Kinetic mixing and symmetry breaking dependent interactions of the dark photon

TL;DR

This paper analyzes how kinetic mixing affects symmetry breaking and interactions in a U(1) x U(1) gauge theory, providing a framework for understanding dark photon couplings without assuming small mixing.

Contribution

It introduces a basis transformation to diagonalize kinetic mixing in a U(1) x U(1) gauge theory, enabling explicit analysis of dark photon interactions and symmetry breaking effects.

Findings

Derived analytical formulas for dark photon couplings.

Established a lower bound on kinetic mixing parameter.

Linked the model to dark matter phenomenology.

Abstract

We examine spontaneous symmetry breaking of a renormalisable U(1) x U(1) gauge theory coupled to fermions when kinetic mixing is present. We do not assume that the kinetic mixing parameter is small. A rotation plus scaling is used to remove the mixing and put the gauge kinetic terms in the canonical form. Fermion currents are also rotated in a non-orthogonal way by this basis transformation. Through suitable redefinitions the interaction is cast into a diagonal form. This framework, where mixing is absent, is used for subsequent analysis. The symmetry breaking determines the fermionic current which couples to the massless gauge boson. The strength of this coupling as well as the couplings of the massive gauge boson are extracted. This formulation is used to consider a gauged model for dark matter by identifying the massless gauge boson with the photon and the massive state to its dark counterpart. Matching the coupling of the residual symmetry with that of the photon sets a lower bound on the kinetic mixing parameter. We present analytical formulae of the couplings of the dark photon in this model and indicate some physics consequences.