标题： 水平$U(1)_H$对称性：一个非异常模型 显示英文标题

标题： Horizontal $U(1)_H$ symmetry: a non-anomalous model

摘要： 自发破缺的阿贝尔规范对称性可以解释最小超对称标准模型中的费米子质量层次。 在大多数情况下，假设$U(1)_H$对称性是反常的。 然而，非反常模型也是可行的，并且产生有趣的物理现象。 规范反常的抵消意味着以下结果：对于最多两代，轻子和下型夸克的 Yukawa 耦合可以统一。 $\mu$项必然稍微低于超对称破缺尺度。 超势具有意外的$B$和$L$对称性，在超对称极限下 R-宇称自动被守恒。 反常抵消还意味着夸克质量矩阵的行列式必须为零，这只有当$m_{up}=0$时才可能实现。 这解决了强 CP 问题，并为该模型提供了明确的低能检验。 显示英文摘要

摘要： Spontaneously broken Abelian gauge symmetries can explain the fermion mass hierarchies of the minimal supersymmetric standard model. In most cases it is assumed that the $U(1)_H$ symmetry is anomalous. However, non-anomalous models are also viable and yield an interesting phenomenology. Cancellation of the gauge anomalies implies the following results: unification of leptons and down-type quarks Yukawa couplings is allowed at most for two generations. The $\mu$ term is necessarily somewhat below the supersymmetry breaking scale. The superpotential has accidental $B$ and $L$ symmetries, and R-parity is automatically conserved in the supersymmetric limit. Anomaly canncellation also implies that the determinant of the quark mass matrix must vanish, wich is possible only if $m_{up}=0$. This solves the strong CP problem and provides an unambiguous low energy test of the model.