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Measurement of Upsilon (1S) Production at BaBar So, Rocky Yat Cheung 2008

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Measurement of Upsilon(1S) Production atBABARInclusive Measurement at the Upsilon(4S)byRocky Yat Cheung SoA THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFBachelor of ScienceinThe Faculty of Science(Honours Biophysics)The University Of British Columbia(Vancouver, Canada)April 14th, 2008c Rocky Yat Cheung So 2008AbstractBABAR is a particle physics experiment at the Stanford Linear Accelerator Center (SLAC). Thepurpose of BABAR is to study matter-antimatter asymmetry in the bottom quark system. AtSLAC, electons and positrons collide, which annihilate and decay into a variety of daughters. AnUpsilon(4S) meson is one of the possible daughters. An Upsilon(4S) decays into a B meson and B mesonmore than 96% of the time. A B meson has an anti-bottom quark and a B meson has a bottomquark. The purpose of this thesis is to measure how many Upsilon(1S) originated from Upsilon(4S) in theentire BABAR data set. This thesis compares on-peak data and off-peak data. On-peak data wastaken at center of mass energy 10.58GeV . One of the possible interactions is e+e- arrowrightUpsilon(4S) sincethe mass of Upsilon(4S) is 10.58GeV/c2. Off-peak data, taken at center of mass energy 10.54GeV , isnot enough to have any BB pairs because 10.54GeV is less than the mass of an Upsilon(4S). Thisthesis can be useful for BABAR physicist because it helps set an upper limit on how many BBpairs there are in the entire BABAR data set. In other words, it sets an upper limit on how muchmore than 96% does Upsilon(4S) decay to BB. Measurement the decay of Upsilon(4S) arrowright Upsilon(1S) + X giveevidence for non BB decays of the Upsilon(4S). The final results of this study shows that there were(110 ? 3) ? 105 Upsilon(1S) on-peak, of which (10 ? 9) ? 105 originated from an Upsilon(4S). Increasingthe centre of mass energy from 10.54GeV to 10.58GeV increases the Upsilon(1S) production by (10 ?8)%.iiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview of the BABAR Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Anatomy of SLAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 The BABAR Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Laboratory Frame and Centre of Mass Frame . . . . . . . . . . . . . . . . . . . . . 31.5 Bottomonium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.6 Motivation for the Measurement of Upsilon(1S) at Upsilon(4S) . . . . . . . . . . . . . . . . . 42 Particle Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1 Physics of Muon and Electron Identification . . . . . . . . . . . . . . . . . . . . . 93.2 Candidates Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3 Monte Carlo Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Analysis Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1 Detector Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Upsilon(1S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.3 Detection Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.4 Angular Distributions of Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . 164.5 Angular Distribution of Detected Upsilon(1S) . . . . . . . . . . . . . . . . . . . . . . . . 164.6 Calculated Number of Events Expected . . . . . . . . . . . . . . . . . . . . . . . . 214.6.1 ISR Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.6.2 Feed Down Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.1 Comparison of On-peak and Off-peak Data . . . . . . . . . . . . . . . . . . . . . . 245.2 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25iiiTable of Contents5.3 Attempt to Measure chibJ (3P) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.4 Attempt to Measure Upsilon(2S) and Upsilon(3S) . . . . . . . . . . . . . . . . . . . . . . . . 26Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30AppendicesA Comparison of SP1072 and SP3981 . . . . . . . . . . . . . . . . . . . . . . . . . . 31ivList of Tables2.1 Mass of Upsilon species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.1 Summary of the data sets, versions used, integrated luminosities, and number ofUpsilon(4S) in each Run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Angles selection in laboratory frame and centre of mass frame. . . . . . . . . . . . 113.3 Summary of Monte Carlo sample used. . . . . . . . . . . . . . . . . . . . . . . . . . 114.1 Detection efficiencies of different signal Monte Carlo types of different Runs. . . . . 164.2 Upsilon dielectron widths and ISR cross sections. . . . . . . . . . . . . . . . . . . . . . . 224.3 Number of ISR Upsilon produced and decayed into muon pairs. . . . . . . . . . . . . . . 224.4 Number of Upsilon(1S) from known feed down events. . . . . . . . . . . . . . . . . . . . 235.1 Summary of uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.2 chibJ (3P) masses and energy of the photon that decayed with it. . . . . . . . . . . . 25vList of Figures1.1 SLAC and the PEP-II Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The BABAR detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 The BABAR coordinates system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 BABAR boost protractor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 A spectrum of bottomonium species. . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 Feynman diagram of the quark pair and lepton pair production . . . . . . . . . . . 62.2 Flow chart of on-peak processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Flow chart of off-peak processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.1 Ratio of E/p for particles of different energies. . . . . . . . . . . . . . . . . . . . . 