- Physical Review Journals
All JournalsPhysics Magazine

Physical Review C

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

Magnetic properties of the hadron resonance gas with physical magnetic moments

Rupam Samanta* and Wojciech Broniowski†

  • *Contact author: rupam.samanta@ifj.edu.pl
  • †Contact author: wojciech.broniowski@ifj.edu.pl
PDF

Phys. Rev. C 112, 045202 – Published 14 October, 2025

DOI: https://doi.org/10.1103/th4j-whrv

Abstract

We study magnetic properties of the hadron resonance gas in the presence of a strong (0≤B≤0.15GeV2) magnetic field, using physical values of the magnetic moments of hadrons, i.e., including their anomalous parts. The values of these moments are taken from experiment, or when unavailable, from theoretical estimates. We evaluate the conserved charge susceptibilities, finding the expected sizable effects of the anomalous magnetic moments, in particular for the octet baryons, such as the proton and neutron, where they are exceptionally large. We also study in detail the large effects of the magnetic moments of the Δ(1232) states, for which various theoretical estimates and experimental values differ significantly. We compare our model results with the lattice quantum chromodynamics data and find reasonable agreement within the model uncertainty.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (68)

  1. D. E. Kharzeev, K. Landsteiner, A. Schmitt, and H.-U. Yee, Strongly interacting matter in magnetic fields: An overview, Lect. Notes Phys. 871, 1 (2013).
  2. J. O. Andersen, W. R. Naylor, and A. Tranberg, Phase diagram of QCD in a magnetic field: A review, Rev. Mod. Phys. 88, 025001 (2016).
  3. X.-G. Huang, Electromagnetic fields and anomalous transports in heavy-ion collisions — A pedagogical review, Rep. Prog. Phys. 79, 076302 (2016).
  4. P. Adhikari et al., Strongly interacting matter in extreme magnetic fields, arXiv:2412.18632.
  5. A. K. Harding and D. Lai, Physics of strongly magnetized neutron stars, Rep. Prog. Phys. 69, 2631 (2006).
  6. G. S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S. D. Katz, S. Krieg, A. Schafer, and K. K. Szabo, The QCD phase diagram for external magnetic fields, J. High Energy Phys. 02 (2012) 044.
  7. A. Bazavov et al., Fluctuations and correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model, Phys. Rev. D 86, 034509 (2012).
  8. G. Endrödi, QCD equation of state at nonzero magnetic fields in the hadron resonance gas model, J. High Energy Phys. 04 (2013) 023.
  9. G. S. Bali, F. Bruckmann, G. Endrödi, S. D. Katz, and A. Schäfer, The QCD equation of state in background magnetic fields, J. High Energy Phys. 08 (2014) 177.
  10. R. Bellwied, S. Borsanyi, Z. Fodor, J. N. Guenther, J. Noronha-Hostler, P. Parotto, A. Pasztor, C. Ratti, and J. M. Stafford, Off-diagonal correlators of conserved charges from lattice QCD and how to relate them to experiment, Phys. Rev. D 101, 034506 (2020).
  11. G. S. Bali, G. Endrődi, and S. Piemonte, Magnetic susceptibility of QCD matter and its decomposition from the lattice, J. High Energy Phys. 07 (2020) 183.
  12. D. Bollweg et al. (HotQCD Collaboration), Second order cumulants of conserved charge fluctuations revisited: Vanishing chemical potentials, Phys. Rev. D 104, 074512 (2021).
  13. H.-T. Ding, J.-B. Gu, A. Kumar, S.-T. Li, and J.-H. Liu, Baryon electric charge correlation as a magnetometer of QCD, Phys. Rev. Lett. 132, 201903 (2024).
  14. H.-T. Ding, J.-B. Gu, A. Kumar, and S.-T. Li, Second order fluctuations of conserved charges in external magnetic fields, Phys. Rev. D 111, 114522 (2025).
  15. M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Signatures of the tricritical point in QCD, Phys. Rev. Lett. 81, 4816 (1998).
