Open Access

Energy Independence of the Collins Asymmetry in $p^{↑} p$ Collisions

B. E. Aboona⁵⁸, J. Adam¹⁷, L. Adamczyk³, I. Aggarwal⁴⁵, M. M. Aggarwal⁴⁵, Z. Ahammed⁶⁶, A. K. Alshammri³³, E. C. Aschenauer⁷, S. Aslam²² et al. (STAR Collaboration)

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Gibson⁶⁵, A. Giri²⁵, K. Gopal²⁸, X. Gou⁵², D. Grosnick⁶⁵, A. Gu²⁶, J. Gu²², A. Gupta³², W. Guryn⁷, A. Hamed⁵, R. J. Hamilton⁷⁰, J. Han¹³, X. Han⁴⁴, S. Harabasz¹⁸, M. D. Harasty¹⁰, J. W. Harris⁷⁰, H. Harrison-Smith³⁴, L. B. Havener⁷⁰, X. H. He³¹, Y. He⁵², N. Herrmann²⁴, L. Holub¹⁷, C. Hu⁶³, Q. Hu³¹, Y. Hu³⁶, H. Huang^42,1, H. Z. Huang¹¹, S. L. Huang⁵⁵, T. Huang¹⁴, Y. Huang²⁰, Y. Huang³¹, Y. Huang²², M. Isshiki⁶², W. W. Jacobs³⁰, A. Jalotra³², C. Jena²⁸, A. Jentsch⁷, Y. Ji³⁶, J. Jia^55,7, X. Jiang¹³, C. Jin⁴⁷, Y. Jin¹³, N. Jindal⁴⁴, X. Ju⁴⁹, E. G. Judd⁹, S. Kabana⁵⁶, D. Kalinkin³⁴, J. Kang⁵¹, K. Kang⁶¹, A. R. Kanuganti⁷, D. Kapukchyan¹², K. Kauder⁷, D. Keane³³, M. Kesler³³, A. Khanal⁶⁸, Y. V. Khyzhniak⁴⁴, D. P. Kikoła⁶⁷, J. Kim⁷, D. Kincses²⁰, I. Kisel²¹, A. Kiselev⁷, A. G. Knospe³⁷, J. Kołaś⁶⁷, B. Korodi⁴⁴, L. K. Kosarzewski⁴⁴, L. Kumar⁴⁵, M. C. Labonte¹⁰, R. Lacey⁵⁵, J. M. Landgraf⁷, C. Larson³⁴, J. Lauret⁷, A. Lebedev⁷, J. H. Lee⁷, Y. H. Leung²⁴, C. Li¹³, D. Li⁴⁹, H-S. Li⁴⁶, H. Li⁶⁹, H. Li²³, H. Li¹³, W. Li⁴⁷, X. Li⁴⁹, X. Li⁴⁹, Y. Li⁶¹, Z. Li⁵⁰, Z. Li⁴⁹, X. Liang¹², R. Licenik^43,17, T. Lin⁵², Y. Lin²³, M. A. Lisa⁴⁴, C. Liu³¹, G. Liu⁵⁰, H. Liu²⁶, L. Liu¹³, L. Liu²², Z. Liu²², Z. Liu¹³, T. Ljubicic⁴⁷, O. Lomicky¹⁷, E. M. Loyd¹², T. Lu³¹, J. Luo⁴⁹, X. F. Luo¹³, L. Ma²², R. Ma⁷, Y. G. Ma²², N. Magdy⁵⁹, D. Mallick¹³, R. Manikandhan²⁵, C. Markert⁶⁰, O. Matonoha¹⁷, K. Mi⁶³, S. Mioduszewski⁵⁸, B. Mohanty⁴¹, B. Mondal⁴¹, M. M. Mondal³⁸, I. Mooney⁷⁰, J. Mrazkova^43,17, M. I. Nagy²⁰, C. J. Naim⁵⁵, A. S. Nain⁴⁵, J. D. Nam⁵⁷, M. Nasim²⁷, H. Nasrulloh⁴⁹, J. M. Nelson⁹, M. Nie⁵², G. Nigmatkulov¹⁴, T. Niida⁶², T. Nonaka⁶², G. Odyniec³⁶, A. Ogawa⁷, S. Oh⁵¹, K. Okubo⁶², B. S. Page⁷, S. Pal¹⁷, A. Pandav³⁶, A. Panday²⁷, A. K. Pandey⁶⁷, T. Pani⁴⁸, A. Paul¹², S. Paul⁵⁵, D. Pawlowska⁶⁷, C. Perkins⁹, S. Ping²², J. Pluta⁶⁷, B. R. Pokhrel⁵⁷, I. D. Ponce