[Paper Review] Developments in heavy quarkonium spectroscopy

S. Eidelman, J.J. Hernandez+3 more|arXiv (Cornell University)|May 18, 2012

Quantum Chromodynamics and Particle Interactions10 citations

TL;DR

This paper summarizes recent experimental advances in heavy quarkonium spectroscopy from 2010 to 2012, focusing on newly observed states such as the $h_{b}(1P)$, $h_{b}(2P)$, $ heta_{b}(10860)$, and $ar{b}c$ states, along with the first observation of $ar{b}c$ states at the LHC. Key results include the confirmation of the $ heta_{b}(10860)$ via dipion transitions, precise mass measurements of $ heta_{b}$ states, and the first observation of $ar{b}c$ states at the LHC, significantly advancing the understanding of bottomonium and charmonium spectroscopy.

ABSTRACT

We summarize recent developments in heavy quarkonium spectroscopy, relying on previous review articles for the bulk of material available prior to mid-2010. This note is intended as a mini-review to appear in the 2012 Review of Particle Physics published by the Particle Data Group.

Motivation & Objective

• To summarize recent experimental developments in heavy quarkonium spectroscopy not covered in prior reviews, particularly those from 2010 onward.
• To report on the discovery and characterization of new conventional quarkonium states, including $h_{b}(1P)$, $h_{b}(2P)$, and $ heta_{b}(10860)$, in bottomonium and charmonium systems.
• To present the first observation of $ar{b}c$ states at the LHC via $pp$ collisions, detected through $ar{b}c \to \gamma \Upsilon(1S,2S)$ decays.
• To refine the mass and branching fraction measurements of the $ heta_{b}(10860)$ and $ heta_{b}(10890)$ states through dipion transitions from $eta(5S)$ and $eta(3S)$ decays.
• To improve the world average of the $ heta_{b}(10860)$ mass and hyperfine splitting by combining new data from Belle and Baryon-antibaryon experiments.

Proposed method

• Utilized data from BESIII, Belle, CLEO, B-Factory, and ATLAS experiments to identify new quarkonium states via invariant mass reconstruction and peak fitting.
• Applied Dalitz plot analysis to study ${{ m ar{b}c}} \to \pi^+ \pi^- \Upsilon(1S)$ and ${{ m ar{b}c}} \to \pi^+ \pi^- \Upsilon(2S)$ transitions, identifying resonant structures consistent with $Z_b^+$ states.
• Performed angular analysis on $\pi^+ \pi^-$ final states to determine quantum numbers, favoring $J^P = 1^+$ for $Z_b^+$ states and confirming negative $G$-parity.
• Reconstructed $\Upsilon(1S)$ and $\Upsilon(2S)$ via $\mu^+ \mu^-$ decay and combined with photons to identify $\chi_{bJ}(nP)$ states in $pp$ collisions at $\sqrt{s} = 7$ TeV.
• Used $e^+e^-$ and $pp$ collision data to extract $\eta_b(1S)$ mass and $h_b(1P) \to \gamma \eta_b(1S)$ branching fraction via recoil mass analysis.
• Combined multiple experimental measurements using inverse-square-error-weighted averaging with $\chi^2$-based uncertainty inflation to improve world averages.

Experimental results

Research questions

• RQ1 What are the properties of the newly observed $h_{b}(1P)$ and $h_{b}(2P)$ states in bottomonium spectroscopy?
• RQ2 Can the $Z_b^+$ states observed in $\Upsilon(5S)$ decays be consistently described as molecular states with $J^P = 1^+$ and negative $G$-parity?
• RQ3 What is the mass and branching fraction of the $h_b(1P) \to \gamma \eta_b(1S)$ transition, and how does it affect the hyperfine splitting?
• RQ4 How do the $\chi_{bJ}(3P)$ states manifest in $pp$ collisions at the LHC, and what is their significance in the context of bottomonium spectroscopy?
• RQ5 What is the role of $\theta_b$ states in the $\Upsilon(5S)$ decay, and how do their masses and widths compare across different experiments?

Key findings

• The $h_{b}(1P)$ state was observed by Belle in $\Upsilon(5S) \to \pi^+ \pi^- h_b(1P)$ with a significance of 5.5 $\sigma$, confirming its existence and assigning it $J^{PC} = 1^{+-}$.
• The $h_{b}(2P)$ state was observed by Belle in $\Upsilon(5S) \to \pi^+ \pi^- h_b(2P)$ with a significance of 11.2 $\sigma$, establishing it as a new excited bottomonium state.
• The $\theta_b(10860)$ state was confirmed via dipion transitions from $\Upsilon(5S)$, with a mass of $10860 \pm 2$ MeV and a width of $15 \pm 2$ MeV, consistent with a $J^P = 1^+$ assignment.
• The $\theta_b(10890)$ state was observed with a mass of $10890 \pm 2$ MeV and a width of $12 \pm 2$ MeV, also consistent with $J^P = 1^+$ and negative $G$-parity.
• The $\eta_b(1S)$ mass was measured by Belle as $9391.0 \pm 2.8$ MeV, with a $h_b(1P) \to \gamma \eta_b(1S)$ branching fraction of $(49.8 \pm 6.8^{+10.9}_{-5.2})\%$, reducing the world average hyperfine splitting by nearly 5 MeV.
• The $\chi_{bJ}(3P)$ triplet was observed at the LHC by ATLAS in $pp$ collisions at $\sqrt{s} = 7$ TeV, with a significance exceeding 6 $\sigma$ for both unconverted and converted photons, marking the first observation of this state.