Analysis of the decay constants of the heavy pseudoscalar mesons with QCD sum rules

In this article, we recalculate the contributions of all vacuum condensates up to dimension-6, in particular the one-loop corrections to the quark condensates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\alpha_s}\left\langle {\overline{q}q} \right\rangle $\end{document} and partial one-loop corrections to the four-quark condensates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \alpha_s^2{{\left\langle {\overline{q}q} \right\rangle}^2} $\end{document}, in the operator product expansion. Then we study the masses and decay constants of the heavy pseudoscalar mesons D, Ds, B and Bs using the QCD sum rules with two choices: I we choose the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \overline{MS} $\end{document} masses by setting m = m(μ) and take perturbative corrections up to the order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{O}\left( {{\alpha_s}} \right) $\end{document}; II we choose the pole masses m, take perturbative corrections up to the order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{O}\left( {\alpha_s^2} \right) $\end{document} and set the energy-scale to be the heavy quark pole mass μ = mQ. In the case of I, the predictions fD = (208 ± 11) MeV and fB = (189 ± 15) MeV are consistent with the experimental data within uncertainties, while the prediction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {f_{{{D_s}}}}=\left( {241\pm 12} \right) $\end{document} MeV is below the lower bound of the experimental data \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {f_{{{D_s}}}}=\left( {260.0\pm 5.4} \right) $\end{document} MeV. In the case of II, the predictions fD = (211 ± 14) MeV, fB = (190 ± 17) MeV, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {f_{{{D_s}}}}=\left( {258\pm 13} \right) $\end{document} MeV and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{{f_{{{D_s}}}}}} \left/ {{{f_D}}} \right.}=1.22\pm 0.08 $\end{document} are all in excellent agreements with the experimental data within uncertainties.