Di-Higgs Production and Trilinear Higgs Self-Coupling in the scNMSSM: Qualitative Implications for the Electroweak Phase Transition at large {\lambda} and Low tan\b{eta}

Abstract

The trilinear Higgs self-coupling and di-Higgs production cross section are investigated in the semi-constrained NMSSM (scNMSSM) at large-$\lambda$ / low-$\tan\beta$ 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 $S_{13}^2 < 0.05$, all found in the mass range $m_{h_1} \in [122.0,\,125.0]~\text{GeV}$ --- a feature that reflects an intrinsic property of the scNMSSM at large-$\lambda$ / low-$\tan\beta$, where doublet-dominated configurations are kinematically confined below ${\sim}125~\text{GeV}$. The trilinear coupling ratio is found to be universally suppressed: $\kappa_\lambda = 0.884$--$0.982$, $\langle\kappa_\lambda\rangle = 0.944 \pm 0.018$. The non-resonant di-Higgs cross section at $\sqrt{s} = 13.6~\text{TeV}$ lies in the range $30.3$--$36.9~\text{fb}$ ($0.88$--$1.05\,\sigma_{\rm SM}$), with the resonant contribution via $gg \to h_3 \to h_1h_1$ negligible ($\leq 0.004~\text{fb}$). 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 $\kappa_\lambda$ 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.