Four-quark operators and non-leptonic weak transitions

Matrix elements of four-quark operators are studied with two approaches. First inclusively; we consider two-point functions of four-quark operators. We compute their corresponding spectral function at very short distances using perturbative QCD with inclusion of O(αs) corrections; and at very long distances, using the chiral effective realization of QCD in terms of Goldstone particles. A qualitative picture emerges which requires, for consistency between the two extreme behaviours, a large coupling constant for ΔI = 1/2 transitions. The other,more direct approach, consists of calculating the effective action of four-quark operators by integrating out the quark field in a gluonic background and in the presence of a source term which triggers spontaneous chiral symmetry breaking. This way we compute the coupling constants of the lowest-order effective chiral lagrangian with ΔS = 1 (ΔI = 1/2 and 3/2) and ΔS = 2 (the so called B-factor). The calculations include the well-known O(Nc2) contributions as well as the subleading O(Nc) with inclusion of the O(αsNc) terms. The picture which emerges at this approximation is already very encouraging. Comparison with other approaches is also made. (orig.)