First Measurement of the Form Factors in the Decays D0 to rho- e+ nu_e and D+ to rho0 e+ nu_e

Using the entire CLEO-c psi(3770) to DDbar event sample, corresponding to an integrated luminosity of 818 pb^-1 and approximately 5.4 x 10^6 DDbar events, we measure the form factors for the decays D0 to rho- e+ nu_e and D+ to rho0 e+ nu_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)/A_1(0) = 1.48 +- 0.15 +- 0.05 and A_2(0)/A_1(0)= 0.83 +- 0.11 +- 0.04. Assuming CKM unitarity, the known D meson lifetimes and our measured branching fractions we obtain the form factor normalizations A_1(0), A_2(0), and V(0). We also present a measurement of the branching fraction for D^+ to omega e^+ nu_e with improved precision.