Parametrisations of the D -> K l nu form factor and the determination of \hat{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 g_{D_s^* D K}. The latter is related to the normalised coupling \hat{g} releveant 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 parametrisations of the form factors by determining the value of \hat{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.

arXiv comment16 pages, 2 figures. A few references added. Accepted for publication in JoPG

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• Determination of the strong coupling $g_{B^{\ast }B\pi }$ from semi-leptonic $B\to \pi \ell \nu$ decay
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• Theory of Semileptonic Charm Decays
• Semileptonic decays of heavy mesons with artificial neural networks