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

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