Whether there exists a massive electroweak (EW) theory, without a Higgs spontaneous symmetry breaking mechanism, that is gauge invariant and renormalizable is investigated. A Stueckelberg formalism for massive \(W\) and \(Z\) bosons is used to derive a gauge invariant EW theory. Negative energy scalar fields that emerge from the gauge invariance of the Lagrangian are removed by invoking an indefinite metric in Hilbert space. A unitary S-matrix and a positive energy spectrum can be obtained by using the PT symmetric formulation of the pseudo-Hermitian Hamiltonian. The theory predicts that if for a system of particles the scalar boson energy \(E_s < \lambda^{1/2}M_W\), where \(\lambda\) is a gauge parameter and \(M_W\) is the \(W\) boson mass, then as \(\lambda\rightarrow\infty\) the scalar boson mass \(\mu=\lambda^{1/2}M_W\) tends to infinity. The theory is perturbatively renormalizable and does not violate longitudinally polarized \(W_L W_L\rightarrow W_L W_L\) scattering in the energy range \(E < \lambda^{1/2}M_W\) for which the scalar bosons have an undetected mass. This means that with this scenario the EW theory can only be treated as an effective renomalizable theory and not as a UV complete theory.

http://arxiv.org/abs/1109.5383
High Energy Physics – Phenomenology (hep-ph); High Energy Physics – Theory (hep-th)