COULOMB'S LAW CORRECTIONS FROM A GAUGE-KINETIC MIXING

We study the connection or equivalence between two well-known extensions of the Standard Model, that is, for the coupling between the familiar massless electromagnetism U(1)(QED) and a hidden-sector U(1)(h), and axionic electrodynamics. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is an alternative to the Wilson loop approach. When we compute in this way the static quantum potential for the coupling between the familiar massless electromagnetism U(1)(QED) and a hidden-sector U(1)(h), the result of this calculation is a Yukawa correction to the usual static Coulomb potential. Previously,(14) we have shown that axionic electrodynamics has a different structure which is reflected in a confining piece. Therefore, both extensions of the Standard Model are not equivalent. Interestingly, when the above calculation is done inside a superconducting box, the Coulombic piece disappears leading to a screening phase.