We present a measurement of the branching fraction for the rare decays B→ρeν and extract a value for the magnitude of Vub, one of the smallest elements of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix. The results are given for five different calculations of form factors used to parametrize the hadronic current in semileptonic decays. Using a sample of 55×106 BB ̄ ̄ ̄ meson pairs recorded with the BABAR detector at the PEP-II e+e− storage ring, we obtain B(B0→ρ−e+ν)=(3.29±0.42±0.47±0.55)×10−4 and |Vub|=(3.64±0.22±0.25+0.39−0.56)×10−3, where the uncertainties are statistical, systematic, and theoretical, respectively.
