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We perform a multivariate analysis of Higgs-pair production via the decaychannel $HH \to b\bar b \gamma\gamma$ at the future 100 TeV $pp$ collider todetermine the trilinear Higgs self--coupling (THSC) $\lambda_{3H}$, which takesthe value of 1 in the standard model. We consider all known backgroundprocesses. For the signal we adopt the most recent event generator of {\ttPOWHEG-BOX-V2} to exploit the NLO distributions for Toolkit for MultivariateData Analysis (TMVA). Through the technique of Boosted Decision Tree (BDT)analysis trained for $\lambda_{3H}=1$, compared to the the conventionalcut-and-count approach, the signal-to-background ratio improves tremendouslyfrom about $1/10$ to $1$ and the significance can reach up to $20.5$ with aluminosity of 3 ab$^{-1}$ without including systematic uncertainties. Inaddition, by implementing a likelihood fitting of the signal-plus-background$M_{\gamma\gamma b b}$ distribution with optimized bin sizes, it is possible todetermine the THSC with the precision of 7.5\% at 68\% CL even at the earlystage of 100 TeV hadron collider with 3 ab$^{-1}$.

Measuring the trilinear Higgs boson self--coupling at the 100 TeV hadron collider via multivariate analysis