4-QUARK OPERATORS AND NONLEPTONIC 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 functions at very short distances using perturbative QCD with inclusion of O(alpha-s) 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 DELTA-I = 1/2 transitions. The other, more direct approach, consists of calculating the effective action of four-quark operators by integrating out the quark fields in a gluonic background and in the presence of a source term which triggers spontaneous chiral symmetry breaking. The procedure follows the method elaborated recently in ref [1]. This way we compute the coupling constants of the lowest-order effective chiral lagrangian with DELTA-S = 1 (DELTA-I = 1/2 and 3/2) and DELTA-S = 2 (the so called B-factor.) The calculations include the well-known O(N(c)2) contributions as well as the subleading O(N(c)) with inclusion of the O(alpha-s(N)c) terms. The picture which emerges at this approximation is already very encouraging. Comparison with other approaches is also made.