Amplitude analysis and branching fraction calculations of $B_c$ meson decays into $B_s\pi$, $DK\pi$ and $D_{s}KK$ final state mesons

Abstract

In this study, several newly observed decay modes of the $B_c^{+}$ meson of the form $B_c^{+}\to D{h}^{+}{h}^{-}$, where $D$ denotes a charmed meson and $h^{\pm }$ represents a charged pion or kaon, have been investigated. The decay channels $B_c^{+}\to D^{+}{K}^{+}{\pi }^{-}$, $B_c^{+}\to D^{\ast +}{K}^{+}{\pi }^{-}$ and $B_c^{+}\to D_s^{+}{K}^{+}{K}^{-}$ were observed for the first time. The LHCb Collaboration has measured their branching fractions relative to the reference decay $B_c^{+}\to B_s^0{\pi }^{+}$, and reported experimental values including ${\mathcal{R}}^{\exp }(B_c^{+}\to D^{+}{K}^{+}{\pi }^{-})=(1.96\pm 0.23\pm 0.08\pm 0.10)\times 10^{-3}$ , ${\mathcal{R}}^{\exp }(B_c^{+}\to D^{\ast +}{K}^{+}{\pi }^{-})=(3.67\pm 0.55\pm 0.24\pm 0.20)\times 10^{-3}$ and ${\mathcal{R}}^{\exp }(B_c^{+}\to D_s^{+}{K}^{+}{K}^{-})=(1.61\pm 0.35\pm 0.13\pm 0.07)\times 10^{-3}$. In this regard, by performing precise calculations using the factorization approach, we have computed similar branching ratio values, including $\mathcal{R}(B_c^{+}\to D^{+}{K}^{+}{\pi }^{-})=(1.70\pm 0.08)\times 10^{-3}$, $\mathcal{R}(B_c^{+}\to D^{\ast +}{K}^{+}{\pi }^{-})=(3.63\pm 0.45)\times 10^{-3}$ and $\mathcal{R}(B_c^{+}\to D_s^{+}{K}^{+}{K}^{-})=(1.09\pm 0.08)\times 10^{-3}$. 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.