- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Hybrid renormalization with gradient flow for baryon quasidistribution amplitudes

Jia-Lu Zhang* and Mu-Hua Zhang

  • *Contact author: elpsycongr00@sjtu.edu.cn
PDF

Phys. Rev. D 113, 014501 – Published 5 January, 2026

DOI: https://doi.org/10.1103/rm4s-wlfq

Abstract

We establish a factorization relation between baryon quasidistribution amplitudes (quasi-DAs) defined with gradient flow and their counterparts renormalized in the MS¯ scheme. Working beyond the small flow-time limit, we perform a complete one-loop calculation that yields the full matching kernel and the associated Wilson-line linear divergence for flowed quasi-DAs. Building on this relation, we formulate a hybrid renormalization scheme that combines ratio scheme with gradient-flow matching, thereby replacing fit-dependent self-renormalization and improving theoretical control over scheme conversion. The framework enables a systematic connection between lattice QCD matrix elements and continuum baryon quasi-DAs, with reduced renormalization uncertainties and clear guidance for practical lattice analyses.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (105)

  1. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).
  2. V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112, 173 (1984).
  3. L. Mankiewicz, G. Piller, and T. Weigl, Eur. Phys. J. C 5, 119 (1998).
  4. X. Ji, Phys. Rev. Lett. 110, 262002 (2013).
  5. X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014).
  6. T. Izubuchi, X. Ji, L. Jin, I. W. Stewart, and Y. Zhao, Phys. Rev. D 98, 056004 (2018).
  7. A. V. Radyushkin, Phys. Rev. D 96, 034025 (2017).
  8. A. V. Radyushkin, Phys. Rev. D 100, 116011 (2019).
  9. Y. Q. Ma and J. W. Qiu, Phys. Rev. D 98, 074021 (2018).
  10. Y. Q. Ma and J. W. Qiu, Phys. Rev. Lett. 120, 022003 (2018).
  11. C. Han and J. Zhang, Phys. Rev. D 109, 014034 (2024).
  12. C. Han, W. Wang, J. Zeng, and J. L. Zhang, J. High Energy Phys. 07 (2024) 019.
  13. Z. F. Deng, C. Han, W. Wang, J. Zeng, and J. L. Zhang, J. High Energy Phys. 07 (2023) 191.
  14. C. Han, W. Wang, J. L. Zhang, and J. H. Zhang, Phys. Rev. D 110, 094038 (2024).
  15. W. Wang, X. Y. Han, J. Hua, X. Ji, C. D. Lü, A. Schäfer, Y. Su, J. Xu, Y. Yang, and J. H. Zhang et al., Proc. Sci. QCHSC24 (2025) 111 [arXiv:2504.02453].
  16. M. H. Chu et al. (Lattice Parton Collaboration), Phys. Rev. D 111, 034510 (2025).
  17. C. Han, Y. Su, W. Wang, and J. L. Zhang, J. High Energy Phys. 12 (2023) 044.
  18. S. M. Hu, W. Wang, J. Xu, and S. Zhao, Phys. Rev. D 109, 034001 (2024).
  19. J. Hua et al. (Lattice Parton Collaboration), Phys. Rev. Lett. 129, 132001 (2022).
  20. J. Hua, M.-H. Chu, P. Sun, W. Wang, J. Xu, Y.-B. Yang, J.-H. Zhang, and Q.-A. Zhang (Lattice Parton Collaboration), Phys. Rev. Lett. 127, 062002 (2021).
