Numerical study of the equation of state for two flavor QCD at non-zero baryon density

TL;DR

This study calculates the equation of state for two-flavor QCD at finite temperature and density, revealing critical behavior near phase transitions and supporting the hadron resonance gas model below the critical temperature.

Contribution

It provides a sixth-order Taylor expansion of the QCD partition function derivatives at non-zero chemical potential, offering new insights into the phase structure.

Findings

Quark number density fluctuations increase near the phase transition.

Susceptibilities develop a peak with increasing chemical potential.

Results align with the hadron resonance gas model below T_c.

Abstract

We discuss the equation of state (EoS) for two flavor QCD at non-zero temperature and density. Derivatives of $\ln Z$ with respect to quark chemical potential $\mu_q$ are calculated up to sixth order. From this Taylor series, the pressure, quark number density and associated susceptibilities are estimated as functions of temperature and $\mu_q$. It is found that the fluctuations in the quark number density increase in the vicinity of the phase transition temperature and the susceptibilities start to develop a pronounced peak as $\mu_q$ is increased. This suggests the presence of a critical endpoint in the $(\mu_q, T)$ plane. Moreover, we comment on the hadron resonance gas model, which explains well our simulation results below $T_c$.