Measurement of ϕ-meson production at forward rapidity in p+p collisions at √s = 510 GeV and its energy dependence from √s = 200 GeV to 7 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Measurement of ϕ-meson production at forward rapidity in p+p collisions at √s = 510 GeV and its energy dependence from √s = 200 GeV to 7 TeV © the Authors, 2018. Funded by SCOAP3. Published version PHENIX Collaboration PHENIX Collaboration. (2018). Measurement of ϕ-meson production at forward rapidity in p+p collisions at √s = 510 GeV and its energy dependence from √s = 200 GeV to 7 TeV. Physical Review D, 98(9), Article 092006. https://doi.org/10.1103/PhysRevD.98.092006 2018 Measurement of ϕ-meson production at forward rapidity in p+pcollisions at ffiffi s p= 510 GeV and its energy dependence from ffiffi s p= 200 GeV to 7 TeV A. Adare,12 C. Aidala,42 N. N. Ajitanand,59,* Y. Akiba,54,55,†R. Akimoto,11 M. Alfred,23 N. Apadula,28,60 Y. Aramaki,54 H. Asano,34,54 E. T. Atomssa,60 T. C. Awes,50 B. Azmoun,7V. Babintsev,24 A. Bagoly,16 M. Bai,6N. S. Bandara,41 B. Bannier,60 K. N. Barish,8S. Bathe,5,55 A. Bazilevsky,7M. Beaumier,8S. Beckman,12 R. Belmont,12,42 A. Berdnikov,57 Y. Berdnikov,57 D. Black,8M. Boer,37 J. S. Bok,48 K. Boyle,55 M. L. Brooks,37 J. Bryslawskyj,5,8 H. Buesching,7 V. Bumazhnov,24 S. Campbell,13,28 V. Canoa Roman,60 C.-H. Chen,55 C. Y. Chi,13 M. Chiu,7I. J. Choi,25 J. B. Choi,10,* T. Chujo,63 Z. Citron,65 M. Connors,20,55 M. Csanád,16 T. Csörgő,17,66 T. W. Danley,49 A. Datta,47 M. S. Daugherity,1 G. David,7,60 K. DeBlasio,47 K. Dehmelt,60 A. Denisov,24 A. Deshpande,55,60 E. J. Desmond,7L. Ding,28 A. Dion,60 J. H. Do,67 A. Drees,60 K. A. Drees,6J. M. Durham,37 A. Durum,24 A. Enokizono,54,56 H. En’yo,54 S. Esumi,63 B. Fadem,43 W. Fan,60 N. Feege,60 D. E. Fields,47 M. Finger,9M. Finger, Jr.,9S. L. Fokin,33 J. E. Frantz,49 A. Franz,7A. D. Frawley,19 Y. Fukuda,63 C. Gal,60 P. Gallus,14 P. Garg,3,60 H. Ge,60 F. Giordano,25 A. Glenn,36 Y. Goto,54,55 N. Grau,2S. V. Greene,64 M. Grosse Perdekamp,25 Y. Gu,59 T. Gunji,11 H. Guragain,20 T. Hachiya,54,55 J. S. Haggerty,7K. I. Hahn,18 H. Hamagaki,11 S. Y. Han,18 J. Hanks,60 S. Hasegawa,29 T. O. S. Haseler,20 X. He,20 T. K. Hemmick,60 J. C. Hill,28 K. Hill,12 A. Hodges,20 R. S. Hollis,8K. Homma,22 B. Hong,32 T. Hoshino,22 N. Hotvedt,28 J. Huang,7,37 S. Huang,64 Y. Ikeda,54 K. Imai,29 Y. Imazu,54 J. Imrek,15 M. Inaba,63 A. Iordanova,8D. Isenhower,1D. Ivanishchev,53 B. V. Jacak,60 S. J. Jeon,44 M. Jezghani,20 Z. Ji,60 J. Jia,7,59 X. Jiang,37 B. M. Johnson,7,20 E. Joo,32 K. S. Joo,44 V. Jorjadze,60 D. Jouan,51 D. S. Jumper,25 J. H. Kang,67 J. S. Kang,21 S. Karthas,60 D. Kawall,41 A. V. Kazantsev,33 J. A. Key,47 V. Khachatryan,60 A. Khanzadeev,53 K. Kihara,63 C. Kim,8,32 D. H. Kim,18 D. J. Kim,30 E.-J. Kim,10 H.-J. Kim,67 M. Kim,58 M. H. Kim,32 Y. K. Kim,21 D. Kincses,16 E. Kistenev,7J. Klatsky,19 D. Kleinjan,8P. Kline,60 T. Koblesky,12 M. Kofarago,16,66 J. Koster,55 D. Kotov,53,57 S. Kudo,63 B. Kurgyis,16 K. Kurita,56 M. Kurosawa,54,55 Y. Kwon,67 R. Lacey,59 J. G. Lajoie,28 A. Lebedev,28 K. B. Lee,37 S. H. Lee,28,60 M. J. Leitch,37 M. Leitgab,25 Y. H. Leung,60 N. A. Lewis,42 X. Li,37 S. H. Lim,37,67 M. X. Liu,37 S. Lökös,16 D. Lynch,7Y. I. Makdisi,6M. Makek,65,68 A. Manion,60 V. I. Manko,33 E. Mannel,7H. Masuda,56 M. McCumber,37 P. L. McGaughey,37 D. McGlinchey,12,37 C. McKinney,25 A. Meles,48 M. Mendoza,8B. Meredith,13 W. J. Metzger,17 Y. Miake,63 A. C. Mignerey,40 D. E. Mihalik,60 A. J. Miller,1A. Milov,65 D. K. Mishra,4J. T. Mitchell,7 I. Mitrankov,57 G. Mitsuka,31,55 S. Miyasaka,54,62 S. Mizuno,54,63 P. Montuenga,25 T. Moon,67 D. P. Morrison,7 S. I. Morrow,64 T. V. Moukhanova,33 T. Murakami,34,54 J. Murata,54,56 A. Mwai,59 K. Nagai,62 S. Nagamiya,31,54 K. Nagashima,22 J. L. Nagle,12 M. I. Nagy,16 I. Nakagawa,54,55 H. Nakagomi,54,63 K. Nakano,54,62 C. Nattrass,61 P. K. Netrakanti,4M. Nihashi,22,54 T. Niida,63 R. Nouicer,7,55 T. Novák,17,66 N. Novitzky,30,60 A. S. Nyanin,33 E. O’Brien,7 C. A. Ogilvie,28 J. D. Orjuela Koop,12 J. D. Osborn,42 A. Oskarsson,38 K. Ozawa,31,63 R. Pak,7V. Pantuev,26 V. Papavassiliou,48 J. S. Park,58 S. Park,54,58,60 S. F. Pate,48 L. Patel,20 M. Patel,28 J.-C. Peng,25 W. Peng,64 D. V. Perepelitsa,7,12,13 G. D. N. Perera,48 D. Yu. Peressounko,33 C. E. PerezLara,60 J. Perry,28 R. Petti,7,60 C. Pinkenburg,7 R. Pinson,1R. P. Pisani,7A. Pun,49 M. L. Purschke,7P. V. Radzevich,57 J. Rak,30 I. Ravinovich,65 K. F. Read,50,61 D. Reynolds,59 V. Riabov,46,53 Y. Riabov,53,57 D. Richford,5T. Rinn,28 N. Riveli,49 D. Roach,64 S. D. Rolnick,8M. Rosati,28 Z. Rowan,5J. G. Rubin,42 J. Runchey,28 N. Saito,31 T. Sakaguchi,7H. Sako,29 V. Samsonov,46,53 M. Sarsour,20 K. Sato,63 S. Sato,29 S. Sawada,31 B. Schaefer,64 B. K. Schmoll,61 K. Sedgwick,8J. Seele,55 R. Seidl,54,55 A. Sen,28,61 R. Seto,8P. Sett,4 A. Sexton,40 D. Sharma,60 I. Shein,24 T.