Kinetic and mass mixing with three abelian groups

TL;DR

This paper explores the mixing effects of two additional abelian gauge groups in the Standard Model extension, deriving formulas that relate gauge and mass eigenstates and discussing specific applications.

Contribution

It provides general formulae and approximate expressions for kinetic and mass mixing effects involving two abelian groups in the Standard Model extension.

Findings

Derived general formulas connecting gauge and mass eigenstates.

Applied formulas to specific abelian groups like U(1)_B and U(1)_(L_alpha - L_beta).

Discussed implications for dark matter models.

Abstract

We present the possible mixing effects associated with the low-energy limit of a Standard-Model extension by two abelian gauge groups U(1)_1 x U(1)_2. We derive general formulae and approximate expressions that connect the gauge eigenstates to the mass eigenstates. Applications using the well-studied groups U(1)_B, U(1)_(B-L), U(1)_(L_alpha - L_beta) (L_alpha being lepton flavor numbers), and U(1)_DM (a symmetry acting only on the dark matter sector) are discussed briefly.