  Theoretical arguments and lattice simulations suggest that, beside the known
resonance of mass $m_h=$ 125 GeV, the Higgs field might exhibit a second
resonance with a larger mass $(M_H)^{\rm theor} = 690 \pm 10 ~({\rm stat}) \pm
20 ~({\rm sys})~ {\rm GeV}$ which, however, would couple to longitudinal W's
with the same typical strength as the low-mass state at 125 GeV and thus
represent a relatively narrow resonance mainly produced at LHC by gluon-gluon
fusion. By looking for some evidence in the LHC data, we argue that the
existence of a new resonance in the predicted mass region finds support in two
analyses by ATLAS (searching for heavy resonances decaying into final states
with 4 charged leptons or $\gamma\gamma$ pairs) and in more recent CMS results
(searching for heavy resonances decaying into a pair of $h(125)$ bosons or
looking for $\gamma\gamma$ pairs produced in $pp$ double-diffractive
scattering). Since the correlation of these measurements is very small and
since, having some definite theoretical prediction, local deviations from the
pure background are not downgraded by the look-elsewhere effect, we emphasize
the instability of the present situation that could probably be resolved by
just adding two crucial, missing samples of RUN2 data.
