Resonant Multi-Scalar Production in the Generic Complex Singlet Model in the Multi-TeV Region

We develop benchmarks for resonant di-scalar production in the generic complex singlet scalar extension of the Standard Model (SM), which contains two new scalars. These benchmarks maximize di-scalar resonant production: pp→ h₂ → h₁ h₁/h₁h₃/h₃h₃, where h₁ is the observed SM-like Higgs boson and h2,3 are new scalars. The decays h₂→ h₁h₃ and h₂→ h₃h₃ may be the only way to discover h₃, leading to a discovery of two new scalars at once. Current LHC and projected future collider (HL-LHC, FCC-ee, ILC500) constraints are used to produce benchmarks at the HL-LHC for h₂ masses between 250 GeV and 1 TeV and a future $pp$ collider for h₂ masses between 250 GeV and 12 TeV. We update the current LHC bounds on the singlet-Higgs boson mixing angle. As the mass of h₂ increases, certain limiting behaviors of the maximum rates are uncovered due to theoretical constraints on the parameters. These limits, which can be derived analytically, are BR(h₂→ h₁h₁)→ 0.25, BR(h₂→ h₃h₃)→ 0.5, and BR(h₂→ h₁h₃) → 0. It can also be shown that the maximum rates of pp→ h₂→ h₁h₁/h₃h₃ approach the same value. Hence, all three h₂→ hᵢhⱼ decays are promising discovery modes for h₂ masses below O(1 TeV), while above O(1 TeV) the decays h₂→ h₁h₁/h₃h₃ are more encouraging. Masses for h₃ are chosen to produce a large range of signatures including multi-b, multi-vector boson, and multi-h₁ production. The behavior of the maximum rates imply that in the multi-TeV region this model may be discovered in the Higgs quartet production mode before Higgs triple production is observed. The maximum di- and four Higgs production rates are similar in the multi-TeV range.