Curvature of the critical line on the plane of quark chemical potential and pseudo scalar meson mass for three-flavor QCD

TL;DR

This study explores the phase diagram of three-flavor QCD at finite chemical potential using lattice simulations with Wilson fermions, focusing on locating the critical end point and determining the curvature of the critical line, finding it to be positive.

Contribution

The paper introduces a method to translate lattice bare parameters to physical parameters for Wilson fermions and determines the positive curvature of the critical line in the QCD phase diagram.

Findings

The critical line curvature in the $\mu$-$m_{\pi}$ plane is positive.

A strategy to relate bare lattice parameters to physical parameters is proposed.

Raising chemical potential from a crossover region leads to a first-order transition.

Abstract

We investigate the phase structure of three-flavor QCD in the presence of finite quark chemical potential $\mu/T\lesssim1.2$ by using the non-perturbatively $O(a)$ improved Wilson fermion action on lattices with a fixed temporal extent $N_{\rm t}=6$ and varied spatial linear extents $N_{\rm s}=8,10,12$. Especially, we focus on locating the critical end point that characterizes the phase structure, and extracting the curvature of the critical line on the $\mu$-$m_{\pi}$ plane. For Wilson-type fermions, the correspondence between bare parameters and physical parameters is indirect. Hence we present a strategy to transfer the bare parameter phase structure to the physical one, in order to obtain the curvature. Our conclusion is that the curvature is positive. This implies that, if one starts from a quark mass in the region of crossover at zero chemical potential, one would encounter a first-order phase transition when one raises the chemical potential.