Twisted mass, overlap and Creutz fermions: Cut-off effects at tree-level of perturbation theory

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 kinds of lattice fermions exhibit the expected O(a2) 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.