A comparison of the cut-off effects for Twisted Mass, Overlap and Creutz fermions at tree-level of Perturbation Theory

TL;DR

This paper compares cutoff effects at tree-level for three lattice fermion formulations—twisted mass, overlap, and Creutz—showing they all exhibit similar $O(a^2)$ scaling and have comparable cutoff effects on key physical quantities.

Contribution

It provides a systematic comparison of cutoff effects for three different lattice fermions at tree-level, highlighting their similar scaling and magnitude.

Findings

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

Cutoff effects are comparable across the three formulations.

Quantities like $C_{PS}$, $m_{PS}$, and $f_{PS}$ are similarly affected.

Abstract

In this paper we investigate the cutoff effects at tree-level of perturbation theory for three different lattice regularizations of fermions -- maximally twisted mass Wilson, overlap and Creutz fermions. We show that all three kinds of fermions exhibit the expected $O(a^2)$ scaling behaviour in the lattice spacing. Moreover, the size of these cutoff effects for the considered quantities i.e. the pseudoscalar correlation function $C_{PS}$, the mass $m_{PS}$ and the decay constant $f_{PS}$ is comparable for all of them.