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

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.

44 pages, 1 figure, minor changes, final version accepted by Phys. Rev. D

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• One-loop Self-energies in the Electroweak Model with Nonlinearly Realized Gauge Group
• On the Renormalization of the Complex Scalar Free Field Theory
• Physical unitarity for a massive Yang-Mills theory without the Higgs field: (I) A perturbative treatment
• On the predictivity of the non-renormalizable quantum field theories
• A nonperturbative construction of massive Yang-Mills fields without Higgs fields
• The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories
• The Stueckelberg Mechanism in the presence of Physical Scalar Resonances
• A non-perturbative study of massive gauge theories
• The Electroweak Model based on the Nonlinearly realized Gauge Group. Theoretical Foundations and Phenomenological Prospects
• Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
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