The semileptonic decays $B_c^{\ast }\to {\eta }_c\mathrm{\ell }{\bar{\nu }}_{\mathrm{\ell }}$ with QCD sum rules

In this article, we calculate the $B_c^{\ast }\to {\eta }_c$ form-factors with the three-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 in the future at the LHCb, while the $B_c^{\ast }\to {\eta }_c$ form-factors can be taken as basic input parameters in other phenomenological analysis.