Event Structure and Double Helicity Asymmetry in Jet Production from Polarized p+p Collisions at sqrt(s) = 200 GeV
A. Adare, S. Afanasiev, C. Aidala, N.N. Ajitanand, Y. Akiba, H. Al-Bataineh, J. Alexander, K. Aoki, L. Aphecetche, R. Armendariz, S.H. Aronson, J. Asai, E.T. Atomssa, R. Averbeck, T.C. Awes, B. Azmoun, V. Babintsev, G. Baksay, L. Baksay, A. Baldisseri, K.N. Barish, P.D. Barnes, B. Bassalleck, S. Bathe, S. Batsouli, V. Baublis, A. Bazilevsky, S. Belikov, R. Bennett, Y. Berdnikov, A.A. Bickley, J.G. Boissevain, H. Borel, K. Boyle, M.L. Brooks, H. Buesching, V. Bumazhnov, G. Bunce, S. Butsyk, S. Campbell, B.S. Chang, J.-L. Charvet, S. Chernichenko, J. Chiba, C.Y. Chi, M. Chiu, I.J. Choi, T. Chujo, P. Chung, A. Churyn, V. Cianciolo, C.R. Cleven, B.A. Cole, M.P. Comets, P. Constantin, M. Csanád, T. Csörgő, T. Dahms, K. Das, G. David, M.B. Deaton, K. Dehmelt, H. Delagrange, A. Denisov, D. d'Enterria, A. Deshpande, E.J. Desmond, O. Dietzsch, A. Dion, M. Donadelli, O. Drapier, A. Drees, A.K. Dubey, A. Durum, V. Dzhordzhadze, Y.V. Efremenko, J. Egdemir, F. Ellinghaus, W.S. Emam, A. Enokizono, H. En'yo, S. Esumi, K.O. Eyser, D.E. Fields, M. Finger Jr, M. Finger, F. Fleuret, S.L. Fokin, Z. Fraenkel, J.E. Frantz, A. Franz, A.D. Frawley, K. Fujiwara, Y. Fukao, T. Fusayasu, S. Gadrat, I. Garishvili, A. Glenn, H. Gong, M. Gonin, et al. (276 additional authors not shown)
aa r X i v : . [ h e p - e x ] S e p Event Structure and Double Helicity Asymmetry in Jet Production from Polarized p + p Collisions at √ s = 200 GeV A. Adare, S. Afanasiev, C. Aidala, N.N. Ajitanand, Y. Akiba,
43, 44
H. Al-Bataineh, J. Alexander, K. Aoki,
28, 43
L. Aphecetche, R. Armendariz, S.H. Aronson, J. Asai, E.T. Atomssa, R. Averbeck, T.C. Awes, B. Azmoun, V. Babintsev, G. Baksay, L. Baksay, A. Baldisseri, K.N. Barish, P.D. Barnes, B. Bassalleck, S. Bathe, S. Batsouli, V. Baublis, A. Bazilevsky, S. Belikov, ∗ R. Bennett, Y. Berdnikov, A.A. Bickley, J.G. Boissevain, H. Borel, K. Boyle, M.L. Brooks, H. Buesching, V. Bumazhnov, G. Bunce,
4, 44
S. Butsyk,
31, 50
S. Campbell, B.S. Chang, J.-L. Charvet, S. Chernichenko, J. Chiba, C.Y. Chi, M. Chiu, I.J. Choi, T. Chujo, P. Chung, A. Churyn, V. Cianciolo, C.R. Cleven, B.A. Cole, M.P. Comets, P. Constantin, M. Csan´ad, T. Cs¨org˝o, T. Dahms, K. Das, G. David, M.B. Deaton, K. Dehmelt, H. Delagrange, A. Denisov, D. d’Enterria, A. Deshpande,
44, 50
E.J. Desmond, O. Dietzsch, A. Dion, M. Donadelli, O. Drapier, A. Drees, A.K. Dubey, A. Durum, V. Dzhordzhadze, Y.V. Efremenko, J. Egdemir, F. Ellinghaus, W.S. Emam, A. Enokizono, H. En’yo,
43, 44
S. Esumi, K.O. Eyser, D.E. Fields,
37, 44
M. Finger, Jr.,
6, 23
M. Finger,
6, 23
F. Fleuret, S.L. Fokin, Z. Fraenkel, ∗ J.E. Frantz, A. Franz, A.D. Frawley, K. Fujiwara, Y. Fukao,
28, 43
T. Fusayasu, S. Gadrat, I. Garishvili, A. Glenn, H. Gong, M. Gonin, J. Gosset, Y. Goto,
43, 44
R. Granier de Cassagnac, N. Grau, S.V. Greene, M. Grosse Perdekamp,
20, 44
T. Gunji, H.-˚A. Gustafsson, ∗ T. Hachiya, A. Hadj Henni, C. Haegemann, J.S. Haggerty, H. Hamagaki, R. Han, H. Harada, E.P. Hartouni, K. Haruna, E. Haslum, R. Hayano, M. Heffner, T.K. Hemmick, T. Hester, X. He, H. Hiejima, J.C. Hill, R. Hobbs, M. Hohlmann, W. Holzmann, K. Homma, B. Hong, T. Horaguchi,
43, 53
D. Hornback, T. Ichihara,
43, 44
H. Iinuma,
28, 43
K. Imai,
28, 43
M. Inaba, Y. Inoue,
45, 43
D. Isenhower, L. Isenhower, M. Ishihara, T. Isobe, M. Issah, A. Isupov, B.V. Jacak, † J. Jia, J. Jin, O. Jinnouchi, B.M. Johnson, K.S. Joo, D. Jouan, F. Kajihara, S. Kametani,
8, 56
N. Kamihara, J. Kamin, M. Kaneta, J.H. Kang, H. Kanou,
43, 53
D. Kawall, A.V. Kazantsev, A. Khanzadeev, J. Kikuchi, D.H. Kim, D.J. Kim, E. Kim, E. Kinney, ´A. Kiss, E. Kistenev, A. Kiyomichi, J. Klay, C. Klein-Boesing, L. Kochenda, V. Kochetkov, B. Komkov, M. Konno, D. Kotchetkov, A. Kozlov, A. Kr´al, A. Kravitz, J. Kubart,
6, 21
G.J. Kunde, N. Kurihara, K. Kurita,
45, 43
M.J. Kweon, Y. Kwon,
58, 52
G.S. Kyle, R. Lacey, Y.S. Lai, J.G. Lajoie, A. Lebedev, D.M. Lee, M.K. Lee, T. Lee, M.J. Leitch, M.A.L. Leite, B. Lenzi, T. Liˇska, A. Litvinenko, M.X. Liu, X. Li, B. Love, D. Lynch, C.F. Maguire, Y.I. Makdisi, A. Malakhov, M.D. Malik, V.I. Manko, Y. Mao,
41, 43
L. Maˇsek,
6, 21
H. Masui, F. Matathias, M. McCumber, P.L. McGaughey, Y. Miake, P. Mikeˇs,
6, 21
K. Miki, T.E. Miller, A. Milov, S. Mioduszewski, M. Mishra, J.T. Mitchell, M. Mitrovski, A. Morreale, D.P. Morrison, T.V. Moukhanova, D. Mukhopadhyay, J. Murata,
45, 43
S. Nagamiya, Y. Nagata, J.L. Nagle, M. Naglis, I. Nakagawa,
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Y. Nakamiya, T. Nakamura, K. Nakano,
43, 53
J. Newby, M. Nguyen, B.E. Norman, R. Nouicer, A.S. Nyanin, E. O’Brien, S.X. Oda, C.A. Ogilvie, H. Ohnishi, K. Okada, M. Oka, O.O. Omiwade, A. Oskarsson, M. Ouchida, K. Ozawa, R. Pak, D. Pal, A.P.T. Palounek, V. Pantuev, V. Papavassiliou, J. Park, W.J. Park, S.F. Pate, H. Pei, J.-C. Peng, H. Pereira, V. Peresedov, D.Yu. Peressounko, C. Pinkenburg, M.L. Purschke, A.K. Purwar, H. Qu, J. Rak, A. Rakotozafindrabe, I. Ravinovich, K.F. Read,
39, 52
S. Rembeczki, M. Reuter, K. Reygers, V. Riabov, Y. Riabov, G. Roche, A. Romana, ∗ M. Rosati, S.S.E. Rosendahl, P. Rosnet, P. Rukoyatkin, V.L. Rykov, B. Sahlmueller, N. Saito,
28, 43, 44
T. Sakaguchi, S. Sakai, H. Sakata, V. Samsonov, S. Sato, S. Sawada, J. Seele, R. Seidl, V. Semenov, R. Seto, D. Sharma, I. Shein, A. Shevel,
42, 49
T.-A. Shibata,
43, 53
K. Shigaki, M. Shimomura, K. Shoji,
28, 43
A. Sickles, C.L. Silva, D. Silvermyr, C. Silvestre, K.S. Sim, C.P. Singh, V. Singh, S. Skutnik, M. Sluneˇcka,
6, 23
A. Soldatov, R.A. Soltz, W.E. Sondheim, S.P. Sorensen, I.V. Sourikova, F. Staley, P.W. Stankus, E. Stenlund, M. Stepanov, A. Ster, S.P. Stoll, T. Sugitate, C. Suire, J. Sziklai, T. Tabaru, S. Takagi, E.M. Takagui, A. Taketani,
43, 44
Y. Tanaka, K. Tanida,
43, 44, 48
M.J. Tannenbaum, A. Taranenko, P. Tarj´an, T.L. Thomas, M. Togawa,
28, 43
A. Toia, J. Tojo, L. Tom´aˇsek, H. Torii, R.S. Towell, V-N. Tram, I. Tserruya, Y. Tsuchimoto, C. Vale, H. Valle, H.W. van Hecke, J. Velkovska, R. V´ertesi, A.A. Vinogradov, M. Virius, V. Vrba, E. Vznuzdaev, M. Wagner,
28, 43
D. Walker, X.R. Wang, Y. Watanabe,
43, 44
J. Wessels, S.N. White, D. Winter, C.L. Woody, M. Wysocki, W. Xie, Y.L. Yamaguchi, A. Yanovich, Z. Yasin, J. Ying, S. Yokkaichi,
43, 44
G.R. Young, I. Younus, I.E. Yushmanov, W.A. Zajc, O. Zaudtke, C. Zhang, S. Zhou, J. Zim´anyi, ∗ and L. Zolin (PHENIX Collaboration) Abilene Christian University, Abilene, Texas 79699, USA Department of Physics, Banaras Hindu University, Varanasi 221005, India Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Brookhaven National Laboratory, Upton, New York 11973-5000, USA University of California - Riverside, Riverside, California 92521, USA Charles University, Ovocn´y trh 5, Praha 1, 116 36, Prague, Czech Republic China Institute of Atomic Energy (CIAE), Beijing, People’s Republic of China Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan University of Colorado, Boulder, Colorado 80309, USA Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France Debrecen University, H-4010 Debrecen, Egyetem t´er 1, Hungary ELTE, E¨otv¨os Lor´and University, H - 1117 Budapest, P´azm´any P. s. 1/A, Hungary Florida Institute of Technology, Melbourne, Florida 32901, USA Florida State University, Tallahassee, Florida 32306, USA Georgia State University, Atlanta, Georgia 30303, USA Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic Iowa State University, Ames, Iowa 