On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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98 Chapter 3. Solving the Flavor Problem in Strongly Coupled Theories gR b 0.12 0.11 0.10 0.09 0.08 0.07 99� CL 95� CL 68� CL � 0.06 �0.430 �0.425 �0.420 �0.415 �0.410 � gL b gR b 0.11 0.10 0.09 0.08 99� CL 95� CL 68� CL 0.07 �0.426 �0.424 �0.422 �0.420 �0.418 �0.416 Figure 3.3: The plots show regions of 68%, 95% and 99% probability in the g b L − gb R plane. The best fit value is denoted with a cross and the experimental value with a star. The red colored regions indicate the predicted values of a large set of parameter points for the minimal RS model in the left panel and for the RS model with custodial protection in the right panel. Inserting the predicted SM values gb L = −0.42114 and gb R = 0.077420 [146, Table G3] for the left- and right-handed bottom-quark couplings into the relations (3.12), we obtain for the central values of the quantities in question R 0 b = 0.21474 , Ab = 0.935 , A 0,b FB = 0.1032 . (3.13) In comparison, the experimentally extracted values for the three “pseudo observables” read [146] R0 b = 0.21629 ± 0.00066 , Ab = 0.923 ± 0.020 , A 0,b FB = 0.0992 ± 0.0016 , � gL b ⎛ 1.00 −0.08 ⎞ −0.10 ρ = ⎝ −0.08 1.00 0.06 ⎠ , (3.14) −0.10 0.06 1.00 where ρ is the correlation matrix. This reproduces the deviations listed in Table 3.1. In contrast to the original analysis in [115, Sec. 6.4], the theoretical corrections to R 0 b pull the best fit value 3σ away from the experimental SM value, as can be seen in Figure 3.3, in which the best fit is denoted by a cross and the experimental value by a star. A new physics contribution that would improve this situation needs a large positive correction to gb R of the order of 20% and no contribution to gb L ( while a small negative shift would also improve the fit). As becomes clear from (3.10) and (3.11), RS corrections reduce the SM value of both gb R and gb L in magnitude, which corresponds to a negative shift of gb R and a positive one for gb L , pointing in exactly the oppo- are smaller by a factor of roughly site direction. In addition, the corrections to g b R �
δg b R /δgb L ∼ F (cbR )2 /F (cbL )2 for δg b = (g b RS −gb SM )/gb SM 3.1. Electroweak Precision Observables 99 , which is typically of the order of a few percent, because cbL is more IR localized in order to help realizing the large top mass in (2.158). The scaling on the plot in the left panel of Figure 3.3 however makes the gb R corrections completely invisible. As a consequence, our set of parameter points, which is chosen so that the correct quark masses and mixings are reproduced (see Appendix A for details), lies entirely in the red band shown in the left panel of Figure 3.3 and therefore fails to agree with the experiment within 3σ for the majority of points. Note, that the scaling of Figure 3.3 distorts the fact that there are still 10% of the parameter points in the 3σ ellipse. Translating this into a constraint for MKK would yield a very strong bound. One can invoke the reparametrization invariance introduced in section 2.5 in order to examine the characteristics of the parameter corner which is in agreement with this constraint. By reshuffling between F (cbL ) and F (cbR ) using (2.169), for η < 1, one increases δgb R /δgb L . For η = 1/2(1/3), about 35(45)% of the parameter points do at least not aggravate the already large discrepancy between the SM and the experiment. Thus, parameter points with strongly IR localized right-handed bottom quarks tend to give less dangerous corrections to the global fit in (3.14). It is interesting to discuss the implications for the dual theory of such a considerable reparametrization. Scaling down F (cbL ) will not only enlarge F (cbR ), but also F (ctR ), the zero mode of the right-handed top, which is already strongly IR localized. In a generalization of this shift to all generations, one can assume that all doublets are extremely UV localized and all singlets shifted towards the IR. The dual theory of such a model would have, to a good approximation, only right-handed quarks composites, while the left-handed quarks are elementaries. This right-handed compositeness was found to be a very attractive idea in [149], in which the relevance for the Z¯bb vertex was however not pointed out. In the later sections we will get back to this scenario and check the compatibility with other observables. This situation is also ameliorated by the mixing between the Z zero mode and the additional neutral composite vector bosons of the SU(2)R present in the custodially protected RS model [148]. This is especially intriguing, because as discussed in the previous section, the scalar sector of any extension of the SM should respect the custodial symmetry in order to not get into conflict with the oblique parameters. The mixing eliminates completely the L enhanced term in gb L and increases the L enhanced term in g b R by L → 3c2 w s 2 w L ≈ 10L. Therefore, corrections to g b L are dominated by the terms in the second line of (3.10), which can now account for both negative and positive modifications, controlled by the interplay of the singlet down quark localization parameters of all generations. Choosing the correct quark representations under the enlarged symmetry group and assuming the bulk symmetric under the exchange and make them purely SU(2)L ↔ SU(2)R, will further reduce the correction to g b L
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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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148 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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