Constraints on dark axion portal: missing energy and fermion EDMs

We study a model in which a new interactions between the Standard Model (SM) photon and both the dark photon ($\gamma_D)$ and an ALP ($a$) are described by the dark axion portal operator. The implications of this dark axion portal scenario for electron fixed-target experiments are presented. In particular, we investigate the missing energy signatures associated with production of dark photons and their subsequent invisible decays into stable dark sector fermions, $\gamma_D \to \chi \bar{\chi}$. We discuss the discovery potential for such a scenario and derive projected sensitivity curves for the NA64$e$ and LDMX experiments. Furthermore, novel constraints of the NA64$e$ for $9.37\times 10^{11}$ electrons on target are derived by considering two production mechanisms for invisible states: (i)~the bremsstrahlung-like emission of an $a\gamma_D$ pair, $e N \to e N \gamma^* (\to a \gamma_D)$, and (ii)~the exclusive vector meson photoproduction, $\gamma^* N \to N V$, followed by the invisible decays of vector mesons, $V \to a \gamma_D$. Additionally, the constraints on the parameter space of $CP$-violating, fermion-specific ALP and dark photon couplings are established. These constraints are derived from current experimental bounds on the electric dipole moments (EDMs) of SM fermions, incorporating loop-induced contributions to the EDMs of the electron, muon, and neutron.