Twisted mass, overlap and creutz fermions: cut-off effect at three- level of perturbation theory
K. Cichy1 , L. J. Gonzalez2,3 , K. Jansen 3 , A. Kujawa1 , A. Shindler4
1 Institute of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614 Poznań, Poland
2 Humboldt-Universität zu Berlin, Institut für Physik, Newtonstrasse 15, 12489 Berlin, Germany
3 DESY, Zeuthen, Platanenallee 6, D-15738 Zeuthen, Germany
4 Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
Nuclear Physics, 94, 109 (2008)
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.