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In this paper, we study the FCNC decay processes of $B$ and $B_c$ meson, inwhich one invisible particle is emitted. Both the spin-0 and spin-1 cases areconsidered. The model-independent effective Lagrangian is introduced todescribe the coupling between the light invisible boson and quarks. Theconstraints of the coupling coefficients are extracted by experimental upperlimits of the missing energy in $B$ meson decays. The bounds are used topredict 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 ispseudoscalar or vector, respectively. The maximum branch ratios are achievedwhen $m_\chi\approx3.5- 4$~GeV, where $m_\chi$ is the mass of the invisibleparticle.

The light invisible boson in FCNC decays of $B$ and $B_c$ mesons