## Can Electroweak Theory Without A Higgs Particle Be Renormalizable?

J. W. Moffat

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)