Electroweak Corrections and Unitarity in Linear Moose Models

TL;DR

This work analyzes electroweak corrections in Higgsless models that can be deconstructed into linear moose chains of SU(2) and U(1) gauge groups with localized fermions. By relating four-fermion electroweak amplitudes to the spectrum of vector-boson KK modes and exploiting unitarity constraints, the authors derive closed-form expressions for the relevant correlation functions and electroweak parameters (S, T, δ, Δρ) in terms of heavy-mode sums Σ_i. They show that in Case I (q = N+1) Δρ vanishes and S, T, and δ are controlled by Σ_Z, Σ_W, and related sums, with zero-momentum parameters hat S > 0 and hat T, hat Y fixed by these sums; more generally, S and T combinations obey custodial consistency relations. A key result is that, due to the required heaviness of KK modes to maintain unitarity, the resulting S parameter cannot be small enough to satisfy precision electroweak data, rendering Higgsless moose models with localized fermions disfavored; this conclusion extends beyond the continuum limit to models with only a few extra vector bosons, though it does not apply to Higgs-based 5-D theories where unitarity constraints are absent. The findings highlight a fundamental tension between unitarity in Higgsless theories and EW precision constraints, with implications for deconstructed and higher-dimensional electroweak theories.

Abstract

We calculate the form of the corrections to the electroweak interactions in the class of Higgsless models which can be "deconstructed'' to a chain of SU(2) gauge groups adjacent to a chain of U(1) gauge groups, and with the fermions coupled to any single SU(2) group and to any single U(1) group along the chain. The primary advantage of our technique is that the size of corrections to electroweak processes can be directly related to the spectrum of vector bosons ("KK modes"). In Higgsless models, this spectrum is constrained by unitarity. Our methods also allow for arbitrary background 5-D geometry, spatially dependent gauge-couplings, and brane kinetic energy terms. We find that, due to the size of corrections to electroweak processes in any unitary theory, Higgsless models with localized fermions are disfavored by precision electroweak data. Although we stress our results as they apply to continuum Higgsless 5-D models, they apply to any linear moose model including those with only a few extra vector bosons. Our calculations of electroweak corrections also apply directly to the electroweak gauge sector of 5-D theories with a bulk scalar Higgs boson; the constraints arising from unitarity do not apply in this case.