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 ε3 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^ 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.

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.