Non-perturbative parton mass for the gluon

TL;DR

This paper introduces a gauge-invariant, non-local observable in pure gauge theory that defines a non-perturbative gluon mass, linking it to heavy quarkonium spectra and providing preliminary numerical estimates.

Contribution

It constructs a gauge-invariant observable equivalent to the gluon propagator, enabling a non-perturbative definition of the gluon mass and connecting it to physical spectra.

Findings

Preliminary numerical estimate of gluon mass in 3d SU(2): 0.37(6)g^2.

Inferred gluon mass in QCD: approximately 420 MeV.

Establishes a relation between gluon mass and heavy quarkonium mass splitting.

Abstract

A gauge invariant, non-local observable is constructed in pure gauge theory, which is identical to the gluon propagator in a particular gauge, permitting to define a non-perturbative parton mass for the gluon. This mass can be shown to be related to the 1P-1S mass splitting of heavy quarkonia. Preliminary numerical results for 3d SU(2) yield m_A=0.37(6)g^2, while from the \bar{b}b spectrum one infers m_A\approx 420 MeV for QCD.