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

Abstract

Methods are proposed for measuring the ratio $R^{+/0} = Γ(Υ(4S) \to B^+ B^-)/$ $Γ(Υ(4S) \to \bo \ob)$ without assuming isospin invariance in exclusive hadronic decays such as $B \to J/ψK$. 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 $Γ(B^+ \to X_c^0 \ell^+ ν_\ell) = Γ(B^0 \to X_c^- \ell^+ ν_\ell)$ 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 $ψ'' \equiv ψ(3770)$, is also estimated.