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Chiral magnetic effect and negative magnetoresistance across the phase diagram of finite-density SU(2) gauge theory

P. V. Buividovich1,*, L. von Smekal2,3,†, and D. Smith4,‡

  • *Contact author: pavel.buividovich@liverpool.ac.uk
  • †Contact author: lorenz.smekal@physik.uni-giessen.de
  • ‡Contact author: d.smith@gsi.de
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Phys. Rev. D 114, 054501 – Published 1 September, 2026

DOI: https://doi.org/10.1103/9fzx-jrp8

Abstract

We study the signatures of the chiral magnetic effect (CME) in SU(2) gauge theory with Nf=2 flavors of dynamical fermions at finite temperature T, quark chemical potential μ and a weak external magnetic field eB. We consider both the correlator of the axial density and the vector current, which gives direct access to the out-of-equilibrium CME, and the correlator of two vector currents, which probes the CME indirectly via the enhancement of the longitudinal electric conductivity (negative magnetoresistance, NMR). We find that the CME response extracted from the vector-axial correlator exhibits a rather weak dependence on temperature and density in the quark-gluon plasma regime, and is very close to the universal value for free massless quarks. The CME appears to be mildly suppressed at low temperatures in the hadronic phase. In contrast, the NMR behaves in a qualitatively different way across the phase diagram, and is strongly suppressed at either large densities or temperatures. The magnitude of the NMR response appears to be considerably smaller than the prediction based on the lowest Landau level calculation for free quarks. Our findings suggest that for relatively small magnetic field strengths eB≲mπ2 the relation between the CME and NMR might not be as direct as expected. We also do not find statistically significant indications for an enhancement of the CME or NMR strength in the vicinity of the crossover or second-order phase transition lines in the (μ,T) phase diagram.

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References (92)

