The penguin operators in nonresonant $B^{-}\to M\bar{M}{\pi }^{-}$ $(M={\pi }^{-},K^{-},K^0)$ decays

Abstract

We investigate the contributions coming from the penguin operators in the nonresonant $B^{-}\to M\bar{M}{\pi }^{-}$ ($M={\pi }^{-},K^{-},K^0$) decays. The effective Wilson coefficients of the the strong penguin operators $O_{4,6}$ are found to be relatively larger. We calculate the contributions arising from the $O_4$ and $O_6$ operators in the nonresonant decays $B^{-}\to M\bar{M}{\pi }^{-}$ ($M={\pi }^{-},K^{-},{\bar{K}}^0$) using a model combining heavy quark symmetry and the chiral symmetry, developed previously. We find that the forbidden nonresonant $B^{-}\to K^0{\bar{K}}^0{\pi }^{-}$ decay occurs through the strong penguin operators. These penguin contributions affect the branching ratios for $B^{-}\to M\bar{M}{\pi }^{-}$ ($M={\pi }^{-},K^{-}$) by only a few percent. The branching ratio for $B^{-}\to K^0{\bar{K}}^0{\pi }^{-}$ is estimated to be of the order $10^{-6}$.

Comments: 14 pages, latex, no figures