# Dense quark matter with chiral and isospin imbalance: NJL-model consideration

## TL;DR

This paper explores the phase structure of dense quark matter considering isospin and chiral imbalances using an NJL model, revealing how chiral isospin chemical potential induces pion condensation and examining symmetry properties.

## Contribution

It introduces a generalized NJL model with multiple chemical potentials to analyze the effects of chiral and isospin imbalances on quark matter phases, including pion condensation and symmetry dualities.

## Key findings

- Chiral isospin chemical potential induces pion condensation in asymmetric quark matter.
- Duality between chiral and pion condensates persists even with finite quark masses.
- Temperature effects on phase structure are also analyzed.

## Abstract

Isospin asymmetry is the well-known property of dense quark matter, which exists in the compact stars and is produced in heavy ion collisions. On the other hand, the chiral imbalance between left- and right-handed quarks is another highly anticipated phenomenon that could occur in the dense quark matter. To investigate quark matter under these conditions, we take into account baryon -- $\mu_B$, isospin -- $\mu_I$ and chiral isospin -- $\mu_{I5}$ chemical potentials and study QCD phase portrait using NJL$_4$ model generalized to two massive quarks that could condense into the pion condensation. We have shown that the chiral isospin chemical potential $\mu_{I5}$ generates pion condensation in isospin asymmetric quark matter. Also, we have investigated discrete symmetry (duality) between chiral and pion condensates in the case of massless quarks, which stay relatively instructive even if the quarks have bare mass. To describe hot dense quark matter, in addition to the above-mentioned chemical potentials, we introduce non-zero temperatures into consideration.