Isospin-Driven Splitting of Chemical Potentials in Isobar Collisions from Lattice QCD

Abstract

Strong magnetic fields produced in relativistic heavy-ion collisions can modify fluctuations of conserved charges and, consequently, their associated chemical potentials. We present first-principles $(2+1)$-flavor lattice-QCD results for isospin-driven splittings of conserved-charge chemical potentials between the isobar systems $^{96}_{44}\mathrm{Ru}+^{96}_{44}\mathrm{Ru}$ and $^{96}_{40}\mathrm{Zr}+^{96}_{40}\mathrm{Zr}$ in the QCD crossover region, both at vanishing and nonzero magnetic fields along the pseudo-critical line $T_{pc}(eB)$. We outline a framework that, under strangeness neutrality and charge-to-baryon ratio $r\equiv n_{\rm Q}/n_{\rm B}$, maps the isospin difference between two nuclei, as encoded in $r_{\rm Zr}$ and $r_{\rm Ru}$, onto splitting ratios $Δμ_{\rm Q}/Δμ_{\rm B}$, $Δμ_{\rm S}/Δμ_{\rm B}$, and $Δμ_{\rm S}/Δμ_{\rm Q}$ as functions of $μ_{\rm B}(r_{\rm Ru})/Δμ_{\rm B}$. Using continuum-estimated lattice results for the leading-order coefficients $q_1\equiv(μ_{\rm Q}/μ_{\rm B})_{\rm LO}$ and $s_1\equiv(μ_{\rm S}/μ_{\rm B})_{\rm LO}$, we find that, at vanishing magnetic field, the splitting ratios are of similar magnitude to recent Bayesian extractions from STAR isobar data and yield $Δμ_{\rm Q}<0$ and $Δμ_{\rm S}>0$, with the electric-charge sector dominating. At nonzero magnetic fields, the splitting ratios show only moderate $eB$ dependence. We therefore further examine Ru--Zr differences in the normalized magnetic-field response of chemical-potential ratios, particularly those involving $μ_{\rm Q}/μ_{\rm B}$, which display a pronounced enhancement in lattice QCD. We also present hadron resonance gas (HRG) results and experimentally motivated proxy observables with kinematic cuts to facilitate contact with experiment.