Improving perturbation theory with cactus diagrams

TL;DR

This paper introduces a systematic method to improve lattice gauge theory perturbation calculations by resumming dominant tadpole diagrams, resulting in more accurate renormalization estimates that align better with non-perturbative results.

Contribution

The paper extends the cactus diagram resummation technique to all gluon actions and fermion actions, providing a gauge-invariant, systematic way to improve perturbative results on the lattice.

Findings

Resummation improves agreement with non-perturbative estimates.

Dressed parameters effectively absorb tadpole contributions.

Method is applicable to various gluon and fermion actions.

Abstract

We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik and clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is consistently better as compared to results from bare perturbation theory.