The chiral phase transition and equation of state in the chiral imbalance

TL;DR

This paper investigates how chiral imbalance affects the phase transition and equation of state in quark matter using a new mean-field approach within the Nambu-Jona-Lasinio model, revealing potential first order transitions and implications for quark star properties.

Contribution

A novel self-consistent mean-field model incorporating vector and axial-vector channels to study chiral imbalance effects on phase transition and quark star characteristics.

Findings

Chiral imbalance can induce a first order phase transition.

Chiral imbalance softens the equation of state of quark matter.

Maximum mass and radius of quark stars decrease with increasing chiral chemical potential.

Abstract

The chiral phase transition and equation of state are studied within a new self-consistent mean-field approximation of the two-flavor Nambu$-$Jona-Lasinio model. In this newly developed model, modifications to the chemical potential $\mu$ and chiral chemical potential $\mu_5$ is naturally included by adding vector and axial-vector channels from Fierz-transformed Lagrangian to the standard Lagrangian. In proper-time scheme, the chiral phase transition is a crossover in the $T-\mu$ plane. But when $\mu_5$ is increased, our study shows that there may exist first order phase transition. Furthermore, the chiral imbalance will soften the equation of state of quark matter. The mass-radius relations and tidal deformability of quark stars are calculated. As $\mu_5$ increases, the maximum mass and radius decrease. The vector channel and axial-vector channel have opposite influence on the equation of state. However, when EOS is constrained by astronomical observations, the shape of the mass-radius curve can be used to determine whether there is chiral imbalance in the dense object, and thus indirectly proving the CP violation in the dense matter. Our study shows a different influence of the chiral imbalance on the chiral phase transition in contrary to tree-momentum-cutoff scheme.