# Chiral QCD phase in equilibrium with Hadron Gas and the location of the critical point

## TL;DR

This paper models the QCD phase transition with chiral symmetry restoration, analyzing the hadron gas and quark condensates to locate the critical point in the phase diagram.

## Contribution

It introduces a novel approach combining chiral symmetry restoration with hadron gas models to determine the QCD critical point's location.

## Key findings

- Critical point located at μ_B ≈ 233-267 MeV and T ≈ 153-158 MeV.
- Pion system significantly influences the order of the phase transition.
- The model predicts the transition shifts from crossover to first order under certain conditions.

## Abstract

We develop a description of the equation of state of QCD matter with restored chiral symmetry, which is in thermal and chemical equilibrium with the hadronic phase. The hadron gas is described with thermodynamically consistent volume corrections. The chiral phase is composed of a set of few quark condensates, each of which corresponds to a family of hadrons with specific quark content. On the boundary between the two phases we apply the requirement of conservation of particle numbers per family. We use lattice calculations for temperatures below the transition curve to determine hadronic volumes. We find that the pion system plays decisive role in the shift of the transition from higher order (crossover) to first order. For four volume models we calculate the location of the critical point as function of critical temperature $T_c$ at vanishing baryon density. Particularly, if we additionally impose the equality between the densities of quarks contained in mesons and baryons, we find a critical point residing in the interval of baryon chemical potential $\mu_B \simeq$ 233-267 MeV and of temperature $T \simeq$ 153-158 MeV.