Effects of isospin violation in the $e^+e^- \rightarrow B^{(*)}\bar B^{(*)}$ cross sections

Model estimates are obtained for the influence of Coulomb effects on the ratio of the cross sections for the production of charged and neutral $B\bar B$ and $B^*\bar B^*$ pairs in $e^+e^-$ annihilation. It is shown that the difference between the masses of charged and neutral mesons obtained under the assumption that this ratio is constant on a scale of the order of the beam energy spread can differ from the true one by $\delta M \sim 0.03\,\mbox{MeV}$ at the energy of $\Upsilon (5S)$ and by $\delta M \sim 0.4\,\mbox{MeV}$ at the energy of $\Upsilon (4S)$. Thus, the errors given in the PDG for the difference between the masses of charged and neutral $B$ mesons, based on the results obtained at the energy of $\Upsilon (4S)$, are strongly underestimated. Similar measurements at the energy of $\Upsilon (5S)$ will have an order of magnitude smaller systematic shift for the mass difference. This circumstance should be taken into account when planning future experiments at the $B$ factory in KEK.