  21. W. Wang, Y. M. Wang, J. Xu, and S. Zhao, Phys. Rev. D 102, 011502 (2020).
  22. W. Wang, J. Xu, Q. A. Zhang, and S. Zhao, arXiv:2411.07101.
  23. X. Y. Han et al. (Lattice Parton Collaboration), Phys. Rev. D 111, 034503 (2025).
  24. X. Y. Han, J. Hua, X. Ji, C. D. Lü, W. Wang, J. Xu, Q. A. Zhang, and S. Zhao, Phys. Rev. D 111, L111503 (2025).
  25. V. M. Braun, A. Vladimirov, and J. H. Zhang, Phys. Rev. D 99, 014013 (2019).
  26. M. H. Chu et al. ***(Lattice Parton (LPC) Collaboration), Phys. Rev. D 106, 034509 (2022).
  27. T. Guo, C. Han, W. Wang, and J. L. Zhang, Phys. Rev. D 112, 016013 (2025).
  28. W. Wang, J. Xu, Q. A. Zhang, and S. Zhao, Phys. Rev. D 112, 054044 (2025).
  29. M. H. Chu et al. (Lattice Parton Collaboration), Phys. Rev. D 109, L091503 (2024).
  30. J. C. He, M.-H. Chu, J. Hua, X. Ji, A. Schäfer, Y. Su, W. Wang, Y.-B. Yang, J.-H. Zhang, and Q.-A. Zhang (Lattice Parton Collaboration (LPC), Phys. Rev. D 109, 114513 (2024).
  31. Z. F. Deng, W. Wang, and J. Zeng, J. High Energy Phys. 09 (2022) 046.
  32. Q. A. Zhang, J. Hua, Y. Huo, X. Ji, Y. Liu, Y.-S. Liu, M. Schlemmer, A. Schäfer, P. Sun, W. Wang, and Y.-B. Yang (Lattice Parton Collaboration), Phys. Rev. Lett. 125, 192001 (2020).
  33. W. Wang, J. H. Zhang, S. Zhao, and R. Zhu, Phys. Rev. D 100, 074509 (2019).
  34. R. Zhang, J. Holligan, X. Ji, and Y. Su, Phys. Lett. B 844, 138081 (2023).
  35. X. Xiong, X. Ji, J. H. Zhang, and Y. Zhao, Phys. Rev. D 90, 014051 (2014).
  36. H. W. Lin, J. W. Chen, S. D. Cohen, and X. Ji, Phys. Rev. D 91, 054510 (2015).
  37. C. Alexandrou, K. Cichy, V. Drach, E. Garcia-Ramos, K. Hadjiyiannakou, K. Jansen, F. Steffens, and C. Wiese, Phys. Rev. D 92, 014502 (2015).
  38. J. W. Chen, S. D. Cohen, X. Ji, H. W. Lin, and J. H. Zhang, Nucl. Phys. B911, 246 (2016).
  39. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, F. Steffens, and C. Wiese, Phys. Rev. D 96, 014513 (2017).
  40. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato, and F. Steffens, Phys. Rev. Lett. 121, 112001 (2018).
  41. J. W. Chen, L. Jin, H. W. Lin, Y. S. Liu, Y. B. Yang, J. H. Zhang, and Y. Zhao, arXiv:1803.04393.
  42. W. Wang, S. Zhao, and R. Zhu, Eur. Phys. J. C 78, 147 (2018).
  43. W. Wang and S. Zhao, J. High Energy Phys. 05 (2018) 142.
  44. H. W. Lin, J. W. Chen, X. Ji, L. Jin, R. Li, Y. S. Liu, Y. B. Yang, J. H. Zhang, and Y. Zhao, Phys. Rev. Lett. 121, 242003 (2018).
  45. Y. S. Liu et al. (Lattice Parton Collaboration), Phys. Rev. D 101, 034020 (2020).
  46. C. Alexandrou, K. Cichy, M. Constantinou, K. Jansen, A. Scapellato, and F. Steffens, Phys. Rev. D 98, 091503 (2018).
  47. Y. S. Liu, J. W. Chen, L. Jin, R. Li, H. W. Lin, Y. B. Yang, J. H. Zhang, and Y. Zhao, arXiv:1810.05043.
