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In this work we calculate the corrections to the amputated Green's functionsof 4-fermion operators, in 1-loop Lattice Perturbation theory. One of the novelaspects of our calculations is that they are carried out to O(a^2) (a: latticespacing). We employ the Wilson/clover action for massless fermions (alsoapplicable for the twisted mass action in the chiral limit) and a family ofSymanzik improved actions for gluons. Our calculations have been carried out ina general covariant gauge. Results have been obtained for several popularchoices of values for the Symanzik coefficients. While our Green's functioncalculations regard any pointlike 4-fermion operators which do not mix withlower dimension ones, we pay particular attention to DF=2 operators, bothParity Conserving and Parity Violating (F: flavour). We compute theperturbative renormalization constants for a complete basis of 4-fermionoperators and we study their mixing pattern. For some of the actions consideredhere, even O(a^0) results did not exist in the literature to date. Thecorrection terms which we calculate are essential ingredients for minimizingthe lattice artifacts which are present in non-perturbative evaluations ofrenormalization constants with the RI'-MOM method. Our perturbative results,for the matrix elements of DF=2 operators and for the correspondingrenormalization matrices, depend on a large number of parameters: couplingconstant, number of colors, lattice spacing, external momentum, cloverparameter, Symanzik coefficients, gauge parameter. To make these results mosteasily accessible, we have included them in the distribution package of thispaper, as an ASCII file named: 4-fermi.m; the file is best perused asMathematica input. The main results of this work have been applied to improvenon-perturbative estimates of the B_K-parameter in N_F=2 twisted mass latticeQCD.

Perturbative renormalization factors and O(a^2) corrections for lattice 4-fermion operators with improved fermion/gluon actions