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研究生:林修賢
研究生(外文):HSIU-HSIEN LIN
論文名稱:用直接量測物理量表述CKM矩陣與夸克-輕子互補性研究
論文名稱(外文):Parameterizations of CKM Matrix and Quark-Lepton Complementarity using Direct Measurable Quantities
指導教授:何小剛
指導教授(外文):XIAO-GANG HE
口試委員:張寶棣耿朝強阮自強陳泉宏
口試委員(外文):PAO-TI CHANGCHAO-QIANG GENGTZU-CHIANG YUANCHUAN-HUNG CHEN
口試日期:2013-05-22
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:英文
論文頁數:51
中文關鍵詞:參數化CP 破壞CKM 矩陣么正夸克混合輕子混合二次參數不變性
外文關鍵詞:parameterizationCP violationCKM matrixunitarityquark mixinglepton mixingreparameterization invariance
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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
References 40


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