微中子震盪暗示微中子有質量, 標準模型不能解釋, 因而有許多新提出的理論, 像是seesaw mechanism, discrete flavor symmetry model, 本研究將利用非常流行的A4模型, 在A4模型中, 利用將可能項列出, 致使簡化模型變成一般化, 從而在A4模型預測U13的微小值.

Neutrino oscillation is an interesting experiment that implies neutrinos have masses. As we know the standard model dose not explain this phenomenon.
There are so many models beyond standard model try to explain this phenomenon, such as seesaw mechanism(LR Symmetry Model can be its framework), discrete flavor symmetry models etc.. In this paper we introduce to the popular A4 flavor symmetry model. One light sterile neutrino can be easily accommodated in the A4 model. The simplied case, we find out Ue3 of neutrino mixing matrix is zero. From the latter experiment data appears to theta(13) =\= 0 , therefor we extended simplied case to general case, the deviation from simplied model is discussed numerically.

1 Introduction
2 The discrete flavor symmetry models
2.1 group theory
2.1.1 S3 group
2.1.2 S4 group
2.1.3 A4 group
2.2 A flavor Symmetry model with A4
2.3 The breaking of SO(3) to A4
2.3.1 The connection between A4 and SO(3)
2.3.2 A model based on SO(3) 􀀀to A4
3 Introduction to neutrino mixing matrix
3.1 Trimaximal
3.2 Bimaximal
3.3 Tri-Bimaximal
3.4 Modfications to the Tri-Bimaximal neutrino mixing
3.4.1 Tri-Bimaximal neutrino mixing in the A4 model
3.4.2 Deviation from Tri-Bimaximal in A4 flavor symmetry
4 One light sterile neutrino in A4 flavor Symmetry model
4.1 Mixing matrix
4.2 One sterile neutrino from A4 model
4.2.1 The simplied case
4.2.2 In general case
4.2.3 Discussion34
4.2.4 Conclusion
5 Appendix: Group theory

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