Isospin inBdecays and the(B0B¯0)/(B+B−)production ratio

Abstract

Methods are proposed for measuring the ratio ${R}^{+/0}=\ensuremath{\Gamma}(\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}{B}^{+}{B}^{\ensuremath{-}})/\ensuremath{\Gamma}(\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}{B}^{0}{\overline{B}}^{0})$ without assuming isospin invariance in exclusive hadronic decays such as $B\ensuremath{\rightarrow}J/\ensuremath{\psi}K$. 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 $\ensuremath{\Gamma}({B}^{+}\ensuremath{\rightarrow}{X}_{c}^{0}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})=\ensuremath{\Gamma}({B}^{0}\ensuremath{\rightarrow}{X}_{c}^{\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})$ is expected to hold at the subpercent 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 ${D}^{+}{D}^{\ensuremath{-}}/{D}^{0}{\overline{D}}^{0}$ ratio at the ${\ensuremath{\psi}}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\equiv}\ensuremath{\psi}(3770)$, is also estimated.