Predictions for hadronic transitions in thebb¯system

Within the framework of the multipole expansion of quantum chromodynamics, we propose a model to compute the rates of hadronic transitions in the $b\overline{b}$ system and heavier $Q\overline{Q}$ states. Rates and estimated branching ratios of various transitions are given. The predicted result for ${\Upsilon }^{\prime }\to \Upsilon \pi \pi$ agrees with recent measurements. We discuss the spin-flip $\pi \pi$ transitions ${\Upsilon }^{\prime \prime }\to 1{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\pi \pi$ and $2{}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\pi \pi$ which can be used to reach the spin-singlet states $1{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$.