Correlating Resonant Di-Higgs and Tri-Higgs Production to H → V V in the Two-Higgs-doublet Model

The observation of resonant di-Higgs production, which would strongly suggest the existence of a new heavy neutral scalar H , has been searched for extensively at the LHC. In the two-Higgs doublet model (2HDM) with m H ≫ m h , where h is the Higgs boson of mass 125 GeV observed at the LHC, we show that a direct correlation emerges between Br ( H → h h ) and Br ( H → V V ) , with V = Z , W , which depends only on m H (and m V ). In particular, for heavy scalar masses between 500 GeV and 1 TeV, we find that Br ( H → h h ) / Br ( H → Z Z ) ≈ 9.4 ± 0.25 . Moreover, H → h h is a dominant decay mode over a significant region of the parameter space and serves as the primary probe for a heavy scalar resonance at current and future hadron colliders. The origin of these predictions is most transparent in the Higgs basis, where the term in the scalar potential proportional to H 1 † H 1 H 1 † H 2 (and its Hermitian conjugate) generates the leading contributions to the H h h and H h h h couplings in the decoupling limit of the 2HDM. Additionally, the latter coupling governs the resonant prompt tri-Higgs production via H → h h h , which is also directly correlated to H → h h (and H → V V ), and can yield rates large enough to be measured at the High-Luminosity LHC.