Twisted Mass, Overlap and Creutz Fermions: Cut-off Effects at Tree-level of Perturbation Theory

TL;DR

This paper compares cutoff effects at tree-level for three lattice fermion formulations, showing they all exhibit similar O(a^2) scaling and analyzing effects of deviations from ideal conditions.

Contribution

It provides a comparative analysis of cutoff effects for twisted mass, overlap, and Creutz fermions at tree-level perturbation theory, including non-ideal scenarios.

Findings

All three fermion types show O(a^2) scaling behavior.

Cutoff effects are comparable across the three formulations.

Deviations from maximal twist or mass matching affect cutoff effects.

Abstract

We study cutoff effects at tree-level of perturbation theory for maximally twisted mass Wilson, overlap and the recently proposed Creutz fermions. We demonstrate that all three kind of lattice fermions exhibit the expected O(a^2) scaling behaviour in the lattice spacing. In addition, the sizes of these cutoff effects are comparable for the three kinds of lattice fermions considered here. Furthermore, we analyze situations when twisted mass fermions are not exactly at maximal twist and when overlap fermions are studied in comparison to twisted mass fermions when the quark masses are not matched.