  48. J. H. Zhang, J. W. Chen, L. Jin, H. W. Lin, A. Schäfer, and Y. Zhao, Phys. Rev. D 100, 034505 (2019).
  49. T. Izubuchi, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky, C. Shugert, and S. Syritsyn, Phys. Rev. D 100, 034516 (2019).
  50. L. B. Chen, W. Wang, and R. Zhu, Phys. Rev. D 102, 011503 (2020).
  51. L. B. Chen, W. Wang, and R. Zhu, J. High Energy Phys. 10 (2020) 079.
  52. L. B. Chen, W. Wang, and R. Zhu, Phys. Rev. Lett. 126, 072002 (2021).
  53. C. Shugert, X. Gao, T. Izubichi, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, and Y. Zhao, arXiv:2001.11650.
  54. Y. Chai, Y. Li, S. Xia, C. Alexandrou, K. Cichy, M. Constantinou, X. Feng, K. Hadjiyiannakou, K. Jansen, and G. Koutsou et al., Phys. Rev. D 102, 014508 (2020).
  55. H. W. Lin, J. W. Chen, Z. Fan, J. H. Zhang, and R. Zhang, Phys. Rev. D 103, 014516 (2021).
  56. Z. Fan, X. Gao, R. Li, H. W. Lin, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, Y. B. Yang, and R. Zhang, Phys. Rev. D 102, 074504 (2020).
  57. X. Gao, K. Lee, S. Mukherjee, C. Shugert, and Y. Zhao, Phys. Rev. D 103, 094504 (2021).
  58. X. Gao, A. D. Hanlon, S. Mukherjee, P. Petreczky, P. Scior, S. Syritsyn, and Y. Zhao, Phys. Rev. Lett. 128, 142003 (2022).
  59. X. Gao, A. D. Hanlon, N. Karthik, S. Mukherjee, P. Petreczky, P. Scior, S. Shi, S. Syritsyn, Y. Zhao, and K. Zhou, Phys. Rev. D 106, 114510 (2022).
  60. Y. Su, J. Holligan, X. Ji, F. Yao, J. H. Zhang, and R. Zhang, Nucl. Phys. B991, 116201 (2023).
  61. F. Yao et al. (Lattice Parton Collaboration), Phys. Rev. Lett. 131, 261901 (2023).
  62. X. Gao, A. D. Hanlon, J. Holligan, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, and Y. Zhao, Phys. Rev. D 107, 074509 (2023).
  63. X. Gao, A. D. Hanlon, S. Mukherjee, P. Petreczky, Q. Shi, S. Syritsyn, and Y. Zhao, Phys. Rev. D 109, 054506 (2024).
  64. X. Gao, W. Y. Liu, and Y. Zhao, Phys. Rev. D 109, 094506 (2024).
  65. C. Chen, Y. Geng, L. Liu, P. Sun, Y.-B. Yang, F. Yao, J.-H. Zhang, and K. Zhang (CLQCD and Lattice Parton Collaborations), Phys. Rev. D 111, 074506 (2025).
  66. J. Holligan and H. W. Lin, J. Phys. G 51, 065101 (2024).
  67. J. Holligan and H. W. Lin, Phys. Lett. B 854, 138731 (2024).
  68. M. Constantinou and H. Panagopoulos, Phys. Rev. D 96, 054506 (2017).
  69. I. W. Stewart and Y. Zhao, Phys. Rev. D 97, 054512 (2018).
  70. K. Zhang, Y.-K. Huo, X. Ji, A. Schäfer, C.-J. Shi, P. Sun, W. Wang, Y.-B. Yang, and J.-H. Zhang (Lattice Parton Collaboration), Phys. Rev. D 110, 074505 (2024).
  71. Y. K. Huo et al. (Lattice Parton (LPC) Collaboration), Nucl. Phys. B969, 115443 (2021).
  72. X. Ji, Y. Liu, A. Schäfer, W. Wang, Y. B. Yang, J. H. Zhang, and Y. Zhao, Nucl. Phys. B964, 115311 (2021).
  73. C. Y. Chou and J. W. Chen, Phys. Rev. D 106, 014507 (2022).
