Analysis of the strong vertices of ${\Sigma }_c\Delta D^{\ast }$ and ${\Sigma }_b\Delta B^{\ast }$ in QCD sum rules

Abstract

In this work, we analyze the strong vertices ${\Sigma }_c\Delta D^{\ast }$ and ${\Sigma }_b\Delta B^{\ast }$ using the three-point QCD sum rules under the tensor structures $i{\epsilon }^{\rho \tau \alpha \beta }{p}_{\alpha }{p}_{\beta }^{\prime }$, $p^{\rho }{p}^{\prime \tau }$ and $p^{\rho }{p}^{\tau }$. We firstly calculate the momentum dependent strong coupling constants $g(Q^2)$ by considering contributions of the perturbative part and the condensate terms $⟨\overline{q}q⟩$, $⟨g_s^{2}GG⟩$, $⟨\overline{q}{g}_s\sigma Gq⟩$ 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 $g_{1{\Sigma }_c\Delta D^{\ast }}=5.13_{-0.49}^{+0.39}$ GeV${}^{-1}$, $g_{2{\Sigma }_c\Delta D^{\ast }}=-3.03_{-0.35}^{+0.27}$ GeV${}^{-2}$, $g_{3{\Sigma }_c\Delta D^{\ast }}=17.64_{-1.95}^{+1.51}$ GeV${}^{-2}$, $g_{1{\Sigma }_b\Delta B^{\ast }}=20.97_{-2.39}^{+2.15}$ GeV${}^{-1}$, $g_{2{\Sigma }_b\Delta B^{\ast }}=-11.42_{-1.28}^{+1.17}$ GeV${}^{-2}$ and $g_{3{\Sigma }_b\Delta B^{\ast }}=24.87_{-2.82}^{+2.57}$ GeV${}^{-2}$. These strong coupling constants are important parameters which can help us to understand the strong decay behaviors of hadrons.

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