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

TL;DR

This paper establishes a direct correlation between the branching ratios of heavy scalar H decaying into di-Higgs, tri-Higgs, and vector bosons in the 2HDM, providing testable predictions for the LHC.

Contribution

It reveals a novel relationship between Br(H→hh), Br(H→VV), and Br(H→hhh) in the 2HDM, enabling new experimental probes of the model at the LHC.

Findings

Br(H→hh)/Br(H→ZZ) ≈ 9.5 for 500 GeV to 1 TeV H masses

The Hhh coupling dominates in the decoupling limit, affecting tri-Higgs production

Predicted rates for H→hhh could be measurable at the High-Luminosity LHC

Abstract

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 $m_H\gg m_h$, where $h$ is the Higgs boson of mass 125 GeV observed at the LHC, we show that a direct correlation emerges between Br$(H\to hh)$ and Br$(H\to VV)$, 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($H\to hh$)/ Br($H\to ZZ)\approx 9.5$. The origin of this prediction is most transparent in the Higgs basis, where the term in the scalar potential proportional to $\mathcal H_1^\dagger \mathcal H_1 \mathcal H_1^\dagger \mathcal H_2$ (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 $H\to hhh$, which is also directly correlated to $H\to hh$ (and $H\to VV$), and can yield rates large enough to be measured at the High-Luminosity LHC.