QCD in strong magnetic fields: fluctuations of conserved charges and EoS

TL;DR

This work investigates QCD in strong magnetic fields using (2+1)-flavor lattice QCD with physical pion mass to quantify how magnetic fields modify fluctuations of conserved charges and the equation of state. It demonstrates that the baryon-electric charge correlation $\chi^{\rm BQ}_{11}$ is a highly sensitive magnetometer, with robust HRG-based proxies that connect lattice results to STAR/ALICE detector acceptances. The leading-order EoS coefficients exhibit non-monotonic, nonperturbative temperature dependence and band-crossings at large $eB$, revealing a $T_{pc}$-lowering effect and a gradual approach to a magnetized ideal-gas regime. Collectively, the results provide lattice QCD benchmarks for interpreting heavy-ion collision data under strong magnetic fields and highlight new observables to probe magnetized QCD matter across centrality classes.

Abstract

Strong magnetic fields can profoundly affect the equilibrium properties, characterized by the equation of state and bulk thermodynamics of strongly interacting matter. Although such fields are expected in off-central heavy-ion collisions, directly measuring their experimental imprints remains extremely challenging. To address this, we propose the baryon-electric charge correlations $χ^{\rm BQ}_{11}$ and the chemical potential ratio $μ_{\rm Q}/μ_{\rm B}$ as magnetic-field-sensitive probes, based on (2+1)-flavor QCD lattice simulations at physical pion masses. Along the transition line, $χ^{\rm BQ}_{11}$ and $(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ in Pb-Pb collisions increase by factors of 2.1 and 2.4 at $eB \simeq 8M_π^2$, respectively. To bridge theoretical predictions and experimental observations, we construct HRG-based proxies and apply systematic kinematic cuts to emulate STAR and ALICE detector acceptances. Furthermore, we extend this investigation to the QCD equation of state, and examine the leading-order thermodynamic coefficients for strangeness-neutral scenarios up to $eB \simeq 0.8 {\rm GeV}^2 \sim 45 m_π^2$, revealing intriguing non-monotonic structures.

Figures (6)

• Figure 1: Results for $\chi^{\rm Q}_{2}$ and $\chi^{\rm BQ}_{11}$ versus $eB$ at $T=145~{\rm MeV}$. Bands represent lattice data, while solid and broken lines represent HRG results. Figure is taken from Ref. Ding:2025jfz.
• Figure 2: $R_{cp}$-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 transition line $T_{pc}(eB)$. Figure is taken from Ref. Ding:2025jfz.
• Figure 3: $R_{cp}$-like ratio $R(\left(\mu_{\rm Q}/\mu_{\rm B} \right)_{\rm LO})$ along transition line $T_{pc}(eB)$ for various HIC systems. Figure is taken from Ref. Ding:2023bft.
• Figure 4: Electric charge over baryon chemical potential, $-q_1\equiv -\left(\mu_{\rm Q}/\mu_{\rm B}\right)_{\rm LO}$, for system with $\hat{n}_{\rm S}=0$ and $r\equiv n^{\rm Q}/n^{\rm B}=0.4$. Figure is taken from Ref.Ding:2025nyh.
• Figure 5: Same as Fig. \ref{['fig:q1']} but for strangeness over baryon chemical potential, $s_1\equiv\left({{{\mu}_{\rm S}}}/{{{\mu}_{\rm B}}}\right)_{\text{LO}}$. Figure is taken from Ref. Ding:2025nyh.