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Form Factors for Semileptonic B -> pi and D -> pi Decays from the Omnes Representation

We use the Omnes representation to obtain the q-squared dependence of the form factors f+ and f0 for semileptonic H -> pi decays from the elastic pi H -> pi H scattering amplitudes, where H denotes a B or D meson. The scattering amplitudes used satisfy elastic unitarity and are calculated from two-particle irreducible amplitudes obtained using tree-level heavy meson chiral perturbation theory (HMChPT). The q-squared 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 q-squared found in sumrule calculations.