- 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

Second-order chiral kinetic theory from the Wigner function approach

Shi-Zheng Yang1,2,*, Shu-Xiang Ma3,†, and Jian-Hua Gao4,5,‡

  • 1Institute of Frontier and Interdisciplinary Science, Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, Shandong 266237, China
  • 2Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 3School of Space Science and Technology, Shandong University, Weihai, Shandong 264209, China
  • 4Shandong Provincial Key Laboratory of Nuclear Science, Nuclear Energy Technology and Comprehensive Utilization, Weihai Frontier Innovation Institute of Nuclear Technology, School of Nuclear Science, Energy and Power Engineering, Shandong University, Shandong 250061, China
  • 5Weihai Research Institute of Industrial Technology of Shandong University, Weihai 264209, China

  • *Contact author: yangsz@ustc.edu.cn
  • †Contact author: shuxiangma@mail.sdu.edu.cn
  • ‡Contact author: gaojh@sdu.edu.cn
PDF

Phys. Rev. D 112, 016001 – Published 2 July, 2025

DOI: https://doi.org/10.1103/r12y-8g4k

Abstract

We present a systematic method to derive the chiral kinetic theory from the Wigner equations based on quantum field theory order by order. We take special effort to derive the chiral kinetic theory in seven-dimensional phase space from the eight-dimensional chiral kinetic theory. We give the seven-dimensional chiral kinetic theory up to second order of semiclassical expansion. We find some new second-order contributions compared with other approaches.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (58)

