Essence of the vacuum quark condensate

TL;DR

The paper demonstrates that the vacuum quark condensate is fundamentally linked to the properties of hadrons, such as the pseudoscalar meson decay constant, and is not a constant filling all spacetime, but rather a hadron-intrinsic property.

Contribution

It clarifies the nature of the quark condensate as a hadron property rather than a spacetime-filling constant, using gauge-invariant transition amplitudes.

Findings

Quark condensate is equivalent to the pseudoscalar meson decay constant in the chiral limit.

Both are obtained from gauge-invariant hadron-to-vacuum transition amplitudes.

The condensate can be understood through hadron wavefunctions, not as a constant mass-scale.

Abstract

We show that the chiral-limit vacuum quark condensate is qualitatively equivalent to the pseudoscalar meson leptonic decay constant in the sense that they are both obtained as the chiral-limit value of well-defined gauge-invariant hadron-to-vacuum transition amplitudes that possess a spectral representation in terms of the current-quark mass. Thus, whereas it might sometimes be convenient to imagine otherwise, neither is essentially a constant mass-scale that fills all spacetime. This means, in particular, that the quark condensate can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions.