# Dependence of the static quark free energy on $\mu_B$ and the crossover temperature of $N_f = 2+1$ QCD

## TL;DR

This study investigates how the static quark free energy varies with baryon chemical potential in $N_f=2+1$ QCD across a broad temperature range, revealing sensitivity to the chiral crossover and aligning with perturbative predictions at high temperatures.

## Contribution

It provides the first detailed analysis of the dependence of static quark free energy on $$ in $N_f=2+1$ QCD using both Taylor expansion and analytic continuation methods.

## Key findings

- The $$-susceptibility peaks around 150 MeV, indicating sensitivity to the chiral crossover.
- Results are consistent between Taylor expansion and analytic continuation approaches.
- High-temperature behavior matches perturbative theoretical expectations.

## Abstract

We study the dependence of the static quark free energy on the baryon chemical potential for $N_f = 2+1$ QCD with physical quark masses, in a range of temperature spanning from 120~MeV up to 1~GeV and adopting a stout staggered discretization with two different values of the Euclidean temporal extension, $N_t = 6$ and $N_t = 8$. In order to deal with the sign problem, we exploit both Taylor expansion and analytic continuation, obtaining consistent results. We show that the dependence of the free energy on $\mu_B$ is sensitive to the location of the chiral crossover, in particular the $\mu_B$-susceptibility, i.e. the linear term in $\mu_B^2$ in the Taylor expansion of the free energy, has a peak around 150 MeV. We also discuss the behavior expected in the high temperature regime based on perturbation theory, and obtain a good quantitative agreement with numerical results.