SU(2) Kinetic Mixing Terms and Spontaneous Symmetry Breaking

TL;DR

This paper explores a non-abelian SU(2) gauge theory with kinetic mixing, demonstrating spontaneous symmetry breaking and mass generation for particles, along with instanton solutions with a modified coupling.

Contribution

It extends the Holdom model to non-abelian SU(2), revealing spontaneous symmetry breaking and new instanton solutions with a redefined coupling.

Findings

Residual gauge and Lorentz symmetries are spontaneously broken.

Particles acquire masses through the symmetry breaking mechanism.

The model admits instanton solutions with a redefined coupling constant.

Abstract

The non-abelian generalization of the Holdom model --{\it i.e.} a theory with two gauge fields coupled to the kinetic mixing term $g {tr}(F_{\mu \nu} (A) F_{\mu \nu} (B))$-- is considered. Contrarily to the abelian case, the group structure $G\times G$ is explicitly broken to $G$. For SU(2) this fact implies that the residual gauge symmetry as well as the Lorentz symmetry is spontaneusly broken. We show that this mechanism provides of masses for the involved particles. Also, the model presents instanton solutions with a redefined coupling constant.