On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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62 Chapter 2. The Randall Sundrum Model and its Holographic Interpretation (DD) When a Higgs vev is turned on on the IR brane, the higgsing generates mass correction to the bosonic composites. We expect therefore the same contributions as in the (DN) scenario, however additional ∆F = 2 contributions should appear. The situation in the UV is unchanged (still Dirichlet BCs) and since there is no mixing, no extra flavor diagonal or ∆F = 1 terms should appear. Accordingly, we find, D ξ=1 µν (q, t; t ′ ) = ηµν L 4πrc M 2 KK which perfectly agrees with the expectations. � t 2 < − t 2 t ′2� , (2.85) (NN) If one allows for Neumann BCs on both branes, the situation changes significantly. There is still the exclusively composite exchange like in the (DN) scenario, however as Neumann BCs in the UV correspond to gauge fields in the elementary sector the mixing term in (2.41) becomes active and allows for all the additional diagrams shown on the left hand side. We cannot reproduce a one-to-one correspondence for each diagram here, because there exist many diagrams contributing to the same terms. However, one can infer that in contrast to the (DD) scenario no additional ∆F = 2 contributions should appear. Also, the existence of a pure gauge boson diagram will lead to a flavor diagonal term independent of the KK scale. There should be additional flavor-diagonal contributions as well, from the diagram with mixing into the composite boson and back. We find D ξ=1 µν (q, t; t ′ ) =− ηµν 2πrcp 2 + ηµν 4πrc M 2 KK � Lt 2
(ND) and all possible Higgs insertions 2.3. Profiles of Gauge Bosons 63 This is the “messiest” scenario, in the sense that all possible diagrams in Figure 2.7 contribute to the propagator, besides the pure gauge boson propagator, because it will be massive due to mixing with a composite which breaks the gauge symmetry. In the language of Section 2.2, the group I is empty here. The corresponding propagator should have flavordiagonal, ∆F = 1 and additional ∆F = 2 contributions and we find D ξ=1 µν (q, t; t ′ ) = ηµν L 4πrc M 2 KK � t 2 < − t 2 − t ′2 + 1 � . (2.87) This is not exactly what one would expect. The Higgs corrections to the ∆F = 2 contributions we found for (DD) BCs are absent. This can not be explained by a direct cancellation between diagrams, because all other diagrams will not lead to ∆F = 2 effects. Also, the flavordiagonal factor is much larger compared to (NN) BCs, which can only be explained by the Higgs insertions there having a large effect. We will close this section with the introduction of the KK decomposition for the different scenarios just introduced and a discussion of the behavior of the profile functions for the lightest modes. The generic bulk Lagrangian (2.53) suggests a KK decomposition in t-notation � � Aµ(xµ, t) = A5(xµ, t) 1 � � An µ(xµ) χn(t) √ rc � . (2.88) n MKK A n 5 (xµ) ∂tχn(t) If this decomposition is inserted into equation (2.53), one finds the important relation (valid in Feynman gauge) iDµν(q, t; t ′ ) = ∞� n=0 −iηµν q 2 − x 2 n + iɛ χn(t)χn(t ′ ) , (2.89) in which xn ≡ mn/MKK and mn denotes the mass of the nth KK mode. This shows how the 5D propagator is equivalent to the exchange of the whole KK tower and represents another connection to the strongly coupled dual theory, compare (2.42). It also follows that the normalization of the kinetic terms imposes the orthonormality relation 2π L � 1 ɛ dt t χm(t)χn(t) = δmn . (2.90) Further, all terms including derivatives with respect to φ and the bulk mass have to be matched to a 4D mass term for each mode. The resulting equations are called EOM, and read for the vector component � 1 − t∂t t ∂t + c2 A t2 � χn(t) = x 2 nχn(t) . (2.91)
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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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112 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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On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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