Kinetic coupling and dark matter on the lattice

We study a $U(1)\otimes U(1)$ system coupled to scalar fields. Initially the model is studied in a novel continuum formulation and study of the appropriate diagonalizations is performed. Three models are examined, in two of which the scalar field couples with both gauge fields while in the third one the scalar field couples only to the dark photon. The model is then treated on a space-time lattice. We determine the phase diagram for various values of the kinetic coupling parameter. Then there follows the determination of masses for the scalar fields and the massive gauge fields, as well as the fine structure constants for the massless gauge fields.