General Sum Rules for WW Scattering in Higgsless Models: Equivalence Theorem and Deconstruction Identities

TL;DR

This paper derives general sum rules for gauge boson and Nambu-Goldstone boson scattering in deconstructed Higgsless models, using the Equivalence Theorem, and explores their implications for 5D models and inelastic channels.

Contribution

It establishes universal sum rules valid for arbitrary deconstructed Higgsless models, connecting 4D and 5D theories, and clarifies the role of inelastic channels and higher KK modes.

Findings

Sum rules hold for arbitrary deconstructed models.

Ignoring higher KK modes is inconsistent with inelastic channels.

Sum rules reduce to elastic case and include 5D geometries.

Abstract

We analyze inelastic 2 to 2 scattering amplitudes for gauge bosons and Nambu-Goldstone bosons in deconstructed Higgsless models. Using the (KK) Equivalence Theorem in 4D (5D), we derive a set of general sum rules among the boson masses and multi-boson couplings that are valid for arbitrary deconstructed models. Taking the continuum limit, our results naturally include the 5D Higgsless model sum rules for arbitrary 5D geometry and boundary conditions; they also reduce to the elastic sum rules when applied to the special case of elastic scattering. For the case of linear deconstructed Higgsless models, we demonstrate that the sum rules can also be derived from a set of general deconstruction identities and completeness relations. We apply these sum rules to the deconstructed 3-site Higgsless model and its extensions; we show that in 5D ignoring all higher KK modes (n>1) is inconsistent once the inelastic channels become important. Finally, we discuss how our results generalize beyond the case of linear Higgsless models.