CP Violation in Dual Dark Matter

In this paper we study the consequences of extending dual symmetry (DuSy) to include a generic $C_μ$ vector field as a dual partner of the photon $A_μ$. A new combined field, the complex $Z^\prime_μ$, is obtained from $C_μ$ and $A_μ$. The promotion of dual symmetry to a local symmetry for $Z^\prime_μ$ implies in the inclusion of an extra complex vector field $W_μ$ with a complex gauge transformation. A dual dark matter (DM) Lagrangian ${\cal L}_{\rm DDM}$ is obtained from the general DuSy invariant Lagrangian ${\cal L}_{\rm DuSy}$. Our tentative conjecture is to interpret $W_μ$ as the actual weak interaction charged gauge boson $W^{\pm}_μ$, which leads us to speculate about a possible extra CP violation scenarios for future calculations.

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