Validity of chiral perturbation theory for K0-K0 mixing

Chiral perturbation theory relates the |ΔS|=2 matrix element 〈K―0|(s―d)V-A×(s―d)V-A|K0〉 to the |ΔS|=1 matrix element 〈π+π0|(s―d)V-A(u―u)V-A+(s―u)V-A×(u―d)V-A-(s―d)V-A(d―d)V-A|K+〉. The latter matrix element is measured in K+→π+π0 decay and the former matrix element is relevant for the predictions that the standard model makes for CP nonconservation in K0-K―0 mixing. In this paper the corrections of order mK4 lnmK2 to lowest-order chiral perturbation theory (i.e., order mK2) for these matrix elements are computed. The correction is large for the |ΔS|=2 matrix element indicating a breakdown of chiral perturbation theory.