On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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172 Chapter 4. The Asymmetry in Top Pair Production ctL ctR ˜C V uū/αs ˜C A uū/αs ˜C V d ¯ d /αs ˜C A d ¯ d /αs ˜C V tū/αs −0.46 0.11 14.5 −2.66 · 10 −2 14.3 −17.5 · 10 −2 −12.8 · 10 −4 −0.47 0.50 17.6 −5.82 · 10 −2 17.6 −6.41 · 10 −2 −20.2 · 10 −4 −0.49 1.00 19.4 −22.2 · 10 −2 19.6 −11.3 · 10 −2 15.5 · 10 −4 Table 4.2: Results for the Wilson coefficients corresponding to three different parameter points. The numbers shown correspond to the RS model with SU(3)D × SU(3)S × SU(2)L × U(1)Y bulk gauge symmetry and brane-localized Higgs sector. The coefficients scale as (1 TeV/MKK) 2 . Further details are given in the text. Since cuR < −1/2 for all parameter points, this would only allow for a positive contribution to A (0) uū,RS+A , if either ctR < −1/2 as well or cuR > −1/2, which both are choices that will undermine the generation of flavor hierarchies with O(1) Yukawa couplings or the RS GIM suppression of FCNCs. In addition, because the contributions to S (0) uū,RS+A are enhanced as well, which leads to a further suppression by the total inclusive cross section in the denominator of are strictly negative, and larger then in the minimal (4.27), the contributions to At FB model. However, the absolute size of the corrections that can be generated in the extended model is still an order of magnitude too small for realistic values of MKK, because all contributions to the asymmetric cross section feel the localization of the light up quarks. It is interesting to note, that one can understand from the dual theory, why the new resonances although they couple almost purely axial to quarks, and the tops are extremely IR localized, do not lead to larger effects. The deeper reason for this is the fact, that unlike for the gluon, for the axigluon there is no elementary field in the dual Lagrangian. In the analysis of the bulk gauge boson propagator in Section 2.3, we found, that only for Neumann BCs in the UV, which corresponds to the existence of an elementary field in the dual theory, terms which are proportional to only one of the bulk coordinates t or t ′ appear in the small momentum expansion. This makes sense, because we could also show that these terms are related to diagrams which mix the composites with the elementary bosons. As a consequence, the gluon KK tower does contribute terms which are only proportional to the top localization to CV uū, because there are diagrams with the gluon coupling to up quarks and then mixing into its composite partner, which couples strongly to the tops. On the other hand, the axigluon KK modes always contribute terms suppressed by the zero mode profiles of the up quark to CA uū, because the only possible diagrams include the axigluon composites coupling to the composite partners of the up quarks, and the mixing between up composites and elementaries is suppressed by exactly those ZMA profiles. In contrast, an RS axigluon with only Dirichlet BCs in the IR (due to an IR brane Higgs sector) and Neumann BCs in the UV would lead to a sum over the KK tower of the type (2.87), which in turn would furnish a sizable contribution to At FB . In order to make these results comparable to the findings in the minimal model, we give the Wilson coefficients in the extended model in Table 4.2 for the same reference
4.6. Axigluon Contributions to the Cross Section and the Asymmetry 173 A t FB �� 8.8 8.6 8.4 8.2 8.0 SU�3�S � SU�3�D 2 4 6 8 10 MKK �TeV� tanΒ�0.5 Figure 4.9: A t FB in the extended RS model with SU(3)D × SU(3)S strong interaction bulk gauge group, plotted for the complete dataset versus MKK. The red line indicates the SM value. points and for θ = 45 ◦ and tan β = 1/2. We refrain from giving the result for the coefficient of the scalar operator even though it may be larger by a factor of a few, depending on the different contributions from the extended Higgs sector, the generic suppression of these contributions will prevail in the extended model. 11 Note, that for tan β = 1/2, the contributions to ˜ C V uū in Table 4.2 are already large, but still feasible, as can be seen from the green points plotted in Figure 4.10. Further, the analogue of the scatter plot in Figure 4.8 for the forward backward asymmetry versus the KK scale is shown in Figure 4.9 for the extended model and θ = 45 ◦ and tan β = 1/2. One can see, that the effects are enhanced due to the relocalization of the top quarks, but still do not exceed −0.5% even for extremely small KK scales and go invariably in the wrong direction for a possible explanation of the measured asymmetry. We can conclude from the results found in both the minimal and the extended RS model, that without invoking additional ad hoc assumptions about the flavor structure of the light-quark sector, the RS model and the corresponding strongly coupled theories can not explain the asymmetry, even if a resonance with purely axial couplings is introduced. There thus seems to be a generic tension between having large effects in At FB and achieving a natural solution to the flavor problem. 11 This is the case, because the couplings to quarks are still proportional to the Yukawa couplings for all new scalar fields.
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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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92 Chapter 3. Solving the Flavor Pr
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100 Chapter 3. Solving the Flavor P
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Page 188 and 189: 178 Appendix A. Generating Paramete
Page 190 and 191: 180 Appendix A. Generating Paramete
Page 192 and 193: 182 Appendix B. Neutral Meson Mixin
Page 194 and 195: 184 Appendix B. Neutral Meson Mixin
Page 197 and 198: C Input Parameters This appendix is
Page 199: Parameter Value ± Error Reference
Page 202 and 203: 192 Appendix D. Higgs Potential for
Page 204 and 205: 194 Bibliography [13] S. Dimopoulos
Page 206 and 207: 196 Bibliography [43] G. Nordström
Page 208 and 209: 198 Bibliography [72] K. S. Babu,
Page 210 and 211: 200 Bibliography [104] R. Contino a
Page 212 and 213: 202 Bibliography [133] M. Baak, M.
Page 214 and 215: 204 Bibliography [160] J. Charles,
Page 216 and 217: 206 Bibliography [185] C. Csaki, G.
Page 218 and 219: 208 Bibliography [213] E. Thomson e
Page 220: 210 Bibliography [239] V. Ahrens, A
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