Probing gluon spin-momentum correlations in transversely polarized protons through midrapidity isolated direct photons in p^\uparrow+p collisions at \sqrt{s}=200 GeV
U.A. Acharya, C. Aidala, Y. Akiba, M. Alfred, V. Andrieux, N. Apadula, H. Asano, B. Azmoun, V. Babintsev, N.S. Bandara, K.N. Barish, S. Bathe, A. Bazilevsky, M. Beaumier, R. Belmont, A. Berdnikov, Y. Berdnikov, B. Blankenship, D.S. Blau, J.S. Bok, M.L. Brooks, J. Bryslawskyj, V. Bumazhnov, S. Campbell, V. Canoa Roman, R. Cervantes, C.Y. Chi, M. Chiu, I.J. Choi, J.B. Choi, Z. Citron, M. Connors, R. Corliss, Y. Corrales N. Cronin, M. Csanád, T. Csörg?, T.W. Danley, M.S. Daugherity, G. David, K. DeBlasio, K. Dehmelt, A. Denisov, A. Deshpande, E.J. Desmond, A. Dion, D. Dixit, J.H. Do, A. Drees, K.A. Drees, J.M. Durham, A. Durum, A. Enokizono, H. En'yo, R. Esha, S. Esumi, B. Fadem, W. Fan, N. Feege, D.E. Fields, M. Finger, M. Finger Jr., D. Fitzgerald, S.L. Fokin, J.E. Frantz, A. Franz, A.D. Frawley, Y. Fukuda, C. Gal, P. Gallus, P. Garg, H. Ge, M. Giles, F. Giordano, Y. Goto, N. Grau, S.V. Greene, M. Grosse Perdekamp, T. Gunji, H. Guragain, T. Hachiya, J.S. Haggerty, K.I. Hahn, H. Hamagaki, H.F. Hamilton, S.Y. Han, J. Hanks, S. Hasegawa, T.O.S. Haseler, X. He, T.K. Hemmick, J.C. Hill, K. Hill, A. Hodges, R.S. Hollis, K. Homma, B. Hong, T. Hoshino, N. Hotvedt, J. Huang, S. Huang, et al. (205 additional authors not shown)
PProbing gluon spin-momentum correlations in transversely polarized protons throughmidrapidity isolated direct photons in p ↑ + p collisions at √ s = 200 GeV
U.A. Acharya, C. Aidala, Y. Akiba,
53, 54, ∗ M. Alfred, V. Andrieux, N. Apadula, H. Asano,
33, 53
B. Azmoun, V. Babintsev, N.S. Bandara, K.N. Barish, S. Bathe,
5, 54
A. Bazilevsky, M. Beaumier, R. Belmont,
11, 46
A. Berdnikov, Y. Berdnikov, B. Blankenship, D.S. Blau,
32, 43
J.S. Bok, M.L. Brooks, J. Bryslawskyj,
5, 8
V. Bumazhnov, S. Campbell, V. Canoa Roman, R. Cervantes, C.Y. Chi, M. Chiu, I.J. Choi, J.B. Choi, † Z. Citron, M. Connors,
20, 54
R. Corliss, Y. Corrales Morales, N. Cronin, M. Csan´ad, T. Cs¨org˝o,
16, 65
T.W. Danley, M.S. Daugherity, G. David,
7, 59
K. DeBlasio, K. Dehmelt, A. Denisov, A. Deshpande,
54, 59
E.J. Desmond, A. Dion, D. Dixit, J.H. Do, A. Drees, K.A. Drees, J.M. Durham, A. Durum, A. Enokizono,
53, 55
H. En’yo, R. Esha, S. Esumi, B. Fadem, W. Fan, N. Feege, D.E. Fields, M. Finger, M. Finger, Jr., D. Fitzgerald, S.L. Fokin, J.E. Frantz, A. Franz, A.D. Frawley, Y. Fukuda, C. Gal, P. Gallus, P. Garg,
3, 59
H. Ge, M. Giles, F. Giordano, Y. Goto,
53, 54
N. Grau, S.V. Greene, M. Grosse Perdekamp, T. Gunji, H. Guragain, T. Hachiya,
42, 53, 54
J.S. Haggerty, K.I. Hahn, H. Hamagaki, H.F. Hamilton, S.Y. Han,
17, 31
J. Hanks, S. Hasegawa, T.O.S. Haseler, X. He, T.K. Hemmick, J.C. Hill, K. Hill, A. Hodges, R.S. Hollis, K. Homma, B. Hong, T. Hoshino, N. Hotvedt, J. Huang, S. Huang, K. Imai, M. Inaba, A. Iordanova, D. Isenhower, D. Ivanishchev, B.V. Jacak, M. Jezghani, Z. Ji, X. Jiang, B.M. Johnson,
7, 20
D. Jouan, D.S. Jumper, J.H. Kang, D. Kapukchyan, S. Karthas, D. Kawall, A.V. Kazantsev, V. Khachatryan, A. Khanzadeev, A. Khatiwada, C. Kim,
8, 31
E.-J. Kim, M. Kim, D. Kincses, A. Kingan, E. Kistenev, J. Klatsky, P. Kline, T. Koblesky, D. Kotov,
51, 56
S. Kudo, B. Kurgyis, K. Kurita, Y. Kwon, J.G. Lajoie, D. Larionova, M. Larionova, A. Lebedev, S. Lee, S.H. Lee,
27, 40, 59
M.J. Leitch, Y.H. Leung, N.A. Lewis, X. Li, S.H. Lim,
35, 52, 66
M.X. Liu, V.-R. Loggins, S. L¨ok¨os, K. Lovasz, D. Lynch, T. Majoros, Y.I. Makdisi, M. Makek, V.I. Manko, E. Mannel, M. McCumber, P.L. McGaughey, D. McGlinchey,
11, 35
C. McKinney, M. Mendoza, A.C. Mignerey, A. Milov, D.K. Mishra, J.T. Mitchell, Iu. Mitrankov, G. Mitsuka,
30, 54
S. Miyasaka,
53, 61
S. Mizuno,
53, 62
M.M. Mondal, P. Montuenga, T. Moon,
31, 66
D.P. Morrison, B. Mulilo,
31, 53
T. Murakami,
33, 53
J. Murata,
53, 55
K. Nagai, K. Nagashima, T. Nagashima, J.L. Nagle, M.I. Nagy, I. Nakagawa,
53, 54
K. Nakano,
53, 61
C. Nattrass, S. Nelson, T. Niida, R. Nouicer,
7, 54
T. Nov´ak,
16, 65
N. Novitzky,
59, 62
A.S. Nyanin, E. O’Brien, C.A. Ogilvie, J.D. Orjuela Koop, J.D. Osborn,
40, 48
A. Oskarsson, G.J. Ottino, K. Ozawa,
30, 62
V. Pantuev, V. Papavassiliou, J.S. Park, S. Park,
53, 57, 59
S.F. Pate, M. Patel, W. Peng, D.V. Perepelitsa,
7, 11
G.D.N. Perera, D.Yu. Peressounko, C.E. PerezLara, J. Perry, R. Petti, M. Phipps,
