Phenomenology of the new light Higgs bosons in Gildener-Weinberg model

TL;DR

Gildener-Weinberg models predict new light Higgs bosons below 500 GeV with distinctive couplings, and their detection at current or near-future colliders could confirm these models' unique phenomenology.

Contribution

This paper calculates specific Higgs self-couplings in GW models and highlights their universal bounds and experimental signatures, emphasizing the importance of collider searches for new Higgs states.

Findings

Sum rule bounds new Higgs masses below 500 GeV.

Calculated Higgs self-couplings are twice and four times the Standard Model values.

Detection of these couplings requires future high-energy colliders.

Abstract

Gildener-Weinberg (GW) models of electroweak symmetry breaking are especially interesting because the low mass and nearly Standard Model couplings of the $125\,{\rm GeV}$ Higgs boson, $H$, are protected by approximate scale symmetry. Another important but so far under-appreciated feature of these models is that a sum rule bounds the masses of the new charged and neutral Higgs bosons appearing in {\em all} these models to be below about $500\,{\rm GeV}$. Therefore, they are within reach of LHC data currently or soon to be in hand. Also so far unnoticed of these models, certain cubic and quartic Higgs scalar couplings vanish at the classical level. This is due to spontaneous breaking of the scale symmetry. These couplings become nonzero from explicit scale breaking in the Coleman-Weinberg loop expansion of the effective potential. In a two-Higgs doublet GW model, we calculate $\lambda_{HHH} \simeq 2(\lambda_{HHH})_{\rm SM} = 64\,{\rm GeV}$. This corresponds to $\sigma(pp \to HH) \cong 15$--$20\,{\rm fb}$, its {\em minimum} value for $\sqrt{s} = 13$--$14\,{\rm TeV}$ at the LHC. It will require at least the $27\,{\rm TeV}$ HE-LHC to observe this cross section. We also find $\lambda_{HHHH} \simeq 4(\lambda_{HHHH})_{\rm SM} = 0.129$, whose observation in $pp \to HHH$ requires a $100\,{\rm TeV}$ collider. Because of the above-mentioned sum rule, these results apply to {\em all} GW models. In view of this unpromising forecast, we stress that LHC searches for the new relatively light Higgs bosons of GW models are by far the surest way to test them in this decade.