Parametrisations of the D -> K l nu form factor and the determination of g
Abstract
The vector form factor f+(t) of the semileptonic decay D -> K l nu, measured recently with a high accuracy, can be used to determine the strong coupling constant gDs* D K. The latter is related to the normalised coupling g releveant in heavy-meson chiral perturbation theory. This determination relies on the estimation of the residue of the form factor at the Ds* pole and thus on an extrapolation of the form factor in the unphysical region (mD-mK)2<t<(mD+mK)2. We test this extrapolation for several parametrisations of the form factors by determining the value of g, whose value can be compared to other (experimental and theoretical) estimates. Several unsophisticated parametrisations, differing by the amount of physical information that they embed, are shown to pass this test. An apparently more elaborated parametrisation of form factors, the so-called z-expansion, is at variance with the other models, and we point out some significant shortcomings of this parametrisation for the problem under consideration.