104.1 Invariant mass of muon pairs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Data VS background Monte Carlo at MUpsilon(1S) . . . . . . . . . . . . . . . . . . . . . 134.3 Number of Upsilon(1S) arrowright?+?- detected on-peak. . . . . . . . . . . . . . . . . . . . . . 144.4 Number of Upsilon(1S) arrowright?+?- detected off-peak. . . . . . . . . . . . . . . . . . . . . . 154.5 Background Monte Carlo angular distributions in the forward direction. . . . . . . 174.6 Background Monte Carlo angular distributions in the backward direction . . . . . 174.7 Angular distribution at signal region and outside signal region. . . . . . . . . . . . 184.8 Angular distribution of detected Upsilon(1S) on-peak . . . . . . . . . . . . . . . . . . . . 194.9 Angular distribution of detected Upsilon(1S) off-peak . . . . . . . . . . . . . . . . . . . . 205.1 Invariant mass of two muons plus one photon greater than 500MeV . . . . . . . . . 275.2 On-peak data and background Monte Carlo at Upsilon(2S) region. . . . . . . . . . . . . 275.3 On-peak data and background Monte Carlo at Upsilon(3S) region. . . . . . . . . . . . . 285.4 On-peak data minus background Monte Carlo at Upsilon(2S) region. . . . . . . . . . . . 285.5 Off-peak data minus background Monte Carlo at Upsilon(2S) region. . . . . . . . . . . . 29A.1 On-peak comparison of muon angular distribution. . . . . . . . . . . . . . . . . . . 31A.2 Off-peak comparison of muon angular distribution. . . . . . . . . . . . . . . . . . . 31A.3 On-peak differences of muon angular distribution between data and Monte Carlo. . 32A.4 Off-peak differences of muon angular distribution between data and Monte Carlo. . 32viAcknowledgementsI would like to thank Dr. Christopher Hearty for the many hours he spent supervising thisresearch. He identified the project and gave me brilliant ideas for this data analysis.Also, thanks to Doug Maas for setting up and maintaining the computer I used for the analysis,and thanks to Dr. Robert Kiefl and Dr. Michael Hasinoff for coordinating the Physics 449 course.Finally, I would like to thank my family for their support, especially my father, Wing KeungSo, who always reminds me to do my best and never give up.viiChapter 1Introduction1.1 Overview of the BABAR ExperimentThe BABAR experiment takes place at the Stanford Linear Accelerator Center (SLAC) in Cali-fornia, USA. It studies matter-antimatter asymmetry in the bottom quark system. Mesons areproduced in SLAC by colliding positrons to electrons head on at speeds close to the speed of light.Electrons are accelerated to 9GeV and positrons are accelerated to 3.1GeV . Since electrons andpositrons are each other?s anti-particle, they annihilate when they hit each other, making anUpsilon(4S) particle a fraction of the time. This Upsilon(4S) particle subsequently decays into a pair of Bmesons (one B and one B). These are what BABAR physicists are interested in. By studyingthe differences between how a B and a B evolve, BABAR physicists can better understand thematter-antimatter asymmetry, which can help explain why the universe is dominated with matterinstead of antimatter.1.2 Anatomy of SLACSLAC has an accelerator and a detector. The accelerator is linear and injects electrons andpositrons into the Positron Electron Project II (PEP-II) ring. The detector is made of manydifferent components. Figure 1.1 [1] shows how the linac feeds electrons and positrons into twoseperate rings.Figure 1.1: SLAC and the PEP-II RingsUsing electromagnetic fields, electrons and positrons are accelerated down the linac and movedinto the PEP-II rings where they begin to travel in opposite directions. The two beams are steeredto hit each other at the BABAR detector, where data is taken.1Chapter 1. IntroductionFigure 1.2: The BABAR detectorFigure 1.3: The BABAR coordinates system.The BABAR detector is able identify and measure the energy, momentum, azimuthal angle phi,and polar angle theta of a charged track. It has five different detectors to do this as shown in Figure1.2 [1]. The Silicon Vertex Tracker records where the track originates (where the vertex of aninteraction is). The Drift Chamber measures the momentum of a track. The Detector of InternallyReflected Cherenkov light detects and identifies hadrons. The Cesium Iodide calorimeter measuresphoton energies. Finally, the Instrumented Flux Return identifies muons and neutral hadrons.1.3 The BABAR Coordinate SystemThroughout this thesis, the BABAR coordinates convention will be used (see Figure 1.3). Thez-axis points in the direction of the electron beam. The x-axis horizontally points away from thePEP-II ring. theta is the angle a charged track makes with the z-axis. phi is the angle a charged trackmakes with the x-axis in the x-y plane.2Chapter 1. Introduction1.4 Laboratory Frame and Centre of Mass FrameIn the laboratory frame, the electrons are accelerated to 9GeV and positrons to 3.1GeV. Aftertheir collision, the Upsilon(4S) continues to move in the electron?s initial direction for momentum to beconserved. The BABAR experiment is designed to do this so we can resolve the decay vertex of theB mesons. Since the total mass of BB is 10.54GeV [4], BB move almost as fast as the Upsilon(4S) inthe laboratory frame. If the electron and positron beams are symmetric in the laboratory frame,then the B mesons would decay at the centre of mass and we cannot see which one decayed first.We can Lorentz transform from the laboratory frame to the centre of mass frame. At theGeV scale, electrons and positrons can be considered massless (m is zero in Einstein?s energymomentum relation E2 = p2c2 + m2c4).Lab Frame9GeV e- arrowrightarrowleft3.1GeV e+Energy of collision = 12.1GeV = EMomentum of collision = 5.9GeV = pzCentre of Mass Frame5.29GeV e- arrowrightarrowleft5.29GeV e+Energy of collision = 10.58GeV = EprimeMomentum of collision = 0GeV = pprimezpprimez = gamma(pz -betaE)beta = pz/E = 0.487gamma = 1.15betagamma = 0.56Therefore, the centre of mass frame is travelling along the z-axis at about half the speed oflight relative to the laboratory frame. This thesis analyses muon data in the centre of mass frame.The relationship between theta in the laboratory frame and thetaprime in the centre of mass frame is:costhetaprime = (costheta -beta)/(1 -betacostheta) (1.1)Azimuthal angle does not change in a boost along the z axis.phiprime = phi (1.2)Figure 1.4 shows how theta in one frame is related to the other.1.5 BottomoniumBottomonium is a general term that applies to any meson that has one bottom quark and oneanti-bottom quark. States with different quantum numbers have different names. For example,a bottomonium with quantum numbers JPC = 1-- is called an Upsilon, where J is the total angularmomentum, P is the parity quantum number, and C is the charge conjugation quantum number.A chibJ is a bottomonium with quantum number JPC = 0,1,2++. J can be 0, 1,or 2, which3Chapter 1. IntroductionFigure 1.4: BABAR boost protractor.corresponds to three states for each of the chibJ(mP). Figure 1.5 [2] shows different bottomoniumspecies, their respective quantum numbers, and a few of their decay modes.Figure 1.5: A spectrum of bottomonium species.1.6 Motivation for the Measurement of Upsilon(1S) at Upsilon(4S)BABAR physicists are interested in B mesons. At BABAR, BB pairs are created by the productionof an Upsilon(4S). Upsilon(4S) decays into BB mesons more than 96% of the time (95% confidence interval)[3]. BABAR physicists would like to know how many B mesons there are in the entire BABAR dataset. Therefore, if we can measure how often an Upsilon(4S) decays into an Upsilon(1S), it gives us moreinformation on the upper limit of how many BB mesons were produced. The BABAR experiment4Chapter 1. Introductiontook data at two energies: on-peak (radicals = 10.58GeV) and off-peak (radicals = 10.54GeV). An Upsilon(4S)has a mass of 10.58GeV , so on-peak data can have Upsilon(4S) in them. Off-peak energy is slightlybelow that required to make an Upsilon(4S), so Upsilon(4S) would not be present in the data. By comparingthe two data sets, the number of Upsilon(1S) decayed from an Upsilon(4S) can be measured.The branching fraction B(Upsilon(4S) arrowrightUpsilon(1S) + anything) is measured to be less than 4 ?10-3[3]. The measurement of this thesis is not a branching fraction. It is an inclusive measurementthat includes any Upsilon(1S) that originated from an Upsilon(4S) regardless of whether it decayed into achibJ, Upsilon(3S), or Upsilon(2S) first, or directly to Upsilon(1S) in the process.This thesis also attempts to show evidence for chibJ in the 3P state. This state has never beenobserved directly before.Heavy quarkonia interactions are important for testing of lattice quantum chromodynamics(LQCD). Many heavy quarkonia are studied by measuring their decays. The Upsilon(4S) is above openflavour threshold. Thus, this study can be useful for LQCD theorists.5Chapter 2Particle InteractionsAt BABAR, an electron-positron collision annihilates and makes a virtual photon, which decaysinto quark pairs or lepton pairs. Figure 2.1 are the Feynman diagrams for the two interactions.Figure 2.1: Feynman diagram of the quark pair and lepton pair production. The first Feyn-man diagram is the production of quark-antiquark pairs. The second Feynman diagram is theproduction of lepton-antilepton pairs. Time goes from left to right.When a quark pair is produced, they hadronize [4]. In the case of bottom quark pairs, theyhadronize to an Upsilon. Since the quantum numbers of a photon and an Upsilon are both JPC = 1--, Upsilon isthe only bottomonium species that can be made. Thus, a chibJ cannot be made initially.At such high energies, photons can be emitted from any of the four legs in the above Feynmandiagrams. The photon would carry away some energy and momentum. If the photon was emittedin the two initial legs, the collision would have energy less than the 10.58GeV or 10.54GeV .e+e- arrowrightgammaqqe+e- arrowrightgammalscript+lscript-Any photon emitted from a lepton prefers to point along the direction of its parent lepton.Therefore, if a photon is emitted initially, the lepton final states would also preferentially pointin the initial directions. e+e- arrowright gamma?+?- has an angular distribution peaked in the forward andbackward directions.If a bottom quark pair is created, an Upsilon(4S) can be made only if there were no photons. Itwould be completely stationary in the centre of mass frame. If a photon is emitted before thecollision, it would carry away some energy and there would not be enough energy to make anUpsilon(4S). However, Upsilon(nS), where n = 1,2,3, can be made even if a photon carried away someenergy. This is because the masses of Upsilon(nS) are lower than the energy of the collision. Themasses of Upsilon species are given in Table 2.1 [3].In this process, the photon associated with an Upsilon(nS), is called an initial state radiationphoton, or gammaISR.6Chapter 2. Particle InteractionsMass (GeV )Upsilon(1S) 9.46030 ?0.00026Upsilon(2S) 10.02326 ?0.00031Upsilon(3S) 10.3552 ?0.0005Upsilon(4S) 10.5794 ?0.0012Table 2.1: Mass of Upsilon species.e+e- arrowrightgammaUpsilon(nS)In the off-peak data set, many of the Upsilon particles come from the ISR process. The others comefrom the feed down of intermediate decays such as Upsilon(3S) arrowrightX arrowrightUpsilon(1S).Similarly, in the on-peak data set, there are many Upsilon(nS) from the ISR process, but there arealso decays from the Upsilon(4S). One of these known decays is Upsilon(4S) arrowrightpi+pi-Upsilon(nS) [5].There are even more feed down processes because an Upsilon(4S) may decay into Upsilon(3S) or otherbottomonium species, which may end up decaying into an Upsilon(1S). Figure 1.5 shows how anUpsilon(3S) can decay into gamma + chib2(2P), which may subsequently decays into omega + Upsilon(1S). Figure 1.5 isa simplification of the cascade of events that can make a Upsilon(1S). In reality, there are many moreintermediate decays possible.This thesis analyses muon data collected in the BABAR experiment. There are many back-ground muon events in the form of e+e- arrowrightgamma?