The ΔI=1/2 rule and (B)over-cap-BK at O(p4) in the chiral expansion

yWe calculate the hadronic matrix elements to O(p(4)) in the chiral expansion for the (Delta S = 1) K-0 --> 2 pi decays and the (Delta S = 2) <(K)over bar (0)> - K-0 oscillation, This is done within the framework of the chiral quark model, The chiral coefficients thus determined depend on the values of the quark and gluon condensates and the constituent quark mass, We show that it is possible to fit the Delta I = 1/2 rule of kaon decays with values of the condensates close to those obtained by QCD sum rules. The renormalization invariant amplitudes are obtained by matching the hadronic matrix elements and their chiral corrections to the short-distance NLO Wilson coefficients. For the same input values, we study the parameter (B) over cap(K)$ of kaon oscillation and find (B) over cap(K)$ = 1.1 +/- 0.2. As an independent check, we determine (B) over cap(K)$ from the experimental value of the K-L-K-S mass difference by using our calculation of the long-distance contributions. The destructive interplay between the short-and long-distance amplitudes yields (B) over cap(K)$ = 1.2 +/- 0.1, in agreement with the direct calculation. (C) 1998 Elsevier Science B.V.