Vacuum pseudoscalar susceptibility

TL;DR

This paper derives a model-independent expression for the pion susceptibility in QCD, linking it to the pion-pole contribution and the vacuum chiral susceptibility, clarifying discrepancies in previous estimates.

Contribution

It presents a novel, model-independent derivation of the pion susceptibility in QCD, connecting it to fundamental vacuum properties and explaining prior estimate mismatches.

Findings

Pion susceptibility expressed as sum of pion-pole and chiral susceptibility terms

Provides a straightforward explanation for discrepancies in previous estimates

Enhances understanding of QCD vacuum responses near the chiral limit

Abstract

We derive a novel model-independent result for the pion susceptibility in QCD via the isovector-pseudoscalar vacuum polarisation. In the neighbourhood of the chiral-limit, the pion susceptibility can be expressed as a sum of two independent terms. The first expresses the pion-pole contribution. The second is identical to the vacuum chiral susceptibility, which describes the response of QCD's ground-state to a fluctuation in the current-quark mass. In this result one finds a straightforward explanation of a mismatch between extant estimates of the pion susceptibility.