-A. Shibata,54,62 K. Shigaki,22 M. Shimomura,28,45 P. Shukla,4A. Sickles,7,25 C. L. Silva,37 D. Silvermyr,38,50 B. K. Singh,3C. P. Singh,3V. Singh,3M. J. Skoby,42 M. Slunečka,9R. A. Soltz,36 W. E. Sondheim,37 S. P. Sorensen,61 I. V. Sourikova,7P. W. Stankus,50 M. Stepanov,41,* S. P. Stoll,7T. Sugitate,22 A. Sukhanov,7T. Sumita,54 J. Sun,60 J. Sziklai,66 A. Takahara,11 A. Takeda,45 A. Taketani,54,55 K. Tanida,29,55,58 M. J. Tannenbaum,7S. Tarafdar,64,65 A. Taranenko,46,59 G. Tarnai,15 R. Tieulent,39 A. Timilsina,28 T. Todoroki,54,55,63 M. Tomášek,14 H. Torii,11 C. L. Towell,1M. Towell,1R. Towell,1R. S. Towell,1I. Tserruya,65 Y. Ueda,22 B. Ujvari,15 H. W. van Hecke,37 M. Vargyas,16,66 S. Vazquez-Carson,12 J. Velkovska,64 M. Virius,14 V. Vrba,14,27 E. Vznuzdaev,53 X. R. Wang,48,55 Z. Wang,5D. Watanabe,22 Y. Watanabe,54,55 Y. S. Watanabe,11,31 F. Wei,48 S. Whitaker,28 S. Wolin,25 C. P. Wong,20 C. L. Woody,7M. Wysocki,50 B. Xia,49 C. Xu,48 Q. Xu,64 L. Xue,20 S. 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Zou8 (PHENIX Collaboration) 1Abilene Christian University, Abilene, Texas 79699, USA 2Department of Physics, Augustana University, Sioux Falls, South Dakota 57197, USA PHYSICAL REVIEW D 98, 092006 (2018) 2470-0010=2018=98(9)=092006(13) 092006-1 Published by the American Physical Society 3Department of Physics, Banaras Hindu University, Varanasi 221005, India 4Bhabha Atomic Research Centre, Bombay 400 085, India 5Baruch College, City University of New York, New York, New York, 10010 USA 6Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA 7Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA 8University of California-Riverside, Riverside, California 92521, USA 9Charles University, Ovocný trh 5, Praha 1, 116 36, Prague, Czech Republic 10Chonbuk National University, Jeonju, 561-756, Korea 11Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan 12University of Colorado, Boulder, Colorado 80309, USA 13Columbia University, New York, New York 10027 and Nevis Laboratories, Irvington, New York 10533, USA 14Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic 15Debrecen University, H-4010 Debrecen, Egyetem t´er 1, Hungary 16ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary 17Eszterházy Károly University, Károly Róbert Campus, H-3200 Gyöngyös, Mátrai út 36, Hungary 18Ewha Womans University, Seoul 120-750, Korea 19Florida State University, Tallahassee, Florida 32306, USA 20Georgia State University, Atlanta, Georgia 30303, USA 21Hanyang University, Seoul 133-792, Korea 22Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan 23Department of Physics and Astronomy, Howard University, Washington, D.C. 20059, USA 24IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia 25University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 26Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia 27Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic 28Iowa State University, Ames, Iowa 50011, USA 29Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan 30Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland 31KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan 32Korea University, Seoul, 02841, Korea 33National Research Center “Kurchatov Institute,”Moscow, 123098 Russia 34Kyoto University, Kyoto 606-8502, Japan 35Physics Department, Lahore University of Management Sciences, Lahore 54792, Pakistan 36Lawrence Livermore National Laboratory, Livermore, California 94550, USA 37Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 38Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden 39IPNL, CNRS/IN2P3, Univ Lyon, Universit´e Lyon 1, F-69622, Villeurbanne, France 40University of Maryland, College Park, Maryland 20742, USA 41Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA 42Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA 43Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA 44Myongji University, Yongin, Kyonggido 449-728, Korea 45Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan 46National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia 47University of New Mexico, Albuquerque, New Mexico 87131, USA 48New Mexico State University, Las Cruces, New Mexico 88003, USA 49Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA 50Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 51IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, BP1, F-91406, Orsay, France 52Peking University, Beijing 100871, People’s Republic of China 53PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia 54RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan 55RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA A. ADARE et al. PHYS. REV. D 98, 092006 (2018) 092006-2 56Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan 57Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia 58Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea 59Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA 60Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA 61University of Tennessee, Knoxville, Tennessee 37996, USA 62Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan 63Tomonaga Center for the History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan 64Vanderbilt University, Nashville, Tennessee 37235, USA 65Weizmann Institute, Rehovot 76100, Israel 66Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Hungarian Academy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary 67Yonsei University, IPAP, Seoul 120-749, Korea 68Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32 HR-10002 Zagreb, Croatia (Received 6 October 2017; published 9 November 2018; corrected 16 November 2018) The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section of ϕð1020Þ-meson production at forward rapidity in pþpcollisions at ffiffiffi s p¼510 GeV via the dimuon decay channel. The partial cross section in the rapidity and pTranges 1.2<jyj<2.2and 2<p T<7GeV=c is σϕ¼½2.28 0.09ðstatÞ0.14ðsystÞ0.27ðnormÞ×10−2mb. The energy dependence of σϕ(1.2<jyj<2.2;2<p T<5GeV=c) is studied using the PHENIX measurements at ffiffiffi s p¼200 and 510 GeV and the Large Hadron Collider measurements at ffiffiffi s p¼2.76 and 7 TeV. The experimental results are compared to various event generator predictions ( PYTHIA 6, PYTHIA 8, PHOJET , AMPT , EPOS 3, and EPOS - LHC ). DOI: 10.1103/PhysRevD.98.092006 I. INTRODUCTION The ϕð1020Þ-vector-meson production in pþpcollisions was intensively studied by various experiments at different colliding energies and in different rapidity ranges [1–18]. It is the lightest bound state of sand ¯ s quarks and is considered a good probe to study strangeness production in pþpcollisions. Production of ϕmesons from an initial nonstrange colliding system, such as pþpcollisions, is substantially suppressed in comparison to ωand ρvector mesons due to the Okubo-Zweig-Iizuka rule [19–21].Theϕ-meson production at low transverse momentum is dominated by soft processes and is sensitive to the hadronization mechanism, while hard processes become dominant at higher transverse momentum. In pþpcollisions, the production of strangeness is in general not well described by generators such as PYTHIA , which tend to underestimate the production of strange particles [10, 22–24].Thestudy of ϕ-meson production in pþpcollisions is an important tool to study QCD, providing data to tune phenomenological QCD models in which an interplay is mandatory between perturbative QCD calculations, used in particular for hard parton production dominant at higher pT, and phenomenological QCD models, needed to describe the nonperturbative hadronization into strange hadrons like the ϕmeson. In addition, recently, a long-range near-side angular correlation was observed in pþpcollisions at LHC energies [25–27], which led to the observation of collectivity in pþpcollisions [28]. This observation generated various explanations [29], including those based on the color-glass-condensate model [30], and collective hydrodynamic flow [31] or color reconnection [32,33]. Being the heaviest easily accessible meson made of light quarks, ϕ-meson production provides the largest lever arm accessible to study effects that scale with mass, as should be the case for collective effects [34]. The study of ϕ-meson production in pþpcollisions can be an important tool to gain insight into new phenomena, such as long-range angular correlations, that would have a direct impact in the field of relativistic heavy-ion collisions. The ϕ-meson production is an excellent observable to *Deceased. †PHENIX Spokesperson: [email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. MEASUREMENT OF ϕ-MESON PRODUCTION AT …PHYS. REV. D 98, 092006 (2018) 092006-3 probe the strangeness enhancement in the quark-gluon plasma created in heavy-ion collisions [35–37]. We report the ϕ-meson-production cross section measured in pþpcollisions at ffiffiffi s p¼510 GeV. The analysis uses a data sample of 144.6pb−1of integrated luminosity obtained by the PHENIX experiment in 2013. The cross section is averaged over the rapidity (y) interval 1.2< jyj<2.2and reported in several bins of transverse momentum (pT) in the range 2<p T<7GeV=c. The results are