7, 24
C. Pinkenburg, R.P. Pisani, M. Potekhin, A. Pun, M.L. Purschke, P.V. Radzevich, N. Ramasubramanian, K.F. Read,
48, 60
D. Reynolds, V. Riabov,
43, 51
Y. Riabov,
51, 56
T. Rinn,
24, 27
S.D. Rolnick, M. Rosati, Z. Rowan, J. Runchey, A.S. Safonov, T. Sakaguchi, H. Sako, V. Samsonov,
43, 51
M. Sarsour, S. Sato, B. Schaefer, B.K. Schmoll, K. Sedgwick, R. Seidl,
53, 54
A. Sen,
27, 60
R. Seto, A. Sexton, D Sharma, D. Sharma, I. Shein, T.-A. Shibata,
53, 61
K. Shigaki, M. Shimomura,
27, 42
T. Shioya, P. Shukla, A. Sickles, C.L. Silva, D. Silvermyr, B.K. Singh, C.P. Singh, V. Singh, M. Sluneˇcka, K.L. Smith, M. Snowball, R.A. Soltz, W.E. Sondheim, S.P. Sorensen, I.V. Sourikova, P.W. Stankus, S.P. Stoll, T. Sugitate, A. Sukhanov, T. Sumita, J. Sun, Z. Sun, J. Sziklai, K. Tanida,
28, 54, 57
M.J. Tannenbaum, S. Tarafdar,
63, 64
G. Tarnai, R. Tieulent,
20, 37
A. Timilsina, T. Todoroki,
54, 62
M. Tom´aˇsek, C.L. Towell, R.S. Towell, I. Tserruya, Y. Ueda, B. Ujvari, H.W. van Hecke, J. Velkovska, M. Virius, V. Vrba,
13, 26
N. Vukman, X.R. Wang,
45, 54
Y.S. Watanabe, C.P. Wong,
20, 35
C.L. Woody, C. Xu, Q. Xu, L. Xue, S. Yalcin, Y.L. Yamaguchi, H. Yamamoto, A. Yanovich, J.H. Yoo, I. Yoon, H. Yu,
45, 50
I.E. Yushmanov, W.A. Zajc, A. Zelenski, S. Zharko, and L. Zou (PHENIX Collaboration) Abilene Christian University, Abilene, Texas 79699, USA Department of Physics, Augustana University, Sioux Falls, South Dakota 57197, USA Department of Physics, Banaras Hindu University, Varanasi 221005, India Bhabha Atomic Research Centre, Bombay 400 085, India Baruch College, City University of New York, New York, New York, 10010 USA Collider-Accelerator Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA a r X i v : . [ h e p - e x ] F e b Physics Department, 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 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 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 Eszterh´azy K´aroly University, K´aroly R´obert Campus, H-3200 Gy¨ongy¨os, M´atrai ´ut 36, Hungary Ewha Womans University, Seoul 120-750, Korea Florida A&M University, Tallahassee, FL 32307, USA Florida State University, Tallahassee, Florida 32306, USA Georgia State University, Atlanta, Georgia 30303, USA Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan Department of Physics and Astronomy, Howard University, Washington, DC 20059, USA 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 for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia 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 Advanced Science Research Center, Japan Atomic Energy Agency, 2-4Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan Jeonbuk National University, Jeonju, 54896, Korea KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan Korea University, Seoul 02841, Korea National Research Center “Kurchatov Institute”, Moscow, 123098 Russia Kyoto University, Kyoto 606-8502, Japan Lawrence Livermore National Laboratory, Livermore, California 94550, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden IPNL, CNRS/IN2P3, Univ Lyon, Universit´e Lyon 1, F-69622, Villeurbanne, France University of Maryland, College Park, Maryland 20742, USA Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia University of New Mexico, Albuquerque, New Mexico 87131, USA New Mexico State University, Las Cruces, New Mexico 88003, USA Physics and Astronomy Department, University of North Carolina at Greensboro, Greensboro, North Carolina 27412, USA Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, BP1, F-91406, Orsay, France Peking University, Beijing 100871, People’s Republic of China PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia Pusan National University, Pusan 46241, Korea 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, 195251 Russia Department of Physics and Astronomy, Seoul National University, Seoul 151-742, 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 11794-3800, USA University of Tennessee, Knoxville, Tennessee 37996, USA Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan Tomonaga Center for the History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan Vanderbilt University, Nashville, Tennessee 37235, USA Weizmann Institute, Rehovot 76100, Israel Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, HungarianAcademy of Sciences (Wigner RCP, RMKI) H-1525 Budapest 114, POBox 49, Budapest, Hungary Yonsei University, IPAP, Seoul 120-749, Korea Department of Physics, Faculty of Science, University of Zagreb, Bijeniˇcka c. 32 HR-10002 Zagreb, Croatia (Dated: March 1, 2021)
