On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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156 Chapter 4. The Asymmetry in Top Pair Production ) 2 xf(x,Q 1.2 1 0.8 0.6 0.4 0.2 0 10 -4 10 g/10 c, c -3 MSTW 2008 NLO PDFs (68% C.L.) s, s 10 2 2 Q = 10 GeV -2 u d u d -1 10 1 x ) 2 xf(x,Q 1.2 1 0.8 0.6 0.4 0.2 0 10 -4 b, b 10 -3 c, c 2 4 2 Q = 10 GeV 10 g/10 s, s -2 u d d u -1 10 1 x Figure 4.4: Figure shows a plot of the PDFs of the gluon and the valence and sea quarks in the proton for Q 2 = 10 GeV 2 and Q 2 = 10 4 GeV 2 . They are taken from the homepage of the MSTW collaboration and were computed using MSTW2008NLO [228]. from which the former has the same color flow as the t channel diagram and thus leads to interference [229]. The common characteristic of models featuring large t channel currents is a sizable flavor off-diagonal coupling between the up (or down) and the top quark, while other flavor changing couplings have to be under control in order to not violate bounds from FCNCs. This can be realized by a W ′ or Z ′ gauge boson with accordingly adjusted couplings, so that the relevant interaction terms read � LZ ′ /W ′ ∋ ¯t g Z′ V + g Z′ � A γ5 γ µ Z ′ � µu + ¯t W ′ gV + g W ′ A γ5 � γ µ W ′ µd . (4.43) The corresponding expressions for the cross sections will not be explicitly repeated here and can be found for the Z ′ in [230, Sec VI] and for the W ′ in [231, Sec.II]. In the case of interference between t and s channel, both vector and axial vector couplings contribute equally to the cross section and the asymmetry and one has therefore more freedom to choose the couplings. If there is no flavor diagonal coupling however, the new gauge bosons are forced to decay into top quarks which will yield a clear signal of like sign leptons. Searches for this final state already place very strong bounds on the parameter space of these resonances, except for a Z ′ , W ′ which is too light to decay into the top [232, 233]. This typically excludes models with resonances in the few 100 GeV range which is preferred in order to explain the large asymmetry assuming perturbative couplings. Analogous considerations apply to a scalar with flavor off-diagonal couplings. The
4.4. Cross Section and Asymmetry in the Minimal RS Model 157 interaction terms for different color representations in the Lagrangian read [234] Lφ ∋ ¯t(g φ V + gφ Aγ5)φ a 1,8 ˜ T a 1,8u + ¯t c (g φ V + gφ Aγ5)φ a 3,6 ˜ T a 3,6u , (4.44) in which the subscript identifies the color representation of the scalar as singlet, triplet, sextet or octet, ˜ T a denotes the corresponding SU(3)C Clebsch Gordon coefficient which connects it to the two quarks and t c = iγ 0 γ 2 t. The corresponding contribution to the cross section can be found in [234, Sec. III] and we content ourselves with quoting the result, that the sextet and triplet color representation can accommodate the asymmetry while the color singlet and octet runs into trouble with other observables. Taking into account the LHC measurements does require similar adaptations as in the case of s channel models and leads to a modification of the already very tuned flavor-changing couplings. 4.4 Cross Section and Asymmetry in the Minimal RS Model In the RS model, many of the contributions described in Section 4.3 are generated. Since left- and right-handed fermions are localized at different points in the bulk, the KK gluon couplings to quarks are in general not purely vector-like, but receive nonvanishing axial-vector components. These couplings generate a charge asymmetry in top-quark pair production at the Born level, which is associated to quark-antiquark annihilation q¯q → t¯t and proceeds through tree-level exchange of KK gluons in the s channel. Further corrections to A t FB arise from the fact that the couplings of KK gluons and photons, the Z boson and its KK excitations, as well as the Higgs boson are flavor non-diagonal, leading to the flavor-changing uū → t¯t transition which affects the t channel. 5 The corresponding diagrams are shown in Figure 4.5. On the other hand, the gluon-fusion channel gg → t¯t does not receive a correction at Born level, since owing to the orthonormality of gauge-boson wave functions the coupling of two gluons to a KK gluon is zero. Leading Order Contributions of the RS Model with and without Custodial Protection The effective Lagrangian needed to account for the effects of intermediate vector and scalar states reads Leff = � � � C (V,8) q¯q,AB Q(V,8) q¯q,AB + C(V,8) tū,AB Q(V,8) tū,AB + C(V,1) tū,AB Q(V,1) tū,AB + C(S,1) tū,AB Q(S,1) � tū,AB , q,u A,B=L,R (4.45) 5 In principle, also the d ¯ d → t¯t transition receives corrections due to the t channel exchange of the W boson and its KK partners. However, these effects are negligibly small for viable values of MKK and will therefore be ignored in the following.
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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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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,
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206 Bibliography [185] C. Csaki, G.
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210 Bibliography [239] V. Ahrens, A
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