- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Accessing Nucleon Transversity with One-Point Energy Correlators

Mei-Sen Gao1,*, Zhong-Bo Kang2,3,4,†, Wanchen Li1,‡, and Ding Yu Shao1,5,6,7,§

  • 1Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
  • 2Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
  • 3Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles, California 90095, USA
  • 4Center for Frontiers in Nuclear Science, Stony Brook University, Stony Brook, New York 11794, USA
  • 5Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University, Shanghai 200433, China
  • 6Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University, Shanghai 200438, China
  • 7Center for High Energy Physics, Peking University, Beijing 100871, China

  • *Contact author: msgao@fudan.edu.cn
  • †Contact author: zkang@physics.ucla.edu
  • ‡Contact author: wanchenli@fudan.edu.cn
  • §Contact author: dyshao@fudan.edu.cn
PDF

Phys. Rev. Lett. 136, 151902 – Published 17 April, 2026

DOI: https://doi.org/10.1103/1lz2-3fm9

Abstract

We propose a novel probe of the nucleon’s transversity distribution h1q using the one-point energy correlator (OPEC), an infrared-and-collinear safe jet substructure observable. We demonstrate that in transversely polarized p↑p collisions, the OPEC exhibits a single-spin asymmetry (SSA) with a clean sin(ϕs−ϕn) angular dependence. This method probes SSA over a much wider kinematic range in the angular scale θn compared to traditional measurements of hadron transverse momentum j⊥, establishing a complementary and systematically distinct channel to study the nucleon’s three-dimensional structure at the RHIC and the future electron-ion collider.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (105)

