Isospin in $B$ Decays and the $(B^0 \bar B^0)/(B^+ B^-)$ Production   Ratio
  Methods are proposed for measuring the ratio $R^{+/0} = \Gamma(\Upsilon(4S) \to B^+ B^-)/$ $\Gamma(\Upsilon(4S) \to \bo \ob)$ without assuming isospin invariance in exclusive hadronic decays such as $B \to J/\psi K$. The validity of isospin invariance in various B decays is discussed. Isospin violations are expected to be especially small in inclusive semileptonic decays, so that $\Gamma(B^+ \to X_c^0 \ell^+ \nu_\ell) = \Gamma(B^0 \to X_c^- \ell^+ \nu_\ell)$ is expected to hold at the sub-percent level. Suggestions are made for utilizing this relation. The accuracy of a ``double-tag'' method for obtaining $R^{+/0}$, such as that used for measuring the $D^+ D^-/D^0 \od$ ratio at the $\psi'' \equiv \psi(3770)$, is also estimated. 
Michael Gronau, Yuval Grossman, and Jonathan L. Rosner