臺灣博碩士論文加值系統

In the most of parameterizations for Cabibbo-Kobayashi-Masjawa (CKM) matrix,the mixing angles and CP violating phase chosen are not direct measurable quantities and depend on parametrizations. Using the measurable quantities to
study the CKM matrix would be interesting. In this thesis, we propose to use experimentally measurable CP violating quantities, α, β or γ in the unitarity triangle as the phase in the CKM matrix, and construct explicit α, β and γ parameterizations. Approximate Wolfenstein-like expressions are also suggested. Since β is the most accurately measured among these three phase angles, we therefore consider the β parameterization the best one to use. Moreover, it is fascinating to research the connection between quark and lepton mixing. We also study the Quark-Lepton Complementarity (QLC) between mixing angles, the sum of an angle in quark mixing and the corresponding angle in lepton mixing is π/4. Experimentally in the CK parameterization, two such relations exist approximately. However, these QLC relations are accidental which only manifest themselves in the CK parameterization. We propose reparameterization invariant expressions for the complementarity relations
in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that |Vus/Vud|+|Ve2/Ve1|+|Vus/Vud||Ve2/Ve1| = 1
and |Vcb/Vtb| + |Vμ3/Vτ3| + |Vcb/Vtb||Vμ3/Vτ3| = 1. Expressions with deviations from exact complementarity are obtained. Implications of these relations are also discussed.

1 Introduction 1
2 The Standard Model and Unitary Matrix 3
2.1 The Standard Model Lagrangian and Higgs Mechanism . . . . . . . . 3
2.2 The CP Violation and CKM Matrix . . . . . . . . . . . . . . . . . . . 7
2.2.1 The Elements of CKM Matrix . . . . . . . . . . . . . . . . . . 8
2.2.2 The Parametrizations of CKM Matrix . . . . . . . . . . . . . 9
2.2.3 The Phases of CKM Matrix . . . . . . . . . . . . . . . . . . . 13
2.3 The Neutrino Oscillation and PMNS Matrix . . . . . . . . . . . . . . 15
2.3.1 The Three Mixing Angles of PMNS Matrix . . . . . . . . . . . 17
2.3.2 The Global Fitting Results of PMNS Matrix . . . . . . . . . . 20
3 The α, β and γ Parametrizations of CKM Matrix 24
3.1 The α, β and γ Parametrizations . . . . . . . . . . . . . . . . . . . . 25
3.2 Relations Between Different Parametrizations . . . . . . . . . . . . . 29
3.3 Wolfenstein-like Expansions . . . . . . . . . . . . . . . . . . . . . . . 30
4 The Quark-Lepton Complementarity 33
4.1 The Quark-Lepton Complementarity Relations . . . . . . . . . . . . . 33
4.2 Reparametrization Invariance of QLC Relations . . . . . . . . . . . . 34
4.3 A Confliction Between QLC and Tribimaximal Mixing Matrix. . . . . 35
4.4 Deviations of QLC relations . . . . . . . . . . . . . . . . . . . . . . . 37
5 Conclusion 39
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