Spin polarized phases in strongly interacting matter: interplay between axial-vector and tensor mean fields

Abstract

The spontaneous spin polarization of strongly interacting matter due to axial-vector and tensor type interactions is studied at zero temperature and high baryon-number densities. We start with the mean-field Lagrangian for the axial-vector and tensor interaction channels, and find in the chiral limit that the spin polarization due to the tensor mean field ($U$) takes place first as the density increases for sufficiently strong coupling constants, and then that due to the axial-vector mean field ($A$) emerges in the region of finite tensor mean field. This can be understood that making the axial-vector mean field finite requires a broken chiral symmetry somehow, which is achieved by the finite tensor mean field in the present case. It is also found from symmetry argument that there appear the type I (II) Nambu-Goldstone modes with a linear (quadratic) dispersion in the spin polarized phase with $U\ne 0$ and $A=0$ ($U\ne 0$ and $A\ne 0$), although these two phases exhibit the same symmetry breaking pattern.

arXiv comment9pages , 5 figures. Version accepted in PRD. Baryon number density has been added in Fig 3, and misprints were corrected

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• Axial-Vector and Tensor Spin Polarization and Chiral Restoration in Quark Matter