Analysis of the strong vertices of $$\Sigma _{c}\Delta D^{*}$$ and $$\Sigma _{b}\Delta B^{
Jie Lu (Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, People’s Republic of China, Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding, 071000, China); Guo-Liang Yu (Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, People’s Republic of China, Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding, 071000, China); Zhi-Gang Wang (Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, People’s Republic of China); Bin Wu (Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, People’s Republic of China)
In this work, we analyze the strong vertices $$\Sigma _{c}\Delta D^{*}$$ and $$\Sigma _{b}\Delta B^{*}$$ using the three-point QCD sum rules under the tensor structures $$i\epsilon ^{\rho \tau \alpha \beta }p_{\alpha }p_{\beta }$$ , $$p^{\rho }p'^{\tau }$$ and $$p^{\rho }p^{\tau }$$ . We firstly calculate the momentum dependent strong coupling constants $$g(Q^{2})$$ by considering contributions of the perturbative part and the condensate terms $$\langle {\overline{q}}q\rangle $$ , $$\langle g_{s}^{2}GG \rangle $$ , $$\langle {\overline{q}}g_{s}\sigma Gq\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_{1\Sigma _{c}\Delta D^{*}}=5.13^{+0.39}_{-0.49}\,\hbox {GeV}^{-1}$$ , $$g_{2\Sigma _{c}\Delta D^{*}}=-3.03^{+0.27}_{-0.35}\,\hbox {GeV}^{-2}$$ , $$g_{3\Sigma _{c}\Delta D^{*}}=17.64^{+1.51}_{-1.95}\,\hbox {GeV}^{-2}$$ , $$g_{1\Sigma _{b}\Delta B^{*}}=20.97^{+2.15}_{-2.39}\,\hbox {GeV}^{-1}$$ , $$g_{2\Sigma _{b}\Delta B^{*}}=-11.42^{+1.17}_{-1.28}\,\hbox {GeV}^{-2}$$ and $$g_{3\Sigma _{b}\Delta B^{*}}=24.87^{+2.57}_{-2.82}\,\hbox {GeV}^{-2}$$ . These strong coupling constants are important parameters which can help us to understand the strong decay behaviors of hadrons.