Does The Lattice Zero Momentum Gluon Propagator for Pure Gauge SU(3) Yang-Mills Theory Vanish in the Infinite Volume Limit?

TL;DR

This study examines the behavior of the gluon propagator at zero momentum in SU(3) Yang-Mills theory, finding evidence for its vanishing in the infinite volume limit, consistent with certain theoretical conditions.

Contribution

The paper provides a robust analysis of the zero momentum gluon propagator in SU(3) gauge theory, supporting the vanishing result and exploring alternative scenarios.

Findings

Zero momentum gluon propagator vanishes in the infinite volume limit.

Results are consistent with the Gribov-Zwanziger horizon condition.

Contradicts similar analysis in SU(2) gauge theory.

Abstract

The Cucchieri-Mendes bounds for the gluon propagator are discussed for the four dimensional pure gauge SU(3) theory. Assuming a pure power law dependence on the inverse of the lattice volume, the lattice data gives a vanishing zero momentum gluon propagator in the infinite volume limit. Our investigation shows that this result is robust against variations of the lattice volumes and corrections to the power law. Moreover, it is consistent with the Gribov-Zwanziger horizon condition and contradicts the SU(2) analysis, which assumed the same type of dependence on the inverse of the volume. Our analysis considers also more general ansatze that, although not conclusive, open the possibility of having $D(0) \ne 0$ in the infinite volume limit. A solution to this puzzle requires further investigations.