Abstract
The annihilation of the ${B}_{c}$ meson to leptons and inclusive light hadrons is analyzed in the framework of nonrelativistic QCD (NRQCD) factorization. We find that the decay mode, which escapes from the helicity suppression, contributes a sizable fraction width. The branching ratio due to the contributions from the color-singlet component of the ${B}_{c}$ meson can be of the order of ${10}^{\ensuremath{-}2}.$ The contributions from the color-octet components are estimated. With the consideration of the NRQCD velocity scaling rule, we find that the color-octet contributions are sizable too, especially in a certain phase space of the annihilation. They are greater than (or comparable to) those from the color-singlet component. A few observables on the spectrum of charged leptons $(e,\ensuremath{\mu})$ relevant to the contributions are suggested that may be used as measurements of the evidence of the color-octet components in future ${B}_{c}$ experiments. A kind of typical ``long-distance contributions'' in the annihilation is also estimated.
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