Analysis of the strong coupling constant $G_{D_s^{\ast }{D}_s\varphi }$ and the decay width of $D_s^{\ast }\to D_s\gamma$ with QCD sum rules

In this article, we calculate the form factors and the coupling constant of the vertex $D_s^{\ast }{D}_s\varphi$ using the three-point QCD sum rules. We consider the contributions of the vacuum condensates up to dimension $7$ in the operator product expansion(OPE). And all possible off-shell cases are considered, $\varphi$, $D_s$ and $D_s^{\ast }$, resulting in three different form factors. Then we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant for the process. Our analysis indicates that the coupling constant for this vertex is $G_{Ds\ast Ds\varphi }=4.12\pm 0.70Ge{V}^{-1}$. The results of this work are very useful in the other phenomenological analysis. As an application, we calculate the coupling constant for the decay channel $D_s^{\ast }\to D_s\gamma$ and analyze the width of this decay with the assumption of the vector meson dominance of the intermediate $\varphi (1020)$. Our final result about the decay width of this decay channel is $\mathrm{\Gamma }=0.59\pm 0.15keV$.