The ΔI = 12 rule and BK at O(p4) in the chiral expansion Original Research Article

We calculate the hadronic matrix elements to O(p4) in the chiral expansion for the (ΔS=1) Ko → 2π decays and the (ΔS = 2) k0−K0 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 ΔI = 12 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 B̂K of kaon oscillation and find B̂K = 1.1 ± 0.2. As an independent check, we determine B̂K from the experimental value of the KL-KS mass difference by using our calculation of the long-distance contributions. The destructive interplay between the short- and long-distance amplitudes yields B̂K = 1.2 ± 0.1, in agreement with the direct calculation.