Con - quark.hiroshima-u.ac.jp · con v oluted r.BW + radiativ e tail Breit-Wigner. The rst term and second is for! mesons. third term, Breit-Winger, is for mesons. The n um b er of!

Study of ! and � Produ tionvia Di-Ele tron De ay Channelin Proton+Proton Collisions at ps = 200 GeVKotaro M Kijima (M060291)Graduate S hool of S ien e, Hiroshima UniversityFebruary 28, 2008

1

Contents1 Introdu tion 81.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 101.1.1 CERN-SPS CERES/NA45 . . . . . . . . . . . . . . . . 101.1.2 CERN-SPS NA60 . . . . . . . . . . . . . . . . . . . . . 101.1.3 KEK-PS E325 . . . . . . . . . . . . . . . . . . . . . . . 112 Experimental Setup 152.1 RHIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 PHENIX Dete tor overview . . . . . . . . . . . . . . . . . . . 172.3 Beam Dete tors . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.1 Beam Beam Counters (BBC) . . . . . . . . . . . . . . 172.3.2 Zero Degree Counters (ZDC) . . . . . . . . . . . . . . 182.4 Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Central Arm Dete tors . . . . . . . . . . . . . . . . . . . . . . 192.5.1 Drift Chamber (DC) . . . . . . . . . . . . . . . . . . . 202.5.2 Pad Chamber (PC) . . . . . . . . . . . . . . . . . . . . 202.5.3 Ring Image Cherenkov Counters (RICH) . . . . . . . . 222.5.4 Ele tro Magneti Calorimeter (EMC) . . . . . . . . . . 222.6 Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.6.1 Overview of Data A quisition system (DAQ) . . . . . . 242.6.2 EMCal RICH level 1 Trigger . . . . . . . . . . . . . . . 273 Analysis 293.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Event Sele tion . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3 Tra k sele tion and ele tron identi� ation . . . . . . . . . . . 293.3.1 Tra k Quality . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Fidu ial ut . . . . . . . . . . . . . . . . . . . . . . . . 303.3.3 eID parameters . . . . . . . . . . . . . . . . . . . . . . 303.3.4 DC ghost tra k reje tion . . . . . . . . . . . . . . . . . 343.3.5 RICH ring sharing reje tion . . . . . . . . . . . . . . . 342

CONTENTS 33.4 Signal Extra tion . . . . . . . . . . . . . . . . . . . . . . . . . 373.4.1 Pair re onstru tion . . . . . . . . . . . . . . . . . . . . 373.4.2 ba kground subtra tion . . . . . . . . . . . . . . . . . . 373.4.3 Spe tral Shape of Resonan es . . . . . . . . . . . . . . 383.4.4 Radiative tail orre tion . . . . . . . . . . . . . . . . . 413.4.5 Signal Counting . . . . . . . . . . . . . . . . . . . . . . 423.5 EÆ ien y evaluation . . . . . . . . . . . . . . . . . . . . . . . 443.5.1 Geometri al A eptan e and Ele tron ID EÆ ien y . . 453.5.2 Trigger eÆ ien y . . . . . . . . . . . . . . . . . . . . . 453.5.3 bin shift orre tion . . . . . . . . . . . . . . . . . . . . 463.6 Systemati Errors . . . . . . . . . . . . . . . . . . . . . . . . . 503.6.1 Signal ounting . . . . . . . . . . . . . . . . . . . . . . 513.6.2 geometri al a eptan e al ulation . . . . . . . . . . . 523.6.3 ele tron ID eÆ ien y . . . . . . . . . . . . . . . . . . . 573.6.4 trigger eÆ ien y . . . . . . . . . . . . . . . . . . . . . 573.6.5 Bin shift orre tion . . . . . . . . . . . . . . . . . . . . 583.6.6 Total systemati error . . . . . . . . . . . . . . . . . . 594 Results and Dis ussion 604.1 Mass shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2 Invariant ross se tion . . . . . . . . . . . . . . . . . . . . . . 605 Con lusion 68

List of Figures1.1 Density and temperature dependen e of < �qq > [4℄ . . . . . . 101.2 The magnitude of the thermal u-quark ondensate as a fun tionof temperature, at zero baryon density [4℄. . . . . . . . . . . . 111.3 Mass of �; ! and � meson as a fun tion of density [6℄ . . . . . 121.4 Invariant e+e� mass spe trum ompared to the expe tationfrom hadroni de ay at the CERES/NA45 experiment [9℄ . . . 121.5 Ex ess mass spe tra of �+�� at the NA60 experiment. Theknown de ay �! e�e+ (solid line) and the level of un orre ted harm de ay (dashed line) are shown omparison. [10℄ . . . . . 131.6 Invariant mass spe tra of e+e� divided into � for the (a)Cand (b)Cu target at KEK-PS E325 experiment. The solid linesrepresent the �t result with an expe ted �! e+e� shape anda quadrati ba kground [12℄ . . . . . . . . . . . . . . . . . . . 141.7 Invariant mass spe tra of e+e� for the (a)C and (b)Cu targetat KEK-PS E325 experiment. The solid lines ate the �t result,whi h is the sum of the known hadroni de ays together withthe ombinatorial ba kground. [13℄ . . . . . . . . . . . . . . . 142.1 RHIC omplex . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 overview of The PHENIX Dete tor . . . . . . . . . . . . . . . 172.3 pi ture of the one element of Beam-Beam Counter . . . . . . 182.4 s hemati view of the ZDC lo ation in luding de e tion of pro-tons and harged fragments . . . . . . . . . . . . . . . . . . . 192.5 overview of the Magnet [27℄ . . . . . . . . . . . . . . . . . . . 202.6 The layout of wire position of DC. The X1 and X2 wire ellsruns in parallel to the beam to perform pre ise tra k measure-ments in r-�. U1, V1, U2, V2 wires have stereo angle of about6Æ relative to the X wires and measure the z oordination oftra k. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7 the pad and pixel geometry(left), A ell de�ned by three pixelsis at the enter of the right pi ture. . . . . . . . . . . . . . . 214

LIST OF FIGURES 52.8 A ut through view of RICH dete tor . . . . . . . . . . . . . . 222.9 Interior view of a lead-s intillator alorimeter module . . . . . 232.10 Exploded view of a lead-glass dete tor supermodule . . . . . . 242.11 The PHENIX Dete tor on�guration [27℄ . . . . . . . . . . . . 252.12 blo k diagram of DAQ [27℄ . . . . . . . . . . . . . . . . . . . . 272.13 s hemati view of EMCal RICH level1 Trigger: Both the super-Module of EMCal and RICH are �red for e+,e�. Only theEMCal is �red for photon, while only the RICH is �red forhigh pT pion. We are able to e�e tively olle t the eventsin luding e+e� pair. . . . . . . . . . . . . . . . . . . . . . . . 283.1 Collision vertex distribution measured by beam dete tor. Theevents in yellow band range are sele ted for this analysis. . . . 303.2 Ne � Np as fun tion as run number. The Green line is themean of Ne � Np, and blue line is its RMS. . . . . . . . . . . 313.3 Alpha versus bord distribution for both side of the DC eastand DC west. The left and right �gures show before and afterremoving the dead and unstable regions, respe tively. . . . . . 323.4 Hot and dead map. The blank area is removed in this analysis 333.5 distribution of number of �red PMT's on RICH . . . . . . . . 343.6 distribution of the displa ement between proje tion and re on-stru ted ring enter . . . . . . . . . . . . . . . . . . . . . . . . 343.7 distribution of E/p -1 normalized by its �. E means energydeposited into EMCal, and p means parti le momentum. . . . 353.8 distribution of tra k mat hing in � dire tion normalized by its � 353.9 distribution of tra k mat hing in z dire tion normalized by its � 353.10 GhostTra ks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.11 ring sharing tra ks. . . . . . . . . . . . . . . . . . . . . . . . . 363.12 s hemati of re onstru tion: the solid magenta and light bluelines show the re onstru tion pro ess in "same event" and"event mixing", respe tively. . . . . . . . . . . . . . . . . . . . 383.13 invariant e+e� mass spe trum. The blue line indi ate ombi-natorial ba kground evaluated by the event mixing method. . 393.14 Invariant mass spe tra divided by pT bins. The blue line indi- ate ombinatorial ba kground evaluated by the event mixingmethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.15 Diagrams for �nal state radiation [30℄. The de ay into e+e� is des ribed by (a). The infrared divergen e in the de ay is an eled by interferen e with the diagrams in (b). . . . . . . . 413.16 e+e� mass spe trum in the radiative de ay � ! e+e� forEmin = 10MeV(orange) smeared with 10MeV(red). . . . . . . 42

