Parametrisations of the D -> K l nu form factor and the determination of \hat{g}

TL;DR

This paper evaluates different parametrisations of the D -> K l nu form factor to accurately determine the strong coupling constant , highlighting the strengths and weaknesses of each approach, including the z-expansion.

Contribution

It compares various form factor parametrisations for D -> K l nu decay to assess their effectiveness in determining , revealing limitations of the z-expansion method.

Findings

Several simple parametrisations successfully estimate .

The z-expansion shows significant shortcomings for this application.

Some models embed more physical information, improving extrapolation accuracy.

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.