On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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66 Chapter 2. The Randall Sundrum Model and its Holographic Interpretation modifications. The 5D Lagrangian is given by the terms in (2.12) minus the SU(3)C terms and (2.13). Analogue to the SM, we define and W ± 1 � 1 M = √ WM ∓ iW 2 2 � M , ZM = AM = MW = vg5 1 � g2 5 + g ′2 � g5W 5 3 M − g ′ � 5BM , (2.94) 1 � g 2 5 + g ′2 5 � ′ g 5W 3 � M + g5BM , 2 , MZ = v� g 2 5 2 + g′2 5 , (2.95) where g5 and g ′ 5 are the 5D gauge couplings of SU(2)L and U(1)Y , respectively. The covariant derivative acting on the Higgs reads DµH = 1 � −i √ 2 √ 2 � ∂µϕ + + MW W + � � µ + terms bi-linear in fields, (2.96) ∂µh + i (∂µϕ3 + MZ Zµ) and the brane Higgs involves in accordance with (2.76) the following gauge fixing terms, LGF = − 1 � ∂ 2ξ µ � 1 Aµ − ξ MKKt ∂t t A5 �� 2 − 1 � ∂ 2ξ µ Zµ − ξ � δ(t − 1) kMZ ϕ3 + 2MKK t∂t 2 − 1 � ∂ ξ µ W + µ − ξ � 2 � × ∂ µ W − µ − ξ 2 δ(t − 1) kMW ϕ + + 2MKK t∂t 1 t Z5 ��2 1 t W + 5 � δ(t − 1) kMW ϕ − 1 + 2MKK t∂t t W − 5 �� , (2.97) in which (2.55) has been applied in changing to t-coordinates for all scalar components. More generally, the gauge fixing parameters could have been chosen different for each gauge fixing term, but for convenience they are set equal. We will in the following concentrate on terms quadratic in the fields. It is however straightforward to implement three and four gauge boson terms. Accounting for the kinetic terms of the gauge bosons and the Higgs, as well as for the gauge fixing terms, results in the
action � S ∋ d 4 x r 2π � 1 dt L ɛ t � − 1 4 FµνF µν − 1 2ξ (∂µ Aµ) 2 + 1 � ∂µA5∂ 2 µ A5 + M 2 KK ∂tAµ∂tA µ� � ∂µZ5∂ µ Z5 + M 2 KK ∂tZµ∂tZ µ� − 1 4 ZµνZ µν − 1 2ξ (∂µ Zµ) 2 + 1 2 − 1 2 W + µνW −µν − 1 + k δ(t − 1) 2 − ξ � 1 MKK t∂t 2 − ξ � 4 2.3. Profiles of Gauge Bosons 67 ξ ∂µ W + µ ∂ ν W − ν + � ∂µW + 5 ∂µ W − 5 + M 2 KK ∂tW + µ ∂tW −µ� � 1 2 ∂µh∂ µ h − λv 2 h 2 + ∂µϕ + ∂ µ ϕ − + 1 2 ∂µϕ3∂ µ ϕ3 � 2 − ξ � 8 + M 2 Z 2 ZµZ µ + M 2 W W + µ W −µ �2 t A5 1 δ(t − 1) kMZ ϕ3 + 2MKK t∂t t Z5 δ(t − 1)kMW ϕ + �� 1 + MKKt∂t δ(t − 1) kMW ϕ − 1 + MKKt∂t t W + 5 In the next step, analogue to (2.88), we decompose the fields in KK modes, Aµ(x, t) = 1 √ rc Zµ(x, t) = 1 √ rc W ± µ (x, t) = 1 √ rc � n � n � n A (n) µ (x) χ A n (t) , A5(x, t) = MKK √ rc Z (n) µ (x) χ Z n (t) , Z5(x, t) = MKK √ rc W ±(n) µ (x) χ W n (t) , W ± MKK 5 (x, t) = √ rc � n � n � n t W − 5 a A n ϕ (n) A (x) ∂t χ A n (t) , a Z n ϕ (n) Z (x) ∂t χ Z n (t) , (2.98) � �� . a W n ϕ ±(n) W (x) ∂t χ W n (t) , (2.99) and expand the would-be Goldstone bosons in (2.96) in the same basis of mass eigenstates as the scalars, ϕ ± (x) = � n b W n ϕ ±(n) W (x) , ϕ3(x) = � We obtain the EOM (2.91) with the replacement c 2 A → 1 2 δ(t − 1− )k M 2 a M 2 KK n b Z n ϕ (n) Z (x) . (2.100) = δ(t − 1 − )L v2 4g2 4 4M 2 , (2.101) KK where the last equality holds for Ma = MW and also for Ma = MZ, if g2 4 by (g ′2 4 + g2 4 ). In the following, we denote both fields by Ma, with the corresponding replacements for the couplings implied. Consequentially, the orthonormality relation is replaced
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On the Flavor Problem in Strongly C
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UNIVERSITY OF MAINZ ABSTRACT THEORE
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Contents Acknowledgements vii Prefa
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Acknowledgements First and foremost
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x One of the most fascinating insig
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2 Chapter 1. Introduction: Problems
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10 Chapter 1. Introduction: Problem
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116 Chapter 3. Solving the Flavor P
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146 Chapter 4. The Asymmetry in Top
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176 Chapter 5. Conclusions describe
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178 Appendix A. Generating Paramete
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180 Appendix A. Generating Paramete
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182 Appendix B. Neutral Meson Mixin
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184 Appendix B. Neutral Meson Mixin
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C Input Parameters This appendix is
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Parameter Value ± Error Reference
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192 Appendix D. Higgs Potential for
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194 Bibliography [13] S. Dimopoulos
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196 Bibliography [43] G. Nordström
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198 Bibliography [72] K. S. Babu,
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200 Bibliography [104] R. Contino a
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202 Bibliography [133] M. Baak, M.
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204 Bibliography [160] J. Charles,
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206 Bibliography [185] C. Csaki, G.
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208 Bibliography [213] E. Thomson e
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210 Bibliography [239] V. Ahrens, A
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