Measurement of the $D^0 \to π^- e^+ ν_e$ differential decay branching fraction as a function of $q^2$ and study of form factor parameterizations

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 D0→π-e+νe. We measure the ratio of branching fractions, RD=B(D0→π-e+νe)/B(D0→K-π+)=0.0713±0.0017stat±0.0024syst, and use the present world average for B(D0→K-π+) to obtain B(D0→π-e+νe)=(2.770±0.068stat±0.092syst±0.037ext)×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+,Dπ(q2), and the normalization |Vcd|×f+,Dπ(q2=0)=0.1374±0.0038stat±0.0022syst±0.0009ext. is extracted from a fit to data. Using the most recent LQCD prediction of f+,Dπ(q2=0)=0.666±0.029, we obtain |Vcd|=0.206±0.007exp±0.009LQCD. Assuming, instead, |Vcd|=|Vus|=0.2252±0.0009, we obtain f+,Dπ(q2=0)=0.610±0.020exp±0.005ext. The q2 dependence of f+,Dπ(q2) is compared to a variety of multipole parametrizations. This information is applied to B0→π-e+νe decays and, combined with an earlier B0→π-e+νe measurement by BABAR, is used to derive estimates of |Vub|.