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In this article, we study momentum dependence of the hadronic couplingconstants $G_{B_c^* B_c \Upsilon}$, $G_{B_c^* B_c J/\psi}$, $G_{B_c B_c\Upsilon}$ and $G_{B_c B_c J/\psi}$ with the off-shell $\Upsilon$ and $J/\psi$using the three-point QCD sum rules. Then we fit the hadronic couplingconstants into analytical functions and extrapolate them into deep time-likeregions to obtain the on-shell values  $ G_{B_c^*B_c\Upsilon}(q^2=M_{\Upsilon}^2)$, $ G_{B_c^*B_cJ/\psi}(q^2=M_{J/\psi}^2)$, $ G_{B_cB_c\Upsilon}(q^2=M_{\Upsilon}^2)$ and $G_{B_cB_c J/\psi}(q^2=M_{J/\psi}^2)$ for the first time. Those hadroniccoupling constants can be taken as basic input parameters in phenomenologicalanalysis.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Analysis of hadronic coupling constants $G_{B_c^*B_c\Upsilon}$,  $G_{B_c^*B_c J/\psi}$, $G_{B_cB_c\Upsilon}$ and $G_{B_cB_c J/\psi}$ with QCD  sum rules