Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors

TL;DR

This paper calculates the dominant two-loop corrections to Higgs self-couplings in extended scalar sector models, providing detailed formulas and analyzing their impact on non-decoupling effects and precision measurements.

Contribution

It offers the first comprehensive two-loop correction calculations for Higgs self-couplings in various BSM models, including explicit formulas and scheme conversions.

Findings

Two-loop corrections are about 20% of one-loop corrections for bb

Non-decoupling effects at one loop are not significantly altered at two loops

Higher-order corrections are necessary for precise future Higgs coupling measurements

Abstract

We compute the dominant two-loop corrections to the Higgs trilinear coupling $\lambda_{hhh}$ and to the Higgs quartic coupling $\lambda_{hhhh}$ in models with extended Higgs sectors, using the effective-potential approximation. We provide in this paper all necessary details about our calculations, and present general $\overline{\text{MS}}$ expressions for derivatives of the integrals appearing in the effective potential at two loops. We also consider three particular Beyond-the-Standard-Model (BSM) scenarios -- namely a typical scenario of an Inert Doublet Model (IDM), and scenarios of a Two-Higgs-Doublet Model (2HDM) and of a Higgs Singlet Model (HSM) without scalar mixing -- and we include all the necessary finite counterterms to obtain (in addition to $\overline{\text{MS}}$ results) on-shell scheme expressions for the corrections to the Higgs self-couplings. With these analytic results, we investigate the possible magnitude of two-loop BSM contributions to the Higgs self-couplings and the fate of the non-decoupling effects that are known to appear at one loop. We find that, at least as long as pertubative unitarity conditions are fulfilled, the size of two-loop corrections remains well below that of one-loop corrections. Typically, two-loop contributions to $\lambda_{hhh}$ amount to approximately 20% of those at one loop, implying that the non-decoupling effects observed at one loop are not significantly modified, but also meaning that higher-order corrections need to be taken into account for the future perspective of precise measurements of the Higgs trilinear coupling.