Light front distribution of the chiral condensate

TL;DR

This paper investigates the distribution of the chiral condensate within the pion using light-front projection techniques, revealing its concentration near the domain boundaries and emphasizing the importance of many-particle Fock states in QCD.

Contribution

It provides a model-independent calculation of the chiral condensate distribution in the pion using Dyson-Schwinger equations, highlighting the role of Fock states and dismissing zero modes.

Findings

Condensate distribution is concentrated near the boundaries of its support.

Many-particle Fock states dominate the generation of the chiral condensate.

Light-front zero modes are not materially involved in the condensate formation.

Abstract

The pseudoscalar projection of the pion's Poincare'-covariant Bethe-Salpeter amplitude onto the light-front may be understood to provide the probability distribution of the chiral condensate within the pion. Unlike the parton distribution amplitudes usually considered and as befitting a collective effect, this condensate distribution receives contributions from all Fock space components of the pion's light-front wave-function. We compute this condensate distribution using the Dyson-Schwinger equation (DSE) framework and show the result to be a model-independent feature of quantum chromodynamics (QCD). Our analysis establishes that this condensate is concentrated in the neighbourhood of the boundaries of the distribution's domain of support. It thereby confirms the dominant role played by many-particle Fock states within the pion's light-front wave function in generating the chiral condensate on the light-front and verifies that light-front longitudinal zero modes do not play a material role in that process.