ϒfamily of resonances above threshold

Abstract

The coupled-channel method developed previously is applied to the $b\overline{b}$ system of resonances above the threshold for Zweig-allowed decays ($2m_B$). The structure of $\Delta R$ is calculated for representative values of $\Delta M=m\left(4\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)-2\mathrm{}{m}_B$. Typically the $4{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ resonance has a complex structure with a total width 10-40 MeV and $\Delta R\left(\mathrm{peak}\right)\sim 1-3$. This structure has a strong $\Delta M$ dependence which may allow the determination of $m_B$ from the observed structure of $\Delta R$ in the ${\Upsilon }^{\prime \prime \prime }$ region. The contribution of each exclusive channel is shown. Higher $b\overline{b}$ resonances are briefly discussed.