Resummation scheme for 3d Yang-Mills and the two-loop magnetic mass for hot gauge theories

Abstract

Perturbation theory for non-Abelian gauge theories at finite temperature is plagued by infrared divergences caused by magnetic soft modes $\sim g^{2}T$, which correspond to the fields of a 3d Yang-Mills theory. We revisit a gauge invariant resummation scheme to solve this problem by self-consistent mass generation using an auxiliary scalar field, improving over previous attempts in two respects. First, we generalise earlier SU(2) treatments to SU(N). Second, we obtain a gauge independent two-loop gap equation, correcting an error in the literature. The resulting two-loop approximation to the magnetic mass represents a $\sim 15$ correction to the leading one-loop value, indicating a reasonable convergence of the resummation.

16 pages, 3 figures

References in corpus (4)

• Four-loop screened perturbation theory
• A unitary and renormalizable model for massive Yang-Mills fields without Higgs fields
• Massive gluon propagator at zero and finite temperature
• Gauge-invariant Mass Terms and Wave Functions

Cited by in corpus (9)

• Massless Mode and Positivity Violation in Hot QCD
• Stabilizing perturbative Yang-Mills thermodynamics with Gribov quantization
• Debye screening mass of hot Yang-Mills theory to three-loop order
• Magnetic confinement and the Linde problem
• Recent progress in hard-thermal-loop QCD thermodynamics and collective excitations
• Implementation of chromomagnetic gluons in Yang-Mills thermodynamics
• The regularization and determination of the Yang-Mills vacuum wave functional in three dimensions at O(e^2)
• The Yang-Mills Vacuum Wave Functional in 2+1 Dimensions
• Interplay between chromoelectric and chromomagnetic gluons in Yang-Mills thermodynamics