  Dark photons $\bar \gamma$ mediating long-range forces in a dark sector are
predicted by various new physics scenarios, and are being intensively searched
for in experiments. We extend a previous study of a new discovery process for
dark photons proceedings via Higgs-boson production at the LHC. Thanks to the
non-decoupling properties of the Higgs boson, BR($H\to \gamma\bar \gamma$)
values up to a few percent are possible for a massless dark photon, even for
heavy dark-sector scenarios. The corresponding signature consists (for a Higgs
boson at rest) of a striking monochromatic photon with energy $E_{\gamma}=
m_H/2$, and similar amount of missing energy. We perform a model independent
analysis at the LHC of both the gluon-fusion and VBF Higgs production
mechanisms at 14 TeV, including parton-shower effects, and updating our
previous parton-level analysis at 8 TeV in the gluon-fusion channel by a more
realistic background modeling. We find that a $5\sigma$ sensitivity can be
reached in the gluon-fusion channel for BR($H\to \gamma\bar
\gamma)\simeq\,$0.1% with an integrated luminosity of $L\simeq 300\, {\rm
fb}^{-1}$. The corresponding VBF reach is instead restricted to 1%. Such decay
rates can be naturally obtained in dark-photon scenarios arising from unbroken
$U(1)_F$ models explaining the origin and hierarchy of the Yukawa couplings,
strongly motivating the search for this exotic Higgs decay at the LHC.
