Physical Review Letters ( IF 8.385 ) Pub Date : 2021-02-22 , DOI: 10.1103/physrevlett.126.082001
H.-T. Ding; S.-T. Li; Swagato Mukherjee; A. Tomiya; X.-D. Wang; Y. Zhang

We introduce novel relations between the derivatives [${\partial }^{n}\rho \left(\lambda ,{m}_{l}\right)/\partial {m}_{l}^{n}$] of the Dirac eigenvalue spectrum [$\rho \left(\lambda ,{m}_{l}\right)$] 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 ${\partial }^{n}\rho \left(\lambda ,{m}_{l}\right)/\partial {m}_{l}^{n}$ ($n=1$, 2, 3) for ${m}_{l}$ corresponding to pion masses ${m}_{\pi }=160–55\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{MeV}$ 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 $\rho \left(\lambda \to 0,{m}_{l}\right)$ 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 $a\to 0$, and its amplitude is proportional to ${m}_{l}^{2}$. We demonstrate that this $\rho \left(\lambda \to 0,{m}_{l}\right)$ 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.

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