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

TL;DR

This paper develops a dispersion relation approach to calculate the S parameter in a minimal composite Higgs model, incorporating effects of a light Higgs and strong sector contributions with high accuracy.

Contribution

It generalizes the Peskin-Takeuchi formula to include a light Higgs, combining IR and UV effects with finite matching for improved precision.

Findings

Derived a dispersion relation for the S parameter in composite Higgs models

Included both IR Higgs effects and UV strong sector contributions

Validated the formula with toy models using Vector Meson Dominance

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.