[Paper Review] Comment on "On the Origin of the OZI Rule in QCD", by N. Isgur and H. B. Thacker

Thomas Schaefer, Edward Shuryak|ArXiv.org|May 30, 2000

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper argues that instantons in QCD explain the sign and magnitude of OZI-violating amplitudes across all mesonic channels—not just the η′ meson—resolving a long-standing issue in hadronic spectroscopy. It demonstrates that instantons predict the correct sign of the scalar channel amplitude, contradicting Isgur and Thacker's initial claim, and shows that instantons are compatible with the large Nc limit, contrary to their conclusion.

ABSTRACT

We comment on the recent paper (hep-lat/0005006) by Isgur and Thacker on the origin of the OZI rule in QCD. We show that instantons explain the sign and magnitude of the observed OZI-violating amplitude in all mesonic channels, not just in the $η'$ channel. We comment on the role of instantons in hadronic spectroscopy and the relation between instantons and the large $N_c$ limit of QCD.

Motivation & Objective

• To clarify the physical origin of the large OZI-violating amplitude in the η′ meson and other mesonic channels.
• To correct the sign of the OZI-violating amplitude in the scalar 0++ channel as claimed by Isgur and Thacker, showing it should be opposite to that in the pseudoscalar channel.
• To demonstrate that instantons are consistent with the large Nc limit of QCD, countering Isgur and Thacker's assertion that large Nc rules out instanton contributions.
• To explain why OZI violation is short-distance in nature, pointing to instantons rather than confinement as the source.
• To highlight phenomenological conspiracies among hadronic amplitudes and show that instantons naturally account for such cancellations.

Proposed method

• Analyzes the effective instanton-induced interaction in QCD using the t’Hooft interaction Lagrangian, which couples to bilinear quark currents with specific isospin and Dirac structure.
• Uses the effective Lagrangian $ L = Gig[(ar{ ho} au_a ho)^2 - (ar{ ho} ho)^2 - (ar{ ho}i ilde{ ho} au_a)^2 + (ar{ ho}i ilde{ ho})^2ig] $ to derive the sign of OZI-violating amplitudes in different channels.
• Compares instanton predictions with lattice QCD results, particularly the topological susceptibility $ \chi_{\text{top}} $, which is shown to be dominated by instantons.
• Applies the Witten-Veneziano relation to connect the $ \eta' $ mass to $ \chi_{\text{top}} $, confirming that instantons explain the $ \eta' $ mass splitting.
• Examines the behavior of hadronic correlation functions in the vector and scalar channels, showing that cancellations between amplitudes are consistent with instanton physics.
• Uses spectral representations and data from $ e^+e^- \to \text{hadrons} $ to verify that duality holds over long distances, implying fine-tuned cancellations explained by instantons.

Experimental results

Research questions

• RQ1 Why is the OZI-violating amplitude in the scalar 0++ channel opposite in sign to that in the pseudoscalar 0-+ channel?
• RQ2 Can instantons explain the magnitude and sign of OZI violation in all mesonic channels, not just the η′ meson?
• RQ3 Are instantons compatible with the large Nc limit of QCD, especially given claims that large Nc and instantons are incompatible?
• RQ4 What is the role of instantons in chiral symmetry breaking and the formation of light scalar mesons like the σ?
• RQ5 Why do hadronic amplitudes conspire to produce approximate duality in correlation functions, and can instantons explain this?

Key findings

• Instantons predict that the OZI-violating amplitude in the scalar 0++ channel is opposite in sign to that in the pseudoscalar 0-+ channel, which matches the corrected result of Isgur and Thacker.
• The magnitude and sign of OZI violation in the η′ channel are explained by instantons, and this mechanism extends to all mesonic channels.
• The topological susceptibility $ \chi_{\text{top}} $, measured in lattice QCD, is dominated by instantons, confirming their role in the $ \eta' $ mass problem.
• Instantons are compatible with the large Nc limit of QCD, particularly in the regime where monopoles condense and Higgs VEVs are tuned to $ O(1/N_c) $, allowing instantons to remain relevant.
• The smallness of OZI violation in the vector channel is explained by the vanishing of direct instanton contributions to disconnected correlators, with corrections suppressed.
• Phenomenological analysis of hadronic correlation functions shows that cancellations between amplitudes—e.g., in the vector channel—require fine-tuning that instantons naturally account for, especially at short distances.