Volume behaviour of quark condensate, pion mass and decay constant from Dyson-Schwinger equations

TL;DR

This paper investigates how finite volume impacts key QCD observables like the quark condensate, pion mass, and decay constant using Dyson-Schwinger and Bethe-Salpeter equations, highlighting significant effects at small volumes.

Contribution

It introduces a truncation scheme including pion cloud effects to study volume dependence of pion-related observables within Dyson-Schwinger framework.

Findings

Large volume effects observed below (1.8 fm)^4

Quantitative comparison with other approaches

Insights into finite volume impacts on QCD observables

Abstract

We solve the coupled system of Dyson-Schwinger and Bethe-Salpeter equations for the quark propagator and the pion Bethe-Salpeter amplitude on a finite volume. To this end we use a truncation scheme that includes pion cloud effects in the quark propagator and light mesons. We study volume effects in the quark condensate, the pion mass and the pion decay constant and compare to corresponding results in other approaches. In general we find large effects for volumes below V=(1.8 fm)^4.