The QCD thermal phase transition in the presence of a small chemical potential

TL;DR

This paper introduces a new Taylor expansion method to study the QCD phase transition at small chemical potentials, providing predictions consistent with reweighting techniques and analyzing effects on the equation of state.

Contribution

The paper develops a novel approach using derivatives at zero chemical potential to explore QCD thermal properties, applicable for small chemical potentials relevant to RHIC.

Findings

Taylor expansion accurately predicts critical temperature shift

Method agrees with reweighting estimates for small μ

Analyzes effects of isoscalar and isovector chemical potentials

Abstract

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $\mu$. Derivatives of the phase transition point with respect to $\mu$ are computed at $\mu=0$ for 2 flavors of p-4 improved staggered fermions with $ma=0.1,0.2$ on a $16^3\times4$ lattice. The resulting Taylor expansion is well behaved for the small values of $\mu_{\rm q}/T_c\sim0.1$ relevant for RHIC phenomenology, and predicts a critical curve $T_c(\mu)$ in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of $\mu\not=0$ on the equation of state, and comment on the complex phase of the fermion determinant in QCD with $\mu\not=0$.