Isospin in $B$ Decays and the $(B^0{\bar{B}}^0)\mathrm{/}(B^{+}{B}^{-})$ Production Ratio

Methods are proposed for measuring the ratio $R^{+/0} = \Gamma(\Upsilon(4S) \to B^+ B^-)/$ $\mathrm{\Gamma }(\mathrm{{\rm Y}}(4S)\to \text{bo}\text{ob})$ without assuming isospin invariance in exclusive hadronic decays such as $B\to J\mathrm{/}\psi K$. 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 $\mathrm{\Gamma }(B^{+}\to X_c^0{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }})=\mathrm{\Gamma }(B^0\to X_c^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }})$ 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 $R^{+\mathrm{/}0}$, such as that used for measuring the $D^{+}{D}^{-}\mathrm{/}{D}^0\text{od}$ ratio at the ${\psi }^{\mathrm{\prime }\mathrm{\prime }}\equiv \psi (3770)$, is also estimated.