  We study the shape parameters of the $D\pi$ scalar and vector form factors
using as input dispersion relations and unitarity for the moments of suitable
heavy-light correlators evaluated with Operator Product Expansions, including
$O(\alpha_s^2)$ terms in perturbative QCD. For the scalar form factor, a low
energy theorem and phase information on the unitarity cut are implemented to
further constrain the shape parameters. We finally determine points on the real
axis and isolate regions in the complex energy plane where zeros of the form
factors are excluded.
