Amplitude analysis and branching fraction calculations of $B_c$ meson decays into $B_s\pi$, $DK\pi$ and $D_sKK$ final state mesons

Abstract

In this study, several newly observed decay modes of the $B_c^+$ meson of the form $B_c^+\rightarrow Dh^+h^-$, where $D$ denotes a charmed meson and $h^{\pm}$ represents a charged pion or kaon, have been investigated. The decay channels $B_c^+\rightarrow D^{+}K^+\pi^{-}$, $B_c^+\rightarrow D^{*+}K^+\pi^{-}$ and $B_c^+\rightarrow D_s^+K^+K^-$ were observed for the first time. The LHCb Collaboration has measured their branching fractions relative to the reference decay $B_c^+\rightarrow B_s^0\pi^+$, and reported experimental values including $\mathcal{R}^{\exp}(B_c^+\rightarrow D^{+}K^+\pi^{-})=(1.96\pm0.23\pm0.08\pm0.10)\times 10^{-3}$ , $\mathcal{R}^{\exp}(B_c^+\rightarrow D^{*+}K^+\pi^{-})=(3.67\pm0.55\pm0.24\pm0.20)\times10^{-3}$ and $\mathcal{R}^{\exp}(B_c^+\rightarrow D_s^+K^+K^{-})=(1.61\pm0.35\pm0.13\pm0.07)\times 10^{-3}$. In this regard, by performing precise calculations using the factorization approach, we have computed similar branching ratio values, including $\mathcal{R}(B_c^+\rightarrow D^{+}K^+\pi^{-})=(1.70\pm0.08)\times 10^{-3}$, $\mathcal{R}(B_c^+\rightarrow D^{*+}K^+\pi^{-})=(3.63\pm0.45)\times 10^{-3}$ and $\mathcal{R}(B_c^+\rightarrow D_s^+K^+K^{-})=(1.09\pm0.08)\times 10^{-3}$. The obtained theoretical results show good consistency with the recent experimental measurements reported by the LHCb collaboration, confirming the effectiveness of the factorization formalism in describing these $B_c^+$ decay modes.