Two-Loop ${\cal O}((\alpha_t+\alpha_\lambda+\alpha_\kappa)^2)$ Corrections to the Higgs Boson Masses in the CP-Violating NMSSM

TL;DR

This paper computes two-loop corrections to the Higgs boson masses in the CP-violating NMSSM, improving the precision of theoretical predictions by implementing advanced regularisation and renormalisation techniques.

Contribution

It introduces a comprehensive two-loop correction calculation for the NMSSM Higgs masses using a mixed renormalisation scheme and compares three infrared divergence regularisation methods.

Findings

Corrections increase with λ and κ, remaining below 3% of previous results.

The renormalisation scheme and scale dependence are typical of two-loop calculations.

Infrared divergences can be efficiently managed with a regulator mass.

Abstract

We present our computation of the ${\cal O}((\alpha_t+\alpha_\lambda+\alpha_\kappa)^2)$ two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed $\overline{\mbox{DR}}$-on-shell (OS) renormalisation scheme for the Higgs sector and apply both $\overline{\mbox{DR}}$ and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising $\lambda$ and $\kappa$, remaining overall below about 3\% compared to our previously computed ${\cal O}(\alpha_t(\alpha_t+\alpha_s))$ corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.