Pinto⁷⁰, M. Posik⁵⁷, E. Pottebaum⁷⁰, S. Prodhan²⁸, T. L. Protzman³⁷, A. Prozorov¹⁷, V. Prozorova¹⁷, N. K. Pruthi⁴⁵, M. Przybycien³, J. Putschke⁶⁸, Y. Qi¹³, Z. Qin⁶¹, H. Qiu³¹, C. Racz¹², S. K. Radhakrishnan³³, A. Rana⁴⁵, R. L. Ray⁶⁰, R. Reed³⁷, C. W. Robertson⁴⁶, M. Robotkova^43,17, M. A. Rosales Aguilar³⁴, D. Roy⁴⁸, P. Roy Chowdhury⁶⁷, L. Ruan⁷, A. K. Sahoo²⁷, N. R. Sahoo²⁸, H. Sako⁶², S. Salur⁴⁸, S. S. Sambyal³², J. K. Sandhu³⁷, S. Sato⁶², B. C. Schaefer³⁷, N. Schmitz³⁹, F-J. Seck¹⁸, J. Seger¹⁶, R. Seto¹², P. Seyboth³⁹, N. Shah²⁹, P. V. Shanmuganathan⁷, T. Shao²², M. Sharma³², N. Sharma²⁷, R. Sharma²⁸, S. R. Sharma²⁸, A. I. Sheikh³³, D. Shen⁵², D. Y. Shen³¹, K. Shen⁴⁹, S. Shi¹³, Y. Shi⁵², E. Shulga⁷, F. Si⁴⁹, J. Singh⁵⁶, S. Singha³¹, P. Sinha²⁸, M. J. Skoby^6,46, N. Smirnov⁷⁰, Y. Söhngen²⁴, Y. Song⁷⁰, T. D. S. Stanislaus⁶⁵, M. Stefaniak⁴⁴, Y. Su⁴⁹, M. Sumbera⁴³, X. Sun³¹, Y. Sun⁴⁹, B. Surrow⁵⁷, M. Svoboda^43,17, Z. W. Sweger¹⁰, A. C. Tamis⁷⁰, A. H. Tang⁷, Z. Tang⁴⁹, T. Tarnowsky⁴⁰, J. H. Thomas³⁶, A. R. Timmins²⁵, D. Tlusty¹⁶, D. Torres Valladares⁴⁷, S. Trentalange¹¹, P. Tribedy⁷, S. K. Tripathy⁶⁷, T. Truhlar¹⁷, B. A. Trzeciak¹⁷, O. D. Tsai^11,7, C. Y. Tsang^33,7, Z. Tu⁷, J. E. Tyler⁵⁸, T. Ullrich⁷, D. G. Underwood^4,65, G. Van Buren⁷, J. Vanek⁷, I. Vassiliev²¹, F. Videbæk⁷, S. A. Voloshin⁶⁸, F. Wang⁴⁶, G. Wang¹¹, G. Wang¹³, J. S. Wang²⁶, J. Wang⁵², K. Wang⁴⁹, X. Wang⁵², Y. Wang⁴⁹, Y. Wang¹³, Y. Wang⁶¹, Z. Wang²², Z. Wang⁵², Z. Y. Wang²², A. J. Watroba³, J. C. Webb⁷, P. C. Weidenkaff²⁴, G. D. Westfall⁴⁰, D. Wielanek⁶⁷, H. Wieman³⁶, G. Wilks¹⁴, S. W. Wissink³⁰, R. Witt⁶⁴, C. P. Wong⁷, J. Wu⁶³, X. Wu¹¹, X. Wu⁴⁹, X. Wu¹³, B. Xi²², Y. Xiao²², Z. G. Xiao⁶¹, G. Xie⁶³, W. Xie⁴⁶, H. Xu²⁶, N. Xu¹³, Q. H. Xu⁵², Y. Xu⁵², Y. Xu²², Y. Xu¹³, Y. Xu³¹, Z. Xu³³, Z. Xu⁴, G. Yan⁵², Z. Yan⁵⁵, C. Yang⁵², Q. Yang⁵², S. Yang⁵⁰, Y. Yang^1,42, Z. Ye⁵⁰, Z. Ye³⁶, L. Yi⁵², Y. Yu⁵², H. Zbroszczyk⁶⁷, W. Zha⁴⁹, C. Zhang²², D. Zhang⁵⁰, J. Zhang⁵², L. Zhang¹³, S. Zhang¹⁵, W. Zhang⁵⁰, X. Zhang³¹, Y. Zhang³¹, Y. Zhang⁴⁹, Y. Zhang ⁵², Y. Zhang²³, Z. Zhang⁷, Z. Zhang¹⁴, F. Zhao³⁵, J. Zhao²², S. Zhou¹³, Y. Zhou¹³, X. Zhu⁶¹, M. Zurek^4,7, and M. Zyzak²¹ (STAR Collaboration)

