Measurement of the Relative Branching Fractions of Bbar --> D/D*/D** l^- anti-nu_l Decays in Events with a Fully Reconstructed B Meson

We determine the relative branching fractions of semileptonic B decays to charmed final states. The measurement is performed on the recoil from a fully reconstructed B meson in a sample of 362 million BBbar pairs collected at the Upsilon(4S) resonance with the BaBar detector. A simultaneous fit to a set of discriminating variables is performed on a sample of Bbar --> D X l^- anti-nu_l decays to determine the contributions from the different channels. We measure Gamma(B- --> D l^- anti-nu_l)/Gamma (B- --> D X l^- anti-nu_l)= 0.227 +/- 0.014 +/- 0.016, Gamma(B- --> D* l^- anti-nu_l)/Gamma (B- --> D X l^- anti-nu_l)= 0.582 +/- 0.018 +/- 0.030 and Gamma(B- --> D** l^- anti-nu_l)/Gamma (B- --> D X l^- anti-nu_l)= 0.191 +/- 0.013 +/- 0.019 for the charged B sample, and Gamma(B0bar --> D l^- anti-nu_l)/Gamma (B0bar --> D X l^- anti-nu_l)= 0.215 +/- 0.016 +/- 0.013, Gamma(B0bar --> D* l^- anti-nu_l)/Gamma (B0bar --> D X l^- anti-nu_l)= 0.537 +/- 0.031 +/- 0.036 and Gamma(B0bar --> D** l^- anti-nu_l)/Gamma (B0bar --> D X l^- anti-nu_l)= 0.248 +/- 0.032 +/- 0.030 for the neutral B sample, where uncertainties are statistical and systematic, respectively.