Study of $\eta$ and dipion transitions in ${\rm Y}\left(4S\right)$ decays to lower bottomonia

Here, we study hadronic transitions between bottomonium states using $496{\mathrm{fb}}^{-1}$ data collected at the ${\rm Y}\left(4S\right)$ resonance with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. We measure $B\left({\rm Y}\right(4S)\to {\pi }^{+}{\pi }^{-}{\rm Y}(1S\left)\right)=(8.2\pm 0.5\left(\text{stat}\right)\pm 0.4\left(\text{syst}\right))\times {10}^{-5}$, $B\left({\rm Y}\right(4S)\to {\pi }^{+}{\pi }^{-}{\rm Y}(2S\left)\right)=(7.9\pm 1.0\left(\text{stat}\right)\pm 0.4\left(\text{syst}\right))\times {10}^{-5}$, and $B\left({\rm Y}\right(4S)\to \eta {\rm Y}(1S\left)\right)=(1.70\pm 0.23\left(\text{stat}\right)\pm 0.08\left(\text{syst}\right))\times {10}^{-4}$. We measure the ratio of branching fractions $R=B\left({\rm Y}\right(4S)\to \eta {\rm Y}(1S\left)\right)/B\left({\rm Y}\right(4S)\to {\pi }^{+}{\pi }^{-}{\rm Y}(1S\left)\right)=2.07\pm 0.30\left(\text{stat}\right)\pm 0.11\left(\text{syst}\right)$. We search for the decay ${\rm Y}\left(1{{}_{3}D}_{1,2}\right)\to \eta {\rm Y}\left(1S\right)$, but do not find significant evidence for such a transition. We also measure the initial-state radiation production cross sections of the ${\rm Y}(2S,3S)$ resonances and we find values compatible with the expected ones. Finally, the analysis of the ${\rm Y}\left(4S\right)\to {\pi }^{+}{\pi }^{-}{\rm Y}\left(1S\right)$ events reflects indications for a resonant contribution due to the $f_0\left(980\right)$ meson.