On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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104 Chapter 3. Solving the Flavor Problem in Strongly Coupled Theories measures the magnitude of the mass difference ∆ms relative to the one in the SM, while the phase φBs affects the coefficients of sin(∆Mst) in the time-dependent asymmetry of Bs → ψφ. One obtains [161] where Sψφ = sin(2|βs| − 2φBs) , (3.28) Vts = −|Vts| e −iβs , (3.29) and βs ≈ −1◦ . In the presence of a non-vanishing phase φBs, the time-dependent asymmetry measures therefore ϕs = |βs| − φBs, and not βs. Generally, (3.28) is only correct if only an negligible weak phase is present in the decay amplitude Bs → ψφ, which is the case for the SM. This assumption can be adopted in the RS model, because corrections to charged-current interactions are suppressed by m 2 W /M 2 KK and numer- ically arg(V ∗ cb Vcs) < 0.001 ◦ , and also the matrix elements in right-handed chargedcurrent interactions (VR)22 and (VR)23 do not exceed the level of 10 −5 in magnitude [115]. These tiny corrections can be safely neglected for all practical purposes. The width differences ∆Γs and the semileptonic CP asymmetries A s SL ∆Γs Γs � � ∆ms = − Γs A s � Γs 12 SL = Im M s � 12 with [158] � � Γs 12 Re M s 12 SM exp SM � � Γs 12 Re M s � cos 2φBs CBs 12 SM � � cos 2φBs Γs 12 − Re CBs M s 12 SM � Γs 12 − Im M s � 12 SM take the form � sin 2φBs , CBs sin 2φBs , (3.30) CBs = (−4.97 ± 0.94) · 10 −3 � Γs 12 , Im M s � = (2.06 ± 0.57) · 10 12 SM −5 . (3.31) In Figure 3.4, the width difference of the mass eigenstates normalized to the total width (3.30) is plotted against Sψφ as given in (3.28), which encodes the CP violation from mixing (see Appendix B for details). The SM prediction for this phase is extremely small and precise [160], 2β SM s = 0.0363 +0.0016 −0.0015 . (3.32) and therefore a good place to constrain new physics effects. Shaded yellow and blue are the 68% and 95% CL regions obtained from a global fit based on the most recent combination of measurements of the semileptonic CP asymmetry As SL , the mass difference ∆mBs, the phase φBs as well as ∆Γs [159]. Shown in red are parameter points which fulfill the constraints from Z → b¯b and from ɛK, which is discussed in Section 3.3. It is interesting to note, that the phase showed a 3σ deviation from the SM phase, based on a combination of almost one third of the DØ and CDF data back in 2008 [162]. New physics in general can accommodate a large phase. However it is hard to
�� 0.6 0.4 0.2 0.0 95 � CL 68 � CL � 0.2 �1.0 � 0.5 0.0 0.5 1.0 SΨΦ 3.2. RS GIM Working 105 Figure 3.4: Predictions for Sψφ versus ∆Γs/Γs in the custodially protected RS model with extended electroweak symmetry group. The red points reproduce the measured value of the Zb ¯ b couplings and of ɛK at the 99% and 95% CL. The black bar indicates the SM prediction and error and the yellow (gray) contours the experimentally preferred regions of 68% (95%) probability. generate in the RS model once the constraints from the Z → b ¯ b analysis and K − ¯ Kmixing are taken into account, as becomes clear from Figure 3.4, but can already be seen in our analysis in [150, Sec.5.4.2]. The 3σ discrepancy slowly melted away over the years by analyzing more and more data and the full CDF dataset (10fb −1 ) finally shows agreement with the SM within 1σ [163]. Even smaller errors could be obtained from the LHCb measurements [164], which also provide the dominant input for the combination [159] and are therefore the root for the small errors in our global fit 5 . The fact that the RS prediction does generically agree with this very constraining experimental results even for a KK scale of a few TeV, is an indication of the impressive range of the RS-GIM mechanism. B Meson Decays to Muons One might object, that ∆F = 2 observables are not the best place for a stress test of the RS-GIM mechanism, because the tensor structures (2.176) which enter the Wilson coefficients are sensitive to the fermion localization on both vertices, i.e. proportional to ∼ mbms/v 2 in the case of Bs − ¯ Bs mixing. We will therefore examine ∆F = 1 observables, again selected by the criteria that they depend on the localization of the 5 It should be noted, that the LHCb analysis did also resolve the long standing sign ambiguity of ∆Γs in favor of the SM [165].
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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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154 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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