  1. M. S. Abdallah et al. (STAR Collaboration), Phys. Rev. C 105, 014901 (2022).
  2. B. Aboona et al. (STAR Collaboration), Phys. Lett. B 839, 137779 (2023).
  3. D. E. Kharzeev, J. Liao, and S. Shi, Phys. Rev. C 106, L051903 (2022).
  4. R. A. Lacey and N. Magdy, arXiv:2206.05773.
  5. H.-S. Li, Y. Feng, and F. Wang, Phys. Rev. C 112, 054901 (2025).
  6. S. Guo, L. Wang, K. Zhou, and G.-L. Ma, Chin. Phys. Lett. 42, 110101 (2025).
  7. Y. Feng, S. A. Voloshin, and F. Wang, Phys. Rev. Res. 7, 031001 (2025).
  8. W. Li, Q. Shou, and F. Wang, Eur. Phys. J. Special Topics (2026), 10.1140/epjs/s11734-026-02225-x.
  9. STAR Collaboration, arXiv:2506.00275.
  10. K. Ikeda, D. E. Kharzeev, and Y. Kikuchi, Phys. Rev. D 103, L071502 (2021).
  11. G. Fejős and D. Suenaga, Phys. Rev. D 112, 114028 (2025).
  12. A. Gynther, K. Landsteiner, F. Pena-Benitez, and A. Rebhan, J. High Energy Phys. 02 (2011) 110.
  13. A. Rebhan, A. Schmitt, and S. A. Stricker, J. High Energy Phys. 01 (2010) 026.
  14. P. V. Buividovich, M. N. Chernodub, E. V. Luschevskaya, and M. I. Polikarpov, Phys. Rev. D 80, 054503 (2009).
  15. A. Yamamoto, Phys. Rev. D 84, 114504 (2011).
  16. A. Yamamoto, Phys. Rev. Lett. 107, 031601 (2011).
  17. B. B. Brandt, G. Endrődi, E. Garnacho-Velasco, and G. Markó, J. High Energy Phys. 09 (2024) 092.
  18. J. B. Kogut, D. K. Sinclair, S. J. Hands, and S. E. Morrison, Phys. Rev. D 64, 094505 (2001).
  19. J. B. Kogut, M. A. Stephanov, D. Toublan, J. J. M. Verbaarschot, and A. Zhitnitsky, Nucl. Phys. B582, 477 (2000).
  20. K. Iida, E. Itou, K. Murakami, and D. Suenaga, arXiv:2606.13974.
  21. V. V. Braguta, E. Ilgenfritz, A. Y. Kotov, A. V. Molochkov, and A. A. Nikolaev, Phys. Rev. D 94, 114510 (2016).
  22. J. Wilhelm, L. Holicki, D. Smith, B. Wellegehausen, and L. von Smekal, Phys. Rev. D 100, 114507 (2019).
  23. D. Lawlor, S. Hands, S. Kim, and J.-I. Skullerud, EPJ Web Conf. 274, 07012 (2022).
  24. S. Hands, S. Kim, and J. Skullerud, Eur. Phys. J. C 48, 193 (2006).
  25. S. Hands, S. Kim, and J. Skullerud, Phys. Rev. D 81, 091502(R) (2010).
  26. N. Strodthoff, B. Schaefer, and L. von Smekal, Phys. Rev. D 85, 074007 (2012).
  27. S. Cotter, P. Giudice, S. Hands, and J. Skullerud, Phys. Rev. D 87, 034507 (2013).
  28. N. Strodthoff and L. von Smekal, Phys. Lett. B 731, 350 (2014).
  29. T. Boz, P. Giudice, S. Hands, J. Skullerud, and A. G. Williams, AIP Conf. Proc. 1701, 060019 (2016).
  30. V. G. Bornyakov, V. V. Braguta, E. Ilgenfritz, A. Y. Kotov, A. V. Molochkov, and A. A. Nikolaev, J. High Energy Phys. 03 (2018) 161.
  31. L. Holicki, J. Wilhelm, D. Smith, B. Wellegehausen, and L. von Smekal, Proc. Sci. LATTICE2016 (2017) 052. [arXiv:1701.04664].
  32. K. Iida, E. Itou, and T. Lee, J. High Energy Phys. 01 (2020) 181.
  33. R. Contant and M. Q. Huber, Phys. Rev. D 101, 014016 (2020).
  34. T. Boz, P. Giudice, S. Hands, and J. Skullerud, Phys. Rev. D 101, 074506 (2020).
  35. P. V. Buividovich, D. Smith, and L. von Smekal, Phys. Rev. D 102, 094510 (2020).
  36. L. McLerran and R. D. Pisarski, Nucl. Phys. A796, 83 (2007).
  37. G. Endrődi, Phys. Rev. D 90, 094501 (2014).
  38. B. B. Brandt, V. Chelnokov, G. Endrodi, G. Marko, D. Scheid, and L. von Smekal, arXiv:2502.04025.
  39. T. D. Cohen, Phys. Rev. Lett. 91, 032002 (2003).
  40. K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Nucl. Phys. A836, 311 (2010).
  41. P. V. Buividovich, M. N. Chernodub, D. E. Kharzeev, T. Kalaydzhyan, E. V. Luschevskaya, and M. I. Polikarpov, Phys. Rev. Lett. 105, 132001 (2010).
  42. G. Almirante, N. Astrakhantsev, V. V. Braguta, M. D’Elia, L. Maio, M. Naviglio, F. Sanfilippo, and A. Trunin, Phys. Rev. D 111, 034505 (2025).
  43. N. Y. Astrakhantsev, V. V. Braguta, M. D’Elia, A. Y. Kotov, A. A. Nikolaev, and F. Sanfilippo, Phys. Rev. D 102, 054516 (2020).
  44. Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosic, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu, and T. Valla, Nat. Phys. 12, 550 (2016).
  45. Y.-W. Sun and Q. Yang, J. High Energy Phys. 09 (2016) 122.
  46. K. Fukushima and A. Okutsu, Phys. Rev. D 105, 054016 (2022).
  47. D. L. Boyda, V. V. Braguta, M. I. Katsnelson, and A. Y. Kotov, Ann. Phys. (Amsterdam) 396, 78 (2018).
  48. P. V. Buividovich, Phys. Rev. D 110, 094508 (2024).
