Ideal fermion delocalization in Higgsless models

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.

Multigauge-boson vertices and chiral Lagrangian parameters in Higgsless models with ideal fermion delocalization

“…The moose diagram [30] for the deconstruction corresponding to these models is shown in figure 1. The fermions derive their SU (2) W properties from a linear combination § of all of the SU (2) groups -in a manner related to the W boson profile as required for ideal delocalzation [36]. For the purposes of the analyses presented here, we will take the U (1) properties of the fermions to arise from the single U (1) group.…”

“…Ideal fermion delocalization takes its name from the fact that it is constructed in such a way as to minimize the size of precision electroweak corrections, as discussed in [36]. For example, the S parameter can be calculated from the T 3 -Y correlation function [22,24] arising from Z-exchange, and we therefore find: …”

“…We explore two possibilities, brane-localized fermions (which are phenomenologically disfavored [24] because this predicts sizeable precision electroweak corrections) and ideally-delocalized fermions as defined in [36] (which are favored because they yield small electroweak corrections).…”

“…We examined the case of a fermion whose SU (2) properties arise from two adjacent sites [34], and confirmed that (even in that simple case) it is possible to minimize the electroweak parameter αS by choosing a suitable amount of fermion delocalization. In subsequent work [36], we studied the properties of deconstructed Higgsless models with fermions whose SU (2) properties arise from delocalization over many sites of the deconstructed lattice. In an arbitrary Higgsless model we showed that if the probability distribution of the delocalized fermions is related to the W wavefunction (a condition we call "ideal" delocalization), in flat space and AdS 5 for example (assuming the absence of brane kinetic energy terms for the gauge fields)…”

A Three Site Higgsless Model

“…In deconstructed language, delocalization means allowing fermions to derive electroweak properties from more than one site on the lattice of gauge groups [31,32]. We then showed [33] for an arbitrary Higgsless model that choosing the probability distribution of the delocalized fermions to be related to the wavefunction of the W boson makes three (Ŝ,T , W ) of the leading zero-momentum precision electroweak parameters defined by Barbieri, et. al. [24,25] vanish at tree-level.…”