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: $pp\rightarrow h_2 \rightarrow h_1 h_1/h_1h_3/h_3h_3$, where $h_1$ is the observed SM-like Higgs boson and $h_{2,3}$ are new scalars. The decays $h_2\rightarrow h_1h_3$ and $h_2\rightarrow h_3h_3$ may be the only way to discover $h_3$, 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 $h_2$ masses between 250 GeV and 1 TeV and a future $pp$ collider for $h_2$ masses between 250 GeV and 12 TeV. We update the current LHC bounds on the singlet-Higgs boson mixing angle. As the mass of $h_2$ 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 ${\rm BR}(h_2\rightarrow h_1h_1)\rightarrow 0.25$, ${\rm BR}(h_2\rightarrow h_3h_3)\rightarrow 0.5$, and ${\rm BR}(h_2\rightarrow h_1h_3) \rightarrow 0$. It can also be shown that the maximum rates of $pp\rightarrow h_2\rightarrow h_1h_1/h_3h_3$ approach the same value. Hence, all three $h_2\rightarrow h_ih_j$ decays are promising discovery modes for $h_2$ masses below $\mathcal{O}(1\,{\rm TeV})$, while above $\mathcal{O}(1\,{\rm TeV})$ the decays $h_2\rightarrow h_1h_1/h_3h_3$ are more encouraging. Masses for $h_3$ are chosen to produce a large range of signatures including multi-b, multi-vector boson, and multi-$h_1$ 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.