Massive Yang-Mills theory based on the nonlinearly realized gauge group

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 $\otimes$ $SU(2{)}_R$ 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.

Figure 1

A weak-power-counting violating graph.