compared to several model predictions [24,34,38–41] and to the measurements previously reported by the PHENIX experiment at ffiffiffi s p¼200 GeV [15] and by the LHC experiments measuring the ϕ-meson-production cross section at forward rapidity at ffiffiffi s p¼2.76 and 7 TeV [10–13,17]. Measurements from experiments at the Relativistic Heavy Ion Collider (RHIC) and the LHC allow extracting the energy dependence of the ϕ-meson-production cross section in the rapidity range 1.2<y<2.2, which provides information to further constrain model predictions. II. EXPERIMENTAL SETUP A complete description of the PHENIX detector can be found in Ref. [42]. The results presented here are obtained by measuringtheϕmesonviaitsμþμ−decaychannelusingboth PHENIX muon spectrometers covering forward and backward pseudorapidities, 1.2<jηj<2.2, and the full azimuth. Each muon arm spectrometer comprises hadron absorbers, a muon tracker (MuTr), which resides in a radial field magnet, and a muon identifier (MuID). The absorbers are situated in front of the MuTr to provide hadron (mostly pion and kaon) rejection and are built of 19 cm of copper, 60 cm of iron, and 36.2 cm of stainless steel. The MuTr comprises three sets of cathode strip chambers in a radial magnetic field with an integrated bending power of 0.8 Tesla meters. The final component is the MuID, which has five alternating steel absorbers and Iarocci tubes to further reduce the number of punch-through hadrons misidentified as muons. Muon candidates are identified by reconstructed tracks in the MuTr matched to MuID tracks that penetrate through to the last MuID plane. Another detector system relevant to this analysis is the beam-beam counter (BBC), comprising two arrays of 64 Čerenkov counters, located on both sides of the interaction point and covering the pseudorapidity 3.1<jηj<3.9. The BBC system is used to measure the pþpcollision vertex position along the beam axis (zvtx) with 2 cm resolution and to provide the minimum bias (MB) trigger. III. DATA ANALYSIS The results presented here are based on the data sample collected by PHENIX during the 2013 pþp run at ffiffiffi s p¼510 GeV. The BBC counters provide the MB trigger, which requires at least one hit in each of the BBCs. Events, in coincidence with the MB trigger, containing a muon pair within the acceptance of the spectrometer are selected by the level-1 dimuon trigger requiring that at least two tracks penetrate through the MuID to its last layer. A total of 5.3×108dimuon triggered events are recorded, which corresponds to a sampled integrated luminosity of 144.6pb−1. A. Raw yield extraction A set of quality assurance cuts is applied to the data to select pþpevents and muon candidates as well as to improve the signal-to-background ratio. Good pþp events are selected by requiring that the collision occurs in the fiducial interaction region jzvtxj<30 cm as measured by the BBC. No selection is made on the event’s charged particle multiplicity. The MuTr tracks are matched to the MuID tracks at the first MuID layer in both the position and angle. In addition, the track is required to have more than a minimum number of possible hits in the MuTr (12 out of the maximum 16) and MuID (6 out of the maximum 10), and cuts on the individual track χ2values are applied. Furthermore, there is a minimum allowed single muon momentum along the beam axis, pz, which is reconstructed and energy-loss corrected at the collision vertex, of 2.4GeV=c corresponding to the momentum cut effectively imposed by the absorbers. Finally, a cut on the χ2of the fit to the common vertex of the two candidate tracks near the interaction point is made. The invariant mass distribution is formed by combining muon candidate tracks of opposite charges. This unlikesign dimuon spectrum is composed of correlated and uncorrelated pairs. In the low-mass region (below ≈1.5GeV=c2), the correlated pairs arise from the twobody and Dalitz decays of the light neutral mesons η,ρ,ω, η0, and ϕas well as semimuonic decays of correlated charmed hadrons (and beauty in a negligible contribution). The uncorrelated pairs are mainly coming from semimuonic decays of pions and kaons and punch-through hadrons and form the so-called combinatorial background. The ratio of the ϕ-meson signal over the combinatorial background is of the order of 0.7. This combinatorial background is estimated using two methods: the first one derives the combinatorial background from the distribution formed within the same event by the muon candidates of the same sign (like-sign pairs), and the second one derives the combinatorial background from the pairs formed by muon candidates of