- 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

Parton distributions from boosted fields in the Coulomb gauge

Xiang Gao1, Wei-Yang Liu2, and Yong Zhao1

  • 1Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
  • 2Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794–3800, USA

PDF

Phys. Rev. D 109, 094506 – Published 10 May, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.094506

Abstract

We propose a new method to calculate parton distribution functions (PDFs) from lattice correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used gauge-invariant Wilson-line operators, these correlations greatly simplify the renormalization thanks to the absence of linear power divergence. Additionally, they enable access to larger off-axis momenta under preserved 3D rotational symmetry, as well as enhanced long-range precision that facilitates the Fourier transform. We verify the factorization formula that relates this new observable to the quark PDF at one-loop order in perturbation theory. Moreover, through a lattice calculation of the pion valence quark PDF, we demonstrate the aforementioned advantage and features of the Coulomb gauge correlation and show that it yields consistent results with the gauge-invariant method. This opens the door to a more efficient way to calculate parton physics on the lattice.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (77)

  1. R. L. Workman et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  2. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
  3. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  4. X. Ji, Phys. Rev. Lett. 110, 262002 (2013).
  5. X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014).
  6. X. Ji, Y.-S. Liu, Y. Liu, J.-H. Zhang, and Y. Zhao, Rev. Mod. Phys. 93, 035005 (2021).
  7. X. Ji, arXiv:2007.06613.
  8. K.-F. Liu and S.-J. Dong, Phys. Rev. Lett. 72, 1790 (1994).
  9. W. Detmold and C. J. D. Lin, Phys. Rev. D 73, 014501 (2006).
  10. V. Braun and D. Müller, Eur. Phys. J. C 55, 349 (2008).
  11. A. J. Chambers, R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, A. Schiller, K. Somfleth, R. D. Young, and J. M. Zanotti, Phys. Rev. Lett. 118, 242001 (2017).
  12. A. V. Radyushkin, Phys. Rev. D 96, 034025 (2017).
  13. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. Lett. 120, 022003 (2018).
  14. M. Constantinou et al., Prog. Part. Nucl. Phys. 121, 103908 (2021).
  15. R. Boussarie et al., arXiv:2304.03302.
  16. G. S. Bali, B. Lang, B. U. Musch, and A. Schäfer, Phys. Rev. D 93, 094515 (2016).
  17. B. U. Musch, P. Hagler, J. W. Negele, and A. Schafer, Phys. Rev. D 83, 094507 (2011).
  18. H. Dorn, Fortschr. Phys. 34, 11 (1986).
  19. L. Maiani, G. Martinelli, and C. T. Sachrajda, Nucl. Phys. B368, 281 (1992).
  20. X. Ji, J.-H. Zhang, and Y. Zhao, Phys. Rev. Lett. 120, 112001 (2018).
  21. T. Ishikawa, Y.-Q. Ma, J.-W. Qiu, and S. Yoshida, Phys. Rev. D 96, 094019 (2017).
  22. J. Green, K. Jansen, and F. Steffens, Phys. Rev. Lett. 121, 022004 (2018).
  23. X. Ji, Y. Liu, A. Schäfer, W. Wang, Y.-B. Yang, J.-H. Zhang, and Y. Zhao, Nucl. Phys. B964, 115311 (2021).
  24. J. Holligan, X. Ji, H.-W. Lin, Y. Su, and R. Zhang, Nucl. Phys. B993, 116282 (2023).
  25. R. Zhang, J. Holligan, X. Ji, and Y. Su, Phys. Lett. B 844, 138081 (2023).
  26. G. S. Bali, C. Bauer, A. Pineda, and C. Torrero, Phys. Rev. D 87, 094517 (2013).
  27. Y. Hatta, X. Ji, and Y. Zhao, Phys. Rev. D 89, 085030 (2014).
  28. T. Izubuchi, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky, C. Shugert, and S. Syritsyn, Phys. Rev. D 100, 034516 (2019).
  29. X. Gao, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky, C. Shugert, S. Syritsyn, and Y. Zhao, Phys. Rev. D 102, 094513 (2020).
  30. X. Ji, J.-H. Zhang, and Y. Zhao, Phys. Rev. Lett. 111, 112002 (2013).
  31. X. Ji, J.-H. Zhang, and Y. Zhao, Phys. Lett. B 743, 180 (2015).
  32. Y.-B. Yang, R. S. Sufian, A. Alexandru, T. Draper, M. J. Glatzmaier, K.-F. Liu, and Y. Zhao, Phys. Rev. Lett. 118, 102001 (2017).
  33. R. Gupta, D. Daniel, and J. Grandy, Phys. Rev. D 48, 3330 (1993).
  34. T. Izubuchi, X. Ji, L. Jin, I. W. Stewart, and Y. Zhao, Phys. Rev. D 98, 056004 (2018).
