Moose models with vanishing $S$ parameter

Abstract

In the linear moose framework, which naturally emerges in deconstruction models, we show that there is a unique solution for the vanishing of the $S$ parameter at the lowest order in the weak interactions. We consider an effective gauge theory based on $K$ SU(2) gauge groups, $K+1$ chiral fields and electroweak groups $SU(2)_L$ and $U(1)_Y$ at the ends of the chain of the moose. $S$ vanishes when a link in the moose chain is cut. As a consequence one has to introduce a dynamical non local field connecting the two ends of the moose. Then the model acquires an additional custodial symmetry which protects this result. We examine also the possibility of a strong suppression of $S$ through an exponential behavior of the link couplings as suggested by Randall Sundrum metric.