# Fate of the Critical Line and Chiral Transition in Finite-Temperature Lattice QCD with the Wilson Quark Action

## TL;DR

This paper investigates the finite-temperature phase structure of lattice QCD with Wilson quarks, revealing a cusp in the critical line and clarifying the relationship between the critical line and thermal transition.

## Contribution

It provides new insights into the behavior of the critical line and thermal transition in lattice QCD with Wilson quarks, especially the cusp formation and the line's trajectory.

## Key findings

- Critical line forms a cusp at finite temperature.
- Thermal transition line passes the cusp tip without touching the critical line.
- Previous results are reinterpreted in light of the cusp formation.

## Abstract

Finite-temperature phase structure of lattice QCD with the Wilson quark action is analyzed. We show that the critical line at finite temperatures, defined to be the line of vanishing pion screening mass, turns back toward strong coupling, forming a cusp on the $(\beta, K)$ plane, and that the line of thermal transition runs past the tip of the cusp without touching the critical line. Previous results are discussed in the light of our findings.