Eur. Phys. J. A (2023) 59: 195
https://doi.org/10.1140/epja/s10050-023-01115-3

Regular Article - Theoretical Physics

The strong vertices of charmed mesons D, $D^{\ast }$ and charmonia $J/\psi$, ${\eta }_c$

¹ Department of Mathematics and Physics, North China Electric Power University, 071003, Baoding, People’s Republic of China
² Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, 071000, Baoding, People’s Republic of China

^b yuguoliang2011@163.com

Received: 13 June 2023
Accepted: 17 August 2023
Published online: 31 August 2023

Abstract

In this work, the strong coupling constants of the vertices $DDJ/\psi$, $D{D}^{\ast }J/\psi$, $D^{\ast }{D}^{\ast }J/\psi$, $D{D}^{\ast }{\eta }_c$ and $D^{\ast }{D}^{\ast }{\eta }_c$ 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 $⟨\overline{q}q⟩$, $⟨\overline{q}{g}_s\sigma Gq⟩$, $⟨g_s^2{G}^2⟩$, $⟨f^3{G}^3⟩$ 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, $g_{DDJ/\psi }=5.{01}_{-0.16}^{+0.58}$, $g_{D{D}^{\ast }J/\psi }=3.{55}_{-0.21}^{+0.20}$GeV${}^{-1}$, $g_{D^{\ast }{D}^{\ast }J/\psi }=5.{10}_{-0.43}^{+0.59}$, $g_{D{D}^{\ast }{\eta }_c}=3.{68}_{-0.11}^{+0.39}$ and $g_{D^{\ast }{D}^{\ast }{\eta }_c}=4.{87}_{-0.40}^{+0.42}$GeV${}^{-1}$.