O (a(2)) corrections to the one-loop propagator and bilinears of cloverfermions with Symanzik improved gluons

Abstract

We calculate corrections to the fermion propagator and to the Green'sfunctions of all fermion bilinear operators of the form (Psi) over barGamma Psi, to one-loop in perturbation theory.We employ the Wilson/clover action for fermions and the Symanzikimproved action for gluons.The novel aspect of our calculations is that they are carried out tosecond order in the lattice spacing, O (a(2)). Consequently, they haveaddressed a number of new issues, most notably the appearance of loopintegrands with strong IR divergences (convergent only beyond 6dimensions). Such integrands are not present in O (a(1)) improvementcalculations; there, IR divergent terms are seen to have the samestructure as in the O (a(0)) case, by virtue of parity underintegration, and they can thus be handled by well-known techniques. Weexplain how to correctly extract the full O (a(2)) dependence; in fact,our method is generalizable to any order in a.The O (a(2)) corrections to the quark propagator and Green's functionscomputed in this paper are useful to improve the nonperturbative RI-MOMdetermination of renormalization constants for quark bilinear operators.Our results depend on a large number of parameters: coupling constant,number of colors, lattice spacing, external momentum, clover parameter,Symanzik coefficients, gauge parameter. To make these results mosteasily accessible to the reader, we have included them in thedistribution package of this paper, as an ASCII file named: Oa2results.m; the file is best perused as Mathematica input.