Chirally improving Wilson fermions 2. Four-quark operators

In this paper we discuss how the peculiar properties of twisted mass lattice QCD at maximal twist can be employed to set up a consistent computational scheme in which, despite the explicit breaking of chiral symmetry induced by the presence of the Wilson and mass terms in the action, it is possible to completely bypass the problem of wrong chirality and parity mixings in the computation of the CP-conserving matrix elements of the ΔS = 1,2 effective weak hamiltonian, and at the same time have a positive determinant for pairs of non-degenerate quarks, as well as absence of O(a) discretization effects in on-shell quantities with no need of improving lattice action and operators. (author)