One-loop corrections to the ρ parameter in higgsless models

A large class of deconstructed Higgsless model is known to satisfy the tree-level experimental bounds on the electroweak precision parameters. In particular, an approximate custodial symmetry insures that the tree-level ρ parameter is exactly one, for arbitrary values of the model parameters, and regardless of fermion delocalization. In this note we expand on previous work by considering the fermionic one-loop contributions to ρ, which are essentially due to loops with top and bottom modes. We analyze the dependence on 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, to quickly stabilize for large values of N. Experimental upper bounds on ρ translate into lower bounds on the mass of the heavy fermions. These, however, are weakly correlated with N, and the three-site model (N = 1) turns out to be already an excellent approximation for the continuum model (N → ∞)