Studying spin-momentum correlations in hadronic collisions offers a glimpse into a three-dimensional picture of proton structure. The transverse single-spin asymmetry for midrapidityisolated direct photons in p ↑ + p collisions at √ s = 200 GeV is measured with the PHENIX detectorat the Relativistic Heavy Ion Collider (RHIC). Because direct photons in particular are producedfrom the hard scattering and do not interact via the strong force, this measurement is a cleanprobe of initial-state spin-momentum correlations inside the proton and is in particular sensitiveto gluon interference effects within the proton. This is the first time direct photons have beenused as a probe of spin-momentum correlations at RHIC. The uncertainties on the results are afifty-fold improvement with respect to those of the one prior measurement for the same observable,from the Fermilab E704 experiment. These results constrain gluon spin-momentum correlations intransversely polarized protons. Unlike lepton-hadron scattering, proton-proton colli-sions are sensitive to gluon scattering at leading order.Direct photons are produced directly in the hard scat-tering of partons and, because they do not interact viathe strong force, are a phenomenologically clean probeof the structure of the proton. At large transverse mo-mentum, direct photons are produced at leading ordervia the quantum chromodynamics (QCD) 2-to-2 hardscattering subprocesses quark-gluon Compton scatter-ing ( g + q → γ + q ) and quark-antiquark annihilation(¯ q + q → γ + g ). Compton scattering dominates at midra-pidity [1] because the proton is being probed at moderatelongitudinal momentum fraction, x , where gluons are theprimary constituents of the proton. Thus midrapiditydirect photon measurements are a clean probe of gluonstructure within the proton.Transverse single-spin asymmetries (TSSAs) inhadronic collisions are sensitive to various spin-momentum correlations, i.e. correlations between thedirections of the spin and momentum of partons and/orhadrons involved in a scattering event. In collisionsbetween one transversely polarized proton and oneunpolarized proton, the TSSA describes the azimuthal-angular dependence of particle production relative tothe transverse polarization direction. TSSAs have beenmeasured to be as large as 40% in forward chargedpion production [2–5] and significantly nonzero forwardneutral pion asymmetries have been measured withtransverse momentum up to p T ≈ /c [6]. In thiscontext, p T serves as proxy for a hard-scattering energy( Q ) that is well into the perturbative regime of QCD.Next-to-leading-order perturbative QCD calculations,which only include effects from high energy partonscattering predict that these asymmetries should besmall and fall off as m q /Q [7], where m q is the baremass of the quark. Thus, to explain these large TSSAs,they must be considered in the context of the dynamicspresent in proton-proton collisions that cannot becalculated perturbatively, namely dynamics describingproton structure and/or the process of hadronization.One approach toward explaining the large measuredTSSAs is through transverse-momentum-dependent(TMD) functions. These functions depend on the soft-scale-parton transverse momentum, k T , in addition to the partonic longitudinal momentum fraction x and Q ,where k T (cid:28) Q . TMD functions can be directly ex-tracted from measurements that are sensitive to two mo-mentum scales, such as semi-inclusive deep-inelastic scat-tering (SIDIS) where the angle and energy of the scat-tered electron can be used to directly measure the hard-scale Q and the transverse momentum of the measuredhadron relates to the soft scales k T of TMD parton dis-tribution functions (PDFs) and fragmentation functions.The Sivers function is a PDF that describes the struc-ture of the transversely polarized proton and correlatesthe transverse spin of the proton and k T of the partonwithin it [8]. The quark Sivers function has been ex-tracted through polarized SIDIS measurements, but thegluon Sivers function has remained comparatively lessconstrained because SIDIS is not sensitive to gluons atleading order [9]. The direct photon TSSA in proton-proton