Kinetic coupling and dark matter on the lattice

TL;DR

This paper investigates a coupled $U(1)\otimes U(1)$ gauge-scalar system using both continuum and lattice approaches, analyzing phase diagrams, mass spectra, and coupling constants to understand dark matter interactions.

Contribution

It introduces a novel continuum formulation for the $U(1)\otimes U(1)$ system and explores its phase structure and particle spectra on the lattice.

Findings

Determined phase diagrams for various kinetic couplings.

Calculated masses of scalar and gauge fields.

Measured fine structure constants for massless gauge fields.

Abstract

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.