Chiral symmetry restoration and eigenvalue density of Dirac operator

We reinvestigate constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature, employing the overlap Dirac operator with the exact chiral symmetry at finite lattice spacings to avoid possible ultra-violet(UV) divergences. Studying multi-point correlation functions in various channels in the thermodynamical limit, we obtain stronger constraints than those found in the previous studies that not only the eigenvalue density at the origin but also its first and second derivatives vanish in the chiral limit of 2 flavor QCD. In addition we show that the axial U(1) anomaly becomes invisible in susceptibilities of scalar and pseudo scalar mesons.