¹Academia Sinica, Taipei 115
²Abilene Christian University, Abilene, Texas 79699
³AGH University of Krakow, FPACS, Cracow 30-059, Poland
⁴Argonne National Laboratory, Argonne, Illinois 60439
⁵American University in Cairo, New Cairo 11835, Egypt
⁶Ball State University, Muncie, Indiana, 47306
⁷Brookhaven National Laboratory, Upton, New York 11973
⁸University of Calabria and INFN-Cosenza, Rende 87036, Italy
⁹University of California, Berkeley, California 94720
¹⁰University of California, Davis, California 95616
¹¹University of California, Los Angeles, California 90095
¹²University of California, Riverside, California 92521
¹³Central China Normal University, Wuhan, Hubei 430079
¹⁴University of Illinois at Chicago, Chicago, Illinois 60607
¹⁵Chongqing University, Chongqing, 401331
¹⁶Creighton University, Omaha, Nebraska 68178
¹⁷Czech Technical University in Prague, FNSPE, Prague 115 19, Czech Republic
¹⁸Technische Universität Darmstadt, Darmstadt 64289, Germany
¹⁹National Institute of Technology Durgapur, Durgapur 713209, India
²⁰ELTE Eötvös Loránd University, Budapest, Hungary H-1117
²¹Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany
²²Fudan University, Shanghai, 200433
²³Guangxi Normal University, Guilin, 541004
²⁴University of Heidelberg, Heidelberg 69120, Germany
²⁵University of Houston, Houston, Texas 77204
²⁶Huzhou University, Huzhou, Zhejiang 313000
²⁷Indian Institute of Science Education and Research (IISER), Berhampur 760010, India
²⁸Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India
²⁹Indian Institute Technology, Patna, Bihar 801106, India
³⁰Indiana University, Bloomington, Indiana 47408
³¹Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu 730000
³²University of Jammu, Jammu 180001, India
³³Kent State University, Kent, Ohio 44242
³⁴University of Kentucky, Lexington, Kentucky 40506-0055
³⁵Lanzhou University, Lanzhou, 730000
³⁶Lawrence Berkeley National Laboratory, Berkeley, California 94720
³⁷Lehigh University, Bethlehem, Pennsylvania 18015
³⁸Lovely Professional University, Pagwara, Panjab 144411, India
³⁹Max-Planck-Institut für Physik, Munich 80805, Germany
⁴⁰Michigan State University, East Lansing, Michigan 48824
⁴¹National Institute of Science Education and Research, HBNI, Jatni 752050, India
⁴²National Cheng Kung University, Tainan 70101
⁴³Nuclear Physics Institute of the CAS, Rez 250 68, Czech Republic
⁴⁴The Ohio State University, Columbus, Ohio 43210
⁴⁵Panjab University, Chandigarh 160014, India
⁴⁶Purdue University, West Lafayette, Indiana 47907
⁴⁷Rice University, Houston, Texas 77251
⁴⁸Rutgers University, Piscataway, New Jersey 08854
⁴⁹University of Science and Technology of China, Hefei, Anhui 230026
⁵⁰South China Normal University, Guangzhou, Guangdong 510631
⁵¹Sejong University, Seoul, 05006, Republic of Korea
⁵²Shandong University, Qingdao, Shandong 266237
⁵³Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800
⁵⁴Southern Connecticut State University, New Haven, Connecticut 06515
⁵⁵State University of New York, Stony Brook, New York 11794
⁵⁶Instituto de Alta Investigación, Universidad de Tarapacá, Arica 1000000, Chile
⁵⁷Temple University, Philadelphia, Pennsylvania 19122
⁵⁸Texas A&M University, College Station, Texas 77843
⁵⁹Texas Southern University, Houston, Texas, 77004
⁶⁰University of Texas, Austin, Texas 78712
⁶¹Tsinghua University, Beijing 100084
⁶²University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
⁶³University of Chinese Academy of Sciences, Beijing, 101408
⁶⁴United States Naval Academy, Annapolis, Maryland 21402
⁶⁵Valparaiso University, Valparaiso, Indiana 46383
⁶⁶Variable Energy Cyclotron Centre, Kolkata 700064, India
⁶⁷Warsaw University of Technology, Warsaw 00-661, Poland
⁶⁸Wayne State University, Detroit, Michigan 48201
⁶⁹Wuhan University of Science and Technology, Wuhan, Hubei 430065
⁷⁰Yale University, New Haven, Connecticut 06520

