= '''The 331 Model''' =

==  '''Authors''' ==
* Dong-Ming Zhang (zhangdongming@pku.edu.cn)
 * Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing
* Qing-Hong Cao (qinghongcao@pku.edu.cn)
 * Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing
 * Collaborative Innovation Center of Qantum Matter, Beijing
 * Center for High Energy Physics, Peking University, Beijing

== '''Model Description''' ==
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. 
There are different versions of this model which can be characterized by a
parameter called beta. Models with different beta have new particles with different electric charges.
But in general, they all have the same features. 
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.  
ii) One of the three quark generations is different from the
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.
iii) Peccei-Quinn (PQ) symmetry which can solve the strong CP problem is a natural result of
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. 
iiii) With the extension of gauge group, particles in the 331 model are richer than the SM.

== '''References''' ==
* arXiv:1611.09337

== '''Model Files''' ==
* 331.fr: The 331 model file for general beta.
* 331_-1.fr: The 331 model file for beta=-1/\sqrt(3).
* 331_1.fr: The 331 model file for beta=+1/\sqrt(3).
* 331_-3.fr: The 331 model file for beta=-sqrt(3).
* 331_3.fr: The 331 model file for beta=+sqrt(3).
* 331.nb: The Mathematica notebook to load the above model files.[[BR]]
Notes:
* 331.fr is only used to calculate the Feynman rules for general beta, but is not used to extract the UFO or CHO model file.
* 331_*.fr are used to both calculate the Feynman rules and extract the UFO or CHO model file.
* The '~' in front of some particlename in 331_-1.fr and 331_1.fr represents that it's a Z2 odd neutral particle. 
* The '~' makes it possible that the CHO model file extracted from 331_-1.fr and 331_1.fr be implemented into the MicrOMEGAs to calculate the relic density and so on.