Studies of Hadron Spectroscopy at Belle and Belle II

TL;DR

Belle and Belle II investigate hadron spectroscopy in the GeV region using initial-state radiation and energy scans near $\Upsilon$ resonances to probe exotic hadronic states beyond conventional $q\bar{q}$. The work reports clear ISR-driven observations of the $Y(4260)$ in $J/\psi\pi^+\pi^-$ and the $Z_c(3900)^{\pm}$ in $\pi J/\psi$, along with a first evidence for $e^+e^- \to \eta \Upsilon(2S)$ near $\Upsilon(10753)$ and a possible near-threshold state near the $B^*\bar{B}^*$ threshold. It also delivers a world-leading precision measurement of the mass difference $\Delta m = m(B^0)-m(B^+)$, constraining quark-model parameters and the isovector $B\bar{B}$ interaction. Collectively, these results showcase Belle II's capabilities for high-precision hadron spectroscopy and set the stage for more extensive studies with larger data samples.

Abstract

The Belle and Belle II experiments have collected an 1.6 ab$^{-1}$ sample of $e^+e^-$ collision data at center-of-mass energies near the $Υ(nS)$ resonances. In particular, the Belle II experiment collected a 19.2 fb$^{-1}$ sample of data at center-of-mass energies near the $Υ(10753)$ resonance. We study the following processes: $e^+e^-\to Υ(nS)η$, $e^+e^-\to γX_b(χ_{bJ}π^+π^-)$, and $e^{+}e^{-}\toχ_{bJ}(1P) γ$. These results provide additional information about the nature of the $Υ(10753)$ resonance and nearby structures. In addition, we measure the $B^{0}$ and $B^+$ meson mass difference, and $σ\left(e^+ e^-\to J/ψp\bar{p}\right)$ over a range of center-of-mass energies accessed via initial-state radiation.

Figures (3)

• Figure 1: (a) Invariant mass distributions of the $\pi \pi J/\psi$ system. The black dots with error bars represent the selected data (signal + background), and the green shaded histograms are background estimates from the normalized $J/\psi$ sidebands. (b) Resonance-model fit to $M_\text{max}(\pi J/\psi)$ in the $\Upsilon(4260)$$M(\pi^+\pi^-J/\psi)$ region. The black dots with error bars represent background-subtracted data, the blue curve represents the total fit, the red dashed curve represents the reweighted MC shape for pure phase-space based on BESIII result at $\sqrt{s} = 4.26\GeV$BESIII_for_ISR, and the red solid curve represents the $Z_c (3900)^\pm$ signal.
• Figure 2: (a) Average center of mass energy $\sqrt{s}$ as a function of time for data collected by Belle II in 2020 and 2021. Taken from BelleII_CM_over_time. (b) Average energy of the colliding beams as a function of the binned average energy of the $B\bar{B}$ pair. The black and red dots correspond to the Belle and Belle II data, respectively. Horizontal error bars indicate $\bar{E}_{B\bar{B}}$ bins, while vertical error bars show statistical uncertainty in $\bar{E}_\text{cm}$.
• Figure 3: (a) $\tilde{M}_{\mathrm{bc}}$ distribution for $B^+$ from Belle shown as black dots. The red solid line represents the fit, the red dashed line the background contribution, and the black dashed line the broken signal, i.e. signal events where one of the final state particles originates from background. (b) Energy dependence of the ratio $\mathcal{R}$ of visible cross sections. The dots with error bars show the direct measurement performed using Belle II data. The vertical inner and outer error bars show statistical and total uncorrelated uncertainties, respectively. The horizontal error bars show statistical uncertainty. The red curve represents the fit result.