+?-. We are interested in the signal events. Theseevents come from Upsilon decays into muon pairs Upsilon(1S) arrowright?+?-.The BABAR experiment recorded muon energies and momenta for every event. This givestheir 4-momentum vector. Adding the muons? 4-momenta and squaring it gives the invariantmass squared. If the two muons decayed from an Upsilon(1S), this would necessarily be equal to themass of an Upsilon(1S).(p?+ + p?-)2 = MUpsilon(1S)2Figures 2.2 and 2.3 summarizes the processes relevant to this thesis.7Chapter 2. Particle InteractionsFigure 2.2: Flow chart of on-peak processes.Figure 2.3: Flow chart of off-peak processes.8Chapter 3DataThe BABAR experiment started taking data in 1999. It takes data for 9 months in a year. Eachyear?s data set is called a Run. This analysis uses data from Run 1 to Run 6. Table 3.1 summarizesthe data sets used in this analysis.Data Set Integrated Luminosity (pb-1) Number of Upsilon(4S) (106)AllEventsSkim-Run1-OffPeak-R22d-v07 2620 0AllEventsSkim-Run2-OffPeak-R22d-v07 6920 0AllEventsSkim-Run3-OffPeak-R22d-v04 2470 0AllEventsSkim-Run4-OffPeak-R22d-v07 10100 0AllEventsSkim-Run5-OffPeak-R22d-v07 14500 0AllEventsSkim-Run6-OffPeak-R22d-v07 7280 0Total Off-Peak Data 43900 0AllEventsSkim-Run1-OnPeak-R22d-v07 20400 22.39 ?0.25AllEventsSkim-Run2-OnPeak-R22d-v07 61100 67.39 ?0.74AllEventsSkim-Run3-OnPeak-R22d-v04 32300 35.57 ?0.39AllEventsSkim-Run4-OnPeak-R22d-v07 100000 110.45 ?1.22AllEventsSkim-Run5-OnPeak-R22d-v07 133000 147.19 ?1.62AllEventsSkim-Run6-OnPeak-R22d-v07 76200 82.04 ?0.90Total On-Peak Data 423000 465.04 ?5.15Table 3.1: Summary of the data sets, versions used, integrated luminosities, and number ofUpsilon(4S) in each Run.3.1 Physics of Muon and Electron IdentificationThe BABAR detector measures leptons as charged tracks. When a high energy electron movesthrough a medium, it can emit a photon. This photon can subsequently create an electron-positron pair by pair production. The electron and positron can further emit photons, which willproduce pairs and so on until the particles have insufficient energy to produce more particles.This phenomenon is called electromagnetic shower [6]. Muons and electrons have distinct showershapes. By analyzing the shape of a shower, a detector can identity an electron from a muon.The ratio of the energy deposited in a shower to the momentum of the electron, E/pc, is nearlyone[7]. This means that electrons deposit most of their energy in its shower. However, sincemuons do not shower like electrons, they deposit a lot less energy as electrons. The E/pc ratioand distribution are characteristic for different particles. Figure 3.1 [7] shows how differentparticles deposit different amounts of energy.9Chapter 3. DataFigure 3.1: Ratio of E/p for particles of different energies.3.2 Candidates SelectionThe major goal of this analysis is to measure how many Upsilon(1S) there are in the on-peak data set.Data in the BABAR experiment are recorded as individual events. Data used in this analysisare muon events that satisfy the following:? there were two charged tracks originating from one vertex,? one of the charged tracks was identified as a muon,? the two charged tracks had total energies that range from 8 to 12 GeV in the centre of massframe,? and the event passed the BGFmumu filter (a reconstructing software filter that roughlyidentifies dimuon events e+e- arrowright?+?-).The BABAR detector is cylindrical. It ?wraps? around the beam pipe and there are no detectorsalong the beam direction. BABAR is known to be capable of measuring polar angles theta from 0.41to 2.54 radians in the laboratory frame. The corresponding angles in the centre of mass frameare given in Table 3.2.Along with the above criteria, muons with costheta from -0.78 to 0.78 were selected instead offrom -0.94 to 0.78. This is done to avoid any bias from having more muons in the backwardsdirection of the data set.10Chapter 3. Datatheta (radians) costheta thetaprime (radians) costhetaprime0.41 0.92 0.68 0.782.54 -0.83 2.78 -0.94Table 3.2: Angles selection in laboratory frame and centre of mass frame.The muon pairs are reconstructed to Upsilon candidates. The four-momentum of these candidatesare simply the sum of the four-vector of the muon pair.3.3 Monte Carlo SampleBoth the on-peak and off-peak data involve many different processes; some of which we knowand some we do not know about. To model the BABAR data, Monte Carlo simulations were used.Monte Carlo simulations are useful because they can model different processes separately.Monte Carlo sample comes from computer-generated events. These events are then modelledto go through the BABAR detector. It includes any resolution effects in the detector. It modelsif a detector will detect the charged tracks and if it will satisfy the reconstruction criteria. Table3.3 summarizes the Monte Carlo samples used in this analysis. There are two different modelsfor the background process SP1072 and SP3981. This study uses SP3981 because it is believedto be the better one. A comparison of SP1072 and SP3981 is given in Appendix A.Decay Mode SP Number of Events Number of Eventsmodenum On-Peak Off-Peak?+?-(gamma) 1072 1.2096060 ?107 6.37691 ?105?+?