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 ⊗ 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.

Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled to the nonlinear sigma model constraint (flat connection formalism).The construction is based on a local functional equation, which overcomes the problems due to the presence (already at one loop) of non chiral symmetric divergences. The subtraction procedure of the divergences in the loop expansion is performed by means of minimal subtraction of properly normalized amplitudes in dimensional regularization.In this paper we complete the study of this subtraction procedure by giving the formal proof that it is symmetric to all orders in the loopwise expansion. We provide further arguments on the issue that, within our subtraction strategy, only two parameters can be consistently used as physical constants. 1

In the present paper, that is the second part devoted to the construction of an electroweak model based on a nonlinear realization of the gauge group SU (2)⊗U (1), we study the tree-level vertex functional with all the sources necessary for the functional formulation of the relevant symmetries (Local Functional Equation, Slavnov-Taylor identity, Landau Gauge Equation) and for the symmetric removal of the divergences. The Weak Power Counting criterion is proven in the presence of the novel sources. The local invariant solutions of the functional equations are constructed in order to represent the counterterms for the one-loop subtractions. The bleaching technique is fully extended to the fermion sector.The neutral sector of the vector mesons is analyzed in detail in order to identify the physical fields for the photon and the Z boson. The identities necessary for the decoupling of the unphysical modes are fully analyzed. These latter results are crucially bound to the Landau gauge used throughout the paper.