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

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