Open Access

Transverse single-spin asymmetry of forward $η$ mesons in $p^{↑} + p$ collisions at $\sqrt{s} = 200 GeV$

N. J. Abdulameer^15,22, U. Acharya ¹⁹, C. Aidala ^38,43, N. N. Ajitanand^62,*, Y. Akiba ^57,58,†, R. Akimoto¹¹, J. Alexander⁶², D. Anderson²⁷, S. Antsupov⁶⁰ et al. (PHENIX Collaboration)

S. Antsupov⁶⁰, K. Aoki^31,57, N. Apadula ^27,63, H. Asano^34,57, E. T. Atomssa⁶³, T. C. Awes⁵⁴, B. Azmoun ⁷, V. Babintsev²³, M. Bai⁶, X. Bai¹⁰, B. Bannier⁶³, E. Bannikov⁶⁰, K. N. Barish ⁸, S. Bathe ^5,58, V. Baublis⁵⁶, C. Baumann⁷, S. Baumgart⁵⁷, A. Bazilevsky ⁷, M. Beaumier⁸, R. Belmont ^12,52, A. Berdnikov ⁶⁰, Y. Berdnikov ⁶⁰, L. Bichon⁶⁹, D. Black⁸, B. Blankenship⁶⁹, D. S. Blau^33,49, J. S. Bok⁵¹, V. Borisov⁶⁰, K. Boyle⁵⁸, M. L. Brooks³⁸, J. Bryslawskyj ^5,8, H. Buesching⁷, V. Bumazhnov²³, S. Butsyk⁵⁰, S. Campbell^13,27, P. Chaitanya⁶³, C.-H. Chen⁵⁸, D. Chen ⁶³, M. Chiu ⁷, C. Y. Chi¹³, I. J. Choi²⁴, J. B. Choi^29,*, S. Choi⁶¹, P. Christiansen³⁹, T. Chujo ⁶⁷, V. Cianciolo⁵⁴, B. A. Cole¹³, M. Connors ^19,58, R. Corliss ⁶³, N. Cronin^45,63, N. Crossette⁴⁵, M. Csanád¹⁶, T. Csörgő^42,71, L. D’Orazio⁴⁰, A. Datta⁵⁰, M. S. Daugherity¹, G. David^7,63, K. Dehmelt ⁶³, A. Denisov²³, A. Deshpande ^58,63, E. J. Desmond⁷, L. Ding²⁷, V. Doomra⁶³, J. H. Do⁷², O. Drapier³⁵, A. Drees ⁶³, K. A. Drees⁶, J. M. Durham ³⁸, A. Durum²³, T. Engelmore¹³, A. Enokizono ^57,59, R. Esha ⁶³, K. O. Eyser⁷, B. Fadem⁴⁵, D. E. Fields⁵⁰, M. Finger, Jr.⁹, M. Finger⁹, D. Firak ^15,63, D. Fitzgerald ⁴³, F. Fleuret³⁵, S. L. Fokin³³, J. E. Frantz⁵³, A. Franz ⁷, A. D. Frawley¹⁸, Y. Fukao³¹, T. Fusayasu⁴⁷, K. Gainey¹, C. Gal⁶³, P. Garg ^3,63, A. Garishvili⁶⁵, I. Garishvili³⁷, F. Giordano²⁴, A. Glenn³⁷, X. Gong⁶², M. Gonin³⁵, Y. Goto^57,58, R. Granier de Cassagnac³⁵, N. Grau², S. V. Greene ⁶⁹, M. Grosse Perdekamp²⁴, T. Gunji ¹¹, T. Guo ⁶³, H. Guragain¹⁹, Y. Gu⁶², J. S. Haggerty ⁷, K. I. Hahn¹⁷, H. Hamagaki ¹¹, J. Hanks⁶³, K. Hashimoto^57,59, R. Hayano¹¹, T. K. Hemmick ⁶³, T. Hester⁸, X. He ¹⁹, J. C. Hill²⁷, A. Hodges ^19,24, R. S. Hollis⁸, K. Homma²¹, B. Hong ³², T. Hoshino²¹, J. Huang^7,38, T. Ichihara^57,58, Y. Ikeda⁵⁷, K. Imai²⁸, Y. Imazu⁵⁷, M. Inaba ⁶⁷, A. Iordanova⁸, D. Isenhower¹, A. Isinhue⁴⁵, D. Ivanishchev⁵⁶, B. V. Jacak ⁶³, S. J. Jeon⁴⁶, M. Jezghani¹⁹, X. Jiang ³⁸, Z. Ji ⁶³, B. M. Johnson ^7,19, K. S. Joo⁴⁶, D. Jouan⁵⁵, D. S. Jumper²⁴, J. Kamin⁶³, S. Kanda^11,31, B. H. Kang²⁰, J. H. Kang⁷², J. S. Kang²⁰, J. Kapustinsky³⁸, G. Kasza^42,71, D. Kawall⁴¹, A. V. Kazantsev³³, J. A. Key⁵⁰, V. Khachatryan⁶³, P. K. Khandai³, A. Khanzadeev ⁵⁶, K. M. Kijima²¹, C. Kim ³², D. J. Kim ³⁰, E.-J. Kim ²⁹, Y.