Benchmarks for Higgs boson pair production and heavy Higgs boson searches in the two-Higgs-doublet model of type II

The search for additional Higgs particles and the exact measurements of Higgs (self-)couplings is a major goal of future collider experiments. In this paper we investigate the possible sizes of new physics signals in these searches in the context of the $CP$-conserving two-Higgs-doublet model (2HDM) of type II. Using current constraints from flavor, electroweak precision, and Higgs signal strength data, we determine the allowed sizes of the triple-Higgs couplings and the branching fractions of the heavy Higgs bosons into lighter Higgs bosons. Identifying the observed Higgs resonance with the light $CP$-even 2HDM Higgs boson $h$, we find that the $hhh$ coupling cannot exceed its Standard Model (SM) value, but can be reduced by a factor of 0.56 at the $2\ensuremath{\sigma}$ level. The branching fractions of the heavy neutral Higgs bosons $H$ and $A$ into two-fermion or two-vector-boson final states can be reduced by factors of 0.4 and 0.01, respectively, if decays into a lighter Higgs boson are possible and if the mass of the decaying Higgs is below the $t\overline{t}$ threshold. To facilitate future studies of collider signatures in 2HDM scenarios with large triple-Higgs couplings or decay modes of the heavy Higgs bosons not covered by the SM Higgs searches we provide a set of benchmark points which exhibit these features and agree with all current constraints. We also discuss the effect of the heavy Higgs bosons on the $gg\ensuremath{\rightarrow}hh$ cross section at a 14 TeV LHC for some of these benchmarks. For ${m}_{H}$ below the $hh$ threshold we see a reduction of the SM $gg\ensuremath{\rightarrow}hh$ cross section due to destructive interference, but for ${m}_{H}$ above the $hh$ threshold current constraints allow enhancement factors above 50. An enhancement factor of 6 is still possible in scenarios in which the heavy Higgs particles would not be discovered by standard searches after $300\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data.