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

AbstractIt is shown that a 25(20)% difference between the decay constants $$f_{D_s } $$ ($$f_{B_s} $$) and fD(fB) occurs due to large differences in the pole masses of the s and d(u) quarks. The values ηD = $$f_{D_s } $$ /fD ∼ 1.23(15), recently observed in the CLEO experiment, and ηB = $$f_{B_s } $$ /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.