This paper studies a simple extension of the laws of electricity and magnetism that adds a second photon living in a “dark” sector. The new photon couples to magnetic charges (monopoles) instead of electric charges. If the two photons mix slightly, ordinary electrons and dark monopoles each pick up the other kind of charge and become dyons — particles that carry both electric and magnetic charge. The authors work out how this idea would show up in a few precise experiments and estimate how large the mixing can be without contradicting current data.

At a basic level the model has three new ingredients: a dark photon, magnetic monopoles in the dark sector, and a small kinetic mixing between the ordinary and dark photon fields. Kinetic mixing is a standard way to provide a weak portal between otherwise separate sectors: it lets the two photon fields influence each other a little. When the authors diagonalize the photon fields to move to the usually observed particles, the electron acquires a tiny magnetic charge while the dark monopole gets a small electric charge. A quantum consistency condition (a version of the Schwinger quantization rule) links the size of the electric and magnetic charges and is modified by the mixing.

The paper checks two kinds of experimental consequences. First, the new dark photon would add a small contribution to the electron’s anomalous magnetic moment, a quantity measured and calculated to very high precision. The observed difference between experiment and the standard theory is Δa_e = −2(26)×10^−12, consistent with zero given the uncertainty. Taking that difference as an upper limit on any dark-photon contribution, the authors estimate an upper bound on the kinetic mixing of order 10^−4. A similar check with the muon’s magnetic moment gives a weaker bound because the muon measurements have larger uncertainties, so both analyses point to a mixing no larger than about 10^−4.