Analysis of the strong vertices of $$\Sigma _{c}\Delta D^{*}$$ and $$\Sigma _{b}\Delta B^{*}$$ in QCD sum rules

Abstract

In this work, we analyze the strong vertices $$\Sigma _{c}\Delta D^{*}$$ Σ c Δ D ∗ and $$\Sigma _{b}\Delta B^{*}$$ Σ b Δ B ∗ using the three-point QCD sum rules under the tensor structures $$i\epsilon ^{\rho \tau \alpha \beta }p_{\alpha }p_{\beta }$$ i ϵ ρ τ α β p α p β , $$p^{\rho }p'^{\tau }$$ p ρ p ′ τ and $$p^{\rho }p^{\tau }$$ p ρ p τ . We firstly calculate the momentum dependent strong coupling constants $$g(Q^{2})$$ g ( Q 2 ) by considering contributions of the perturbative part and the condensate terms $$\langle {\overline{q}}q\rangle $$ ⟨ q ¯ q ⟩ , $$\langle g_{s}^{2}GG \rangle $$ ⟨ g s 2 G G ⟩ , $$\langle {\overline{q}}g_{s}\sigma Gq\rangle $$ ⟨ q ¯ g s σ G q ⟩ and $$\langle {\overline{q}}q\rangle ^{2}$$ ⟨ 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 $$g_{1\Sigma _{c}\Delta D^{*}}=5.13^{+0.39}_{-0.49}\,\hbox {GeV}^{-1}$$ g 1 Σ c Δ D ∗ = 5 . 13 - 0.49 + 0.39 GeV - 1 , $$g_{2\Sigma _{c}\Delta D^{*}}=-3.03^{+0.27}_{-0.35}\,\hbox {GeV}^{-2}$$ g 2 Σ c Δ D ∗ = - 3 . 03 - 0.35 + 0.27 GeV - 2 , $$g_{3\Sigma _{c}\Delta D^{*}}=17.64^{+1.51}_{-1.95}\,\hbox {GeV}^{-2}$$ g 3 Σ c Δ D ∗ = 17 . 64 - 1.95 + 1.51 GeV - 2 , $$g_{1\Sigma _{b}\Delta B^{*}}=20.97^{+2.15}_{-2.39}\,\hbox {GeV}^{-1}$$ g 1 Σ b Δ B ∗ = 20 . 97 - 2.39 + 2.15 GeV - 1 , $$g_{2\Sigma _{b}\Delta B^{*}}=-11.42^{+1.17}_{-1.28}\,\hbox {GeV}^{-2}$$ g 2 Σ b Δ B ∗ = - 11 . 42 - 1.28 + 1.17 GeV - 2 and $$g_{3\Sigma _{b}\Delta B^{*}}=24.87^{+2.57}_{-2.82}\,\hbox {GeV}^{-2}$$ g 3 Σ b Δ B ∗ = 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.