-J. Kim²⁴, Y. K. Kim²⁰, E. Kistenev⁷, J. Klatsky¹⁸, D. Kleinjan⁸, P. Kline⁶³, T. Koblesky¹², M. Kofarago^16,71, B. Komkov⁵⁶, J. Koster⁵⁸, D. Kotchetkov⁵³, D. Kotov ^56,60, L. Kovacs¹⁶, F. Krizek³⁰, K. Kurita⁵⁹, M. Kurosawa^57,58, Y. Kwon ⁷², Y. S. Lai¹³, J. G. Lajoie^27,54, A. Lebedev ²⁷, D. M. Lee³⁸, G. H. Lee²⁹, J. Lee^17,64, K. B. Lee³⁸, K. S. Lee³², S. H. Lee ^27,63, M. J. Leitch ³⁸, M. Leitgab²⁴, B. Lewis⁶³, X. Li¹⁰, X. Li³⁸, S. H. Lim ⁷², M. X. Liu ³⁸, D. A. Loomis ⁴³, D. Lynch⁷, S. Lökös⁷¹, C. F. Maguire⁶⁹, Y. I. Makdisi⁶, M. Makek^70,73, A. Manion⁶³, V. I. Manko³³, E. Mannel ⁷, M. McCumber^12,38, P. L. McGaughey³⁸, D. McGlinchey^12,18,38, C. McKinney²⁴, A. Meles⁵¹, M. Mendoza⁸, B. Meredith²⁴, Y. Miake⁶⁷, T. Mibe³¹, A. C. Mignerey ⁴⁰, A. Milov ⁷⁰, D. K. Mishra⁴, J. T. Mitchell⁷, M. Mitrankova^60,63, Iu. Mitrankov^60,63, S. Miyasaka^57,66, S. Mizuno^57,67, A. K. Mohanty⁴, S. Mohapatra⁶², D. P. Morrison ⁷, M. Moskowitz⁴⁵, T. V. Moukhanova³³, B. Mulilo^32,57,74, T. Murakami ^34,57, J. Murata^57,59, A. Mwai⁶², T. Nagae³⁴, S. Nagamiya^31,57, J. L. Nagle ¹², M. I. Nagy¹⁶, I. Nakagawa ^57,58, Y. Nakamiya²¹, K. R. Nakamura^34,57, T. Nakamura⁵⁷, K. Nakano^57,66, C. Nattrass ⁶⁵, P. K. Netrakanti⁴, M. Nihashi^21,57, T. Niida⁶⁷, R. Nouicer^7,58, N. Novitzky ^30,63, T. Novák^42,71, G. Nukazuka ^57,58, A. S. Nyanin³³, E. O’Brien ⁷, C. A. Ogilvie²⁷, H. Oide¹¹, K. Okada⁵⁸, M. Orosz^15,22, A. Oskarsson³⁹, K. Ozawa^31,67, R. Pak⁷, V. Pantuev ²⁵, V. Papavassiliou⁵¹, I. H. Park^17,64, J. S. Park⁶¹, S. Park ^44,57,61,63, S. K. Park³², L. Patel¹⁹, S. F. Pate ⁵¹, J.-C. Peng²⁴, D. V. Perepelitsa ^12,13, G. D. N. Perera⁵¹, D. Yu. Peressounko³³, J. Perry²⁷, R. Petti^7,63, C. Pinkenburg ⁷, R. P. Pisani⁷, M. Potekhin⁷, M. L. Purschke⁷, H. Qu¹, J. Rak³⁰, I. Ravinovich ⁷⁰, K. F. Read ^54,65, D. Reynolds⁶², V. Riabov ^49,56, Y. Riabov^56,60, E. Richardson⁴⁰, D. Richford ^5,68, N. Riveli⁵³, D. Roach⁶⁹, S. D. Rolnick⁸, M. Rosati ²⁷, M. S. Ryu²⁰, B. Sahlmueller⁶³, N. Saito³¹, T. Sakaguchi ⁷, H. Sako²⁸, V. Samsonov^49,56, M. Sarsour ¹⁹, S. Sato²⁸, S. Sawada³¹, K. Sedgwick⁸, J. Seele⁵⁸, R. Seidl ^57,58, Y. Sekiguchi¹¹, A. Seleznev⁶⁰, A. Sen^19,27, R. Seto⁸, P. Sett⁴, D. Sharma ⁶³, A. Shaver²⁷, I. Shein²³, T.-A. Shibata^57,66, K. Shigaki ²¹, M. Shimomura ^27,48, K. Shoji⁵⁷, P. Shukla⁴, A. Sickles ^7,24, C. L. Silva³⁸, D. Silvermyr ^39,54, B. K. Singh³, C. P. Singh³, V. Singh ³, M. Skolnik⁴⁵, M. Slunečka⁹, K. L. Smith ^18,38, S. Solano⁴⁵, R. A. Soltz ³⁷, W. E. Sondheim³⁸, S. P. Sorensen ⁶⁵, I. V. Sourikova⁷, P. W. Stankus⁵⁴, P. Steinberg⁷, E. Stenlund³⁹, M. Stepanov⁴¹, A. Ster⁷¹, S. P. Stoll⁷, M. R. Stone¹², T. Sugitate²¹, A. Sukhanov⁷, J. Sun ⁶³, Z. Sun ^15,22,63, A. Takahara¹¹, A. Taketani^57,58, Y. Tanaka⁴⁷, K. Tanida^28,58,61, M. J. Tannenbaum⁷, S. Tarafdar ^3,69, A. Taranenko^49,62, E. Tennant⁵¹, A. Timilsina²⁷, T. Todoroki^57,58,67, M. Tomášek^14,26, H. Torii¹¹, R. S. Towell ¹, I. Tserruya ⁷⁰, B. Ujvari ^15,22, H. W. van Hecke³⁸, M. Vargyas^16,71, E. Vazquez-Zambrano¹³, A. Veicht¹³, J. Velkovska ⁶⁹, M. Virius¹⁴, V. Vrba^14,26, E. Vznuzdaev⁵⁶, R. Vértesi⁷¹, X. R. Wang^51,58, D. Watanabe²¹, K. Watanabe^57,59, Y. Watanabe^57,58, Y. S. Watanabe^11,31, F. Wei⁵¹, S. Whitaker²⁷, S. Wolin²⁴, C. L. Woody⁷, M. Wysocki⁵⁴, B. Xia⁵³, Y. L. Yamaguchi^11,63, A. Yanovich²³, S. Yokkaichi^57,58, I. Yoon ⁶¹, I. Younus^36,50, Z. You³⁸, I. E. Yushmanov³³, W. A. Zajc ¹³, A. Zelenski⁶, and S. Zhou¹⁰ (PHENIX Collaboration)

