# Chiral restoration temperature at finite spin density in QCD

## TL;DR

This study explores how finite spin density influences the chiral phase transition temperature in QCD, revealing a transition from crossover to first-order and identifying a critical end-point through an extended phase diagram.

## Contribution

It introduces a method to extend the QCD phase diagram at finite spin density using the linear sigma model and lattice data comparison, addressing regularization ambiguities.

## Key findings

- Chiral transition temperature decreases with increasing spin potential.
- Transition changes from crossover to first-order at a critical end-point.
- Chiral symmetry restoration occurs at high spin potentials regardless of temperature.

## Abstract

We investigate the impact of a uniform spin density on the critical temperature of the chiral phase transition in finite-temperature QCD in the scope of the linear sigma model. We demonstrate that at a finite spin potential $\mu_\Sigma$, corresponding to a finite spin density, the predictive power of the model is challenged by an ambiguity associated with a contribution of the vacuum renormalization term to the free energy. Eliminating the regularization freedom through comparison with recent low-$\mu_{\Sigma}$ lattice data, we extend the phase diagram of QCD at finite spin density to regions inaccessible to lattice simulations. We show that, as the spin potential increases, the temperature of the chiral crossover transition diminishes and the chiral crossover turns into a first-order transition at a second-order critical end-point $(T,\mu_\Sigma)_\mathrm{CEP}\simeq (0.142,0.098)$ GeV. With increasing spin potential, the critical temperature touches the zero-temperature axis at $\mu_{\Sigma} = 0.310$ GeV, implying that the chiral symmetry is restored at higher potentials at any temperature.