-(gamma) 3981 2.837796 ?108 6.689054 ?107Upsilon(4S) arrowrightpi+pi-Upsilon(nS) arrowrightpi+pi-lscript+lscript- 5467 145000 0Upsilon(4S) arrowrightgammachibJ(3P) arrowrightgammagammaUpsilon(nS) arrowrightgammagammalscript+lscript- 8249 350000 0gammaUpsilon(nS) arrowrightgammalscript+lscript- 8268 1053000 0Table 3.3: Summary of Monte Carlo sample used.11Chapter 4Analysis ProceduresROOT was used to analyse data from the BABAR database in ntuples format [8]. Figure 4.1 is amass plot of the invariant muon pair mass on-peak and off-peak.Figure 4.1: Invariant mass of muon pairs.4.1 Detector ResolutionMost of the data are background events in the form of e+e- arrowright gamma?+?-. The peaks of the twohistograms occur slightly below their centre of mass energy because many events have lost energyvia photon emission. It becomes an asymmetric Gaussian because events can only lose energyand move to the left side of the Gaussian instead of moving to the heavier side of the Gaussian.The BABAR detector has a resolution. If an event had an invariant muon pair mass M, it is12Chapter 4. Analysis Proceduresgoing to be measured with a variance of sigma2. The higher side of the Gaussian has energy higherthan the centre of mass energy, so almost all the events there had no photons. The width ofthe higher energy side would be the approximate resolution of the detector because it is mostlyevents of centre of mass energy.This width is approximately 70MeV . The detector?s resolution is assumed to be constantfrom 8GeV to 12GeV .4.2 Upsilon(1S)If the BABAR detector detects signal from Upsilon(1S), we expect to see an excess of events at the massof Upsilon(1S) over background events. A Gaussian with mean at MUpsilon(1S) and width sigma is expected.The integral of this Gaussian would be the total number of Upsilon(1S) we detected.The Monte Carlo for background events e+e- arrowright?+?-gamma is plotted with the data at the Upsilon(1S)region ?4sigma. The mass region outside of 3sigma have neglible signal. The Monte Carlo was scaled sothe number of events at those regions is equal to the data. Those events are purely backgroundevents. Figure 4.2 shows the excess of events at the Upsilon(1S) region compared to background MonteCarlo.Figure 4.2: Data VS background Monte Carlo at MUpsilon(1S)Then the background Monte Carlo events are subtracted from data to obtain the distribution13Chapter 4. Analysis Proceduresof signal events.Figure 4.3: Number of Upsilon(1S) arrowright?+?- detected on-peak.This was fitted to a Gaussian in Figure 4.3. There are (1.644 ? 0.04) ? 105 Upsilon(1S) arrowright ?+?-events in this Gaussian. Dividing this by the branching fraction B(Upsilon(1S) arrowright ?+?-) = (2.48 ?0.05)%, this corresponds to (6.63 ?0.16) ?106 Upsilon(1S) detected.The corresponding plot is given in Figure 4.4 for off-peak. There are (6.5 ?0.4) ?105 Upsilon(1S)detected off-peak.4.3 Detection EfficienciesThe number of Upsilon(1S) detected is less than the actual number of Upsilon(1S) produced because theBABAR detector has a detection efficiency less than 100%. Efficiencies are estimated using signalMonte Carlo sample.Events were generated in signal Monte Carlo samples. As shown in Table 3.3, these wereUpsilon(nS) arrowright?+?- events. Of these samples, Events that had an Upsilon(1S) generated and a muon pairgenerated right after were selected. These are the actual number of events of interest generated.Of these events, the exact same selection criteria used for candidate selection in data were applied.These events are the simulated events that survive to the detector and gets detected. Therefore,the efficiency epsilon1 is14Chapter 4. Analysis ProceduresFigure 4.4: Number of Upsilon(1S) arrowright?+?- detected off-peak.15Chapter 4. Analysis Proceduresepsilon1 = #surviving#generated (4.1)These efficiencies are listed in Table 4.1 for different Runs for each signal Monte Carlo type.Their uncertainties are radicalbign ?epsilon1(1 -epsilon1), where n is the number of generated events of interest.Run Upsilon(4S) arrowrightpipiUpsilon(nS) Upsilon(4S) arrowright gammachibJ(3P) arrowrightgammagammaUpsilon(nS) gammaISRUpsilon(nS)1 0.668 ?0.014 0.664 ?0.012 0.592 ?0.0082 0.678 ?0.008 0.670 ?0.007 0.604 ?0.0053 0.679 ?0.010 0.661 ?0.010 0.601 ?0.0064 - 0.673 ?0.005 0.605 ?0.0045 0.687 ?0.005 0.668 ?0.005 0.604 ?0.0036 0.679 ?0.010 - -Table 4.1: Detection efficiencies of different signal Monte Carlo types of different Runs. MonteCarlo samples were not available for every Run.Different signal types have different efficiencies because they have different angular distribu-tions. The BABAR detector does not have a uniform detection efficiency over all polar angles.4.4 Angular Distributions of Monte Carlo SamplesKnowing the number of Upsilon(1S) detected is not enough to determine if it decayed from an Upsilon(4S),decayed from a cascade of feed down events, or directly from an ISR event. Monte Carlo samplescan be used to model the angular distributions of background events and different signal types.The angular distribution of Upsilon(4S) arrowrightpi+pi-Upsilon(nS) and Upsilon(4S) arrowrightgammachibJ(3P) arrowrightgammagammaUpsilon(nS) eventsare uniform. This is because in the event an Upsilon(4S) is made, it is stationary in the centre of massframe. Its daughters would not inherit any momentum, and there is no preferred direction.In ISR events, since an ISR photon carried away some momentum, the Upsilon(nS) particle isnot stationary in the centre of mass frame when it gets created. ISR photons have angulardistributions peaked in the forward and backward directions. To conserve momentum, the ISRphoton and the Upsilon candidate would have to point back to back in the centre of mass frame.Background Monte Carlo also have sharp spikes in the forwards and backwards region.4.5 Angular Distribution of Detected Upsilon(1S)The shape angular distribution of detected Upsilon(1S) can tell what they are composed of. It is acombination of a uniform distribution of Upsilon(1S) decayed from Upsilon(4S) and a peaked distributionof ISR Upsilon. Since the number of background events is big compared to signal events, the accuracyof Monte Carlo angular distributions is very critical. In order to avoid any inaccurate modellingof the angular distribution of background events by Monte Carlo, data itself can also model theangular distributions of background events. The following is a description of how this was done.Outside the signal region, since there is no Upsilon(1S), we can expect those events are purelybackground. That is, the events from 9.12 - 9.22GeV and 9.70 - 9.80GeV are expected to be16Chapter 4. Analysis Proceduresonly e+e- arrowrightgamma?