  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 $E_s < \mu=\lambda^{1/2}M_W$,
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 $E < \mu=\lambda^{1/2}M_W$ for which the scalar bosons have decoupled and
they 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.
