Gauge kinetic mixing and dark topological defects

Takashi Hiramatsu,Masahiro Ibe,Soma Yamaguchi,Motoo Suzuki

doi:10.1007/jhep12(2021)122

Abstract

We discuss how the topological defects in the dark sector affect the Standard Model sector when the dark photon has a kinetic mixing with the QED photon. In particular, we consider the dark photon appearing in the successive gauge symmetry breaking, SU(2) → U(1) → ℤ2, where the remaining ℤ2 is the center of SU(2). In this model, the monopole is trapped into the cosmic strings and forms the so-called bead solution. As we will discuss, the dark cosmic string induces the QED magnetic flux inside the dark string through the kinetic mixing. The dark monopole, on the other hand, does not induce the QED magnetic flux in the U(1) symmetric phase, even in the presence of the kinetic mixing. Finally, we show that the dark bead solution induces a spherically symmetric QED magnetic flux through the kinetic mixing. The induced flux looks like the QED magnetic monopole viewed from a distance, although QED satisfies the Bianchi identity everywhere, which we call a pseudo magnetic monopole.

Highlights

A dark photon with a mass would associate with spontaneously broken U(1) gauge symmetry.2 For several reasons, it is more desirable to associate the dark photon with a non-Abelian gauge symmetry
Let us assume that the dark monopole is formed at the first phase transition, SU(2)D → U(1)D
We discussed how the topological defects in the dark sector affect the SM sector through the gauge kinetic mixing between the QED photon and the dark photon

Summary

Cosmic string

Let us consider the dark photon model based on the U(1)D gauge theory coupling to the QED photon, L. In the presence of the kinetic mixing, the field equations of the QED and the dark photon are given by,. JQμED and JDμ denote the charge currents coupling to the QED and the dark photons, respectively. For JQμED = 0, we find that the QED gauge field follows the dark photon configuration, Fμν = F μν ,. In the canonically normalized basis, there is no kinetic mixing between Xμ and Xμ, and the configuration of the shifted QED is trivial around the dark string solution of Xμ, i.e., Xμ = 0. The magnetic flux of the dark cosmic string is given by, Xsμdxμ (2.22) In this shifted basis, the AB phases on the QED charged particles appear through the direct coupling to the dark photon, Xμ,. Again, the AB phase of the QED charged particle with the charge q is given by, qWQED

Monopole

Gauge kinetic mixing and beads

Numerical simulation

Conclusion

B The magnetic field of a finite solenoid

C Stream line