Analysis of U$_A$(1) symmetry-breaking and restoration effects on the scalar-pseudoscalar spectrum
We explore patterns of effective restoration of the chiral U$_A$(1) symmetry using an extended three-flavor Nambu-Jona-Lasinio model that incorporates explicitly the axial anomaly through the 't Hooft interaction, and assuming that the coefficient of the anomaly term is temperature and density dependent. The special case of explicit breaking of chiral symmetry without U$_A$(1) anomaly is also considered, since this scenario can provide additional information allowing to understand the interplay between the U$_A$(1) anomaly and (spontaneous) chiral symmetry breaking effects. The pseudoscalar and scalar sectors are analyzed in detail bearing in mind the identification of chiral partners and the study of its convergence. We also concentrate on the behavior of the mixing angles that give us relevant information on the issue under discussion. In the region of temperatures (densities) studied, we do not observe signs indicating a full restoration of U(3)$\otimes$U(3) symmetry as, for instance, the degeneracy of both $a_0$ and $f_0$ mesons with the pion. As we work in a real world scenario ($m_u=m_d<<m_s$), we only observe the return to symmetries of the classical QCD Lagrangian in the non-strange sector.