LIST OF FIGURES 63.17 Invariant mass spe tra divided by pT bins after ba kgroundsubtra tion. The bla k line are the �tting result, whi h is sumof the known de ays, ! (left magenta line), � (right magentaline), � (light blue line), radiative de ay of ! and � (blue line). 433.18 Demonstration of tra ks de ayed from 10 � mesons. The redline indi ate e+ or e�, blue dotted line indi ate photons andbla k line indi ate herenkov photon radiated in RICH. EM-Cal, PC and DC are drawn. . . . . . . . . . . . . . . . . . . . 443.19 Invariant mass spe trum of single ! for all pT . . . . . . . . . 453.20 Invariant mass spe trum of single � for all pT . . . . . . . . . 453.21 Comparison of DC phi distribution in the real data(red) andthe simulation(blue). The simulation phi distribution is weightedby appropriate ele tron pT distribution. The data is res aledsu h that the integral of the phi distribution in the real dataand in the simulation agree. The middle and the bottom panelshows the phi distribution in the South side(zed<0)and theNorth side(zed>0), respe tively. The top panel shows the phidistribution for North and South side. The pT range of theele tron is 0.3<pT<4.0 GeV/ for borht of the real data andsimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.22 Total re onstru tion eÆ ien y of !(blue) and �(red) in ludinga eptan e is shown as a fun tion of pT . . . . . . . . . . . . . 483.23 ERT Ele tron trigger eÆ ien y for single ele tron is shown asa fun tion of momentum. . . . . . . . . . . . . . . . . . . . . . 493.24 ERT Ele tron trigger eÆ ien y for !(blue) and �(red) areshown as a fun tion of pT . . . . . . . . . . . . . . . . . . . . . 503.25 Invariant mass spe trum divided by pT . Ba kground shape wasestimated as exponential(blue). The bla k line are the �ttingresult, whi h is sum of the ba kground and known de ays, !(left magenta line), � (right magenta line), � (light blue line),radiative de ay of ! and � (Orange line) . . . . . . . . . . . . 533.26 Invariant mass spe trum divided by pT . Ba kground shapewas estimated as power law fun tion(blue). The bla k line arethe �tting result, whi h is sum of the ba kground and knownde ays, ! (left magenta line), � (right magenta line), � (lightblue line), radiative de ay of ! and � (Orange line) . . . . . . 543.27 phi distribution for the real data(red) and the simulation(blue).Simulation data is normalized in -0.6<�<-0.2 . . . . . . . . . 553.28 phi distribution for the real data(red) and the simulation(blue).Simulation data is normalized in 0.7<�<0.85 . . . . . . . . . . 55

LIST OF FIGURES 73.29 phi distribution for the real data(red) and the simulation(blue).Simulation data is normalized in 2.3<�<2.45 . . . . . . . . . . 563.30 phi distribution for the real data(red) and the simulation(blue).Simulation data is normalized in 2.5<�<2.9 . . . . . . . . . . 563.31 single ele tron ERT trigger eÆ ien y of a se tor0. the red dashline shows ase1 and the blue dash line shows ase2. . . . . . . 574.1 position of mass enter of ! as a fun tion of pT . The error isonly statisti al error. The PDG value [29℄ of mass enter of !is des ribed in this �gure as m, and � means total de ay widthof ! (See table 3.2). . . . . . . . . . . . . . . . . . . . . . . . 624.2 mass enter of � as a fun tion of pT . The error is only statisti alerror. The PDG value [29℄ of mass enter of � is des ribed inthis �gure as m, and � means total de ay width of � (See table3.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.3 mass enter of ! as a fun tion of pT . The blue points areobtained by �tting result for real data analysis. the orange linesindi ate 1� of dete tor mass resolution obtained by simulation. 644.4 mass enter of � as a fun tion of pT . The blue points areobtained by �tting result for real data analysis. the orange linesindi ate 1� of dete tor mass resolution obtained by simulation. 654.5 Invariant ross se tion for ! as a fun tion of pT . The red pointis our result, ! ! e+e�. The blue and light blue points indi ate! ! �0�+��, ! ! �0 , respe tively. The bra ket and grayband indi ate systemati error. . . . . . . . . . . . . . . . . . 664.6 Invariant ross se tion for � as a fun tion of pT . The redpoint is our result, � ! e+e�. The green points indi ate� ! K+K�. The bra ket and gray band indi ate systemati error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Chapter 1Introdu tionThe all matters onstru ting "our world" onsist of elementary parti le, quarksand leptons. For instan e, the Hydrogen atom is omposed of an ele tronand a proton. Where the ele tron is a point parti le whi h is lassi�ed intolepton, the proton is known to be a omposite parti le onsisting of threequarks, whi h are held together by gluons. The state of the nu lear matteris des ribed by the Quantum Chromo-Dynami s(QCD).Mass [MeV= 2℄quark Bare Quark Const. Quarkdown 3 - 6 � 300up 1.5 - 5 � 300strange 60 - 170 � 450 harm 1100 - 1400bottom 4100 - 4400top 168 � 103 - 179 � 103Table 1.1: mass of the quarks:Listed are the mass of "bare" quarks( urrentquark) whi h would be measured in the limit Q2 !1 as well as the mass of onstituent quarks, i.e., the e�e tive mass of quarks bound in hadrons. [2℄The most of light hadron masses are generated due to the spontaneousbreaking of the hiral symmetry. Due to the e�e t of hiral symmetry restora-tion, the mass of the hadron, espe ially light ve tor mesons(�, !, � ), maybe shifted and/or modi�ed in the hot matter reated by the heavy ion olli-sions. The study of mass modi� ation is an important topi to understandthe me hanism of generation of hadron mass.8

CHAPTER 1. INTRODUCTION 9Latti e QCD simulations indi ate a tenden y towards hiral restorationat temperatures T �150-200 MeV [3℄. The density dependen e in addition totemperature dependen e of the hiral symmetry was al ulated. Figure 1.1shows the s hemati behavior of the < �qq >, whi h is the order parameterof the symmetry, al ulated with the Nambu and Jona-Lasinio (NJL) model[4℄. A ording to the al ulation, the < �qq > shows the sudden drop at the riti al temperature as expe ted by latti e al ulation (See Figure 1.2). Onthe other hand, the < �qq > de reases linearly to the density and the hiralsymmetry will restore even at the normal nu lear density.Hatsuda and Lee al ulated the density dependen e of the mass of theve tor mesons based on QCD sum rules to rea h the on lusion that the massshift is approximately linear to the density in 0 < � < 2�0, and signi� antlyde ease for �, ! and � at normal density shown in Figure 1.3.Therefore, low-mass ve tor mesons are onsidered the most sensitive probeof hiral symmetry restoration. Over the past few de ades, a onsiderablenumber of studies have been ondu ted on mass shift and/or modi� ation.In the next se tion, we are going to introdu e the interesting results reportedfrom CERES/NA45, NA60 and KEK-PS E325.The Relativisti Heavy Ion Collider (RHIC) is onstru ted at BrookhavenNational Laboratory (BNL) to provide ollisions of heavy ion at the enterof mass energy (psNN) up to 200GeV and proton at the enter of massenergy (ps) up to 500GeV. The Pioneering High Energy Nu lear Intera tioneXperiment (PHENIX) is one of four experiments in RHIC and spe ializedexperiment for measurement of lepton and photon. The one of the main goalin the PHENIX experiment is to observe the mass shift or modi� ation of lowmass ve tor mesons (�, !, �) in high temperature system reated by heavyion ollisions due to the Chiral Symmetry Restoration, in omparison withthe result on normal density su h as KEK-PS E325 experimentThe study of the light ve tor mesons in proton+proton ollisions is animportant baseline for the various heavy ions ollisions su h as Au+Au,Cu+Cu and d+Au. We, The PHENIX ollaboration, re orded the data inproton+proton ollisions at ps = 200GeV during the year 2005.The purpose of this work is to �nd out whether mass shift are observed ornot in proton+proton ollisions and to provide referen e data for baseline ofheavy ion ollisons. To study !/� meson produ tion, their di-ele tron de ay hannel was used. Unlike hadrons, ele trons do not intera t strongly with themedium. The measurement of ele tron pairs from ve tor meson is thereforea good probe to study hiral symmetry restoration sin e ele trons arry theoriginal information.In Chapter 2, we will introdu e the setup of the PHENIX experiment. In

CHAPTER 1. INTRODUCTION 10Chapter 3, we will des ribe the detailed pro edure of this work. In Chapter4, the result of this work are shown and dis ussed about it. Chapter 5, wewill on lude this work.

Figure 1.1: Density and temperature dependen e of < �qq > [4℄1.1 Experimental results1.1.1 CERN-SPS CERES/NA45The CERES/NA45 experiment [8℄ measured e+e� pair produ tion in entralPb-Au ollision 158A GeV at CERN-SPS. A signi� ant ex ess of the e+e�pair yield over the expe tation from hadron de ay was observed. The date learly favor a substantial in-medium broadening of the � mesons spe tralfun tion over a density-dependent shift of the � pole mass at SPS energy [9℄.1.1.2 CERN-SPS NA60The NA60 experiment measured low mass muon pair in 158AGeV Indium+Indium ollisions at the CERN-SPS. a peaked stru ture is seen in all ases, broad-ening strongly with entrality, but remaining essentially entered around theposition of the nominal � pole. At the same time, the total yield in reases rel-ative to the o ktail �, their ratio rea hing values above 4 for M<0.9 GeV/ 2in the most entral bin [10℄. Su h values are onsistent with the results foundby CERES/NA45.

CHAPTER 1. INTRODUCTION 11

temperature T [MeV]Figure 1.2: The magnitude of the thermal u-quark ondensate as a fun tionof temperature, at zero baryon density [4℄.1.1.3 KEK-PS E325The KEK-PS E325 experiment [11℄ was ondu ted at the KEK 12-GeVProton-Syn hrotron, in order to sear h for in-medium mass modi� ation ofve tor mesons in the rea tion 12GeV proton + A ! �, !, � + X ! e+e�+ X 0. The data obtained with a opper target revealed a signi� ant ex- ess on the low-mass side of the � meson peak in the � � < 1.25 region(See Fig.1.6), Added to this, also the ex ess on the low-mass side of the !peak(See Fig.1.7) due to the spe tral shape modi� ation of �, ! and �mesons,respe tively[12℄[13℄.

