Study of $B_c^{+}$ decays to the $K^{+}{K}^{-}{\pi }^{+}$ final state by using $B_s^0$, ${\chi }_{c0}$ and $D^0$ resonances and weak annihilation nonresonant topologys

In this research the weak decay of $B_c^{+}$ decays to the $K^{+}{K}^{-}{\pi }^{+}$ final state, which is observed by LHCb collaboration for the first time, is calculated in the quasi-two-body decays which takes into account the $B_s^0$, ${\chi }_{c0}$ and $D^0$ resonances and weak annihilation nonresonant contributions. In this process, the $B_c^{+}$ meson decays first into $B_s^0{\pi }^{+}$, ${\chi }_{c0}{\pi }^{+}$ and $D^0{\pi }^{+}$ intermediate states, and then the $B_s^0$, ${\chi }_{c0}$ and $D^0$ resonances decay into $K^{+}{K}^{-}$ components, which undergo final state interaction. The mode of the $B^+_c\rightarrow D^0(\rightarrow K^-\pi^+)K^+$ is also associated to the calculation, in this mode the intermediate resonance $D^0$ decays to the $K^{-}{\pi }^{+}$ final mesons. The resonances $B_s^0$, ${\chi }_{c0}$ and $D^0$ effects in the $B^+_c\rightarrow B^0_s(\rightarrow K^+K^-)\pi^+$,$B^+c\rightarrow \chi{c0}(\rightarrow K^+K^-)\pi^+$and$B^+_c\rightarrow D^0(\rightarrow K^+K^-)\pi^+, D^0(\rightarrow K^-\pi^+)K^+$ decays are described in terms of the quasi-two-body modes. There is a weak annihilation nonresonant contribution in which $B_c^{+}$ decays to the $K^{+}{K}^{-}{\pi }^{+}$ directly, so the point-like 3-body matrix element $⟨K^{+}{K}^{-}{\pi }^{+}\mathrm{\mid }u\bar{d}\mathrm{\mid }0⟩$ is also considered. The decay mode of the $B_c^{+}\to {\bar{K}}^{\ast 0}(892)K^{+}$ is contributed to the annihilation contribution. The branching ratios of quasi-two-body decays expand in the range from $1.98\times {10}^{-6}$ to $7.32\times {10}^{-6}$.