  35. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. D 98, 074021 (2018).
  36. X. Xiong, X. Ji, J.-H. Zhang, and Y. Zhao, Phys. Rev. D 90, 014051 (2014).
  37. K. Orginos, A. Radyushkin, J. Karpie, and S. Zafeiropoulos, Phys. Rev. D 96, 094503 (2017).
  38. X. Ji, J.-H. Zhang, and Y. Zhao, Nucl. Phys. B924, 366 (2017).
  39. A. Bazavov et al. (HotQCD Collaboration), Phys. Rev. D 90, 094503 (2014).
  40. E. Follana, Q. Mason, C. Davies, K. Hornbostel, G. P. Lepage, J. Shigemitsu, H. Trottier, and K. Wong (HPQCD and UKQCD Collaborations), Phys. Rev. D 75, 054502 (2007).
  41. A. Hasenfratz and F. Knechtli, Phys. Rev. D 64, 034504 (2001).
  42. E. Shintani, R. Arthur, T. Blum, T. Izubuchi, C. Jung, and C. Lehner, Phys. Rev. D 91, 114511 (2015).
  43. C. T. H. Davies, G. G. Batrouni, G. R. Katz, A. S. Kronfeld, G. P. Lepage, K. G. Wilson, P. Rossi, and B. Svetitsky, Phys. Rev. D 37, 1581 (1988).
  44. R. J. Hudspith (RBC and UKQCD Collaborations), Comput. Phys. Commun. 187, 115 (2015).
  45. V. N. Gribov, Nucl. Phys. B139, 1 (1978).
  46. I. M. Singer, Commun. Math. Phys. 60, 7 (1978).
  47. L. Giusti, M. L. Paciello, C. Parrinello, S. Petrarca, and B. Taglienti, Int. J. Mod. Phys. A 16, 3487 (2001).
  48. G. Burgio, M. Schrock, H. Reinhardt, and M. Quandt, Phys. Rev. D 86, 014506 (2012).
  49. A. Maas, Ann. Phys. (Amsterdam) 387, 29 (2017).
  50. G. Burgio, M. Quandt, H. Reinhardt, and H. Vogt, Phys. Rev. D 95, 014503 (2017).
  51. D. Zwanziger, Nucl. Phys. B518, 237 (1998).
  52. L. Baulieu and D. Zwanziger, Nucl. Phys. B548, 527 (1999).
  53. A. Niegawa, Phys. Rev. D 74, 045021 (2006).
  54. A. Niegawa, M. Inui, and H. Kohyama, Phys. Rev. D 74, 105016 (2006).
  55. X. Gao, A. D. Hanlon, S. Mukherjee, P. Petreczky, P. Scior, S. Syritsyn, and Y. Zhao, Phys. Rev. Lett. 128, 142003 (2022).
  56. Y.-K. Huo et al. (Lattice Parton Collaboration (LPC), Nucl. Phys. B969, 115443 (2021).
  57. X. Gao, K. Lee, S. Mukherjee, C. Shugert, and Y. Zhao, Phys. Rev. D 103, 094504 (2021).
  58. Y. Su, J. Holligan, X. Ji, F. Yao, J.-H. Zhang, and R. Zhang, Nucl. Phys. B991, 116201 (2023).
  59. X. Ji, Y. Liu, and Y. Su, J. High Energy Phys. 08 (2023) 037.
  60. I. Novikov et al., Phys. Rev. D 102, 014040 (2020).
  61. P. C. Barry, C.-R. Ji, N. Sato, and W. Melnitchouk (Jefferson Lab Angular Momentum (JAM) Collaboration), Phys. Rev. Lett. 127, 232001 (2021).
  62. M. Constantinou, H. Panagopoulos, and G. Spanoudes, Phys. Rev. D 99, 074508 (2019).
  63. M. A. Ebert, I. W. Stewart, and Y. Zhao, J. High Energy Phys. 03 (2020) 099.
  64. P. Shanahan, M. L. Wagman, and Y. Zhao, Phys. Rev. D 101, 074505 (2020).
  65. J. R. Green, K. Jansen, and F. Steffens, Phys. Rev. D 101, 074509 (2020).
  66. Y. Ji, J.-H. Zhang, S. Zhao, and R. Zhu, Phys. Rev. D 104, 094510 (2021).
  67. K. Zhang, X. Ji, Y.-B. Yang, F. Yao, and J.-H. Zhang (Lattice Parton Collaboration (LPC), Phys. Rev. Lett. 129, 082002 (2022).
  68. C. Alexandrou et al., Phys. Rev. D 108, 114503 (2023).
  69. M. A. Ebert, I. W. Stewart, and Y. Zhao, Phys. Rev. D 99, 034505 (2019).
  70. M. A. Ebert, I. W. Stewart, and Y. Zhao, J. High Energy Phys. 09 (2019) 037.
  71. X. Ji, Y. Liu, and Y.-S. Liu, Nucl. Phys. B955, 115054 (2020).
  72. X. Ji, Y. Liu, and Y.-S. Liu, Phys. Lett. B 811, 135946 (2020).
  73. M. A. Ebert, S. T. Schindler, I. W. Stewart, and Y. Zhao, J. High Energy Phys. 04 (2022) 178.
  74. A. Pochinsky, qlua lattice software suite, https://usqcd.lns.mit.edu/qlua (2008–present).
  75. M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi, Comput. Phys. Commun. 181, 1517 (2010).
  76. R. Babich, M. A. Clark, B. Joo, G. Shi, R. C. Brower, and S. Gottlieb, in Proceedings of the SC11 International Conference for High Performance Computing, Networking, Storage and Analysis (2011), arXiv:1109.2935.
  77. T. DeGrand and C. DeTar, Lattice Methods for Quantum Chromodynamics (World Scientific, Singapore, 2006).

Outline

Information

Phys. Rev. D 109, 094506– Published 10 May, 2024
  • Received 7 July 2023
  • Accepted 11 April 2024
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