Measurement of the D^0→π^−e^+ν_e differential decay branching fraction as a function of q^2 and study of form factor parametrizations

Based on a sample of 500 million e^+e^−→cc events recorded by the BABAR detector at c.m. energies of close to 10.6 GeV, we report on a study of the decay D^0→π^−e^+ν_e. We measure the ratio of branching fractions, R_D=B(D^0→π^−e^+ν_e)/B(D^0→K^−π^+)=0.0713±0.0017_(stat)±0.0024_(syst), and use the present world average for B(D^0→K^−π^+) to obtain B(D^0→π^−e^+ν_e)= 2.770±0.068_(stat)±0.092_(syst)±0.037_(ext))×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 q^2, 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(q^2), and the normalization V_(cd)|×f^π_+,D(q^2=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)(q^2=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)(q^2=0)=0.610±0.020_(exp)±0.005_(ext). The q^2 dependence of f^π_(+,D)(q^2) is compared to a variety of multipole parametrizations. This information is applied to B^0→π^−e^+ν_e decays and, combined with an earlier B^0→π^−e^+ν_e measurement by BABAR, is used to derive estimates of |V_(ub)|