Spin polarization and chiral condensation in a ()-flavor Nambu–Jona-Lasinio model at finite temperature and baryon chemical potential

Abstract

We investigate the ferromagnetic (spin polarization) condensation in (2+1 )-flavor Nambu–Jona-Lasinio (NJL) model with nonzero 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 that may be generated due to nonperturbative effects in QCD. In this investigation, we study the interplay between the 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 an additional 𝐹8∼⟨ ¯ 𝜓 ⁢Σ𝑧⁢𝜆8⁢𝜓⟩ along with a 𝐹3∼⟨ ¯ 𝜓 ⁢Σ𝑧⁢𝜆3⁢𝜓⟩ condensate associated with the 𝜆8 flavor generator. We find nonzero values of the two spin condensates in the chirally restored phase. Beyond a certain temperature, the spin polarization condensates vanish for any value of quark chemical potential. The spin condensates affect the chiral phase transition, quark masses, and quark dispersion relation. Thermodynamic behaviors of 𝐹3 and 𝐹8 are found to be different, and they affect the quark masses differently. We discuss the phase diagram in the temperature and chemical potential plane in the presence of such condensates.