Coulomb's law corrections from a gauge-kinetic mixing

TL;DR

This paper investigates how gauge-kinetic mixing between visible and hidden U(1) gauge fields modifies the static potential, revealing Yukawa corrections and screening effects in different environments.

Contribution

It introduces a gauge-invariant, path-dependent formalism to analyze Coulomb's law corrections from gauge-kinetic mixing, providing new insights into potential screening phenomena.

Findings

Static potential includes Yukawa correction due to gauge mixing.

Screening phase occurs inside a superconducting environment.

Potential transitions from Coulombic to Yukawa form depending on conditions.

Abstract

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.