50011, USA Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academyof Sciences (MTA KFKI RMKI), H-1525 Budapest 114, POBox 49, Budapest, Hungary Korea University, Seoul, 136-701, Korea Russian Research Center “Kurchatov Institute”, Moscow, Russia Kyoto University, Kyoto 606-8502, Japan Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France Lawrence Livermore National Laboratory, Livermore, California 94550, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA LPC, Universit´e Blaise Pascal, CNRS-IN2P3, Clermont-Fd, 63177 Aubiere Cedex, France Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden Institut f¨ur Kernphysik, University of Muenster, D-48149 Muenster, Germany Myongji University, Yongin, Kyonggido 449-728, Korea Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan University of New Mexico, Albuquerque, New Mexico 87131, USA New Mexico State University, Las Cruces, New Mexico 88003, USA Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France Peking University, Beijing, People’s Republic of China PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Saint Petersburg State Polytechnic University, St. Petersburg, Russia Universidade de S˜ao Paulo, Instituto de F´ısica, Caixa Postal 66318, S˜ao Paulo CEP05315-970, Brazil Seoul National University, Seoul, Korea Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Universit´e de Nantes) BP 20722 - 44307, Nantes, France University of Tennessee, Knoxville, Tennessee 37996, USA Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan Vanderbilt University, Nashville, Tennessee 37235, USA Waseda University, Advanced Research Institute for Science andEngineering, 17 Kikui-cho, Shinjuku-ku, Tokyo 162-0044, Japan Weizmann Institute, Rehovot 76100, Israel Yonsei University, IPAP, Seoul 120-749, Korea (Dated: June 6, 2018)
We report on the event structure and double helicity asymmetry ( A L L ) of jet production in lon-gitudinally polarized p+p collisions at √ s =200 GeV. Photons and charged particles were measuredby the PHENIX experiment at midrapidity | η | < .
35 with the requirement of a high-momentum( > c ) photon in the event. Event structure, such as multiplicity, p T density and thrustin the PHENIX acceptance, were measured and compared with the pythia event generator andthe geant detector simulation. The shape of jets and the underlying event were well reproducedat this collision energy. For the measurement of jet A LL , photons and charged particles wereclustered with a seed-cone algorithm to obtain the cluster p T sum ( p reco T ). The effect of detectorresponse and the underlying events on p reco T was evaluated with the simulation. The productionrate of reconstructed jets is satisfactorily reproduced with the NLO pQCD jet production crosssection. For 4 < p reco T <
12 GeV/ c with an average beam polarization of h P i = 49% we mea-sured A LL = − . ± . stat at the lowest p reco T bin (4–5 GeV/ c ) and − . ± . stat atthe highest p reco T bin (10–12 GeV/ c ) with a beam polarization scale error of 9.4% and a p T scaleerror of 10%. Jets in the measured p reco T range arise primarily from hard-scattered gluons withmomentum fraction 0 . < x < . pythia . The measured A LL is compared withpredictions that assume various ∆ G ( x ) distributions based on the GRSV parameterization. Thepresent result imposes the limit − . < R . . dx ∆ G ( x, µ = 1GeV ) < . R . . dx ∆ G ( x, µ = 1GeV ) < . PACS numbers: 25.75.Dw
I. INTRODUCTION
The motivation of this measurement is to understandthe spin structure of the proton, particularly the contri-bution of the gluon spin (∆ G ) to the proton spin. Theproton spin can be represented as12 proton = 12 X f ∆ q f + ∆ G + L q + L g , (1)where ∆ G is the gluon spin, i.e. the integral of the po-larized gluon distribution function, ∆ G = R dx ∆ G ( x ), P ∆ q is the quark spin, and L q and L g are the orbitalangular momenta of quarks and gluons in the proton. Itwas found by the EMC experiment at CERN in 1987 thatthe quark spin contribution to the proton spin is only(12 ± ± P ∆ q more precisely. The recentanalysis by the HERMES experiment [3] reported that P ∆ q = 0 . ± . . ) ± . . ) ± . . )at a hard-scattering scale µ ∼ , which is onlyabout 30% of the proton spin. Consequently, the major-ity of the proton spin should be carried by the remainingcomponents.Jet production from longitudinally-polarized p + p colli-sions is suited for the measurement of ∆ G because gluon-involved scatterings, such as q + g → q + g or g + g → g + g ,dominate the cross section. The double helicity asymme-try A LL ≡ σ ++ − σ + − σ ++ + σ + − , (2) ∗ Deceased † PHENIX Spokesperson: [email protected] is the asymmetry in cross section between two beam he-licity states. In the A LL measurement, many systematicerrors cancel out so that high precision can be achieved.Another motivation of this measurement is to studythe event structure of p + p collisions. A high-energy p + p collision produces not only hard scattered par-tons but also many particles that originate from softinteractions which we call the ‘underlying event’. The pythia event generator phenomenologically models theunderlying event on the Multi-Parton Interaction (MPI)scheme [4], and can reproduce the event structure of p + ¯ p collisions measured by the CDF experiment at √ s = 1.8TeV [5]. We present measurements of event structure atlower collision energy, √ s = 200 GeV, and compare themwith those simulated by pythia in order to examine thevalidity of the pythia MPI scheme. One of the goals ofthe PHENIX experiment at the Relativistic Heavy IonCollider (RHIC) is the determination of ∆ G . PHENIXhas published results on single particle production; the A LL of π production was reported in [6, 7]. This pa-per reports a measurement of jet production. For ∆ G ,it is valuable to determine the parton kinematics follow-ing the collision in order to better control the x range.In this work we reconstruct jets, observing a larger frac-tion of the parton´s momentum. This allows improvedreconstruction of the original parton kinematics and bet-ter statistical accuracy for higher x gluons. Since π ’s in p + p collisions are produced via jet fragmentation, themeasurements of jet and π with same data set have astatistical overlap. The size of the overlap was estimatedto be 40-60% depending on the jet p T . Even in suchoverlapped events, measured p T of jets does not correlatewith that of π s, and thus the two measurements have anindependent sensitivity on x . The fraction of q + g sub-process is larger than q + q and g + g subprocesses in thepresent jet measurement, making it sensitive to the signof ∆ G . The STAR experiment at RHIC is also measuringinclusive jets to determine ∆ G [8]. These measurementshave different types of systematic uncertainties and thusone can provide a systematic check for the other.The remainder of this paper is organized as follows.In Section II, the parts of the PHENIX detector that isrelevant to the jet measurement are described. In Sec-tion III, analysis methods such as particle clustering andsimulation studies are discussed. In Section IV, resultson event structure, jet production rate and beam-helicityasymmetries are shown. II. EXPERIMENTAL SETUP
The PHENIX detector [9] can be grouped into threeparts; the Inner Detectors, the Central Arms and theMuon Arms. The schematic drawing of the PHENIXdetector is shown in Fig. 1. In this measurement, theCentral Arms were used to detect photons and chargedparticles in jets, and the Inner Detectors to obtain thecollision vertex and beam luminosity.
