On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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152 Chapter 4. The Asymmetry in Top Pair Production (b) are related by � � dσa � = −dσa � , (4.34) (a) (b) one can infer that the overall contribution must be proportional to A (1) q¯q ∼ 1 16N 2 αsd C 2 abc . (4.35) Note, that one factor αs is factored out in (4.28) and another one in (4.20), so that the A (n) ij will always be linear in αs although the overall contributions are ∼ α3 s. One can conclude, that the Born-Box diagram interference in Figure 4.2 gives a positive overall contribution, while the contributions from interference of initial- with final state radiation diagrams enter with the opposite sign. The exact computation reveals, that the latter are smaller, so that one ends up with a net positive asymmetry. The exact formulas are compiled in [215, App. A] and will not be repeated here. The final result can however be described by the parametrization A (1) q¯q = αs d 2 abc 16N 2 c � 5.994 βρ 1 + 17.948 β − 20.391 β 2 + 6.291 β 3 � + 0.253 ln (1 − β) , (4.36) which approximates the exact result with permille level accuracy. It has been obtained by integrating the expressions for the charge-asymmetric contributions to the differential t¯t production cross section over the relevant phase space. 2 Employing Nc = 3, d2 abc = � N 2 c − 1 � � N 2 c − 4 � /Nc = 40/3, mt = 173.1 GeV, and αs(mt) = 0.126, one can plot (4.36) as a function of the square root of the CM energy √ s. This is shown by the solid black plot in the left panel of Figure 4.3, while in the right panel A (1) q¯q is multiplied with the up-quark PDFs ffuū(ˆs/s, µf ) and also plotted in solid black. In both cases the function peaks at √ s ≈ 420 GeV, i.e. around the t¯t threshold. The right panel shows also, that the integrated asymmetry (4.29) will be saturated long before the upper integration limit s is reached, which is rooted in the fact that the quark luminosities behave roughly like 1/ˆs 2 . These results can be compared with the plots of the exact calculation, which can be found in [215, Fig. 7]. 4.3 New Physics and the Forward-Backward Asymmetry Since it is the only observable dealt with in this thesis, which shows significant deviations from the SM and because top physics are largely unaffected by hadronic uncertainties, it makes sense to categorize what kind of new physics would be able to explain the observed deviation. Severely constrained by the requirement to achieve agreement with the SM regarding the other observables introduced in Section 4.1, the vast space of new physics models can be reduced to two different classes, new physics 2 The numerical integration has been performed using the Vegas Monte Carlo algorithm imple- mented in the CUBA library [223]
A (1) q¯q 0.15 0.10 0.05 0.00 4.3. New Physics and the Forward-Backward Asymmetry 153 500 1000 1500 2000 √ ˆs [GeV] dσa/d √ ˆs [fb/GeV] 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 400 500 600 700 800 900 1000 √ ˆs [GeV] Figure 4.3: The asymmetric coefficient A (1) q¯q (left panel) and the differential hadronic asymmetry dσa/d √ ˆs (right panel) as functions of √ ˆs in the SM plotted in solid black and in the minimal RS model plotted in dashed black. which contribute through the s channel and new physics which contribute through the t or u channel. New Physics in the s Channel From the SM calculation it is clear, that if the effect is due to s channel exchange of some new resonances, it will only lead to an asymmetry if these new resonances have sizable axial vector couplings to the SM quarks. In addition, the vector couplings should be under control in order not to induce a large contribution to the total inclusive cross section. Direct searches do also prefer heavy resonances, so that the interference with the gluon s channel diagram will give the dominant contributions, while the new physics squared contribution can be neglected away from the resonance peak. Such an interference term from new physics in the s channel can only contribute to the asymmetry if the new resonance is a spin 1 boson, which is a consequence of the Dirac structure. Scalar color octets do not contribute to the asymmetry even if they have purely axial couplings, compare [224, Sec. II], and references therein, while colored spin 2 resonances exchanged in the s channel do not interfere with gluons at all [225]. Such a new resonance will thus lead to an additional term in the Lagrangian LA ∋ gsT a � qi ¯qi gV + gqi A γ5 � µ a γ Aµ qi , (4.37)
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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
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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
Page 208 and 209: 198 Bibliography [72] K. S. Babu,
Page 210 and 211: 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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