Hadronic transitions ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(1S\right)\mathrm{}$

Using a $73.6{\mathrm{pb}}^{\mathrm{-}1}$ data sample of ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}$ events collected with the CLEO II detector at the Cornell Electron Storage Ring, we have investigated the hadronic transitions between the ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}$ and the ${\rm Y}\mathrm{}\left(1S\right).$ The dipion transition ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(1S\right)\mathrm{}{\pi }^{+}{\pi }^{-}$ was studied using two different analysis techniques. Selecting events in which ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}\to e^{+}{e}^{-},{\mu }^{+}{\mu }^{-}$ (“exclusive” analysis), and using the ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}$ leptonic branching fractions world averages from the PDG review, we obtained $\mathcal{B}\left({\rm Y}\mathrm{}\right(2S)\mathrm{}\to {\rm Y}\mathrm{}(1S\left)\mathrm{}{\pi }^{+}{\pi }^{-}\right)=0.189\mathrm{}\pm 0.004\pm 0.010,$ while using a method allowing ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}\to \mathrm{anything}$ (“inclusive” analysis) we obtained $\mathcal{B}\left({\rm Y}\mathrm{}\right(2S)\mathrm{}\to {\rm Y}\mathrm{}(1S\left)\mathrm{}{\pi }^{+}{\pi }^{-}\right)=0.196\mathrm{}\pm 0.002\pm \mathrm{0.010.}$ The appropriate weighted average of the two measurements gives $\mathcal{B}\left({\rm Y}\mathrm{}\right(2S)\mathrm{}\to {\rm Y}\mathrm{}(1S\left)\mathrm{}{\pi }^{+}{\pi }^{-}\right)=0.192\mathrm{}\pm 0.002\pm \mathrm{0.010.}$ Combining the exclusive and inclusive results we derive the ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}$ leptonic branching fractions ${\mathcal{B}}_{\mathrm{ee}}=0.0229\mathrm{}\pm 0.0008\pm 0.0011$ and ${\mathcal{B}}_{\mu \mu }=0.0249\mathrm{}\pm 0.0008\pm \mathrm{0.0013.}$ We also studied ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(1S\right)\mathrm{}{\pi }^0{\pi }^0$ and obtained $\mathcal{B}\left({\rm Y}\mathrm{}\right(2S)\mathrm{}\to {\rm Y}\mathrm{}(1S\left)\mathrm{}{\pi }^0{\pi }^0\right)=0.092\mathrm{}\pm 0.006\pm \mathrm{0.008.}$ Parameters of the ππ system (dipion invariant mass spectra, angular distributions) were analyzed and found to be consistent with current theoretical models. Lastly, we searched for the η and single ${\pi }^0$ transitions and obtained the 90% confidence level upper limits $\mathcal{B}\left({\rm Y}\mathrm{}\right(2S)\mathrm{}\to {\rm Y}\mathrm{}(1S\left)\mathrm{}\eta \right)<0.0028\mathrm{}$ and $\mathcal{B}\left({\rm Y}\mathrm{}\right(2S)\mathrm{}\to {\rm Y}\mathrm{}(1S\left)\mathrm{}{\pi }^0\right)<\mathrm{0.0011.}\mathrm{}$