A Three Site Higgsless Model

TL;DR

The paper presents a minimal three-site Higgsless model with an SU(2)×SU(2)×U(1) gauge structure that reproduces a BESS-like gauge sector while focusing on fermion-sector dynamics to achieve ideal fermion delocalization. By solving the gauge and fermion sectors and enforcing ideal delocalization, the authors show that the light fermions couple to the Standard Model W with near-SM strength and that the heavy vector states (W′/Z′) are fermiophobic, allowing them to be relatively light (as low as ~380 GeV) while heavy fermion partners must lie above ~1.8 TeV. They compute one-loop corrections to αT and Z→bb, derive bounds on the heavy spectrum from EW precision data and b→sγ, and construct a large-M EFT with a toy UV completion to explicitly demonstrate decoupling of the bulk fermions. The results illustrate how a very small deconstructed model can capture key Higgsless phenomena and remain compatible with precision constraints, while offering a tractable framework for collider phenomenology and implementation in matrix-element event generators.

Abstract

We analyze the spectrum and properties of a highly-deconstructed Higgsless model with only three sites. Such a model contains sufficient complexity to incorporate interesting physics issues related to fermion masses and electroweak observables, yet remains simple enough that it could be encoded in a Matrix Element Generator program for use with Monte Carlo simulations. The gauge sector of this model is equivalent to that of the BESS model; the new physics of interest here lies in the fermion sector. We analyze the form of the fermion Yukawa couplings required to produce the ideal fermion delocalization that causes tree-level precision electroweak corrections to vanish. We discuss the size of one-loop corrections to b \to s γ, the weak-isospin violating parameter αT and the decay Z \to b \bar{b}. We find that the new fermiophobic vector states (the analogs of the gauge-boson KK modes in a continuum model) can be reasonably light, with a mass as low as 380 GeV, while the extra (approximately vectorial) quark and lepton states (the analogs of the fermion KK modes) must be heavier than 1.8 TeV.

Figures (5)

• Figure 1: Mass-mixing diagram which yields the operator in eqn. (\ref{['eq:seesawmassM']}) when integrating out the bulk fermion (interior fermion line) at tree-level.
• Figure 2: Coupling diagram which yields the operator in eqn. (\ref{['eq:couplingmixM']}) when integrating out the bulk fermion at tree-level.
• Figure 3: Loop Diagram giving the leading contribution to $\alpha T$, as encoded in the operator of eqn. (\ref{['eq:deltarhopM']}).
• Figure 4: Loop Diagram giving leading contribution to the nonuniversal correction to $Z \to b\bar{b}$. Here $\pi$ corresponds to a quantum charged "eaten" Goldstone boson, and the vertex involving the fermions, $\Phi^\dagger_1$ and $\pi$ is to be interpreted using the "background field" method to preserve chiral invariance. This diagram, and those like it, give rise to the operator in eqn. (\ref{['eq:zbbopM']}) in the low-energy theory.
• Figure 5: A potentially large correction to $Z\to b\bar{b}$ in extra-dimensional models Oliver:2002up. Due to ideal delocalization, however, the $W'tb$ coupling vanishes, and this contribution is small in the three site model described here.