opposite charges (unlike-sign pairs) coming from different events (mixed event). The normalization of the mass distribution of the combinatorial background using the same-event like-sign dimuon distributions (Nþþ and N−−) is calculated as NCB ¼2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi NþþN−− p. The mixed-event like-sign dimuon mass distribution is normalized to the same-event like-sign combinatorial background distribution in the invariant mass range 0.2–2.5GeV=c2. This factor is then used to normalize the mixed-event unlike-sign dimuon mass distribution. A. ADARE et al. PHYS. REV. D 98, 092006 (2018) 092006-4 Figure 1shows the unlike-sign dimuon spectrum together with the combinatorial background estimated by both methods that agree within 15% in the invariant mass range of interest (0.8<M μμ <1.3GeV=c2). The signal invariant mass spectrum is extracted by first subtracting the uncorrelated combinatorial background spectra from the unlike-sign spectra. The signal spectra are then fitted to extract the ϕcontribution. The mass resolution of both muon spectrometers is estimated using Monte Carlo simulation to be 93 ð94ÞMeV=c2 for the lowest pTbin (2<p T<2.5GeV=c) and up to 114 ð111ÞMeV=c2for the highest pTbin (5<p T< 7GeV=c) for the negative (positive) pseudorapidity muon spectrometer. Those resolutions being greater than the natural widths of the ϕand ω, the two-body decay of ϕ and ωcontributions are described by Gaussians, while the two-body decay of the ρ-meson contribution is described by a Breit-Wigner distribution convoluted with a Gaussian. The contribution from ρdimuon decay is fixed by the assumption that the production cross sections of ρand ωare related such as σρ¼1.15 ×σω, as measured in Ref. [12] and used in previous PHENIX analysis related to ϕ-meson production in the dimuon decay channel [15,43,44].To evaluate the shape of the correlated background, a PYTHIA [45] MB simulation followed by GEANT 3[46] transport and detector response simulation of the PHENIX detector is performed. The correlated background distribution is found to be well described by an exponential plus a polynomial of first order (χ2/ndf ≤1). To summarize, eight free parameters are needed to describe the signal spectrum: two parameters for the ϕand (ωþρ) signal normalizations, two parameters to describe relative changes of Gaussian widths and central masses with respect to simulation estimates, and four parameters to describe the correlated background distribution and its normalization. The starting values of the free parameters describing the shapes of the different distributions are taken to be the ones from the Monte Carlo simulation. Figure 2shows the fit results for the entire pTrange at backward rapidity. Extracted peak positions and widths are found to be in good agreement with Monte Carlo simulations. B. Detector acceptance and reconstruction efficiency The product of detector acceptance and reconstruction efficiency, Aϵrec, of dimuon decays of ϕmesons is determined by the full event reconstruction of the ϕ-meson signal run through a full GEANT 3simulation of the 2013 PHENIX detector setup and embedded in MB real data. The pTdistribution of the simulated ϕ-meson signal is iteratively reweighted to match the data pTdistribution, the initial pTdistribution being obtained from PYTHIA 6[45] using tune ATLAS _ CSC [38]. The embedded simulated events are then reconstructed in the same manner as data with the same cuts applied as in the real data analysis. The Aϵrec factor is extracted from the simulation as the ratio of reconstructed ϕdistribution over the generated one in the same kinematic range. Figure 3shows the Aϵrec as a function of ϕ-meson pTand rapidity. The main sources of the relative difference between both spectrometers Aϵrec are different detection efficiencies of the MuTr and MuID systems and different amounts of absorber material. C. Differential cross section extraction The pT-dependent differential cross section is calculated according to d2σϕ dpTdy¼Nraw AϵrecΔpTΔyBRϕ→μþμ− σBBC pp ϵBBCNBBC MB ;ð1Þ where BRϕ→μþμ−¼ð2.87 0.19Þ×10−4is the branching ratio of ϕdecay to dimuon [47].Nraw is the extracted ϕraw yield for each pTbin, NBBC MB ¼4.16 ×1012 is the number of sampled MB events. The BBC trigger samples a cross section of σBBC pp ¼32.53.2mb in pþpcollisions, ) 2 c (GeV/ μμ M 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 ) 2 cdN/dM (per 40 MeV/ 0 1000 2000 3000 4000 5000 6000 7000 Unlike sign pairs Bkg - like-sign pairs Bkg - Event Mixing =510 GeVspp c < 7 GeV/ T 2 < p -2.2 < y < -1.2 FIG. 1. Unlike-sign dimuon invariant mass spectrum before background subtraction (solid [black] circles) and uncorrelated background distribution estimated using like-sign pairs (open [black] circles) and the event-mixing technique (solid [red] curve). ) 2 (GeV/c μμ M 0.4 0.6 0.8 1 1.2 1.4 1.6 ) 2 cdN/dM (per 40 MeV/ 0 1000 2000 3000 4000 5000 6000 /ndf = 1.0 2 χ φ ω+ρ Corr. Bkg. =510 GeVspp c < 7 GeV/ T 2 < p -2.2 < y < -1.2 FIG. 2. Unlike-sign signal (solid [black] points) fitted by the sum of three components: ϕmeson (long dash [red] curve), ρþω mesons (short dash [green] curve), and correlated background (dot dash [blue] curve); see the text for details. MEASUREMENT OF ϕ-MESON PRODUCTION AT …PHYS. REV. D 98, 092006 (2018) 092006-5 according to Vernier scans; however, it samples a larger fraction of the cross section when the collision includes a hard scattering process [48]. Studies with high pTπ0yields show an increase of the luminosity scanned by the BBC by a factor of 1=ϵBBC,ϵBBC ¼0.91 0.04 [49]. The inelastic cross sections given by PYTHIA 8[50] for ffiffiffi s p¼500 and 510 GeV pþpcollisions differ by 0.3%; therefore, no correction or additional systematic uncertainty is added. D. Systematic uncertainties The main source of systematic uncertainties in the signal extraction comes from the uncorrelated and correlated background distributions used. To estimate this uncertainty, the extracted ϕraw yields are compared using the following two methods: i) the mixing and like-sign pair methods are separately used for subtraction of uncorrelated background, and ii) the correlated background is fit by an exponential plus first-order polynomial and by an exponential plus second-order polynomial. The extracted ϕraw yields are consistent among all different fit trials. The quadratic mean of the raw yields extracted from the trials is used as the central value, and the uncertainty on the central value is the quadratic mean of the uncertainties of all the trials. Table I summarizes the systematic uncertainties. Type A is a point-to-point uncorrelated uncertainty that allows the data points to move independently with respect to one another and are added in quadrature with statistical uncertainties. Asystematicuncertainty equal to the difference between the central and the extreme values of the extracted yields accounts for the systematic uncertainty related to the background description as a whole. The systematic uncertainty associated with the signal extraction method ranges from 3% to 23%, depending on the pTbin and the muon spectrometer considered (negative/positive rapidity). Type B is a point-to-point correlated uncertainty that allows the data points to move coherently. To evaluate the Aϵrec systematic uncertainty, different pTand rapidity input distributions of the simulated ϕmesons are used. The pT distribution is allowed to vary over the range of the data statistical uncertainty (statistical plus type-A systematics uncertainties added in quadrature; see above), yielding an up to 8% uncertainty. The rapidity distribution shapes given by five generator models ( PYTHIA 6, PYTHIA 8, PHOJET , EPOS 3, and EPOS - LHC ) are used as input rapidity distributions of the simulated ϕmesons, resulting in up to 5% uncertainty. The relative systematic uncertainty of acceptance caused by the fluctuation of the vertex width is estimated to be 3.5% [51]. A 4% uncertainty from the measured MuID tube efficiency and a 2% uncertainty from MuTr chamber efficiency are assigned [15]. Simulation parameters are adjusted in order to reproduce the tracking efficiency observed in the data. While the relative tracking efficiency is validated using J=ψ→μμ data, data-driven evaluation of the absolute tracking efficiency is not available. Therefore, we assign 10% uncertainty for the absolute tracking efficiency as a conservative value [51]. Finally, type C is an overall normalization uncertainty, which allows the data points to move together by a common multiplicative factor. Type C is composed of 10% uncertainty assigned for the BBC cross section and efficiency uncertainties and a 6.6% uncertainty from the measurement of BRϕ→μþμ−. y 3−2−1−0123 )c (GeV/ T p 0 1 2 3 4 5 6 7 8 rec ∈A 5− 10 4− 10 3− 10 2− 10 1− 10 1 (a) )c (GeV/ T p 234567 rec ∈ A 3− 10 2− 10 1− 10 μμ→φ 1.2 < y < 2.2 -2.2 < y < -1.2 (b) FIG. 3. Aϵrec for ϕdetection in forward (1.2<y<2.2) and backward (−2.2<y<−1.2) muon spectrometers (a) in the pTrapidity plane and (b) integrated in rapidity per spectrometer for each pTbin considered in the analysis. TABLE I. Systematic uncertainties associated with the differential cross section calculation. Type Origin Value A Signal extraction 3%–23% BAϵrec:pTinput distribution 2%–8% BAϵrec: Rapidity