Testing Improved Actions

TL;DR

This paper introduces a new improved gauge action called the square Symanzik action, which simplifies the gauge field propagator and is tested through analytical and Monte Carlo methods in finite volume gauge theories.

Contribution

The paper presents the development of the square Symanzik improved action, including its parameters and Lambda value, and discusses its properties and issues such as unitarity violations.

Findings

The gauge field propagator is greatly simplified with the new action.

Monte Carlo results demonstrate the behavior of the improved action.

Discussion of unitarity violations at the lattice cutoff scale.

Abstract

We discuss testing improved actions in the context of finite volume gauge theories, where both results for the continuum and the Wilson lattice action are known analytically for volumes up to 0.7 fermi across. A new improved action is introduced, obtained by adding a 2 x 2 plaquette to the L\"uscher-Weisz Symanzik action, for which the gauge field propagator greatly simplifies. We call this the square Symanzik action. We present the tree-level parameters of this improved action and the value of its Lambda parameter. We also give some Monte Carlo results and discuss some of the issues related to violations of unitarity at the scale of the lattice cutoff due to next-to-nearest coupling in the time direction.