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.
Highlights
Particle physics have problems that can be solved using gauged Uð1Þm ≡ Uð1Þ1 × Uð1Þ2 × ... × Uð1Þm extensions of the Standard Model (SM) featuring multiple Z0 bosons [1]
In order to be well behaved at high energies, a gauge symmetry must be free of anomalies [19,20,21,22]
In composite gauge theories, there is a subset of fermions that independently cancel anomalies, and one can use these different subsets to add free parameters that are available because they enter linearly in the equations for fermion charges
Summary
Particle physics have problems that can be solved using gauged Uð1Þm ≡ Uð1Þ1 × Uð1Þ2 × ... × Uð1Þm extensions of the Standard Model (SM) featuring multiple Z0 bosons [1]. × Uð1Þm extensions of the Standard Model (SM) featuring multiple Z0 bosons [1]. General solutions to the anomaly cancellation equations are not always useful because free parameters may be trapped in complicated polynomial expressions. In composite gauge theories, there is a subset of fermions that independently cancel anomalies, and one can use these different subsets to add free parameters that are available because they enter linearly in the equations for fermion charges. We will construct composite anomaly-free Uð1Þm gauge extensions of the SM. IVand V we will make the construction using one-family and twofamilies anomaly-free Uð1Þ extensions as building blocks in each case, and in Sec. VI we will present other extensions that can be made with additional charged Weyl fermions
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