On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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150 Chapter 4. The Asymmetry in Top Pair Production Following [222], we introduce the charge-asymmetric (a) and -symmetric (s) averaged differential cross sections. In the former case, we define � dσa 1 dσ ≡ d cos θ 2 p¯p→t¯tX � dσp¯p→¯ttX − , (4.23) d cos θ d cos θ with dσ p¯p→t¯tX /d cos θ given in (4.19). The corresponding expression for the chargesymmetric averaged differential cross section dσs/d cos θ is simply obtained from the above by changing the minus into a plus sign. The notation indicates that in the process labeled by the superscript p¯p → t¯tX (p¯p → ¯ttX) the angle θ corresponds to the scattering angle of the top (antitop) quark in the partonic CM frame. Using (4.23) one can derive various physical observables in t¯t production. For example, the total hadronic cross section is given by σ t¯t = � 1 The total t¯t charge asymmetry can then be defined as −1 � 1 A t 0 c ≡ � 1 0 d cos θ dσs . (4.24) d cos θ d cos θ dσa d cos θ d cos θ dσs d cos θ . (4.25) Since QCD is symmetric under charge conjugation, it allows to identify dσp¯p→¯ttX � � � � d cos θ = dσp¯p→t¯tX � � � � d cos θ , (4.26) � cos θ=c � cos θ=−c for any fixed value c. As mentioned in the previous section, the charge asymmetry can then be understood as a forward-backward asymmetry � 1 A t c = A t 0 FB ≡ � 1 0 σa = αs m 2 t d cos θ dσp¯p→t¯tX d cos θ − � 0 d cos θ dσp¯p→t¯tX d cos θ + i,j 4m 2 t −1 � 0 −1 d cos θ dσp¯p→t¯tX d cos θ d cos θ dσp¯p→t¯tX d cos θ = σa . (4.27) σs It makes sense to express contributions to the symmetric and asymmetric cross section already at the level of the hard scattering kernels, σs = αs m2 � � s t i,j 4m2 dˆs s t ffij � � � � 4m2 t ˆs/s, µf Sij . (4.28) ˆs � � s dˆs s ffij � � � � 4m2 t ˆs/s, µf Aij , (4.29) ˆs
¯q q (a) t ¯t 4.2. The Forward-Backward Asymmetry in the SM 151 ¯q q Figure 4.2: Cut diagrams which contribute to the charge asymmetry at O(α 3 s) in QCD. The cuts refer to the initial- and final state interference and the box diagram- Born level interference respectively. with the corresponding expansion (4.20). Since the coefficients (4.21) and (4.22) are symmetric under cos θ → − cos θ, one finds for the LO SM coefficients S (0) πβρ q¯q = αs S (0) gg = αs 27 πβρ 192 ¯q q (2 + ρ) , (4.30) � 1 β ln � � 1 + β �16 2 + 16ρ + ρ 1 − β � � − 28 − 31ρ , (4.31) A (0) q¯q = A (0) gg = 0 . (4.32) This result is not surprising, considering that QCD couples purely vectorially and that the diagrams in (4.16) do not discriminate between the final quark and antiquark. At NLO however, there are diagrams which are odd under the exchange of the final state top with the final state antitop. In this case, a vector coupling contributes maximally. The diagrams in question are shown in the form of cut diagrams in Figure 4.2 and refer to the interference of initial- and final-state radiation and the interference of the box with the born level diagram. In principle, there is also a small contribution from different quark-gluon scattering amplitudes, but their contribution to the asymmetry is roughly an order of magnitude smaller compared to the ones discussed here, see [215, Fig.4]. The same holds true for QCD-electroweak interference, which can be obtained from replacing the s-channel gluon or one of the gluons in the box in Figure 4.2 by Z or γ, for which α 3 s → αeα 2 s. The diagrams (a) and (b) in Figure 4.2 have the color structure [215] C (a) = 1 N 2 � Tr T C a T b T c� � Tr T a T c T b� = 1 C (b) = 1 N 2 Tr C 16N 2 C � T a T b T c� � Tr T b T c T a� = 1 16N 2 C (b) t ¯t � 2 fabc + d 2 � abc � 2 − fabc + d 2 � abc , (4.33) in which Ta = λ a /2 are the SU(3)C generators with λ a the Gellmann matrices, and fabc denote the structure constants and dabc the totally symmetric d symbols of SU(3)C. Since the color-stripped contributions to the asymmetry from the diagrams (a) and ¯q q
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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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Page 110 and 111: 100 Chapter 3. Solving the Flavor P
Page 156 and 157: 146 Chapter 4. The Asymmetry in Top
Page 186 and 187: 176 Chapter 5. Conclusions describe
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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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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