A QCD sum rules calculation of the ${\eta }_c{D}^{\ast }D$ and ${\eta }_c{D}_s^{\ast }{D}_s$ form factors and strong coupling constants

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