Axial Anomaly Of QCD At High Temperature From Lattice QCD

The nature of chiral phase transition for QCD with two light quark flavors is not yet completely understood.This is primarily because that one has to understand whether or not the anomalous U(1)symmetry in the flavor sector is effectively restored along with the chiral symmetry.In QCD how axial anomaly manifests itself in the two-point correlation functions of isotriplet scalar and pseudoscalar mesons can be answered only non-perturbatively.Lattice QCD has emerged as the most successful nonperturbative tool to study this problem and has led to quite a few independent studies.However,up to now,there is still no consensus within the lattice community on whether the ax-ial anomaly remains manifested or disappear in the two point correlation functions at the chiral phase transition temperature due to the lack of state-of-the-art lattice QCD calculations with controlled continuum and chiral extrapolations.In this thesis,we investigate the Dirac eigenvalue spectrum(p(?,m,))to gain more insight into the axial anomaly in QCD,and study its microscopic origin.We introduce novel relations between the derivatives((?)?(?,ml)/(?)mln)of the Dirac eigenvalue spec-trum with respect to the light sea quark mass(ml)and the(n+1)-point correlations among the eigenvalues(A)of the massless Dirac operator.Based on these relations,for the first time,we present lattice QCD results for(?)n?(?,ml)/(?)mln(n=1,2,3)for ml corre-sponding 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 and the tree-level Symanzik gauge action.The strange quark mass ms was tuned to its physical value.To perform the continuum ex-trapolation,we chose three different lattice spacings a=(TN?)-1=0.12,0.08,0.06 fm which corresponds to lattice temporal extents N?=8,12,16.To investigate the volume dependence,the spatial extents(N?)of the lattices were chosen to have aspect ratios in the range of N?/N?=4-9.We find no evidence of a gap opening up in the infrared region of the Dirac eigen-value spectrum even at T?1.6Tc,with Tc being the chiral phase transition tempera-tore.Instead,we find that in the small eigenvalue region,the Dirac eigenvalue spectrum?(?? 0,ml)develops a peaked structure.This peaked structure,which arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum,be-comes sharper as a?0,and its amplitude is proportional to the quark mass square.We demonstrate that this ?(??0,ml)is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudo-scalar mesons.After con-tinuum and chiral extrapolations,we find that the axial anomaly remains manifested in two-point correlation functions of scalar and pseudo-scalar mesons in the chiral limit.These suggest that for T(?)1.6Tc the microscopic origin of axial anomaly is driven by the weakly interacting(quasi)instanton gas motivated ?(??0,ml?0)?ml2?(?),and the chiral phase transition in(2+1)-flavor QCD is 2nd order belonging to the three-dimensional O(4)universality class.