Topological charge renormalization: A test case for 3-loop vacuum calculations using overlap fermions and Symanzik improved gluons

TL;DR

This paper performs a detailed perturbative calculation of the topological charge renormalization in lattice QCD using overlap fermions and Symanzik improved gluons, including a three-loop analysis of the susceptibility.

Contribution

It provides the first three-loop calculation of the additive renormalization of the topological susceptibility with these lattice actions.

Findings

One-loop multiplicative renormalization of topological charge density computed.

Three-loop power divergent additive renormalization of susceptibility obtained.

Results facilitate more accurate lattice QCD topological studies.

Abstract

We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power divergent additive renormalization of the topological susceptibility is calculated to 3 loops.