+?-. We expect that some combination of the lower region and the upper regionof the data gives the angular distribution of the e+e- arrowrightgamma?+?- at the signal region.Figure 4.5: Background Monte Carlo angular distributions in the forward direction.Figure 4.6: Background Monte Carlo angular distributions in the backward directionTo determine the weighting ratio, we looked at the angular distributions of background MonteCarlo and tried to emulate the signal region by adding the lower region to upper region with dif-ferent proportions. The angular distributions in the forward and backwards region of backgroundMonte Carlo are plotted in Figures 4.5 and 4.6. Theses plot show that lower the invariant mass,the more sharply peaked the angular distributions are in the forwards and backwards direction.By adding a 9.12 - 9.22GeV distribution to a 9.70 - 9.80GeV distribution, a new distributionthat is almost identical to the one at signal region is obtained. The weighting was 53% lowerregion and 47% upper region. This weighting ratio was obtained by trial and error.Using the outside regions does not give the exact angular distribution at the signal region.With background Monte Carlo, taking the actual angular distribution at the signal region and17Chapter 4. Analysis Proceduressubtracting the lower and upper region gives the disagreement. This disagreement should besimilar to the disagreement for data.In the actual BABAR data, 53% of the lower region and 47% of the upper region was addedto the disagreement obtained from background Monte Carlo. Figure 4.7 is an on-peak plot of theangular distribution at signal region with the distribution outside the signal region. This is usedas the angular distribution of e+e- arrowrightgamma?+?- in the signal region.Figure 4.7: Angular distribution at signal region and outside signal region.This was subtracted from the angular distribution of the data at the signal region. Theresulting plot is the angular distribution of the detected Upsilon(1S). Figure 4.8 is on-peak and Figure4.9 is off-peak.The Upsilon(1S) in both the on-peak and off-data set is also peaked in the forward and backwardregion. This indicates that many of these are ISR Upsilon.4.6 Calculated Number of Events Expected4.6.1 ISR EventsISR processes have been studied before [9] [10]. In these studies, the predicted cross section forISR events were accurate up to the fine structure constant squared, alpha2.18Chapter 4. Analysis ProceduresFigure 4.8: Angular distribution of detected Upsilon(1S) on-peak19Chapter 4. Analysis ProceduresFigure 4.9: Angular distribution of detected Upsilon(1S) off-peak20Chapter 4. Analysis ProceduressigmagammaISRUpsilon(nS)(s) = 12pi2GeeM(nS)sW(s,1 -M2(nS)s ) (4.2)x = 1 - M2(nS)s (4.3)W(s,x) = deltabetaxbeta-1 - beta2 (2 -x) + beta28braceleftbigg(2 -x)[3ln(1 -x) -4lnx] -4ln(1 -x)x -6 + xbracerightbigg(4.4)delta = 1 + alphapi(32L + 13pi2 -2) + (alphapi)2delta2 (4.5)delta2 = (98 -2zeta2)L2 -(4516 - 112 zeta2 -3zeta3)L - 65zeta22 - 92zeta3 -6zeta2ln2 + 38zeta2 + 5712 (4.6)beta = 2alphapi (L -1) (4.7)zeta2 = 1.64493407 (4.8)zeta3 = 1.2020569 (4.9)L = 2lnradicalsme (4.10)me is the mass of an election. radicals is the centre of mass energy. Gee is the dielectron width.M(nS) is the mass of an Upsilon(nS). beta in the above equations is not the fraction of the speed of light.Plugging in the on-peak and off-peak centre of mass energies and the Upsilon masses gives the crosssection for the interactions. Multiplying this by the integrated luminosities and efficiency of eachrun gives the number of Upsilon(1S) that we expect to detect. Table 4.2 lists the dielectron widths andISR cross sections for different Upsilon. Table 4.3 lists the number of Upsilon we expect to be produced andthe number of Upsilon arrowright?+?- events.Dielectron width On-peak ISR Off-peak ISRGee (keV) [3] cross section (pb) cross section (pb)Upsilon(1S) 1.340 ?0.0018 19.60 20.42Upsilon(2S) 0.612 ?0.011 17.11 18.48Upsilon(3S) 0.272 ?0.008 28.63 34.54Table 4.2: Upsilon dielectron widths and ISR cross sections.21Chapter 4. Analysis ProceduresB(Upsilon arrowright?+?-)(%) On-peak ISR Upsilon Upsilon arrowright?+?- Off-peak ISR Upsilon Upsilon arrowright?+?