Deconstructed Higgsless models with one-site delocalization

Abstract

In this note we calculate the form of electroweak corrections in deconstructed Higgsless models for the case of a fermion whose weak properties arise from two adjacent $SU(2)$ groups on the deconstructed lattice. We show that, as recently proposed in the continuum, it is possible for the value of the electroweak parameter $\ensuremath{\alpha}S$ to be small in such a model. In addition, by working in the deconstructed limit, we may directly evaluate the size of off-$Z$-pole electroweak corrections arising from the exchange of Kaluza-Klein modes; this has not been studied in the continuum. The size of these corrections is summarized by the electroweak parameter $\ensuremath{\alpha}\ensuremath{\delta}$. In one-site delocalized Higgsless models with small values of $\ensuremath{\alpha}S$, we show that the amount of delocalization is bounded from above, and must be less than 25% at 95% C.L. We discuss the relation of these calculations to our previous calculations in deconstructed Higgsless models, and to models of extended technicolor. We present numerical results for a four-site model, illustrating our analytic calculations.