# Chiral crossover in QCD at zero and non-zero chemical potentials

## TL;DR

This study uses lattice QCD to determine the pseudo-critical temperatures of QCD chiral crossovers at various chemical potentials, providing precise parametrizations and insights relevant for heavy-ion collision conditions.

## Contribution

It offers the first detailed lattice QCD determination of the curvature parameters of the QCD phase boundary at finite chemical potentials.

## Key findings

- Precise value for $T_c(0) = 156.5 \,\mathrm{MeV}$.
- Determined curvature coefficients $\,\kappa_2^X$ and $\,\kappa_4^X$ for different chemical potentials.
- QCD phase boundary lines are close to chemical freeze-out conditions in heavy-ion collisions.

## Abstract

We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon ($B$), strangeness ($S$), electric charge ($Q$), and isospin ($I$) chemical potentials $\mu_{X=B,Q,S,I}$. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as $ T_c(\mu_X) = T_c(0) \left[ 1 -\kappa_2^{X}(\mu_{X}/T_c(0))^2 -\kappa_4^{X}(\mu_{X}/T_c(0))^4 \right] $, we determined $\kappa_2^X$ and $\kappa_4^X$ from Taylor expansions of chiral observables in $\mu_X$. We obtained a precise result for $T_c(0)=(156.5\pm1.5)\;\mathrm{MeV}$. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., $\mu_{S}(T,\mu_{B})$ and $\mu_{Q}(T,\mu_{B})$ fixed from strangeness-neutrality and isospin-imbalance, we found $\kappa_2^B=0.012(4)$ and $\kappa_4^B=0.000(4)$. For $\mu_{B}\lesssim300\;\mathrm{MeV}$, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of $0.42(6)\;\mathrm{GeV/fm}^3$ and constant entropy density of $3.7(5)\;\mathrm{fm}^{-3}$.