We present an investigation of the total decay rate of the (ground state) B_c
meson within the framework of the relativistic constituent quark model
formulated on the light-front (LF). The exclusive semileptonic (SL) and
nonleptonic (NL) beauty and charm decays of the B_c meson are described through
vector and axial hadronic form factors, which are calculated in terms of a
constituent quark model LF wave functions. The latter ones are derived via the
Hamiltonian LF formalism using as input the update versions of the constituent
quark model. The inclusive SL and NL partial rates are calculated within a
convolution approach inspired by the partonic model and involving the same B_c
wave function which is used for evaluation of the exclusive modes. The
framework incorporates systematically 84 exclusive and 44 inclusive partial
rates corresponding to the underlying \bar{b}\to\bar{c} and c\to s quark
decays. Based on our approach we find\tau_{B_c}=0.59 \pm 0.06 ps where the
theoretical uncertainty is dominated by the uncertainty in the choice of LF
wave functions and the threshold values for the hadron continuum. For the
branching fractions of the B^+_c \to J/\psi\mu^+\nu_{\mu} and B_c^+\to
J/\psi\pi^+ decays we obtain 1.6 % and 0.1 %, respectively.Comment: 10 pages, LaTeX, 1 ps figur
