Improving lattice perturbation theory

TL;DR

This paper presents an analytical approach to tadpole renormalization in lattice gauge theory using Cayley parametrization, improving numerical results and gauge potential approximations.

Contribution

It introduces Cayley parametrization for lattice gauge potentials, simplifying tadpole renormalization and improving the accuracy of lattice perturbation theory results.

Findings

Cayley parametrization simplifies tadpole renormalization.

Gauge potentials closely match continuum form.

Tadpole renormalized coupling aligns better with numerical values.

Abstract

Lepage and Mackenzie have shown that tadpole renormalization and systematic improvement of lattice perturbation theory can lead to much improved numerical results in lattice gauge theory. It is shown that lattice perturbation theory using the Cayley parametrization of unitary matrices gives a simple analytical approach to tadpole renormalization, and that the Cayley parametrization gives lattice gauge potentials gauge transformations close to the continuum form. For example, at the lowest order in perturbation theory, for SU(3) lattice gauge theory, at $\beta=6,$ the `tadpole renormalized' coupling $\tilde g^2 = {4\over 3} g^2,$ to be compared to the non-perturbative numerical value $\tilde g^2 = 1.7 g^2.$