On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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82 Chapter 2. The Randall Sundrum Model and its Holographic Interpretation and |F (cd1 )| 1 ∼md |F (cu3 )| mt λ3 |F (cu1 )| mu 1 ∼ |F (cu3 )| mt λ3 |F (cd2 )| ms 1 ∼ |F (cu3 )| mt λ2 |F (cu2 )| mc 1 ∼ |F (cu3 )| mt λ2 |F (cd3 )| mb ∼ , (2.168) |F (cu3)| mt which in turn make the hierarchical structure of the rotation matrices (2.159) and (2.160) clearly visible. Because only ratios or products of profile functions are fixed by the above relations, there is some freedom in rescaling a given set of profile functions and Yukawa matrices and still end up with a set of parameters, that reproduces all physical input parameters. From (2.158) it is evident that this can either be done by reshuffling between the singlet and doublet profiles and keeping the Yukawas unchanged, F (cQi or by rescaling both the profiles and the Yukawas 1 ) → ηF (cQi ), F (cqi ) → F (cqi ) , (2.169) η F (cQi ) → ηF (cQi ), F (cqi ) → ηqF (cqi ) , Y q → 1 Y q . (2.170) ηηq This freedom will be referred to as reparametrization invariance and will be a convenient tool in estimating whether regions of parameter space which are not covered directly in the numerical analyses would change the conclusions without the need to generate a whole new set of parameter points. One should be careful in taking advantage of this freedom, because a rescaling of the Yukawa matrix should not clash with the assumption of order one Yukawa couplings. Also, one should be aware that a large reparametrization of the zero mode profiles implies changes of the localization parameters, which can lead to a shift of some profiles from the UV in the IR and result in severe bounds from FCNCs, as we will see in the next section. The range of sensible values for η and ηq is therefore not unlimited. In the dual theory, the zero mode profiles are equivalent to the functions defined below (2.47) and the bulk parameters to the anomalous dimensions of the composite quark partners. Referring to Section 1.1, the profile functions can be understood as the mixing angles (1.30), so that the equations (1.31), (2.47) and (2.154) are basically the same in different languages. The derivation of hierarchies in the quark sector in the dual theory is explained in the corresponding Sections 1.1 and 2.2. Reparametrization invariance is the freedom of choosing the degree of compositeness in the dual theory and corresponds to a reshuffling between the c-parameters in (2.46). Therefore, the dual theory allows for a better understanding of the the limitations of the rescaling parameters η, ηq. Based on Figure 2.3, one can see that a rescaling of the profile functions of the light quarks towards the IR will not affect the generation of the masses and mixing angles, but will make the light quarks more and more composite, which in turn would not only lead to
2.5. Hierarchies in Quark Masses and Mixings and the RS GIM Mechanism 83 qi qj t t ′ Figure 2.10: Four fermion diagram leading to ∆F = 1 and ∆F = 2 processes. FCNCs, but also imply form factors (see [125, Sec. 3.3] for explicit calculations) clearly in tension with the most recent experimental limits on quark compositeness [126]. The RS-GIM Mechanism The Higgs, being confined to the IR brane is in the dual theory interpreted as a fully composite state, and its overlap with the zero modes of the light flavor quarks is small, because they correspond to mostly elementary states which do not couple to the Higgs. Similarly, gauge boson KK modes are almost entirely composites and are therefore localized towards the IR brane. As a byproduct of the mass generation by an IR brane localized Higgs, this also keeps the couplings between light flavor quarks and these new resonances small. Most importantly, FCNCs which appear at tree level due to the couplings being non-universal in flavor space are exponentially suppressed by the zero mode profile functions (2.151). This is called the RS-GIM mechanism, in reference to the SM GIM mechanism, which explains why loop-level FCNCs in the SM are small. Both rely on the fact, that small quark masses enter in the couplings. In both cases, the absence or even the equality of all quark masses (bulk mass parameters) would eliminate FCNCs. One could worry that effects in the RS model might still be significantly to large, because they appear at tree level, while SM FCNCs are suppressed by a loop factor. This is however balanced by the KK modes being heavy, so that the new physics scale provides an additional suppression. All experimental evidence points in the direction of small FCNCs in very good agreement with the SM and thus the requirement 1 M 2 × m KK 2 q ≈ 1 16π 2 × m2 q M 2 W qk ql (2.171) can be understood as a very rough estimate of the new physics scale expected if an RS-GIM mechanism is realized in nature. Remarkably, this puts it in the ballpark of MKK ∼ 4πMW , which is what one would expect from a model designed to solve the gauge hierarchy problem. It should be stressed, that it is especially noteworthy if not unique, that flavor points to the TeV scale in a new physics model with no additional assumptions regarding couplings in the flavor sector (a.k.a. MFV).
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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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132 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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