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

Abstract

Gildener-Weinberg (GW) models of electroweak symmetry breaking are especially interesting because the low mass and nearly Standard Model couplings of the 125 GeV Higgs boson $H$ are protected by approximate scale symmetry. Another important but so far underappreciated feature of these models is that a sum rule bounds the masses of the new charged and neutral Higgs bosons appearing in all these models to be below about 500 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 ${\ensuremath{\lambda}}_{HHH}\ensuremath{\simeq}2({\ensuremath{\lambda}}_{HHH}{)}_{\mathrm{SM}}=64\text{ }\text{ }\mathrm{GeV}$. This corresponds to $\ensuremath{\sigma}(pp\ensuremath{\rightarrow}HH)\ensuremath{\cong}15--20\text{ }\text{ }\mathrm{fb}$, its minimum value for $\sqrt{s}=13--14\text{ }\text{ }\mathrm{TeV}$ at the LHC. It will require at least the 27 TeV HE-LHC to observe this cross section. We also find ${\ensuremath{\lambda}}_{HHHH}\ensuremath{\simeq}4({\ensuremath{\lambda}}_{HHHH}{)}_{\mathrm{SM}}=0.129$, whose observation in $pp\ensuremath{\rightarrow}HHH$ requires a 100 TeV collider. Because of the above-mentioned sum rule, these results apply to 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.