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Phys. Rev. Lett. 135, 261902 – Published 26 December, 2025

DOI: https://doi.org/10.1103/jgsw-zhny

Abstract

The STAR experiment reports new, high-precision measurements of the transverse single-spin asymmetries for $π^{\pm}$ within jets, namely the Collins asymmetries, from transversely polarized $p^{↑} p$ collisions at $\sqrt{s} = 510 GeV$ . The energy-scaled distribution of jet transverse momentum, $x_{T} = 2 p_{T, jet} / \sqrt{s}$ , shows a remarkable consistency for Collins asymmetries of $π^{\pm}$ in jets between $\sqrt{s} = 200 GeV$ and 510 GeV. This indicates that the Collins asymmetries are nearly energy independent, with, at most, a very weak scale dependence in $p^{↑} p$ collisions. These results extend to high-momentum scales ( $Q^{2} \leq 3400 {GeV}^{2}$ ) and enable unique tests of evolution and universality in the transverse-momentum-dependent formalism, thus providing important constraints for the Collins fragmentation functions.

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Phys. Rev. Lett. 135, 261902– Published 26 December, 2025

Vol. 135, Iss. 26 — 31 December 2025

Received 23 July 2025
Revised 5 November 2025
Accepted 12 November 2025

DOI: https://doi.org/10.1103/jgsw-zhny

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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Energy Independence of the Collins Asymmetry in $p^{↑} p$ Collisions

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Energy Independence of the Collins Asymmetry in p↑p Collisions

Abstract

Physics Subject Headings (PhySH)

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References (59)

Energy Independence of the Collins Asymmetry in $p^{↑} p$ Collisions