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 arecent proposal of an electroweak model based on a nonlinearly realized gauge group $\mathrm{SU}(2)\otimes\mathrm U(1)$, 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.