Di-Higgs Production and Trilinear Higgs Self-Coupling in the scNMSSM: Qualitative Implications for the Electroweak Phase Transition at large λ 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: ${\kappa }_{\lambda }=0.884$--$0.982$, $⟨{\kappa }_{\lambda }⟩=0.944\pm 0.018$. The non-resonant di-Higgs cross section at $\sqrt{s}=13.6\text{TeV}$ lies in the range $30.3$--$36.9\text{fb}$ ($0.88$--$1.05{\sigma }_{\mathrm{SM}}$), with the resonant contribution via $gg\to h_3\to h_1{h}_1$ negligible ($\le 0.004\text{fb}$). 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.

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