First measurement of the form factors in the decays D0 → ρ- e+ ν(e) and D+ → ρ0 e+ ν(e)

The beauty to up quark coupling constant |V(ub)| can be extracted from B → ρ e+ ν(e) combined with the form factors for D → K* e+ ν(e) and B → V ℓ+ ℓ- and D → ρ e+ ν(e). Using the entire CLEO-c ψ(3770) → DD event sample, corresponding to an integrated luminosity of 818 pb(-1) and approximately 5.4×10(6) DD events, we measure the form factors for the decays D0 → ρ- e+ ν(e) and D+ → ρ0 e+ ν(e) for the first time and the branching fractions with improved precision. A four-dimensional unbinned maximum likelihood fit determines the form factor ratios to be V(0)/A1(0)=1.48±0.15±0.05 and A2(0)/A1(0)=0.83±0.11±0.04. Assuming Cabibbo-Kobayashi-Maskawa unitarity, the known D meson lifetimes, and our measured branching fractions we obtain the form factor normalizations A1(0), A2(0), and V(0). We also present a measurement of the branching fraction for D+ → ω e+ ν(e) with improved precision.