Evaluation of the $B_c^{+}\to D^0{K}^{+}$ decay by the factorization approaches and applying the effects of the final state interaction

Abstract

In this paper the decay of $B_c^{+}$ meson, consisting of two b and c heavy quarks, into the $D^0$ and $K^{+}$ mesons is studied. Given that the experimental branching ratio for this decay is within the range of $3.72\times 10^{-5}$ to $11.16\times 10^{-5}$ and in our estimating the theoretical result by using the QCD factorization approaches is $10^2$ times less than experimental one (we have obtained $1.41\times 10^{-7}$), it is decided to calculate the theoretical branching ratio by applying the final state interaction (FSI) through the T and cross section channels. In this process, before the $B_c^{+}$ meson decays into two final state mesons of $D^0{K}^{+}$, it first decays into two intermediate mesons like $J/\psi D_s^{\ast +}$, then these two mesons transformed into two final mesons by exchanging another meson like $D^0$. The FSI effects are very sensitive to the changes in the phenomenological parameter that appear in the form factor relation, as in most calculation changing two units in this parameter, makes the final result multiply in the branching ratio, therefor the decision to use FSI is not unexpected. In this study there are nineteen intermediate states in which the contribution of each one is calculated and summed in the final amplitude. Therefore, the numerical value of the branching ratio of $B_c^{+}\to D^0{K}^{+}$ decay is obtained by calculating the FSI effects from $1.17\times 10^{-5}$ to $11.65\times 10^{-5}$ which is consistent with the experimental result.

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