[Paper Review] Observation of the bottomonium ground state, eta_b, at BaBar

P. Grenier|arXiv (Cornell University)|Sep 9, 2008

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper reports the first observation of the bottomonium ground state, η_b(1S), via the radiative decay Υ(3S) → γη_b in 109 million Υ(3S) events collected by the BaBar experiment at SLAC. The signal, observed at a photon energy of 921.2 ± 2.1(stat) ± 2.4(syst) MeV, corresponds to an η_b mass of 9388.9 ± 3.1(stat) ± 2.7(syst) MeV/c² and a hyperfine splitting of 71.4 ± 2.3(stat) ± 2.7(syst) MeV/c², with a branching fraction of (4.8 ± 0.5 ± 1.2) × 10⁻⁴.

ABSTRACT

We present the first observation of the bottomonium ground state eta_b(1S) in the photon energy spectrum using a sample of 109+/-1 million of Upsilon(3S) events recorded at the Upsilon(3S) energy with the BaBar detector at the PEP-II B factory at SLAC. A peak at E_gamma = 921.2 {+2.1}{-2.8}(stat) +/- 2.4(syst) MeV observed with a significance of 10 standard deviations in the photon energy spectrum is interpretated as being due to the radiative transition Upsilon(3S) -> gamma eta_b(1S). This photon energy corresponds to an eta_b(1S) mass of 9388.9 {+3.1}{-2.3}(stat) +/- 2.7(syst) MeV/c2. The hyperfine Upsilon(1S)-eta_b(1S) mass splitting is 71.4 {+2.3}{-3.1}(stat) +/- 2.7(syst) MeV/c2. The branching fraction for this radiative Υ(3S) decay is obtained as (4.8 +/- 0.5(stat) +/- 1.2 (syst)) x 10^(-4).

Motivation & Objective

• To observe the long-sought bottomonium ground state η_b(1S), which had not been detected despite decades of bottomonium spectroscopy.
• To measure the hyperfine splitting between the Υ(1S) and η_b(1S) states, a key test of QCD models and spin-dependent interactions.
• To determine the branching fraction for the radiative decay Υ(3S) → γη_b, providing a benchmark for theoretical calculations.
• To validate the signal interpretation by distinguishing it from dominant background sources, including χ_bJ(2P) and ISR processes.

Proposed method

• A binned maximum likelihood fit was performed on the inclusive photon energy spectrum in the center-of-mass frame to extract the signal.
• Background contributions were modeled as a non-peaking continuum (from q̄q and bottomonium decays) and two peaking components: χ_bJ(2P) → γΥ(1S) and ISR γ_ISRΥ(1S).
• Signal selection used kinematic and topological criteria: minimum four tracks, Fox-Wolfram moment ratio < 0.98, photon isolation, and angular cuts on thrust axis to suppress continuum events.
• A veto on π⁰ → γγ decays was applied by rejecting photon pairs with invariant mass within 15 MeV of the π⁰ mass.
• The signal PDF was modeled as a Gaussian with a width fixed at 10 MeV, based on theoretical estimates, and the fit included calibration of the photon energy scale using the χ_bJ(2P) peak position.
• Systematic uncertainties were evaluated by varying the η_b width (5–20 MeV), ISR yield, and PDF parameters within ±1σ.

Experimental results

Research questions

• RQ1 Can the η_b(1S) ground state be observed in the radiative decay Υ(3S) → γη_b?
• RQ2 What is the precise mass of the η_b(1S) state, and how does it compare to theoretical predictions?
• RQ3 What is the hyperfine splitting between the Υ(1S) and η_b(1S) states, and how does it constrain QCD models?
• RQ4 What is the branching fraction for the decay Υ(3S) → γη_b, and how does it compare to theoretical expectations?

Key findings

• The η_b(1S) was observed with a significance of 10 standard deviations in the photon energy spectrum.
• The signal peak is located at E_γ = 921.2 ± 2.1(stat) ± 2.4(syst) MeV, corresponding to an η_b mass of 9388.9 ± 3.1(stat) ± 2.7(syst) MeV/c².
• The hyperfine splitting between Υ(1S) and η_b(1S) is measured as 71.4 ± 2.3(stat) ± 2.7(syst) MeV/c².
• The branching fraction for Υ(3S) → γη_b is (4.8 ± 0.5 ± 1.2) × 10⁻⁴, with the dominant systematic uncertainty arising from reconstruction efficiency.
• The photon energy calibration was determined to be 3.8 ± 2.0 MeV by comparing the χ_bJ(2P) peak position to the PDG value.
• The signal yield was measured as 19,200 ± 2,000(stat) ± 2,100(syst) events, confirming a robust observation.