Chiral susceptibility and the scalar Ward identity

TL;DR

This paper explores the calculation of chiral susceptibility in QCD using a nonperturbative, symmetry-preserving approach, demonstrating its consistency across different vertex ansätze and its role in identifying chiral symmetry breaking.

Contribution

It introduces a method to compute chiral susceptibility via the scalar Ward identity, independent of the kernel ansatz, enabling consistent results across different vertex models.

Findings

Chiral susceptibility can be calculated consistently using the scalar Ward identity.

Results are robust across different vertex ansätze with minor quantitative differences.

Susceptibility helps identify the coupling strength domain for chiral symmetry breaking.

Abstract

The chiral susceptibility is given by the scalar vacuum polarisation at zero total momentum. This follows directly from the expression for the vacuum quark condensate so long as a nonperturbative symmetry preserving truncation scheme is employed. For QCD in-vacuum the susceptibility can rigorously be defined via a Pauli-Villars regularisation procedure. Owing to the scalar Ward identity, irrespective of the form or Ansatz for the kernel of the gap equation, the consistent scalar vertex at zero total momentum can automatically be obtained and hence the consistent susceptibility. This enables calculation of the chiral susceptibility for markedly different vertex Ansaetze. For the two cases considered, the results were consistent and the minor quantitative differences easily understood. The susceptibility can be used to demarcate the domain of coupling strength within a theory upon which chiral symmetry is dynamically broken. Degenerate massless scalar and pseudoscalar bound-states appear at the critical coupling for dynamical chiral symmetry breaking.