Charm rescattering contribution in rare $B^+_c \to K^+ K^- \pi^+$ decay

Abstract

Following the experimental results from LHCb on the rare decay $B^+_c \to K^-K^+\pi^+$, we investigate the possibility where this process is dominated by a double charm rescattering. The $B_c$ decay to double charm channels have a weak topology that is favoured in comparison with the direct production of $K^-K^+\pi^+$ in the final state, suppressed by quark annihilation. The decay amplitude for $B^+_c \to K^-K^+\pi^+$ with $B_c$ decaying first to double charm channels is described by a charm penguin diagram, represented by charm hadronic triangle loops, which reach the final state of interest after $D\bar{D}\to K\bar{K}$ or $ D^+ D^-_s \to \pi^+ K^-$ transitions. We show that these processes give rise to non-resonant amplitudes with a clear signature in the Dalitz plot. In a near future, the new data from LHCb run II will be able to confirme if the main hypotheses of this work is correct and the dominant mechanism to produce $K^+K^+\pi^-$ from the decay of $B^+_c$ is through charm rescattering.