Search for $h_b(2P)\to\gamma\chi_{bJ}(1P)$ at $\sqrt{s} = 10.860$ GeV

TL;DR

This study searches for hindered M1 transitions in bottomonium, setting upper limits on their branching fractions, which constrains coupled-channel models predicting enhanced transition rates.

Contribution

First experimental search for $h_b(2P) o \gamma\, ext{chi}_{bJ}(1P)$ transitions, providing upper limits that inform theoretical models.

Findings

No significant signals found for the transitions.

Upper limits set on branching fractions at 90% CL.

Results constrain parameters of coupled-channel models.

Abstract

In the bottomonium sector, the hindered magnetic dipole (M1) transitions between P-wave states $h_b(2P) \rightarrow \chi_{bJ}(1P) \gamma$, $J=0, \, 1, \, 2$, are expected to be severely suppressed according to the Relativized Quark Model, due to the spin flip of the $b$ quark. Nevertheless, a recent model following the coupled-channel approach predicts the corresponding branching fractions to be enhanced by orders of magnitude. In this Letter, we report the first search for such transitions. We find no significant signals and set upper limits at 90% CL on the corresponding branching fractions: $\mathcal{B}[h_b(2P)\to\gamma\chi_{b0}(1P)] < 2.7 \times 10^{-1}$, $\mathcal{B}[h_b(2P)\to\gamma\chi_{b1}(1P)] < 5.4 \times 10^{-3}$ and $\mathcal{B}[h_b(2P)\to\gamma\chi_{b2}(1P)] < 1.3 \times 10^{-2}$. These values help to constrain the parameters of the coupled-channel models. The results are obtained using a $121.4 \, fb^{-1}$ data sample taken around $\sqrt{s}= 10.860 \, GeV$ with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.