A phenomenological analysis of the scalar meson f0(980) is performed that relies on the quasi-two body decays D and Ds -> f0(980)P, with P=pi, K. The two-body branching ratios are deduced from experimental data on D or Ds -> pi pi pi, K Kbar pi and from the f0(980) -> pi+ pi- and f0(980) -> K+ K- branching fractions. Within a covariant quark model, the scalar form factors F0(q2) for the transitions D and Ds -> f0(980) are computed. The weak D decay amplitudes, in which these form factors enter, are obtained in the naive factorization approach assuming a quark-antiquark state for the scalar and pseudoscalar mesons. They allow to extract information on the f0(980) wave function in terms of u-ubar, d-dbar and s-sbar pairs as well as on the mixing angle between the strange and non-strange components. The weak transition form factors are modeled by the one-loop triangular diagram using two different relativistic approaches: covariant light-front dynamics and dispersion relations. We use the information found on the f0(980) structure to evaluate the scalar and vector form factors in the transitions D and Ds -> f0(980), as well as to make predictions for B and Bs -> f0(980), for the entire kinematically allowed momentum range of q2.
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