Di-Higgs Production and Trilinear Higgs Self-Coupling in the scNMSSM: Qualitative Implications for the Electroweak Phase Transition at large λ and low tan β

The trilinear Higgs self-coupling and di-Higgs production cross section are investigated in the semi-constrained NMSSM (scNMSSM) at large-[Formula: see text] / low-[Formula: see text] with full two-loop precision. A random scan of one million parameter points subject to theoretical, collider, flavor, and dark matter constraints yields 66 SM-like points with singlet fraction [Formula: see text], all found in the mass range [Formula: see text] — a feature that reflects an intrinsic property of the scNMSSM at large-[Formula: see text] / low-[Formula: see text], where doublet-dominated configurations are kinematically confined below [Formula: see text]. The trilinear coupling ratio is found to be universally suppressed: [Formula: see text], [Formula: see text]. The non-resonant di-Higgs cross section at [Formula: see text] lies in the range [Formula: see text] ([Formula: see text]), with the resonant contribution via [Formula: see text] negligible ([Formula: see text]). All predictions are consistent with current ATLAS+CMS di-Higgs upper limits and is expected to be probed at the HL-LHC. These results are discussed in the context of the electroweak phase transition, where the universal suppression of [Formula: see text] is qualitatively consistent with a modified Higgs potential that could support a strengthened first-order transition. A quantitative determination of the phase transition strength via finite-temperature analysis is left for future work.