中国物理学会高能物理分会第十三届全国粒子物理学术会议（2021）

We introduce novel relations between the derivatives ($\partial^n \rho/\partial m_l^n$) of the Dirac eigenvalue spectrum ($\rho$) with respect to the light sea quark mass ($m_l$) and the $(n+1)$-point correlations among the eigenvalues ($\lambda$) of the massless Dirac operator. Using these relations we present lattice QCD results for $\partial^n \rho/\partial m_l^n$ ($n=1, 2, 3$) 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 $\rho(\lambda\to0,m_l)$ 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 $a\to0$, and its amplitude is proportional to $m_l^2$. We demonstrate that this $\rho(\lambda\to0,m_l)$ is responsible for the manifestations of axial anomaly in 2-point correlation functions of light scalar and pseudo-scalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in 2-point correlation functions of scalar and pseudo-scalar mesons in the chiral limit. The talk is based on Phys.Rev.Lett. 126 (2021) 8, 082001.