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Fluctuations and correlations of net baryon number, electric charge and strangeness in a background magnetic field

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Abstract

We present results on the second-order fluctuations of and correlations among net baryon number, electric charge and strangeness in (2 + 1)-flavor lattice QCD in the presence of a background magnetic field. Simulations are performed using the tree-level improved gauge action and the highly improved staggered quark (HISQ) action with a fixed scale approach (\(a\simeq \) 0.117 fm). The light quark mass is set to be 1/10 of the physical strange quark mass and the corresponding pion mass is about 220 MeV at vanishing magnetic field. Simulations are performed on \(32^3\times N_\tau \) lattices with 9 values of \(N_\tau \) varying from 96 to 6 corresponding to temperatures ranging from zero up to 281 MeV. The magnetic field strength eB is simulated with 15 different values up to \(\sim \)2.5 GeV\(^2\) at each nonzero temperature. We find that quadratic fluctuations and correlations do not show any singular behavior at zero temperature in the current window of eB while they develop peaked structures at nonzero temperatures as eB grows. By comparing the electric charge-related fluctuations and correlations with hadron resonance gas model calculations and ideal gas limits we find that the changes in degrees of freedom start at lower temperatures in stronger magnetic fields. Significant effects induced by magnetic fields on the isospin symmetry and ratios of net baryon number and baryon-strangeness correlation to strangeness fluctuation are observed, which could be useful for probing the existence of a magnetic field in heavy-ion collision experiments.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: As further studies on these data will be carried on by us, we will not make the data public at the moment.]

Change history

  • 29 July 2021

    The original online version of this article was revised: The corresponding author remark in brackets was removed for the author H.-T. Ding.

Notes

  1. Here we neglect the term arising from the vacuum energy, as which receives no contributions to the fluctuations and correlations of B, Q and S.

  2. One can also construct quantities without \(\chi _2^\mathrm{S}\) to reflect the isospin symmetry breaking, e.g. \((\chi _2^\mathrm{Q}- 2\chi _{11}^\mathrm{BQ})/(\chi _2^\mathrm{Q}+\chi _{11}^\mathrm{BQ})\), and \(0.5(2\chi _2^\mathrm{B}- \chi _{11}^\mathrm{BQ})/(\chi _2^\mathrm{B}+\chi _{11}^\mathrm{BQ})\). Both of these two quantities approach to \(\chi _2^d/\chi _2^u\) in the high-temperature limit.

  3. Here in the HRG calculations we adopt the PDG hadron spectrum except that at \(eB=0\) masses of pion, kaon and \(\rho \) determined in our current lattice setup are used instead of those listed in PDG.

  4. The eB-dependence seen at \(T\simeq 70\) MeV could be due to the statistics-hungry nature of the observables at low temperature and insufficient statistics we have in the simulation, similar in the cases of \(\chi _{2}^\mathrm{Q}\) and \(\chi _{11}^\mathrm{BQ}\).

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Acknowledgements

We thank Frithjof Karsch and Swagato Mukherjee for useful discussions, and the HotQCD collaboration for sharing its software suite based on which the codes used in the current study for generating gauge configurations and computing the Taylor expansion coefficients in nonzero magnetic fields are developed. This work was supported by the NSFC under Grant Numbers 11535012, 11775096 and 11947237. The numerical simulations have been performed on the GPU cluster in the Nuclear Science Computing Center at Central China Normal University (NSC\(^3\)).

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Authors and Affiliations

  1. Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan, 430079, China

    H.-T. Ding, S.-T. Li, Q. Shi & X.-D. Wang

  2. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, 730000, China

    S.-T. Li

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  1. H.-T. Ding
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  2. S.-T. Li
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  3. Q. Shi
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  4. X.-D. Wang
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Correspondence to H.-T. Ding.

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Communicated by Carsten Urbach

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Ding, HT., Li, ST., Shi, Q. et al. Fluctuations and correlations of net baryon number, electric charge and strangeness in a background magnetic field. Eur. Phys. J. A 57, 202 (2021). https://doi.org/10.1140/epja/s10050-021-00519-3

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  • DOI: https://doi.org/10.1140/epja/s10050-021-00519-3

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