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The Inclusive Decays $B\to D X$ 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 $D^{*0}$. Here B is the mixture of B_d and B_u from $Υ(4S)$ 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 is propagated from other measurements): ${\cal B}(B\to D^0 X) = (0.636\pm 0.014\pm 0.019\pm 0.018), {\cal B}(B\to D^+ X) = (0.235\pm 0.009\pm 0.009\pm 0.024), {\cal B}(B\to D^{*0} X) = (0.247\pm 0.012\pm 0.018\pm 0.018), {\cal B}(B\to D^{*+} X) = (0.239\pm 0.011\pm 0.014\pm 0.009)$. The following ratio of branching ratios is not affected by most of the systematic errors: ${\cal B}(B\to D^{*0} X)/{\cal B}(B\to D^{*+} X) = (1.03\pm 0.07\pm 0.09\pm 0.08).$ We also report the first measurement of the momentum-dependent $D^{*0}$ 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 $\bar c$ quarks produced in B decay to be $< n_c > = 1.10\pm 0.05$.