Behavior of the topological susceptibility at finite T and μ and signs of restoration of chiral symmetries

We investigate the possible restoration of chiral and axial symmetries across the phase transition at finite temperature and chemical potential, by analyzing the behavior of several physics quantities, such as the quark condensates and the topological susceptibility, the respective derivatives in order to chemical potential, and the masses of meson chiral partners. We discuss whether only chiral symmetry or both chiral and axial symmetries are restored and what is the role of the strange quark. The results are compared with recent lattice results. PACS. 11.30.Rd – 11.10.Wx – 14.40.Aq Understanding the rich content of the QCD phase diagram is a major challenge nowadays. Phase transitions, associated to deconfinement, restoration of chiral and axial UA(1) symmetries are expected to occur at high density and /or temperature. A question that has attracted a lot of attention is whether these phase transitions take place simultaneously and which observables could signal its occurrence. The UA(1) symmetry is explicitly broken at the quantum level by the axial anomaly, that may be described at the semiclassical level by instantons, giving a mass to η in the chiral limit, which implies that, in the real world, this meson is not a remnant of a Goldstone boson. The UA(1) anomaly causes flavor mixing, which has the effect of lifting the degeneracy between several mesons. So, the effective restoration of this symmetry should have relevant consequences on the meson masses as well as on the phenomenology of meson mixing angles. In particular, the η mass should decrease and this meson should degenerate with other Goldstone bosons. There are several reasons to expect that the singlet axial symmetry might be restored. In fact, large instantons are supposed to be suppressed at high densities or temperatures, and interactions between instantons contribute to eliminate fluctuations of the topological charge, what implies that the effects of the anomaly could disappear [1]. The topological susceptibility, χ, is related to the η mass through the Witten-Veneziano formula, and the behavior of χ and its slope are relevant to understand the possible restoration of the UA(1) symmetry [2,3,4,5]. The topological susceptibility is defined as: