  In one of our recent papers, a second Higgs-like boson $h'$ with the mass
near 0.5~TeV was predicted from a dual holographic model (borrowed from the
AdS/QCD approach) for a hypothetical strongly-coupled BSM sector. In the
present work, we reproduce this prediction within the framework of more
traditional phenomenological approaches to effective description of a
strongly-coupled field theory -- the Nambu--Jona-Lasinio model and spectral sum
rules. A good quantitative agreement between these three drastically different
methods is obtained. Interestingly, the existence of the $h'$ with the
predicted mass turns out to be a minimal possibility to cancel the quadratic
divergence in the vacuum energy density. We argue also that the dominant
channel for the production of $h'$ should be $h\rightarrow h'h$, where $h$ is
the standard Higgs boson. Hence, the $H(650)$ resonance observed recently at
the LHC can be naturally interpreted as an enhancement due to the
$hh'$-threshold. Within the considered scenario, the $h$ and $h'$ bosons in a
conjectured BSM theory play the role of the $\pi$ and $\sigma$ mesons in
low-energy descriptions of QCD. Our result can be understood as a quantitative
consequence of universality of strong coupling regime in both theories, i.e.,
the prediction represents a BSM analogue of the numerical QCD relation
$m_\sigma\simeq 4m_\pi$. We argue that the obtained result is a
model-independent consequence of the assumed universality.
