The hMSSM approach for Higgs self-couplings revisited

TL;DR

This paper revisits the calculation of Higgs self-couplings in the hMSSM, comparing it with a full MSSM approach, and identifies missing contributions that improve the approximation's accuracy.

Contribution

It provides a detailed comparison between the hMSSM approximation and full MSSM calculations for Higgs decay processes, highlighting necessary corrections for better accuracy.

Findings

Good agreement between hMSSM and MSSM when top quark contributions are included.

Identification of missing top quark contributions in the hMSSM self-couplings.

Analysis of momentum-dependent and kinetic corrections in Higgs decay calculations.

Abstract

We compare the decay of the heavy Higgs boson into two SM-like Higgs bosons, $H\to hh$, calculated in a Feynman-diagrammatic approach at the one-loop level based on the one hand on the full effective potential involving the top quark and stops in the Minimal Supersymmetric Standard Model (MSSM) accompanied by the matched Two-Higgs-Doublet Model (2HDM) as its low-energy limit and on the other hand on the hMSSM approximation. We identify missing contributions due to the top quark in the Higgs self-couplings of the hMSSM, that - when taken into account - lead to a good agreement between the hMSSM and a full MSSM calculation, at least in the limit of the Higgsino mass parameter $\mu$ being small compared to the stop spectrum. We also thoroughly analyze momentum-dependent and kinetic corrections intrinsic to the Feynman-diagrammatic approach and the matching to the effective Lagrangian, respectively, for both our calculation in the MSSM and the hMSSM and for the latter suggest to include additional corrections from the top quark, which are independent of the unknown supersymmetric spectrum.