We discuss the decay of $B_c$ mesons into two light mesons $(\pi ,K^{(*)},{\eta }^{(\prime )},\rho ,\omega ,\varphi )$. All these decay channels come from a single type of diagram, namely, tree annihilation. This allows us to derive extremely simple $SU(3)$ relations among these processes. The size of annihilation contributions is an important issue in $B$ physics, and we provide two different estimates in the case of nonleptonic charmless $B_c$ decays, either a comparison with annihilation decays of heavy-light mesons or a perturbative model inspired by QCD factorization. We finally discuss a possible search for these channels at LHCb.

• Received 19 August 2009

DOI:https://doi.org/10.1103/PhysRevD.80.114031