Correlating Resonant Di-Higgs and Tri-Higgs Production to H→ VV in the 2HDM

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→ hh) and Br(H→ VV), 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→ hh)/ Br(H→ ZZ)≈ 9.5. The origin of this prediction 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 Hhh and Hhhh couplings in the decoupling limit of the 2HDM. Moreover, the latter coupling governs the resonant prompt tri-Higgs production via H→ hhh, which is also directly correlated to H→ hh (and H→ VV), and can yield rates large enough to be measured at the High-Luminosity LHC.