  In the region of invariant mass 620$\div$740 GeV, we have analyzed the ATLAS
sample of 4-lepton events that could indicate a new scalar resonance produced
mainly via gluon-gluon fusion. These data suggest the existence of a new heavy
state $H$ whose mass $660\div 680$ GeV would fit well with the theoretical
range $M_H = 690 \pm 10 ~({\rm stat}) \pm 20 ~({\rm sys})~ {\rm GeV}$ for the
hypothetical second resonance of the Higgs field that has been recently
proposed and which would couple to longitudinal W's with the same typical
strength of the low-mass state at $125$ GeV. Since the total width $\Gamma_H$
is very poorly determined, to sharpen the analysis of the precious ATLAS data,
we have considered a particular correlation between resonating peak cross
section $\sigma_R(pp\to H \to 4l)$ and the ratio $\gamma_H=\Gamma_H/M_H$. This
correlation should be nearly insensitive to the precise value of $\Gamma_H$ and
mainly determined by the lower mass $m_h=$ 125 GeV. Equivalently, if this
correlation holds true, one could also fit $m_h$ from the 4-lepton data in the
high-mass range 620$\div$740 GeV. The result $(m_h)^{\rm fit} \sim (125 \pm
13)$ GeV reproduces the direct measurement of the Higgs particle mass and thus
supports the idea that $m_h$ and $M_H$ are the masses of two different
excitations of the same field. Therefore, if we combine with the excess at 680
GeV in the ATLAS $\gamma\gamma$ distribution, there are now two signals for a
new resonance in the same mass region. Even though, quantitatively, the global
statistical significance of each effect is modest, still the sharp correlation
$\gamma_H-\sigma_R$ in the 4-lepton channel should induce to consider seriously
these indications.
