Does the three site Higgsless model survive the electroweak precision tests at loop?

Abstract

We complete the list of one-loop renormalization group equations and matching conditions relevant for the computation of the electroweak precision parameters $S$ and $T$ in the three site Higgsless model. We obtain one-loop formulas for $S$ and $T$ expressed in terms of physical observables such as the Kaluza-Klein (KK) gauge boson mass ${M}_{{W}^{\ensuremath{'}}}$, the KK fermion mass $M$, and the KK gauge boson (${W}^{\ensuremath{'}}$) couplings with light quarks and leptons ${g}_{{W}^{\ensuremath{'}}ff}$. It is shown that these physical observables, ${M}_{{W}^{\ensuremath{'}}}$, $M$, and ${g}_{{W}^{\ensuremath{'}}ff}$ are severely constrained by the electroweak precision data. Unlike the tree level analysis on the ideally delocalized fermion, we find that perfect fermiophobity of ${W}^{\ensuremath{'}}$ is ruled out by the precision data. We also study the cutoff dependence of our analysis. Although the model is nonrenormalizable, the dependence on the cutoff parameter $\ensuremath{\Lambda}$ is shown to be nonsignificant.