Study of $B^+_c$ decays to the $K^+K^-\pi^+$ final state by using $B^0_s$, $\chi_{c0}$ and $D^0$ resonances and weak annihilation nonresonant topologys

Abstract

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 $B^0_s$, $\chi_{c0}$ and $D^0$ resonances and weak annihilation nonresonant contributions. In this process, the $B^+_c$ meson decays first into $B^0_s\pi^+$, $\chi_{c0}\pi^+$ and $D^0\pi^+$ intermediate states, and then the $B^0_s$, $\chi_{c0}$ 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 $B^0_s$, $\chi_{c0}$ 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 $\langle K^+K^-\pi^+|u\bar{d}|0\rangle$ is also considered. The decay mode of the $B^+_c\rightarrow \bar{K}^{*0}(892)K^+$ is contributed to the annihilation contribution. The branching ratios of quasi-two-body decays expand in the range from $1.98\times10^{-6}$ to $7.32\times10^{-6}$.