[Paper Review] Effective Mass Generation of Off-diagonal Gluons as the Origin of Infrared Abelian Dominance in the Maximally Abelian Gauge in QCD

K. Amemiya, Hideo Suganuma|arXiv (Cornell University)|Nov 28, 1998

High-Energy Particle Collisions Research7 citations

TL;DR

This paper identifies the effective mass generation of off-diagonal gluons as the origin of infrared abelian dominance in the maximally abelian (MA) gauge of SU(2) lattice QCD. Using the U(1)₃ Landau gauge fixing, it shows that off-diagonal gluons acquire a mass of approximately 0.94 GeV at distances r ≥ 0.2 fm, explaining why abelian-like dynamics dominate at long distances.

ABSTRACT

We study the origin of the abelian dominance in the maximally abelian (MA) gauge for the long-distance physics in terms of the interaction range mediated by gluons. In the MA gauge, diagonal gluon components behave as neutral gauge fields like photons, and off-diagonal gluon components behave as charged matter fields on the residual abelian gauge symmetry. We study the gluon propagator in the MA gauge with the U(1)$_3$ Landau gauge fixing using the SU(2) lattice QCD with $ 2.2 \\le \\beta \\le 2.4$ and $12^3 \ imes 24$. We find the abelian dominance for the gluon propagator in the MA gauge in the infrared region. The off-diagonal charged gluon behaves as a massive vector boson with the effective mass $M_{\ m ch} \\simeq 0.94$ GeV in the region of $r \\gsim 0.2$ fm. The origin of the infrared abelian dominance is physically explained as the generation of the charged gluon mass $M_{\ m ch}$ induced by the MA gauge fixing, and the charged-gluon mass generation predicts general abelian dominances for the long-distance physics in QCD in the MA gauge.

Motivation & Objective

• To understand the physical origin of infrared abelian dominance in the maximally abelian (MA) gauge of QCD.
• To investigate how the interaction range of gluons contributes to abelian dominance in long-distance QCD physics.
• To determine whether the MA gauge fixing mechanism generates effective masses for off-diagonal gluons.
• To establish a connection between off-diagonal gluon mass generation and the dominance of abelian-like dynamics at infrared scales.

Proposed method

• Performing SU(2) lattice QCD simulations with β values between 2.2 and 2.4 on a 12³ × 24 spatial-temporal lattice.
• Applying the U(1)₃ Landau gauge fixing condition to isolate the maximally abelian gauge configuration.
• Computing the gluon propagator in the MA gauge to analyze the long-distance behavior of diagonal and off-diagonal gluon components.
• Analyzing the spatial dependence of the gluon propagator to extract the effective mass of off-diagonal gluons in the infrared region.
• Using the observed propagator behavior to infer the effective mass of charged gluons via the exponential decay of correlation functions.
• Comparing the behavior of diagonal and off-diagonal gluons to confirm abelian dominance in the infrared limit.

Experimental results

Research questions

• RQ1 What is the physical mechanism responsible for infrared abelian dominance in the maximally abelian gauge of QCD?
• RQ2 How does the MA gauge fixing condition lead to effective mass generation in off-diagonal gluons?
• RQ3 What is the magnitude of the effective mass generated for off-diagonal gluons in the infrared region?
• RQ4 Does the effective mass of off-diagonal gluons explain the dominance of abelian-like dynamics in long-distance QCD?
• RQ5 Can the observed mass generation in off-diagonal gluons be universally linked to abelian dominance in QCD at long distances?

Key findings

• The off-diagonal gluons in the MA gauge acquire an effective mass of approximately 0.94 GeV at distances r ≥ 0.2 fm.
• The gluon propagator in the MA gauge exhibits abelian dominance in the infrared region, with off-diagonal components showing suppressed long-range behavior.
• The effective mass generation of off-diagonal gluons is directly induced by the MA gauge fixing condition.
• The massive behavior of off-diagonal gluons explains the suppression of non-abelian contributions at long distances.
• The observed effective mass supports a general mechanism for abelian dominance in long-distance QCD physics within the MA gauge framework.
• The results confirm that the MA gauge fixing leads to a dynamical mass gap for charged gluons, consistent with infrared abelian dominance.