On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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136 Chapter 3. Solving the Flavor Problem in Strongly Coupled Theories �ΕK � 1000 10 0.1 0.001 10 �5 tanΒ�0.1 tanΒ�0.5 tanΒ�1 tanΒ�2 tanΒ�5 2 4 6 8 10 MKK �TeV � Figure 3.10: Plot of the fit to |ɛK| versus MKK for six different values of tan β, in which the curves are from left to right for tan β = 0.1, 0.5, 1, 2, 5. for 2 < tan β < 5, the bound becomes as bad as in the minimal model. Therefore, if the extended color symmetry group is realized in nature, very small tan β < 2 are a necessary prediction for the minimal Higgs sector. Note, that implementing a custodial protection will shift the extracted value for MKK from Figure 3.7 by roughly a TeV, for the reasons explained in Section 3.7. This induces a tension, because even for tan β < 1 the extracted bound becomes MKK > 4 TeV. Another new source of contributions to ɛK arise from the exchange of the neutral color octets in the extended Higgs sector. In general, such a new scalar can lead to large FCNCs, but not if it couples proportional to the Yukawas, for details compare the model-independent analysis [197]. Such a MFV coupling is naturally implemented here and the flavor changing couplings arise only due to the mixing between fermion zero mode and KK modes as in the case of a brane-localized color singlet [196]. It is straightforward to determine the size of these FCNCs by inserting (3.85) into (3.60) and compare the result with the FCNC inducing couplings of the brane localized SM Higgs in (2.189). One can immediately read off that the couplings will be enhanced compared to the singlet scalars by a factor of √ 2NC. However, on the basis of (2.189) and (2.184), this still results in an overall suppression of v 4 /(m 2 O M 4 KK ) for the octet contribution to the Wilson coefficients, in which mO denotes the mass of the octet scalar. 13 We find that they can be neglected for realistic masses for the color octet. 13 Note, that the mass of the octet depends sensitively on the choice of parameters in the Higgs potential and is not trivially connected to the SM Higgs mass.
3.7 Flavor Observables and LHC Bounds 3.7. Flavor Observables and LHC Bounds 137 As elaborated in the last section, the extension of the color gauge group in the bulk makes it necessary to introduce an extended scalar sector and as a consequence changes the localization of the quarks along the extra dimension. Therefore not only observables in which the new axigluon resonances directly mediate FCNCs change in the extended model, but also processes which involve only photon or Z exchange. In this section we will therefore comment on the new contributions to observables discussed in the earlier sections of this chapter and repeat the numerical analyses with the axigluon contributions as well as the fermion localization implemented. . We will also analyze the bounds from direct detection experiments for the color octet and axigluon resonances at the LHC. Electroweak Precision Observables The modification of the strongly coupled sector will not give direct contributions to the oblique parameters and the relocalization of the fermions does also not affect the analysis in Section 3.1, because only flavor universal contributions have been considered there. In principle, a color octet, electroweak doublet scalar leads to modifications of the electroweak gauge boson propagators via loop insertions. A model independent analysis yields an upper bound on the mass splitting between charged and neutral color octets of O(50) GeV in order to agree with the T parameter [198]. This splitting depends on the parameters in the Higgs potential and can be used as a constraint for generating the physical spectrum. Note also, that we have not considered loops of KK fermions or gauge bosons in Section 3.1, which might change these conclusions. Corrections to the Z → b ¯ b vertex depend sensitively on the localization of the bottom quark. The extended color sector shifts all right-handed quarks closer to the IR brane, so that effectively only modifications to the coupling of the Z to right-handed b quarks gb R in (3.11) play a role.14 From (3.108) one can infer that the relocalization amounts to a factor p2 d of the RS contribution δgb R . Since these corrections go in the wrong direction and are already enhanced in the custodial model, the Z ¯ bb constraint also prefers small tan β, which is in line with the parameter region favored by ɛK. The resulting scatter plot in the extended model is shown for tan β = 1/2 and θ = 45 ◦ in Figure 3.11, and despite the misleading scaling, still more than 95% do agree with the measurements at 99% CL. Flavor Violating Observables Although the extended gauge sector leads to smaller values for ɛK, the contributions to ∆B = 2 observables as discussed in Section 2.6 may be even larger in the RS model with extended color gauge group. The reason is, that for K − ¯ K mixing the mixed 14 There is also a modification for the second term in (3.10), but this term is suppressed by m 2 b/m 2 Z.
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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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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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