Parametrizations of the D → Kellν form factor and the determination of ĝ

The vector form factor f₊(t) of the semileptonic decay D → Kellν, measured recently with a high accuracy, can be used to determine the strong coupling constant g_{D_s^* D K} . The latter is related to the normalized coupling \hat g relevant in heavy-meson chiral perturbation theory. This determination relies on the estimation of the residue of the form factor at the D*_s pole and thus on an extrapolation of the form factor in the unphysical region (m_D - m_K)² < t < (m_D + m_K)². We test this extrapolation for several parametrizations of the form factors by determining the value of ĝ, whose value can be compared to other (experimental and theoretical) estimates. Several unsophisticated parametrizations, differing by the amount of physical information that they embed, are shown to pass this test. An apparently more elaborated parametrization of form factors, the so-called z-expansion, is at variance with the other models, and we point out some significant shortcomings of this parametrization for the problem under consideration.