The Order $\mathcal{O}(\alpha_t\alpha_s)$ Corrections to the Trilinear Higgs Self-Couplings in the Complex NMSSM

TL;DR

This paper calculates two-loop order corrections to the trilinear Higgs self-couplings in the complex NMSSM, improving theoretical precision and reducing uncertainties in Higgs mass and coupling predictions.

Contribution

It provides the first two-loop ${ m O}(\a_t \a_s)$ corrections to Higgs self-couplings in the CP-violating NMSSM, using two renormalization schemes and analyzing their impact.

Findings

Two-loop corrections are about 10% in studied scenarios.

Inclusion of two-loop corrections reduces theoretical uncertainties.

Renormalization scheme choice affects the size of corrections.

Abstract

A consistent interpretation of the Higgs data requires the same precision in the Higgs boson masses and in the trilinear Higgs self-couplings, which are related through their common origin from the Higgs potential. In this work we provide the two-loop corrections at order ${\cal O}(\alpha_t \alpha_s)$ in the approximation of vanishing external momenta to the trilinear Higgs self-couplings in the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM). In the top/stop sector two different renormalization schemes have been implemented, the OS and the $\overline{\text{DR}}$ scheme. The two-loop corrections to the self-couplings are of the order of 10\% in the investigated scenarios. The theoretical error, estimated both from the variation of the renormalization scale and from the change of the top/stop sector renormalization scheme, has been shown to be reduced due to the inclusion of the two-loop corrections.