Dark photon relic dark matter production through the dark axion portal

We present a new mechanism to produce the dark photon ($\gamma'$) in the early universe with a help of the axion ($a$) using a recently proposed dark axion portal. The dark photon, a light gauge boson in the dark sector, can be a relic dark matter if its lifetime is long enough. The main process we consider is a variant of the Primakoff process $f a \to f \gamma'$ mediated by a photon, which is possible with the axion--photon--dark photon coupling. The axion is thermalized in the early universe because of the strong interaction and it can contribute to the non-thermal dark photon production through the dark axion portal coupling. It provides a two-component dark matter sector, and the relic density deficit issue of the axion dark matter can be addressed by the compensation with the dark photon. The dark photon dark matter can also address the reported 3.5 keV $X$-ray excess via the $\gamma' \to \gamma a$ decay.