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

Bhatnagar, S. ; Kulshreshtha, D. S. ; Mitra, A. N. (1991) How big are the decay constants fP of heavy-light mesons? Physics Letters B, 263 (3-4). pp. 485-490. ISSN 0370-2693

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The quark loop diagram for fP 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 (fp ∼ mQ) 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 fp=fo+ δf in which the second term is an unequal-mass cut-off shell contribution. The ratio δf/fo 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/fo increases up to the D-B region (where its effect is 15-20%), before tapering off for higher mQ values. The total ƒP values are on the low side (fo< 150 MeV, fB< 100 MeV. A brief comparison is given with lattice measurements.

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