One-loop corrections to theSparameter in the four-site model

Abstract

We compute the leading chiral-logarithmic corrections to the $S$ parameter in the four-site Higgsless model. In addition to the usual electroweak gauge bosons of the standard model, this model contains two sets of heavy charged and neutral gauge bosons. In the continuum limit, the latter gauge bosons can be identified with the first excited Kaluza-Klein states of the ${W}^{\ifmmode\pm\else\textpm\fi{}}$ and $Z$ bosons of a warped extra-dimensional model with an $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}$ bulk gauge symmetry. We consider delocalized fermions and show that the delocalization parameter must be considerably tuned from its tree-level ideal value in order to reconcile experimental constraints with the one-loop results. Hence, the delocalization of fermions does not solve the problem of large contributions to the $S$ parameter in this class of theories and significant contributions to $S$ can potentially occur at one-loop.