On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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26 Chapter 1. Introduction: Problems beyond the Standard Model where the 5D curvature, derived from GMN, and the 4D curvature, derived from the 4D block of GMN, gµν = e −2σ ηµν, are related by R5(G) = e 2σ(φ) R4(g) + . . . up to terms which vanish upon φ-integration or cancel with cosmological constant terms. Matching with the 4D Einstein-Hilbert action implies that M 2 Pl = M 3 Pl(5) k � 1 − e −2krcπ� , (1.53) which, as a consequence of the strong curvature, is largely independent of the radius rc, in contrast to (1.47). Likewise, the masses of the KK excitations are not tied to the radius of the extra dimension, but depend on the curvature scale mn ∼ nMKK, where MKK ≡ ke krcπ = k ΛIR ΛUV . (1.54) The observation, that (1.53) is not sensitive to the limit rc → ∞ led to a subsequent paper of Randall and Sundrum, in which they proposed a model with an infinite warped extra dimension as an alternative to compactification [56]. Equation (1.50) suggests, that solving the hierarchy problem only require the Higgs to stay at the IR brane. The conclusions are not altered if all other SM fields are promoted to bulk fields, which was explored soon after the original paper for bulk gauge bosons in [57], and bulk fermions in [58, 59]. Similar to the split fermion idea in UED, a localization in the bulk will lead to a suppression of dangerous higher dimensional operators, because the overlaps of the extra dimensional wavefunctions determine the size of the couplings. Due to the warping it can also accommodate hierarchical fermion masses and mixings coming from anarchic 5D Yukawa couplings, as well as a suppression of tree-level flavor violating effects. These features will be elaborated on in Section 2.4 and 2.5. In the context of the AdS/CFT duality, it can be motivated, that the RS model is dual to a strong interacting four dimensional theory, see Section 2.2. Therefore, many concepts introduced in Section 1.1 have an alternative, so called holographic 5D description, which may at first glance look like an entirely different theory. So is for example the warped higgsless model dual to a walking TC theory [63]. The warped version of a gauge-Higgs unification model is a dual description of a composite pseudo-Nambu Goldstone Higgs 19 [62, Sec.4] and the mechanism of collective symmetry breaking can be implemented by an enlarged bulk gauge group [60]. It is interesting to note, that this dual description for the RS scenario, where gravity is in the bulk and the graviton can therefore be understood as a composite of the brane Yang-Mills theory seemingly contradicts a no-go theorem, the Weinberg-Witten theorem [79]. It states among other things, that a massless graviton cannot be a composite state. Very reminiscent of the Coleman-Mandula theorem and SUSY, the AdS/CFT correspondence makes use of a loophole, because the 5D graviton can be described by a composite state on the four dimensional boundary, see [80] for details. 19 An indication of this relation may be that the extra-dimensional components of the gauge fields transforms under the 5D gauge symmetry like under a shift symmetry.
u,c,t q γ W q u,c,t s 1.2. Solutions to the Flavor Problem 27 Figure 1.8: Diagrams contributing to FCNCs in the SM. 1.2 Solutions to the Flavor Problem s ¯d u c t u c t The famous question of “Who ordered the muon?” has now been escalated to “Why does Nature repeat herself ?” Frank Wilcek & Anthony Zee Hierarchies in the flavor sector are not radiatively unstable and might therefore be considered a less severe problem then the gauge hierarchy problem. However, if the hierarchy problem is solved by new physics at the electroweak scale, one immediately runs into trouble with flavor observables. The reason is, that in the SM, the Z boson, the gluon and the photon couple flavor universal and as a consequence, flavor changing neutral currents (FCNCs) are loop-suppressed. Furthermore, these loop processes are additionally suppressed due to the so called GIM mechanism [67]. It is based on the fact, that flavor-violating diagrams, like the ones shown in Figure 1.8 can be described by an effective Hamiltonian H = � i Ci Oi (1.55) Λ2 with four quark operators Oi and Wilson coefficients CPenguin ∼ � λiF (mi) , CBox ∼ � i=u,c,t i,j=u,c,t d ¯s λiλj ˜ F (mi, mj) , (1.56) for the Penguin and Box diagram respectively. In this notation, the CKM factors are ⎧ ⎪⎨ V λi = ⎪⎩ ∗ isVid for K decays and K0 − ¯ K0 V − mixing, ∗ ibVid for Bd decays and B0 d − ¯ B0 d− mixing, (1.57) V ∗ ib Vis for Bs decays and B 0 s − ¯ B 0 s − mixing, so that in all cases unitarity of the CKM matrix enforces λu + λc + λt = 0 . (1.58) In the limit of equal quark masses, these processes would never occur through SM physics alone. This is rooted in the fact that the SM gauge interactions respect the
Page 1 and 2: On the Flavor Problem in Strongly C
Page 3 and 4: UNIVERSITY OF MAINZ ABSTRACT THEORE
Page 5 and 6: Contents Acknowledgements vii Prefa
Page 7: Acknowledgements First and foremost
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100 Chapter 3. Solving the Flavor P
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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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210 Bibliography [239] V. Ahrens, A
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