collisions has been shown to be sensitive to thegluon Sivers function [10], but the k T moment of TMDfunctions must be used to apply these functions to thesingle-scale inclusive TSSAs measured in proton-protoncollisions.Twist-3 correlation functions are another approach to-ward describing TSSAs. Unlike TMD functions, collineartwist-3 correlation functions depend only on a singlescale, the hard scale Q . Twist-3 functions describe spin-momentum correlations generated by the quantum me-chanical interference between scattering off of one par-ton versus scattering off of two. There are two differenttypes: the quark-gluon-quark ( qgq ) correlation functionsand the trigluon ( ggg ) correlation function. In the con-text of proton structure, qgq correlation functions de-scribe the interference between scattering off of a singlequark in the proton versus scattering off of a quark, whichcarries the same flavor and the same momentum fractionand an additional gluon. Analogously, the trigluon corre-lation describes the interference between scattering off ofone gluon in the proton versus scattering off of two. Ad-ditional twist-3 collinear correlation functions describingspin-momentum correlations in the process of hadroniza-tion also exist, but are not relevant to the productionof direct photons. Collinear twist-3 functions have beenshown to be related to the k T moment of TMD func-tions [11, 12]. For example, the Efremov-Teryaev-Qiu-Sterman (ETQS) function is a qgq correlation functionfor the polarized proton [13–15] that is related to the k T moment of the Sivers TMD PDF. The ETQS functionhas also been extracted from fits to inclusive TSSAs inproton-proton collisions [16, 17], and the forward directphoton TSSA has been suggested to be dominated bythis ETQS function [18]. The fact that both TMD andcollinear twist-3 functions are nonzero reflects that scat-tering partons do in fact interact with the color fieldspresent inside the proton, which goes beyond traditionalassumptions present in hadronic collision studies.Multiple observables can provide sensitivity to the ggg correlation function. Midrapidity inclusive hadron TSSAmeasurements are sensitive to gluon spin-momentum cor-relations in the proton but also include potential ef-fects from hadronization and final-state color interac-tions. Heavy flavor production at the Relativistic HeavyIon Collider (RHIC) is dominated by gluon-gluon fusionand thus particularly sensitive to gluons in the proton.A heavy flavor hadron TSSA measurement [19] has beenused to estimate the trigluon correlation function in thetransversely polarized proton assuming no effects fromhadronization or final-state color interactions [20]. Themidrapidity isolated direct photon TSSA is instead aclean probe of the trigluon correlation function because itis insensitive to hadronization effects as well as final-statecolor interactions [21].The only previously published direct photon TSSAmeasurement is the Fermilab E704 result, which useda 200 GeV /c polarized proton beam on an unpolarizedproton target ( √ s = 19 . . < p γT < . /c [22]. The PHENIX results presented in thisLetter measure photons with p γT > /c with totaluncertainties up to a factor of 50 smaller than the E704measurements. This measurement will constrain trigluoncorrelations in transversely polarized protons.The presented direct photon measurement was per-formed with the PHENIX experiment in the central ra-pidity region | η | < .
35, using p ↑ + p collisions at √ s =200 GeV. The data set was collected in 2015 and corre-sponds to an integrated luminosity of approximately 60pb − . Direct photons were reconstructed using similartechniques to a previously published direct photon crosssection result at √ s = 200 GeV [23]. The asymmetry wasmeasured with transversely polarized proton beams atRHIC where the clockwise and counter-clockwise beamshad an average polarization of 0 . ± .
02 and 0 . ± . φ = π/ | η | < .
35 in pseudorapidity. Photons are identi-fied through clusters in the electromagnetic calorimeter(EMCal), which has two detector arms: the west andthe east. The west arm comprises four sectors of sam-pling lead-scintillator (PbSc) calorimeters with granu-larity δφ × δη = 0 . × .
011 and the east arm com-prises two more PbSc sectors along with two sectors ofˇCerenkov lead-glass (PbGl) calorimeters with granularity δφ × δη = 0 . × .