WestSouth
Side ViewBeam View
PHENIX Detector
NorthEast
MuTrMuID MuIDMVDMVDPbSc PbScPbSc PbScPbSc PbGlPbSc PbGlTOF
PC1
PC1PC3aerogel PC2Central MagnetCentralMagnet N o r t h M uon M agne t S ou t h M uon M agne t TECPC3BBBBRICH RICHDC DC ZDC NorthZDC South
FIG. 1: (color online) PHENIX detector.
A. Inner detectors
The Inner Detectors include the Beam-Beam Counters(BBC) and the Zero-Degree Calorimeters (ZDC). The BBC is composed of two identical sets of countersplaced at both the north and south sides of the colli-sion point with a 144 cm distance [10]. Each counteris composed of 64 sets of PMT plus a 3-cm quartzˇCerenkov radiator. The BBC covers a pseudorapidity of3 . < | η | < . z -vertex,and beam luminosity. The timing and z -vertex resolutionin p + p collisions are about 100 ps and 2 cm, respectively.The ZDC is comprised of two sets of hadronic calorime-ters placed at the north and south sides of the collisionpoint with a 18 m distance [11]. It covers a 10 cm ×
10 cm area perpendicular to the beam direction, whichcorresponds to 2.8 mrad when viewed from the collisionpoint. It consists of alternating layers of tungsten ab-sorbers and sampling fibers, and is 150 radiation lengthsand 5.1 interaction lengths in depth. It measures neu-trons in forward and backward regions and is used as alocal polarimeter which assures that the beam polariza-tion is correctly longitudinal or transverse at the interac-tion region by observing the left-right asymmetry in the ~p + p → neutron + X scattering cross section [12, 13]. B. Central Arms
The Central Arms consist of a tracking system andan electromagnetic calorimeter (EMCal). Pad cham-bers (PC) and drift chambers (DC) were used to detectcharged particles in jets, and the EMCal was used todetect photons in jets.The EMCal system [14] is located at a distance of5 m from the interaction point. The system consistsof four sectors in each of the East and West Arms,and each sector has a size of 2 × . The system iscomposed of two types of calorimeter, lead scintillator(PbSc) and lead glass (PbGl). One PbSc module has asize of 5.5 × × corresponding to 18.0 radiationlengths. One PbGl module has a size of 4.0 × × corresponding to 14.4 radiation lengths. The energyresolution is ∼
7% at E = 1 GeV.The DC system [15] is located in the region from 2 to2.4 m from the interaction point to measure the positionand momentum of charged particles. The DC systemconsists of one frame in each of the East and West Arms.Each chamber has a size of 2.5 m × ◦ in z - φ directionwith cylindrical shape, and is composed of 80 sense planeswith a 2-2.5 cm drift space in the φ direction. Each senseplane has 24 wires, which precisely measure r - φ position,and 16 tilted wires, which measure z position.The PC system [15] is composed of multi-wire propor-tional chambers in three separate layers, which are calledPC1, PC2 and PC3, of the Central Arms tracking sys-tem. The PC1 is located behind the DC and is used forpattern recognition together with the DC by providingthe z coordinate. The PC1 consists of a single plane ofanode and field wires lying in a gas volume between twocathode planes. One cathode is segmented into pixelswith a size of ∼ . × . , and signals from thepixels are read out.Charged particle tracks are reconstructed using the in-formation from the DC and the PC1 [16]. The magneticfield between the collision vertex and the DC is axial,and thus bends particles in the x - y plane. The field is soweak at the outer area from the DC that particle trackscan be assumed to be straight. A track reconstruction isperformed in the DC first, and then reconstructed tracksare associated with hits in the PC1. The momentum res-olution is given by σ p /p (%) = 1 . · p (GeV /c ) ⊕ . C. Trigger
The PHENIX experiment has various trigger configu-rations to efficiently select many type of interesting rareevents. This measurement required the coincidence oftwo triggers; a minimum bias (MB) trigger issued by theBBC, and a high-energy photon trigger issued by theEMCal.The MB trigger in p + p collisions requires one chargedparticle in both the north and south sides of the BBC.The reconstructed z -vertex is required to be within ± ∼
30 cm. The efficiency, f MB , of the MB trigger for high- p T QCD scatterings such as jet production is 0 . ± . π yieldswith and without the MB trigger requirement.The high-energy photon trigger is fired when the sumof energy deposits in 4 × φ ≃ ∆ η ≃ .
04) is above a threshold, ∼ . ∼ . × × × E ∼ III. ANALYSIS METHODSA. Outline
This analysis used 2.3 pb − of data that were takenwith the MB + high-energy-photon trigger in 2005. Inaddition, ∼ − of data that were taken with theMB trigger alone were used for systematic error stud-ies. Photons were detected with the EMCal, and chargedparticles were detected with the DC and PC1. Measuredparticles in each PHENIX Central Arm were clusteredusing a cone method to form a ‘reconstructed jet’ and itstransverse momentum ( p reco T ). Because of the finite sizeof the acceptance ( | η | < . A LL of inclusive jet pro-duction were calculated as a function of jet transversemomentum ( p NLO T ) within the framework of a next-to-leading-order perturbative QCD (NLO pQCD). This cal-culation predicted various A LL ’s by assuming various∆ G ( x ) distributions.A simulation with the pythia event generator [4] andthe geant detector simulation package [17] was per-formed to understand the effects of the detector response,the underlying events and the jet-definition differencebetween the measurement and the theory calculation. pythia simulates parton-parton hard scatterings in p + p collisions at leading order (LO) in α s with phenomeno-logical initial and final-state radiation and hadroniza-tion. geant simulates the acceptance and response ofthe PHENIX detector. We define a jet at the partoniclevel in pythia . The effect of the detector response andthe underlying events was evaluated as the statistical re-lation between the jets defined in pythia and the recon-structed jets. We assume p PY T = p NLO T within an uncer-tainty that will be explained in a later section, and thenwe obtained the relation between the NLO calculationand the measurement.To confirm that the simulation reproduces well the realdata in terms of event structure, namely spatial distribu-tion of particles in an event, quantities sensitive to eventstructure were measured. Those include particle mul-tiplicity, transverse-momentum density, thrust distribu-tion and jet-production rate. A comparison was madebetween the real data and the simulation output.We derive the predictions of the measured A LL by con-verting the NLO calculation with the relation between p NLO T and p reco T . A χ test between the measured andpredicted A LL ’s was performed to determine the most-probable ∆ G .The definitions and relations of jets in this measure-ment are summarized in Tab. I and Fig. 2. B. Particle Clustering with Cone Method
A jet in one PHENIX Central Arm is constructed withphotons and charged particles detected with the EMCal,the DC and the PC1 of the Central Arm. A seed-conealgorithm, described below, is used for the cluster finding.
TABLE I: Definitions of jets adopted in this measurement.Reconstructed jet( p reco T ) Hadronic jet made with measurableparticles after hadronizationwith a cone size of R = 0 . pythia ( p PY T ) Partonic jet in pythia without cone.jet in NLO calcula-tion( p NLO T ) Partonic jet in NLO pQCD calc.with a cone size of δ = 1 .
