Measurement of the Ratio ${\cal B}\xspace(\B^+ \to X e ν)$ / ${\cal B}\xspace(\B^0 \to X e ν)

We report measurements of the inclusive electron momentum spectra in decays of charged and neutral B mesons, and of the ratio of semileptonic branching fractions ${\cal B}\xspace(\B^+ \to X e \nu)$ and ${\cal B}\xspace(\B^0 \to X e \nu)$. These were performed on a sample of 231 million $B\kern 0.18em\bar{\kern -0.18em B}{}\xspace$ events recorded with the \mbox{\slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller A\kern-0.2em R}} detector at the $\Upsilon{(4S)}\xspace$ resonance. Events are selected by fully reconstructing a hadronic decay of one $B$ meson and identifying an electron among the decay products of the recoiling $\Bbar$ meson. We obtain ${\cal B}\xspace(\Bu \to X e \nu)$/${\cal B}\xspace(\Bz \to X e \nu)$ = $1.084 \pm 0.041_{\mathrm{(stat)}}\xspace\pm 0.025_{\mathrm{(syst)}}\xspace$.