Self energy of massive lattice fermions

We address the perturbative renormalization of massive lattice fermions. We derive expressions—valid to all orders in perturbation theory and for all values of the bare fermion mass—for the rest mass, the kinetic mass, and the wave-function renormalization factor. We obtain the fermion’s self energy at the one-loop level with a mass-dependent, $O\left(a\right)\mathrm{}$ improved action. Numerical results for two interesting special cases, the Wilson and Sheikholeslami-Wohlert actions, are given. The mass dependence of these results smoothly connects the massless and infinite-mass limits, as expected. Combined with Monte Carlo calculations our results can be employed to determine the quark masses in common renormalization schemes.