  16. M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Event-by-event fluctuations in heavy ion collisions and the QCD critical point, Phys. Rev. D 60, 114028 (1999).
  17. Z. Fodor and S. D. Katz, Critical point of QCD at finite t and mu, lattice results for physical quark masses, J. High Energy Phys. 04 (2004) 050.
  18. Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, The order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature (London) 443, 675 (2006).
  19. A. Bazavov et al., The chiral and deconfinement aspects of the QCD transition, Phys. Rev. D 85, 054503 (2012).
  20. V. A. Miransky and I. A. Shovkovy, Magnetic catalysis and anisotropic confinement in QCD, Phys. Rev. D 66, 045006 (2002).
  21. G. S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S. D. Katz, and A. Schafer, QCD quark condensate in external magnetic fields, Phys. Rev. D 86, 071502(R) (2012).
  22. N. Mueller and J. M. Pawlowski, Magnetic catalysis and inverse magnetic catalysis in QCD, Phys. Rev. D 91, 116010 (2015).
  23. E. Fermi, High-energy nuclear events, Prog. Theor. Phys. 5, 570 (1950).
  24. I. Y. Pomeranchuk, On the theory of multiple particle production in a single collision, Dokl. Akad. Nauk SSSR 78, 889 (1951).
  25. R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3, 147 (1965).
  26. P. Koch, B. Muller, and J. Rafelski, Strangeness in relativistic heavy ion collisions, Phys. Rep. 142, 167 (1986).
  27. R. Dashen, S.-K. Ma, and H. J. Bernstein, S matrix formulation of statistical mechanics, Phys. Rev. 187, 345 (1969).
  28. R. Venugopalan and M. Prakash, Thermal properties of interacting hadrons, Nucl. Phys. A 546, 718 (1992).
  29. W. Florkowski, Phenomenology of Ultra-Relativistic Heavy-Ion Collisions (World Scientific, Singapore, 2010).
  30. A. Andronic, P. Braun-Munzinger, and J. Stachel, Hadron production in central nucleus-nucleus collisions at chemical freeze-out, Nucl. Phys. A 772, 167 (2006).
  31. W. Broniowski and W. Florkowski, Explanation of the RHIC p⊥ spectra in a thermal model with expansion, Phys. Rev. Lett. 87, 272302 (2001).
  32. S. Jeon and V. Koch, Charged particle ratio fluctuation as a signal for QGP, Phys. Rev. Lett. 85, 2076 (2000).
  33. M. Asakawa, U. W. Heinz, and B. Muller, Fluctuation probes of quark deconfinement, Phys. Rev. Lett. 85, 2072 (2000).
  34. S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, Fluctuations of conserved charges at finite temperature from lattice QCD, J. High Energy Phys. 01 (2012) 138.
  35. R. Bellwied, S. Borsanyi, Z. Fodor, S. D. Katz, A. Pasztor, C. Ratti, and K. K. Szabo, Fluctuations and correlations in high temperature QCD, Phys. Rev. D 92, 114505 (2015).
  36. S. Borsanyi, Z. Fodor, J. N. Guenther, S. K. Katz, K. K. Szabo, A. Pasztor, I. Portillo, and C. Ratti, Higher order fluctuations and correlations of conserved charges from lattice QCD, J. High Energy Phys. 10 (2018) 205.
  37. M. Marczenko, M. Szymański, P. M. Lo, B. Karmakar, P. Huovinen, C. Sasaki, and K. Redlich, Magnetic effects in the hadron resonance gas, Phys. Rev. C 110, 065203 (2024).
  38. V. Vovchenko, Magnetic field effect on hadron yield ratios and fluctuations in a hadron resonance gas, Phys. Rev. C 110, 034914 (2024).
  39. A. Bhattacharyya, S. K. Ghosh, R. Ray, and S. Samanta, Exploring effects of magnetic field on the hadron resonance gas, Europhys. Lett. 115, 62003 (2016).
  40. W.-Y. Tsai and A. Yildiz, Motion of charged particles in a homogeneous magnetic field, Phys. Rev. D 4, 3643 (1971).
  41. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, Course of Theoretical Physics, Vol. 5 (Butterworth-Heinemann, Oxford, 1980).
  42. M. Gurtler et al., Vector meson electromagnetic form factors, PoS LATTICE2008, 051 (2008).
  43. D. Djukanovic, E. Epelbaum, J. Gegelia, and U. G. Meissner, The magnetic moment of the ρ-meson, Phys. Lett. B 730, 115 (2014).
