W_L W_L Scattering in Higgsless Models: Identifying Better Effective Theories

TL;DR

This paper evaluates how well simplified three-site models replicate the W_L W_L scattering behavior of continuum Higgsless models, proposing modifications to improve their accuracy and analyzing collider phenomenology implications.

Contribution

It introduces sum rules to compare Higgsless models and extends the three-site model to better approximate continuum theories, enhancing understanding of their collider phenomenology.

Findings

The three-site model can closely mimic continuum models with certain extensions.

Sum rules effectively measure the accuracy of simplified models.

The ring model with hidden local symmetry parameter 'a' can replicate continuum scattering.

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 (KK) 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 KK 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 ("BESS' 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 rho-meson dominance of pion-pion 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' line shape and ZWW coupling at a high-energy lepton collider.