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In this work, we calculate the form factors and the coupling constant of thestrange-charmed vertex $J/\psi D_s^* D_s$ in the framework of the QCD sum rulesby studying their three-point correlation functions. All the possible off-shellcases are considered, $D_s$, $D_s^*$ and $J/\psi$, resulting in three differentform factors. These form factors are extrapolated to the pole of theirrespective off-shell mesons, giving the same coupling constant for the process.Our final result for the $J/\psi D_s^* D_s$ coupling constant is $g_{J/\psiD^*_s D_s} = 4.30^{+0.42}_{-0.37}\text{GeV}^{-1}$.

A QCD sum rules calculation of the $J/\psi D_s^* D_s$ strong coupling constant