008 [25].The PHENIX central tracking system uses pad cham-bers and a drift chamber to measure the position ofcharged particle tracks [26]. The beam-beam counters(BBC) are far-forward arrays of quartz ˇCerenkov radia-tors that cover the full azimuth and 3 . < | η | < . p T photons are selected through an EMCal-based high-energy photon trigger that is taken in coincidence withthis minimum-bias trigger.All photons used in the asymmetry calculation are re-quired to pass the following cuts. A shower shape cutselects clusters whose energy distribution is consistentwith a parameterized profile from a photon shower. Thisreduces the contribution of clusters from hadrons alongwith merged photons from high energy π decays, whichresolve as a single cluster in the EMCal. A time-of-flightcut suppresses the contribution of EMCal noise, wherethe timing of the cluster is measured by the EMCal andthe time zero reference of the event is provided by theBBC. A charged-track-veto cut eliminates clusters thatgeometrically match with a charged track and uses thetrack position measured directly in front of the EMCal.This cut reduces the background from electrons as well ascharged hadrons that were not eliminated by the showershape cut.Direct photon candidates are also required to pass tag-ging cuts that reduce the hadronic decay background byeliminating photons that are tagged as coming from ei-ther π → γγ or η → γγ decays. The candidate di-rect photon is matched with a partner photon in thesame event and same EMCal arm, which has passed aminimum-energy cut of 0.5 GeV. A photon is consid-ered tagged as coming from a π → γγ ( η → γγ ) decayif it is matched into a photon pair with invariant mass105 < M γγ <
165 MeV /c (480 < M γγ <
620 MeV /c ),which corresponds roughly to a ± σ window around theobserved π and η peaks.Additionally, direct photon candidates have to pass anisolation cut, which further reduces the contribution ofdecay photons [23]. Ref. [1] estimates that the contribu-tion of the next-to-leading-order fragmentation photonsto the isolated direct photon sample is less than 15% forphotons with p T > /c . The photon isolation cutrequires that the sum of the particles’ energy surroundingthe photon in a cone of radius r = (cid:112) (∆ η ) + (∆ φ ) < . E cone < E γ · E cone , an EMCal cluster must have energylarger than 0 .
15 GeV and a charged track needs to havea momentum above 0 . /c . To provide a more in-clusive sample of the particles surrounding the photon,the clusters and tracks that are included in the E cone sum are only required to pass a minimum set of qualitycuts. The charged track veto cut is still used to ensurecharged particles are not double counted by the energythat they deposit in the EMCal. The shower-shape cutis not applied to EMCal clusters to ensure that neutralhadrons and charged hadrons that were not reconstructedas charged tracks can still contribute to E cone .The asymmetry measurement is formed from pho-tons that satisfy these criteria, using similar techniquesto previously published PHENIX TSSAs which includeRefs. [19] and [28]. The TSSA is determined using the relative luminosity formula : A N = 1 P (cid:104) cos( φ ) (cid:105) N ↑ − R N ↓ N ↑ + R N ↓ , (1)where R = L ↑ / L ↓ is the relative luminosity of collisionsfor when the beam was polarized up versus down. P is the average polarization of the beam and (cid:104) cos( φ ) (cid:105) isthe acceptance factor accounting for the azimuthal cov-erage of each detector arm. In Eq. (1), N refers to theparticle yield and the up ( ↑ ) or down ( ↓ ) arrow super-scripts refer to the direction of the beam polarization.The asymmetries are calculated separately for each armof the detector and averaged together for the final result,weighted by the statistical uncertainty.The main source of direct-photon background comesfrom decay photons that were not eliminated by the tag-ging cut because their partner photon was not measured.This can occur because the partner photon was out ofacceptance, hit a dead area of the detector, or did notpass the minimum-energy cut. To calculate the isolateddirect-photon asymmetry, A dir N , the candidate isolateddirect-photon asymmetry, A iso N , must be corrected for thecontribution from background: A dir N = A iso N − r π A iso ,π N − r η A iso ,ηN − r π − r η . (2)This expression removes the effects of background asym-metries from isolated π photons, A iso ,π N , and isolated η photons, A iso ,ηN , where r π and r η are the backgroundfractions due to photons from π and η decays, respec-tively. Because the midrapidity π and η TSSAs have been measured to be consistent with zero to high statis-tical precision [28] and their isolated asymmetries werealso confirmed to be consistent with zero, A iso ,π N and A iso ,ηN are set to zero in Eq. (2). The systematic uncer-tainty due to setting the background asymmetries to zerodominates the total