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In this work, we use the QCD sum rule method to study the radiative decays ofthe vector and axial-vector $B_c$ mesons to each of three charmed strangemesons, $D_s$, $D^*_s$ and $D_{s1}$, through their dominant weak annihilationchannels. We calculate all relevant transition form factors, which are used toestimate the branching fractions at different channels. The order of branchingratios are obtained to be in the order of $ 10^{-6} - 10^{-5} $, which may bechecked via differnet experiments.

Rare Radiative Decays of Vector and Axial-Vector $B_{c}$ Mesons to $ (D_{s}, D^{*}_{s}, D_{s1}) $ Final States