Probing triple-Higgs productions via $4b2\gamma$ decay channel at a 100 TeV hadron collider

The quartic self-coupling of the Standard Model Higgs boson can only be measured by observing the triple-Higgs production process, but it is challenging for the LHC Run 2 or International Linear Collider (ILC) at a few TeV because of its extremely small production rate. In this paper, we present a detailed Monte Carlo simulation study of the triple-Higgs production through gluon fusion at a 100 TeV hadron collider and explore the feasibility of observing this production mode. We focus on the decay channel $HHH\to b\overline{b}b\overline{b}\gamma \gamma$, investigating detector effects and optimizing the kinematic cuts to discriminate the signal from the backgrounds. Our study shows that, in order to observe the Standard Model triple-Higgs signal, the integrated luminosity of a 100 TeV hadron collider should be greater than $1.8\times {10}^4{\mathrm{ab}}^{-1}$. We also explore the dependence of the cross section upon the trilinear (${\lambda }_3$) and quartic (${\lambda }_4$) self-couplings of the Higgs. We find that, through a search in the triple-Higgs production, the parameters ${\lambda }_3$ and ${\lambda }_4$ can be restricted to the ranges $[-1,5]$ and $[-20,30]$, respectively. We also examine how new physics can change the production rate of triple-Higgs events. For example, in the singlet extension of the Standard Model, we find that the triple-Higgs production rate can be increased by a factor of $\mathcal{O}(10)$.

Figure 1

Distributions of the (a) invariant mass of two Higgs $m_{HH}$ and (b) invariant mass of three Higgs $m_{HHH}$ at the leading-order parton level are shown.

Figure 2

The distributions of (a) the number of jets for the fully hadronic final states and (b) missing energy transverse for the semileptonic and dileptonic final states for both the signal and the background $pp\to t\overline{t}H$ at the detector level are demonstrated.

Figure 3

The distributions of the minima of ${\chi }^2$ are shown.

Figure 4

The distributions of the (a) reconstructed top mass and (b) reconstructed $W$ mass.

Figure 5

The distributions of the (a) recontructed Higgs mass, (b) invariant mass of two photons, (c) invariant mass of the hardronic Higgs, and (d) total invariant mass of three Higgses.

Figure 6

The response of the discriminants to the signal and background in two multivariate analyses, (a) the BDT method and (b) the MLP neural network method.

Figure 7

The example Feynman diagrams of the process $gg\to HHH$ in the SM.

Figure 8

(a) The fitted cross section when ${\lambda }_3=1$; (b) the feasibility contours of $\sigma (pp\to hhh)$ in the ${\lambda }_4-{\lambda }_3$ plane.

Figure 9

Extra Feynman diagrams which contribute to the process $gg\to HHH$ in the Higgs singlet model are provided.

Figure 10

The detector level distributions of (a) the invariant mass of three Higgs bosons and (b) the invariant mass of di-Higgs bosons on three benchmark points of the $\text{singlet}+\mathrm{SM}$ model, compared to the distributions of the SM signal and backgrounds.

Figure 11

The transverse momentum distributions of (a) the third and (b) the fourth hardest tagged $b$ jets.