The S parameter for a light composite Higgs: a dispersion relation approach

We derive a dispersion relation for the S parameter in the SO(5)/SO(4) Minimal Composite Higgs model. This generalizes the Peskin-Takeuchi formula to the case when a light Higgs boson is present in the spectrum. Our result combines an IR effect due to the reduction in the Higgs boson couplings with a UV contribution from the strong sector. It also includes a finite matching term, achieving a very good relative accuracy O(m(h)/m(rho)). We apply our formula in several toy examples, modeling the UV spectral density via Vector Meson Dominance.