Analysis of the strong vertices of $\hat{I}{\pounds }_c\hat{I}”D^{\ast }$ and $\hat{I}{\pounds }_b\hat{I}”B^{\ast }$ in QCD sum rules

Abstract

In this work, we analyze the strong vertices $\hat{I}{\pounds }_c\hat{I}”D^{\ast }$ and $\hat{I}{\pounds }_b\hat{I}”B^{\ast }$ using the three-point QCD sum rules under the tensor structures $i\hat{I}{\mu }^{\ddot{I}\ddot{I}„\hat{I}\pm {\hat{I}}^2}{p}_{\hat{I}}\pm p_{\hat{I}}^2$, $p^{\ddot{I}}p^{\prime \ddot{I}}„$ and $p^{\ddot{I}}p^{\ddot{I}}„$. We firstly calculate the momentum dependent strong coupling constants $g(Q^2)$ by considering contributions of the perturbative part and the condensate terms $⟨\overline{q}q⟩$, $⟨g_s^{2}GG⟩$, $⟨\overline{q}{g}_s\ddot{I}ƒGq⟩$ and $⟨\overline{q}q{⟩}^2$. By fitting these coupling constants into analytical functions and extrapolating them into time-like regions, we then obtain the on-shell values of strong coupling constants for these vertices. The results are $g_{1\hat{I}{\pounds }_c\hat{I}”D^{\ast }}=5.13_{-0.49}^{+0.39}$ GeV${}^{-1}$, $g_{2\hat{I}{\pounds }_c\hat{I}”D^{\ast }}=-3.03_{-0.35}^{+0.27}$ GeV${}^{-2}$, $g_{3\hat{I}{\pounds }_c\hat{I}”D^{\ast }}=17.64_{-1.95}^{+1.51}$ GeV${}^{-2}$, $g_{1\hat{I}{\pounds }_b\hat{I}”B^{\ast }}=20.97_{-2.39}^{+2.15}$ GeV${}^{-1}$, $g_{2\hat{I}{\pounds }_b\hat{I}”B^{\ast }}=-11.42_{-1.28}^{+1.17}$ GeV${}^{-2}$ and $g_{3\hat{I}{\pounds }_b\hat{I}”B^{\ast }}=24.87_{-2.82}^{+2.57}$ GeV${}^{-2}$. These strong coupling constants are important parameters which can help us to understand the strong decay behaviors of hadrons.