Ideal Fermion Delocalization in Higgsless Models

TL;DR

This paper addresses precision electroweak constraints in Higgsless models by analyzing deconstructed moose setups where SM fermions are delocalized across multiple sites. By deriving neutral and charged current correlation functions and enforcing spectral-residue consistency, the authors connect the fermion profile to the $W$-boson wavefunction and identify an 'ideal delocalization' that cancels leading non-physical corrections. They show that for ideally delocalized fermions, the oblique parameters $\hat{S}$, $\hat{T}$, and $W$ vanish at tree level, with $Y$ given by $Y = M_W^2 (\Sigma_W-\Sigma_Z)$, and they provide explicit forms for the normalization of the fermion distribution. The results extend to continuum warped and flat Higgsless models, where the same cancellations occur (up to small corrections), and offer a broadly applicable method to suppress precision electroweak constraints in Higgsless linear moose models, including those with a small number of extra vector bosons.

Abstract

In this note we examine the properties of deconstructed Higgsless models for the case of a fermion whose SU(2) properties arise from delocalization over many sites of the deconstructed lattice. We derive expressions for the correlation functions and use these to establish a generalized consistency relation among correlation functions. We discuss the form of the W boson wavefunction and show that if the probability distribution of the delocalized fermions is appropriately related to the W wavefunction, then deviations in precision electroweak parameters are minimized. In particular, we show that this "ideal fermion delocalization" results in the vanishing of three of the four leading zero-momentum electroweak parameters defined by Barbieri, et. al. We then discuss ideal fermion delocalization in the context of two continuum Higgsless models, one in Anti-deSitter space and one in flat space. Our results may be applied to any Higgsless linear moose model with multiple SU(2) groups, including those with only a few extra vector bosons.