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

## TL;DR

This paper calculates two-loop ${
m O}(\a_t^2)$ corrections to neutral Higgs boson masses in the CP-violating NMSSM, improving the precision of Higgs spectrum predictions in supersymmetric models.

## Contribution

It provides the first implementation of ${
m O}(\a_t^2)$ corrections in the NMSSMCALC code, enhancing the accuracy of Higgs mass calculations in the CP-violating NMSSM.

## Key findings

- Corrections add 4-7% to the Higgs mass with $ar{ ext{DR}}$ renormalization.
- Corrections reduce the Higgs mass by 6-9% with OS renormalization.
- Theoretical uncertainties are analyzed via scale and scheme variations.

## Abstract

We present our calculation of the two-loop corrections of ${\cal O}(\alpha_t^2)$ to the neutral Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM). The calculation is performed in the Feynman diagrammatic approach in the gaugeless limit at vanishing external momentum. We apply a mixed $\overline{\mathrm{DR}}$-on-shell (OS) renormalization scheme for the NMSSM input parameters. Furthermore, we exploit a $\overline{\mathrm{DR}}$ as well as an OS renormalization in the top/stop sector. The corrections are implemented in the Fortran code NMSSMCALC for the calculation of the Higgs spectrum both in the CP-conserving and CP-violating NMSSM. The code also provides the Higgs boson decays including the state-of-the-art higher-order corrections. The corrections computed in this work improve the already available corrections in NMSSMCALC which are the full one-loop corrections without any approximation and the two-loop ${\cal O}(\alpha_t \alpha_s)$ corrections in the gaugeless limit and at vanishing external momentum. Depending on the chosen parameter point, we find that the ${\cal O}(\alpha_t \alpha_s + \alpha_t^2)$ corrections add about 4-7% to the one-loop mass of the SM-like Higgs boson for $\overline{\mathrm{DR}}$ renormalization in the top/stop sector and they reduce the mass by about 6-9% if OS renormalization is applied. For an estimate of the theoretical uncertainty we vary the renormalization scale and change the renormalization scheme and show that care has to be taken in the corresponding interpretation.