One-Loop Corrections to the S and T Parameters in a Three Site Higgsless Model

Abstract

In this paper we compute the one-loop chiral logarithmic corrections to the $S$ and $T$ parameters in a highly deconstructed Higgsless model with only three sites. In addition to the electroweak gauge bosons, this model contains a single extra triplet of vector states (which we denote ${\ensuremath{\rho}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${\ensuremath{\rho}}^{0}$), rather than an infinite tower of Kaluza-Klein modes. We compute the corrections to $S$ and $T$ in 't Hooft-Feynman gauge, including the ghost, unphysical Goldstone-boson, and appropriate pinch contributions required to obtain gauge-invariant results for the one-loop self-energy functions. We demonstrate that the chiral-logarithmic corrections naturally separate into two parts, a model-independent part arising from scaling below the $\ensuremath{\rho}$ mass, which has the same form as the large Higgs-mass dependence of the $S$ or $T$ parameter in the standard model, and a second model-dependent contribution arising from scaling between the $\ensuremath{\rho}$ mass and the cutoff of the model. The form of the universal part of the one-loop result allows us to correctly interpret the phenomenologically derived limits on the $S$ and $T$ parameters (which depend on a reference Higgs-boson mass) in this three-site Higgsless model. Higgsless models may be viewed as dual to models of dynamical symmetry breaking akin to ``walking technicolor,'' and in these terms our calculation is the first to compute the subleading $1/N$ corrections to the $S$ and $T$ parameters. We also discuss the reduction of the model to the ``two-site'' model, which is the usual electroweak chiral Lagrangian, noting the ``nondecoupling'' contributions present in the limit ${M}_{\ensuremath{\rho}}\ensuremath{\rightarrow}\ensuremath{\infty}$.