Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-06-17
Chin.J.Phys. 38 (2000) 783
Physics
High Energy Physics
High Energy Physics - Phenomenology
19 pages, 1 figure. Errors in the 66 and 88 entries of the constant matrices are corrected
Scientific paper
The $K\to\pi\pi$ 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 $\Delta I=3/2 K\to\pi\pi$ amplitude $A_2$ and the enhancement of the $\Delta I=1/2 A_0$ amplitude, are phenomenologically extracted from the measured $K^+\to\pi^+\pi^0$ 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 $\Delta I=1/2$ rule. Comparison of the present analysis with the chiral-loop approach is given.
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