Cutoff effects for Wilson twisted mass fermions at tree-level of perturbation theory

TL;DR

This paper analyzes cutoff effects at tree-level for Wilson and Wilson twisted mass fermions, showing automatic O(a) improvement at maximal twist and comparing scaling violations in different fermion formulations.

Contribution

It demonstrates that Wilson twisted mass fermions exhibit automatic O(a) improvement at maximal twist even with O(a) cutoff effects and compares scaling violations between Wilson and twisted mass fermions.

Findings

Wilson and mass average methods are equivalent and lead to O(a) improvement.

Automatic O(a) improvement works at maximal twist even with O(a) cutoff effects.

Scaling violations are O(a^2) for Wilson and O(a^4) for twisted mass fermions in the chiral limit.

Abstract

We study cutoff effects at tree-level of perturbation theory for standard Wilson and Wilson twisted mass fermionic lattice actions with Nf=2 flavour degenerate quarks. The discretization effects are investigated by computing the mass spectrum and decay amplitudes for different hadron interpolating fields and the scaling behaviour towards the continuum limit is analyzed. It is shown that the Wilson and the mass average methods are equivalent and lead to O(a) improved R5-parity even lattice observables. We also demonstrate that automatic O(a) improvement works in case of Wilson twisted mass fermions at maximal twist and that this improvement is realized even if the condition of maximal twist is achieved only up to O(a) cutoff effects. We demonstrate that in the chiral limit standard Wilson fermions show scaling violations of O(a^2) while for maximally twisted mass fermions these violations are only of O(a^4). For our analytical calculations, lattices with sizes L=aN and periodic boundary conditions in the spatial directions have been chosen while infinite extension in the time direction is considered.