First Measurement Of The Form Factors In The Decays D-0 -> Rho(-)E(+)Nu(E) And D+ -> Rho(0)E(+)Nu(E)

The beauty to up quark coupling constant \V-ub\ can be extracted from B --> rho e(+)nu(e) combined with the form factors for D --> K*e(+)nu(e) and B --> Vl(+)l(-) and D --> rho e(+)nu(e). Using the entire CLEO-c psi(3770) --> D (D) over bar event sample, corresponding to an integrated luminosity of 818 pb(-1) and approximately 5.4 x 10(6) D (D) over bar events, we measure the form factors for the decays D-0 --> rho(-)e(+)nu(e) and D+ --> rho(0)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 Cabibbo-Kobayashi-Maskawa 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+ --> omega e(+)nu(e) with improved precision. DOI: 10.1103/PhysRevLett.110.131802