[Paper Review] Two-photon decay of light scalars: a comparison of tetraquark and quarkonium assignments

Francesco Giacosa|ArXiv.org|Dec 2, 2007

Quantum Chromodynamics and Particle Interactions2 references6 citations

TL;DR

This paper compares two-photon decay rates of light scalar mesons (f₀(600) and f₀(980)) under quarkonium and tetraquark assignments using SU(3) symmetry and effective Lagrangians. It finds that the two-photon width of f₀(600) is less than 1 keV in both frameworks, indicating that γγ decay rates alone are insufficient to distinguish between quarkonium and tetraquark structures for these states.

ABSTRACT

Two-photon decays of light scalar mesons are discussed within the quarkonium and tetraquark asignements: in both cases the decay rate of the sigma resonances turns out to be smaller than 1 keV.

Motivation & Objective

• To assess whether two-photon decay widths can distinguish between quarkonium and tetraquark interpretations of light scalar mesons.
• To evaluate the consistency of γγ decay rates with SU(3) symmetry and effective field theory in both quarkonium and tetraquark frameworks.
• To test the viability of the tetraquark model by comparing predicted γγ rates with experimental data, especially for f₀(600) and f₀(980).
• To examine the role of next-to-leading-order contributions (quark-antiquark annihilation) in tetraquark γγ decays.

Proposed method

• Uses an effective Lagrangian approach with SU(3) flavor symmetry to compute γγ decay rates for scalar quarkonia, parameterized by coupling constants and mixing angles.
• Applies the same formalism to tetraquark states, including two distinct contributions: quark-line switching (c₁^γγ) and quark-antiquark annihilation (c₂^γγ).
• Derives decay width formulas based on matrix elements of the electromagnetic current, incorporating mass dependence and mixing between bare states.
• Fixes mixing angles φ_S from strong decay data (φ_S = -12.8°) and uses experimental γγ rate ratios to constrain c₂^γγ/c₁^γγ.
• Performs consistency checks using known pseudoscalar nonet decays (π⁰, η, η′) to validate the formalism before applying it to scalars.
• Compares theoretical predictions with experimental data, particularly the γγ width of f₀(980) and the ratio Γ(f₀(980)γγ)/Γ(a₀⁰γγ), to test model viability.

Experimental results

Research questions

• RQ1 What is the predicted two-photon decay width of f₀(600) under the quarkonium assignment, and how does it compare to experimental limits?
• RQ2 Can the tetraquark model reproduce the observed γγ decay rates of light scalars, particularly f₀(600) and f₀(980), with realistic mixing angles?
• RQ3 How do the two contributions (c₁^γγ and c₂^γγ) in the tetraquark Lagrangian affect the γγ decay amplitude, and what constraints do data impose on their ratio?
• RQ4 Does the γγ decay width of f₀(600) remain below 1 keV in both quarkonium and tetraquark models, suggesting a limitation in using this decay mode for state identification?
• RQ5 Is the large mixing angle required by the tetraquark model to fit γγ data consistent with the observed mass degeneracy between a₀(980) and f₀(980)?

Key findings

• The two-photon decay width of f₀(600) is predicted to be less than 1 keV in the quarkonium assignment, consistent with microscopic calculations.
• In the tetraquark model, the γγ width of f₀(600) remains below 1 keV even when including the next-to-leading-order annihilation term (c₂^γγ), with the ratio Γ(f₀(600)γγ)/Γ(a₀⁰γγ) ≤ 0.35.
• The mixing angle φ_S = -12.8°, fixed from strong decays, leads to a γγ width for f₀(600) that is well below 1 keV in the tetraquark framework.
• The inclusion of the c₂^γγ term significantly enhances the amplitude for f_B^{[4q]} → γγ, improving phenomenological consistency despite the small γγ rate.
• The experimental ratio Γ(f₀(980)γγ)/Γ(a₀⁰γγ) ≈ 1.30 ± 0.8 implies a large mixing angle in the tetraquark model, which would break the mass degeneracy between f₀(980) and a₀(980), making this scenario disfavored.
• The study concludes that two-photon decay widths alone are insufficient to distinguish between quarkonium and tetraquark assignments for light scalar mesons, as both predict very small widths for f₀(600).