CHAPTER 1. INTRODUCTION 12M /M

*

ρ/ρ0

ρ,ω meson

φ meson

Figure 1.3: Mass of �; ! and � meson as a fun tion of density [6℄

Figure 1.4: Invariant e+e� mass spe trum ompared to the expe tation fromhadroni de ay at the CERES/NA45 experiment [9℄


Figure 1.5: Ex ess mass spe tra of �+�� at the NA60 experiment. The knownde ay �! e�e+ (solid line) and the level of un orre ted harm de ay (dashedline) are shown omparison. [10℄


Figure 1.6: Invariant mass spe tra ofe+e� divided into � for the (a)C and(b)Cu target at KEK-PS E325 exper-iment. The solid lines represent the�t result with an expe ted �! e+e�shape and a quadrati ba kground[12℄Figure 1.7: Invariant mass spe tra ofe+e� for the (a)C and (b)Cu targetat KEK-PS E325 experiment. Thesolid lines ate the �t result, whi h isthe sum of the known hadroni de- ays together with the ombinatorialba kground. [13℄

Chapter 2Experimental SetupThe RHIC omplex and PHENIX dete tor are overviewed in this hapter.The des ription of the RHIC omplex is des ribed in Se tion 2.1, and thePHENIX dete ors is des ribed in Se tion 2.2.2.1 RHICThe Relativisti Heavy Ion Collider (RHIC) [14℄ at Brookhaven National Lab-oratory (BNL) in the United State was built to study the nu lear physi s. Themaximum energy at RHIC for heavy ion is 100GeV per un leon and that forproton is 250GeV. The heavy ion and proton produ ed at the sour e are trans-ported through a Tandem Van de Graa� and proton lina , respe tively, anda elerate at Booster Syn hrotron and the Alternating Gradient Syn hrotron(AGS), after that, inje ted to RHIC. The RHIC ring has a ir umferen e of3.8km with the maximum bun h of 120 and the designed luminosity is 2 �1026 m�2 s�2 for Au ion and 2 � 1032 m�2 s�2 for proton. The RHIC onsists of two quasi- ir ular on entri rings, one("Blue Ring") for lo k-wise and the other("Yellow Ring) for ounter- lo kwise. The rings ross atsix intera tion points. Four experiments, PHENIX, STAR, BRAHMS andPHOBS are build in ea h one of six intera tion points.The PHENIX, the Pioneering High Energy Nu lear Intera tion eXperi-ment [15℄, is one of four experiments and spe ialized experiment for measure-ment of lepton and photon. In this analysis, the data olle ted by PHENIXwas used. The Dete tor design is des ribed in the next subse tion.15

CHAPTER 2. EXPERIMENTAL SETUP 16

PHENIX

PHOBOS BRAHMS

STAR

Figure 2.1: RHIC omplex


Figure 2.2: overview of The PHENIX Dete tor2.2 PHENIX Dete tor overviewThe PHENIX dete tor onsists of 2 entral arms [20℄ [21℄ [23℄ whi h haspseudo-rapidity overage of � 3.5 and 180Æ azimuthal angle in total, 2 muonarms [24℄ whi h has pseudo-rapidity overage of � (1.2-2.4), and beam dete -tors [16℄ whi h is near the beam pipe.2.3 Beam Dete torsThe main purpose of inner dete tors is make triggers and to measure theluminosity and entrality in heavy ion ollisions. In this se tion, mainly BBCand ZDC are dis ribed.2.3.1 Beam Beam Counters (BBC)Beam Beam Counters(BBC) [17℄ are lo ated on North and South side at144.35 m along beam pipe from the ollision point and overs the pseude-rapidity from 3.0 to 3.9. Ea h of them onsists of 64 elements, whi h ea h ofthem is quartz Cherenkov ounter. BBC have four major tasks, to trigger theMinimum Bias events, to measure the ollision vertex, to obtain the ollisiontime and determine entrality. In addition, the rea tion plain is determined

CHAPTER 2. EXPERIMENTAL SETUP 18by hit pattern of BBC. The ollision vertex and time are determined by thedi�eren e and average time to north and South ounters; ollision vertex = (TS � TN )2 � (2.1) ollision time = TS + TN � (2� L)= 2 (2.2)where TN and TS are the averaged hit time of in oming parti les, is thelight velosity and L is the distan e from z = 0 to both BBCs, L = 144.35 m.

Figure 2.3: pi ture of the one element of Beam-Beam Counter2.3.2 Zero Degree Counters (ZDC)Zero Degree Calorimeters(ZDC) [18℄ are hadron alorimeter lo ated at 18mNorth and South side along beam pipe from the ollision point. Sin e the bothnorth and south ZDC sit at just the upstream of the last bending magnet onthe RHIC ring, most of harged parti les are swept out from the a eptan e.So, ZDC works as the minimum bias trigger ounter and monitor the beamluminosity sin e ZDC measured neutrons from spe tator part of heavy ion ollision.


Beam - Axis [m]

[cm

]

Figure 2.4: s hemati view of the ZDC lo ation in luding de e tion of protonsand harged fragments2.4 MagnetThe PHENIX has three magnet systems [19℄, one is the entral magnet, othersare north and south muon magnets. The entral magnet provide a magneti �eld around the ollision point whi h is parallel to the beam. And the Centralmagnet onsist of inner and outer oil, whi h an be optimized separately,together, or in opposition. During the run for this work, both inner andouter magnets are energized and integrated magneti �eld is 1.15 T �m. themomentum of harged parti les an be obtained by measuring the urvatureof the tra k whi h is bended due to magneti �eld.2.5 Central Arm Dete torsThe entral arm dete tors an measure harged hadron, ele tron and pho-ton, and onsists of three parts : the tra king system , parti le identi� a-tion system and ele tro magneti alorimeter. The Drift Chamber(DC) andPad Chamber(PC) form the tra king unit and measures the momentum of harged parti les from ollisions. The Ring-Imaging Cherenkov(RICH) andthe Time-of-Fight(ToF) provide identi� ation of harged parti les. Addition-ally, Ele tro Magneti Calorimeter(EMCal) is used to measure the spatialposition and energy of ele trons and photons.


2.02.00.00.0 4.04.0 Z (m)Z (m)-2.0-2.0-4.0-4.0

PH ENIX

Magnetic field lines for the two Central Magnet coils in combined (++) modeMagnetic field lines for the two Central Magnet coils in combined (++) modeFigure 2.5: overview of the Magnet [27℄2.5.1 Drift Chamber (DC)The Drift Chambers(DC) are ylindri ally shaped and lo ated in the regionfrom 2 to 2.4 m from the beam axis and 2 m along the beam axis. This pla esthem in a residual magnet �eld with a maximum of 0.6 kG. Fig.2.11 is shownposition of DCs relative to the other dete tors. Ea h DC measures hargedparti le traje tories to determine transverse momentum of ea h parti les. TheDC also parti ipates in the pattern re ognition at high parti le tra k densitiesby providing position information that is used to link tra ks thought thevarious PHENIX dete tors.2.5.2 Pad Chamber (PC)The PHENIX Pad Chambers(PC) are multiwire proportional hambers thatform three separate layers. Ea h dete tors onsists of a single plane of wireinside a gas volume bounded by two athode plane. One athode is �nelysegmented int an array of pixels. The harge indu ed on a number of pixelswhen a harged parti le starts an avalan he on an anode wire, is read outthorough spe ially designed read out ele troni s. The PC system determinesspa e points along the straight line parti le traje tories outside the magneti

CHAPTER 2. EXPERIMENTAL SETUP 21�eld. Fig.2.11 shows position of PCs relative to the other dete tors. Theinnermost pad hamber alled PC1 is essential for determining the three-dimensional momentum ve tor by providing the z oordinate at the exit ofthe DC.

Figure 2.6: The layout of wire position of DC. The X1 and X2 wire ells runsin parallel to the beam to perform pre ise tra k measurements in r-�. U1,V1, U2, V2 wires have stereo angle of about 6Æ relative to the X wires andmeasure the z oordination of tra k.

Figure 2.7: the pad and pixel geometry(left), A ell de�ned by three pixels isat the enter of the right pi ture.

CHAPTER 2. EXPERIMENTAL SETUP 222.5.3 Ring Image Cherenkov Counters (RICH)The Ring Image Cherenkov Counters(RICH) [22℄ is o upies the radial regionbetween 2.575 and 4.1 m from the beam line. Ea h of the dete tors in theeast and west entral arms has a volume of 40 m2. the minimum thi kness ofthe radiator gas, whi h is CO2, is 87 m, the maximum is about 150 m. TheRICH is provides e/� dis rimination below the � Cherenkov threshold, whi his set at 4.65 GeV/ . The Cherenkov photon produ ed in the radiator gasare re e ted on the mirror and are dete ted by the photon multiplier tubes(PMTs). The average size of the Cherenkov ring is 8 m and average numberof the Cherenkov photon produ ed by ele tron is 10.8 on the plane where thePMTs are sitting. Fig.ri h show the ut through view of RICH dete tor.

Figure 2.8: A ut through view of RICH dete tor2.5.4 Ele tro Magneti Calorimeter (EMC)The Ele tro Magneti Calorimeter (EMCal) is designed primarily to measurethe energies and spatial position of photon and ele trons. It also plays a majorrole of in parti le identi� ation and is an important part of the PHENIXtrigger system. The EMCal system an trigger on rare events with hightransverse momentum photons and ele trons. The EMCal system onsists of atotal of 24768 individual dete tor modules divided between the Pb-S intillator

CHAPTER 2. EXPERIMENTAL SETUP 23 alorimeter (PbS ), whi h provides 6 se tors of entral arm and the Pb-Glass alorimeter (PbGl) omprised of 2 se tors.The PbS is a sampling alorimeter made of alternating tile of Pb ands intillator onsisting of 15552 individual towers and overing an area of ap-proximately 48 m2. The basi blo k is a module onsisting of 4 towers, whi hare opti ally isolated, and are read out individually. The tower has 5.52 �5.25 m2 ross se tion and 3.75 m in length. Figure 2.9 show the interiorview of the module. A super-module is omposed of 12 � 12 towers and ase tor is omposed of 18(12�12) super-modules.The PbGl is a Cherenkov type alorimeter. A lead glass has 4.0 � 4.0 m2 ross se tion and 40 m length. Figure 2.10 shows the interior viewof one super-module, omposed by 4 � 6 towers. A se tor is omposed of192(12�12) super-modules.