1. Event and particle selections
To select the energy region where the efficiency of thehigh- p T photon trigger is in the plateau, at least onephoton with p T > . /c is required in each event.This requirement causes a bias towards jets that includemostly high- p T π , η , etc. or radiated photons.To collect photons from all EMCal hits, a p T cut, acharged track veto, and an EMCal shower shape cut wereapplied. The p T cut required the p T of each EMCal hitto be > . /c in order to eliminate hits likely to bedominated by electronics noise in the detector. It alsoeliminates charged hadron hits because the measured en-ergy of minimum ionization particles by PbSc peaks at0.25 GeV. and that of π ± with momentum of 1 GeV/ c inthe PbGl result in a distribution peaked around 0.4 GeV,with a broad tail to lower energy. The charged trackveto reduces charged particle contamination by checkingwhether each EMCal hit has a matched charged trackwithin 3 σ of their position resolutions. The shower shapecut reduces hadron contamination by comparing the frac-tion of energy deposits in every EMCal module of a hitwith the fraction predicted by a model of shower shape.This cut eliminates half of hadron hits and statistically1% of photon hits. These cuts made the contaminationof charged and neutral hadrons negligible.All charged particles detected with the DC and thePC1 were required to have p T ranging from 0.4 to 4.0GeV/ c . Below the lower limit, the acceptance is stronglydistorted due to a large bending angle and thus becomesshifted from that of photons. The upper limit eliminatesfake high- p T tracks which originate from low- p T particles that are produced from a decay or a conversion in themagnetic field. Note that this limit causes a bias towardsjets that include fewer charged particles.
2. Cluster finding algorithm
All particles that satisfy the experimental cuts in onearm were used as a seed in cluster finding. Starting withthe momentum direction of a seed particle as a tempo-rary cone axis, we calculated the next temporary coneaxis with particles which are in the cone. The distancebetween the cone axis ( η C , φ C ) and the momentum di-rection of each particle ( η i , φ i ) is defined as R i ≡ q ( η i − η C ) + ( φ i − φ C ) . (3)The cone radius R was set to 0.3, which was about a halfof the η acceptance of the detector. The next temporarycone axis ~e next is calculated as a vector sum of momentaof particles in the cone: ~e next ≡ ~p reco | ~p reco | , ~p reco ≡ X i ∈ cone ~p i . (4)This procedure was iterated until the temporary coneaxis became stable.The cluster finding is done with all seed particles, andthen each seed particle has one cone and some conescan be the same or overlapped. The cone which has thelargest p reco T in an event is used in the event. For mea-surements of event structure we also define the sum ofmomenta of all particles in one arm: ~p sum ≡ X i ∈ arm ~p i . (5)An evaluation of p reco T without seed has been done us-ing a part of the statistics in order to check the effect ofthe use of a seed. Every direction in the ( η , φ ) space witha step of δη = δφ = 0 .
01 within the Central Arm accep-tance has been used as an initial cone direction in eachevent. All steps except the choice of the initial cone di-rections is the same as the original algorithm. The yieldof reconstructed jets with the seedless method was largerthan that with the seed method by ∼
20% at p reco T = 4GeV/ c , ∼
10% at p reco T = 8 GeV/ c and ∼
5% at p reco T = 12GeV/ c . This deviation is compensated in the relation be-tween p reco T and p PY T estimated with the simulation, andtherefore the p reco T difference between the two methods ofcluster finding is smaller than the deviation above. C. Simulation Study
1. Simulation settings
The pythia version 6.220 was used. Only QCD high- p T processes were generated by setting the process switch(“MSEL”) to 1 and the lower cutoff of partonic transversemomentum (“CKIN(3)”) to 1.5 GeV/ c . The parametermodification reduces the time for event generation anddoes not affect any physics results in the measured p T region, as it has been confirmed by comparing p reco T dis-tribution etc. to those without the parameter modifica-tion. We call a pythia simulation with these conditions‘ pythia default’. Hadron-hadron collisions have a so-called ‘underlying event’, which comes from the breakupof the incident nucleons. The pythia simulation repro-duces the underlying event with the Multi-Parton Inter-action (MPI) mechanism. The CDF experiment at theTevatron showed that the pythia simulation did not re-produce the event structure well and modeled a set oftuned parameters called ‘tune A’ [5, 18]. Modified orimportant parameters are listed in Tab. II. TABLE II: Important or modified (Used) parameters in the pythia
MPI setting.Parameter Default Used NoteMSTP(81) 1 1 MPI master switch.MSTP(82) 1 4 double-Gaussian matter distri-bution used.PARP(82) 1.9 2.0 turn-off p T for MPI at the ref-erence energy scale PARP(89)PARP(83) 0.5 0.5 the fraction of the core Gaus-sian matter to total hadronicmatterPARP(84) 0.2 0.4 the radius of the core GaussianmatterPARP(85) 0.33 0.9 the probability that two glu-ons are produced in MPI withcolors connecting to nearestneighborsPARP(86) 0.66 0.95 the probability that two glu-ons are produced in MPI withthe PARP(85) condition or asa closed loopPARP(89) 1000 1800 reference energy scale for theturn-off p T PARP(90) 0.16 0.25 energy dependence of the turn-off p T PARP(67) 1.0 4.0 hard-scattering scale µ multi-plied by this sets the maximumparton virtuality in initial-state radiationMSTP(51) 7 7 CTEQ 5L PDF used.MSTP(91) 1 1 Gaussian k T used.PARP(91) 1.0 1.0 width of k T distribution.PARP(93) 5.0 5.0 upper cutoff for k T dist. We call a pythia simulation with the tune-A setting‘ pythia
MPI’, although it has been adopted as defaultvalues in the pythia version 6.226 and later.We use the output of the ‘ pythia default’ and the‘ pythia
MPI’ simulations to estimate the effect of the underlying event on our measurement.The PHENIX experiment has developed its own geant π (2 γ ), π ± , K ± and p ± .
2. Relation between p reco T and p PY T The pythia + geant simulation was used to evaluatethe effect of the detector response and the underlyingevent on the p reco T measurement. The p T of a jet in pythia , which is represented by p PY T in this paper, shouldbe defined so that it is comparable with the theoreticaljet in order to evaluate the relation between the NLOcalculation and the measurement. The event-by-eventtransition from the jet in pythia ( p PY T ) to the recon-structed jet ( p reco T ) is simulated to obtain the statisticalrelation between them.A jet in pythia is defined as a hard-scattered partonthat has not undergone final-state parton splits, namelyparticle number 7 or 8 in the pythia event list. A simu-lated reconstructed jet is associated with one of the twopartons by minimizing the angle ∆ R = p ∆ η + ∆ φ .Figure 3 shows the ratio p reco T /p PY T at each p reco T bin, andFig. 4 shows the mean value of the ratios as a function of p reco T . The ratio of the pythia MPI output is ∼
80% onaverage and is larger than that of the pythia default out-put due to the contribution from the underlying event.The relation between reconstructed jets and jets in pythia can be characterized by multiple effects. Someparticles in a jet can leak from the cone because of thelimited acceptance, the small cone size and the absence ofa detector for neutral hadrons. Some particles producedby the underlying event can be included in the cone andcontaminate p reco T , and thus the ratio p reco T /p PY T can ex-ceed one. The p PY T of events that are in a p reco T bin isdistributed widely due to the finite p T resolution of thePHENIX Central Arm. Because a gluon jet is softer andbroader than quark jet [19, 20], the high- p T photon re-quirement has lower efficiency for gluon jets. Thereforethe ratio of p reco T to p PY T for gluon jets is smaller thanquark jets on average.Figure 5 shows the relative yields of quark+quark( q + q ), quark+gluon ( q + g ) and gluon+gluon ( g + g )subprocesses as a function of p PY T at each p reco T bin. Fig-ure 6 shows the fraction of g + g , q + g and q + q sub-processes as a function of p reco T . These were evaluatedwith the simulation. As explained above, the gg subpro-cess is suppressed in this measurement. The dominantsubprocess is q + g throughout the p reco T range. F r a c t i o n recoT PYTHIA defaultPYTHIA MPI recoT recoT recoT recoT recoT recoT
10 < p
PYT / p recoT p recoT
11 < p
FIG. 3: (color online) Distributions of the ratio p reco T /p PY T evaluated with (dashed black) pythia default and (solidgreen) pythia MPI. (GeV/c) recoT p > P Y T / p rec o T < p FIG. 4: (color online) The mean value of ratio p reco T /p PY T asfunctions of p reco T .
