Form factors for semileptonic B→π and D→π decays from the Omnès representation

We use the Omnès representation to obtain the q2 dependence of the form factors f+,0(q2) for semileptonic H→π decays from elastic πH→πH scattering amplitudes, where H denotes a B or D meson. The amplitudes used satisfy elastic unitarity and are obtained from two-particle irreducible amplitudes calculated in tree-level heavy meson chiral perturbation theory (HMChPT). The q2-dependences for the form factors agree with lattice QCD results when the HMChPT coupling constant, g, takes values smaller than 0.32, and confirm the milder dependence of f0 on q2 found in sumrule calculations.