Detecting a Fifth-Force Gauge Boson via Superconducting Josephson Junctions

A new fifth force between particles carrying $B-L$ charges is well-motivated by the intriguing $U(1{)}_{B-L}$ extension of the standard model. The gauge boson mediator, Féeton, also serves as a dark matter candidate. In this letter, we propose a novel experimental design to detect the quantum phase difference caused by this fifth force using a superconducting Josephson junction. We find that the experiment has the best sensitivity to the gauge coupling when the gauge boson is within the mass range of $0.01$eV to $10$eV, which is an interesting mass region for the Féeton dark matter. This opens up a new avenue for the measurement of new physics at small scale below millimeter.