Dark-photon searches via $ZH$ production at $e^+e^-$ colliders

We study the $ZH$ associated production followed by the Higgs $H\to \gamma \bar{\gamma}$ decay into a photon plus an invisible and massless dark photon, at future high-energy $e^+e^-$ facilities. Large $H\to \gamma \bar{\gamma}$ decay rates (with branching ratios up to a few percent) are allowed, thanks to possible non-decoupling properties of the Higgs boson under specific conditions, and unsuppressed dark-photon couplings in the dark sector. Such large decay rates can be obtained in the framework of recent flavor models that aim to naturally explain the observed spread in the fermion mass spectrum. We analyze the experimental prospects for observing the $e^+e^-\rightarrow ZH$ process followed by the semi invisible Higgs decay into a photon plus a massless invisible system. Search strategies for both the leptonic and the hadronic final states (arising from $Z\rightarrow \mu^+\mu^-$ and $Z\rightarrow q\bar{q}$, respectively) are outlined. We find that a $5\sigma$ sensitivity to a branching fraction $BR_{\gamma\bar{\gamma}}\sim 3\times 10^{-4}$ can be achieved by combining the two channels with an integrated luminosity of 10 ab$^{-1}$ at a c.m. energy of 240 GeV. This is considerably better than the corresponding sensitivity in alternative channels previously studied at lepton colliders. The analysis is model independent, and its results can be straightforwardly applied to the search of any Higgs two-body decay into a photon plus an undetected light particle.