Analysis of the strong vertices of $Σ_{c}ΔD^{*}$ and $Σ_{b}ΔB^{*}$ in QCD sum rules

Abstract

In this work, we analyze the strong vertices $Σ_{c}ΔD^{*}$ and $Σ_{b}ΔB^{*}$ using the three-point QCD sum rules under the tensor structures $iε^{ρταβ}p_αp'_β$, $p^ρp'^τ$ and $p^ρp^τ$. We firstly calculate the momentum dependent strong coupling constants $g(Q^{2})$ by considering contributions of the perturbative part and the condensate terms $\langle\overline{q}q\rangle$, $\langle g_{s}^{2}GG \rangle$, $\langle\overline{q}g_{s}σGq\rangle$ and $\langle\overline{q}q\rangle^{2}$. 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 $g_{1Σ_{c}ΔD^{*}}=5.13^{+0.39}_{-0.49}$ GeV$^{-1}$, $g_{2Σ_{c}ΔD^{*}}=-3.03^{+0.27}_{-0.35}$ GeV$^{-2}$, $g_{3Σ_{c}ΔD^{*}}=17.64^{+1.51}_{-1.95}$ GeV$^{-2}$, $g_{1Σ_{b}ΔB^{*}}=20.97^{+2.15}_{-2.39}$ GeV$^{-1}$, $g_{2Σ_{b}ΔB^{*}}=-11.42^{+1.17}_{-1.28}$ GeV$^{-2}$ and $g_{3Σ_{b}ΔB^{*}}=24.87^{+2.57}_{-2.82}$ GeV$^{-2}$. These strong coupling constants are important parameters which can help us to understand the strong decay behaviors of hadrons.