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The quartic self-coupling of the Standard Model Higgs boson can only bemeasured by observing the triple-Higgs production process, but it ischallenging for the Large Hadron Collider (LHC) Run 2 or International LinearCollider (ILC) at a few TeV because of its extremely small production rate. Inthis paper, we present a detailed Monte Carlo simulation study of thetriple-Higgs production through gluon fusion at a 100 TeV hadron collider andexplore the feasibility of observing this production mode. We focus on thedecay channel $HHH\rightarrow b\bar{b}b\bar{b}\gamma\gamma$, investigatingdetector effects and optimizing the kinematic cuts to discriminate the signalfrom the backgrounds. Our study shows that, in order to observe the StandardModel triple-Higgs signal, the integrated luminosity of a 100 TeV hadroncollider should be greater than $1.8\times 10^4$ ab$^{-1}$. We also explore thedependence of the cross section upon the trilinear ($\lambda_3$) and quartic($\lambda_4$) self-couplings of the Higgs. We find that, through a search inthe triple-Higgs production, the parameters $\lambda_3$ and $\lambda_4$ can berestricted to the ranges $[-1, 5]$ and $[-20, 30]$, respectively. We alsoexamine 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 thetriple-Higgs production rate can be increased by a factor of $\mathcal{O}(10)$.

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