On the hypothesis of a second Higgs boson near 0.5 TeV

Recently, a second Higgs-like boson $h'$ with the mass near 0.5~TeV was predicted from a dual holographic model describing the hypothetical strongly-coupled sector beyond the Standard Model. We analyze under what conditions this prediction can be reproduced within the framework of more traditional models for describing a strongly-coupled field theory -- the spectral sum rules and the Nambu--Jona-Lasinio model in the scalar channel. It is shown that the results of both approaches are close and lead to this prediction if the covariant four-momentum cutoff in them is identified with the unitarity bound on the Higgs boson mass, and also under the assumption that the strongly coupled sector beyond the Standard Model is described by some quantum field theory based on the $SU(2)$ gauge group. We also present additional arguments suggesting that a mass of about 0.5 TeV would be natural for a heavy analogue of the Higgs boson, if it exists.