Heaviside transform with respect to the mass in QCD

TL;DR

This paper introduces a Heaviside transform approach with respect to quark mass in QCD, revealing that at high momentum transfer, the transformed propagator simplifies the analysis of chiral symmetry breaking, and facilitates estimating the quark condensate.

Contribution

It proposes a novel Heaviside transform method with respect to quark mass in QCD, simplifying the analysis of dynamical chiral symmetry breaking effects.

Findings

Transformed propagator behaves softly at high momentum transfer.

Massless approximation is more convenient in the transformed space.

Estimated the quark condensate in the massless limit.

Abstract

We propose the use of Heaviside transform with respect to the quark mass to investigate dynamical aspects of QCD. We show that at large momentum transfer the transformed propagator of massive quarks behaves softly and thus the dominant effect of explicit chiral symmetry breaking disappears through Heaviside transform. This suggests that the massless approximation would be more convenient to do in the transformed quantity than in the original one. As an example of explicit approximation, we estimate the massless value of the quark condensate.