Measurement of the Branching Fractions for Inclusive $B^-$ and $\bar B^0$ Decays to Flavor-tagged $D$, $D_s$ and $Λ_c$

We report on the inclusive branching fractions of $B^-$ and of ${\bar B}^0$ mesons decaying to ${D^0 X}$, ${{\bar D}^0 X}$, ${D^+ X}$, ${D^- X}$, ${D_s^+ X}$, ${D_s^- X}$, ${\Lambda_c^+ X}$, ${{\bar \Lambda}_c^- X}$, based on a sample of 88.9 million $B \bar B$ events recorded with the $BABAR$ detector at the $\Upsilon(4S)$ resonance. Events are selected by completely reconstructing one $B$ and searching for a reconstructed charmed particle in the rest of the event. We measure the number of charmed and of anti-charmed particles per $B$ decay and derive the total charm yield per $B^-$ decay, $n_c^- = 1.313 \pm 0.037 \pm 0.062 ^{+0.063}_{-0.042} $, and per ${\bar B}^0$ decay, $n_c^0 = 1.276 \pm 0.062 \pm 0.058 ^{+0.066}_{-0.046}$ where the first uncertainty is statistical, the second is systematic, and the third reflects the charm branching-fraction uncertainties.