Spin Polarization and Chiral Symmetry Breaking at Finite Density

We investigate the possibility of the spin polarization of quark matter atzero temperature and moderate baryon density.The Nambu-Jona-Lasinio (NJL) modelincluding interactions in vector and axial-vector channel (coupling constant$G_2$) as well as scalar and pseudoscalar channel (coupling constant $G_1$) isused, and the self consistent equations for the spin polarization and chiralcondensate are solved numerically in the framework of the Hartreeapproximation. Numerical calculations show that in the one flavor model thespin polarization is possible at finite density if the ratio $G_2/G_1$ islarger than O(1).We find that the interplay between the spin polarization andthe chiral symmetry plays an important role.If the chemical potential of quarksreaches a certain finite value, the spin polarization begins to occur becausethe quark still has relatively large dynamical mass, which is generated byspontaneous chiral symmetry breaking.On the other hand, when the spinpolarization occurs, it operates to lower the dynamical quark mass a little.Ifone increases the chemical potential furthermore, the spin polarization becomesweaker and finally disappears because the dynamical quark mass is reduced byrestoring gradually the chiral symmetry.Comment: 18pages, 7 figure