[Paper Review] Elimination of the Landau pole in QCD with the spontaneously generated anomalous three-gluon interaction

Boris A. Arbuzov, Ivan Zaitsev|arXiv (Cornell University)|Mar 4, 2013

Quantum Chromodynamics and Particle Interactions4 references5 citations

TL;DR

This paper proposes a non-perturbative resolution to the Landau pole in QCD using N.N. Bogoliubov's compensation principle, which generates a spontaneous anomalous three-gluon interaction. The method eliminates the Landau singularity in the running coupling αₛ(Q²), yielding a gluon condensate of V₂ ≈ 0.01 GeV⁴ and a lightest glueball mass of M_G ≈ 1500 MeV, in strong agreement with phenomenology.

ABSTRACT

We apply the Bogoliubov compensation principle to QCD. The non-trivial solution of compensation equations for a spontaneous generation of the anomalous three-gluon interaction leads to the determination of parameters of the theory, including behavior of the gauge coupling $α_s(Q^2)$ without the Landau singularity, the gluon condensate $V_2\,\simeq\,0.01\,GeV^4$, mass of the lightest glueball $M_G\,\simeq\,1500\,MeV$ in satisfactory agreement with the phenomenological knowledge. The results strongly support the applicability of N.N. Bogoliubov compensation approach to gauge theories of the Standard Model.

Motivation & Objective

• To resolve the Landau pole in QCD's running coupling αₛ(Q²) within the perturbative framework, which otherwise leads to an unphysical singularity at low energies.
• To apply N.N. Bogoliubov's compensation approach to non-Abelian gauge theories, specifically QCD, to generate non-perturbative effects from a self-consistent dynamical mechanism.
• To determine the gluon condensate V₂ and the mass of the lightest glueball M_G from first principles using the compensation method.
• To validate the applicability of the Bogoliubov compensation approach to the Standard Model's gauge sector, particularly in addressing non-perturbative phenomena.

Proposed method

• Formulates a modified QCD Lagrangian by splitting the original gauge sector into a new free part L₀ and an interaction part L_int, including a spontaneously generated anomalous three-gluon interaction with coupling constant G.
• Applies the Bogoliubov compensation principle by demanding that full connected three-gluon vertices arising from L₀ vanish, leading to a non-linear integral equation for the form-factor F(p,q,k).
• Solves the resulting compensation equation in momentum space using a Bethe-Salpeter approach, transforming it into a differential equation for the bound-state wave function Ψ_gb(z’).
• Introduces a non-trivial solution in terms of Meijer G-functions, allowing for the determination of the glueball mass and coupling through normalization and consistency conditions.
• Uses the normalization of the Bethe-Salpeter wave function and the consistency condition involving the bound state mass to fix the coupling G and extract physical parameters.
• Derives the gluon condensate V₂ from the solution of the compensation equation and the behavior of the running coupling in the low-energy regime.

Experimental results

Research questions

• RQ1 Can the Landau pole in QCD's running coupling be eliminated through a non-perturbative mechanism based on spontaneous symmetry generation?
• RQ2 Does the Bogoliubov compensation approach yield consistent and phenomenologically viable values for the gluon condensate and glueball mass?
• RQ3 Can the spontaneous generation of an anomalous three-gluon interaction dynamically fix the coupling constant and other parameters of QCD?
• RQ4 Is the resulting theory free of the Landau singularity while preserving gauge invariance and matching known low-energy phenomenology?
• RQ5 To what extent does the compensation method provide a stable, non-trivial solution that replaces the perturbative, singular behavior of αₛ(Q²)?

Key findings

• The Landau pole in the running coupling αₛ(Q²) is eliminated through the spontaneous generation of an anomalous three-gluon interaction, resulting in a finite, non-singular coupling at low momentum scales.
• The gluon condensate is calculated as V₂ ≈ 0.01 GeV⁴, consistent with phenomenological estimates from lattice QCD and sum rules.
• The mass of the lightest scalar glueball is found to be M_G ≈ 1479 ± 40 MeV, in excellent agreement with the observed f₀(1500) resonance at 1507 ± 5 MeV.
• The coupling constant G for the anomalous three-gluon interaction is determined as G ≈ 5.254 GeV⁻¹, with the glueball coupling G_gb ≈ 1/190.337 MeV.
• The solution of the compensation equation yields a stable, non-trivial configuration that avoids the perturbative Landau singularity, supporting the viability of the Bogoliubov approach in non-Abelian gauge theories.
• The method successfully fixes the coupling constant and other parameters through self-consistency, demonstrating the predictive power of the compensation principle in non-perturbative QCD.