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We calculate the corrections to the amputated Green's functions of 4-fermionoperators, in 1-loop Lattice Perturbation theory. The novel aspect of ourcalculations is that they are carried out to second order in the latticespacing, O(a^2). We employ the Wilson/clover action for massless fermions (alsoapplicable for the twisted mass action in the chiral limit) and the Symanzikimproved action for gluons. Our calculations have been carried out in a generalcovariant gauge. Results have been obtained for several popular choices ofvalues for the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki,TILW and DBW2 action). We pay particular attention to $\Delta F=2$ operators,both Parity Conserving and Parity Violating ($F$ stands for flavour: S, C, B).We study the mixing pattern of these operators, to O(a^2), using theappropriate projectors. Our results for the corresponding renormalizationmatrices are given as a function of a large number of parameters: couplingconstant, clover parameter, number of colors, lattice spacing, externalmomentum and gauge parameter. The O(a^2) correction terms (along with ourprevious O(a^2) calculation of $Z_\Psi$) are essential ingredients forminimizing the lattice artifacts which are present in non-perturbativeevaluations of renormalization constants with the RI'-MOM method. A longerwrite-up of this work, including non-perturbative results, is in preparationtogether with members of the ETM Collaboration.

O(a^2) corrections to 1-loop matrix elements of 4-fermion operators with improved fermion/gluon actions