Parametrisations of the D -> K l nu form factor and the determination of $\hat{g}$
Résumé
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 g_{D_s^* D K}, which is related to the normalised coupling \hat{g}. This is achieved through the estimation of the residue of the form factor at the D_s^* pole, which requires an extrapolation of the form factor in the unphysical region (m_D-m_K)^2 < t < (m_D+m_K)^2. We consider several unsophisticated parametrisations which yield results agreeing with most of the other determinations of \hat{g}. 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 drawbacks of this parametrisation for the problem under consideration.