  In this paper, we study the FCNC decay processes of $B$ and $B_c$ meson, in
which one invisible particle is emitted. Both the spin-0 and spin-1 cases are
considered. The model-independent effective Lagrangian is introduced to
describe the coupling between the light invisible boson and quarks. The
constraints of the coupling coefficients are extracted by experimental upper
limits of the missing energy in $B$ meson decays. The bounds are used to
predict the upper limits of branching fractions of corresponding $B_c$ decays,
which are of the order of $10^{-6}$ or $10^{-5}$ when final meson is
pseudoscalar or vector, respectively. The maximum branch ratios are achieved
when $m_\chi\approx3.5- 4$~GeV, where $m_\chi$ is the mass of the invisible
particle.
