[Paper Review] QCD phenomenology with infrared finite SDE solutions

A. A. Natale|arXiv (Cornell University)|Oct 29, 2009

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes a consistent framework—Dynamical Perturbation Theory (DPT)—to incorporate infrared-finite Schwinger-Dyson equation (SDE) solutions with a dynamically generated gluon mass into perturbative QCD. By using IR-finite gluon propagators and coupling constants, the approach eliminates unphysical singularities and successfully fits experimental hadronic data across diverse processes, yielding a dynamical gluon mass of $ m_g \approx 300-400 \, \text{MeV} $, consistent with lattice QCD and Cornwall's earlier predictions.

ABSTRACT

Recent progress in the solution of Schwinger-Dyson equations (SDE), as well as lattice simulation of pure glue QCD, indicate that the gluon propagator and coupling constant are infrared (IR) finite. We discuss how this non-perturbative information can be introduced into the QCD perturbative expansion in a consistent scheme, showing some examples of tree level hadronic reactions that successfully fit the experimental data with the gluon propagator and coupling constant depending on a dynamically generated gluon mass. This infrared mass scale acts as a natural cutoff and eliminates some of the ad hoc parameters usually found in perturbative QCD calculations. The application of these IR finite Green's functions in the case of higher order terms of the perturbative expansion is commented.

Motivation & Objective

• To address the unphysical infrared singularities in perturbative QCD caused by the Landau pole in the coupling constant.
• To incorporate non-perturbative SDE and lattice QCD results—showing an infrared-finite gluon propagator and coupling—into a consistent perturbative framework.
• To test whether a dynamically generated gluon mass scale can improve agreement between theoretical predictions and experimental hadronic observables.
• To reduce reliance on ad hoc parameters in phenomenological QCD calculations by introducing a natural infrared cutoff via the dynamical gluon mass.
• To explore the viability of the DPT scheme for higher-order corrections using IR-finite Green’s functions.

Proposed method

• Adopt the Dynamical Perturbation Theory (DPT) scheme to embed non-perturbative SDE solutions with a dynamical gluon mass into perturbative QCD calculations.
• Use an infrared-finite gluon propagator of the form $ D_{\mu\nu}(k^2) \propto \frac{P_{\mu\nu}(k^2)}{k^2 + m_g^2} $, where $ m_g $ is a dynamically generated mass scale.
• Employ an effective coupling constant $ \bar{\alpha}_{sd}(0) = \frac{1}{4\pi b \ln(4m_g^2 / \Lambda^2)} $, which remains finite in the infrared.
• Apply the IR-finite propagator and coupling to tree-level hadronic processes such as nucleon beta decay and the Bjorken sum rule.
• Fit experimental data—e.g., from Jefferson Lab on $ \Gamma^{p-n}_1(Q^2) $—to extract the gluon mass scale $ m_g $.
• Assess the impact of the dynamical mass on higher-order corrections, suggesting that power corrections may be softened by the IR-finite structure.

Experimental results

Research questions

• RQ1 Can the infrared-finite gluon propagator and coupling constant from SDE and lattice QCD be consistently embedded into perturbative QCD using DPT?
• RQ2 Does the inclusion of a dynamically generated gluon mass improve the agreement between theoretical predictions and experimental data in hadronic processes?
• RQ3 What is the quantitative value of the dynamical gluon mass scale $ m_g $, and is it consistent across different observables with varying energy and mass scales?
• RQ4 How does the DPT scheme with IR-finite Green’s functions affect the behavior of higher-order perturbative corrections in QCD?
• RQ5 Can the DPT framework reduce the number of arbitrary parameters typically required in phenomenological QCD models?

Key findings

• The effective coupling constant $ \bar{\alpha}_{sd} $, derived from experimental data on the nucleon structure function $ \Gamma^{p-n}_1(Q^2) $, shows an excellent fit with the IR-finite form predicted by SDE and lattice QCD.
• The extracted dynamical gluon mass scale is $ m_g \approx 300-400 \, \text{MeV} $, consistent with previous phenomenological estimates and Cornwall’s earlier predictions.
• The IR-finite coupling and propagator structure eliminate unphysical Landau singularities and provide a natural infrared cutoff, reducing reliance on ad hoc parameters.
• The agreement between theory and experiment is impressive across different processes and energy scales, suggesting a universal dynamical gluon mass scale of order $ 2\Lambda_{QCD} $.
• Preliminary analysis indicates that the DPT approach with IR-finite Green’s functions may soften power corrections and improve convergence of the perturbative series.
• The results strongly support the existence of a dynamically generated gluon mass in QCD, corroborating SDE and lattice QCD findings.