systematic uncertainty of the direct-photon asymmetry for all p T bins. It is assigned by in-tegrating the inclusive midrapidity π and η TSSAs overphoton p T and propagating their uncertainties throughEq. (2).The background fraction calculation is performed bytaking the ratio of measured photon yields: N iso ,h tag /N iso ,where N iso is the isolated direct photon candidate sam-ple. N iso ,h tag is the number of photons that were tagged ascoming from a diphoton decay of hadron h and pass thephoton pair isolation cut, E cone − E partner < E γ · E partner . Tagged photons that pass this cut would havebeen included in the isolated direct photon candidatesample had their partner photon not been detected. Sim-ulations are used to calculate how to convert from thenumber of tagged decay photons to the number of de-cay photons where the partner photon was missed. Thebackground fraction, r h , for photons from π and η me-son decays is calculated separately to account for theirdifferences in particle production and decay kinematics, r h = R h N iso ,h tag N iso , (3)where R h is the one-miss ratio for the decay of hadron h .It is the ratio in single particle Monte Carlo of the num-ber of photons for which only one of the simulated decayphotons was reconstructed to the number of photons inwhich both decay photons were reconstructed [23]. Thesesimulations include the geometry, resolution, and con-figuration of the dead areas of the EMCal and use thepreviously measured π [29] and η [30] cross sections.The background fractions for photons from π ( η ) de-cays are plotted in Fig. 1 and are systematically largerin the east arm versus the west due to the PbGl sectorshaving slightly more dead area compared to the PbScsectors. The uncertainty on the background fraction ispropagated through Eq. (2) to assign an additional sys-tematic uncertainty to the direct-photon asymmetry.A similar method to Eq. (3) is used to find the contri-bution of merged π decay photons. The equivalent R h is calculated using simulated h → γγ decays, taking theratio of the number of reconstructed EMCal clusters pro-duced by merged decay photons divided by the numberof reconstructed clusters associated with a single decayphoton. The contribution from merged photon clusterswas found to be less than 0.2%, small compared to theup to 50% background fraction due to the one-miss ef-fects, and the contribution from merged η decays wasconfirmed to be negligible. [GeV/c] T p5 6 7 8 9 10 11 12 p r (a) [GeV/c] T p5 6 7 8 9 10 11 12 h r PHENIX (b)
FIG. 1. The fractional contribution of photons from (a) π and (b) η decays to the isolated direct photon candidate sam-ple. An additional systematic study is performed by calcu-lating the asymmetry with the square root formula : A N = 1 P (cid:104) cos( φ ) (cid:105) (cid:113) N ↑ L N ↓ R − (cid:113) N ↓ L N ↑ R (cid:113) N ↑ L N ↓ R + (cid:113) N ↓ L N ↑ R , (4)where the L and R subscripts refer to yields to the leftand to the right of the polarized-beam-going direction, re-spectively. This result is verified to be consistent with therelative luminosity formula results from Eq. (1) and thedifferences between these results are assigned as an addi-tional systematic uncertainty due to possible variationsin detector performance and beam conditions. Anotherstudy using bunch shuffling found no additional system-atic effects. Bunch shuffling is a technique that random-izes the bunch-by-bunch beam polarization directions toconfirm that the variations present in the data are con-sistent with what is expected by statistical variation. TABLE I. The measured A N of isolated direct photons in p ↑ + p collisions at √ s =200 GeV as a function of p T . Anadditional scale uncertainty of 3.4% due to the polarizationuncertainty is not included. (cid:104) p T (cid:105) [GeV /c ] A dir N σ stat σ syst The results for the A N of isolated direct photons, A dir N ,at midrapidity in p ↑ + p collisions at √ s = 200 GeV areshown in Table I and in Fig. 2, where the shaded [gray]bands represent the systematic uncertainty and the ver-tical bars represent the statistical uncertainty. The mea- [GeV/c] T p5 6 7 8 9 10 11 12 N d i r A - qgq Contributionggg Contribution Model 1, min/maxggg Contribution Model 2, min/max |<0.35 h = 200 GeV, |s + X, iso g fi + p › p PHENIX
FIG. 2. Transverse single-spin asymmetry of isolated directphotons measured at midrapidity | η | < .
35 in p ↑ + p collisionsat √ s = 200 GeV. An additional scale uncertainty of 3.4% dueto the polarization uncertainty is not shown. surement is consistent with zero to within 1% across theentire p T range. Figure 2 also shows predictions fromcollinear twist-3 correlation functions. The solid [green]curve shows the contribution of qgq correlation functionsto the direct-photon asymmetry which is calculated usingfunctions that were published in Ref. [18] that are inte-grated over the | η | < .
