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

TL;DR

This work develops and applies a Taylor-expansion-based reweighting framework to study the QCD thermal transition at small quark chemical potential $\mu$ for $N_f=2$ with $p_4$-improved staggered fermions on a $16^3\times4$ lattice. By computing derivatives of the reweighting factor and fermionic observables at $\mu=0$, the authors extract the curvature of the transition line $T_c(\mu)$, finding a negative but modest $d^2 T_c/d\mu_q^2$ and thus $T_c$ decreasing with increasing $\mu$ in the RHIC-relevant regime, with weak quark-mass dependence. They also quantify the effect of $\mu$ on the equation of state and quark-number susceptibilities, showing only small changes near $\mu_q/T_c \sim 0.1$, and assess the complex phase of the determinant, finding the sign problem to be mild in the explored region. The results are consistent with reweighting studies and offer a scalable method to probe QCD thermodynamics at small densities, with potential extensions to larger volumes and higher-order terms.

Abstract

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $μ$. Derivatives of the phase transition point with respect to $μ$ are computed at $μ=0$ 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 $μ_{\rm q}/T_c\sim0.1$ relevant for RHIC phenomenology, and predicts a critical curve $T_c(μ)$ 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 $μ\not=0$ on the equation of state, and comment on the complex phase of the fermion determinant in QCD with $μ\not=0$.

Figures (25)

• Figure 1: Quark mass dependence of $\chi_L$ as a function of $\beta$ at $m_0=0.1$.
• Figure 2: Quark mass dependence of $\chi_L$ as a function of $\beta$ at $m_0=0.2$.
• Figure 3: Quark mass dependence of $\chi_{\bar{\psi}\psi}$ as a function of $\beta$ at $m_0=0.1$.
• Figure 4: Quark mass dependence of $\chi_{\bar{\psi}\psi}$ as a function of $\beta$ at $m_0=0.2$.
• Figure 5: $\beta_c(m)$ determined by $\chi_L$ around $m_0=0.2$.