Higgs-Higgs scattering and the (non-)existence of the Higgsonium

TL;DR

This paper investigates the potential for Higgs-Higgs bound states (Higgsonium) in various Higgs potentials, confirming their absence in the Standard Model and exploring conditions for their possible formation in non-SM scenarios.

Contribution

It provides a detailed analysis of Higgs-Higgs scattering, refines unitarization methods, and establishes bounds on parameters for Higgsonium formation beyond the Standard Model.

Findings

No Higgsonium in the Standard Model.

Refined unitarization methods and scattering length calculations.

Conditions for bound state formation in non-SM potentials.

Abstract

We study the Higgs-Higgs scattering process and the possible emergence of a Higgs-Higgs bound state (Higgsonium) in any Higgs potential with the vacuum expectation value and second derivative matching the corresponding values from the Standard Model (SM). From the tree-level Higgs-Higgs scattering amplitude, we construct the unitarized amplitude using two different unitarization schemes (the well-known on-shell and N/D methods). We reproduce the known result that there is no Higgsonium state in the SM and, in addition, we determine the S-, D-, and G-wave SM scattering lengths, both at tree-level and upon unitarization. In doing so, we refine previous results by checking the convergence of the N/D approach. Next, we extend the calculation for non-SM potentials and investigate under which conditions a formation of a bound state close to the Higgs-Higgs threshold is possible. In this way, the assumption that no Higgsonium exist, imposes certain bounds on the values of the self-interaction parameters that complement those imposed by the vacuum stability condition.