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| 1 | = '''The 331 Model''' = |

| 2 | |

| 3 | == '''Author''' == |

| 4 | * Dong-Ming Zhang (zhangdongming@pku.edu.cn) |

| 5 | * School of Physics, Peking University |

| 6 | |

| 7 | == '''Model Description''' == |

| 8 | The 331 model is a simple extension of the SM based on the gauge group SU(3)_C x SU(3)_L x U(1)_X. |

| 9 | There are different versions of this model which can be characterized by a |

| 10 | parameter called beta. Models with different beta have new particles with different electric charges. |

| 11 | But in general, they all have the same features. |

| 12 | i) Unlike the SM that anomaly cancellation is fulfilled within each generation, the gauge anomaly is cancelled in the 331 model when considering all the generations. In particular, the number of triplets must be equal to the number of anti-triplets in fermion sector, due to the nontrivial SU(3) gauge structure. The number of generations N must be a multiple of three. On the other hand, in order to ensure QCD an asymptotic free theory, the number of generations N has to be smaller than six. So N is equal to three. That explains why the SM has three generations. |

| 13 | ii) One of the three quark generations is different from the |

| 14 | other two, making sure that the anomaly is free, which leads to tree-level Flavour Changing Neutral Current (FCNC) through a new neutral gauge boson Z'. And if we choose the third generation of quark as a different one, the heavy top quark mass may be explained. |

| 15 | iii) Peccei-Quinn (PQ) symmetry which can solve the strong CP problem is a natural result of |

| 16 | gauge invariance in the 331 model. Thus PQ symmetry does not suffer from quantum corrections, which means it is not a classical symmetry but a quantum-level one. |

| 17 | iiii) With the extension of gauge group, particles in the 331 model are richer than the SM. |

| 18 | |

| 19 | == '''References''' == |

| 20 | * arXiv:1611.09337 |

| 21 | |

| 22 | == '''Model Files''' == |

| 23 | |

| 24 | == '''Instructions''' == |