  We consider the vector and scalar form factors of the charm-changing current
responsible for the semileptonic decay D\rightarrow \pi l \nu. 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, we constrain the shape parameters of the form
factors and find exclusion regions for zeros on the real axis and in the
complex plane. For the scalar form factor, a low energy theorem and phase
information on the unitarity cut are also implemented to further constrain the
shape parameters. We finally propose new analytic expressions for the $D\pi$
form factors, derive constraints on the relevant coefficients from unitarity
and analyticity, and briefly discuss the usefulness of the new parametrizations
for describing semileptonic data.
