Running mass ms at low scale from the heavy-light meson decay constants

It is shown that a 25(20)% difference between the decay constants \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f_{D_s } $$ \end{document} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{B_s} $$\end{document}) and fD(fB) occurs due to large differences in the pole masses of the s and d(u) quarks. The values ηD = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f_{D_s } $$ \end{document}/fD ∼ 1.23(15), recently observed in the CLEO experiment, and ηB = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f_{B_s } $$ \end{document}/fB ∼ 1.20, obtained in unquenched lattice QCD, can be reached only if, in the relativistic Hamiltonian the running mass, ms at low scale is ms(∼0.5 GeV) = 170–200 MeV. Our results follow from the analytical expression for the pseudoscalar decay constant fP based on the path-integral representation of the meson Green’s function.