3. Relation between p PY T and p NLO T The cross section and the A LL of inclusive jet pro-duction in | η | < .
35 at √ s = 200 GeV were calculatedwithin the NLO pQCD framework with the CTEQ6Munpolarized PDF under the Small Cone Approximation(SCA) [21–23]. We adopted a cone size of δ = 1 . (GeV/c) PYT p < 12 GeV/c recoT
11 < p < 11 GeV/c recoT
10 < p < 10 GeV/c recoT < 9 GeV/c recoT < 8 GeV/c recoT < 7 GeV/c recoT < 6 GeV/c recoT R e l a t i v e y i e l d < 5 GeV/c recoT FIG. 5: (color online) The relative yields of q + q , q + g and g + g subprocesses in the pythia + geant simulation. Theresults with all the subprocesses combined are also shown. µ = p T , 2 p T and p T / p NLO T needs to be connected with p PY T in order toevaluate the relation between the NLO calculation andthe measurement, where the relation between p PY T and p reco T was obtained from the pythia + geant simulation.We assume p PY T = p NLO T , and thus the relation betweenthe jet in pythia and the measurement can be inter-preted as the relation between the NLO calculation andthe measurement. However the definition of p PY T and p NLO T has a discrepancy, and they become close to eachother only as the cone half-aperture ( δ ) in the theorybecomes large. Therefore we set δ to 1.0, which is theupper limit where the SCA is applicable, and evaluatedthe discrepancy between p PY T and p NLO T with δ = 1 . δ = 1 . pythia simulation; the former is related to (GeV/c) recoT p Subp r o ce ss f r a c t i o n FIG. 6: (color online) Subprocess fractions of reconstructedjets as functions of p T . It was evaluated with the pythia MPIand geant simulation. It should be noted that the gluon-quark reaction is the dominant reaction in all the momentumregion from 4 to 12 GeV/ c . (GeV/c) jetT p ) ( pb / G e V / dp s E d
10 pQCD NLO = 1 d | < 0.35, h | FIG. 7: Unpolarized jet cross section at a pseudorapidity | η | < .
35 with a cone half-aperture δ = 1. It was calculatedat NLO under the SCA with three factorization scales, µ = p T ( solid line ), 2 p T ( lower dashed line ) and p T / upperdashed line ). the angle between two splitting partons and the latter isrelated to the angle between stable particles.
4. Uncertainty due to difference in jet definitions
The uncertainty due to the jet-definition difference be-tween the pythia and NLO calculations with δ = 1 . pythia . One definition is the jet in pythia defined above. The other assumes a cluster of partonswith a cone size of δ = 1 . pythia , where partonsoriginating from the underlying event are excluded. Forthe latter definition the jet p T is denoted p in cone T . Since p in cone T and p NLO T are defined similarly, i.e. both at thepartonic level and with the same cone size δ , we assume that the scales of p in cone T and p NLO T are the same. Thenthe difference between p in cone T and p PY T , which can beevaluated using pythia , is considered to be the differ-ence between p NLO T and p PY T .Figure 8 shows distributions of the fraction p in cone T /p PY T at three typical p PY T bins. This indi-cates that the p T scales of the two jet definitions havea 10% difference on average in the p T range of thesemeasurements. Therefore the uncertainty due to thejet-definition difference between pythia and the NLOcalculation with δ = 1 . p T scale. PYT / p in coneT p E v e n t f r a c t i o n PYT / p in coneT range,
PYT p 5 - 6 GeV/c, 0.9215 - 16 GeV/c, 0.9325 - 26 GeV/c, 0.91
FIG. 8: (color online) Distributions of the fraction p in cone T /p PY T evaluated with a pythia simulation at three typ-ical p PY T bins.
5. Reproducibility Check
Figure 9 shows the distribution of p reco T measured withthe clustering method described above. The simulationoutputs have been normalized so that they match the realdata at p T ∼ c . The slope of the pythia MPI out-put agrees better with that of the real data, where thatof the pythia default output is less steep. The relativeyield between the real data and the pythia
MPI outputis consistent within ±
10% over five orders of magnitude.Figure 10 shows distributions of the fraction p trig γT /p reco T , where p trig γT is p T of the trigger photon. Thelower cutoff of the distributions is due to the minimum p T of the trigger photon ( > c ). The rightmost bin( p trig γT /p reco T ∼
1) contains events in which only a triggerphoton exists. Such events can occur by the limited ac-ceptance, by the EMCal masked area (particles except atrigger photon in jet are not detected), by EMCal noise orby direct photon events. The difference between the realdata and the simulation outputs in the rightmost bin mayindicate that these effects are not completely reproducedby the simulation, but the difference is small ( < Y i e l d ( a r b i t r a r y un i t) Real dataPYTHIA defaultPYTHIA MPIsimulations are normalized to ~ 8 GeV/c T match real data at p (GeV/c) recoT p S i m u l a t i o n / R e a l d a t a FIG. 9: (color online) Reconstructed-jet yields as a functionof p reco T . The red, black and green points correspond to thereal data, the pythia default output and the pythia MPIoutput, respectively. The simulation outputs have been nor-malized so that they match the real data at p T = 8 GeV/ c .The ratio of the yields between the simulations and the realdata is shown at bottom. IV. RESULTS AND DISCUSSIONSA. Event structure
1. Multiplicity
Multiplicity is defined as the number of particles whichsatisfy the experimental cuts in one event. Figure 11(a)and (b) show the mean value of multiplicity in the CentralArm vs p sum T and in the cluster vs p reco T . The multiplici-ties in the arm and in the cluster of the simulation out-puts agree, on the whole, with that of the real data. The pythia MPI output is larger than the pythia defaultoutput as expected, and the real data are closer to the pythia default output. On the other hand, the p reco T dis-tributions (Fig. 9) shows better agreement between thereal data and the pythia MPI output. This indicatesthat the pythia
MPI reproduces the sum of p T of parti-cles well, which is less sensitive to particle fragmentationprocess, while it does not reproduce the particle multi-plicity very well. The reproducibility of the summed p T is checked in measurements described later.Figure 11(c) and (d) show the ratio of charged-particlemultiplicity to photon multiplicity in the Central Arm F r a c t i o n recoT Real dataPYTHIA defaultPYTHIA MPI recoT recoT recoT recoT recoT recoT
10 < p recoT / p trig phT p recoT
11 < p
FIG. 10: (color online) The fraction of p T of the triggerphoton in each p reco T . and in the cluster. The real data lies below the pythia default and MPI results for both multiplicities. This in-dicates that the effect of the underlying event in the ra-tios is small, and the difference between the real data andthe pythia results is mainly caused by the imbalance be-tween photons and charged particles in jet. Figure 11(e)and (f) show the ratio of the sum of charged-particle p T to the sum of photon p T . These have the same tendencyas the multiplicity ratios.
2. Transverse momentum density
The p T density, D P T (∆ φ ), is defined as D p T (∆ φ ) ≡ * δφ X i in[∆ φ, ∆ φ + δφ ] p T i + event , (6)where ∆ φ is φ angle with respect to the direction of atrigger photon in event, δφ is an area width in φ direc-tion, and p T i is transverse momentum of i -th particle inevent. The p T density means the area-normalized totaltransverse momentum in an area of δφ × δη at a distance∆ φ from trigger photon, where δη is the width of theCentral Arm acceptance.1 (GeV/c) sumT p4 6 8 10 12 1400.20.40.60.811.21.4 sum phT / p sum chT (e) p sum ph / n sum ch (c) n (a) photon + charged multiplicity in arm Real dataPYTHIA defaultPYTHIA MPI (GeV/c) recoT p4 6 8 10 12 1400.20.40.60.811.21.4 reco phT / p reco chT (f) p reco ph / n reco ch (d) n (b) photon + charged multiplicity in reco. jet
FIG. 11: (color online) (a) : Mean multiplicity in the CentralArm vs p sum T . (b) : Mean multiplicity in the cluster vs p reco T . (c) : The ratio of charged multiplicity to photon multiplicityin the Central Arm. (d) : Same as (c) but in the cluster. (e) :The ratio of charged p T to photon p T in the Central Arm. (f) : Same as (e) but in the cluster. We name the region at ∆ φ . . φ & . D p T in the transverse region is sen-sitive to the underlying event. FIG. 12: (color online) Measurement condition of the p T density. The arc and the × mark represent one Central Armand the collision point in the beam view. As illustrated in Fig. 12, to avoid the effect of thePHENIX Central Arm acceptance in the calculation of D p T , we limited the φ direction of the trigger photonsto less than 20 ◦ from one edge of the PHENIX CentralArms, and we did not use photons and charged particleswhich were in the φ area between the trigger photon andthe near edge. With this method the D p T distributionis not affected by the finite acceptance of the PHENIX Central Arms up to 70 ◦ ( ∼ ( G e V / c / r a d ) f ) / d T i p i S d ( -1 < 5 GeV/c sumT Real dataPYTHIA defaultPYTHIA MPI -1 < 6 GeV/c sumT -1 < 7 GeV/c sumT -1 < 8 GeV/c sumT -1 < 9 GeV/c sumT -1 < 10 GeV/c sumT -1 < 11 GeV/c sumT
10 < p from trigger photon f D -1 < 12 GeV/c sumT
11 < p
FIG. 13: (color online) p T density, D P T = d Σ i p Ti /dφ (GeV/ c /rad), in each p sum T bin. Trigger photons are includedin the leftmost points. Figure 13 shows the D p T distributions for each p sum T range. In the “toward” region, the simulation outputsagree well with the real data. It shows that the shapeof jets produced by the simulation is consistent with thereal data. In the “transverse” region, the pythia defaultoutput is generally smaller than the real data. This isan indication that the pythia default does not containsufficient total p T of soft particles from the underlyingevent. The pythia MPI output agrees with the real datawell.
