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

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 $B_s^0$, ${\chi }_{c0}$ 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 $B_c^{+}\to D^0(\to K^{-}{\pi }^{+})K^{+}$ 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 $B_c^{+}\to B_s^0(\to K^{+}{K}^{-}){\pi }^{+}$, $B_c^{+}\to {\chi }_{c0}(\to K^{+}{K}^{-}){\pi }^{+}$ and $B_c^{+}\to D^0(\to K^{+}{K}^{-}){\pi }^{+},D^0(\to K^{-}{\pi }^{+})K^{+}$ 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 $⟨K^{+}{K}^{-}{\pi }^{+}|u\bar{d}|0⟩$ 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 $7.32\times 10^{-6}$.

Comments: Repeated topic