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

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.

💡 Research Summary

In this work the authors present continuum‑extrapolated (2+1)‑flavor lattice QCD results obtained with the highly improved staggered quark (HISQ) action at the physical pion mass, focusing on second‑order fluctuations of the conserved charges (baryon number B, electric charge Q, strangeness S) and on the leading‑order equation of state (EoS) in the presence of strong external magnetic fields. The study covers magnetic field strengths up to eB≈0.8 GeV² (≈45 Mπ²) and temperatures around the pseudo‑critical line T_pc(eB).

A key finding is the extreme sensitivity of the baryon–electric charge correlation χ_BQ^11 to the magnetic field. Double ratios of the form R_cp≈χ_BQ^11/χ_Q² and χ_BQ^11/χ_QS^11, evaluated along the transition line, increase by factors of about 2 and 2.25 respectively at eB≈8 Mπ². This makes χ_BQ^11 a natural “magnetometer” for QCD. To connect with experiment, the authors construct hadron‑resonance‑gas (HRG) based proxy observables by mapping net‑B, Q, S onto measurable final‑state hadrons (π, p, K) with appropriate decay weights. They then impose realistic kinematic cuts that mimic the STAR and ALICE acceptances (p_T and η windows). Even after these cuts, the proxy double ratios retain roughly 80 % of the lattice magnetic sensitivity, predicting up to 25 % (for χ_BQ^11/χ_Q²) and 60 % (for χ_BQ^11/χ_QS^11) enhancements at eB≈8 Mπ². Recent STAR and ALICE measurements of χ_BQ^11/χ_Q² show centrality‑dependent increases consistent with these predictions, and the authors propose χ_BQ^11/χ_QS^11 as an even more sensitive observable.

The second part of the paper addresses the EoS under the constraints of strangeness neutrality (n_S=0) and a fixed charge‑to‑baryon ratio n_Q/n_B=r, appropriate for heavy‑ion collisions (r≈0.4 for Pb–Au). By expanding the pressure in the conserved‑charge chemical potentials and eliminating μ_Q and μ_S in favor of μ_B, the authors obtain the leading‑order chemical‑potential ratio q₁≡(μ_Q/μ_B)_LO and the pressure coefficient P₂, which governs the μ_B² dependence of the pressure. Lattice results show that q₁ is negative throughout the explored (T, eB) region, becomes more negative with increasing magnetic field, and exhibits temperature‑dependent sign‑changes (hierarchy reversals) around eB≈0.15 GeV². These reversals are not reproduced by the HRG model, indicating genuine non‑perturbative QCD effects. The dependence of q₁ on the isospin parameter r is also studied: at zero field the sign change occurs near r≈0.5, while strong fields shift the zero‑crossing to larger r, and in the magnetized ideal‑gas limit q₁ remains negative for all r.

The pressure coefficient P₂ combines diagonal susceptibilities (χ_B², χ_Q², χ_S²) with the mixed susceptibilities weighted by q₁, s₁ (μ_S/μ_B) and shows a rich structure. At zero field P₂ rises monotonically with temperature, but for strong magnetic fields it develops non‑monotonic temperature bands, crossing points, and hierarchy reversals, reflecting the intricate interplay between thermal excitations and Landau quantization. Comparisons with both a QM‑HRG (including all quark‑model states) and a PDG‑HRG reveal that the HRG description captures the qualitative trend at low fields but fails to reproduce the band crossings and saturation behavior at high eB.

Overall, the paper provides the first continuum‑extrapolated lattice QCD benchmark for conserved‑charge fluctuations and the leading‑order EoS in strong magnetic fields at physical quark masses. It demonstrates that χ_BQ^11 can serve as a robust experimental probe of magnetic fields in relativistic heavy‑ion collisions, and it delivers quantitative predictions for μ_Q/μ_B and the pressure response under realistic heavy‑ion constraints. The results have implications for the phenomenology of magnetized quark‑gluon plasma, the interpretation of fluctuation measurements at RHIC and the LHC, and for theoretical modeling of magnetized QCD matter in astrophysical and early‑universe contexts.