Chiral condensate and the equation of state at nonzero baryon density from the hadron resonance gas model with a repulsive mean field

We study the QCD equation of state and the chiral condensate using the hadron resonance gas model with repulsive mean-field interactions. We find that the repulsive interactions improve the agreement with the lattice results on the derivatives of the pressure with respect to the baryon chemical potential up to eighth order. From the temperature dependence of the chiral condensate we estimate the crossover temperature as a function of baryon chemical potential, $T_{pc}\left({\mu }_B\right)$. We find that the chiral crossover line starts to deviate significantly from the chemical freeze-out line already for ${\mu }_B>400\mathrm{MeV}$. Furthermore, we find that the chiral pseudocritical line can be parametrized as $T_{pc}\left({\mu }_B\right)/T_{pc}\left(0\right)=1-{\kappa }_2{[{\mu }_B/T_{pc}\left(0\right)]}^2-{\kappa }_4{[{\mu }_B/T_{pc}\left(0\right)]}^4$ with ${\kappa }_2=0.0150\left(2\right)$ and ${\kappa }_4=3.1\left(6\right)\times {10}^{-5}$, which are in agreement with lattice QCD results for small values of ${\mu }_B$. For the first time we find a tiny but nonzero value of ${\kappa }_4$ in our study.