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Leading-order QCD equation of state in strong magnetic fields at nonzero baryon chemical potential

Heng-Tong Ding, Jin-Biao Gu, Arpith Kumar, and Sheng-Tai Li

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Phys. Rev. D 112, 094508 – Published 18 November, 2025

DOI: https://doi.org/10.1103/qpds-94pf

Abstract

We present continuum-estimated (2+1)-flavor lattice QCD results for the leading-order Taylor expansion coefficients of the equation of state in strong magnetic fields and at nonzero baryon chemical potential. Simulations employ the highly improved staggered quark action with physical pion masses on lattices of temporal extent Nτ=8, 12, covering 145  MeV≲T≲165  MeV and eB≲0.8  GeV2, imposing strangeness neutrality with baseline results at electric charge to baryon number ratio r=0.4. We determine the T–eB dependence of q1 and s1 (electric charge and strangeness chemical potential ratios), pressure coefficient P2, baryon number density coefficient N1B, and energy-related coefficients Θ2 (trace anomaly), ε2 (energy density), and σ2 (entropy density). Magnetic fields induce temperature-band crossings for q1 and P2 and nonmonotonic structures in the energy-related coefficients, with Θ2 at strong fields possibly vanishing or turning negative at higher T, indicating dominance of the pressure term over the energy contribution. We also examine the r-dependence, finding that r=0 (charge-neutral matter) shows the most muted magnetic-field enhancement of P2 despite larger |q1|, providing a useful reference for neutron-star–relevant conditions. Comparisons with the hadron resonance gas model show qualitative agreement at low T and weak eB, with clear deviations near the crossover and at strong fields. These results provide useful input for constraining models and effective theories of QCD matter in strong magnetic fields at finite baryon density.

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Phys. Rev. D 112, 094508– Published 18 November, 2025
  • Received 12 August 2025
  • Accepted 8 October 2025
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