Renormalization of the topological charge density in QCD with dimensional regularization

TL;DR

This paper proves that in dimensionally regularized QCD, the topological charge density's renormalization involves only an additive term linked to the axial current divergence, valid at all perturbation orders.

Contribution

It demonstrates that the renormalization of the topological charge density in QCD is simpler than expected, requiring only a specific additive renormalization at all orders of perturbation theory.

Findings

Renormalization involves only an additive term proportional to the axial current divergence.

The proof uses BRS analysis and algebraic properties of the charge density.

Valid for all orders of perturbation theory.

Abstract

To all orders of perturbation theory, the renormalization of the topological charge density in dimensionally regularized QCD is shown to require no more than an additive renormalization proportional to the divergence of the flavour-singlet axial current. The proof is based on the standard BRS analysis of the QCD vertex functional in the background gauge and exploits the special algebraic properties of the charge density through the Stora--Zumino chain of descent equations.