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A search is reported for long-lived dark photons with masses between 0.1 GeVand 15 GeV, from exotic decays of Higgs bosons produced viavector-boson-fusion. Events that contain displaced collimated Standard Modelfermions reconstructed in the calorimeter or muon spectrometer are probed. Thissearch uses the full LHC Run 2 (2015-2018) data sample collected inproton-proton collisions at $\sqrt{s}=13$ TeV, corresponding to an integratedluminosity of 139 $fb^{-1}$. Dominant backgrounds from Standard Model processesand non-collision sources are estimated by using data-driven techniques. Theobserved event yields in the signal regions are consistent with the expectedbackground. Upper limits on the Higgs boson to dark photon branching fractionare reported as a function of the dark-photon mean proper decay length or ofthe dark-photon mass and the coupling between the Standard Model and thepotential dark sector. This search is combined with previous ATLAS searchesobtained in the gluon-gluon fusion and \textit{WH} production modes. Abranching fraction above 10\% is excluded at 95\% CL for a 125 GeV Higgs bosondecaying into two dark photons for dark-photon mean proper decay lengthsbetween 173 and 1296 mm and mass of 10 GeV.

Search for light long-lived neutral particles from Higgs boson decays  via vector-boson-fusion production from $pp$ collisions at $\sqrt{s}=13$ TeV  with the ATLAS detector