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

Vanamali Shastry; Francesco Giacosa

doi:10.1140/epjc/s10052-023-11883-3

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 713
https://doi.org/10.1140/epjc/s10052-023-11883-3

Regular Article - Theoretical Physics

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

Vanamali Shastry¹^a and Francesco Giacosa¹^,2

¹ Institute of Physics, Jan Kochanowski University, ul. Uniwersytecka 7, 25-406, Kielce, Poland
² Institute for Theoretical Physics, Johann Wolfgang Goethe-University, Max von Laue-Str. 1, 60438, Frankfurt, Germany

^a vanamalishastry@gmail.com

Received: 9 January 2023
Accepted: 30 July 2023
Published online: 9 August 2023

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.

© The Author(s) 2023

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