Neutral Higgs production at proton colliders in the CP-conserving NMSSM

We discuss neutral Higgs boson production through gluon fusion and bottom-quark annihilation in the CP-conserving $\mathbb{Z}_3$-invariant Next-to-Minimal Supersymmetric Standard Model (NMSSM) at proton colliders. For gluon fusion we adapt known asymptotic expansions in supersymmetric particles for the inclusion of next-to-leading order contributions of squarks and gluinos from the Minimal Supersymmetric Standard Model (MSSM) and include electro-weak corrections involving light quarks. Together with the resummation of higher order sbottom contributions in the bottom-quark Yukawa coupling for both production processes we thus present accurate cross section predictions implemented in a new release of the code SusHi. We elaborate on the new features of an additional SU$(2)_L$ singlet in the production of CP-even and -odd Higgs bosons with respect to the MSSM and include a short discussion of theory uncertainties.