Kinetic and mass mixing with three abelian groups

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×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)Lα−Lβ (Lα being lepton flavor numbers), and U(1)DM (a symmetry acting only on the dark matter sector) are discussed briefly.