The generating functional for hadronic weak interactions and its quenched approximation

We derive the generating functional of |ΔS| = 1, 2 hadronic weak interactions at one loop for a generic number of flavours and its counterpart in the quenched approximation. A systematic analysis of the ultraviolet divergences in the full theory (with and without a singlet dynamical field) and in the quenched case is performed. We show that the quenched chiral logarithms in the presence of weak interactions amount to a redefinition of the weak mass term in the ΔS = ±1 weak effective Lagrangian at leading order. Finally, we apply the results to BK and K → ππ matrix elements with ΔI = 1/2, 3/2 to analyze the modifications induced by quenching on the coeffcients of chiral logarithms in the one-loop corrections.