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from October 30, 2021 to November 2, 2021
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Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD


  • Dr. 瑜 张


In this talk I will present the novel relations between the quark mass derivatives [$\partial^n \rho(\lambda,m_l)/\partial m_l^n$] of the Dirac eigenvalue spectrum and the $(n+1)$-point correlations among the eigenvalues. Using these relations we present lattice QCD results for $\partial^n \rho(\lambda,m_l)/\partial m_l^n$ ($n=1, 2, 3$) 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. 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 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. This talk is based on PRL 126 (2021) 082001.