On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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164 Chapter 4. The Asymmetry in Top Pair Production The main lesson learned from the way the charge asymmetry arises in QCD is that beyond LO vector couplings alone are sufficient to generate non-vanishing values of At FB . In the case of the EFT (4.45) this means that cut diagrams like the ones shown in Figure 4.6, can give a sizable contribution to the charge asymmetry if the combination CV q¯q = � C (V,8) � q¯q,� + C(V,8) q¯q,⊥ of Wilson coefficients is large enough. In fact, from (4.50), (4.52), and (4.73) it is not difficult to see that in the case of the RS model NLO corrections to σa should dominate over the LO ones, if the condition 7 αs 4π (1 + ctL + ctR ) � L eL(1+cu L +cu R ) (4.64) is fulfilled. For example, employing ctL = −0.34, cuL = −0.63, and cuR = −0.68, the above formula tells us that for ctR = 0.57 the NLO contributions are bigger than the LO corrections by a factor of roughly 25. This suggests that it might be possible to generate values of At FB that can reach the percent level with typical and completely natural choices of parameters. Notice that in contrast to QCD, in the RS framework the Feynman graphs displayed in 4.6 are not the only sources of charge-asymmetric contributions. Self-energy, vertex, and counterterm diagrams as well as box diagrams involving the virtual exchange of one zero-mode and one KK gluon might also give a contribution to At FB at NLO. As in Chapter 3, we will however not implement KK modes in loops as it is technically involved to compute the nested sums over KK modes in these diagrams. Also, those corrections are, like the Born-level contribution, all exponentially suppressed by the UV localization of the light-quark fields (and the small axial-vector coupling of the light quarks for what concerns the contributions from the operators Q (V,8) q¯q,AB ). Compared to the tree-level corrections, these contributions are thus suppressed by an additional loop factor, so that they can be ignored for all practical purposes in this particular observable. The relevant contributions to At FB arising in the RS model beyond LO include the graphs depicted in Figure 4.6. After integrating over cos θ, one obtains in the partonic CM frame (q¯q = uū, d ¯ d) A (1) q¯q,RS = ˆs 16παs C V q¯q A (1) q¯q , (4.65) where A (1) q¯q denotes the NLO asymmetric SM coefficient, given in (4.36), and C V q¯q the Wilson coefficient including the vector couplings as defined below (4.52). Employing an exemplary value of C q¯q V = 10 TeV−2 , Figure 4.3 shows A (1) q¯q,RS in the left panel and A (1) q¯q,RS multiplied with the up-quark PDFs in the right panel, both plotted against the CM energy √ s in dashed black. This has to be compared with the solid black plots in Figure 4.3 , which shows the same plots for the SM expressions. Clearly, the peak at the t¯t threshold is washed-out in the RS model, because the extra factor ˆs in (4.65) prevents the function from dropping off for large CM energies. This is a consequence of the fact that the new physics is considered heavy, which means that interference terms scale as ˆs/m2 A , compare (4.38), and is symbolized by the propagators being replaced by contact interactions in Figure 4.6. 7 This inequality should be considered only as a crude approximation valid up to a factor of O(1).
4.5 Numerical Analysis 4.5. Numerical Analysis 165 The Wilson coefficients appearing in the effective Lagrangian (4.45) are constrained by the measurements of the forward-backward asymmetry At FB , the total cross section σt¯t, and the t¯t invariant mass spectrum dσt¯t/dMt¯t. In Section 4.1 the experimental values for the cross section (4.3) and the forward backward asymmetry in the CM frame (4.7) are quoted. In addition, we will include in the analysis the last bin of the invariant t¯t mass spectrum, Mt¯t ∈ [800, 1400] GeV, which is most sensitive to new physics [236], � �Mt¯t ∈ [800,1400] GeV dσt¯t dM t¯t exp = (0.068 ± 0.032stat. ± 0.015syst. ± 0.004lumi.) fb GeV . (4.66) Here the quoted individual errors are of statistical and systematic origin, and due to the luminosity uncertainty, respectively. The above results should be compared to the predictions obtained in the SM supplemented by the dimension-six operators (4.45). Ignoring tiny contributions related to the (anti)strange-, (anti)charm-, and (anti)bottom-quark content of the proton (antiproton), and using the dimensionless coefficients ˜C V q¯q ≡ 1 TeV 2 C V q¯q , (4.67) ˜C V tū ≡ 1 TeV 2 � 1/3 C (V,8) tū,� − 2C(V,1) tū,� one obtains for the cross section � (σt¯t)RS = 1 + 0.053 � C˜ V uū + ˜ C V � tū − 0.612 C˜ S tū + 0.008 ˜ C V d ¯ � �6.73 � +0.52 d −0.80 pb , (4.68) and for the last bin of the invariant mass spectrum � �Mt¯t ∈ [800,1400] GeV dσt¯t = (4.69) dMt¯t RS � 1 + 0.33 � C˜ V uū + ˜ C V � tū − 0.81 C˜ S tū + 0.02 ˜ C V d ¯ � �0.061 � +0.012 fb d −0.006 GeV . All Wilson coefficients in the above expressions are understood to be evaluated at mt. The numerical factors multiplying ˜ CS tū correspond to a Higgs mass of mh = 115 GeV. 8 The RG evolution of the Wilson coefficients from MKK to mt is achieved with the formula (4.56). The dependence of σ t¯t and dσ t¯t/dM t¯t on ˜ C P ij � , has been obtained by convoluting the kernels (4.50) with the parton luminosities ffij(ˆs/s, µf ) by means of the charge-symmetric analog of formula (4.28), using MSTW2008LO PDFs [228] with renormalization and factorization scales fixed to µr = µf = mt = 173.1 GeV. The corresponding value of the strong coupling constant is αs(MZ) = 0.139, which translates into αs(mt) = 0.126 using one-loop RG running. The total cross section 8 The conclusions will not depend on the Higgs mass, so that it is unnecessary to update the calculation with the measured value here.
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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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92 Chapter 3. Solving the Flavor Pr
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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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On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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