WLWLscattering in Higgsless models: Identifying better effective theories

Abstract

The three-site model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this paper we analyze how well the three-site model performs as a general exemplar of Higgsless models in describing ${W}_{L}{W}_{L}$ scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. We show that the size of the four-point vertex for the (unphysical) Nambu-Goldstone modes and the degree to which the sum rules are saturated by contributions from the lowest-lying Kaluza-Klein resonances both provide good measures of the extent to which a highly deconstructed theory can accurately describe the low-energy physics of a continuum 5D Higgsless model. After comparing the three-site model to flat and warped continuum models, we analyze extensions of the three-site model to a longer open linear moose with an additional $U(1)$ group and to a ring (``breaking electroweak symmetry strongly'' or ``hidden local symmetry'') model with three sites and three links. Both cases may be readily analyzed in the framework of the general sum rules. We demonstrate that ${W}_{L}{W}_{L}$ scattering in the ring model can very closely approximate scattering in the continuum models, provided that the hidden local symmetry parameter $a$ is chosen to mimic $\ensuremath{\rho}$-meson dominance of $\ensuremath{\pi}\ensuremath{\pi}$ scattering in QCD. The hadron and lepton collider phenomenology of both extended models is briefly discussed, with a focus on the complementary information to be gained from precision measurements of the ${Z}^{\ensuremath{'}}$ line shape and $ZWW$ coupling at a high-energy lepton collider.