Study of the Hadronic Transitions $\Upsilon$(2S)$\rightarrow (\eta,\pi^0)\Upsilon$(1S) at Belle

TL;DR

This study measures the branching ratios of rare hadronic transitions from $S$ to $
S$ involving $$ and $$ mesons, providing new experimental data on these processes.

Contribution

First measurement of the branching ratios for $S o
S $ and $S o
S $ transitions at Belle, improving understanding of bottomonium hadronic transitions.

Findings

Measured $rac{S o
S }{S o
S  ext{-}$ transitions ratio as (1.99±0.14±0.11)×10^{-3}.

Set an upper limit for $S o
S $ transition at 2.3×10^{-4} (90% CL).

Calculated $S o
S $ branching fraction as (3.57±0.25±0.21)×10^{-4}.

Abstract

We study the rare hadronic transitions $\Upsilon(2S)\rightarrow \Upsilon(1S)\eta$ and $\Upsilon(2S)\rightarrow \Upsilon(1S)\pi^0$ using a sample of 158 $\times 10^6$ $\Upsilon(2S)$ decays collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We observe the $\eta$ meson decay to $\gamma\gamma$ and $\pi^+\pi^-\pi^0$ final states; the $\Upsilon(1S)$ is reconstructed in the $\mu^+\mu^-$ and $e^+e^-$ decay modes. We measure the ratios of branching fractions (${\mathcal B}$) $\frac{{\mathcal B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\eta)}{{\mathcal B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^+\pi^-)}$ = (1.99$\pm$0.14 (stat) $\pm$0.11 (syst)) $\times 10^{-3}$ and $\frac{{\mathcal B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^0)}{{\mathcal B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^+\pi^-)} < 2.3 \times 10^{-4}$ at the 90% confidence level (CL). Assuming the value ${\mathcal B}(\Upsilon(2S) \rightarrow \Upsilon(1S)\pi^-\pi^+)$ = (17.92$\pm$0.26)%, we obtain $ {\mathcal B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\eta) = (3.57 \pm 0.25 ({\rm stat})\ \pm 0.21 ({\rm syst}))\times 10^{-4} $ and $ {\mathcal B}(\Upsilon(2S)\rightarrow\Upsilon(1S)\pi^0) < 4.1\times 10^{-5}\ ({\rm 90%\ CL}). $