Abstract
We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1)_A$ symmetries. For that purpose, we exploit QCD Ward Identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests $U(1)_A$ partner restoration if chiral symmetry partners are also degenerated. This is also confirmed by the ChPT analysis when the light chiral limit is reached. Partner degeneration for the $I=1/2$ sector, the behavior of $I=0$ mixing and the temperature scaling of meson masses predicted by WI are also studied. Special attention is paid to the connection of our results with recent lattice analyses.
Highlights
The nature of chiral symmetry restoration is an essential ingredient of the phase diagram of QCD
We consider the low-energy realization of QCD provided by Uð3Þ chiral perturbation theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved
We have performed a detailed analysis of the correlators and susceptibilities corresponding to the scalar and pseudoscalar meson nonets, both from general arguments in terms of Ward identities and from the model-independent description provided by Uð3Þ chiral perturbation theory
Summary
The nature of chiral symmetry restoration is an essential ingredient of the phase diagram of QCD. For Nf 1⁄4 2 þ 1 flavors and nonzero quark masses, it has been found in [4,5] that the Uð1ÞA symmetry in terms of π − a0 partner degeneration is restored well above Tc, i.e., the chiral transition temperature where π − σ states degenerate. These results are consistent with previous analysis of screening masses by the same group [40].
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