Sphalerons in composite and non-standard Higgs models

TL;DR

This paper investigates how different Higgs potential structures in composite and non-standard models affect sphaleron energies, which are crucial for understanding electroweak symmetry breaking and baryogenesis.

Contribution

It calculates sphaleron energies in composite and deformed Higgs models, revealing potential deviations from the Standard Model and the existence of a second sphaleron branch.

Findings

Sphaleron energy deviations could be detectable at 10% measurement precision.

A second sphaleron branch with higher energy exists in composite Higgs models.

Sphaleron energy is sensitive to the global structure of the Higgs potential.

Abstract

After the discovery of the Higgs boson and the rather precise measurement of all electroweak boson's masses the local structure of the electroweak symmetry breaking potential is already quite well established. However, despite being a key ingredient to a fundamental understanding of the underlying mechanism of electroweak symmetry breaking, the global structure of the electroweak potential remains entirely unknown. The existence of sphalerons, unstable solutions of the classical action of motion that are interpolating between topologically distinct vacua, is a direct consequence of the Standard Model's $\mathrm{SU}(2)_L$ gauge group. Nevertheless, the sphaleron energy depends on the shape of the Higgs potential away from the minimum and can therefore be a litmus test for its global structure. Focusing on two scenarios, the minimal composite Higgs model $\mathrm{SO}(5)/\mathrm{SO}(4)$ or an elementary Higgs with a deformed electroweak potential, we calculate the change of the sphaleron energy compared to the Standard Model prediction. We find that the sphaleron energy would have to be measured to $\mathcal{O}(10)\%$ accuracy to exclude sizeable global deviations from the Standard Model Higgs potential. We further find that because of the periodicity of the scalar potential in composite Higgs models a second sphaleron branch with larger energy arises.