Physics

Chiral anomaly

Mathematical physics

Particle physics

Quantum chromodynamics

Anomaly (physics)

Neutrino

Eigenvalues and eigenvectors

Quantum electrodynamics

Dirac (video compression format)

Quantum mechanics

Chiral perturbation theory

Physical Review Letters

We introduce novel relations between the derivatives [$\partial^{n}\rho(\lambda, m_{l})/\partial m_{l}^n$] of the Dirac eigenvalue spectrum [$\rho(\lambda, m_{l})$] 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 $\partial^{n}\rho(\lambda, m_{l})/\partial m_{l}^n$ ($n=1, 2, 3$) 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, 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 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.

Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD