Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD

We introduce novel relations between the derivatives ^n (, m₋) /m₋^n of the Dirac eigenvalue spectrum (, m₋) with respect to the light sea quark mass (m₋) and the (n+1) -point correlations among the eigenvalues () of the massless Dirac operator. Using these relations we present lattice QCD results for ^n (, m₋) /m₋^n (n=1, 2, 3) for m₋ corresponding to pion masses m_=160--55 MeV and at a temperature of about 1. 6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings a=0. 12, 0. 08, 0. 06 fm, and lattices having aspect ratios 4--9. We find that (0, m₋) develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as a0, and its amplitude is proportional to m₋^2. We demonstrate that this (0, m₋) is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.