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

TL;DR

This paper explores the hypothesis that the rare decay $B^+_c o K^+ K^- o \pi^+$ is dominated by charm rescattering processes, using charm penguin diagrams and triangle loops to explain non-resonant amplitudes observed in Dalitz plots.

Contribution

It introduces a model where charm rescattering via triangle loops explains the decay mechanism, contrasting with direct production and quark annihilation.

Findings

Rescattering processes produce distinctive non-resonant signatures in Dalitz plots.

The model predicts charm rescattering as the dominant mechanism for the decay.

Future LHCb data can test the validity of the rescattering hypothesis.

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.