Disentangling the high- and low-cutoff scales via the trilinear Higgs couplings in the type-I two-Higgs-doublet model

The type-I two-Higgs-doublet model in the inverted Higgs scenario can retain the theoretical stability all the way up to the Planck scale. The Planck-scale cutoff ΛcutPlanck directly impacts the mass spectra such that all the extra Higgs boson masses should be light below about 160 GeV. However, the observation of the light masses of new Higgs bosons does not indicate the high-cutoff scale because a low-cutoff scale can also accommodate the light masses. Over the viable parameter points that satisfy the theoretical requirements and the experimental constraints, we show that the trilinear Higgs couplings for low Λcut are entirely different from those for the Planck-scale cutoff. The most sensitive coupling to the cutoff scale is from the h-h-h vertex, where h is the lighter CP-even Higgs boson at a mass below 125 GeV. The gluon fusion processes of gg→hh and gg→AA are insensitive to the cutoff scale, yielding a small variation of the production cross sections, O(1) fb, according to Λcut. The smoking-gun signature is from the triple Higgs production of qq¯′→W∗→H±hh, which solely depends on the h-h-h vertex. The cross section for Λcut=1 TeV is about 103 times larger than that for the Planck-scale cutoff. Since the decay modes of H±→W∗h/W∗A and h/A→bb are dominant, the process yields the 6b+ℓν final state, which enjoys an almost background-free environment. Consequently, the precision measurement of pp→H±hh can probe the cutoff scale of the model.