Nonlinearly Realized Gauge Group Research Articles

Erratum: One-loop self-energy and counterterms in a massive Yang-Mills theory based on the nonlinearly realized gauge group [Phys. Rev. D77, 105012 (2008)

Erratum: One-loop self-energy and counterterms in a massive Yang-Mills theory based on the nonlinearly realized gauge group [Phys. Rev. D<b>77</b>, 105012 (2008)

Erratum: One-loop self-energies in the electroweak model with a nonlinearly realized gauge group [Phys. Rev. D79, 125028 (2009)

Erratum: One-loop self-energies in the electroweak model with a nonlinearly realized gauge group [Phys. Rev. D<b>79</b>, 125028 (2009)

Of higgs, unitarity and other questions

On the verge of conclusive checks on the Standard Model by the LHC, we discuss some of the basic assumptions. The reason for this analysis stems from a recent proposal of an electroweak model based on a nonlinearly realized gauge group SU(2) ⊗ U(1), where, in the perturbative approximation, there is no Higgs boson. The model enjoys the Slavnov-Taylor identities and therefore the perturbative unitarity. On the other hand, it is commonly believed that the existence of the Higgs boson is entangled with the property of unitarity, when high energy processes are considered. The argument is based mostly on the Froissart bound and on the equivalence theorem. In this paper we briefly review some of our objections to the validity of such arguments. Some open questions are pointed out, in particular on the limit of zero mass for the vector mesons and on the fate of the longitudinal polarizations.

One-loop self-energies in the electroweak model with a nonlinearly realized gauge group

We evaluate at one loop the self-energies for the $W$, $Z$ mesons in the electroweak model where the gauge group is nonlinearly realized. In this model the Higgs boson parameters are absent, while a second mass parameter appears together with a scale for the radiative corrections. We estimate these parameters in a simplified fit on leptons and gauge bosons data. We check physical unitarity and the absence of infrared divergences. Landau gauge is used. As a reference for future higher order computations, the regularized $D$-dimensional amplitudes are provided. Eventually the limit $D\ensuremath{\rightarrow}4$ is taken on physical amplitudes.

THE SU(2) ⊗ U(1) ELECTROWEAK MODEL BASED ON THE NONLINEARLY REALIZED GAUGE GROUP

The electroweak model is formulated on the nonlinearly realized gauge group SU (2) ⊗ U (1). This implies that in perturbation theory no Higgs field is present. This paper provides the effective action at the tree level, the Slavnov–Taylor identity (necessary for the proof of physical unitarity), the local functional equation (used for the control of the amplitudes involving the Goldstone bosons) and the subtraction procedure (nonstandard, since the theory is not power-counting renormalizable). Particular attention is devoted to the number of independent parameters relevant for the vector mesons; in fact, there is the possibility of introducing two mass parameters. With this choice the relation between the ratio of the intermediate vector meson masses and the Weinberg angle depends on an extra free parameter. We briefly outline a method for dealing with γ5 in dimensional regularization. The model is formulated in the Landau gauge for sake of simplicity and conciseness. The QED Ward identity has a simple and intriguing form.

One-loop self-energy and counterterms in a massive Yang-Mills theory based on the nonlinearly realized gauge group

In this paper we evaluate the self-energy of the vector mesons at one loop in our recently proposed subtraction scheme for massive nonlinearly realized SU(2) Yang-Mills theory. We check the fulfillment of physical unitarity. The resulting self-mass can be compared with the value obtained in the massive Yang-Mills theory based on the Higgs mechanism, consisting in extra terms due to the presence of the Higgs boson (tadpoles included). Moreover we evaluate all the one-loop counterterms necessary for the next order calculations. By construction they satisfy all the equations of the model (Slavnov-Taylor, local functional equation and Landau gauge equation). They are sufficient to make all the one-loop amplitudes finite through the hierarchy encoded in the local functional equation.

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 $D\ensuremath{-}4$ 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 $\ensuremath{\bigotimes}$ $SU(2{)}_{R}$ 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.