input distribution 3%–5% BAϵrec: Vertex width fluctuation 3.5% BAϵrec: MuID hit efficiency 4% BAϵrec: MuTr hit efficiency 2% BAϵrec: MuTr tracking efficiency 10% C MB trigger efficiency 10% CBr ϕ→μþμ−6.6% A. ADARE et al. PHYS. REV. D 98, 092006 (2018) 092006-6 IV. RESULTS The pT-differential cross section is calculated independently for each muon arm, and then the results are combined using the best-linear-unbiased-estimate method [52]. The pTintegrated (2<p T<7GeV=c) cross section dσϕ=dyis given in Table II. Results obtained using the two muon spectrometers are consistent within uncertainties. Combining both arm results, the integrated cross section in the kinematic range 2<p T<7GeV=c and 1.2<jyj< 2.2is σϕ¼2.28 0.09ðstatÞ0.14ðsystÞ×10−2mb, to which a 12% normalization uncertainty applies. The ϕ-meson-differential cross section as a function of pTmeasured in pþpcollisions at ffiffiffi s p¼510 GeV is shown in Fig. 4and listed in Table III. The data points are bin shifted in pTusing the Lafferty and Wyatt method [53] to correct for the finite width of the pTbins. The data are fitted by a Tsallis function [54] with a resulting χ2=ndf ¼0.66. The results are compared to calculations performed using six different generator models: PYTHIA 6[45] using tune ATLAS_CSC [38], PYTHIA 8.210 [50] using tune Monash2013 [24], PHOJET 1.12 [39], EPOS 3.117 [34], EPOS - LHC [40], and AMPT v1.26 [41]. Data and models are compared as the ratio of the model prediction over the Tsallis fit of the data. The AMPT simulation is done with the default AMPT model version 1.26 (without string melting), in which the initial conditions are determined by HIJING [55]. Parton scattering is done using Zhang’s parton-cascade model [56]. The hadronization is accomplished using the Lund string fragmentation model [57,58]. The final-state hadronic interactions are based on “a relativistic transport” model [59]. We used the set of parameters tabulated in Ref. [60] describing both the charged particle distribution and elliptic flow measured in Au þAu collisions at the RHIC. The Lund string fragmentation parameters are a¼0.5and b¼0.9GeV−2, the QCD coupling constant is αs¼0.33, and the screening mass is μ¼3.2fm−1, leading to a parton-scattering cross section of 1.5 mb. Besides their production from the fragmentation of excited strings in the initial collisions, ϕmesons can also be produced and absorbed from hadronic matter via various TABLE II. The ϕ-meson-production cross section dσϕ=dyin pþpcollisions at ffiffiffi s p¼510 GeV integrated in the transverse momentum range 2<p T<7GeV=c. The first uncertainty represents the statistical and type-A systematic uncertainties, while the second is the systematic uncertainty of type B, and the third one is the additional 12% type-C normalization systematic uncertainty. yrange dσϕ=dy(mb) 1.2<y<2.2ð2.13 0.14 0.16 0.26Þ×10−2 −2.2<y<−1.2ð2.46 0.12 0.18 0.30Þ×10−2 1.2<jyj<2.2ð2.28 0.09 0.14 0.27Þ×10−2 123456 )c (GeV/ T p 4− 10 2− 10 1 dy (mb/GeV) T p/d φ σ 2 d (a) = 510 GeVspp, 1.2 < |y| < 2.2 PHENIX Tsallis fit 123456 )c (GeV/ T p 1 2 Model/Data fit Pythia6 Pythia8 PHOJET AMPT EPOS-LHC (b) 01234567 )c (GeV/ T p 1 2 Model/Data fit EPOS3 Full No-Casc No-Hydro/No-Casc (c) FIG. 4. (a) d2σϕ=dpTdymeasurements in pþpcollisions at ffiffiffi s p¼510 GeV fitted by a Tsallis function. Error bars represent the statistical uncertainty, and the boxes represent the type-B and type-C systematic uncertainties added in quadrature. (b) and (c) Comparison between the data and predictions of six models ( PYTHIA 6using the tune ATLAS _ CSC , PYTHIA 8 using tune M ONASH 2013, PHOJET 1.12, EPOS - LHC , AMPT v1.26, and EPOS 3.117) shown as the ratio of the model to the data fitted by a Tsallis function. (c) The data are compared to EPOS 3 predictions using three different options of the model (see the text for details). TABLE III. The ϕ-meson-differential-production cross section d2σϕ=dpTdyfor 1.2<jyj<2.2in pþpcollisions at ffiffiffi s p¼510 GeV. ˜ pTis the pTat which the data point is plotted (see the text for details). The first uncertainty represents the statistical and type-A systematic uncertainties, while the second is the systematic uncertainty of type B, and the third one is the additional 12% type-C normalization systematic uncertainty. pTrange (GeV=c) ˜ pT (GeV=c)d 2σϕ=dpTdy½mb=ðGeV=cÞ 2.0–2.5 2.24 ð2.16 0.17 0.23 0.26Þ×10−2 2.5–3.0 2.74 ð1.20 0.05 0.12 0.14Þ×10−2 3.0–3.5 3.24 ð6.26 0.36 0.61 0.75Þ×10−3 3.5–4.0 3.74 ð2.70 0.20 0.30 0.32Þ×10−3 4.0–5.0 4.44 ð1.06 0.07 0.11 0.13Þ×10−3 5.0–7.0 5.79 ð1.97 0.19 0.20 0.24Þ×10−4 MEASUREMENT OF ϕ-MESON PRODUCTION AT …PHYS. REV. D 98, 092006 (2018) 092006-7 hadronic