Analysis of the strong vertices of ΣcΔD∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}\\Delta D^{*}$$\\end{document} and ΣbΔB∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{b}\\Delta B^{*}$$\\end{document} in QCD sum rules

Abstract

In this work, we analyze the strong vertices ΣcΔD∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}\\Delta D^{*}$$\\end{document} and ΣbΔB∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{b}\\Delta B^{*}$$\\end{document} using the three-point QCD sum rules under the tensor structures iϵρταβpαpβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i\\epsilon ^{\\rho \ au \\alpha \\beta }p_{\\alpha }p_{\\beta }$$\\end{document}, pρp′τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{\\rho }p'^{\ au }$$\\end{document} and pρpτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{\\rho }p^{\ au }$$\\end{document}. We firstly calculate the momentum dependent strong coupling constants g(Q2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g(Q^{2})$$\\end{document} by considering contributions of the perturbative part and the condensate terms ⟨q¯q⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle {\\overline{q}}q\\rangle $$\\end{document}, ⟨gs2GG⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle g_{s}^{2}GG \\rangle $$\\end{document}, ⟨q¯gsσGq⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle {\\overline{q}}g_{s}\\sigma Gq\\rangle $$\\end{document} and ⟨q¯q⟩2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle {\\overline{q}}q\\rangle ^{2}$$\\end{document}. 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 g1ΣcΔD∗=5.13-0.49+0.39GeV-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{1\\Sigma _{c}\\Delta D^{*}}=5.13^{+0.39}_{-0.49}\\,\\hbox {GeV}^{-1}$$\\end{document}, g2ΣcΔD∗=-3.03-0.35+0.27GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{2\\Sigma _{c}\\Delta D^{*}}=-3.03^{+0.27}_{-0.35}\\,\\hbox {GeV}^{-2}$$\\end{document}, g3ΣcΔD∗=17.64-1.95+1.51GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{3\\Sigma _{c}\\Delta D^{*}}=17.64^{+1.51}_{-1.95}\\,\\hbox {GeV}^{-2}$$\\end{document}, g1ΣbΔB∗=20.97-2.39+2.15GeV-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{1\\Sigma _{b}\\Delta B^{*}}=20.97^{+2.15}_{-2.39}\\,\\hbox {GeV}^{-1}$$\\end{document}, g2ΣbΔB∗=-11.42-1.28+1.17GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{2\\Sigma _{b}\\Delta B^{*}}=-11.42^{+1.17}_{-1.28}\\,\\hbox {GeV}^{-2}$$\\end{document} and g3ΣbΔB∗=24.87-2.82+2.57GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{3\\Sigma _{b}\\Delta B^{*}}=24.87^{+2.57}_{-2.82}\\,\\hbox {GeV}^{-2}$$\\end{document}. These strong coupling constants are important parameters which can help us to understand the strong decay behaviors of hadrons.