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) 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 0(1)(B), U(1)(B-L). 0(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. (C) 2011 Elsevier B.V. All rights reserved.