3. Thrust distribution in PHENIX Central Arm
We evaluated the thrust variable defined in the CERN-ISR era with particles in one PHENIX Central Arm(∆ η = 0 .
7, ∆ φ = 90 o ): T P H ≡ max u P i | p i · u | P i | p i | = P i | p i · ˆ p | P i | p i | (7)ˆ p = P i p i | P i p i | , (8)2where u is a unit vector which is called the thrust axisand is directed to maximize T , and p i is a momentumof each particle in one arm. If only particles in a halfsphere in an event are used, T P H can be written as theright-side formula in Eq. 7.The distribution of T P H of isotropic events in thePHENIX Central Arm acceptance for each p sum T bin wassimulated with the following method. First, the crosssection of inclusive particle production is assumed tobe proportional to exp( − p T (GeV /c )) and is indepen-dent of η and φ . Second, the same cuts as the experi-mental conditions are applied numerically: the geomet-rical acceptance ( | η | < .
35, ∆ φ = 90 o ), the momen-tum limit ( p T > . /c ), and one high- p T particle( p T > . /c ). Third, the distribution of T P H ofisotropic events was calculated for each number of par-ticles in one event ( f n ( T ) for n = 1 , , , . . . ). The T P H distribution of n = 2 events is particularly steep. Thuswe applied a cut of n ≥ T P H measurement. The f T is evaluated as the sum of f n ( T )’s weighted by theprobability ( ǫ n ) that the number of particles per event is n : f ( T ) = X n ǫ n f n ( T ) , ǫ n = N n evt N evt , (9)where ǫ n was derived from the real data.Figure 14 shows the T P H distribution in each p sum T range. The pythia MPI output agrees with the real datawell. The pythia default has a steeper slope, which indi-cates that the number of particles in the vicinity of jetsin the pythia default is insufficient. In the real data,the pythia default output and the pythia
MPI output,the T P H distribution becomes sharper as p sum T increases.This is due to the fact that the transverse momentum( j T ) of a jet is independent of its longitudinal momen-tum and is almost constant.If the real data includes a contribution from non-jet(isotropic) events, the T P H distribution of the real datais a mixture of the distribution of the simulation outputand the distribution of the isotropic case. The contri-bution from non-jet events can be judged to be negligi-ble because the pythia
MPI output reproduces the dataeven though it does not have isotropic events.
B. Jet production rate
1. Evaluation method (measurement)
The jet production rate Y , namely the yield of recon-structed jets per unit luminosity, is defined with mea-sured quantities as Y i ≡ N ireco L · f MB · f ph , (10)where L is the integrated luminosity; f MB and f ph arethe efficiencies of the MB trigger (see Sec. II C) and Thrust in PHENIX < 12 GeV/c sumT
11 < p < 11 GeV/c sumT
10 < p < 10 GeV/c sumT < 9 GeV/c sumT < 8 GeV/c sumT < 7 GeV/c sumT < 6 GeV/c sumT F r a c t i o n < 5 GeV/c sumT Real dataPYTHIA defaultPYTHIA MPIIsotropic event
FIG. 14: (color online) T PH distribution in each p sum T bin. Alldistributions have been normalized so that their areas wereequal to one another. The purple lines are the distributionsof isotropic events in the acceptance of the PHENIX CentralArms, which are evaluated with Eq. 9. the high- p T photon trigger, respectively; N ireco is thereconstructed-jet yield in a i -th p reco T bin. The high- p T photon trigger efficiency f ph was estimated to be0 . ± .
02, where the inefficiency is caused by the 10% ofthe EMCal acceptance where the trigger was disabled dueto electronics noise. The inefficiency is slightly smallerthan the disabled acceptance because a particle clutercan contain multiple high- p T photons.
2. Evaluation method (prediction)
On the other hand, the variable Y is expressed withtheoretical and simulation quantities as Y i ≡ X j f ij · ǫ jtrig + acc · Y jtheo , (11)where the label i and j are the indices of p reco T and p NLO T bins, respectively. The Y jtheo is a jet production ratewithin | η | < .
35 in a j -th p NLO T bin, which is theoreti-cally calculated. The ǫ jtrig + acc is a high- p T -photon triggerefficiency and acceptance correction, which is evaluated3with the pythia + geant simulation. The ǫ jtrig + acc ·Y jtheo is a yield of jets that include a high- p T photon within | η | < .
35. The f ij is the probability that a jet withina j -th p NLO T bin is detected as a reconstructed jet withina i -th p reco T bin. This method uses the relative p reco T dis-tribution in each p NLO T bin and thus the slope of the p PY T distribution in the simulation does not affect the resultof Y i .The correction factor ǫ jtrig + acc is a fraction, whose nu-merator is the number of events in which at least onephoton with p T > c is detected, and whose de-nominator is the number of events in which jets are in | η | < .
35. The condition “ p T > c ” in the numer-ator corrects a high- p T photon efficency, i.e. the probabil-ity that a high- p T photon in jets must be detected withthe EMCal. The condition “ | η | < .
35” in the denomina-tor and the absence of it in the numerator corrects an ac-ceptance for jets, i.e. the fact that a part of reconstructed-jets does originate from jets with | η | > .
35. Figure 15shows ǫ jtrig + acc as a function of p NLO T estimated with the pythia default and MPI simulations. (GeV/c) PYT p T r i gg er e ff i c i e n c y + a ce p t a n ce c o rrec t i o n -3 -2 -1
10 PYTHIA defaultPYTHIA MPI
FIG. 15: (color online) The correction factor ǫ jtrig + acc forhigh- p T photon trigger efficiency and acceptance effect. The pythia default ( black ) and the pythia MPI setting ( green )were used.
To estimate a systematic error related to the simula-tion reproducibility of high- p T photon, we evaluated, inboth the real data and the simulations, the ratio ( r ) ofthe reconstructed-jet yields in the high- p T photon trig-gered sample to that in the MB triggered sample. The r of the pythia MPI output is 5% at p reco T = 4 GeV/ c and50% at p reco T = 12 GeV/ c , and is consistent with that ofthe real data within ± pythia MPI simulation. The r of the pythia defaultoutput is smaller by 20-30% than that of the real data.
3. Result
Figure 16 shows the jet production rate. The mainsystematic errors are listed in Tab. III. The main uncer- tainties of the measurement are the BBC cross sectionand the EMCal energy scale. These errors are fully cor-related bin-to-bin. The error on the EMCal energy scaleincludes both the change of p T of individual photons andthe change of the threshold of the high- p T photon require-ment. In comparing the measurement and the calcula-tion, the 10% p T scale uncertainty of the jet definitionsin the pythia simulation and the NLO pQCD theorymakes a 30% error at low p T or 70% at high p T , and isthe largest source. The uncertainty of the renormaliza-tion and factorization scales in the NLO jet productioncross section makes a 30% error. The calculation with pythia MPI agrees with the measurement within errorsover the measured range 4 < p reco T <
15 GeV/ c . R ec o n s t r u c t e d -j e t y i e l d ( pb ) Measurement systematic errorCalculation systematic error T /2 or 2p T = p m with different theory scales (GeV/c) recoT p4 6 8 10 12 14 M e a s u re m e n t / c a l c u l a t i o n FIG. 16: (color online) (top) Reconstructed jet yield and(bottom) the ratio of the real data to the calculations. (redpoints) Real data with the (gray band) experimental system-atic error. (black curves) pythia
MPI calculation with theoryfactorization scales of (solid curve) p T , (upper dashed curve) p T /
2, and (lower dashed curve) 2 p T . (dotted curves) Varia-tion caused by 10% p T scale uncertainty around the calcula-tion. Statistical uncertainties are smaller than the size of thepoints. The result with pythia default is smaller than theresult with pythia
MPI by 50% at p reco T = 4 GeV/ c ,by 35% at p reco T = 9 GeV/ c and by 20% at p reco T = 14GeV/ c . It can be fully explained by the difference visi-ble in Fig. 15 between pythia default and pythia MPI.According to the comparisons of the event structure, pythia
MPI reproduces the spatial distribution of parti-cle momenta in one event much better than the pythia default. Therefore, for the jet production rate evaluated4
TABLE III: Main systematic errors of the jet production rate.Source Size Size on rateMeasurementLuminosity 9.7% 9.7%EMCal energy scale 1.5% 7-6%Tracking momentum scale 1.5% 0-3%CalculationJet definition 10% in p T p T photon fragmentation – 10%Simulation statistics – 2-5% with pythia MPI simulation, the error due to possibleinsufficient tunings of pythia
MPI should be smallerthan the difference of the jet production rate betweenthe pythia
MPI simulation and the pythia default sim-ulation.
