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In this article, we calculate the $B_c^* \to \eta_c$ form-factors with thethree-point QCD sum rules, then study the semileptonic decays $B_c^* \to \eta_c\ell \bar{\nu}_{\ell}$. The tiny decay widths may be observed experimentally inthe future at the LHCb, while the $B_c^* \to \eta_c$ form-factors can be takenas basic input parameters in other phenomenological analysis.

The semileptonic decays $B_c^* \to \eta_c \ell \bar{\nu}_{\ell} $ with QCD sum rules