Vacuum Polarization and Chiral Lattice Fermions

TL;DR

This paper calculates the vacuum polarization for chiral fermions on a 4D lattice using the overlap method, confirming gauge invariance and matching continuum results, including Standard Model RG functions, with no residual lattice artifacts.

Contribution

It demonstrates that the overlap prescription provides a gauge invariant regularization of chiral fermions on the lattice, reproducing continuum physics without lattice artifacts.

Findings

Overlap regularization is gauge invariant.

Reproduces continuum Feynman graph results.

No residual lattice artifacts or dependence on Wilson mass.

Abstract

The vacuum polarization due to chiral fermions on a 4--dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge invariant regularization of the fermion vacuum amplitude. Its low energy -- long wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan--Symanzik RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson--type mass parameters.