Higgsless Electroweak Symmetry Breaking from Theory Space

TL;DR

Problem: achieve electroweak symmetry breaking without a Higgs while preserving unitarity in $W_LW_L$ scattering. Approach: a deconstructed theory-space chain $U(1)\times [SU(2)]^N\times SU(2)_{N+1}$ with nonlinear Sigma fields and tunable end couplings, whose heavy vector tower restores (delays) unitarity. Key findings: the leading energy-growing term scales as $R \sim {g^2\over (N+1)^2}$, so unitarity violation is postponed; in the $N+1\to\infty$ limit the model becomes a 5D $SU(2)$ gauge theory on an interval with boundary terms, yielding SM-like $W$ and $Z$ as light KK states. Precision constraints, especially on the $S$ parameter, restrict the allowed scale of the heavy states and present a tension for simple fermion embeddings. Significance: demonstrates a calculable Higgsless mechanism with a simpler gauge-sector structure than previous proposals, highlighting both its promise for delaying unitarity violation and the challenges posed by electroweak precision data.

Abstract

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 $Σ$ 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.