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

TL;DR

The paper studies resonant di-Higgs production as a probe of a heavy neutral scalar $H$ in the 2HDM within the decoupling/alignment regime. It shows that Br$(H\to hh)$ and Br$(H\to VV)$ are directly correlated, governed by the leading $Hhh$ coupling produced by the Higgs-basis term proportional to $Z_6$, and that the same coupling controls resonant tri-Higgs production via $H\to hhh$. The authors derive simple, $m_H$-dependent relations among decay widths, e.g. $\Gamma(H\to hh)/\Gamma(H\to ZZ)\approx 9.5$ and $\Gamma(H\to hhh)/\Gamma(H\to ZZ)\in[0.01,0.1]$ for $500\text{GeV}<m_H<1\text{TeV}$, with the results largely independent of Yukawa couplings in this limit. They assess current LHC constraints and HL-LHC prospects, finding that resonant $pp\to H\to hhh$ could yield measurable rates (of order $0.1$ fb at 14 TeV) and thus provide a robust test of the 2HDM; the analysis extends to CP-violating cases, where the relevant couplings are controlled by Re$(Z_6 e^{-i\eta})$ and Im$(Z_6 e^{-i\eta})$.

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.

Figures (2)

• Figure 1: 2HDM predictions for $\Gamma(H\to hh)/\Gamma(H\to ZZ)$ (left axis, red) and $\Gamma(H\to hhh)/\Gamma(H\to ZZ)$ (right axis, blue) under the assumption that $|Z_6|\lesssim 1$ [which implies that the Higgs alignment limit is approximately realized in light of Eq. (\ref{['cbmadecoup']})].
• Figure 2: Allowed regions in the $a_{F}$ vs. $c_{\beta-\alpha}$ plane for $m_H\approx m_A\approx m_{H^\pm}\approx 800$ GeV, where $a_F\equiv a_U=a_D=a_E$. The contour lines show $\sigma(pp\to H \to hhh)$ in units of femtobarn (fb) for $\sqrt{s}=14$ TeV. The regions outside the dashed lines are excluded by $H\to t\bar{t}$ and $A\to t\bar{t}$ searches at the LHC. Note that in the decoupling limit with $|Z_6|\lesssim 1$, Eq. (\ref{['cbmadecoup']}) implies that $|c_{\beta-\alpha}|\lesssim 0.1$.