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

TL;DR

This paper investigates how the trilinear Higgs couplings in the type-I two-Higgs-doublet model can reveal the high or low cutoff scale, with specific focus on the triple Higgs production process as a key signature.

Contribution

It demonstrates that the $h$-$h$-$h$ vertex coupling varies significantly with the cutoff scale, providing a potential method to distinguish between high and low cutoff scenarios.

Findings

The $h$-$h$-$h$ coupling is highly sensitive to the cutoff scale.

The triple Higgs production cross section differs by about three orders of magnitude between low and high cutoff scales.

The $6b+ ext{lepton}+ ext{neutrino}$ final state offers a nearly background-free signature for probing the cutoff scale.

Abstract

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-cutoff scale, $\Lambda_{\rm cut}^{\rm Planck}$, 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 $\Lambda_{\rm cut}$ are entirely different from those for the Planck-cutoff scale. 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. Among the multi-Higgs productions mediated by Higgs bosons, the gluon fusion processes of $gg \to h h $ and $gg \to AA$ are insensitive to the cutoff scale, yielding a small variation of $\mathcal{O}(1)\,{\rm fb}$ according to $\Lambda_{\rm cut}$. The smoking-gun signature is from the triple Higgs production of $q\bar{q}' \to W^* \to H^\pm hh$, which solely depends on the $h$-$h$-$h$ vertex. The cross section for $\Lambda_{\rm cut}=1\,{\rm TeV}$ is about $10^3$ times larger than that for the Planck-cutoff scale. Since the decay modes of $H^\pm \to W^* h/W^* A$ and $h/A \to bb$ are dominant, the process yields the $6b+\ell\nu$ final state, which enjoys an almost background-free environment. Consequently, the precision measurement of $pp \to H^\pm hh$ can probe the cutoff scale of the model.