[Paper Review] Gluon Mass from Instantons

Marcus Hütter|arXiv (Cornell University)|Jan 18, 1995

Particle physics theoretical and experimental studies2 references3 citations

TL;DR

This paper calculates the momentum-dependent gluon propagator in an instanton background using background-$\xi$-gauge, demonstrating that the gluon acquires a mass of approximately 400 MeV at low momentum ($p^2 \ll 1$), independent of the gauge parameter $\xi$. The result suggests a dynamical gluon mass generation mechanism via nonperturbative instanton effects in QCD.

ABSTRACT

The gluon propagator is calculated in the instanton background in a form appropriate for extracting the momentum dependent gluon mass. In background-$ξ$-gauge we get for the mass $400$MeV for small $p^2$ independent of the gauge parameter $ξ$.

Motivation & Objective

• To investigate the origin of gluon mass in QCD beyond perturbation theory.
• To determine whether instanton configurations in the QCD vacuum can generate a momentum-dependent gluon mass.
• To examine the gauge dependence of the resulting gluon mass in a nonperturbative framework.
• To provide a quantitative estimate of the gluon mass in the low-momentum regime using instanton-induced effects.

Proposed method

• The gluon propagator is computed in the background-field method using the instanton solution as the background gauge field.
• The calculation is performed in background-$\xi$-gauge to ensure gauge invariance and to test the dependence on the gauge parameter $\xi$.
• The momentum-dependent gluon mass is extracted from the full propagator by analyzing its pole structure and effective mass term.
• The analysis focuses on the low-momentum limit ($p^2 \ll 1$) to determine the effective mass scale.
• The formalism is designed to isolate nonperturbative instanton contributions to the gluon self-energy.
• The final result is checked for independence from the gauge parameter $\xi$, confirming gauge invariance of the mass scale.

Experimental results

Research questions

• RQ1 Can instanton configurations in the QCD vacuum generate a non-zero gluon mass?
• RQ2 What is the magnitude of the effective gluon mass at low momentum in the presence of instantons?
• RQ3 Is the resulting gluon mass independent of the gauge parameter $\xi$, indicating gauge invariance?
• RQ4 How does the momentum dependence of the gluon propagator reflect dynamical mass generation?

Key findings

• The gluon acquires a mass of approximately 400 MeV at low momentum ($p^2 \ll 1$) due to instanton-induced effects.
• The calculated gluon mass is independent of the gauge parameter $\xi$, confirming gauge invariance of the result.
• The mass generation mechanism arises from the nonperturbative structure of the instanton background in the gluon propagator.
• The result is derived in background-$\xi$-gauge, ensuring consistency with gauge theory requirements.
• The momentum-dependent mass is extracted from the full propagator, indicating a dynamically generated mass scale.