The Structure of Corrections to Electroweak Interactions in Higgsless Models

TL;DR

The paper analyzes Higgsless electroweak models realized as deconstructed five-dimensional gauge theories, aiming to compute corrections to electroweak interactions in a broad class of models. Using deconstruction, it derives exact tree-level neutral and charged current current-current correlators in terms of the spectrum of heavy vector bosons, valid for arbitrary 5D geometry, position-dependent couplings, and brane kinetic terms. It shows that nonoblique corrections arise only when isospin violation in the heavy spectrum is sizable and derives a fundamental relation between oblique parameters: $\alpha S - 4 \cos^2\theta_W \alpha T = 4 \sin^2\theta_W \cos^2\theta_W M_Z^2 \Sigma_W$, with $\Sigma_W = \sum_{\hat{n}=1}^N 1/M_{W\hat{n}}^2$, constraining the allowed EW corrections in unitary theories. Depending on the amount of isospin violation, heavy-vector exchanges can be negligible, important in the $J_Y J_Y$ channel, or contribute to both neutral and charged processes through a small parameter $\delta$, with associated shifts in $M_W$, $M_Z$, and the weak mixing angle. The results, applicable to continuum 5D models and to extended gauge-symmetry scenarios motivated by hidden local symmetry, provide a framework for confronting Higgsless theories with precision EW data and guide model-building under unitarity and custodial considerations.

Abstract

Recently, ``Higgsless'' models of electroweak symmetry breaking have been proposed. Based on compactified five-dimensional gauge theories, these models achieve unitarity of electroweak boson self-interactions through the exchange of a tower of massive vector bosons rather than the exchange of a scalar Higgs boson. In this paper, using deconstruction, we analyze the form of the corrections to the electroweak interactions in a large class of these models, allowing for arbitrary 5-D geometry, position-dependent gauge coupling, and brane kinetic energy terms. We show that many models considered in the literature, including those most likely to be phenomenologically viable, are in this class. By analyzing the asymptotic behavior of the correlation function of gauge currents at high momentum, we extract the exact form of the relevant correlation functions at tree-level and compute the corrections to precision electroweak observables in terms of the spectrum of heavy vector bosons. We determine when nonoblique corrections due to the interactions of fermions with the heavy vector bosons become important, and specify the form such interactions can take. In particular we find that in this class of models, so long as the theory remains unitary, S-4 c^2__W T > O(1), where S and T are the usual oblique parameters. We concur with the result of Cacciapaglia et.al. that small or negative S is possible -- though only at the expense of substantial negative T at tree-level. Although we stress our results as they apply to continuum 5-D models, they apply also to models of extended electroweak gauge symmetries motivated by models of hidden local symmetry.