Improved bounds for the slope and curvature of B → D(∗)ℓν form factors

We derive a theoretically allwed domain for the slope ρ2 and curvature c of the physical form factor appearing in the decay B → D∗ℓν. Using heavy-quark symmetry, we relate this function to a particular B → D form factor free of ground-state Bc poles below the threshold for BD production, for which almost model-independent constraints are derived from QCD using unitarity and analyticity. Our results are of interest for the extraction of |Vcb| from the recoil spectrum in exclusive semileptonic B decays. Making conservative estimates of the theoretical uncertainties, we find (up to 1mQ corrections) ρ2 < 1.11 and c ⋍ 0.66ρ2 −0.11. We also derive the corresponding bounds for the form factor in the decay B → D ℓ ν.