Studies of hadron spectroscopy at Belle and Belle II

TL;DR

This work leverages the Belle and Belle II datasets, including a data sample of about $1.6\ \mathrm{ab}^{-1}$ collected near Υ resonances, to probe bottomonium transitions and search for strange-charmed exotics. It reports the first evidence for the spin-symmetry-forbidden transition $h_b(2P)\to Υ(1S)η$ with a branching fraction of about $7.1\times 10^{-3}$, while isospin-violating decays remain unobserved, challenging models with large hadronic-loop contributions. The analysis also observes $P_{c\bar{c}s}(4459)^0 \to J/ψΛ$ in inclusive Υ(1S,2S) decays, with mass and width compatible with LHCb measurements, and sets limits on $P_{c\bar{c}s}(4338)^0$. Together, these results demonstrate Belle/Belle II’s strong potential for hadron spectroscopy and Exotic-State searches, laying groundwork for future, more precise studies with larger data samples.

Abstract

The Belle and Belle II experiments have collected a $1.6\,\mathrm{ab}^{-1}$ sample of $e^+e^-$ collision data at center-of-mass energies near the $Υ(nS)$ resonances. We conduct searches for transitions from the spin-singlet $h_b(1P,2P)$ states to the spin-triplet $Υ(1S)$ and $χ_{bJ}(1P)$ states. We do not find evidence for the $h_b(1P,2P)\to Υ(1S) π^0$ and $h_b(2P) \to χ_{bJ}(1P)γ$ transitions. We find the first evidence for the $h_b(2P)\to Υ(1S)η$ transition. However, the measured branching fraction is lower than expected from related decays. Furthermore, we find evidence for $P_{c\bar c s}(4459)^0 \to J/ψΛ$ decays in inclusive $Υ(1S,2S)$ decays. This is the first evidence for an exotic state produced in $Υ(1S,2S)$ decays.

Figures (3)

• Figure 1: Kinematic distributions in the process $\Upsilon(5S) \to h_b(2P) \pi^+\pi^-$ with $h_b(2P) \to \Upsilon(1S)\eta$. \ref{['fig:U1:2d']} shows the distribution in the invariant mass $M_{\gamma\gamma}$ of the $\gamma\gamma$ system in the decay $\eta\to\gamma\gamma$ versus the invariant mass $M_{\pi\pi}^\mathrm{rec}$ of the system recoiling against the $\pi^+\pi^-$ system, which corresponds to the $h_b(2P)$ decay products, but is calculated from the measured momenta of the $\pi^-$ and $\pi^+$ and the well-known $e^+e^-$ initial state using 4-momentum conservation. The green rectangle indicates the signal region. The red triangular markers show events where $\Upsilon(1S)\to e^+e^-$. The black square markers show events where $\Upsilon(1S)\to e^+e^-$. \ref{['fig:U1:1d']} shows the $M_{\pi\pi}^\mathrm{rec}$ distribution. The red curve indicates the $h_b(2P) \to\Upsilon(1S) \eta$ signal model. The violet curve indicates background from $\Upsilon(5S)\to \chi_{bJ}(1P) \pi^+\pi^-\pi^0$ decays. The blue curve indicates the total model. Taken from ref. Belle:2024qmw.
• Figure 2: Kinematic distribution in the process $\Upsilon(5S) \to h_b(2P) \pi^+\pi^-$ with $h_b(2P) \to \chi_{bJ}(1P) \gamma_1$ and $\chi_{bJ}(1P) \to \Upsilon(1S)\gamma_2$. The vertical axis shows the difference of the invariant masses of the $h_b(2P)$ decay products ($M(\mu\mu\gamma_1\gamma_2)$) and the $\chi_{bJ}$ decay products ($M(\mu\mu\gamma_2)$). The horizontal axis shows the invariant mass $M_\mathrm{rec}(\pi^+\pi^-)$ of the system recoiling against the $\pi^+\pi^-$ system, which corresponds to the $h_b(2P)$ decay products, but is calculated from the measured momenta of the $\pi^-$ and $\pi^+$ and the well-known $e^+e^-$ system using 4-momentum conservation. The orange histogram shows the experimental data. The blue histogram shows the expected background. The red dashed rectangle indicates the signal region. The blue dashed lines indicate the blinded region where where $e^+e^-\to\Upsilon(5S)\to \Upsilon_J(1D)\pi^+\pi^-$ decay may be observed. Taken from ref. Belle:2024jta.
• Figure 3: Kinematic distributions in the inclusive process $\Upsilon(1S,2S) \to P_{c\bar{c} s} + X \to J/\psi \Lambda + X$, where the $J/\psi$ decays to $\ell^+\ell^-$ and the $\Lambda$ to $p \pi^-$. \ref{['fig:Pcc:2D']} shows the distribution in the invariant mass of the $\Lambda$ decay products versus the invariant mass of the $J/\psi$ decay products for $\Upsilon(1S)$ decays. The red box indicates the signal region. The blue and green boxes indicate the sideband regions. For the analogous plot for $\Upsilon(2S)$ decays see fig. 1.(b) in ref. Belle:2025pey. \ref{['fig:Pcc:M2']} shows the distribution in the invariant mass of the $J/\psi \Lambda$ system combined for $\Upsilon(1S)$ and $\Upsilon(2S)$ decays. The black markers show the real data in the signal region. The orange histogram shows the background estimated from the two-dimensional sideband regions. The solid curve indicates the total fit result. The red dashed curve indicates the signal. The brown dashed curve indicates the no-$P_{c\bar{c} s}$ component. The green dashed curve indicates the background from the sidebands. Taken from ref. Belle:2025pey.