35 pseudorapidity range of thePHENIX central arms. This calculation includes con-tributions from the qgq correlation functions present inboth the polarized and unpolarized proton, including theETQS function which is extracted from a global fit inRef. [17]. The error band plotted with the solid [green]curve in Fig. 2 includes uncertainties propagated fromfits to data, but does not include uncertainties associ-ated with assuming functional forms. Quark-flavor de-pendence is not considered in these calculations, includ-ing qgq correlators. Direct-photon production in p + p collisions is four times more sensitive to the up quarkthan the down quark in the proton because of the factorof electric charge squared in the production cross section.Given the small predicted contributions from qgq correlation functions to the midrapidity direct photonTSSA, this measurement can provide a clean extractionof the ggg function. The predicted ranges for the trigluoncorrelation function’s contribution to the direct-photonasymmetry are also plotted in Fig. 2. The dashed [blue]and dotted [red] curves use results that were publishedin Ref. [20] and were reevaluated as a function of pho-ton p T for pseudorapidity η = 0 [31]. Models 1 and 2assume different functional forms for the trigluon cor-relation function in terms of the collinear leading-twistgluon PDF. As this figure clearly shows, this measure-ment has the statistical precision, especially at low p T ,to constrain the trigluon correlation function.In summary, the TSSA of midrapidity isolated directphotons was measured by the PHENIX experiment tobe consistent with zero in the presented p T range, withuncertainties as low as 0.4% in the lowest p T bins. Thisis the first time direct photons have been used to probetransversely polarized proton collisions at RHIC and thefirst measurement of this TSSA in almost 30 years, withsignificantly higher p T reach and up to a fifty-fold im-provement in uncertainty. Direct photons are a cleanprobe of proton structure with no contributions fromfinal-state QCD effects and at midrapidity are particu-larly sensitive to gluon dynamics. When included in theglobal analysis of world TSSA data, this measurementwill constrain gluon spin-momentum correlations in thetransversely polarized proton, marking an important steptoward creating a more three-dimensional picture of pro-ton structure.We thank the staff of the Collider-Accelerator andPhysics Departments at Brookhaven National Labora-tory and the staff of the other PHENIX participat-ing institutions for their vital contributions. We alsothank D. Pitonyak and S. Yoshida for helpful discus-sions. 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 Sci-ences, Vanderbilt University (U.S.A), Ministry of Ed-ucation, Culture, Sports, Science, and Technology andthe Japan Society for the Promotion of Science (Japan),Conselho Nacional de Desenvolvimento Cient´ıfico e Tec-nol´ogico and Funda¸c˜ao de Amparo `a Pesquisa do Es-tado de S˜ao Paulo (Brazil), Natural Science Founda-tion of China (People’s Republic of China), CroatianScience Foundation and Ministry of Science and Educa-tion (Croatia), Ministry of Education, Youth and Sports(Czech Republic), Centre National de la Recherche Sci-entifique, Commissariat `a l’´Energie Atomique, and Insti-tut National de Physique Nucl´eaire et de Physique desParticules (France), Bundesministerium f¨ur Bildung undForschung, Deutscher Akademischer Austausch Dienst,and Alexander von Humboldt Stiftung (Germany), J.Bolyai Research Scholarship, EFOP, the New NationalExcellence Program ( ´UNKP), NKFIH, and OTKA (Hun-gary), Department of Atomic Energy and Department ofScience and Technology (India), Israel Science Founda-tion (Israel), Basic Science Research and SRC(CENuM)Programs through NRF funded by the Ministry of Ed-ucation and the Ministry of Science and ICT (Korea).Physics Department, Lahore University of ManagementSciences (Pakistan), Ministry of Education and Science,Russian Academy of Sciences, Federal Agency of AtomicEnergy (Russia), VR and Wallenberg Foundation (Swe-den), the U.S. Civilian Research and Development Foun-dation for the Independent States of the Former SovietUnion, the Hungarian American Enterprise ScholarshipFund, the US-Hungarian Fulbright Foundation, and theUS-Israel Binational Science Foundation. ∗ PHENIX Spokesperson: [email protected] † Deceased[1] A. Adare et al. (PHENIX Collaboration), “High p T directphoton and π triggered azimuthal jet correlations andmeasurement of k T for isolated direct photons in p + p collisions at √ s = 200 GeV,” Phys. Rev. D , 072001(2010).[2] R. D. Klem, J. E. Bowers, H. W. Courant, H. Kagan,M. L. Marshak, E. A. Peterson, K. Ruddick, W. H.Dragoset, and J. B. Roberts, “Measurement of Asym-metries of Inclusive Pion Production in Proton ProtonInteractions at 6-GeV/c and 11.8-GeV/c,” Phys. Rev.Lett. , 929 (1976).