Deconstructed Higgsless Models with One-Site Delocalization

TL;DR

The paper investigates deconstructed Higgsless models with one-site delocalization, showing that the electroweak parameter $\alpha S$ can be tuned small by appropriately distributing fermion couplings across adjacent SU(2) sites. It directly computes off-$Z$-pole corrections via $\alpha \delta$ arising from KK-mode exchanges within the deconstructed setup and demonstrates that achieving a small $\alpha S$ does not automatically guarantee a small $\alpha\delta$, imposing a bound on the allowed delocalization (about 25% at 95% CL). Through analytic calculations in the limit $g_0,g_{N+1}\ll g_i$ and a four-site numerical example, the work reveals the trade-offs between unitarizing longitudinal $W$ scattering and staying within EW precision constraints. The results illuminate the viability and limitations of Higgsless frameworks with fermion delocalization and connect to broader themes in technicolor/ETC model building, motivating future multi-site analyses. The methodology provides a concrete bridge between deconstruction and continuum approaches, enabling precise, testable predictions for electroweak observables across energy scales.

Abstract

In this note we calculate the form of electroweak corrections in deconstructed Higgsless models for the case of a fermion whose weak properties arise from two adjacent SU(2) groups on the deconstructed lattice. We show that, as recently proposed in the continuum, it is possible for the value of the electroweak parameter alpha S to be small in such a model. In addition, by working in the deconstructed limit, we may directly evaluate the size of off-Z-pole electroweak corrections arising from the exchange of Kaluza-Klein modes; this has not been studied in the continuum. The size of these corrections is summarized by the electroweak parameter alpha delta. In one-site delocalized Higgsless models with small values of alpha S, we show that the amount of delocalization is bounded from above, and must be less than 25% at 95% CL. We discuss the relation of these calculations to our previous calculations in deconstructed Higgsless models, and to models of extended technicolor. We present numerical results for a four-site model, illustrating our analytic calculations.