We construct anomaly-free $U(1{)}_1\times U(1{)}_2\times \dots \times U(1{)}_m$ 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.

• Received 6 August 2020
• Accepted 5 November 2020

DOI:https://doi.org/10.1103/PhysRevD.102.115006

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Published by the American Physical Society