  1. J. P. Ralston and D. E. Soper, Nucl. Phys. B152, 109 (1979).
  2. R. L. Jaffe and X.-D. Ji, Phys. Rev. Lett. 67, 552 (1991).
  3. V. Barone, A. Drago, and P. G. Ratcliffe, Phys. Rep. 359, 1 (2002).
  4. H.-W. Lin et al., Prog. Part. Nucl. Phys. 100, 107 (2018).
  5. J. D. Jackson, S. B. Treiman, and H. W. Wyld, Phys. Rev. 106, 517 (1957).
  6. J. C. Collins, Nucl. Phys. B396, 161 (1993).
  7. J. C. Collins, S. F. Heppelmann, and G. A. Ladinsky, Nucl. Phys. B420, 565 (1994).
  8. Z.-B. Kang, A. Prokudin, P. Sun, and F. Yuan, Phys. Rev. D 93, 014009 (2016).
  9. 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), Phys. Rev. D 102, 054002 (2020).
  10. L. Gamberg, M. Malda, J. A. Miller, D. Pitonyak, A. Prokudin, and N. Sato (Jefferson Lab Angular Momentum (JAM) Collaboration), Phys. Rev. D 106, 034014 (2022).
  11. M. Radici and A. Bacchetta, Phys. Rev. Lett. 120, 192001 (2018).
  12. C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl (JAM Collaboration), Phys. Rev. Lett. 132, 091901 (2024).
  13. C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl (Jefferson Lab Angular Momentum (JAM) Collaboration), Phys. Rev. D 109, 034024 (2024).
  14. X. Gao, A. D. Hanlon, S. Mukherjee, P. Petreczky, Q. Shi, S. Syritsyn, and Y. Zhao, Phys. Rev. D 109, 054506 (2024).
  15. H.-W. Lin, W. Melnitchouk, A. Prokudin, N. Sato, and H. Shows, Phys. Rev. Lett. 120, 152502 (2018).
  16. U. D’Alesio, C. Flore, and A. Prokudin, Phys. Lett. B 803, 135347 (2020).
  17. J. Benel, A. Courtoy, and R. Ferro-Hernandez, Eur. Phys. J. C 80, 465 (2020).
  18. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. Lett. 41, 1585 (1978).
  19. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D 19, 2018 (1979).
  20. T. Kinoshita, J. Math. Phys. (N.Y.) 3, 650 (1962).
  21. T. D. Lee and M. Nauenberg, Phys. Rev. 133, B1549 (1964).
  22. K. Abe et al. (SLD Collaboration), Phys. Rev. D 51, 962 (1995).
  23. O. Adrian et al. (L3 Collaboration), Phys. Lett. B 284, 471 (1992).
  24. P. D. Acton et al. (OPAL Collaboration), Phys. Lett. B 276, 547 (1992).
  25. I. Adachi et al. (TOPAZ Collaboration), Phys. Lett. B 227, 495 (1989).
  26. W. Braunschweig et al. (TASSO Collaboration), Z. Phys. C 36, 349 (1987).
  27. W. Bartel et al. (JADE Collaboration), Z. Phys. C 25, 231 (1984).
  28. E. Fernandez et al., Phys. Rev. D 31, 2724 (1985).
  29. D. R. Wood et al., Phys. Rev. D 37, 3091 (1988).
  30. H. J. Behrend et al. (CELLO Collaboration), Z. Phys. C 14, 95 (1982).
  31. C. Berger et al. (PLUTO Collaboration), Z. Phys. C 28, 365 (1985).
  32. M. Z. Akrawy et al. (OPAL Collaboration), Phys. Lett. B 252, 159 (1990).
  33. D. Decamp et al. (ALEPH Collaboration), Phys. Lett. B 257, 479 (1991).
  34. B. Adeva et al. (L3 Collaboration), Phys. Lett. B 257, 469 (1991).
  35. K. Abe et al. (SLD Collaboration), Phys. Rev. D 50, 5580 (1994).
  36. G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 750, 427 (2015).
  37. M. Aaboud et al. (ATLAS Collaboration), Eur. Phys. J. C 77, 872 (2017).
  38. ATLAS Collaboration, , Report No. ATLAS-CONF-2020-025, ATLAS-CONF-2020-025, 2020.
  39. S. Acharya et al. (ALICE Collaboration), arXiv:2409.12687.
  40. A. Hayrapetyan et al. (CMS Collaboration), Phys. Rev. Lett. 133, 071903 (2024).
  41. V. Chekhovsky et al. (CMS Collaboration), Phys. Lett. B 866, 139556 (2025).
  42. S. Acharya et al. (ALICE Collaboration), arXiv:2504.03431.
  43. G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 07 (2023) 085.
  44. ATLAS Collaboration, Report No. CMS-PAS-HIN-24-019, 2025.
  45. H. T. Li, Y. Makris, and I. Vitev, Phys. Rev. D 103, 094005 (2021).
  46. D. Neill, G. Vita, I. Vitev, and H. X. Zhu, in Snowmass 2021 (2022), arXiv:2203.07113.
  47. Z.-B. Kang, J. Penttala, F. Zhao, and Y. Zhou, Phys. Rev. D 109, 094012 (2024).
  48. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
  49. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  50. X. Liu and H. X. Zhu, Phys. Rev. Lett. 130, 091901 (2023).
  51. H.-Y. Liu, X. Liu, J.-C. Pan, F. Yuan, and H. X. Zhu, Phys. Rev. Lett. 130, 181901 (2023).
  52. H. Cao, X. Liu, and H. X. Zhu, Phys. Rev. D 107, 114008 (2023).
  53. X. L. Li, X. Liu, F. Yuan, and H. X. Zhu, Phys. Rev. D 108, L091502 (2023).
  54. Z.-B. Kang, K. Lee, D. Y. Shao, and F. Zhao, J. High Energy Phys. 03 (2024) 153.
  55. S. Bhattacharya, Z.-B. Kang, D. Padilla, and J. Penttala, arXiv:2504.10475.
