Measurement of the D⁰ → π⁻e⁺ν_e Differential Decay Branching Fraction as a Function of q² and Study of Form Factor Parametrizations

Based on a sample of 500 million e⁺e⁻ → cc̅ events recorded by the BABAR detector at c. m. energies of close to 10.6 GeV, we report on a study of the decay D⁰ → π⁻e⁺ν(e⁻). We measure the ratio of branching fractions, R(D) = ℬ(D⁰ → π⁻e⁺ν(e)) / ℬ(D⁰ → K⁻ π⁺) = 0.0713 ± 0.0017(stat) ± 0.0024(syst) and use the present world average for B(D⁰ → K⁻π⁺) to obtain ℬ(D⁰ → π⁻e⁺ν(e)) = (2.770 ± 0.068(stat) ± 0.092(syst) ± 0.037(ext)) x 10⁻³ where the third error accounts for the uncertainty on the branching fraction for the reference channel. The measured dependence of the differential branching fraction on q², the four-momentum transfer squared between the D and the π meson, is compared to various theoretical predictions for the hadronic form factor, (f^(π)(+,D))(q²), and the normalization |V(cd)| x (f^(π)(+,D)(q² = 0) = 0.1374 ± 0.0038(stat) ± 0.0022(syst) ± 0.0009(ext⋅) is extracted from a fit to data. Using the most recent LQCD prediction of (f^(π))(+,D)(q²) = 0) = 0.666 ± 0.029, we obtain |V(cd)| = 0.206 ± 0.007(exp) ± 0.009(LQCD). Assuming, instead, |V(cd)| = |V(us)| = 0.2252 ± 0.0009, we obtain (f^(π))(+,D)(q²) = 0) = 0.610 ± 0.020(exp) ± 0.005(ext⋅). The q² dependence of f^(π)(+,D)(q² = 0) is compared to a variety of multipole parametrizations. This information is applied to B⁰ → π⁻e⁺ν(e) decays and, combined with an earlier B⁰ → π⁻e⁺ν(e) measurement by BABAR, is used to derive estimates of |V(ub)|.