A scalar gluonium contribution to $K\to \pi \pi$ decay

Abstract

We study a new $K\to \pi \pi$ decay channel with gluons in intermediate state which is normally neglected within the factorization framework. Both short-distance and long-distance parts of the amplitude are calculated. The chiral Lagrangian approach is used for obtaining the long-distance contribution. The nonperturbative contribution gives an additional enhancement to $K\to \pi \pi$ decay amplitude with $\Delta I=1/2$. A sizable violation of factorization in the $p^4$ order of chiral perturbation theory is found.

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