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 ${}_{44}^{96}\mathrm{Ru}{+}_{44}^{96}\mathrm{Ru}$ and ${}_{40}^{96}\mathrm{Zr}{+}_{40}^{96}\mathrm{Zr}$ 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 $r\equiv n_{\mathrm{Q}}/n_{\mathrm{B}}$, maps the isospin difference between two nuclei, as encoded in $r_{\mathrm{Zr}}$ and $r_{\mathrm{Ru}}$, onto splitting ratios $\Delta {\mu }_{\mathrm{Q}}/\Delta {\mu }_{\mathrm{B}}$, $\Delta {\mu }_{\mathrm{S}}/\Delta {\mu }_{\mathrm{B}}$, and $\Delta {\mu }_{\mathrm{S}}/\Delta {\mu }_{\mathrm{Q}}$ as functions of ${\mu }_{\mathrm{B}}(r_{\mathrm{Ru}})/\Delta {\mu }_{\mathrm{B}}$. Using continuum-estimated lattice results for the leading-order coefficients $q_1\equiv ({\mu }_{\mathrm{Q}}/{\mu }_{\mathrm{B}}{)}_{\mathrm{LO}}$ and $s_1\equiv ({\mu }_{\mathrm{S}}/{\mu }_{\mathrm{B}}{)}_{\mathrm{LO}}$, we find that, at vanishing magnetic field, the splitting ratios are of similar magnitude to recent Bayesian extractions from STAR isobar data and yield $\Delta {\mu }_{\mathrm{Q}}<0$ and $\Delta {\mu }_{\mathrm{S}}>0$, 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 ${\mu }_{\mathrm{Q}}/{\mu }_{\mathrm{B}}$, 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.

Comments: 15 pages, 7 figures