The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space

TL;DR

This paper computes the hadronic vacuum polarization function for two light flavors across all momenta using Dyson-Schwinger equations, extracting quark spectral functions from the gap equation, highlighting dynamical chiral symmetry breaking.

Contribution

It introduces a novel method to extract light quark spectral functions from the gap equation and applies Dyson-Schwinger equations in Minkowski space to compute the vacuum polarization.

Findings

First extraction of light quark spectral functions from the gap equation.

Computation of the vacuum polarization function over entire momentum domain.

Emphasis on dynamical chiral symmetry breaking as a key scale.

Abstract

The hadronic vacuum polarization function $\Pi_h$ for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson-Schwinger equations. The analytical continuation of the function $\Pi_h$ is based on the utilization of the Gauge Technique with the entry of QCD Green's functions determined from generalized quark spectral functions. For the first time, the light quark spectral functions are extracted from the solution of the gap equation for the quark propagator. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.