Higgsless Electroweak Symmetry Breaking from Theory Space

We investigate unitarity of $W^+W^-$ scattering in the context of theory space models of the form $U(1)\times {[SU(2)]}^N\times SU(2)_{N+1}$, which are broken down to $U(1)_{EM}$ by non-linear $\Sigma$ fields, without the presence of a physical Higgs Boson. By allowing the couplings of the U(1) and the final $SU(2)_{N+1}$ to vary, we can fit the $W$ and $Z$ masses, and we find that the coefficient of the term in the amplitude that grows as $E^2/m_W^2$ at high energies is suppressed by a factor of $(N+1)^{-2}$. In the $N+1\to\infty$ limit the model becomes a 5-dimensional SU(2) gauge theory defined on an interval, where boundary terms at the two ends of the interval break the SU(2) down to $U(1)_{EM}$. These boundary terms also modify the Kaluza-Klein (KK) mass spectrum, so that the lightest KK states can be identified as the $W$ and $Z$ bosons. The $T$ parameter, which measures custodial symmetry breaking, is naturally small in these models. Depending on how matter fields are included, the strongest experimental constraints come from precision electroweak limits on the $S$ parameter.