Fermion EDMs with Minimal Flavor Violation

We study the electric dipole moments (EDMs) of fermions in the standard model supplemented with right-handed neutrinos and its extension including neutrino seesaw mechanism under the framework of minimal flavor violation (MFV). In the quark sector, we find that the current experimental bound on the neutron EDM does not yield a significant restriction on the scale of MFV. In addition, we consider how MFV may affect the contribution of the strong theta-term to the neutron EDM. For the leptons, the existing EDM data also do not lead to strict limits if neutrinos are Dirac particles. On the other hand, if neutrinos are Majorana in nature, we find that the constraints become substantially stronger. Moreover, the results of the latest search for the electron EDM by the ACME Collaboration are sensitive to the MFV scale of order a few hundred GeV or higher. We also look at constraints from $CP$-violating electron-nucleon interactions that have been probed in atomic and molecular EDM searches.Comment: 27 pages, 6 figures. New materials adde

CP Violation Within and Beyond Standard Model

標準模型(Standard Model)是現今對基本粒子物理(Elementary Particle Physics)最佳的闡述，它擁有許多美妙的對稱，於此同時卻又容許透過小林-益 川機制(KM Mechanism)來達成 CP破壞(CP Violation)，而 CP 破壞除了形而上 的趣味外同時也是致使宇宙擁有物質-反物質不對稱的必要條件，這些事實引導 我們分別探討一個有關在標準模型內的 CP 破壞及另一個在標準模型外的 CP 破 壞之題目。 在第一個題目中，在假設 CP 破壞純然由小林-益川機制提供且 SU(3)味對稱 (Flavor Symmetry)成立的狀況下，我們推導了一有趣的關係式∆ ( ⻒1;0 → ⻓0;+⼚7;− ) = −∆ ( ⻒1;⻖4;0 → ⻓0;−⼚7;+ ) ，在此∆(B → PP)被定義成反粒子的衰變率(Decay Rate)和粒子的衰變率之差，而從最近 LHCb 的數據顯示，這關係式是非常準 確，這也導致探討來自於 SU(3)為對稱之破壞對關係式的修正變得重要。最後 我們也檢查了在其它 B 介子衰變中相似的關係式。 而第二個題目則是有關於一個直接來自 CP 破壞的結果─電子電偶極 ⻔9;⻕0;─而 最近有一最新的⻔9;⻕0;上限來自於 ACME，但是這個上限仍然比標準模型的預測大上 許多個數量級。在我們採取了一個獨立於模型之外的架構─最小味對稱破壞 (Minimal Flavor Violation)─來探討⻔9;⻕0;在電子是狄拉克粒子或是馬約拉納粒 子加上蹺蹺板機制(Seesaw Mechanism)下可能的特性，而我們發現在後者的情 形下⻔9;⻕0;是可以被增強到達現今實驗的上限。1 Introduction 1 2 The Standard Model 4 2.1 The SM Lagrangian and Higgs Mechanism . . . . . . . . . . . . . . . 4 2.2 The CKM matrix and CP Violation . . . . . . . . . . . . . . . . . . . 12 2.3 Neutrino Oscillation and PMNS Matrix . . . . . . . . . . . . . . . . . 16 3 CP Violation in B Meson Decays and Tests for SU(3) Flavor Sym- metry Predictions 20 3.1 SU(3) Flavor Symmetry and Effective Operators . . . . . . . . . . . . 22 3.2 SU(3) Prediction for CP Asymmetry in B0 → K+π− and B0 s → K−π+ with estimation for SU(3) breaking effects . . . . . . . . . . . 26 3.2.1 CP Asymmetry in B0 → K+π− and B0 s → K−π+ . . . . . . 26 3.2.2 SU(3) flavor breaking effects . . . . . . . . . . . . . . . . . . . 27 3.3 CP Asymmetry Relations in Other B → PP and B → PV Decays . . 31 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Analysis of Electron EDM under Minimal Flavor Violation Hy- pothesis 40 4.1 Type-I Seesaw Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Minimal Flavor Violation . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3 MFV Framework on EDM . . . . . . . . . . . . . . . . . . . . . . . . 46 4.4 Numerical Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1 4.5 The Relevant Phenomena . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5.1 Neutron EDM . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5.2 CP-violating electron-neutron interactions . . . . . . . . . . . 56 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5 Conclusion 67 A Some Useful Properties of SU(3) Group 70 B The Amplitude for B to PP and B to PV 72 C Reduction of A 2 BAB 2 74 References 7