Charmonia Production in $W\to (c\bar{c}) D_{s}^{(*)}$ Decays

In the presented paper production of charmonium state $\mathcal{Q}$ in exclusive $W\to\mathcal{Q} D_{s}^{(*)}$ decays is analyzed in the framework of both leading order Nonrelativistic Quantum Chromodynamics (NRQCD) and light-cone expansion (LC) models. Analytical and numerical predictions for the branching fractions of these decays in both approaches are given. The typical value of the branching fractions is $\sim 10^{-11}$ and it turns out the LC results are about 4 times lager than NRQCD ones, so the effect of internal quark should be taken into account. Some estimates of color-octet contributions are presented and it is shown, that these contributions could be comparable with color-singlet results.