On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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170 Chapter 4. The Asymmetry in Top Pair Production 4.6 Axigluon Contributions to the Cross Section and the Asymmetry The conclusions drawn in Section 4.3 and at the end of the last Section suggest that a new resonance with mainly axial vector couplings can bring the measured value of the forward backward asymmetry in agreement with the SM prediction. The model introduced in Chapter 3, which features an extended strong interaction gauge group SU(3)D ×SU(3)S in the bulk fulfills some of the criteria which we identi- fied as essential for a solution of the A t FB puzzle in Section 4.3. It provides a large axial vector coupling with negligible vector coupling component for mixing angles θ ≈ 45 ◦ preferred by the flavor sector. Further, the couplings are large for the top, even larger then in the minimal model, because the extended scalar sector implies extremely IR localized top profiles. In addition, the extended model furnishes a hierarchy between couplings to down and to up type quarks, which is rooted in the different scalar fields which provide their masses. Such a hierarchy might explain why the measurements point to a smaller asymmetry at a machine which collides protons that contain equal shares of ū and ¯ d quarks, compared to a proton-antiproton collider which provides 3/2 more ū than ¯ d in the initial state. From (3.63) and (3.108), one finds that in the model with extended color gauge group the Wilson coefficients in (4.55) take the form � 1 C (V,8) q¯q,� C (V,8) q¯q,⊥ C (V,8) tū,� = − παs 2M 2 KK = − παs 2M 2 KK παs = − M 2 L KK L − (∆′ Q)11 − (∆ ′ Q)33 − p 2 q (∆ ′ q)11 − p 2 q (∆ ′ q)33 � 1 + 2L c 2 θ ( � ∆Q)11 ⊗ ( � ∆Q)33 + p4q s2 ( θ � ∆q)11 ⊗ ( � ∆q)33 − vIR � 2 tθ (∆Q)11(∆Q)33 + p 4 4 qct 2 θ (∆q)11(∆q)33 � �� , (4.72) � 1 L − (∆′ Q)11 − (∆ ′ Q)33 − p 2 q (∆ ′ q)11 − p 2 q (∆ ′ q)33 � 1 c 2 θ + p2qvIR 2 L � � (∆Q)11(∆q)33 + (∆Q)33(∆q)11 � , (∆Q)13 ⊗ ( � ∆Q)31 + p4q s2 (∆q)13 ⊗ ( θ � ∆q)31 − vIR � 2 tθ (∆Q)13(∆Q)31 + p 4 4 qct 2 θ (∆q)13(∆q)31 � � , and C (V,1) tū,� is not modified by the axigluon KK modes, but only by the relocalization of the fermions and is therefore not repeated here. In the above expressions, only O(v 2 /M 2 KK ) contributions are kept, except for terms ∼ vIR, that become significant if the suppression from vIR is balanced by powers of pu, which parametrizes the effect
4.6. Axigluon Contributions to the Cross Section and the Asymmetry 171 of the IR shift of the up-type quarks due to the extended Higgs sector. This factor is defined in (3.105) and is a function of tan β, which is preferred to be small by flavor observables. From the expressions (4.72) one can infer, that the tensor structures contributing to C (V,8) in the minimal model cancel between the gluon and the axigluon contributions, q¯q,⊥ which is expected, because this effect is exactly what renders the contributions to ɛK small. In contrast to the down sector however, the remaining contributions are ∼ vIRp2 u (for up quarks in the initial state), which is not small, because p2 u > p2 d if tan β < 1. The definition of the relocalization factors pu, pd is given in (3.105), and for our reference value tan β = 1/2, one finds p2 u = 15. It follows for the ZMA relations for the symmetric and antisymmetric hard scattering kernels introduced in (4.50) and (4.52) in the case of the extended model, S (0) uū,RS+A A (0) uū,RS+A ∼ αsπ M 2 KK αsπ ∼ − M 2 L KK � F 2 (ctL ) + F 2 (cuL ) + p2 uF 2 (ctR ) + p2 uF 2 (cuR ) − p2 uvIR 4 � , (4.73) � 1 c2 � 4 θ 3 − s2 � vIR θ F 3 2 (ctL )F 2 (cuL ) + p4u s2 � 4 θ 3 − c2 � vIR θ F 3 2 (ctR )F 2 (cuR ) � F 2 (ctL )F 2 (cuR ) + F 2 (ctR )F 2 (cuL ) � � , (4.74) which has to be compared to (4.58). The cancellation of contributions to C (V,1) tū,� are the reason for the absence of a term with overall positive sign in A (0) uū,RS+A , which is not formally of the order v 4 /M 4 KK , because vIR ∼ v 2 /M 2 KK . Keep in mind, that the asymmetric cross section σa in the minimal model is positive, if the condition (4.63) is fulfilled. Naively, one might think that this leads to an even larger set of parameter points for which σa > 0 in the extended model, due to the IR shift of the up-type quark localization parameters. However, condition (4.63) basically ensures ) dominates in A(0) in (4.73). This would not lead that the term ∼ F 2 (ctR )F 2 (cuL uū,RS to a positive asymmetric cross section in the extended model, because this term is suppressed by vIR/p 2 u compared to the leading negative contribution to A (0) uū,RS+A . In this explicit example, we recover the result from Section 4.3, that an axigluon generically generates the wrong sign in the asymmetry. A two Higgs doublet model on the IR brane with tan β < 1 would actually lead to an overall positive σa > 0, but the cancellations in the left-right chirality operator due to the axigluon tower spoils this effect. In writing only the dominant terms in (4.73) and using the approximation (4.60), this becomes even more apparent, S (0) uū,RS+A A (0) uū,RS+A ∼ 2παs M 2 KK 2παs ∼ M 2 L KK p4u s2 θ � 1 2 + p2 u 2 + ctL + p2 � uctR , (4.75) � 4 3 − c2 � vIR θ (1 + 2ctR 3 )(1 + 2cuR )eL(2cuR +1) . (4.76)
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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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100 Chapter 3. Solving the Flavor P
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Page 190 and 191: 180 Appendix A. Generating Paramete
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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
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Page 204 and 205: 194 Bibliography [13] S. Dimopoulos
Page 206 and 207: 196 Bibliography [43] G. Nordström
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