Dirac operator spectral density and low energy sum rules

TL;DR

This paper studies the spectral density of the Euclidean Dirac operator in partially quenched QCD with arbitrary quark masses, connecting it to low energy sum rules and scalar/pseudoscalar correlators.

Contribution

It provides a spectral density representation compatible with low energy sum rules using partially quenched chiral perturbation theory.

Findings

Spectral density derived from partially quenched chiral perturbation theory

Compatibility with established low energy sum rules

Representation of scalar and pseudoscalar correlators in terms of spectral density

Abstract

The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral density, obtained from the partially quenched chiral perturbation theory is shown to be compatible with low energy sum rules, obtained earlier.