Study of $\eta$ and dipion transitions in $\Upsilon(4S)$ decays to lower bottomonia

We study hadronic transitions between bottomonium states using 496 fb$^{-1}$ data collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^{+}e^{-}$ collider. We measure: ${\cal B}(\Upsilon(4S)\to\pi^+\pi^-\Upsilon(1S))=(8.2\pm 0.5 {\rm(stat.)} \pm 0.4 {\rm(syst.)})\times10^{-5}$, ${\cal B}(\Upsilon(4S)\to\pi^+\pi^-\Upsilon(2S))=(7.9\pm 1.0 {\rm(stat.)} \pm 0.4 {\rm(syst.)})\times10^{-5}$, and ${\cal B}(\Upsilon(4S)\to\eta\Upsilon(1S))=(1.70\pm 0.23 {\rm(stat.)} \pm 0.08 {\rm(syst.)})\times10^{-4}$. We measure the ratio of branching fractions ${\cal R} = {\cal B}(\Upsilon(4S)\to\eta\Upsilon(1S))/{\cal B}(\Upsilon(4S)\to\pi^+\pi^-\Upsilon(1S)) = 2.07\pm 0.30 {\rm(stat.)} \pm 0.11 {\rm(syst.)}$. We search for the decay $\Upsilon(1^3D_{1,2})\to\eta\Upsilon(1S)$, but do not find significant evidence for such a transition. We also measure the initial state radiation production cross sections of the $\Upsilon(2S,3S)$ resonances and we find values compatible with the expected ones. Finally, the analysis of the $\Upsilon(4S)\to\pi^+\pi^-\Upsilon(1S)$ events shows indications for a resonant contribution due to the $f_0(980)$ meson.