Dark photon dark matter in quantum electromagnetodynamics and detection at haloscope experiments

The numerous candidates of dark matter (DM) have motivated the search for potential hidden particles in a wide range of mass scales. The dark photon (DP), also called the hidden photon, [1,2] is an appealing candidate of ultralight bosonic DM [3−5] (see a recent review Ref. [6] and references therein). It is a spin-one field particle gauged by an Abelian group in the dark sector. The visible and dark photons interacte through the gauge kinetic mixing between the field strength tensors of Standard Model (SM) electromagnetic gauge group $ U(1)_{\rm EM} $ and dark Abelian gauge group $ U(1)_{\rm D} $ below the electroweak scale

where $ F^{\mu\nu} $ ( $ F^{\mu\nu}_D $ ) is the SM (dark) field strength and $ A_D $ is the dark gauge boson with mass $ m_{D} $ . If the SM particles are uncharged under the dark gauge group, kinetic mixing $ \epsilon\ll 1 $ is generated by integrating new heavy particles charged under both gauge groups at loop level. The two gauge fields can be rotated to get rid of the mixing. Consequenlty, the SM matter current shifts by $A_\mu\to A_\mu - \epsilon A_{D\mu}$ . Based on quantum electrodynamics (QED), the electromagnetic signals from the source of dark photon DM can be searched for in terrestrial experiments [4,7−17].

The description of relativistic electrodynamics may not be as simple as the QED theory. The magnetic monopole is one of the most longstanding and mysterious topics in history [18−26]. In the 1960s, J. S. Schwinger and D. Zwanziger developed generalized electrodynamics with monopoles in the presence of both electric and magnetic charges, called quantum electromagnetodynamics (QEMD) [27−29]. The characteristic feature of QEMD is the substitution of the $ U(1)_{\rm EM} $