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For certain classes of Beyond the Standard Model theories, includingcomposite Higgs models, the coupling of the Higgs to gauge bosons can bedifferent from the Standard Model one. In this case, the multi-boson productionvia vector boson fusion (VBF) can be hugely enhanced in comparison to the SMproduction one due to the lack of cancellation in longitudinal vector bosonscattering. Among these processes, triple Higgs boson production in VBF plays aspecial role - its enhancement is especially spectacular due to the absence ofbackground from transversely polarised vector bosons in the final state. Whilethe rates from $pp\to jjhhh$ production in vector boson fusion are too low atthe LHC and even at future 33 TeV $pp$ colliders, we have found that the 100TeV $pp$ future circular collider (FCC) has the unique opportunity to probe the$hVV$ coupling far beyond the LHC sensitivity. We have evaluated the $pp\tojjhhh$ rates as a function of deviation from the $hVV$ coupling and have foundthat the background is much smaller than the signal for observable signalrates. We also found that the 100 TeV $pp$ FCC can probe the $hVV$ coupling upto the permille level, which is far beyond the LHC reach. These resultshighlight a special role of the $hhh$ VBF production and stress once more theimportance of the 100 TeV $pp$ FCC.

Precise test of Higgs properties via triple Higgs production in VBF at future colliders