微中子震盪和最近測量到的渺子及電子g-2實驗結果沒辦法用標準模型解釋。為了解釋這些現象，我們造了一個模型，並引進了四個標量子(Scalars)和二對向量費米子(Vector Fermions)。模型中只有新粒子帶有U(1)_X電荷，而標準模型粒子都是U(1)_X電中性的，所以新物理的影響至少都是一個迴圈以上的費曼圖修正。數值掃描完成後，我們發現對於正常階層(normal hierarchy)的微中子，△ a_\mu ∈ [5,8] × 10^{-10}；對於相反階層(inverted hierarchy)的微中子，△ a_\mu ∈ [3,5] × 10^{-10}。這是因為味道改變的中性電流(flavor-changing neutral currents)的實驗限制。我們的模型不支持目前實驗與理論的差別。但是如果新的晶格量子色動力學(Lattice QCD)的計算是正確的，標準模型預測的渺子g-2會更大，而△ a_\mu會更小，則我們的模型就有機會成功給出合適的△ a_\mu。我們的模型可以
解釋兩種不同的△ a_e也可以造出正常階層或是相反階層的微中子。其中沒有
任何一個被排除掉。這個模型有可能會產生很大的希格斯子到電子正子對的衰變率(Γ (H → e e))，甚至是標準模型預測的十幾倍大。

We consider a hidden gauged U(1)_X model to explain the observed neutrino oscillation data and anomalous magnetic moments of electron and muon; which cannot be explained by the Standard Model (SM).
This U(1)_X model introduces four exotic scalars and two pairs of vector fermions. Because the SM particles are U(1)_X singlets, neutrino mass generation and △ a_l begin at the one-loop level. In our model, △ a_\mu is strongly constrained by the flavor-changing neutral currents (FCNC). Our numerical study shows that △ a_\mu ∈ [5,8] × 10^{-10} for inverted-ordering (IO) neutrino data and △ a_\mu ∈ [3,5] × 10^{-10} for normal-ordering (NO) neutrino data. If the experimental FCNC constraint is improved in the future, the predicted $\Delta a_\mu$ will be further suppressed. Our model does not support the current experimentally measured $\Delta a_\mu$ but seems to be preferred by the new lattice QCD evaluation on the hadronic contribution to muon g-2. Our model can accommodate either the central value of the measured △ a_e^{Cs} or that of △ a_e^{Rb}. Besides, both NO and IO neutrino mass can be well explained in this model. Our model predicts a large, ~ ten times the SM prediction, Γ (H → e e) Higgs decay rate in some viable model parameter space. Moreover, the effective Higgs-electron Yukawa coupling could be negative in our model.

1 Introduction . . . 1

2 Higgs Mechanism and Neutrino Oscillation . . . 4
2.1 Higgs Mechanism . . . 4
2.2 PMNS Matrix and Lepton Mixing . . . 7
2.3 Neutrino Oscillation . . . 9

3 The Model . . . 11
3.1 The Mixing of H and S2 after SSB . . . 13
3.2 Mixing of the New Fermions . . . 15
3.3 Mixing of New Scalars . . . 17

4 The Flavor Physics . . . 19
4.1 ∆al and l → lγ . . . 19
4.2 Lepton Mass Mixing . . . 21
4.3 Neutrino Mass and The Rank of Matrices . . . 22
4.4 H → ll Decay . . . 24

5 Numerical Analysis 27
5.1 Constraints on the neutrino oscillation and l → l γ . . . 27
5.2 Numerical strategy . . . 28
5.3 Numerical results and discussion . . . 30

6 Conclusion . . . 40

A Calculations . . . 42
A.1 Nonlinear Realization . . . 42
A.2 Calculations about Feynman diagrams . . . 43
A.3 Calculation of li → lj γ . . . . 44
B Benchmark Points . . . 47

Bibliography . . . 49

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