Study of $\hat{I}\cdot$ and dipion transitions in $\hat{I}\yen (4S)$ decays to lower bottomonia

Abstract

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

11 pages, 7 figures, 6 tables. Submitted to PRD