The Delta I=1/2 Rule in Kaon Decays: A New Look

Abstract

The $K\toππ$ decay amplitudes are studied within the framework of generalized factorization in which the effective Wilson coefficients are gauge-invariant, renormalization-scale and -scheme independent while factorization is applied to the tree-level hadronic matrix elements. Nonfactorized contributions to the hadronic matrix elements of (V-A)(V-A) four-quark operators, which are needed to account for the suppression of the $ΔI=3/2 K\toππ$ amplitude $A_2$ and the enhancement of the $ΔI=1/2 A_0$ amplitude, are phenomenologically extracted from the measured $K^+\toπ^+π^0$ decay and found to be large. The $A_0/A_2$ ratio is predicted to lie in the range 15-17 for $m_s(1 GeV)=(127-150)$ MeV. Vertex and penguin-type radiative corrections to the matrix elements of four-quark operators and nonfactorized effects due to soft-gluon exchange account for the bulk of the $ΔI=1/2$ rule. Comparison of the present analysis with the chiral-loop approach is given.

19 pages, 1 figure. Errors in the 66 and 88 entries of the constant matrices are corrected