Charm Penguin in $B^\pm \to K^\pm K^+ K^-$: partonic and hadronic loops

Abstract

Charm penguin diagrams are known to be the main contribution to charmless B decay process with strangeness variation equal to minus one, which is the case of $B^\pm \to K^\pm K^+ K^-$ decay. The large phase space available in this and other B three-body decays allows non trivial final state interactions with all sort of rescattering processes and also access high momentum transfers in the central region of the Dalitz plane. In this work we investigate the charm Penguin contribution to $B^\pm \to K^\pm K^+ K^-$, described by a hadronic triangle loop in nonperturbative regions of the phase space, and by a partonic loop at the quasi perturbative region. These nonresonant amplitudes should have a particular structure in the Dalitz plane and their contributions to the final decay amplitude can be confirmed by a data amplitude analysis in this channel. In particular, the hadronic amplitude has a changing sign in the phase at $D\bar{D}$ threshold which can result in a change of sign for the CP asymmetry.