# Spin Polarization and Chiral Condensation in 2+1 flavor Nambu-Jona-Lasinio model at finite temperature and baryon chemical potential

## TL;DR

This paper explores how spin polarization and chiral condensation interact in a 2+1 flavor NJL model at finite temperature and density, revealing their effects on phase transitions relevant to neutron star physics.

## Contribution

It introduces the study of spin polarization in a 2+1 flavor NJL model, highlighting its impact on chiral symmetry and phase transitions with tensor interactions.

## Key findings

- Spin polarization appears only in the chirally restored phase.
- Spin condensates vanish beyond a certain temperature at high chemical potential.
- Spin polarization acts as a catalyst for chiral symmetry restoration.

## Abstract

We investigate the ferromagnetic (spin polarization) condensation in (2+1) flavor Nambu Jona-Lasinio(NJL) model with non-zero current quark masses at finite temperature and density which may be relevant in the context of neutron stars. The spin polarization condensation arises due to a tensor type interaction which may be generated due to non-perturbative effects in Quantum Chromodynamics(QCD). In this investigation we have shown the interplay between chiral condensate and spin polarization condensation for different values of tensor coupling. Spin polarization in the case of 2+1 flavor is different from two flavor case because of additional F$_8$ condensate associated with $\lambda_8^f$ flavor generator. We find a non-zero value of the two spin condensates in the chirally restored phase. Beyond a certain temperature the spin polarization condensates vanish for rather large quark chemical potentials. The spin condensates affect the chiral phase transition, quark masses, and the quark dispersion relation. The spin polarization condensate appears only in the chiral restored phase for light quarks. For large enough tensor couplings, it is observed that the spin polarization condensate acts as a catalyst for chiral symmetry restoration. Thermodynamic behavior of $F_3$ and $F_8$ are found to be different and they affect the quark masses differently.