Figure 2.9: Interior view of a lead-s intillator alorimeter module


Figure 2.10: Exploded view of a lead-glass dete tor supermodule2.6 Computing2.6.1 Overview of Data A quisition system (DAQ)PHENIX is designed to make measurements on a variety of ollision systemfrom p+p to Au+Au. The o upan y in the dete tor varies from a few tra ksin p+p intera tion to approximately 10% of all dete tor hannels in entralAu+Au intera tions. The intera tion rate at design luminosity varies from afew kHz for Au+Au entral ollisions to approximately 500 kHz for minimumbias p+p ollisions. The PHENIX DAQ system was designed to seamlesslya ommodate improvements in the design luminosity. This was a omplishedthrough the pipelined and deadtimeless features to the dete tor front ends andthe ability to a ommodate higher-level triggers.In PHENIX it is ne essary to measure low-mass lepton pair and low pTparti les in a high-ba kground environment. In order to preserve the highintera tion-rate apability of PHENIX a exible system that permits taggingof events was onstru ted. The On-Line system has two levels of triggeringdenoted of LVL1 and LVL2. The LVL1 trigger is fully pipelined, thereforethe On-Line system is free of deadtime through LVL1. Bu�ering is providedthat is suÆ ient to handle u tuations in the event rate so that deadtimeis redu ed to less than 5% for full RHIC luminosity. The LVL1 trigger andlower levels of the readout are lo k-driven by bun h- rossing signals from


West

South Side View

Beam View

PHENIX Detector

North

East

MuTr

MuID MuIDMVD

MVD

PbSc PbSc

PbSc PbSc

PbSc PbGl

PbSc PbGl

TOF

PC1 PC1

PC3

aerogel

PC2

Central Magnet

CentralMagnet

North M

uon MagnetSouth Muon Magnet

TECPC3

BB

BBRICH RICH

DC DC

ZDC NorthZDC South

Figure 2.11: The PHENIX Dete tor on�guration [27℄

CHAPTER 2. EXPERIMENTAL SETUP 26the 9.4 MHz RHIC lo k. The higher levels of readout and the LVL2 triggerare data-driven where the results of triggering and data pro essing propagateto the next higher level only after pro essing of a given event is ompleted.The general s hemati for the PHENIX On-Line system is shown in Fig.2.12. Signals from the various PHENIX subsystems are pro essed by FrontEnd Ele troni s (FEE) that onvert dete tor signals into digital event frag-ments. This involves analog signal pro essing with ampli� ation and shapingto extra t the optimum time and/or amplitude information, development oftrigger input data and bu�ering to allow time for data pro essing by the LVL1trigger and digitization. This is arried out for all dete tor elements at everybeam rossing syn hronously with the RHIC beam lo k. The timing signalis a harmoni of the RHIC beam lo k and is distributed to the FEM's bythe PHENIX Master Timing System (MTS). The LVL1 trigger provides afast �lter for dis arding empty beam rossings and uninteresting events be-fore the data is fully digitized. It operates in a syn hronous pipelined mode,generates a de ision every 106 ns and has an adjustable laten y of some 40beam rossings.On e an event is a epted the data fragments from the FEM's and primi-tives from the LVL1 trigger move in parallel to the Data Colle tion Modules(DCM). The PHENIX ar hite ture was designed so that all dete tor-spe i� ele troni s end with the FEM's, so that there is a single set of DCM's that ommuni ate with the rest of the DAQ system. The only onne tion betweenthe Intera tion Region (IR) where the FEM's are lo ated and the CountingHouse (CH) where the DCM's are lo ated is by �ber-opti able. The DCM'sperform zero suppression, error he king and data reformating. Many paral-lel data streams from the DCM's are sent to the Event Builder (EvB). TheEvB performs the �nal stage of event assembly and provides an environmentfor the LVL2 trigger to operate. In order to study the rare events for whi hPHENIX was designed, it is ne essary to further redu e the number of a - epted events by at least a fa tor of six. This sele tion is arried out by theLVL2 triggers while the events are being assembled in the Assembly and Trig-ger Pro essors (ATP) in the EvB. The EvB then sends the a epted eventsto the PHENIX On-line Control System (ONCS) for logging and monitor-ing. The logged data, whi h is named as PHENIX Raw Data File(PRDF),are send to RHIC Computing Fa ility(RCF) for sinking on the tape in HighPerforman e Storage System(HPSS). The data in the HPSS are analyzed and onverted into an intermediated data format in the linux omputer at RCFand Computing Center in Japan(CCJ).

CHAPTER 2. EXPERIMENTAL SETUP 27RHIC clocks

20MB/s

250TB/yr

~350000 ch

ATM Switch

MTM

SEB

DCMFEM

Linux Farm

~600 CPU's

Online

Monitoring

ZD

C S

outh

ZD

C N

orth

A S

ubsyst

em

(e.g

. Eas

t DC

)

Data packets

over fiber

Clock, Trigger,

Mode bits

over fiber

Sh

ield W

all

a few

miles la

ter

DCB

PartitionerData Packets

Dat

a Pac

kets

over

NEV

IS T

oken

passing

Bus

over Parallel

FIFO Interface

GTM

GL1

L1

Bu

sy

Bu

sy

Trigger

tape

storage

1.2PB

Clock

Interaction regionCountingroom

RHIC

Computing

Facility

GL1 Global Level 1 Trigger

GTM Granual Timing Module

MTM Master Timing Module

DCB Data Collection Board

DCM Data Collection Module

FEM Front End Module

SEB Sub Event Buffer

ATP Assembly Trigger Processor

Missing:

• ARCNET Serial Interface to FEMs

• High and Low Voltage Control and

associated control systems

• Alarm system

'trigger' is a placeholder

for a much more complex

'Local Level 1' trigger system

SEBSEBSEB

ATP

End

User

Figure 2.12: blo k diagram of DAQ [27℄2.6.2 EMCal RICH level 1 Triggerthe PHENIX has had two kinds of the Level 1 trigger. One is minimumbias trigger whi h is require at least one hit on the north and south BBCs.The other is the EMC al RHIC level 1 trigger(ERT) designed to enhan ethe ele tron, positron, pair of ele tron and positron pair, high pT hargedparti les, and �0. The ERT is ru ial for measurement of e+e� pair due to therare events in luding e+e� pairs. For enhan ement of the e+e� pair sampledevents, the information of RICH and EMCal is used. For this analysis, theERT requires RICH oin iden e with EMCal. The ERT trigger threshold of400MeV is required for EMCal to dis riminate high pT harged pion sin ethe harged pion only deposit the minimum ionized energy into EMCal. Thes hemati view of ERT is shown Figure 2.13.


π

e

γ

collison vertex

EMCal

RICH

±

±

Figure 2.13: s hemati view of EMCal RICH level1 Trigger: Both the super-Module of EMCal and RICH are �red for e+,e�. Only the EMCal is �redfor photon, while only the RICH is �red for high pT pion. We are able toe�e tively olle t the events in luding e+e� pair.

Chapter 3Analysis3.1 Data Setthe PHENIX olle ted the date at proton + proton ollisions in year 2005.The Run number in proton + proton ollisions is from 166030 to 179846. Inthis analysis, we used 16,587 nDST(Data Summary Tape) �les were madefrom PRDF. The total data size of the nDST is approximately 410 GBite.3.2 Event Sele tionThe ele tron yield, whi h is de�ned in Eq.3.1 , for ea h run number is he ked.Ne �Np = Ne=Nevt �Np=Nevt (3.1)where Ne,Np and Nevt in right term are the number of ele trons, the num-ber of positrons and the number of MinBias events, respe tively. Figure.3.2shows Ne � Np as fun tion of run number. The ele tron yield drops after run178937 sin e two of RICH data pa kets were disable after this run.The analysis is restri ted to events with ollision vertex ful�lling jbb zj< 25 m, where bb z is the vertex position found by the BBC. The ollisionvertex distribution is shown Figure 3.1. After these run sele tion and global ut, 56.39 M minimum bias sampled events are used in this analysis.3.3 Tra k sele tion and ele tron identi� ation3.3.1 Tra k QualityThe following tra k quality sele tion is applied:29

CHAPTER 3. ANALYSIS 30

collision vertex [cm] -50 -40 -30 -20 -10 0 10 20 30 40 50

Nu

mb

er

of

even

ts

0

2

4

6

8

10

12

14

610×

Collision vertex

Figure 3.1: Collision vertex distribution measured by beam dete tor. Theevents in yellow band range are sele ted for this analysis.� quality bits = 31 [ 63the value of 31 means the tra ks are required the hit of X1,X2 wire and uniquehit of UV wire, in addition, hit of PC1. the ase of 63, tra ks are additionallyrequired the unique hit of PC1.3.3.2 Fidu ial utTo redu e the systemati un ertainly for the a eptan e, dead and unstableareas of DC and EMCal are removed [35℄. Figure 3.3 shows the areas removeddue to dead and unstable of DC. Figure 3.4 shows the areas removed due todead and warm for se tor-by-se tor of EMCal. In addition that, dead areasof PC1 are removed.3.3.3 eID parametersEle trons are identi�ed with RICH and EMCal. The variables whi h are usedfor ele tron identi� ation are summarized in Table 3.1. In this analysis, thefollowing uts are applied:� number of �red PMT's shown as Fig.3.5: n0 > 2� tra k mat hing to RICH shown as Fig.3.6: disp < 5 m� energy-momentum mat hing shown as Fig.3.7: jdepj < 3�


run number168 170 172 174 176 178 180

310×

>+

x N

e-

<N

e

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4-6

10×run by run efficiency

Figure 3.2: Ne � Np as fun tion as run number. The Green line is the meanof Ne � Np, and blue line is its RMS.� tra k mat hing to EMCal shown as Fig.3.8, 3.9: pem sdphi2 + em sdz2< 4 �


Figure 3.3: Alpha versus bord distribution for both side of the DC east andDC west. The left and right �gures show before and after removing the deadand unstable regions, respe tively.


zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

zsect0 10 20 30 40 50 60 70 80 90

ys

ec

t

0

5

10

15

20

25

30

35

40

45

EMC sect0

Figure 3.4: Hot and dead map. The blank area is removed in this analysis

CHAPTER 3. ANALYSIS 34variable des riptionn0 number of �red PMT's in nominal ring radiusdisp displa ement between the proje tion point onto RICH PMT planeand the ring enter re onstru ted from the �red PMT'se ore energy dete ted at EMCal (summed up for 3 towers)mom transverse momentum by DCem sdphi tra k mat hing in phi dire tion at EMCal surfa e normalized by �em sdz tra k mat hing in z dire tion at EMCal surfa e normalized by �dep e ore/mom �1 normalized by �(mom)Table 3.1: eID parameters list

n02 4 6 8 10 12 14

co

un

t

0

10000

20000

30000

40000

50000

60000

n0

Figure 3.5: distribution of number of�red PMT's on RICHdisp [cm]

0 2 4 6 8 10 12 14

co

un

t

0

1000

2000

3000

4000

5000

6000

7000

disp

Figure 3.6: distribution of the dis-pla ement between proje tion and re- onstru ted ring enter3.3.4 DC ghost tra k reje tionGhost tra ks in the DC are reje ted as follows. If any two tra ks ful�lljDC1zed � DC2zedj < 0.5 m and jDC1phi � DC2phij < 0.02 rad, the one withworse EMCal mat hing is reje ted, as it is likely to be a ghost tra k.3.3.5 RICH ring sharing reje tionTwo tra ks share the same RICH ring when they are parallel to ea h otherwhile passing through the RICH gas. In this ase, one of them is possibly amisidenti�ed hadron. The RICH ghosting phenomenon de reased purity ofele tron and also made orrelation in the invariant mass spe trum around 0.5GeV/ 2. So that su h tra ks need to be reje ted. Fig.3.11 shows orrelation


}σdep [-15 -10 -5 0 5 10

co

un

t

0

10000

20000

30000

40000

50000

60000

70000

80000

dep

Figure 3.7: distribution of E/p -1 normalized by its �. E means energydeposited into EMCal, and p means parti le momentum.]σemcsdphi [

-4 -2 0 2 40

5000

10000

15000

20000

25000

30000

directionφEMCal matching

Figure 3.8: distribution of tra kmat hing in � dire tion normalizedby its �]σemcsdz [

-4 -2 0 2 40

5000

10000

15000

20000

25000

EMCal matching z direction

Figure 3.9: distribution of tra kmat hing in z dire tion normalizedby its �between PFOA and dCROSS. If any two tra ks ful�ll jdCROSSj < 3 � andPFOA < 0.25 rad, both of the tra ks are reje ted. PFOA(Post-Field OpeningAngle) is the angle between two tra k ve tor after they have been de e tedby the PHENIX magnet. dCROSS is de�ned following.dCROSS � q(jRICH1z � RICH2z j=9:55)2 + (jRICH1phi � RICH2phij=0:023)2


Dzed [cm]δ-3 -2 -1 0 1 2 3

DP

hi [r

ad

]δ

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1

10

210

Dzed:Dphi

Figure 3.10: GhostTra ks

}2

+ (cross_phi/0.023)2

sqrt{(cross_dz/9.55)0 2 4 6 8 10 12 14

PF

OA

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

20

40

60

80

100

120

140

160

180

200

dCROSS:PFOA

Figure 3.11: ring sharing tra ks.

CHAPTER 3. ANALYSIS 373.4 Signal Extra tion3.4.1 Pair re onstru tionThe invariant mass Mee is written as,Mee = q(Ee+ + Ee�)2 � ( ~pe+ + ~pe�)2 (3.2)where E is the energy of the parti le, ~p is parti le momentum,(Ee+ + Ee�)2 = (qm2e+ + p2e+ +qm2e� + p2e�)2 (3.3)and, ( ~pe+ + ~pe�)2 = (pe+x + pe�x)2 + (pe+y + pe�y)2 + (pe+z + pe�z)2: (3.4)px, py, pz is written as following,px = p� sin � os�py = p� sin � sin�pz = p� os �where � is the poler angle measured from the beam axis and � is the azimuthalangle.The invariant mass spe trum were derived by ombination all identi�ede+e� pairs. The re onstru ted invariant mass spe trum is divided 6 pT bins,su h as 0<pT<0.5, 0.5<pT<1.0, 1.0<pT<1.5, 1.5<pT<2.0, 2.0<pT<3.0,3.0<pT<4.0.3.4.2 ba kground subtra tionInvariant mass of any e+e� pairs in ea h event was al ulated. Then, toevaluate the mass shape and the number of ! and �, it is ne essary to subtra tthe ba kground from invariant mass spe trum. The sour e of the ba kgroundis listed as following.� Un orrelated e+e� pairs. ( ombinatorial ba kground)� Corre ted e+e� pair from D �D, B �B and Drell-Yan produ tion. ( ontin-uum yield)In this analysis, the ba kground from ontinuum yield are ignored sin ethe main sour e of the ba kground on the mass region of ! and � is from

CHAPTER 3. ANALYSIS 38 ombinatorial ba kground. Event mixing te hnique is used to subtra t the ombinatorial ba kground. Figure 3.12 shows a s hemati view of the eventmixing te hnique. The un orrelated e�e+ pairs are produ ed by using thee� (e+) in urrent event and the e+ (e�) in other events. Figure 3.13 showthe invariant mass spe trum with ombinatorial ba kground evaluated byevent mixing te hnique. The mass spe tra divided into pT bins are shown inFig.3.14 .φ

ω

n th event

n+1 th event

n+2 th event

-

-

-

e+e-

e+ e+ e-

e+ e- e- e-

Figure 3.12: s hemati of re onstru tion: the solid magenta and light bluelines show the re onstru tion pro ess in "same event" and "event mixing",respe tively.3.4.3 Spe tral Shape of Resonan esSpe tral shape of resonan es were generated using the relativisti Breit-Wingerdistribution [28℄ rBR(m) = m2�tot(m)�ee(m)(m2 �m20)2 +m02�tot(m)2 (3.5)with the pole mass, m0, total de ay width, �tot(m) and the energy dependentpartial de ay width of the ve tor meson going to e+e�, �ee(m).


]2invariant mass [GeV/c

0 0.5 1 1.5 2 2.5 3 3.5 4

co

un

t

1

10

210

310

410

invariant mass

Figure 3.13: invariant e+e� mass spe trum. The blue line indi ate ombina-torial ba kground evaluated by the event mixing method.�tot(m) and �ee(m) an be parametrized as�tot(m) = mm0�tot (3.6)�ee(m) = m30m3�ee (3.7)(3.8)where �tot is the natural de ay width, �ee is the partial width of the ve tormeson de aying into e+e�. The values of the natural de ay widths and polemasses of ve tor masons are shown in table 3.2mass [MeV= 2℄ �tot [MeV= 2℄ �ee=�tot� 771.1 149.2 0:454� 10�4! 782.57 8.44 0:695� 10�4� 1019.456 4.26 2:96� 10�4Table 3.2: The pole masses and natural de ay widths of the ve tor mesonstaken from the PDG [29℄


]2invariant mass [GeV/c0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

co

un

t

0

10

20

30

40

50

60

70

h_n_ivmass_ERT_1_fcut2_pT0


co

un

t

0

20

40

60

80

100

120

h_n_invmass_ERT_1_fcut2_pT1


co

un

t

0

10

20

30

40

50

60



co

un

t

0

5

10

15

20

25



co

un

t

0

2

4

6

8

10

12

14

16



co

un

t

0

1

2

3

4

5

6

7

8


0 < pT < 0.5 0.5 < pT < 1.0

1.0 < pT < 1.5 1.5 < pT < 2.0

2.0 < pT < 3.0 3.0 < pT < 4.0

Figure 3.14: Invariant mass spe tra divided by pT bins. The blue line indi ate ombinatorial ba kground evaluated by the event mixing method.

CHAPTER 3. ANALYSIS 413.4.4 Radiative tail orre tionThe radiative orre tion to e+e� was estimated. The observation of radiativede ays J= ! e+e� was reported and the result is onsistent with a QED al ulation based on �nal state radiation [30℄. The radiative de ay is des ribedby the diagrams shown Figure 3.15.

Figure 3.15: Diagrams for �nal state radiation [30℄. The de ay into e+e� is des ribed by (a). The infrared divergen e in the de ay is an eled byinterferen e with the diagrams in (b).An analyti formula for the di-lepton mass spe tra in radiative de ays isderived [31℄. The fra tion of de ays orresponding to the emission of hardphotons isChard = �2� �4 ln M2Emin�lnM2m2l � 1�� 3 lnM2m2l � 23�2 + 112 � (3.9)where Emin is the minimal photon energy, M is a mass of parent parti le andml is a mass of leptons. The di-lepton mass m is shifted by photon emissionm = qM(M � 2E ) � M � E (E �M) (3.10)Hard photon emission ause a tail towards lower mass in the di-leptonmass spe trum. The distribution P (m) of the di-lepton mass in the radiativede ay is des ribed asP (m) = �� 2m(M2 �m2)�1 + m4M4 ��ln 1 + r1� r � r� (3.11)where r = q1� 4m2l =m2 is also a fun tion of m. Figure 3.16 shows the massspe tra in the radiative de ay �! e+e� for Emin = 10MeV.


]2mass [GeV/c0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.10

1

2

3

4

5

6

Figure 3.16: e+e� mass spe trum in the radiative de ay �! e+e� for Emin= 10MeV(orange) smeared with 10MeV(red).3.4.5 Signal CountingFitting fun tion onsists ofGaussian onvoluted r.BW + radiative tail + Breit-Wigner.The �rst term and se ond term is for ! and � mesons. The third term, Breit-Winger, is for � mesons. The number of ! and � mesons are obtained bythe �rst and se ond term. The �tting parameters are the peak amplitude,mass enter and experimental mass resolution, while the width �tot are �xedto PDG value [29℄. The ratio between the number of � and ! are �xed. The� /! ratio is �xed to 1.53, whi h obtained by ration of bran hing into e+e�The �tting result for invariant mass spe tra are shown in Fig.3.17.


