We investigate the decays of $B_c$ meson which is a bound state of $\bar{b}$- and $c$-quark. Quite large number of $B_c$ mesons are expected to be produced in next collider, like LHC. The $B_c$ meson is a source of interesting physics. It will provide unique probe of both strong and weak interactions, and a challenge to understand the effects of strong interactions on the underlying weak decays.
Since the hadronic structure is very different from the light-light or heavy-light quarks bound mesons, the system probes different sector of QCD interaction.
The electron energy spectra and decay widths of inclusive semileptonic decays of $B_c$ meson are studied in the ACCMM model. We obtain the value of the Fermi motion parameter $p_F$ using quantum mechanical variational method. We find that the decay widths are significantly affected by the bound state effects inside the $B_c$ meson. As a result the semileptonic decay rate of $B_c$ through c-quark decay is about the same as that through b-quark decay.
Using the heavy-quark spin symmetry, we study the decay widths of experimentally feasible decay modes of $B_c$ meson. The degree of polarization of the vector particle strongly influences the momentum spectrum of the decay particles as well as the decay rate. We will show that $|V_{cb}|$ quark mixing-matrix element can be determined from the measurement of polarization of vector meson. Especially it is stressed that the measurement of polarization of J/ψ meson in $\bar{B_c}→J/ψ l \bar{ⅴ_l}$ decay process, followed by $J/ψ→l^+ l^-$, will play a special role to extract $|V_{cb}|$ due to experimentally clean signature.
