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We perform a detailed hadron-level study on the sensitivity of Higgs bosonpair production via the $WW^{*}WW^{*}$ channel with the final state $3 \ell 2j$ + missing $E_T$ at the LHC with the collision energy $\sqrt{S} = 14$ TeV anda future 100 TeV collider. To avoid the huge background from $pp \to Z W +\textrm{jets}$ processes, we confine to consider the four lepton patterns:$e^\pm e^\pm \mu^\mp $ and $\mu^\pm \mu^\pm e^\mp$. We propose a partialreconstruction method to determine the most reliable combination. After that,we examine a few crucial observables which can discriminate efficiently signaland background events, especially we notice that the observable $m_{\rm T2}$ isvery efficient. For the LHC 14 TeV collisions, with an accumulated 3000fb$^{-1}$ dataset, we find that the sensitivity of this mode can reach up to1.5 $\sigma$ for the Standard Model and the triple coupling of Higgs boson$\lambda_3$ in the simplest effective theory can be constrained into the range[-1, 8] at $95\%$ confidence level; at a 100 TeV collider with the integratedluminosity 3000 fb$^{-1}$, the sensitivity can reach up to 13 $\sigma$ for theStandard Model and we find that all values of $\lambda_3$ in the effectivetheory can be covered up to 3$\sigma$ even without optimising signals. Toprecisely measure the triple coupling of Higgs boson $\lambda_3=1$ of theStandard Model at a 100 TeV collider, by using the invariant mass of threeleptons which is robust to against the contamination of underlying events andpileup effects and by performing a $\chi^2$ analysis, we find that it can bedetermined into a range [0.8, 1.5] at $95\%$ confidence level.

Probe Higgs boson pair production via the $3 \ell 2 j$ + missing $E_T$ mode