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How axial anomaly manifests itself in the two-point correlation functions of iso-triplet scalar and pseudo-scalar mesons affects the nature of chiral phase transition. In this talk we first review current status on the fate of UA(1) anomaly in the finite temperature lattice QCD, and then present a first continuum and chiral extrapolation of two UA(1) measures in (2+1)-flavor lattice QCD at 1.6Tc. After continuum and chiral extrapolations we find that axial anomaly remains manifested in the 2-point correlation functions of scalar and pseudo-scalar mesons in the chiral limit. To study the origin of the axial anomaly we propose novel relations between the quark mass derivatives of Dirac eigenvalue spectrum $\rho$ and correlation functions among eigenvalues. We find that the peak structure developed in $\rho$ in the infrared region with its height proportional to quark mass squared is responsible for the manifestation of axial anomaly. These findings suggest that the axial anomaly is driven by the weakly interacting (quasi-)instanton gas motived $\rho$ at T>1.6Tc and the chiral phase transition belongs to 3-d O(4) universality class. The talk is based on https://arxiv.org/abs/2010.14836.
Postponed to 14/Jan/2020