Dispersion Relations for Electroweak Observables in Composite Higgs Models

TL;DR

This paper develops dispersion relations for electroweak observables in composite Higgs models, enabling estimation of resonance contributions and revealing the sign dependence of the S parameter on spectral behavior.

Contribution

It introduces modified dispersion relations tailored for composite Higgs models and analyzes the sign variability of the S parameter contribution from spin-1 resonances.

Findings

Dispersion relations can be adapted for composite Higgs models.

The sign of the S parameter contribution depends on spectral asymptotics.

Resonance contributions estimated at 1-loop level.

Abstract

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 $\epsilon_3$ 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 $\hat S$ 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.