¹Abilene Christian University, Abilene, Texas 79699, USA
²Department of Physics, Augustana University, Sioux Falls, South Dakota 57197, USA
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, Faculty of Mathematics and Physics, 180 00 Troja, Prague, Czech Republic
¹⁰Science and Technology on Nuclear Data Laboratory, China Institute of Atomic Energy, Beijing 102413, People’s Republic of China
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 tér 1, Hungary
¹⁶ELTE, Eötvös Loránd University, H-1117 Budapest, Pázmány P. s. 1/A, Hungary
¹⁷Ewha Womans University, Seoul 120-750, Korea
¹⁸Florida State University, Tallahassee, Florida 32306, USA
¹⁹Georgia State University, Atlanta, Georgia 30303, USA
²⁰Hanyang University, Seoul 133-792, Korea
²¹Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
²²HUN-REN ATOMKI, H-4026 Debrecen, Bem tér 18/c, Hungary
²³IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, 142281, Russia
²⁴University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²⁵Institute for Nuclear Research of the Russian Academy of Sciences, prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia
²⁶Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic
²⁷Iowa State University, Ames, Iowa 50011, USA
²⁸Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan
²⁹Jeonbuk National University, Jeonju, 54896, Korea
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
³⁵Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay, F-91128, Palaiseau, France
³⁶Physics Department, Lahore University of Management Sciences, Lahore 54792, Pakistan
³⁷Lawrence Livermore National Laboratory, Livermore, California 94550, USA
³⁸Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
³⁹Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden
⁴⁰University of Maryland, College Park, Maryland 20742, USA
⁴¹Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-9337, USA
⁴²MATE, Institute of Technology, Laboratory of Femtoscopy, Károly Róbert Campus, H-3200 Gyöngyös, Mátrai út 36, Hungary
⁴³Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
⁴⁴Mississippi State University, Mississippi State, Mississippi 39762, USA
⁴⁵Muhlenberg College, Allentown, Pennsylvania 18104-5586, USA
⁴⁶Myongji University, Yongin, Kyonggido 449-728, Korea
⁴⁷Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan
⁴⁸Nara Women’s University, Kita-uoya Nishi-machi Nara 630-8506, Japan
⁴⁹National Research Nuclear University, MEPhI, Moscow Engineering Physics Institute, Moscow, 115409, Russia
⁵⁰University of New Mexico, Albuquerque, New Mexico 87131, USA
⁵¹New Mexico State University, Las Cruces, New Mexico 88003, USA
⁵²Physics and Astronomy Department, University of north Carolina at Greensboro, Greensboro, North Carolina 27412, USA
⁵³Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA
⁵⁴Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁵⁵IPN-Orsay, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, BP1, F-91406, Orsay, France
⁵⁶PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia
⁵⁷RIKEN Nishina Center for Accelerator-Based Science, Wako, Saitama 351-0198, Japan
⁵⁸RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
⁵⁹Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan
⁶⁰Saint Petersburg State Polytechnic University, St. Petersburg, 195251 Russia
⁶¹Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Korea
⁶²Chemistry Department, Stony Brook University, SUNY, Stony Brook, New York 11794-3400, USA
⁶³Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, New York 11794-3800, USA
⁶⁴Sungkyunkwan University, Suwon, 440-746, Korea
⁶⁵University of Tennessee, Knoxville, Tennessee 37996, USA
⁶⁶Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan
⁶⁷Tomonaga Center for the History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
⁶⁸United States Merchant Marine Academy, Kings Point, New York 11024, USA
⁶⁹Vanderbilt University, Nashville, Tennessee 37235, USA
⁷⁰Weizmann Institute, Rehovot 76100, Israel
⁷¹Institute for Particle and Nuclear Physics, HUN-REN Wigner Research Centre for Physics, (HUN-REN Wigner RCP, RMI), H-1525 Budapest 114, P.O. Box 49, Budapest, Hungary
⁷²Yonsei University, IPAP, Seoul 120-749, Korea
⁷³Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32 HR-10002 Zagreb, Croatia
⁷⁴Department of Physics, School of Natural Sciences, University of Zambia, Great East Road Campus, Box 32379, Lusaka, Zambia

