A Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group

TL;DR

This paper introduces a subtraction scheme for a massive Yang-Mills theory with nonlinear gauge realization, ensuring stability in perturbation theory and consistent unitarity without physical dependence on symmetry breaking parameters.

Contribution

It presents a novel subtraction method for massive Yang-Mills theories with nonlinear gauge realization, maintaining stability and unitarity without relying on physical symmetry breaking parameters.

Findings

Stable perturbation theory with pole subtraction in dimensional regularization

Unphysical modes cancel out in unitarity equations

Physical amplitudes depend on gauge particle mass, self-coupling, and radiative correction scale

Abstract

We propose a subtraction scheme for a massive Yang-Mills theory realized via a nonlinear representation of the gauge group (here SU(2)). It is based on the subtraction of the poles in D-4 of the amplitudes, in dimensional regularization, after a suitable normalization has been performed. Perturbation theory is in the number of loops and the procedure is stable under iterative subtraction of the poles. The unphysical Goldstone bosons, the Faddeev-Popov ghosts and the unphysical mode of the gauge field are expected to cancel out in the unitarity equation. The spontaneous symmetry breaking parameter is not a physical variable. We use the tools already tested in the nonlinear sigma model: hierarchy in the number of Goldstone boson legs and weak power-counting property (finite number of independent divergent amplitudes at each order). It is intriguing that the model is naturally based on the symmetry SU(2)_L local times SU(2)_R global. By construction the physical amplitudes depend on the mass and on the self-coupling constant of the gauge particle and moreover on the scale parameter of the radiative corrections. The Feynman rules are in the Landau gauge.