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

TL;DR

This work provides a dispersion-relations-based computation of the S parameter in a light composite Higgs framework, unifying an IR Higgs-coupling suppression with a UV resonance contribution via a finite matching term. The core result is a μ-independent expression that combines a Higgs-loop piece, a dispersive UV integral over the strong-sector spectral density, and a finite matching term, yielding an accuracy of order $O(m_h/m_\rho)$. The approach extends the Peskin-Takeuchi formalism to the MCHM and is demonstrated with toy spectral models, including Vector Meson Dominance, highlighting the roles of Weinberg sum rules and the importance of correct matching. Overall, the paper provides a robust, systematic method to quantify oblique corrections in composite-Higgs theories and guides how future spectral information may refine these precision constraints.

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_ρ). We apply our formula in several toy examples, modeling the UV spectral density via Vector Meson Dominance.