Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature

The chiral susceptibility, or the first derivative of the chiral condensate with respect to the quark mass, is often used as a probe for the QCD phase transition since the chiral condensate is an order parameter of SU(2)L × SU(2)R symmetry breaking. However, the chiral condensate also breaks the axial U(1) symmetry, which is usually not studied as it is already broken by the anomaly and apparently has little impact on the transition. We investigate the susceptibilities in the scalar and pseudoscalar channels in order to quantify how much the axial U(1) breaking contributes to the chiral phase transition. Employing a chirally symmetric lattice Dirac operator and its eigenmode decomposition, we separate the axial U(1) breaking effects from others. Our result in two-flavor QCD indicates that both of the connected and disconnected chiral susceptibilities are dominated by axial U(1) breaking at temperatures T ≳ 190 MeV after the quadratically divergent constant is subtracted.