Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD

We introduce novel relations between the derivatives [partial derivative(n)rho(lambda, m(l))/ partial derivative m(l)(n) of the Dirac eigenvalue spectrum [rho(lambda, m(1))] with respect to the light sea quark mass (m(i)) and the (n + 1)-point correlations among the eigenvalues (lambda) of the massless Dirac operator. Using these relations we present lattice QCD results for partial derivative(n)rho(lambda,m(l)/partial derivative m(l)(n) (n = 1, 2, 3) for m(l) corresponding to pion masses m(pi) = 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 rho(lambda -> 0, m(l)) 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 a -> 0, and its amplitude is proportional to m(l)(2). We demonstrate that this rho(lambda -> 0, m(l)) 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.