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.

中文翻译：

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标准模型的无异常 U(1)m 扩展

我们构建了标准模型的无异常 $U(1)_1\times U(1)_2\times...\times U(1)_m$ 规范扩展。为了执行这种构造，我们将一个和两个费米子族的无异常 $U(1)$ 扩展放在一起。在费米子电荷方程中线性输入的自由参数的可用性和大量不同类别的扩展可能有助于其他对使用它们来解决粒子物理问题感兴趣的模型构建者。