Recent advances on chiral partners and patterns

We review recent results on chiral $SU(2)_L\times SU(2)_R\approx O(4)$ and $U(1)_A$ symmetry restoration in QCD. In particular, we discuss how Ward Identities allow one to derive general results on partner degeneration, which shed light on the distinction between the $O(4)$ and $O(4)\times U(1)_A$ patterns of the chiral transition. For that purpose, susceptibilities associated with the $O(4)$ and $U(1)_A$ symmetries are studied. From this analysis we conclude that in the ideal regime of exact $O(4)$ restoration (formally achieved in the limit of two massless flavours), $U(1)_A$ partners degenerate as well. We also discuss the role of the thermal $f_0(500)$ state to describe thermodynamic observables sensitive to chiral restoration, such as the scalar susceptibility. We pay special attention to the consistency of our results with recent lattice analysis.

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