On tadpole improvement for staggered fermions

One-loop renormalization constants for a number of staggered-fermion operators have large finite parts (see e.g. ref. [1]), which appear not to be explained by gluon-tadpole contributions. This is in contrast to the situation with Wilson fermions, where tadpole improvement [2] appears to work well. Staggered and Wilson fermions differ in the way they deal with the doubling problem: in the Wilson case, they get a mass of the order of the cutoff and decouple, while they are present in the staggered case, yielding a number of continuum flavors which is a multiple of four. The staggered doublers do contribute to loop diagrams, and here I suggest that this may explain why tadpole improvement does not work well for staggered fermions, by considering the one-loop fermion self-energy. Let us first consider the Wilson case. The oneloop self-energy is [3]