Benchmarks for Higgs Pair Production and Heavy Higgs 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 of type II. Using current constraints from flavour, 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 SM value, but can be reduced by a factor of $0.56$ at the 2 $\sigma$ 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 lighter Higgs boson are possible and if the mass of the decaying Higgs is below the $t\bar t$ 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 $gg\to hh$ 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 $gg\to hh$ 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 fb${}^{-1}$ of data.