The Bosonization of the Electroweak Penguin Operators

Abstract

We give the complete $O(p^2)$ bosonization of the electroweak Penguin operators $Q_{7,8}$ and compare the result with that of the gluon Penguin operators $Q_{5,6}$. We find that, in addition to the usual (constant and current-current) parts, there are three new terms not discussed previously in the literature. Two of these are present in the factorization approximation and should be included in the standard definition of the $B_{7,8}$-factors. The impact of these corrections on the direct $CP$-violating parameter ${\epsilon }^{\prime }/\epsilon$ is briefly discussed.

Comments: 9 pages, uuencoded Latex + eps files