  44. A. M. Badalian and Y. A. Simonov, Magnetic moments of mesons, Phys. Rev. D 87, 074012 (2013).
  45. E. V. Luschevskaya, O. E. Solovjeva, O. V. Teryaev, and M. S. Prokudin, Magnetic structure of vector mesons in lattice QCD, EPJ Web Conf. 182, 02077 (2018).
  46. S. Navas et al., Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  47. U.-G. Meissner and S. Steininger, Baryon magnetic moments in chiral perturbation theory, Nucl. Phys. B 499, 349 (1997).
  48. F. X. Lee, S. Moerschbacher, and W. Wilcox, Magnetic moments of vector, axial, and tensor mesons in lattice QCD, Phys. Rev. D 78, 094502 (2008).
  49. G. Lopez Castro and A. Mariano, Determination of the Δ++ magnetic dipole moment, Phys. Lett. B 517, 339 (2001).
  50. F. X. Lee, R. Kelly, L. Zhou, and W. Wilcox, Baryon magnetic moments in the background field method, Phys. Lett. B 627, 71 (2005).
  51. H.-S. Li, Z.-W. Liu, X.-L. Chen, W.-Z. Deng, and S.-L. Zhu, Magnetic moments and electromagnetic form factors of the decuplet baryons in chiral perturbation theory, Phys. Rev. D 95, 076001 (2017).
  52. D. B. Leinweber, T. Draper, and R. M. Woloshyn, Decuplet baryon structure from lattice QCD, Phys. Rev. D 46, 3067 (1992).
  53. T. Bauer, J. Gegelia, and S. Scherer, Magnetic moment of the Roper resonance, Phys. Lett. B 715, 234 (2012).
  54. S. Ferrara, M. Porrati, and V. L. Telegdi, g=2 as the natural value of the tree-level gyromagnetic ratio of elementary particles, Phys. Rev. D 46, 3529 (1992).
  55. F. J. Belinfante, Intrinsic magnetic moment of elementary particles of spin 32, Phys. Rev. 92, 997 (1953).
  56. M. G. de Paoli, D. P. Menezes, L. B. Castro, and C. C. Barros, Jr., The Rarita-Schwinger particles under the influence of strong magnetic fields, J. Phys. G 40, 055007 (2013).
  57. M. Seetharaman, J. Prabhakaran, and P. M. Mathews, Rarita-Schwinger particles in homogeneous magnetic fields, and inconsistencies of spin 3/2 theories, Phys. Rev. D 12, 458 (1975).
  58. U. Yakhshiev, H.-C. Kim, and M. Oka, Nucleon and Δ isobar in a strong magnetic field, Phys. Rev. D 99, 054027 (2019).
  59. Y. Chen and W. Jiang, Nucleons and Δ isobars under strong magnetic fields in Skyrme models, Phys. Rev. C 107, 025201 (2023).
  60. R. K. Pathria and P. D. Beale, Statistical Mechanics, 3rd ed. (Elsevier/Academic Press, Amsterdam/Boston, 2011).
  61. B. Friman, P. M. Lo, M. Marczenko, K. Redlich, and C. Sasaki, Strangeness fluctuations from K−π interactions, Phys. Rev. D 92, 074003 (2015).
  62. V. Skokov, A. Y. Illarionov, and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24, 5925 (2009).
  63. A. Huang, D. She, S. Shi, M. Huang, and J. Liao, Dynamical magnetic fields in heavy-ion collisions, Phys. Rev. C 107, 034901 (2023).
  64. A. Huang, X.-Y. Wu, and M. Huang, Effect of vorticity on the dynamical magnetic fields in heavy-ion collisions, Phys. Rev. D 110, 094032 (2024).
  65. U. Gürsoy, D. Kharzeev, and K. Rajagopal, Magnetohydrodynamics, charged currents and directed flow in heavy ion collisions, Phys. Rev. C 89, 054905 (2014).
  66. B. Abelev et al., Centrality dependence of π, K, and p production in Pb-Pb collisions at sNN = 2.76 TeV, Phys. Rev. C 88, 044910 (2013).
  67. S. Acharya et al., Production of charged pions, kaons, and (anti-)protons in Pb-Pb and inelastic pp collisions at sNN = 5.02 TeV, Phys. Rev. C 101, 044907 (2020).
  68. G. Torrieri, S. Steinke, W. Broniowski, W. Florkowski, J. Letessier, and J. Rafelski, SHARE: Statistical hadronization with resonances, Comput. Phys. Commun. 167, 229 (2005).

Outline

Information

Phys. Rev. C 112, 045202– Published 14 October, 2025
  • Received 22 May 2025
  • Revised 6 August 2025
  • Accepted 11 September 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