reactions (baryon-baryon, meson-baryon, and meson-meson scatterings) [41]. The EPOS 3model includes, in addition to the description of the initial scattering based on a Gribov-Regge approach [61], a viscous hydrodynamic expansion of the created system followed by a hadronization phase and a final-state hadronic cascade using the URQMD model [62,63].In EPOS 3, the hydrodynamic evolution and the hadronic cascade can be turned on or off, separately. The so-called Full version of EPOS 3includes hydrodynamic expansion of the created system followed by a final-state hadronic cascade. The EPOS 3No-Casc version does not include the final-state hadronic cascade, and No-Hydro/No-Casc has both the hydrodynamic and the final-state hadronic cascade turned off. The EPOS - LHC calculation presented in Fig. 4is performed, including a parametrized viscous hydrodynamic expansion of the created partonic system. As shown in panels (b) and (c) of Fig. 4, the experimental data are better reproduced by the AMPT model and by EPOS 3 without the hadronic cascade. The EPOS 3Full and EPOS - LHC overestimate the ϕ-meson production, and PHOJET and PYTHIA models tend to underestimate it by a factor of 2. A previous study of the M ONASH 2013 tune of PYTHIA 8 showed that the calculated transverse-momentum spectra of ϕmesons overestimates the experimental data at very soft momenta (below ∼500 MeV=c) and underestimates it at higher momenta, the overall yield of ϕmesons being correctly reproduced [24]. Additional calculations using the AMPT model with string melting (version 2.26) were performed. The ϕmeson-production yield was found to be a factor of 2 higher than the one extracted using the default AMPT model with approximately the same pTdependence. For clarity, those calculations are not shown in Fig. 4. V. ENERGY DEPENDENCE OF ϕ-MESON PRODUCTION The PHENIX experiment previously measured the ϕmeson cross section at forward rapidity and for 1<p T< 7GeV=c in pþpcollisions at ffiffiffi s p¼200 GeV [15].At the LHC, the ALICE experiment measured the ϕ-mesonproduction cross section via its dimuon decay channel in pþpcollisions at forward rapidity 2.5<y<4.0and for 1<p T<5GeV=c at ffiffiffi s p¼2.76 TeV [17] and 7 TeV [12]. Measurement of the ϕ-meson production was also performed via the KþK−decay channel at midrapidity jyj<0.5and for 0.4<p T<6GeV=c at ffiffiffi s p¼7TeV [13]. The LHCb experiment measured the inclusive ϕmeson-production cross section in the KþK−decay channel in the kinematic range 2.44 <y<4.06 and 0.6< pT<5GeV=c in pþpcollisions at ffiffiffi s p¼7TeV [10]. Figures 5–8show comparisons between d2σϕ=dpTdy measurements at forward rapidities done by PHENIX at ffiffiffi s p¼200 GeV [15], by ALICE at ffiffiffi s p¼2.76 TeV [17] and 7 TeV [12], and by LHCb at ffiffiffi s p¼7TeV [10], respectively, along with model predictions. The AMPT model is in good agreement with the measured cross sections at both RHIC energies but overestimates the production cross section at LHC energies, especially at 7 TeV. The PYTHIA 6and PHOJET calculations at LHC energies are in better agreement with the data than at RHIC energies, in which the models underestimate the measured production cross section. The PYTHIA 8prediction underestimates the cross section for all four energies. Panels (c) of Figs. 4–8show the comparison between the measurements fitted by a Tsallis function and EPOS 3using three different model settings (see above for details). The comparison of those results reveals the effect of the hydrodynamic expansion of the partonic system created in pþpcollisions and of the final-state hadronic cascade on the ϕ-meson production. The hydrodynamic evolution does not impact the ϕ-meson production at RHIC energies [No-Casc and No-Hydro/No-Casc curves are almost identical on panel (c) of Figs 4–8]. A significant effect appears at ffiffiffi s p¼2.76 TeV and becomes stronger at 7 TeV, where the ϕ-meson-production cross section increases by a factor of 2 for the pTrange 1–3GeV=c when turning on the hydrodynamic evolution. The same behavior was already observed for the production of Λ0,Ks, and Ξin pþp collisions at 7 TeV [34], showing that the flow effects increase with the mass of the particle. The final-state )c (GeV/ T p 12 3 45 6 dy (mb/GeV) T p/d φ σ 2 d 4− 10 2− 10 1(a) = 200 GeVspp, 1.2 < |y| < 2.2 PHENIX [PRD 90, 052002 (2014)] Tsallis fit )c (GeV/ T p 12 3 45 6 Model/Data fit 1 2 Pythia6 Pythia8 PHOJET AMPT EPOS-LHC (b) )c (GeV/ T p 01234567 Model/Data fit 1 2 EPOS3 Full No-Casc No-Hydro/No-Casc (c) FIG. 5. Same as Fig. 4for PHENIX measurement at ffiffiffi s p¼ 200 GeV [15]. A. ADARE et al. PHYS. REV. D 98, 092006 (2018) 092006-8