^*Deceased.
^†PHENIX Collaboration Spokesperson.

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Phys. Rev. D 113, 072006 – Published 9 April, 2026

DOI: https://doi.org/10.1103/6vnq-5hfx

Abstract

Utilizing the 2012 transversely polarized proton data from the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, the forward $η$ -meson transverse single-spin asymmetry ( $A_{N}$ ) was measured for $p^{↑} + p$ collisions at $\sqrt{s} = 200 GeV$ as a function of Feynman-x ( $x_{F}$ ) for $0.2 < | x_{F} | < 0.8$ and transverse momentum ( $p_{T}$ ) for $1.0 < p_{T} < 5.0 GeV / c$ . Large asymmetries at positive $x_{F}$ are observed ( $⟨ A_{N} ⟩ = 0.086 \pm 0.019$ ), agreeing well with previous measurements of $π^{0}$ and $η A_{N}$ , but with reach to higher $x_{F}$ and $p_{T}$ . The contribution of initial-state spin-momentum correlations to the asymmetry, as calculated in the collinear twist-3 framework, appears insufficient to describe the data.

Physics Subject Headings (PhySH)

Article Text

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Phys. Rev. D 113, 072006– Published 9 April, 2026

Vol. 113, Iss. 7 — 1 April 2026

Received 19 September 2025
Accepted 20 February 2026

DOI: https://doi.org/10.1103/6vnq-5hfx

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.

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Transverse single-spin asymmetry of forward $η$ mesons in $p^{↑} + p$ collisions at $\sqrt{s} = 200 GeV$

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Transverse single-spin asymmetry of forward η mesons in p↑+p collisions at s=200 GeV

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Transverse single-spin asymmetry of forward $η$ mesons in $p^{↑} + p$ collisions at $\sqrt{s} = 200 GeV$