Topological effects in QCD and the problem of short-distance singularities

TL;DR

This paper discusses a regularization-independent way to define topological charge moments in QCD using correlation functions free of short-distance singularities, grounded in chiral Ward identities.

Contribution

It introduces a novel, unambiguous method to compute topological charge moments in QCD that avoids short-distance singularities and is based on fundamental chiral Ward identities.

Findings

Correlation functions are free of short-distance singularities.

Provides a regularization-independent definition of topological moments.

Connects topological susceptibility to n-point functions of quark densities.

Abstract

The topological susceptibility and the higher moments of the topological charge distribution in QCD are expressed through certain n-point functions of the scalar and pseudo-scalar quark densities at vanishing momenta, which are free of short-distance singularities. Since the normalization of the correlation functions is determined by the non-singlet chiral Ward identities, these formulae provide an unambiguous regularization-independent definition of the moments and thus of the charge distribution.