The annihilation decays $B^-_c \to \eta^{'}(\eta ,\pi^0) l^- \bar{\nu}$

We investigate the simileptonic OZI-forbidden annihilation decays $B^-_c \to \eta^{'}(\eta ,\pi^0) l^- \bar{\nu}$ for $l=\mu,e$ in the perturbative QCD, and carry out a precise calculation without any approximation for the one-loop contributions, which involves integrals of 4- and 5-point loop functions. Our results show that the branching ratios of decays $B^-_c \to \eta^{'} l^- \bar{\nu}$, $B^-_c \to \eta l^- \bar{\nu}$ and $B^-_c \to \pi^0 l^- \bar{\nu}$, turn out to be of orders $10^{-4}$, $10^{-5}$ and $10^{-6}$, respectively, which could be observable in the future experiments at the LHC.