]2invariant mass [GeV/c0.6 0.7 0.8 0.9 1 1.1 1.2

co

un

t

-10

0

10

20

30

40

50 chi2/ndf = 75.95/114


co

un

t

-20

0

20

40

60

80

100 chi2/ndf = 73.25/114

h_subt_pT_2


co

un

t

-10

0

10

20

30

40

50

60

chi2/ndf = 75.89/114

h_subt_pT_3


co

un

t

-5

0

5

10

15

20

25chi2/ndf = 108.50/114

h_subt_pT_4


co

un

t

-2

0

2

4

6

8

10

12

14

16

chi2/ndf = 102.62/114

h_subt_pT_5


co

un

t

-1

0

1

2

3

4

5

6

7

8 chi2/ndf = 156.00/114

h_subt_pT_6

0 < pT <0.5 0.5 < pT <1.0

1.0 < pT <1.5 1.5 < pT <2.0

2.0 < pT <3.0 3.0 < pT <4.0

Figure 3.17: Invariant mass spe tra divided by pT bins after ba kgroundsubtra tion. The bla k line are the �tting result, whi h is sum of the knownde ays, ! (left magenta line), � (right magenta line), � (light blue line),radiative de ay of ! and � (blue line).

CHAPTER 3. ANALYSIS 443.5 EÆ ien y evaluation

Figure 3.18: Demonstration of tra ks de ayed from 10 � mesons. The red lineindi ate e+ or e�, blue dotted line indi ate photons and bla k line indi ate herenkov photon radiated in RICH. EMCal, PC and DC are drawn.To evaluate the eÆ ien y of PHENIX dete tor a eptan e, ele tron iden-ti�ed and ERT trigger eÆ ien y, the simulation study was done. We usethe event generator alled "EXODUS" based on Monte Carlo odes. 10M !mesons and � mesons are generated for following status, and de ayed intoe+e� pair.� rapidity{ range: -0.5<y<0.5, the shape of y distribution: at� pT (transverse momentum){ range: 0.0<pT<5.5, the shape of pT distribution: atThe PHENIX dete tor is very omplex in hara ter with a large variety ofdete tor types and materials inside it. To simulate su h PHENIX dete tor, ”PISA”, PHENIX Integrates Simulation Appli ation [32℄ was introdu ed. ThePISA ode is based heavily on the CERN software libraries [33℄. Spe i� ally,

CHAPTER 3. ANALYSIS 45PISA is the PHENIX implementation of the GEANT geometry and eventparti le tra king software system. Using PISA, a PHENIX simulator an pi kwhi h (or all) aspe ts of the whole PHENIX dete tor geometry to introdu einto an event simulation. [34℄We re onstru t ! and � mesons by al ulating eq. 3.2. The Figure 3.20is invariant mass spe trum of single ! re onstru ted from PISA output.

]2invariant mass [GeV/c0.6 0.65 0.7 0.75 0.8 0.85 0.9

co

un

t

0

2000

4000

6000

8000

10000

12000

Invariant mass at Minimum Bias

Figure 3.19: Invariant mass spe trumof single ! for all pT ]2invariant mass [GeV/c0.9 0.95 1 1.05 1.1 1.15

co

un

t

0

2000

4000

6000

8000

10000

12000

14000

Invariant mass at Minimum Bias

Figure 3.20: Invariant mass spe trumof single � for all pT3.5.1 Geometri al A eptan e and Ele tron ID EÆ- ien yThe eÆ ien y of the PHENIX Geometri al a eptan e and ele tron ID was al ulated as a fun tion of pT. Results are shown in Fig.3.22.In the a eptan e al ulation, it is important that the dete tor a eptan ein the real data and the simulation data agree. In Fig.3.21, we ompare thephi distribution of the data and simulation. Here phi is the � oordinate oftra k in the DC. The phi distribution in the simulation agree with the realdata well.3.5.2 Trigger eÆ ien ySingle ele tron eÆ ien y in ea h EMCal se tor for ERT ele tron is al ulatedas a fun tion of momentum using Minimum Bias sampled events. The resultare shown in Fig.3.23, and alled turn-on urve.Trigger eÆ ien y is al ulated with simulation data and turn-on urve. Turn-on urve is �tted by "Error fun tion(Erf)" ,whi h is integrated gaussian, and

CHAPTER 3. ANALYSIS 46parameterized.f(momentum) = par[0℄� Erf(momentum� par[2℄par[1℄ ) (3.12)A random number is used to see if ea h ele tron from the ! and � wouldhave �red Ele tron trigger in the EMCal se tor that it hit, using pT depen-dent single ele tron eÆ ien ies shown in Fig.3.23. The results are shown inFig.3.24.3.5.3 bin shift orre tionBin shift orre tion was performed in the same way as used in [38℄. Thepro edure is below.1. Fit the pT spe trum with f(pT) = expf-pT/C1 + C2 g2. al ulate bin shift orre tion fa tor3. move the data point verti ally and leave the pT of data point un hanged.The result is shown in Table.3.3pT 0.-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-4.0! 1.084 1.084 1.084 1.084 1.363 1.363� 1.065 1.065 1.065 1.065 1.277 1.277Table 3.3: Corre tion fa tor of bin shift orre tion.


DC phi [rad]-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

0

1000

2000

3000

4000

5000

6000

7000

8000

DC phi

DC phi [rad]-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 40

500

1000

1500

2000

2500

3000

3500

4000

DC phi North

DC phi [rad]-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

0

500

1000

1500

2000

2500

3000

3500

4000

DC phi South

Figure 3.21: Comparison of DC phi distribution in the real data(red) and thesimulation(blue). The simulation phi distribution is weighted by appropriateele tron pT distribution. The data is res aled su h that the integral of thephi distribution in the real data and in the simulation agree. The middle andthe bottom panel shows the phi distribution in the South side(zed<0)and theNorth side(zed>0), respe tively. The top panel shows the phi distribution forNorth and South side. The pT range of the ele tron is 0.3<pT<4.0 GeV/ forborht of the real data and simulation.


pT [GeV/c]0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy [

%]

0

0.005

0.01

0.015

0.02

0.025

0.03

Figure 3.22: Total re onstru tion eÆ ien y of !(blue) and �(red) in ludinga eptan e is shown as a fun tion of pT .


momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2

hrEntries 0

Mean x 0Mean y 0

RMS x 0RMS y 0

hrEntries 0

Mean x 0Mean y 0

RMS x 0RMS y 0

/ ndf 2

χ 801.6 / 38

Prob 0

p0 0.004691± 0.6886

p1 0.03375± 2.361

p2 0.0009595± 0.3234

/ ndf 2

χ 801.6 / 38

Prob 0

p0 0.004691± 0.6886

p1 0.03375± 2.361

p2 0.0009595± 0.3234

WEST 0

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2

hr1Entries 0

Mean x 0Mean y 0

RMS x 0RMS y 0

hr1Entries 0

Mean x 0Mean y 0

RMS x 0RMS y 0

/ ndf 2

χ 1734 / 38Prob 0

p0 0.005689± 0.8856 p1 0.02935± 2.136

p2 0.001002± 0.3094

/ ndf 2

χ 1734 / 38Prob 0

p0 0.005689± 0.8856 p1 0.02935± 2.136

p2 0.001002± 0.3094

WEST 1

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2

hr2

Entries 0Mean x 0Mean y 0

RMS x 0RMS y 0

hr2


RMS x 0RMS y 0

/ ndf 2

χ 1576 / 38Prob 0

p0 0.005161± 0.6559

p1 0.03136± 2.086 p2 0.001025± 0.3139

/ ndf 2

χ 1576 / 38Prob 0

p0 0.005161± 0.6559

p1 0.03136± 2.086 p2 0.001025± 0.3139

WEST 2

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2

hr3


RMS x 0RMS y 0

hr3


RMS x 0RMS y 0

/ ndf 2

χ 2026 / 38Prob 0

p0 0.007069± 0.2874

p1 0.04302± 1.232 p2 0.002307± 0.2539

/ ndf 2

χ 2026 / 38Prob 0

p0 0.007069± 0.2874

p1 0.04302± 1.232 p2 0.002307± 0.2539

WEST 3

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2

hr4Entries 0Mean x 0

Mean y 0RMS x 0RMS y 0



/ ndf 2

χ 129.9 / 38Prob 4.438e-14

p0 0.002527± 0.3202

p1 0.0494± 3.019

p2 0.001018± 0.1795

/ ndf 2

χ 129.9 / 38Prob 4.438e-14

p0 0.002527± 0.3202

p1 0.0494± 3.019

p2 0.001018± 0.1795

EAST 0

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2





/ ndf 2

χ 719.3 / 38

Prob 0

p0 0.00448± 0.5808

p1 0.02275± 1.947

p2 0.0005062± 0.1859

/ ndf 2

χ 719.3 / 38

Prob 0

p0 0.00448± 0.5808

p1 0.02275± 1.947

p2 0.0005062± 0.1859

EAST 1

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2

hr6Entries 0

Mean x 0Mean y 0RMS x 0

RMS y 0

hr6Entries 0


RMS y 0

/ ndf 2

χ 2056 / 38Prob 0

p0 0.004036± 0.8362

p1 0.01555± 1.923

p2 0.0003318± 0.2936

/ ndf 2

χ 2056 / 38Prob 0

p0 0.004036± 0.8362

p1 0.01555± 1.923

p2 0.0003318± 0.2936

EAST 2

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1.2

hr7Entries 0


RMS y 0

hr7Entries 0


RMS y 0

/ ndf 2

χ 942.5 / 38Prob 0

p0 0.003841± 0.7889

p1 0.02132± 2.283

p2 0.0005053± 0.2862

/ ndf 2

χ 942.5 / 38Prob 0

p0 0.003841± 0.7889

p1 0.02132± 2.283

p2 0.0005053± 0.2862

EAST 3

Figure 3.23: ERT Ele tron trigger eÆ ien y for single ele tron is shown as afun tion of momentum.