  56. Z.-B. Kang, J. Penttala, and C. Zhang, arXiv:2410.21435.
  57. A. B. Cuerpo, I. Scimemi, and A. Vladimirov, J. High Energy Phys. 11 (2025) 013.
  58. Y.-K. Song, S.-Y. Wei, L. Yang, and J. Zhou, Phys. Rev. Lett. 136, 131901 (2026).
  59. I. Moult and H. X. Zhu, arXiv:2506.09119.
  60. M. Riembau and M. Son, Phys. Rev. D 111, 014004 (2025).
  61. Z. Mi and Z. Wang, J. High Energy Phys. 11 (2025) 090.
  62. M. Riembau and M. Son, Phys. Rev. Lett. 136, 101901 (2026).
  63. Y. J. Zhu, Phys. Rev. D 113, 014025 (2026).
  64. R. Boussarie et al., arXiv:2304.03302.
  65. F. Yuan, Phys. Rev. Lett. 100, 032003 (2008).
  66. U. D’Alesio, L. Gamberg, Z.-B. Kang, F. Murgia, and C. Pisano, Phys. Lett. B 704, 637 (2011).
  67. U. D’Alesio, F. Murgia, and C. Pisano, Phys. Lett. B 773, 300 (2017).
  68. Z.-B. Kang, A. Prokudin, F. Ringer, and F. Yuan, Phys. Lett. B 774, 635 (2017).
  69. Z.-B. Kang, X. Liu, F. Ringer, and H. Xing, J. High Energy Phys. 11 (2017) 068.
  70. L. Adamczyk et al. (STAR Collaboration), Phys. Rev. D 97, 032004 (2018).
  71. M. Abdallah et al. (STAR Collaboration), Phys. Rev. D 106, 072010 (2022).
  72. Y. Zhang (STAR Collaboration), Proc. Sci. SPIN2023 (2024) 059.
  73. B. Aboona et al. (STAR Collaboration), Phys. Rev. Lett. 135, 261902 (2025).
  74. I. Nakagawa (sPHENIX Collaboration), Ukr. J. Phys. 69, 799 (2024).
  75. M. Procura and I. W. Stewart, Phys. Rev. D 81, 074009 (2010); 83, 039902(E) (2011).
  76. Z.-B. Kang, F. Ringer, and I. Vitev, J. High Energy Phys. 11 (2016) 155.
  77. C. W. Bauer, S. Fleming, and M. E. Luke, Phys. Rev. D 63, 014006 (2000).
  78. C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, Phys. Rev. D 63, 114020 (2001).
  79. C. W. Bauer and I. W. Stewart, Phys. Lett. B 516, 134 (2001).
  80. C. W. Bauer, D. Pirjol, and I. W. Stewart, Phys. Rev. D 65, 054022 (2002).
  81. J. Arrington et al., arXiv:2102.08337.
  82. R. Milton, S. J. Paul, B. Schmookler, M. Arratia, P. Karande, A. Angerami, F. T. Acosta, and B. Nachman, Nucl. Instrum. Methods Phys. Res., Sect. A 1079, 170613 (2025).
  83. J. Owens, Rev. Mod. Phys. 59, 465 (1987).
  84. Z.-B. Kang, F. Yuan, and J. Zhou, Phys. Lett. B 691, 243 (2010).
  85. D. Boer, P. Mulders, and F. Pijlman, Nucl. Phys. B667, 201 (2003).
  86. A. Metz, Phys. Lett. B 549, 139 (2002).
  87. J. C. Collins and A. Metz, Phys. Rev. Lett. 93, 252001 (2004).
  88. F. Yuan and J. Zhou, Phys. Rev. Lett. 103, 052001 (2009).
  89. D. Boer, Z.-B. Kang, W. Vogelsang, and F. Yuan, Phys. Rev. Lett. 105, 202001 (2010).
  90. See Supplemental Material at http://link.aps.org/supplemental/10.1103/1lz2-3fm9 for more details of the theoretical framework of the OPEC FJFs, including factorization, one-loop matching to corresponding collinear counterparts, evolution equations, and theoretical scale uncertainty estimates for the SSA predictions.
  91. Z.-B. Kang, K. Lee, and F. Zhao, Phys. Lett. B 809, 135756 (2020).
  92. Z.-B. Kang, H. Xing, F. Zhao, and Y. Zhou, J. High Energy Phys. 03 (2024) 142.
  93. T. Generet, K. Lee, I. Moult, R. Poncelet, and X. Zhang, J. High Energy Phys. 08 (2025) 015.
  94. M. Cacciari, G. P. Salam, and G. Soyez, J. High Energy Phys. 04 (2008) 063.
  95. J. C. Collins, D. E. Soper, and G. F. Sterman, Nucl. Phys. B250, 199 (1985).
  96. J.-w. Qiu and X.-f. Zhang, Phys. Rev. Lett. 86, 2724 (2001).
  97. F. Landry, R. Brock, P. M. Nadolsky, and C. P. Yuan, Phys. Rev. D 67, 073016 (2003).
  98. P. Sun, J. Isaacson, C. P. Yuan, and F. Yuan, Int. J. Mod. Phys. A 33, 1841006 (2018).
  99. K. Lee and I. Moult, arXiv:2308.01332.
  100. K. Lee and I. Moult, arXiv:2308.00746.
  101. Y. Li, I. Moult, S. S. van Velzen, W. J. Waalewijn, and H. X. Zhu, Phys. Rev. Lett. 128, 182001 (2022).
  102. H. Chen, I. Moult, X. Zhang, and H. X. Zhu, Phys. Rev. D 102, 054012 (2020).
  103. M. Jaarsma, Y. Li, I. Moult, W. J. Waalewijn, and H. X. Zhu, J. High Energy Phys. 12 (2023) 087.
  104. H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. M. Nadolsky, J. Pumplin, and C.-P. Yuan, Phys. Rev. D 82, 074024 (2010).
  105. D. de Florian, R. Sassot, M. Epele, R. J. Hernández-Pinto, and M. Stratmann, Phys. Rev. D 91, 014035 (2015).

Outline

Information

Phys. Rev. Lett. 136, 151902– Published 17 April, 2026
  • Received 30 September 2025
  • Revised 13 February 2026
  • Accepted 31 March 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation