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

Abstract

Methods are proposed for measuring the ratio $R^{+/0}=\Gamma ({\rm Y}(4S)\to B^{+}{B}^{-})/$ $\Gamma ({\rm Y}(4S)\to \text{bo}\text{ob})$ 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 $D^{+}{D}^{-}/D^0\text{od}$ ratio at the ${\psi }^{\prime \prime }\equiv \psi (3770)$, is also estimated.

Comments: 6 pages, no figures, to be published in Phys. Rev. D (Brief Reports). One reference and acknowledgment added; slight text change