K→2πdecays andK−πmatrix elements ofΔS=1transition operators

Abstract

It is pointed out that the $K-\pi$ matrix element given by Shifman, Vainshtein, and Zakharov using the vacuum-insertion method is inconsistent with the chiral-symmetry constraint. The matrix elements of the left-handed current × current operators obtained by this method are however consistent with chiral symmetry and give a qualitative understanding of the $\Delta I=\frac{3}{2}$ $K\to 2\pi$ decay amplitude. The $\Delta I=\frac{1}{2}$ amplitude seems to be dominated by a pure $\Delta I=\frac{1}{2}$ operator as indicated by the calculated $K_L\to 2\gamma$ decay rate; the nature of this interaction is discussed.