[3] D. L. Adams et al. (FNAL-E704 Collaboration), “Ana-lyzing power in inclusive π + and π − production at high x F with a 200-GeV polarized proton beam,” Phys. Lett. , 462 (1991).[4] C.E. Allgower et al. , “Measurement of analyzing powersof π + and π − produced on a hydrogen and a carbontarget with a 22-GeV/c incident polarized proton beam,”Phys. Rev. D , 092008 (2002).[5] I. Arsene et al. (BRAHMS Collaboration), “Single Trans-verse Spin Asymmetries of Identified Charged Hadrons inPolarized p + p Collisions at √ s = 62.4 GeV,” Phys. Rev.Lett. , 042001 (2008).[6] J. Adam et al. (STAR Collaboration), “Comparison oftransverse single-spin asymmetries for forward π pro-duction in polarized pp , p Al and p Au collisions at nu-cleon pair c.m. energy √ s NN = 200 GeV,” (2020),arXiv:2012.07146.[7] G. L. Kane, J. Pumplin, and W. Repko, “TransverseQuark Polarization in Large p T Reactions, e + e − Jets,and Leptoproduction: A Test of QCD,” Phys. Rev. Lett. , 1689 (1978).[8] D. W. Sivers, “Single Spin Production Asymmetries fromthe Hard Scattering of Point-Like Constituents,” Phys.Rev. D , 83 (1990).[9] C. Adolph et al. (COMPASS Collaboration), “First mea-surement of the Sivers asymmetry for gluons using SIDISdata,” Phys. Lett. B , 854 (2017).[10] R. M. Godbole, A. Kaushik, A. Misra, and S. Pad-val, “Probing the Gluon Sivers Function through directphoton production at RHIC,” Phys. Rev. D , 014003(2019).[11] D. Boer, P.J. Mulders, and F. Pijlman, “Universality ofT odd effects in single spin and azimuthal asymmetries,”Nucl. Phys. B667 , 201 (2003).[12] X. Ji, J.-W. Qiu, W. Vogelsang, and F. Yuan, “A Uni-fied picture for single transverse-spin asymmetries in hardprocesses,” Phys. Rev. Lett. , 082002 (2006).[13] A. V. Efremov and O. V. Teryaev, “QCD Asymmetryand Polarized Hadron Structure Functions,” Phys. Lett.B , 383 (1985).[14] J. Qiu and G. F. Sterman, “Single transverse spin asym-metries in direct photon production,” Nucl. Phys. B378 ,52 (1992).[15] J. Qiu and G. F. Sterman, “Single transverse spin asym-metries in hadronic pion production,” Phys. Rev. D ,014004 (1999).[16] K. Kanazawa, Y. Koike, A. Metz, and D. Pitonyak, “To-wards an explanation of transverse single-spin asymme- tries in proton-proton collisions: the role of fragmenta-tion in collinear factorization,” Phys. Rev. D , 111501(2014).[17] J. Cammarota, L. Gamberg, Z.-B. Kang, J. A. Miller,D. Pitonyak, A. Prokudin, T. C. Rogers, and N. Sato(Jefferson Lab Angular Momentum Collaboration), “Ori-gin of single transverse-spin asymmetries in high-energycollisions,” Phys. Rev. D , 054002 (2020).[18] K. Kanazawa, Y. Koike, A. Metz, and D. Pitonyak,“Transverse single-spin asymmetries in p ↑ p → γX fromquark-gluon-quark correlations in the proton,” Phys.Rev. D , 014013 (2015).[19] C. Aidala et al. (PHENIX Collaboration), “Cross sec-tion and transverse single-spin asymmetry of muons fromopen heavy-flavor decays in polarized p + p collisions at √ s = 200 GeV,” Phys. Rev. D , 112001 (2017).[20] Y. Koike and S. Yoshida, “Probing the three-gluon cor-relation functions by the single spin asymmetry in p ↑ p → DX ,” Phys. Rev. D , 014026 (2011).[21] Y. Koike and S. Yoshida, “Three-gluon contribution tothe single spin asymmetry in Drell-Yan and direct-photonprocesses,” Phys. Rev. D , 034030 (2012).[22] D.L. Adams et al. (E704 Collaboration), “Measurementof single spin asymmetry for direct photon productionin p p collisions at 200-GeV/c,” Phys. Lett. B , 569(1995).[23] A. Adare et al. (PHENIX Collaboration), “Direct-Photon Production in p + p Collisions at √ s = 200 GeV at Midrapidity,” Phys. Rev. D , 072008 (2012).[24] W. D. Schmidke et al. (The RHIC Polarime-try Group), “RHIC polarization for Runs 9–17,”https://technotes.bnl.gov/Home/ViewTechNote/209057(2018).[25] L. Aphecetche et al. (PHENIX Collaboration), “PHENIXcalorimeter,” Nucl. Instrum. Methods Phys. Res., Sec. A , 521 (2003).[26] K. Adcox et al. (PHENIX Collaboration), “PHENIX cen-tral arm tracking detectors,” Nucl. Instrum. MethodsPhys. Res., Sec. A , 489 (2003).[27] M. Allen et al. , “PHENIX inner detectors,” Nucl. In-strum. Methods Phys. Res., Sec. A , 549 (2003).[28] C. Aidala et al. , “Transverse single-spin asymmetriesof midrapidity π and η mesons in p + p collisions at √ s = 200 GeV,” (2020), arXiv:2011.14170 and DY12683in production PRD.[29] A. Adare et al. (PHENIX Collaboration), “Inclusivecross-section and double helicity asymmetry for π pro-duction in p + p collisions at √ s = 200 GeV: Implicationsfor the polarized gluon distribution in the proton,” Phys.Rev. D , 051106 (2007).[30] A. Adare et al. (PHENIX Collaboration), “Cross sectionand double helicity asymmetry for η mesons and theircomparison to neutral pion production in p+p collisionsat √ s = 200 GeV,” Phys. Rev. D83