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We use the QCD sum rules for the three point correlation functions to computethe strong coupling constants of the meson vertices $\eta_c D^* D$ and $\eta_cD_s^* D_s$. We consider perturbative and non-perturbative contributions,working up to dimension five on the OPE. The vertices were studied consideringthat each one of its three mesons are off-shell alternately. The vertexcoupling constant is evaluated through the extrapolation of the three differentform factors. The results obtained for the coupling constants are $g_{\eta_cD^* D} = 5.23^{+1.80}_{-1.38}$ and $g_{\eta_c D_s^*  D_s}=5.55^{+1.29}_{-1.55}$.

A QCD sum rules calculation of the $\eta_c D^* D$ and $\eta_c D_s^* D_s$ form factors and strong coupling constants