The S parameter for a Light Composite Higgs: a Dispersion Relation Approach

Abstract

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.

Comments: 21 pages, no figures; v2: references added, typos corrected; v3: accuracy estimate revised, comparison with gauge formalism made more precise, other minor improvements, version to appear in JHEP; v4: misprints corrected, footnote added