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

In this article, we study momentum dependence of the hadronic coupling constants $G_{B_c^* B_c \Upsilon}$, $G_{B_c^* B_c J/\psi}$, $G_{B_c B_c \Upsilon}$ 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 coupling constants into analytical functions and extrapolate them into deep time-like regions to obtain the on-shell values $ G_{B_c^*B_c\Upsilon}(q^2=M_{\Upsilon}^2)$, $ G_{B_c^*B_c J/\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 hadronic coupling constants can be taken as basic input parameters in phenomenological analysis.