See also various models and searches that motivate dark photons in this mass range for dark matter production [15, 16, 17, 18, 19, 20, 21, 22] and for addressing the Hubble tension [23]. In particular, several dark matter production mechanisms point to this mass window [18, 19], given that the matter-radiation equality occurs around the eV temperature scale, similar to the prediction of the hot dark matter paradigm. See also proposals for dark matter decay searches in this mass range [24, 25]. For dark matter searches, one can consider ${\gamma }^{\prime }\to \gamma \varphi$ with $\varphi$ being a light scalar field, producing a narrow line. Furthermore, multilaser collision experiments may probe dark photons in this mass range via the ${\gamma }^{\prime }\gamma \gamma \gamma$ coupling, similar to the ALP search proposed in Ref. [26].

One can easily see that $|\mathcal{M}{|}^2$ with small $m$ reduces to the usual oscillation form multiplied by the wave packet when I take ${\chi }_{\mathrm{mir}}^{\mathrm{eff}}=0$, corresponding to $\mathrm{Im}{\mathrm{\Pi }}_{\mathrm{mir}}\gg m^2$, i.e. when the mirror effectively acts as a perfect “wall.”