We derive dispersion relations for the electroweak oblique observables
measured at LEP in the context of SO(5)/SO(4) composite Higgs models. It is
shown 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. The dispersion relation for the parameter ϵ3 is then used
to estimate the contribution from spin-1 resonances at the 1-loop level.
Finally, it is shown that the sign of the contribution to the S^
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.Comment: 34 pages, 4 figures. v2: a few minor changes, typos corrected, list
of references revise