-Upsilon(1S) 2.48 ?0.05 8300352 205849 896340 22229Upsilon(2S) 1.93 ?0.17 7246524 139858 810872 15650Upsilon(3S) 2.18 ?0.21 12124269 264309 1516103 33051Table 4.3: Number of ISR Upsilon produced and decayed into muon pairs.4.6.2 Feed Down EventsIn both on-peak and off-peak, there are millions of ISR Upsilon(nS). The Upsilon(2S) and Upsilon(3S) coulddecay into an Upsilon(1S). Some of these decays have precisely measured branching fractions. It turnsout that the number of Upsilon(1S) from a cascade of feed down decays is very comparable to the ISRUpsilon(1S) events. Table 4.4 sums up the known decays from higher mass bottomonium species.Origin On-peak Off-peakfeed down Upsilon(1S) feed down Upsilon(1S)Upsilon(2S) 2303525 257760Upsilon(3S) 1693811 211806Upsilon(4S) 75788 0Total 4073124 469566Table 4.4: Number of Upsilon(1S) from known feed down events.The most significant contribution comes from Upsilon(2S). Roughly, 30% of Upsilon(2S) decays into anUpsilon(1S). The total contributions of feed down events add up to almost one half of ISR Upsilon(1S). Theactual contributions should be bigger because there are branching fractions that have not beenmeasured and there may be processes that we do not know of or understand. The feed downfrom Upsilon(4S) in off-peak data is zero because there is no Upsilon(4S).The Upsilon from the cascade of decays have a complicated angular distrubution because there aremany processes involved. Since there is not yet a Monte Carlo for these events, it is very difficultto model the detection efficiency of these events.We predict the angular distribution of these to have a preference in the forward and backwardsdirections but not as sharply peaked. This is because ISR Upsilon(2S) and Upsilon(3S) have momentumin the centre of mass frame. Their daughters inherit some of the momentum. Upsilon also have nopreferred decay direction, so the combined effect of these two would make a distribution preferredforward and backwards.22Chapter 5Results5.1 Comparison of On-peak and Off-peak DataAlthough the energy resolution of the BABAR detector was estimated to be 70MeV , the on-peakGaussian fit at the Upsilon(1S) region has a width of (61 ? 2)MeV and the off-peak has a width of(48 ? 5)MeV . This may mean that the resolution is different for on-peak and off-peak or thereis some process data that we do not know about in the on-peak data set that smeared out thedata.The angular distributions of Upsilon(1S) in the both on-peak data and off-peak data have verysimilar shapes and are both peaked in the forwards and backwards direction. This indicates thatthe on-peak Upsilon(1S) are mostly created in the same mechanism as off-peak.The ratio of luminosities between on-peak and off-peak data is R = 9.7. Scaling the numberof off-peak Upsilon(1S) by this ratio gives a good estimate of how many Upsilon(1S) in the on-peak data didnot originate from an Upsilon(4S).N = nepsilon1B (5.1)n = Nepsilon1B (5.2)nprime = Nprimeepsilon1B (5.3)N is the number of detected Upsilon(1S) on-peak. n is the number of produced Upsilon(1S) on-peak. Nprimeis the number of detected Upsilon(1S) off-peak. nprime is the number of produced Upsilon(1S) off-peak. epsilon1 is thedetection efficiency. B is the branching fraction of Upsilon(1S) arrowright?+?-.The number of Upsilon(1S) that originated from a Upsilon(4S) is thereforedelta = n -nprimeRr (5.4)delta = N -NprimeRrepsilon1B (5.5)r is a correction factor of 0.96, which is equal to the ratio of Upsilon(1S) ISR cross section on-peakto off-peak. delta corresponds to 1.1 ?107 -1.0 ?107 approxequal 1 ?106.To avoid the complications from efficiencies, branching fractions, different resolution widths,and uncertainties, we can simply compare the ratio of detected on-peak events and off peak events.Efficiencies and branching fractions cancel in their ratio N/(NprimeRr). This becomes 164400/(9.7 ?16120 ?0.96) approxequal 1.10. In other words, just by tuning the centre of mass energy up to the mass ofan Upsilon(4S), we get roughly 10% more Upsilon(1S) due to Upsilon(4S) decays.23Chapter 5. ResultsOn-peak and off-peak data both agree that most of the Upsilon(1S) came from ISR production.The decay Upsilon(4S) arrowright Upsilon(1S) must happen at some level. This process is small compared to theISR production of Upsilon(1S).5.2 Error AnalysisThe three fundamental quantities measured are the total number of Upsilon(1S), the number of thisthat originated from an Upsilon(4S), and how many more Upsilon(1S) we get if we go from off-peak toon-peak. The uncertainties involved in these calculations are given in Table 5.1.Parameter UncertaintyRatio of luminosities 1%B(Upsilon(1S) arrowright?+ ?-) 1%N 2.3%Nprime 7.0%Systematic error between data and Monte Carlo 4%Detection efficiencies 1.6%Number of Upsilon(4S) in on-peak data 1.1%Systematic error of ratio of ISR luminosities approxequal 1%Table 5.1: Summary of uncertainties.Therefore, n = (1.10 ? 0.03) ? 107, delta = (1.0 ? 0.9) ? 106, and increasing the centre of massenergy from off-peak to on-peak makes (10 ? 8)% more Upsilon(1S). The uncertainty on delta is hugebecause N approxequal NprimeRr. Of the 4.65 ? 108 Upsilon(4S), 0.22 ? 0.18% eventually end up as an Upsilon(1S).Compared to the branching fraction of Upsilon(4S) arrowright Upsilon(1S) + anything < 0.4% [3], this means thatUpsilon(4S) decayed into Upsilon(1S) directly most of the time instead of by a cascade of decays.5.3 Attempt to Measure chibJ (3P)Upsilon(4S) decays into BB almost all the time. Approximately 1 million out of the 465 million Upsilon(4S)did not decay into BB, which is about 0.2%. Some of these Upsilon(4S) may have decayed into thetheoretical chibJ (3P). chibJ in the (3P) orbital has never been directly observed. The mass of chibJis theoretically between the mass of a Upsilon(3S) and a Upsilon(4S).Mass (GeV ) Energy of photon decayed along (MeV )chib0 (3P) 10.501 79chib1 (3P) 10.516 64chib2 (3P) 10.526 54Table 5.2: chibJ (3P) masses and energy of the photon that decayed with it.Daughters in a 2-body decay in the centre of mass frame of the parent have energies24Chapter 5. ResultsEdaughter1 = Mparent2 -mdaughter12 + mdaughter222Mparentmdaughter1 (5.6)Therefore, photons decayed with chibJ (3P) should have energies approximately from 50 to80MeV in the decay Upsilon(4S) arrowright gammachibJ(3P). This is difficult to distinguish from the backgroundbecause there are many background photons that did not originate from the electron, the positron,or their collision. These background photons also have energies in the order of tens of MeV.Theoretically, chibJ (3P) may also decay radiatively into an Upsilon(1S). The higher mass differencebetween chibJ (3P) and Upsilon(1S) corresponds to a higher energy photon in the order of 1GeV .Unfortunately, this was also very difficult to distinguish from the background. This is becausein the event e+e- arrowrightgamma?