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 f
rom 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.
We propose a model for $D^+ to pi^+ pi^- pi^+$ decays following experimental results which indicate that the two-pion interaction in the $S$-wave is dominated by the scalar resonances $f_0(600)/sigma$ and $f_0(980)$. The weak decay amplitude for $D^+
to R pi^+$, where $R$ is a resonance that subsequently decays into $pi^+pi^-$, is constructed in a factorization approach. In the $S$-wave, we implement the strong decay $Rto pi^-pi^+$ by means of a scalar form factor. This provides a unitary description of the pion-pion interaction in the entire kinematically allowed mass range $m_{pipi}^2$ from threshold to about 3 GeV$^2$. In order to reproduce the experimental Dalitz plot for $Dppp$, we include contributions beyond the $S$-wave. For the $P$-wave, dominated by the $rho(770)^0$, we use a Breit-Wigner description. Higher waves are accounted for by using the usual isobar prescription for the $f_2(1270)$ and $rho(1450)^0$. The major achievement is a good reproduction of the experimental $m_{pipi}^2$ distribution, and of the partial as well as the total $Dppp$ branching ratios. Our values are generally smaller than the experimental ones. We discuss this shortcoming and, as a byproduct, we predict a value for the poorly known $Dto sigma$ transition form factor at $q^2=m_pi^2$.
