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$$_{125}$, a precise knowledge of its production and decay properties is mandatory. While in the Standard Model (SM) these calculations are quite advanced, in many models beyond the SM (BSM) a precise calculation is missing so far. We present the calculation of the Higgs-strahlung cross-sections at e$^+$ e$^-$ colliders for the light neutral Higgs boson production in the next-to-minimal supersymmetric SM (NMSSM) with complex parameters (cNMSSM). The evaluation is based on a full one-loop calculation of the production mechanism e$^+$ e$^-$ -> $h$$_1$$Z$, including soft, hard, and collinear photon radiation. The dependence of the Higgs boson production cross-sections on the relevant cNMSSM parameters is analyzed numerically. In certain scenarios we find sizable corrections to the Higgs-strahlung cross-section. Normally, they reach about 10% of the tree-level results, but can also exceed 20%. Finally, the calculation is compared to the corresponding one in the Minimal Supersymmetric SM (MSSM). The knowledge of the full one-loop contributions to the Higgs-boson production is particularly important for a sound theoretical interpretation of measurements at future e$^+$ e$^-$ colliders such as the ILC, CLIC, LCF, FCC-ee, or CEPC. ... mehrIt is planned to implement the evaluation of the Higgs boson production cross-sections into an add-on package to the code FeynHiggs.