Dispersion relations for electroweak observables in composite Higgs models

We derive dispersion relations for the electroweak oblique observables measured at LEP in the context of SO(5)/SO(4) composite Higgs models. We show how these relations can be used and must be modified when modeling the spectral functions through a low-energy effective description of the strong dynamics. We then use the dispersion relation for the parameter epsilon(3) to estimate the contribution from spin-1 resonances at the one-loop level. Finally, we show that the sign of the contribution to the (S) over cap parameter from the lowest-lying spin-1 states is not necessarily positive definite but depends on the energy scale at which the asymptotic behavior of current correlators is attained.