Abstract
We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
Highlights
The similarities between the nonlinear sigma (NLσ) model in d = 2 spacetime dimensions and Quantum Chromodynamics (QCD) in d = 4 have been reported long ago
We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge
We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function
Summary
For k of the order of the microscopic scale of the theory, one starts with an O(N )-symmetric potential, strongly peaked around a nonzero value, which ensures that the radial modes are frozen and that only the transverse, pseudo-Goldstone degrees of freedom (d.o.f.) contribute These massless modes lead to large infrared fluctuations which, in d = 2, are strong enough to result in an effective symmetry restoration: the minimum of the effective potential decreases with decreasing k and eventually vanishes below some scale kr. First, that there exists some values of the gauge-fixing parameters for which the symmetry of the NLσ sector is radiatively restored and, second, that, whenever this happens, this results in a nonzero gluon mass at tree level
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