How big are the decay constants f_P of heavy-light mesons?

Abstract

The quark loop diagram for f_P for a heavy-light (Qq¯) meson is employed within a Lorentz-invariant framework for addressing a two-fold issue: (i) finite corrections to the asymptotic scaling law (f_p ∼ m_Q^-½) of shifman, Voloshin, Politzer and Wise; (ii) corrections to the static approximation for the heavy-quark propagator in lattice calculations. The loop diagram yields a general two-component structure f_p=f_o+ δf in which the second term is an unequal-mass cut-off shell contribution. The ratio δf/f_o provides a rough index of the nature and extent of both these corrections for heavy-light mesons. Concrete estimates are made in terms of a Bethe-Salpeter model for the vertex function Γ(q) whose parameters are firmly rooted in meson and baryon spectroscopy. It is found that δf/f_o increases up to the D-B region (where its effect is 15-20%), before tapering off for higher m_Q values. The total ƒ_P values are on the low side (f_o< 150 MeV, f_B< 100 MeV. A brief comparison is given with lattice measurements.