+?-, one photon emission events contribute the more than multi-photonevents. These one photon events also have photon energies in the order of 1GeV in the chibJ (3P)rest frame. It is very difficult to resolve background QED photons and chibJ photons. Besides, themasses of chibJ (3P) are already very close to each other.We attempted to measure a chibJ (3P) by plotting the invariant mass of the two muon plusone photon with energy more than 500MeV . This selection was done to avoid any backgroundphotons. If there were chibJ (3P) in the data, there should be excess events at the theoretical chibJ(3P) masses.To do this, the same approach used to plot the angular distributions was used. Figure 5.1shows plots at the lower region and upper region of the invariant muon pair mass. Then we usedthe same weighting factors which we used before (53% and 47%) to emulate the signal region.The resulting plot is also given in Figure 5.1. Most of these events are background events. ThechibJ (3P) signal is probably too small and undistinguishable.5.4 Attempt to Measure Upsilon(2S) and Upsilon(3S)We originally proposed to measure Upsilon(2S) and Upsilon(3S) too. From the expected events calculationin chapter 4, we can expect that Upsilon(2S) and Upsilon(3S) get created in similar amounts by ISR butdiffer in the feed down contributions. At the Upsilon(2S) and Upsilon(3S) regions, there are many morebackground events compared to the Upsilon(1S) region. Excess events are more difficult to be seen.Also, the Monte Carlo and data do not agree as well as it did at the Upsilon(1S) region. The analysismethods used in this study would not work well for a measurement of Upsilon(2S) and Upsilon(3S). Figures5.2 and 5.3 shows how Upsilon are not distinguishable from the on-peak data. We do not see ?Gaussianbumps? at MUpsilon(2S) or MUpsilon(3S).Figure 5.4 is data minus background Monte Carlo on-peak and Figure 5.5 is data minusbackground Monte Carlo off-peak. In both of these plots, Monte Carlo predicts too few eventsabove the mass region of Upsilon(2S). These fits were obtained by fitting a Gaussian plus a third orderpolynomial. It would be difficult to look at the angular distribution of Upsilon(2S) candidates until wehave Monte Carlo that agrees with data better.25Chapter 5. ResultsFigure 5.1: Invariant mass of two muons plus one photon greater than 500MeVFigure 5.2: On-peak data and background Monte Carlo at Upsilon(2S) region.26Chapter 5. ResultsFigure 5.3: On-peak data and background Monte Carlo at Upsilon(3S) region.Figure 5.4: On-peak data minus background Monte Carlo at Upsilon(2S) region.27Chapter 5. ResultsFigure 5.5: Off-peak data minus background Monte Carlo at Upsilon(2S) region.28Bibliography[1] Workbook for BABAR Offline Users.http://www.slac.stanford.edu/BFROOT/www/doc/workbook/detector/detector.html[2] Pedlar Todd K. Contribution to the proceedings for ?Heavy Quarks and Leptons 2006?(HQL06), 16-20 Oct 2006 Munich, Germany.[3] W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: http://pdg.lbl.gov)[4] Griffiths, D. Introduction to elementary particles. New York : J. Wiley and Sons, Inc., 1987.[5] BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 96, 232001 (2006).[6] Perkins, Donald H. Introduction to high energy physics. Cambridge ; New York :Cambridge University Press, 2000.[7] The BABAR Physics Book. http://www.slac.stanford.edu/pubs/slacreports/slac-r-504.html[8] ROOT: An Object Oriented Data Analysis Framework. http://root.cern.ch/[9] Patrignani, Claudia. Study of hadronic transitions of Upsilon(nS) and search for Upsilon(nS) arrowrighteta Upsilon(1S).BABAR Analysis Document # 1784, Version 2. September 25, 2007.[10] Benayoun, M. et al. Spectroscopy at B-Factories Using Hard Photon Emission. InternationalJournal of Modern Physics A. arXiv:hep-ph/9910523v1 27 Oct 1999.29Appendix AComparison of SP1072 and SP3981This thesis uses Monte Carlo modenum SP3981 to model e+e- arrowright ?+?-gamma. Both SP1072 andSP3981 model this process. SP3981 is believed to be better at modelling the background muonprocess, but no one has actually studied their differences. This section compares the two andshows that SP3981 seems better at modelling the actual BABAR data.Figure A.1: On-peak comparison of muon angular distribution.Figure A.2: Off-peak comparison of muon angular distribution.The muon angular distributions in the Run3 data are compared to SP1072 and Run3 SP3981.30Appendix A. Comparison of SP1072 and SP3981Kolmogorov-Smirnov tests returns a score of 0 between data and SP1072 as well as betweendata and SP3981. This is possibly due to the small error bars resulting from high statistics.Figure A.1 is on-peak comparison and Figure A.2 is off-peak comparison. Both the MonteCarlo samples have muon angular distributions that are shaped like the data. However, SP3981appears to resemble data more closely. This is more obvious on-peak than off-peak. SP3981 canalso model the detector defiency more closely at costheta near ?0.55. Figure A.3 is a plot of thedifference between on-peak data and Monte Carlo samples. Figure A.4 is the corresponding plotfor off-peak data. The disagreements appear to be smaller for SP3981.This is a rather coarse study of the two Monte Carlo modes. More vigorous statistical com-parisons can be done to quantify how much better SP3981 is compared to SP1072.Figure A.3: On-peak differences of muon angular distribution between data and Monte Carlo.Figure A.4: Off-peak differences of muon angular distribution between data and Monte Carlo.31

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