Υ dipion transitions at energies near the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$

Using a $4.19{\mathrm{fb}}^{\mathrm{-}1}$ data sample collected with the CLEO II detector at the Cornell Electron Storage Ring, we have searched for dipion transitions between pairs of Υ resonances at center of mass energies $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=10.58\mathrm{}\mathrm{GeV}$ and $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=10.52\mathrm{}\mathrm{GeV}.$ We obtain the 90% confidence level upper limits $\mathcal{B}\left({\rm Y}\mathrm{}\right(4S)\mathrm{}\to {\rm Y}\mathrm{}(2S\left)\mathrm{}{\pi }^{+}{\pi }^{-}\right)<3.9\mathrm{}\times {10}^{-4}$ and $\mathcal{B}\left({\rm Y}\mathrm{}\right(4S)\mathrm{}\to {\rm Y}\mathrm{}(1S\left)\mathrm{}{\pi }^{+}{\pi }^{-}\right)<1.2\mathrm{}\times {10}^{-4}.$ We also observe the transitions ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(1S\right)\mathrm{}{\pi }^{+}{\pi }^{-},$ ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(2S\right)\mathrm{}{\pi }^{+}{\pi }^{-},$ and ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(1S\right)\mathrm{}{\pi }^{+}{\pi }^{-},$ from which we measure the cross sections for the radiative processes $e^{+}{e}^{-}\to {\rm Y}\mathrm{}\left(3S\right)\mathrm{}\gamma$ and $e^{+}{e}^{-}\to {\rm Y}\mathrm{}\left(2S\right)\mathrm{}\gamma .$ We obtain ${\sigma }_{e\overrightarrow{e}{\rm Y}\mathrm{}\left(3S\right)\mathrm{}\gamma }=(17.8\mathrm{}\pm 3.0\pm 1.7)\mathrm{pb}$ and ${\sigma }_{e\overrightarrow{e}{\rm Y}\mathrm{}\left(2S\right)\mathrm{}\gamma }=(15.5\mathrm{}\pm 1.3\pm 1.4)\mathrm{pb}$ at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=10.58\mathrm{}\mathrm{GeV},$ and ${\sigma }_{e\overrightarrow{e}{\rm Y}\mathrm{}\left(3S\right)\mathrm{}\gamma }=(27.3\mathrm{}\pm 5.0\pm 2.6)\mathrm{pb}$ and ${\sigma }_{e\overrightarrow{e}{\rm Y}\mathrm{}\left(2S\right)\mathrm{}\gamma }=(16.3\mathrm{}\pm 1.8\pm 1.5)\mathrm{pb}$ at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=10.52\mathrm{}\mathrm{GeV},$ which we compare with theoretical predictions.