[Paper Review] Linking Dynamical Gluon Mass to Chiral Symmetry Breaking via a QCD Low Energy Effective Field Theory

Orlando Oliveira, W. de Paula+1 more|arXiv (Cornell University)|May 24, 2011

High-Energy Particle Collisions Research7 references3 citations

TL;DR

This paper proposes a low-energy effective field theory for QCD that introduces a color-octet scalar field to dynamically generate a gluon mass, linking it directly to chiral symmetry breaking. The model predicts that the constituent quark mass is proportional to the square of the gluon mass, with chiral symmetry restoration and deconfinement occurring simultaneously at the same critical temperature, and supports the decoupling solution of the Schwinger-Dyson equations via a constant M/m²g ratio.

ABSTRACT

A low energy effective field theory model for QCD with a scalar color octet field is discussed. The model relates the gluon mass, the constituent quark masses and the quark condensate. The gluon mass comes about $\sqrt{N_c}\, Λ_{QCD}$ with the quark condensate being proportional to the gluon mass squared. The model suggests that the restoration of chiral symmetry and the deconfinement transition occur at the same temperature and that, near the transition, the critical exponent for the condensate is twice the gluon mass one. The model also favors the decoupling like solution for the gluon propagator.

Motivation & Objective

• To establish a dynamical link between the gluon mass and chiral symmetry breaking in the non-perturbative regime of QCD.
• To construct a gauge-invariant, flavor-symmetric effective field theory using a color-octet scalar field as a composite operator of the QCD vacuum.
• To test the model's consistency with non-perturbative QCD solutions, particularly the decoupling solution of the Schwinger-Dyson equations and lattice QCD simulations.
• To predict critical exponents for the gluon mass and quark condensate near the chiral phase transition.
• To explore the phenomenological implications of the new scalar field, including its role in quark mass generation and anomalous magnetic moments.

Proposed method

• Introduces a color-octet scalar field φᵃ as a collective excitation of the QCD vacuum, representing multi-gluon and multi-quark correlations.
• Constructs a gauge-invariant effective Lagrangian with the QCD Lagrangian plus a new color-singlet operator: q̄q φᵃφᵃ, which generates quark mass shifts and the quark condensate.
• Assumes a non-zero vacuum expectation value ⟨φᵃφᵃ⟩ = v²δᵃᵇ, which dynamically generates a gluon mass mg ∝ √Nc ΛQCD and breaks chiral symmetry.
• Derives the constituent quark mass M as proportional to mg², leading to a constant ratio M/mg² in the infrared region.
• Uses the decoupling solution of the Schwinger-Dyson equations as a benchmark to test the M/mg² ratio, using quenched lattice gluon and ghost propagators.
• Analyzes the model's implications for the QCD phase diagram, predicting simultaneous deconfinement and chiral symmetry restoration at the same critical temperature.

Experimental results

Research questions

• RQ1 How can a dynamical gluon mass be consistently linked to chiral symmetry breaking in a low-energy effective QCD model?
• RQ2 What is the functional relationship between the constituent quark mass and the dynamically generated gluon mass in the non-perturbative regime?
• RQ3 Does the model predict a simultaneous deconfinement and chiral symmetry restoration transition, consistent with lattice QCD and phase diagram studies?
• RQ4 Is the predicted M/mg² ratio constant in the infrared, as required by the model and supported by non-perturbative solutions?
• RQ5 How does the inclusion of a color-octet scalar field affect the gluon propagator and its compatibility with the decoupling solution of the Schwinger-Dyson equations?

Key findings

• The model predicts a constituent quark mass M proportional to the square of the gluon mass, with M/mg² approximately constant in the infrared region, consistent with the decoupling solution of the Schwinger-Dyson equations.
• The gluon mass mg is dynamically generated via the vacuum expectation value of the color-octet scalar field, with mg ∝ √Nc ΛQCD, and is linked to the quark condensate via ⟨q̄q⟩ ∝ mg².
• The model predicts that chiral symmetry restoration and deconfinement occur simultaneously at the same critical temperature, in agreement with QCD phase diagram studies.
• The critical exponent for the quark condensate is twice that of the gluon mass near the phase transition, i.e., ηq = 2ηg, a testable prediction for lattice QCD.
• The model favors the decoupling solution of the Schwinger-Dyson equations over the scaling solution, as it matches lattice QCD results and supports a massive infrared gluon.
• The scalar field φᵃ is predicted to have a small mass δmϕ ≲ 76 MeV, potentially explaining the absence of observed physical states and possibly relating to a light scalar resonance seen in BABAR data.