Light Neutral Higgs-Boson Production at $e^+e^-$ Colliders in the Complex MSSM and NMSSM: A Full One-Loop Analysis

For future precision analyses of the Higgs boson at $\approx 125$ GeV, $h_{125}$, a precise knowledge of its production and decay properties is mandatory. While in the Standard Model (SM) these calculations are quite advanced, in many models beyond the SM (BSM) a precise calculation is missing so far. We present the calculation of the Higgs-strahlung cross-sections at $e^+e^-$ colliders for the light neutral Higgs boson production in the Next-to-Minimal Supersymmetric SM (NMSSM) with complex parameters (cNMSSM). The evaluation is based on a full one-loop calculation of the production mechanism $e^+e^- \to h_1 Z$, including soft, hard, and collinear photon radiation. The dependence of the Higgs boson production cross-sections on the relevant cNMSSM parameters is analyzed numerically. In certain scenarios we find sizable corrections to the Higgs-strahlung cross-section. Normally, they reach about $10$ of the tree-level results, but can also exceed 20%. Finally, the calculation is compared to the corresponding one in the Minimal Supersymmetric SM (MSSM). The knowledge of the full one-loop contributions to the Higgs-boson production is particularly important for a sound theoretical intemeasurements at future $e^+e^-$ colliders such as the ILC, CLIC, LCF, FCC-ee, or CEPC. It is planned to implement the evaluation of the Higgs boson production cross-sections into an add-on package to the code FeynHiggs.