QCD in strong magnetic fields: fluctuations of conserved charges and equation of state

Abstract

We present continuum-estimated (2+1)-flavor lattice QCD results for second-order fluctuations of conserved charges and the leading-order equation of state in the presence of strong magnetic fields at nonzero baryon chemical potential, using the HISQ action at the physical pion mass. The baryon-electric charge correlation $χ^{\rm BQ}_{11}$ exhibits striking sensitivity to the magnetic field: $R_{cp}$-like double ratios $χ^{\rm BQ}_{11}/χ^{\rm Q}_{2}$ and $χ^{\rm BQ}_{11}/χ^{\rm QS}_{11}$ reach enhancements of $\sim2$ and $\sim2.25$ at $eB \simeq 8M_π^2$ along the transition line, establishing $χ^{\rm BQ}_{11}$ as a magnetometer of QCD. To bridge theoretical predictions and experimental observations, we construct HRG-based proxy observables and apply systematic kinematic cuts emulating STAR and ALICE detector acceptances, which retain $\sim80\%$ of the lattice QCD magnetic sensitivity. Extending to the QCD equation of state under strangeness neutrality and isospin asymmetry, we determine the chemical potential ratio $q_1\equiv(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ and the pressure coefficient $P_2$ for magnetic field strengths up to $eB \simeq 0.8~{\rm GeV}^2 \sim 45 M_π^2$. The results reveal temperature-band crossings, hierarchy reversals, and non-monotonic structures driven by the nontrivial interplay between thermal and magnetic effects.

Figures (3)

• Figure 1: $R_{cp}$-like ratio $R\left(\chi^{\rm BQ}_{11} /\chi^{\rm Q}_{2}\right)$ (left) and $R\left(\chi^{\rm BQ}_{11} /\chi^{\rm QS}_{11}\right)$ (right) along the transition line $T_{pc}(eB)$. Bands represent lattice data, while solid and broken lines represent HRG results. Plots are taken from Ref. Ding:2025jfz.
• Figure 2: Electric charge over baryon chemical potential, $-q_1\equiv -\left(\mu_{\rm Q}/\mu_{\rm B}\right)_{\rm LO}$, for strangeness-neutral systems. Top: $eB$- (left) and $T$-dependence (right) for $^{208}_{82}$Pb$/^{197}_{79}$Au with $r \simeq0.4$. Bottom: $eB$-dependence for various isospin regimes (left) and $r$-dependence for fixed $eB$ (right). Plots are taken from Ref. Ding:2025nyh.
• Figure 3: Leading-order pressure coefficient $P_2$ for strangeness-neutral systems. Top: $eB$- (left) and $T$-dependence (right) for $r=0.4$. Bottom: $P_2(r)/P_2(r=0.5)$ versus $eB$ for various isospin regimes (left) and versus $r$ at fixed $eB$ (right). Plots are taken from Ref. Ding:2025nyh.