  74. R. Narayanan and H. Neuberger, J. High Energy Phys. 03 (2006) 064.
  75. M. Lüscher, J. High Energy Phys. 08 (2010) 071; 03 (2014) 92.
  76. M. Luscher and P. Weisz, J. High Energy Phys. 02 (2011) 051.
  77. M. Luscher, J. High Energy Phys. 04 (2013) 123.
  78. C. Monahan and K. Orginos, EPJ Web Conf. 175, 06004 (2018).
  79. C. Monahan, Phys. Rev. D 97, 054507 (2018).
  80. N. Brambilla and X. P. Wang, J. High Energy Phys. 06 (2024) 210.
  81. A. NieMiera, W. Good, H. W. Lin, and F. Yao, arXiv:2510.17758.
  82. A. Francis, P. Fritzsch, R. Karur, J. Kim, G. Pederiva, D. A. Pefkou, A. Rago, A. Shindler, A. Walker-Loud, and S. Zafeiropoulos, arXiv:2510.26738.
  83. A. Francis, P. Fritzsch, R. V. Harlander, R. Karur, J. Kim, J. T. Kohnen, G. Pederiva, D. A. Pefkou, A. Rago, and A. Shindler et al., arXiv:2509.02472.
  84. V. M. Braun, S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B553, 355 (1999).
  85. V. Braun, R. J. Fries, N. Mahnke, and E. Stein, Nucl. Phys. B589, 381 (2000); B607, 433(E) (2001).
  86. M. Luscher, Commun. Math. Phys. 293, 899 (2010).
  87. M. Lüscher, Proc. Sci. LATTICE2013 (2014) 016 [arXiv:1308.5598].
  88. S. Borsányi et al. (BMW Collaboration), J. High Energy Phys. 09 (2012) 010.
  89. R. Sommer, Proc. Sci. LATTICE2013 (2014) 015 [arXiv:1401.3270].
  90. H. Suzuki, Prog. Theor. Exp. Phys. 2013, 083B03 (2013); 2015, 079201(E) (2015).
  91. H. Makino and H. Suzuki, Prog. Theor. Exp. Phys. 2014, 63B02 (2014); 2015, 079202(E) (2015).
  92. R. V. Harlander, Y. Kluth, and F. Lange, Eur. Phys. J. C 78, 944 (2018); 79, 858(E) (2019).
  93. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG), arXiv:2411.04268.
  94. V. Leino, N. Brambilla, J. Mayer-Steudte, and A. Vairo, EPJ Web Conf. 258, 04009 (2022).
  95. J. Mayer-Steudte, N. Brambilla, V. Leino, and A. Vairo, Proc. Sci. LATTICE2022 (2023) 353 [arXiv:2212.12400].
  96. V. Leino, N. Brambilla, J. Mayer-Steudte, and P. Petreczky, Proc. Sci. LATTICE2022 (2023) 183 [arXiv:2212.10941].
  97. M. Nagatsuka, K. Sakai, and S. Sasaki, Phys. Rev. D 108, 094506 (2023).
  98. F. Lange, Dissertation, RWTH Aachen University, 2021, 10.18154/RWTH-2021-07652.
  99. C. Monahan and K. Orginos, J. High Energy Phys. 03 (2017) 116.
  100. M. Beneke, Phys. Rep. 317, 1 (1999).
  101. M. Beneke and V. M. Braun, Nucl. Phys. B426, 301 (1994).
  102. J. L. Zhang, Phys. Rev. D 112, 094504 (2025).
  103. K. Orginos, A. Radyushkin, J. Karpie, and S. Zafeiropoulos, Phys. Rev. D 96, 094503 (2017).
  104. A. V. Radyushkin, Phys. Lett. B 781, 433 (2018).
  105. H. Bai et al. (LPC Collaboration), arXiv:2508.08971.

Outline

Information

Phys. Rev. D 113, 014501– Published 5 January, 2026
  • Received 20 October 2025
  • Accepted 11 December 2025
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