Precise test of Higgs boson properties via triple Higgs boson production in vector boson fusion at future colliders

For certain classes of beyond the standard model theories, including composite Higgs models, the coupling of the Higgs to gauge bosons can be different from the standard model one. In this case, the multiboson production via vector boson fusion (VBF) can be hugely enhanced in comparison to the SM production one due to the lack of cancellation in longitudinal vector boson scattering. Among these processes, triple Higgs boson production in VBF plays a special role - its enhancement is especially spectacular due to the absence of background from transversely polarized vector bosons in the final state. While the rates from pp→jjhhh production in vector boson fusion are too low at the LHC and even at future 33 TeV pp colliders, we have found that the 100 TeV pp future circular collider (FCC) has the unique opportunity to probe the hVV coupling far beyond the LHC sensitivity. We have evaluated the pp→jjhhh rates as a function of deviation from the hVV coupling and have found that the background is much smaller than the signal for observable signal rates. We also found that the 100 TeV pp FCC can probe the hVV coupling up to the permille level, which is far beyond the LHC reach. These results highlight a special role of the hhh VBF production and stress once more the importance of the 100 TeV pp FCC.