Effects of Fermion Localization in Higgsless Theories and Electroweak Constraints

TL;DR

The paper tackles electroweak precision constraints in Higgsless five-dimensional models where SM fermions are brane-localized, proposing delocalization of light fermions into the bulk as a path to suppress the S parameter while preserving custodial protection of T. The authors analyze a continuum theory-space Higgsless model, showing that with brane-localized fermions the oblique parameters satisfy $\alpha S = 2 s^2 \lambda^2/3$, $\alpha T=0$, $\alpha U=0$, but that allowing bulk leakage for light fermions introduces a cancellation mechanism: $g^{CC}$ and $g^{NC}_3$ acquire a universal suppression $(1- A t_L^2)$, enabling the condition $t_L^2 = \lambda^2/(6A)$ to set $S=0$ while keeping $T=U=0$. The framework is shown to work in both flat and warped backgrounds and provides a principle for reconciling Higgsless models with precision data, though natural mechanisms for the tuning between $\lambda^2$ and $t_L^2$ and third-generation phenomenology remain to be resolved.

Abstract

Extra-dimensional Higgsless models with electroweak symmetry breaking through boundary conditions generically have difficulties with electroweak precision constraints, when the fermions are localized to the ``branes'' in the fifth dimension. In this paper we show that these constraints can be relaxed by allowing the light fermions to have a finite extent into the bulk of the fifth dimension. The $T$ and $U$ electroweak parameters can be naturally suppressed by a custodial symmetry, while the $S$ parameter can be made to vanish through a cancellation, if the leakage into the bulk of the light gauge fields and the light left-handed fermion fields are of the same size. This cancellation is possible while allowing realistic values for the first two generations of fermion masses, although special treatment is probably required for the top quark. We present this idea here in the context of a specific continuum theory-space model; however, it can be applied to any five-dimensional Higgsless model, either with a flat or a warped background.