044% 0.10%Time var. of mu-pair e . 0.032% 0.07%Var. of   R  0.047% 0.11%Total 0.07% 0.16%  X Statistical 0.016% 0.04%Time var. of continuum e . 0.096% 0.21%ISR/2  contribution 0.020% 0.04%Total 0.10% 0.22% "B Statistical 0.004% 0.004%Low track-multiplicity events 0.360% 0.36%BB data/MC comparison 0.404% 0.40%Total 0.54% 0.54% N0B Total 0.6%(9.8) separately we can determine how the uncertainties on   and "B propagateinto uncertainties on N0B.The uncertainties on    and  X combined in quadrature lead to a    valueof  0:12%. This corresponds to a  0:27% uncertainty in N0B while the  "Bvalue of  0:54% corresponds to an uncertainty of  0:54% in N0B. These, addedin quadrature via (9.8) give the total uncertainty of 0.6% on the number of Bmesons.The number of BB events counted in the BABARdataset is (464:8 2:8) 106.The equivalent number given by the existing B Counting code is (465:0 5:1) 106. The number counted in each Run is shown in Table 9.3.Chapter 9. Systematic Uncertainty 89Table 9.3: Number of B mesons events with revised overall uncertainty in Runs1{6.Run 1 Run 2N0B (new cutsets) (22:4  0:1)  106 (67:6  0:4)  106N0B (existing code) (22:4  0:3)  106 (67:4  0:7)  106Run 3 Run 4N0B (new cutsets) (35:7  0:2)  106 (110:7  0:7)  106N0B (existing code) (35:6  0:4)  106 (110:5  1:2)  106Run 5 Run 6N0B (new cutsets) (146:2  0:9)  106 (82:2  0:5)  106N0B (existing code) (147:2  1:6)  106 (82:0  0:9)  106TotalN0B (new cutsets) (464:8  2:8)  106N0B (existing code) (465:0  5:1)  10690Chapter 10SummaryWe have presented a new proposed set of cuts designed to improve the precisionof B Counting at the BABARExperiment. The overall uncertainty in the numberof B mesons counted has been reduced from 1.1% to approximately 0.6%.The largest contributors to uncertainty are from BGFMultiHadron and nTracksdue to inaccuracies in simulating low track-multiplicity events (  0:36%) andfrom the di erences between the ETotal distributions of BB data and MC(  0:40%) .Algorithms implementing these new B Counting selection criteria are beingrun in the Release 24 reprocessing of the BABAR dataset. This ensures analystsrunning on the most recent version of the data will be able to count B mesonswith this improved method. To allow cross-checking, the old tagbits isBCMuMuand isBCMultiHadron are also recalculated during reprocessing.91Appendix AUncertainties of aMulti-Variable FunctionLet f(x1;      ;xm) be an in nitely di erentiable function of m variables (xi),each with an uncertainty  xi. The Taylor series of f expanded around thepoint (a1;      ;am) is:T(x1;      ;xm) =1Xn1=0     1Xnm=0@n1@xn11      @nm@xnmmf(a1;      ;am)n1!       nm!   (x1  a1)n1       (xm  am)nm : (A.1)Assume each xi comes from an independent statistical distribution withmean ^i and standard deviation  xi. If the standard deviations are su cientlysmall, we can approximate f by evaluating the series to  rst order around(^1;      ; ^m). The uncertainty of the function can then be estimated by theequation:[ f(x1;      ;xm)]2 =mXi=1  @f@xi  xi 2; (A.2)where the di erential is evaluated at (^1;      ; ^m). The zeroth order terms areconstant and do not a ect the uncertainty.The expression for     has the same form asf(x1;x2) = x1x2; (A.3)so in this case:( f)2 =   x1^2 2+   ^x1 x2x22 2: (A.4)Similarly,  cont: has the formg(x1;x2;x3;x4) = x1 + x2x3 + x4(A.5)and( g)2 =   x1^3 + ^4 2+   x2^3 + ^4 2+   (^x1 + ^x2) x3(^3 + ^4)2 2++   (^x1 + ^x2) x4(^3 + ^4)2 2: (A.6)92Appendix B  (3S) CountingBetween 