C. Double helicity asymmetry A LL
1. Evaluation method (measurement) A LL is expressed with measured quantities as A LL = 1 | P B || P Y | ( N ++ + N −− ) − R ( N + − + N − + )( N ++ + N −− ) + R ( N + − + N − + )(12) R ≡ L ++ + L −− L + − + L − + , (13)where N ++ etc. are reconstructed-jet yields with collid-ing proton beams having the same (++ or −− ) and op-posite (+ − or − +) helicity; P B and P Y are the beampolarizations; R is the relative luminosity, i.e. the ratioof the luminosity with the same helicity ( L ++ + L −− )to that with the opposite helicity ( L + − + L − + ). A LL ismeasured fill-by-fill and the results are fit to a constant,because the beam polarization and the relative luminos-ity are evaluated fill-by-fill to decrease systematic errors.The average fill length was about five hours. The inte-grated luminosity used was 2.1 pb − . It is 0.1 pb − lessthan the statistics used in the production rate measure-ment because the data with bad conditions on the beampolarization were discarded.The relative luminosity at PHENIX was evaluatedwith the MB trigger counts ( N ++MB and N + − MB ) as R = N ++MB /N + − MB . A possible spin dependence of MB-triggereddata causes an uncertainty on the relative luminosity.The error has been checked by comparing the relativeluminosity with another relative luminosity defined withthe ZDCLL1 trigger counts. The ZDCLL1 trigger is firedwhen both the north ZDC and the south ZDC have a hit and the reconstructed z -vertex is within 30 cm of thecollision point.The beam polarizations were measured with the pCand H-jet polarimeters [24, 25] at the 12 o´clock inter-action point on the RHIC ring. One of the collidingbeam rotating clockwise is called “blue beam”, and theother rotating counterclockwise “yellow beam”. Theluminosity-weighted-average polarizations are 50.3% forthe blue beam and 48.5% for the yellow beam. The sumof statistical and systematic errors on h P B ih P Y i is 9.4%.
2. Evaluation method (prediction)
Polarized/unpolarized cross sections of jet productionfor every subprocess ( q + q , q + g and g + g ) were cal-culated at NLO based on the SCA with a cone size of δ = 1 .
0. The polarized cross sections were calculated us-ing various ∆ G ( x ) in order to compare the measured A LL with various predicted A LL ’s and find the most-probable∆ G ( x ). Figure 17 shows the distributions of the ∆ G ( x )used, and the integrated values are Z dx ∆ G ( x, µ = 0 . )= − .
24 (∆ G = − G ) , − . , − . , − . , − . , − . , − . , − . , G = 0) , .
24 (GRSV − std) , . , . , . , . , .
24 (∆ G = G ) (14)Each ∆ G ( x ) (except the GRSV-std, the ∆ G = G input,the ∆ G = 0 input and the ∆ G = − G input) have beenobtained by refitting the GRSV parameters to the DISdata which were used in the original GRSV analysis [26].It is noted that the DIS data used in GRSV are the dataup to the year 2000 and thus are much less than thatused in the updated analysis, DSSV [27], for example.The polarized PDF in the GRSV parameterization is ofthe form:∆ f ( x, µ ) = N f x α f (1 − x ) β f f ( x, µ ) GRV , (15)where f is u , d , ¯ q or G ; µ = 0 . is the initialscale at which the functional forms are defined as above; f ( x, µ ) GRV is the unpolarized PDF of the GRV98 anal-ysis [28]; N f , α f and β f are free parameters. In the refitof the DIS data, the integral value of ∆ G ( x ) from x = 0to 1 was fixed to its particular value listed above, and theshape of ∆ G ( x ) and the quark-related parameters weremade free. The χ of the refitting to the DIS data is 170for the 209 data points [26] when the integral of ∆ G is0 at the initial µ , for example. In the remainder of this5 Bjorken x -2 -1
10 1 G / G D -1-0.8-0.6-0.4-0.2-00.20.40.60.81 = 1 GeV m G = G D G = +0.70 D G = +0.60 D G = +0.45 D G = +0.30 D GRSV stdG = 0 D G = -0.15 D G = -0.30 D G = -0.45 D G = -0.60 D G = -0.75 D G = -0.90 D G = -1.05 D G = -G D FIG. 17: (color online) Assumed gluon distribution functionsat µ = 1 GeV . The integral R dx ∆ G ( x ) of each distributionat the initial scale µ = 0.4 GeV is, from bottom to top at x = 0 .
15, -1.24 (∆ G = − G ), -1.05, -0.90, -0.75, -0.60, -0.45,-0.30, -0.15, 0 (∆ G = 0), 0.24 (GRSV-std), 0.30, 0.45, 0.60,0.70 and 1.24 (∆ G = G ). paper we concentrate on investigating the χ of the sixdata points of the reconstructed-jet A LL .The various ∆ G ( x ) above were evolved up to a scale µ of every event in the A LL calculation. The A LL ofevery subprocess ( A q + qLL , A q + gLL and A g + gLL ) can be derivedas functions of p NLO T from the unpolarized and polarizedcross sections. The pythia + geant simulation producesthe relative yields of every subprocess ( n q + q ( p NLO T , p reco T ), n q + g ( p NLO T , p reco T ) and n g + g ( p NLO T , p reco T )), as shown inFig. 5. A reco LL ( p reco T ) is calculated as a mean of A q + qLL , A q + gLL and A g + gLL weighted by the fractions of events: A reco LL ( p reco T )= Z dp NLO T X i sub n i sub ( p NLO T , p reco T ) · A i sub LL ( p NLO T ) Z dp NLO T X i sub n i sub ( p NLO T , p reco T ) , (16)where i sub is q + q , q + g and g + g . As an estimation ofsystematic errors, the slope of jet yields and the fractionof subprocesses were compared between the theory cal-culation and the pythia simulation. Note that both theslope and the fraction that we compared have not beenbiased by the high- p T photon and the small cone, sincethe theory calculation cannot provide biased values. Thevariations of A reco LL caused by both the slope differenceand the fraction difference are negligible in comparisonwith other errors.