  1. A. Bzdak and V. Skokov, Phys. Lett. B 710, 171 (2012).
  2. W. T. Deng and X. G. Huang, Phys. Rev. C 85, 044907 (2012).
  3. J. Bloczynski, X. G. Huang, X. Zhang, and J. Liao, Phys. Lett. B 718, 1529 (2013).
  4. Z. T. Liang and X. N. Wang, Phys. Rev. Lett. 94, 102301 (2005); 96, 039901(E) (2006).
  5. Z. T. Liang and X. N. Wang, Phys. Lett. B 629, 20 (2005).
  6. J. H. Gao, S. W. Chen, W. t. Deng, Z. T. Liang, Q. Wang, and X. N. Wang, Phys. Rev. C 77, 044902 (2008).
  7. F. Becattini, F. Piccinini, and J. Rizzo, Phys. Rev. C 77, 024906 (2008).
  8. L. P. Csernai, V. K. Magas, and D. J. Wang, Phys. Rev. C 87, 034906 (2013).
  9. Y. Jiang, Z. W. Lin, and J. Liao, Phys. Rev. C 94, 044910 (2016); 95, 049904(E) (2017).
  10. W. T. Deng and X. G. Huang, Phys. Rev. C 93, 064907 (2016).
  11. L. G. Pang, H. Petersen, Q. Wang, and X. N. Wang, Phys. Rev. Lett. 117, 192301 (2016).
  12. A. Vilenkin, Phys. Rev. D 22, 3080 (1980).
  13. D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, Nucl. Phys. A803, 227 (2008).
  14. K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Phys. Rev. D 78, 074033 (2008).
  15. A. Vilenkin, Phys. Lett. 80B, 150 (1978).
  16. D. Kharzeev and A. Zhitnitsky, Nucl. Phys. A797, 67 (2007).
  17. J. Erdmenger, M. Haack, M. Kaminski, and A. Yarom, J. High Energy Phys. 01 (2009) 055.
  18. N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam, and P. Surowka, J. High Energy Phys. 01 (2011) 094.
  19. D. T. Son and A. R. Zhitnitsky, Phys. Rev. D 70, 074018 (2004).
  20. M. A. Metlitski and A. R. Zhitnitsky, Phys. Rev. D 72, 045011 (2005).
  21. M. A. Stephanov and Y. Yin, Phys. Rev. Lett. 109, 162001 (2012).
  22. J. H. Gao, Z. T. Liang, S. Pu, Q. Wang, and X. N. Wang, Phys. Rev. Lett. 109, 232301 (2012).
  23. D. T. Son and N. Yamamoto, Phys. Rev. D 87, 085016 (2013).
  24. J. W. Chen, S. Pu, Q. Wang, and X. N. Wang, Phys. Rev. Lett. 110, 262301 (2013).
  25. C. Manuel and J. M. Torres-Rincon, Phys. Rev. D 89, 096002 (2014).
  26. J. Y. Chen, D. T. Son, M. A. Stephanov, H. U. Yee, and Y. Yin, Phys. Rev. Lett. 113, 182302 (2014).
  27. J. Y. Chen, D. T. Son, and M. A. Stephanov, Phys. Rev. Lett. 115, 021601 (2015).
  28. Y. Hidaka, S. Pu, and D. L. Yang, Phys. Rev. D 95, 091901 (2017).
  29. N. Mueller and R. Venugopalan, Phys. Rev. D 97, 051901 (2018).
  30. A. Huang, S. Shi, Y. Jiang, J. Liao, and P. Zhuang, Phys. Rev. D 98, 036010 (2018).
  31. Y. Hidaka and D. L. Yang, Phys. Rev. D 98, 016012 (2018).
  32. J. H. Gao, Z. T. Liang, Q. Wang, and X. N. Wang, Phys. Rev. D 98, 036019 (2018).
  33. J. H. Gao, J. Y. Pang, and Q. Wang, Phys. Rev. D 100, 016008 (2019).
  34. Y. C. Liu, L. L. Gao, K. Mameda, and X. G. Huang, Phys. Rev. D 99, 085014 (2019).
  35. Y. C. Liu and X. G. Huang, Nucl. Sci. Tech. 31, 56 (2020).
  36. J. H. Gao, G. L. Ma, S. Pu, and Q. Wang, Nucl. Sci. Tech. 31, 90 (2020).
  37. J. H. Gao, Z. T. Liang, and Q. Wang, Int. J. Mod. Phys. A 36, 2130001 (2021).
  38. Y. Hidaka, S. Pu, Q. Wang, and D. L. Yang, Prog. Part. Nucl. Phys. 127, 103989 (2022).
  39. E. V. Gorbar, V. A. Miransky, I. A. Shovkovy, and P. O. Sukhachov, Phys. Rev. Lett. 118, 127601 (2017).
  40. E. V. Gorbar, V. A. Miransky, I. A. Shovkovy, and P. O. Sukhachov, Phys. Rev. B 95, 115202 (2017).
  41. E. V. Gorbar, V. A. Miransky, I. A. Shovkovy, and P. O. Sukhachov, Phys. Rev. B 95, 115422 (2017).
  42. N. Yamamoto and D. L. Yang, Astrophys. J. 895, 56 (2020).
  43. K. Kamada, N. Yamamoto, and D. L. Yang, Prog. Part. Nucl. Phys. 129, 104016 (2023).
  44. D. E. Kharzeev and H.-U. Yee, Phys. Rev. D 84, 045025 (2011).
  45. N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla, and T. Sharma, J. High Energy Phys. 09 (2012) 046.
  46. S. Bhattacharyya, J. R. David, and S. Thakur, J. High Energy Phys. 01 (2014) 010.
  47. E. Megias and M. Valle, J. High Energy Phys. 11 (2014) 005.
  48. A. Jimenez-Alba and H. U. Yee, Phys. Rev. D 92, 014023 (2015).
  49. D. Satow, Phys. Rev. D 90, 034018 (2014).
  50. E. V. Gorbar, D. O. Rybalka, and I. A. Shovkovy, Phys. Rev. D 95, 096010 (2017).
  51. N. Abbasi, F. Taghinavaz, and O. Tavakol, J. High Energy Phys. 03 (2019) 051.
  52. E. V. Gorbar, V. A. Miransky, I. A. Shovkovy, and P. O. Sukhachov, Phys. Rev. B 95, 205141 (2017).
  53. T. Hayata, Y. Hidaka, and K. Mameda, J. High Energy Phys. 05 (2021) 023.
  54. K. Mameda, Phys. Rev. D 108, 016001 (2023).
  55. U. W. Heinz, Phys. Rev. Lett. 51, 351 (1983).
  56. H. T. Elze, M. Gyulassy, and D. Vasak, Nucl. Phys. B276, 706 (1986).
  57. D. Vasak, M. Gyulassy, and H. T. Elze, Ann. Phys. (N.Y.) 173, 462 (1987).
  58. P. Zhuang and U. W. Heinz, Ann. Phys. (N.Y.) 245, 311 (1996).

Outline

Information

Phys. Rev. D 112, 016001– Published 2 July, 2025
  • Received 13 February 2025
  • Accepted 12 June 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