Anomaly-free $U(1)^m$ extensions of the Standard Model

Abstract: We construct anomaly-free $U(1)_1\times U(1)_2\times...\times U(1)_m$ gauge extensions of the Standard Model. To perform this construction we put together anomaly-free $U(1)$ extensions of one and two families of fermions. The availability of free parameters that enter linearly in the equations for the fermion charges and the large number of different classes of extensions may help other model builders interested in their use to solve problems of particle physics.