Inclusive decays $B\to \mathrm{DX}$ and $B\to D^{*}X$

We report new measurements of the differential and total branching ratios for inclusive $B$ decay to $D^0$, $D^{+}$, and $D^{*+}$ and the first measurement of the same quantities for inclusive $B$ decay to $D^{*0\mathrm{}}$. Here $B$ is the mixture of $B_d$ and $B_u$ from ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ decay. Furthermore, since more than one charm particle (or antiparticle) of the same kind can be produced in $B$ decay, here “inclusive $B$ branching ratio” is used to mean the average number of charm particles and their antiparticles of a certain species produced in $B$ decay. We obtain the following results (the first error is statistical, the second systematic of this analysis, the third propagated from other measurements): $\mathcal{B}(B\to D^{0}X)=(0.636\mathrm{}\pm 0.014\pm 0.019\pm 0.018),$ $\mathcal{B}(B\to D^{+}X)=(0.235\mathrm{}\pm 0.009\pm 0.009\pm 0.024),$ $\mathcal{B}(B\to D^{*0\mathrm{}}X)$$=(0.247\mathrm{}\pm 0.012\pm 0.018\pm 0.018),$ $\mathcal{B}(B\to D^{*+}X)=(0.239\mathrm{}\pm 0.011\pm 0.014\pm 0.009).$ The following ratio of branching ratios is not affected by most of the systematic errors: $\mathcal{B}(B\to D^{*0\mathrm{}}X)/\mathcal{B}(B\to D^{*+}X)$$=(1.03\mathrm{}\pm 0.07\pm 0.09\pm 0.08).$ We also report the first measurement of the momentum-dependent $D^{*0\mathrm{}}$ polarization and a new measurement of the $D^{*+}$ polarization in inclusive $B$ decay. Using these measurements and other CLEO results and making some additional assumptions, we calculate the average number of $c$ and $\overline{c}$ quarks produced in $B$ decay to be $〈n_c〉=1.10\mathrm{}\pm 0.05$.