We have investigated the transitions $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}\Upsilon \mathrm{}\left(1S\right)\mathrm{}$, $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}\Upsilon \mathrm{}\left(2S\right)\mathrm{}$ and the cascade process $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to \Upsilon \mathrm{}\left(2S\right)+X$, $\Upsilon \mathrm{}\left(2S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}\Upsilon \mathrm{}\left(1S\right)\mathrm{}$, both in the exclusive decay mode, with the daughter $\Upsilon$ state decaying into two leptons, and in the inclusive decay mode, with the daughter $\Upsilon$ state decaying hadronically. Results are presented on the branching fractions and properties of the ${\pi }^{+}{\pi }^{-}$ system. The ${\pi }^{+}{\pi }^{-}$ invariant-mass spectra for the decays $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}\Upsilon \mathrm{}\left(1S\right)\mathrm{}$ and $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}\Upsilon \mathrm{}\left(2S\right)\mathrm{}$ are measured and compared with theoretical predictions. We also present the results of a search for the $h_b\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ and $\Upsilon \left(1\mathrm{}{}_{}{}^3{}_{}{}^{}D\right)$ states in inclusive $\Upsilon \mathrm{}\left(3S\right)\mathrm{}$ decays, and for the exclusive decay $\Upsilon \mathrm{}\left(3S\right)\mathrm{}\to \eta \Upsilon \mathrm{}\left(1S\right)\mathrm{}$.

• Received 24 September 1990

DOI:https://doi.org/10.1103/PhysRevD.43.1448