On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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130 Chapter 3. Solving the Flavor Problem in Strongly Coupled Theories to introduce an additional scalar which is either a singlet under the color groups or under the SU(2)L, in order to break the residual U(1) in the potential. The vacuum expectation values of the three scalars are dictated by the symmetries of the vacuum 〈 (Hu) i aα〉 = vu √ δaαδ 2NC i1 , 〈 (Hd) i aα〉 = vd √ δaαδ 2NC i2 , 〈h i 〉 = vℓ √2δ i2 . (3.80) Here, small latin letters from the middle of the alphabet denote SU(2)L indices. The mass term for the electroweak gauge bosons (2.102) and for the axigluon (3.77) change accordingly and one finds, MW = g5 � v2 u + v2 d + v2 ℓ , 2 MZ = MW cw , MA = gs5 � v2 u + v2 d √ . 2NCsθ cθ (3.81) All three scalars are electroweak doublets and consequentially give mass to the electroweak gauge bosons, while only the color-charged fields couple to the axigluon. It follows therefore for the SM vev v = 246 GeV, � v = v2 u + v2 d + v2 ℓ , (3.82) from which one can already infer for the factor introduced in (3.64) that ξ < 1. In order to make this explicit, we will repeat the matching of the 5D to the 4D Lagrangian, which was performed for the electroweak sector in (2.3), for the extended color sector. Therefore, the rotation (3.54) has to be introduced in the Lagrangian for the SU(3)D × SU(3)S bulk gauge fields LSU(3)D×SU(3)S = GKM G LN � − 1 4 (GrD)KL(G r D)MN − 1 4 (GrS)KL(G r � S)MN , (3.83)
which yields L SU(3)D×SU(3)S = GKM G LN − gs5 − g 2 s5 3.6. The Extension of the Scalar Sector 131 � − 1 4 Gr KLG r MN − 1� ∂KA 4 r L − ∂LA r �� K ∂MA r N − ∂NA r � M � f rst (∂KG r L)A s MA t N + (cot θ − tan θ)f rst (∂KA r L)A s MA t N � 1 + 1 2 f rst� ∂KA r L − ∂LA r K �� s GMA t N − G s NA t � M � 4 (cot θ2 + tan θ 2 )f rst f rpq A s KA t LA p M Aq N + 1 4 f rst f rpq� G s KA t L − G s LA t K �� p GMAq N − Gp NAq M + 1 2 (cot θ − tan θ)f rst f rpq (G s KA t L − G s LA t K)A p MAq N + 1 2 f rst f rpq G s KG t LA p MAq � N � . (3.84) Here, the first line corresponds to the color gauge sector of the minimal RS model and the axigluon kinetic term, the second and third line to GAA and AAA vertices and the remaining terms to vertices with four legs. The color-charged scalars are bitriplets under SU(3)D × SU(3)S, so that they can be decomposed into a singlet φ and an octet O r under the diagonal subgroup SU(3)C, (Hu)aα = φu (Hd)aα = φd δaα √ 2NC δaα √ 2NC δaα (S)aα = φS √ 2NC + O r u T r aα + O r d T r aα + O r S T r aα , (3.85) in which the electroweak singlet Higgs is included in order to model the UV BC. The relevant terms in the action are quadratic in the fields. Mass terms for the scalars are omitted, because they depend non-trivially on the various parameters of the Higgs potential given in Appendix D. Including only color charged fields, one finds � S ∋ d 4 x r 2π L � 1 ɛ dt t � LG + LA + k 2 δ(t − 1)LIR + k 2 δ(t − ɛ)LUV � + LGF , (3.86) �
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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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36 Chapter 2. The Randall Sundrum M
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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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On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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