One-loop corrections to the ρ parameter in higgsless models

A large class of deconstructed Higgsless model is known to satisfy thetree-level experimental bounds on the electroweak precision parameters. Inparticular, an approximate custodial symmetry insures that the tree-level$\rho$ parameter is exactly one, for arbitrary values of the model parameters,and regardless of fermion delocalization. In this note we expand on previouswork by considering the fermionic one-loop contributions to $\rho$, which areessentially due to loops with top and bottom modes. We analyze the dependenceon the number $N$ of internal SU(2) sites in models with a ``flat background''.We find that the new-physics contribution rapidly increases with $N$, toquickly stabilize for large values of $N$. Experimental upper bounds on $\rho$translate into lower bounds on the mass of the heavy fermions. These, however,are weakly correlated to $N$, and the three-site model (N=1) turns out to bealready an excellent approximation for the continuum model ($N\to\infty$).Comment: 20 pages, 5 figure