The Trilinear Higgs Self-Couplings at ${\cal O}(\alpha_t^2)$ in the CP-Violating NMSSM

TL;DR

This paper improves predictions of the Higgs trilinear self-couplings in the CP-violating NMSSM by including specific higher-order corrections, aiding the understanding of the Higgs potential and its experimental verification.

Contribution

It provides the ${\cal O}(\alpha_t^2)$ corrections to the Higgs self-couplings in the CP-violating NMSSM, advancing theoretical precision in this area.

Findings

Higher-order corrections are larger than mass corrections.

Corrections show expected perturbative convergence.

Electroweak higher-order corrections may be significant.

Abstract

In supersymmetric theories the Higgs boson masses are derived quantities where higher-order corrections have to be included in order to match the measured Higgs mass value at the precision of current experiments. Closely related through the Higgs potential are the Higgs self-interactions. In addition, the measurement of the trilinear Higgs self-coupling provides the first step towards the reconstruction of the Higgs potential and the experimental verification of the Higgs mechanism sui generis. In this paper, we advance our prediction of the trilinear Higgs self-couplings in the CP-violating Next-to-Minimal Supersymmetric extension of the SM (NMSSM). We provide the ${\cal O}(\alpha_t^2)$ corrections in the gaugeless limit at vanishing external momenta. The higher-order corrections turn out to be larger than the corresponding mass corrections but show the expected perturbative convergence. The inclusion of the loop-corrected effective trilinear Higgs self-coupling in gluon fusion into Higgs pairs and the estimate of the theoretical uncertainty due to missing higher-order corrections indicate that the missing electroweak higher-order corrections may be significant.