Unitarity in composite Higgs approaches with vector resonances

TL;DR

This paper investigates a composite Higgs model with vector resonances, revealing a dynamically generated scalar resonance that influences unitarity in $W_LW_L$ scattering, with implications for the model's phenomenology.

Contribution

It demonstrates the emergence of a scalar resonance in a composite Higgs model with vector resonances using the $K$-matrix method, enhancing understanding of unitarity constraints.

Findings

A scalar resonance appears in $W_LW_L$ scattering amplitude.

The scalar's mass and width are large and inversely related to the vector resonance.

Vector resonances improve unitarity in the scalar-isoscalar channel.

Abstract

We examine a simple Composite Higgs Model (CHM) with vector resonances in addition to the Standard Model (SM) fields in perturbation theory by using the $K$-matrix method to implement unitarity constraints. We find that the $W_LW_L$ scattering amplitude has an additional scalar pole (analogous to the $\sigma$ meson of QCD) as in generic strongly interacting extensions of the SM. The mass and width of this dynamically generated scalar resonance are large and the mass behaves contrary to the vector one, so that when the vector resonance is lighter, the scalar one is heavier, and vice versa. We also attempt an interpretation of this new resonance. Altogether, the presence of the vector state with the symmetries of the CHM improve the low-energy unitarity behavior also in the scalar-isoscalar channel.