3. Result
Figure 18 shows measured A reco LL and four predic-tion curves. Table IV shows the values of measured A reco LL . The measured A LL is consistent with zero, as the χ /n.d.f. between the data points and zero asymmetry( A LL = 0) is 1.3/6. The systematic error of the relativeluminosity is much smaller than the statistical error on A LL and is negligible. On the prediction curves the sys-tematic error related to the fractions of subprocesses aresmaller than the 10% p T scale uncertainty by roughly anorder of magnitude. Therefore it is not included in thisplot. (GeV/c) recoT p4 6 8 10 12 LL J e t A -0.06-0.04-0.0200.020.040.060.08 G=G input D GRSV-stdG=0 input D G=-G input D , 49% pol.) -1 Run5 (2.1 pb9.4% pol. scale error not shown scale error not shown T
10% p
FIG. 18: (color online) Reconstructed-jet A LL as a functionof p reco T . (red points) Measurement with statistical error bars.(black lines) Calculation based on four ∆ G ( x ) functions andthe pythia MPI + geant simulation.TABLE IV: Measured reconstructed-jet A LL . p reco T range and mean (GeV/ c ) A LL stat error4-5, 4.42 -0.0014 0.00375-6, 5.43 -0.0005 0.00596-7, 6.43 0.0058 0.00897-8, 7.44 0.0034 0.01328-10, 8.79 0.0077 0.015210-12, 10.81 -0.0181 0.0282 It has been confirmed with a “bunch shuffling” methodthat the size of the statistical errors assigned is appropri-ate. In this method, the helicity of every beam bunch wasnewly assigned at random and A reco LL was evaluated again.Repeating this random assignment produced a large setof A reco LL values. Its mean value should be of course zeroand was confirmed in this exercise. Its standard devia-tion indicates the size of the statistical fluctuation, andwas consistent with the statistical errors assigned. Thepoint-to-point variance seems smaller than the statisti-cal errors of the data points, but we could not find any6unrecognized cause such as a statistical correlation. Weconclude that the small variance of the data points hap-pened statistically despite its small probability.As a systematic error check, the single spin asymmetry A L was measured. It is defined as A L ≡ σ + − σ − σ + + σ − = 1 P N + − R N − N + + R N − , R ≡ L + L − , (17)where N + and N − are reconstructed-jet yields with onecolliding proton beam having the positive and negativehelicity, respectively; P is the beam polarization; R isthe relative luminosity, i.e. the ratio of the luminositywith the positive helicity ( L + ) to that with the negativehelicity ( L − ). As the jets are produced via the strongforce, A L must be zero under the parity symmetry. Thusany non-zero value indicates systematic errors.Figure 19 shows measured A L . A L was measured forthe polarization of one colliding beam while the otherbeam was assumed to be unpolarized. No significantasymmetry was observed. (GeV/c) recoT p L J e t A -0.03-0.02-0.0100.010.020.03 blue beam pol.yellow beam pol.combined FIG. 19: (color online) Jet A L as a function of p reco T . Theblue and green points are the results using the polarizationsof the blue beam and the yellow beam, respectively. The redpoints are the averages of the blue and green points.
4. Constraint on ∆ G To determine the range of x gluon probed by this mea-surement, the pythia MPI simulation without geant was used to obtain event-by-event x gluon (one value perq-g scattering event, two values per g-g, or none per q-q)and also µ . Figure 20 and 21 show the distributions of x gluon and µ , respectively. The x gluon value where theyield is half maximum is 0.02 at the lower side of the“4 < p reco T <
5” distribution and 0.3 at the upper side ofthe “10 < p reco T <
12” distribution. Therefore we adopta range of 0 . < x gluon < . G ( x )at the measured x gluon range, below the range and abovethe range. The measured x gluon range includes ∼
70% of distributions in all the four GRSV models shown. Withthe same procedure, the µ range probed was estimatedto be 5 < µ <
300 GeV . TABLE V: Partial integral of ∆ G ( x ) at µ = 1 GeV .Model R dx ∆ G ( x ) at each x range10 − -0.02 0.02-0.3 0.3-1 10 − -1∆ G = − G input -0.406 -1.09 -0.208 -1.71(24%) (64%) (12%)∆ G = 0 input 0.00808 0.0644 0.00869 0.0812(10%) (79%) (11%)GRSV-std 0.0684 0.258 0.102 0.427(16%) (60%) (24%)∆ G = G input 0.427 1.22 0.226 1.87(23%) (65%) (12%) gluon x -2 -1
10 1 Y i e l d p er b i n re l a t i v e t o m ax recoT p 4 to 5 5 to 6 6 to 7 7 to 8 8 to 10 10 to 12 FIG. 20: (color online) Distributions of x gluon in events thatinclude a reconstructed jet with 4 < p reco T <
12 GeV/ c . ) (GeV m Y i e l d p er b i n re l a t i v e t o m ax recoT p 4 to 5 5 to 6 6 to 7 7 to 8 8 to 10 10 to 12 FIG. 21: (color online) Distributions of µ in events thatinclude a reconstructed jet with 4 < p reco T <
12 GeV/ c . Figure 22 shows the χ between the 6 data pointsand the prediction curves as a function of the integral7 R . . dx ∆ G ( x, µ = 1) for each prediction curve. Thevalue of µ (= 1 GeV ) has been arbitrarily chosen inorder to show the value of the ∆ G integral in horizon-tal axis. Actual µ used in the A LL calculation variesdepending on jet p T . ) = 1 GeV m G (GRSV, x = [0.02, 0.3], D -1 -0.5 0 0.5 1 ) LL ( J e t A c T
10% pG=-G D G=0 D std G=G D FIG. 22: (color online) χ between the measured A LL andthe calculated A LL as a function of the integrated value of∆ G ( x ). The minimum of the χ is ∼ . G = 0 .
07, namelythe GRSV ∆ G = 0 input. The 95% and 99% confidencelimits are where the χ increases from the minimum by4 and 9, respectively. We obtained − . < Z . . ∆ G GRSV ( x, µ = 1) < . Z . . ∆ G GRSV ( x, µ = 1) < . G ( x ) are not included. Also the fact that the shapeof the polarized PDFs is parameterized into Eq. 15 maycause additional uncertainty in ∆ G ( x ). V. CONCLUSION
We measured the event structure and the double he-licity asymmetry ( A LL ) in jet production at midrapidity( | η | < .
35) in longitudinally polarized p + p collisionsat √ s = 200 GeV were measured. The main motiva-tion is to use this complementary approach to inclusivemeasurements to better understand the contribution ofthe gluon spin (∆ G ) to the proton spin. Because thismeasurement of A LL observes a larger fraction of the jetmomentum, it reaches higher p T and thus higher gluon x . The MPI-enhanced pythia simulation agrees well withthe real data in terms of the event structure: the multi-plicity of photons and charged particles, the p T densityas a function of the azimuthal angle from trigger photon,and the thrust in the PHENIX Central Arm. A smalldifference in the intra-jet structure, namely the fractionsof photons and charged particles in jets, was observedas shown in Fig. 11(c) to (f). Nevertheless, the simula-tion well reproduces the shape of jets and the underlyingevent at this collision energy.In the measurement of jet A LL , measured particleswere clustered by the seed-cone algorithm with a coneradius R = 0 .
3. The relation between p NLO T and p reco T wasevaluated with pythia and geant . The jet productionrate was measured and satisfactorily reproduced by thecalculation based on the NLO pQCD jet production crosssection and the simulation. The jet A LL was measuredat 4 < p reco T <
12 GeV/ c . The main systematic errors area p T scale uncertainty of 10% and a beam polarizationuncertainty of 9.4%. The x gluon range probed by thisjet measurement with 4 < p reco T <
12 GeV/ c is mainly0 . < x < . A LL was compared with the predicted values basedon the GRSV parameterization, and the comparison im-posed the limit − . < R . . dx ∆ G GRSV ( x, µ = 1) < . R . . dx ∆ G GRSV ( x, µ = 1) < . ACKNOWLEDGMENTS
We thank the staff of the Collider-Accelerator andPhysics Departments at Brookhaven National Labora-tory and the staff of the other PHENIX participating in-stitutions for their vital contributions. We also thankWerner Vogelsang for helpful discussions and calcula-tions. We acknowledge support from the Office of Nu-clear Physics in the Office of Science of the Department ofEnergy, the National Science Foundation, Abilene Chris-tian University Research Council, Research Foundationof SUNY, and Dean of the College of Arts and Sciences,Vanderbilt University (U.S.A), Ministry of Education,Culture, Sports, Science, and Technology and the JapanSociety for the Promotion of Science (Japan), ConselhoNacional de Desenvolvimento Cient´ıfico e Tecnol´ogicoand Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜aoPaulo (Brazil), Natural Science Foundation of China(People’s Republic of China), Ministry of Education,Youth and Sports (Czech Republic), Centre Nationalde la Recherche Scientifique, Commissariat `a l’´EnergieAtomique, and Institut National de Physique Nucl´eaireet de Physique des Particules (France), Ministry of In-dustry, Science and Tekhnologies, Bundesministerium f¨urBildung und Forschung, Deutscher Akademischer Aus-8tausch Dienst, and Alexander von Humboldt Stiftung(Germany), Hungarian National Science Fund, OTKA(Hungary), Department of Atomic Energy (India), IsraelScience Foundation (Israel), National Research Founda-tion and WCU program of the Ministry Education Sci-ence and Technology (Korea), Ministry of Education and Science, Russia Academy of Sciences, Federal Agency ofAtomic Energy (Russia), VR and the Wallenberg Foun-dation (Sweden), the U.S. Civilian Research and Devel-opment Foundation for the Independent States of theFormer Soviet Union, the US-Hungarian NSF-OTKA-MTA, and the US-Israel Binational Science Foundation. [1] J. Ashman et al. (European Muon Collaboration), Phys.Lett.
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