The strong vertices of charmed mesons $D$, $D^{\ast }$ and charmonia $J/\ddot{I}ˆ$, $\hat{I}{\cdot }_c$

Abstract

In this work, the strong coupling constants of the vertices $DDJ/\ddot{I}ˆ$, $D{D}^{\ast }J/\ddot{I}ˆ$, $D^{\ast }{D}^{\ast }J/\ddot{I}ˆ$, $D{D}^{\ast }\hat{I}{\cdot }_c$ and $D^{\ast }{D}^{\ast }\hat{I}{\cdot }_c$ are calculated within the framework of the QCD sum rules. For each vertex, we analyze the momentum dependence of the coupling constants by considering all possible off-shell cases. In these analyses, we consider the contributions of the vacuum condensate terms $⟨\overline{q}q⟩$, $⟨\overline{q}{g}_s\ddot{I}ƒGq⟩$, $⟨g_s^2{G}^2⟩$, $⟨f^3{G}^3⟩$ and $⟨\overline{q}q⟩⟨g_s^2{G}^2⟩$. Then, the momentum dependent coupling constants are fitted into analytical functions $g(Q^2)$ and are extrapolated into time-like regions. The values of strong coupling constants are obtained by using on-shell conditions of the intermediate mesons($Q^2=-m^2$). The final results are as follows, $g_{DDJ/\ddot{I}ˆ}=5.01_{-0.16}^{+0.58}$, $g_{D{D}^{\ast }J/\ddot{I}ˆ}=3.55_{-0.21}^{+0.20}$GeV${}^{-1}$, $g_{D^{\ast }{D}^{\ast }J/\ddot{I}ˆ}=5.10_{-0.43}^{+0.59}$, $g_{D{D}^{\ast }\hat{I}{\cdot }_c}=3.68_{-0.11}^{+0.39}$ and $g_{D^{\ast }{D}^{\ast }\hat{I}{\cdot }_c}=4.87_{-0.40}^{+0.42}$GeV${}^{-1}$.