Coulomb's law corrections from a gauge-kinetic mixing

We study the static quantum potential for a gauge theory which includes the mixing between the familiar photon $U(1)_{QED}$ and a second massive gauge field living in the so-called hidden-sector $U(1)_h$. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is alternative to the Wilson loop approach. Our results show that the static potential is a Yukawa correction to the usual static Coulomb potential. Interestingly, when this calculation is done inside a superconducting box, the Coulombic piece disappears leading to a screening phase.