pT [GeV/c]0 1 2 3 4 5

ER

T E

ffic

ien

cy [

%]

0

0.2

0.4

0.6

0.8

1

1.2

Figure 3.24: ERT Ele tron trigger eÆ ien y for !(blue) and �(red) are shownas a fun tion of pT .3.6 Systemati ErrorsThe followings are onsidered and evaluated as sour es of systemati errors.� signal ounting� geometri al a eptan e al ulation� ele tron ID eÆ ien y� ERT Trigger eÆ ien y� Bin shift orre tion

CHAPTER 3. ANALYSIS 513.6.1 Signal ountingThe sour e of systemati error in signal ounting are following.� ambiguity of ba kground shape� ambiguity of rho meson yieldTo estimate the systemati error from ambiguity of ba kground, we as-sumed the other �tting fun tion for ba kground on invariant mass spe tra.Basi method : Event Mixing methodexponential : Exp(C1 � x + C2)power : C1 � Exp(C2 � Log(x) + C3)The total systemati error from ambiguity of ba kground was obtained by al ulating the quadrati sum of systemati error on the ases of ea h other�tting fun tion for ea h pT bin. The �tting results are shown in Figure 3.25,3.26. Systemati errors from ambiguity of ba kground for ! and � is shownin Table 3.4, ??, respe tively.pT 0.-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-4.0pol2 22.6% 0.0% 0.0% 36.5% 15.9% 1.5%power 16.2% 6.1% 2.4% 34.9% 14.0% 2.4%total 27.8% 6.1% 2.4% 50.5% 21.2% 2.9%Table 3.4: Systemati errors from ambiguity of ba kground for ! in ea h pTbins . pT 0.-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-4.0expo 0.7% 8.0% 5.0% 11.5% 2.5% 10.2%power 2.1% 5.8% 5.2% 10.4% 1.5% 3.9%total 2.2% 9.8% 7.2% 15.5% 2.9% 10.9%Table 3.5: Systemati errors from ambiguity of ba kground for � in ea h pTbins .

CHAPTER 3. ANALYSIS 523.6.2 geometri al a eptan e al ulationSour es of systemati error in a eptan e al ulation is di�eren e of �du ialarea between the real data and the simulation. The normalization is done in4 di�erent pla e as shown Fig.3.27 ,3.28 3.29 ,3.30 to estimate the systemati error from a eptan e al ulation. the systemati error was estimated byfollowing al ulation in ea h pT bin.Sys Error = 2 � Dp12 (3.13)D is the deviation whi h is the ratio between number of ! or � mesons forea h ase and number of ! or � for basi ase.The deviation is al ulate from ratio of integral between the real dataand the simulation. The systemati error from a eptan e al ulation wasobtained from Eq.3.13. Then, the D is a largest deviation in all ase. Theresult is shown in Table.3.6.



co

un

t

0

10

20

30

40

50

60

70

chi2/ndf = 149.67/112


co

un

t

0

20

40

60

80

100

120chi2/ndf = 141.29/112



co

un

t

0

10

20

30

40

50

60 chi2/ndf = 151.01/112



co

un

t

0

5

10

15

20

25 chi2/ndf = 165.86/112



co

un

t

0

2

4

6

8

10

12

14

16

chi2/ndf = 134.01/112



co

un

t

0

1

2

3

4

5

6

7

8 chi2/ndf = 41.53/112


0 < pT < 0.5 0.5 < pT < 1.0

1.0 < pT < 1.5 1.5 < pT < 2.0

2.0 < pT < 3.0 3.0 < pT < 4.0

Figure 3.25: Invariant mass spe trum divided by pT . Ba kground shape wasestimated as exponential(blue). The bla k line are the �tting result, whi his sum of the ba kground and known de ays, ! (left magenta line), � (rightmagenta line), � (light blue line), radiative de ay of ! and � (Orange line)



co

un

t

0

10

20

30

40

50

60

70

chi2/ndf =148.34/111



co

un

t

0

20

40

60

80

100

120chi2/ndf =150.00/111



co

un

t

0

10

20

30

40

50

60 chi2/ndf =151.24/111



co

un

t

0

5

10

15

20

25chi2/ndf =164.45/111



co

un

t

0

2

4

6

8

10

12

14

16

chi2/ndf =134.22/111



co

un

t

0

1

2

3

4

5

6

7

8 chi2/ndf =42.37/112


Figure 3.26: Invariant mass spe trum divided by pT . Ba kground shape wasestimated as power law fun tion(blue). The bla k line are the �tting result,whi h is sum of the ba kground and known de ays, ! (left magenta line), �(right magenta line), � (light blue line), radiative de ay of ! and � (Orangeline)


DC phi [rad]-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

0

1000

2000

3000

4000

5000

6000

7000

8000

<-0.2φ-0.6<

Figure 3.27: phi distribution for the real data(red) and the simulation(blue).Simulation data is normalized in -0.6<�<-0.2

DC phi [rad]-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

<0.85φ0.7<

Figure 3.28: phi distribution for the real data(red) and the simulation(blue).Simulation data is normalized in 0.7<�<0.85


DC phi [rad]-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

0

1000

2000

3000

4000

5000

6000

7000

8000

<-2.45φ2.3<


DC phi [rad]-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

0

1000

2000

3000

4000

5000

6000

7000

<2.9φ2.5<


CHAPTER 3. ANALYSIS 57�[rad℄ -0.6<�<-0.2 0.7<�<0.85 2.3<�<2.45 2.5<�<2.9deviation 0.945 1.049 1.079 1.011sys error 4.5%Table 3.6: Systemati errors from a eptan e al ulation.3.6.3 ele tron ID eÆ ien ySystemati error from eID eÆ ien y is assigned to be 8%, sin e the errorassigned in singe ele tron analysis is 4% [39℄.3.6.4 trigger eÆ ien yTo estimate the systemati error from ERT trigger eÆ ien y, parameter ofturn-on urve is hanged to following.1. 1.025 � par[0℄ and 0.99 � par[2℄2. 0.975 � par[0℄ and 1.01 � par[2℄Here, par[0℄ and par[2℄ are parameter of turn-on urve shown Eq.3.12. thevalue of 1.025, 0.975, 0.99 and 1.01 were obtained from the error of �tting.Then, ase 1 means ERT trigger eÆ ien y is higher than basi . ase 2 meansERT trigger eÆ ien y is lower than basi ase. For example, the red dashline in Fig.3.31 shows ase 1, and the blue dash line shows ase 2. Afterthe re al ulating trigger eÆ ien y of ! and �, larger SysError al ulated byEq.3.13 in ea h pT bin was assigned as systemati error. The result is shownin Table.3.7.

momentum0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

nc

y

0

0.2

0.4

0.6

0.8

1

1.2

WEST 0

Figure 3.31: single ele tron ERT trigger eÆ ien y of a se tor0. the red dashline shows ase1 and the blue dash line shows ase2.

CHAPTER 3. ANALYSIS 58pT 0.-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-4.0! 2.4% 1.8% 1.3% 1.3% 1.1% 1.1%� 0.8% 2.2% 1.5% 1.1% 1.2% 0.8%Table 3.7: Systemati errors from ERT trigger eÆ ien y in ea h pT bins .3.6.5 Bin shift orre tionAnother �tting fun tion: par[0℄� (1 + ( pTpar[1℄)2 )�6 (3.14)is bin shift orre tion is tried for evaluation of systemati error. The di�eren eis assigned as the systemati error from bin shift orre tion. The result isshown in Table.3.8.pT 0.-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-4.0! 11.2% 4.6% 1.1% 3.4% 10.0% 1.0%� 8.8% 4.3% 3.1% 2.7% 10.5% 4.7%Table 3.8: Systemati errors from bin shift orre tion in ea h pT bins .

CHAPTER 3. ANALYSIS 593.6.6 Total systemati errorVarious systemati errors are summarized in Table.3.9, 3.10.pT 0.-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-4.0rho 2.3%BG 27.8% 6.1% 2.4% 50.5% 21.2% 2.9%a eptan e 4.5%ele tron ID 8.0%ERT trigger 2.4% 1.8% 1.3% 1.3% 1.1% 1.1%bin shift 11.2% 4.6% 1.1% 3.4% 10.0% 1.0%Total 31.5% 12.3% 9.9% 51.1% 25.3% 10.0%Table 3.9: Total systemati error for !pT 0.-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-3.0 3.0-4.0rho 0.6%BG 2.2% 9.8% 7.2% 15.5% 2.9% 10.9%a eptan e 4.5%ele tron ID 8.0%ERT trigger 0.8% 2.2% 1.5% 1.1% 1.2% 0.8%bin shift 8.8% 4.3% 3.1% 2.7% 10.5% 4.7%Total 12.9% 14.3% 12.2% 18.3% 14.3% 15.0%Table 3.10: Total systemati error for �

Chapter 4Results and Dis ussion4.1 Mass shiftThe enter of mass was obtained as a fun tion of pT by �tting the invariantmass spe tra for both ! and �, respe tively. Figure 4.1 and 4.2 shows theresult of the position of mass enter as a fun tion of pT . The obtained resultswere not onsistent with PDG value [29℄ into the statisti al error.It is ne essary to onsider the simulation result to evaluate dete tor massresolution. The orange line in Figure 4.1 and 4.2 indi ate 1� of dete tormass resolution. The position of the mass enter obtained by real date are onsistent with PDG value, in addition simulated position of mass, withinthe dete tor mass resolution.4.2 Invariant ross se tionInvariant ross se tion in proton+proton ollisions for ! and � mesons are al ulated as following.Ed3�dp3 = 12�pT N! or �Nevent �pT�y �BBC�bias 1�a +eID �ERT (4.1)Here� Nevent is the Number of MinBias sampled events.� �BBC = 23.0[mb℄ is the BBC trigger ross se tion [39℄.� �bias = 0.79 is the BBC trigger eÆ ien y [39℄.� �a +eID is the a eptan e and ele tron re onstru tion eÆ ien y.60

CHAPTER 4. RESULTS AND DISCUSSION 61� �ERT is the ERT trigger eÆ ien y.After bin shift orre tion, we were able to get invariant ross se tion of! and � mesons as a fun tion of pT . The Results are shown in Fig.4.5 and4.6. We ompared with results obtained from study of other de ay hannels,! ! pi0 , ! ! �0�+�� and � ! K+K� in proton+proton ollisions at ps= 200GeV.The result of this analysis are onsistent with the other result withinstatisti al and systemati error.