  49. B. B. Brandt, G. Endrodi, E. Garnacho Velasco, G. Marko, and A. D. M. Valois, Proc. Sci. LATTICE2024 (2025) 196. [arXiv:2502.01155].
  50. G. Inghirami, M. Mace, Y. Hirono, L. Del Zanna, D. E. Kharzeev, and M. Bleicher, Eur. Phys. J. C 80, 293 (2020).
  51. S. A. Voloshin, Phys. Rev. C 70, 057901 (2004).
  52. N. Magdy, S. Shi, J. Liao, N. Ajitanand, and R. A. Lacey, Phys. Rev. C 97, 061901 (2018).
  53. Y. Yin and J. Liao, Phys. Lett. B 756, 42 (2016).
  54. C. Zhang and M. Zubkov, Pis’ma Zh. Eksp. Teor. Fiz. 110, 480 (2019).
  55. C. Zhang and M. Zubkov, J. Phys. A 53, 195002 (2020).
  56. M. A. Zubkov and R. A. Abramchuk, Phys. Rev. D 107, 094021 (2023).
  57. P. V. Buividovich, D. Smith, and L. von Smekal, Phys. Rev. D 104, 014511 (2021).
  58. P. V. Buividovich, D. Smith, and L. von Smekal, Eur. Phys. J. A 57, 293 (2021).
  59. D. Scheffler, C. Schmidt, D. Smith, and L. von Smekal, Proc. Sci. LATTICE2013 (2013) 191. [arXiv:1311.4324].
  60. J. B. Kogut, D. Toublan, and D. K. Sinclair, Phys. Lett. B 514, 77 (2001).
  61. D. B. Renner, W. Schroers, R. Edwards, G. T. Fleming, P. Hagler, J. W. Negele, K. Orginos, A. V. Pochinski, and D. Richards, Nucl. Phys. B, Proc. Suppl. 140, 255 (2005).
  62. R. G. Edwards, G. T. Fleming, P. Hagler, J. W. Negele, K. Orginos, A. Pochinsky, D. B. Renner, D. G. Richards, and W. Schroers, Phys. Rev. Lett. 96, 052001 (2006).
  63. E. Berkowitz, D. Brantley, C. Bouchard, C. Chang, M. A. Clark, N. Garron, B. Joo, T. Kurth, C. Monahan, H. Monge-Camacho, A. Nicholson, K. Orginos, E. Rinaldi, P. Vranas, and A. Walker-Loud, arXiv:1704.01114.
  64. R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, A. Schiller, and J. M. Zanotti, Proc. Sci. LAT2015 (2016) 138. [arXiv:1511.05304].
  65. R. Horsley, S. Kazmin, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, A. Schiller, and J. M. Zanotti, Proc. Sci. LAT2016 (2017) 149. [arXiv:1612.04992].
  66. P. V. Buividovich, J. Phys. Conf. Ser. 607, 012018 (2013).
  67. P. V. Buividovich, Nucl. Phys. A925, 218 (2014).
  68. M. Greif, I. Bouras, Z. Xu, and C. Greiner, Phys. Rev. D 90, 094014 (2014).
  69. A. Puglisi, S. Plumari, and V. Greco, Phys. Rev. D 90, 114009 (2014).
  70. S. Qin, Phys. Lett. B 742, 358 (2015).
  71. M. Greif, C. Greiner, and G. S. Denicol, Phys. Rev. D 93, 096012 (2016).
  72. D. Fernandez-Fraile and A. Gomez Nicola, Phys. Rev. D 73, 045025 (2006).
  73. L. D. McLerran and T. Toimela, Phys. Rev. D 31, 545 (1985).
  74. L. McLerran and V. Skokov, Nucl. Phys. A929, 184 (2014).
  75. A. Dubla, U. Gürsoy, and R. Snellings, Mod. Phys. Lett. A 35, 2050324 (2020).
  76. S. Grieninger, S. Morales-Tejera, and P. G. Romeu, Phys. Rev. D 112, 036003 (2025).
  77. P. Goswami, J. H. Pixley, and S. Das Sarma, Phys. Rev. B 92, 075205 (2015).
  78. E. V. Gorbar, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. B 89, 085126 (2014).
  79. H. B. Meyer, Eur. Phys. J. A 47, 86 (2011).
  80. G. Aarts and A. Nikolaev, Eur. Phys. J. A 57, 118 (2021).
  81. T. Steinert and W. Cassing, Phys. Rev. C 89, 035203 (2014).
  82. O. Soloveva, P. Moreau, and E. Bratkovskaya, Phys. Rev. C 101, 045203 (2020).
  83. R.-A. Tripolt, C. Jung, N. Tanji, L. von Smekal, and J. Wambach, Nucl. Phys. A982, 775 (2019).
  84. G. Kadam, H. Mishra, and L. Thakur, Phys. Rev. D 98, 114001 (2018).
  85. S. Ghosh, Phys. Rev. D 95, 036018 (2017).
  86. M. Ulybyshev, C. Winterowd, and S. Zafeiropoulos, Phys. Rev. B 96, 205115 (2017).
  87. H. Ding, A. Francis, O. Kaczmarek, F. Karsch, E. Laermann, and W. Soeldner, Phys. Rev. D 83, 034504 (2011).
  88. K. Fukushima and Y. Hidaka, J. High Energy Phys. 04 (2020) 162.
  89. A. Shaikh, S. Rath, S. Dash, and B. Panda, Phys. Rev. D 108, 056021 (2023).
  90. L. Thakur and P. K. Srivastava, Phys. Rev. D 100, 076016 (2019).
  91. V. Skokov, A. Illarionov, and V. Toneev, Int. J. Mod. Phys. A 24, 5925 (2009).
  92. K. Tuchin, Phys. Rev. C 88, 024911 (2013).

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Phys. Rev. D 114, 054501– Published 1 September, 2026
  • Received 13 May 2026
  • Accepted 9 July 2026
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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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