22 December 2007 and 29 February 2008 (Run 7), the BABAR detectorrecorded events provided by PEP-II at the  (3S) resonance. Data was providedat the resonance peak with a CM energy of 10.35 GeV (on-peak data) and alsoat approximately 30 MeV below this (o -peak data).The author and Chris Hearty performed an analysis of  (3S) Counting onthis dataset. The methods used were closely based on the work presented inthis thesis and [11], and are described in detail in a BABAR Analysis Document[28].During Run 7, 121.9 million  (3S) mesons were produced. These werecounted to within a systematic uncertainty of 1.0%. Some results utilizing thiswork have been published, including a signi cant observation of the bottomo-nium ground state  b(1S) through the decay  (3S) !  b(1S) [29].93Bibliography[1] D. Besson and T. Skwarnicki, Ann. Rev. Nucl. Part. Sci. 43, 333 (1993).[2] P. F. Harrison and H. R. Quinn [BABAR Collaboration], \The BaBarPhysics Book: Physics at an Asymmetric B Factory," SLAC-R-0504,(1998).[3] B. Aubert et al. [BABAR collaboration], Phys. Rev. Lett. 87, 091801 (2001).[4] J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay, Phys. Rev.Lett. 13, 138 (1964).[5] A. D. Sakharov, Sov. Phys. Usp. 34, 417 (1991).[6] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963).[7] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).[8] K. Lingel, T. Skwarnicki and J. Smith, Annu. Rev. Nucl. Part. Sci. 48, 253(1998).[9] B. Aubert et al. [BABARCollaboration], Phys. Rev. Lett. 98, 211802 (2007).[10] B. Aubert et al. [BABAR Collaboration], Phys. Rev. D 69, 071101 (2004)[11] C. Hearty, \Hadronic Event Selection and B-Counting for Inclusive Char-monium Measurements," BABAR Analysis Document #30 (2000).[12] B. Aubert et al. [BABAR Collaboration], Nucl. Instrum. Meth. A 479, 1(2002).[13] PEP-II Conceptual Design Report, SLAC-418 (1993).[14] BABAR Technical Design Report, SLAC-R-95-457 (1995).[15] G. C. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978).[16] F. Anulli et al., Nucl. Instrum. Meth. A 539, 155 (2005).[17] S. Jadach, B. F. L. Ward and Z. Was, Comput. Phys. Commun. 130, 260(2000).[18] S. Agostinelli et al. [GEANT4 Collaboration], \GEANT4: A simulationtoolkit," Nucl. Instrum. Meth. A 506, 250 (2003).Bibliography 94[19] A. Mohapatra, J. Hollar, H. Band, \Studies of a Neural Net Based MuonSelector for the BABAR Experiment," BABAR Analysis Document #474(2004).[20] R. Hagedorn, Relativistic Kinematics, Reading: Benjamin/Cummings,1963.[21] W. M. Yao et al. [Particle Data Group], \Review of Particle Physics," J.Phys. G 33, 1 (2006). 301{302.[22] M. Peskin and D. Schroeder, An Introduction to Quantum Field Theory,Boulder: Westview Press, 1995. 131{140, 170.[23] T. Sj ostrand, Comput. Phys. Commun. 82, 74 (1994).[24] A. Ryd et al., \EvtGen: A Monte Carlo Generator for B-Physics," BABARAnalysis Document #522 (2003).[25] M. Benayoun, S. I. Eidelman, V. N. Ivanchenko and Z. K. Silagadze, Mod.Phys. Lett. A 14, 2605, (1999) [arXiv:hep-ph/9910523].[26] V. M. Budnev, I. F. Ginzburg, G. V. Meledin and V. G. Serbo, Phys. Rept.15, 181 (1974).[27] B. Aubert et al. [BABARCollaboration], Phys. Rev. Lett. 95, 042001 (2005).[28] G. McGregor and C. Hearty, \Hadronic and    Event Selection for  (3S)Counting," BABAR Analysis Document #2069 (2008).[29] B. Aubert et al. [BABAR Collaboration], \Observation of the bottomoniumground state in the decay  (3S) !  b" [arXiv:hep-ex/0807.1086v2].


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