CHAPTER 4. RESULTS AND DISCUSSION 62

pT [GeV/c]0 0.5 1 1.5 2 2.5 3 3.5 4

]2

ma

ss

[G

eV

/c

0.76

0.765

0.77

0.775

0.78

0.785

0.79

0.795

0.8

m

Γ m -

Γ m +

Figure 4.1: position of mass enter of ! as a fun tion of pT . The error is onlystatisti al error. The PDG value [29℄ of mass enter of ! is des ribed in this�gure as m, and � means total de ay width of ! (See table 3.2).


pT [GeV/c]0 0.5 1 1.5 2 2.5 3 3.5 4

]2

ma

ss

[G

eV

/c

1

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

m

Γ m -

Γ m +

Figure 4.2: mass enter of � as a fun tion of pT . The error is only statisti alerror. The PDG value [29℄ of mass enter of � is des ribed in this �gure asm, and � means total de ay width of � (See table 3.2).


pT [GeV/c]0 0.5 1 1.5 2 2.5 3 3.5 4

]2

ma

ss

[G

eV

/c

0.76

0.765

0.77

0.775

0.78

0.785

0.79

0.795

0.8

m

Γ m -

Γ m +

Figure 4.3: mass enter of ! as a fun tion of pT . The blue points are obtainedby �tting result for real data analysis. the orange lines indi ate 1� of dete tormass resolution obtained by simulation.


pT [GeV/c]0 0.5 1 1.5 2 2.5 3 3.5 4

]2

ma

ss

[G

eV

/c

1

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

m

Γ m -

Γ m +

Figure 4.4: mass enter of � as a fun tion of pT . The blue points are obtainedby �tting result for real data analysis. the orange lines indi ate 1� of dete tormass resolution obtained by simulation.


pT [GeV/c]0 1 2 3 4 5 6 7 8

/dyd

pT

σ

2p

T d

π1/2

-710

-610

-510

-410

-310

-210

-110

1

10

= 200 GeVsp+p at

- e+ e→ ω

-π +π 0π → ω

0π γ → ω

mesonsω/dydpT for σ2pT dπ1/2

Figure 4.5: Invariant ross se tion for ! as a fun tion of pT . The red point isour result, ! ! e+e�. The blue and light blue points indi ate ! ! �0�+��,! ! �0 , respe tively. The bra ket and gray band indi ate systemati error.


pT [GeV/c]0 1 2 3 4 5 6

/dyd

pT

σ

2p

T d

π1/2

-710

-610

-510

-410

-310

-210

-110

1

= 200 GeVsp+p at

- e+ e→ φ

-

K+

K→ φ

mesonsφ/dydpT for σ2pT dπ1/2

Figure 4.6: Invariant ross se tion for � as a fun tion of pT . The red point isour result, � ! e+e�. The green points indi ate � ! K+K�. The bra ketand gray band indi ate systemati error.

Chapter 5Con lusionWe have measured the invariant mass spe tra of e+e� pairs and obtainedprodu tion ross se tion as a fun tion of pT in proton+proton ollisions atsqrts = 200GeV. The goal of this work is to �nd out whether mass shift andmodi� ation of the light ve tor mesons are dete ted or not, in proton+proton ollisions and to provide referen e data as baseline of heavy ion ollision.We identi�ed e+, e� tra ks from large other harged parti le tra ks pro-du ed in the ollision vertex. We re onstru ted the invariant mass spe -trum of e+e� pairs and subtra ted ombinatorial ba kground evaluated byevent mixing method, moreover �tted the resonan e fun tion as known sour e,! ! e+e�, �! e+e�, �! e+e� and radiative tail.We observed no mass shift in proton+proton ollisions. The positionof enter of mass are onsistent with PDG value within the dete tor massresolution obtained by simulation based on Monte Carlo odes. In addition,the invariant ross se tion of ! and � mesons are obtained by orre tingthe a eptan e of PHENIX dete tor, ele tron identi�ed eÆ ien y, and ERTtrigger eÆ ien y. As a onsequen e of omparison with the result of otherde ay hannels, we re ognized that there is no di�eren e.From this view point, we an provide referen e data of ! and � produ tionas baseline of heavy ion ollision. The next step, we will be going on the dataanalysis of heavy ion ollisions, Au+Au and Cu+Cu. There is possibility ofobservation of mass shift and mass modi� ation in heavy ion ollision. Wewill present this results as soon as possible!!68

A knowledgementsI would like to thank the sta� members Sugiate-sensi, Homma-sensei, Torii-san, Horagu hi-san and Shigaki-sensei for their detailed omments, sugges-tions, and onstant support. I ould not write up this paper without yourhelp. I also would like to thank Ozawa-sensei.I wish to thank Tsu himoto-san for giving me very useful advi e to pro eedmy analysis. I also wish to thank Nakamiya-san for dis ussing with me aboutuseful physi s topi s at any time day or night. I would like to thanks Narita-kun and Kubo-san for their en ouragement. I great a knowledge all membersof our lab and H/L PWG.Finally, thanks appre iate my friends, huy 14 members, my brother andmy mother.

69

Bibliography[1℄ K.Yagi, T.Hatuda and Y.Miake Quark-Gluon Plasma[2℄ Phovh.Rith.S holz.Zets he, PARTICLES AND NUCLEI[3℄ John B. Kogut. et al. Phys.Rev.Lett. 50(1983) 393[4℄ M.Lutz, S.Klimt and W.Weise. Nu lear Physi s A 542(1992) 521-558[5℄ G.E.Brown, Mannque Rho. Phys.Rev.Lett. 66(1991) 2720-2723[6℄ K.Yagi, T.Hatuda, H.Shiomi and H.Kuwabara. Prog.Theor.Phys.95(1996) 1009-1028[7℄ T.Hatsuda and T.Kunihiro. Phys.Rept. 247(1994) 2221-367. hep-ph/9504250[8℄ G.Agaki hiev, et al, Nu lear Instruments and Methods A 371(1996) 16-21[9℄ CERES Collaboration, D.Adamova. et al. nu l-ex/0611022[10℄ NA60 Collaboration, R.Arnaldi. et al. Phys.Rev.Lett. 96(2006) 162302[11℄ M.Sekimoto, et al, Nu lear Instruments and Methods A 516(2004) 390-405[12℄ KEK-E325 Collaboration, R.Muto. et al, Phys.Rev.Lett. 98(2007)042501[13℄ M.Naruki, et al, Phys.Rev.Lett. 96(2006) 092301[14℄ Nu lear Instruments and Methods A 499(2003) 235-244[15℄ Nu lear Instruments and Methods A 499(2003) 423-432[16℄ Nu lear Instruments and Methods A 499(2003) 549-55970

BIBLIOGRAPHY 71[17℄ T.Nakamura http://www.phenix.bnl.gov/WWW/run/03/fo us/talks/bb /fo us bb .ppt[18℄ Nu lear Instruments and Methods A 499(2003) 433-436[19℄ Nu lear Instruments and Methods A 499(2003) 480-488[20℄ Nu lear Instruments and Methods A 499(2003) 489-507[21℄ Nu lear Instruments and Methods A 499(2003) 508-520[22℄ Nu lear Instruments and Methods A 433(1999) 143-148[23℄ Nu lear Instruments and Methods A 499(2003) 521-536[24℄ Nu lear Instruments and Methods A 499(2003) 537-548[25℄ Nu lear Instruments and Methods A 499(2003) 560-592[26℄ Nu lear Instruments and Methods A 499(2003) 593-602[27℄ in PHENIX website http://www.phenix.bnl.gov/WWW/run/drawing/[28℄ M.Naruki. PhD thesis, Kyoto Univ., 2006[29℄ K.Hagiwara, et al. Review of Parti le Physi s. Phys:Rev:D, 66:010001,2002.[30℄ Fermilab E760 Collaboration, T.A.Armstrong, et al. Phys.Rev.D54(1996) 7067-7070[31℄ A.Spiridonov hep-ex/ 0510076[32℄ A Primer Manual for the PHENIX Simulation Code PISAhttp://www.phenix.bnl.gov/phenix/WWW/simulation/primer4/[33℄ CERN OÆ ial Website, http://www. ern. h[34℄ M.Ou hida. Master thesis, Hiroshima Univ., 2007[35℄ quality ontrol for RUN5 pp data set. PHENIX analysis note 486[36℄ PHENIX analysis note 550[37℄ PHENIX analysis note 411[38℄ PHENIX analysis note 73[39℄ Single ele trons from heavy � flavor de ays in p +p ollisions at ps = 200GeV . PHENIX analysis note 509

Documents

Con - quark.hiroshima-u.ac.jp · con v oluted r.BW + radiativ e tail Breit-Wigner. The rst term and second is for! mesons. third term, Breit-Winger, is for mesons. The n um b er of!