Perturbative renormalization factors and O(a^{2}) corrections for lattice four-fermion operators with improved fermion/gluon actions

In this work we calculate the corrections to the amputated Green's functions of 4-fermion operators, in 1-loop Lattice Perturbation theory. One of the novel aspects of our calculations is that they are carried out to O(a^2) (a: lattice spacing). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients. While our Green's function calculations regard any pointlike 4-fermion operators which do not mix with lower dimension ones, we pay particular attention to DF=2 operators, both Parity Conserving and Parity Violating (F: flavour). We compute the perturbative renormalization constants for a complete basis of 4-fermion operators and we study their mixing pattern. For some of the actions considered here, even O(a^0) results did not exist in the literature to date. The correction terms which we calculate are essential ingredients for minimizing the lattice artifacts which are present in non-perturbative evaluations of renormalization constants with the RI'-MOM method. Our perturbative results, for the matrix elements of DF=2 operators and for the corresponding renormalization matrices, 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 most easily accessible, we have included them in the distribution package of this paper, as an ASCII file named: 4-fermi.m; the file is best perused as Mathematica input. The main results of this work have been applied to improve non-perturbative estimates of the B_K-parameter in N_F=2 twisted mass lattice QCD.