Exploring Resonant di-Higgs production in the Higgs Singlet Model

TL;DR

This work analyzes a Higgs sector extended by a real singlet without a $Z_2$ symmetry, focusing on resonant di-Higgs production via $gg\to h_2\to h_1h_1$. By fixing the global electroweak minimum and applying unitarity, stability, and experimental constraints, it identifies the remaining free parameters and computes the maximal possible di-Higgs enhancement at hadron colliders. The study finds that resonant enhancements can reach about $\mathcal{O}(10)$, with maxima near $m_2\sim 270$ GeV ($\sim 18$) and $m_2\sim 420$ GeV ($\sim 13$) at $\sqrt{S}=14$ TeV, and that theoretical constraints on the potential often exceed current experimental limits. These results illuminate how vacuum structure and scalar mixing govern beyond-Standard-Model di-Higgs signatures and inform future collider searches at 14 and 100 TeV.

Abstract

We study the enhancement of the di-Higgs production cross section resulting from the resonant decay of a heavy Higgs boson at hadron colliders in a model with a Higgs singlet. This enhancement of the double Higgs production rate is crucial in understanding the structure of the scalar potential and we determine the maximum allowed enhancement such that the electroweak minimum is a global minimum. The di-Higgs production enhancement can be as large as a factor of ~ 18 (13) for the mass of the heavy Higgs around 270 (420) GeV relative to the Standard Model rate at 14 TeV for parameters corresponding to a global electroweak minimum.

Figures (14)

• Figure 1: Structure of the $v^2\neq 0$ vacua in the $b_3$ vs. $a_2$ plane for $m_{2}=370$ GeV, $b_4=1$, and $\cos\theta=\sqrt{0.88}$. The different regions are where the $(v,x)=(v_{EW},0)$ minimum is the lowest lying (white region), $(v_-,x_-)$ is the lowest lying minimum with $v^2_-<0$ (red horizontal lines) and $v^2_->0$ (blue squares), and $(v_+,x_+)$ is the lowest lying minimum with $v^2_+<0$ (green vertical lines), and $v^2_+>0$ (maroon hatched region).
• Figure 2: Constraints on the $(b_3$, $a_2)$ parameter space obtained by requiring that the global minimum is at $(v,x)=(v_{EW}=246~GeV,0)$. Regions enclosed by the lines are allowed. Fig. \ref{['fig:EWmin']}(a) shows the allowed regions with various values of $m_{2}$ for $b_4=1$. The solid (red), dashed (blue), and dash-dotted (black) represent $m_{2}=$ 270, 370, and 500 GeV, respectively. Fig. \ref{['fig:EWmin']}(b) shows the allowed regions with $b_4=1$ (blue dashed) and $b_4=3$ (black solid) for $m_{2}=370$ GeV. The parameters used are $m_{1}=126$ GeV and $\cos\theta = 0.94$.
• Figure 3: Representative diagrams for di-Higgs production corresponding to (a) box diagram, (b) triangle diagram exchanging the light Higgs $h_1$, and (c) triangle diagram exchanging the heavy Higgs $h_2$. The solid lines stand for fermions, where top quark loops give the dominant contributions.
• Figure 4: The branching ratio of $h_2 \to h_1 h_1$ as a function of $b_3$. The parameters used are $m_{1}=126$ GeV, $\cos\theta = 0.94, a_2=0, v_{EW} =246$ GeV, and $b_4=1$. Lines from top to bottom are $m_{2}=270, 370, 420, 500$, and 1000 GeV. The solid (dashed) lines stand for regions that are allowed (excluded) by the requirement of EW stability.
• Figure 5: The ratio of the di-Higgs cross section in the singlet model to that in the SM at (a) $\sqrt{S}=14~ TeV$ and (b) $\sqrt{S}=100~ TeV$ as a function of $b_3$. The parameters used are $m_1=126~ GeV$, $\cos\theta = 0.94$ , $a_2=0$, $v_{EW}=246~ GeV$, and $b_4=1$. The solid (dashed) lines stand for regions that are allowed (excluded) by the requirement of EW stability.