On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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148 Chapter 4. The Asymmetry in Top Pair Production Even though it cannot be transformed in a forward-backward asymmetry1 , the charge asymmetry at the LHC has the same physical origin and possible new physics effects showing up in At FB will also contribute to Ay C . It has been measured at the LHC by both ATLAS [217, 218] and CMS [216] and was found to be in good agreement with the SM [219], (A y C )SM = (1.15 ± 0.6) % , (4.14) (A y C )exp = (0.4 ± 1stat ± 1.1syst) % . (4.15) Here, the quoted experimental value corresponds to the latest CMS result, which is based on 5fb −1 of data. The fact that the asymmetry at the LHC is considerably smaller than at the Tevatron is rooted in the different center of mass energies (CM) of both machines. Since the asymmetries are normalized to the total inclusive cross section, the number of top pairs produced by gluon-gluon fusion contributes to the denominator but not to the numerator as it is a charge symmetric initial state and at LHC energies gluon-gluon fusion is by far the dominating process. We can conclude, that whatever new physics might be responsible for the discrepancy seen at the Tevatron, its contribution to the LHC charge asymmetry should stay within the (still significant) errors. It should further not contribute to the total inclusive cross section which all experiments see in very good agreement with SM predictions, and it must be heavy or broad enough to have escaped direct detection by dijet searches or in the t¯t invariant mass spectrum so far. 4.2 The Forward-Backward Asymmetry in the SM We will concentrate on the Tevatron observables at which t¯t pairs are produced in collisions of protons and antiprotons, p¯p → t¯tX. At the partonic Born-level contributions from quark-antiquark annihilation and gluon fusion arise within the SM q ¯q ¯t q(p1) + ¯q(p2) → t(p3) + ¯t(p4) , t g g ¯t g(p1) + g(p2) → t(p3) + ¯t(p4) , t (4.16) in which the four-momenta p1,2 of the initial state partons can be expressed as the fractions x1,2 of the four-momenta P1,2 of the colliding hadrons, p1,2 = x1,2P1,2. We denote the square of the hadronic CM energy by s = (P1 + P2) 2 and introduce the 1 For more details concerning the different asymmetries and their comparability, see e.g. [220].
kinematic invariants 4.2. The Forward-Backward Asymmetry in the SM 149 ˆs = (p1 + p2) 2 , t1 = (p1 − p3) 2 − m 2 t , u1 = (p2 − p3) 2 − m 2 t . (4.17) The partonic cross section can then be described as a function of ˆs, t1 and u1 and momentum conservation at Born level implies ˆs + t1 + u1 = 0. Since the number of top quarks scattered in forward (backward) direction is given by integrating the differential cross section over the angle θ included by �p1 and �p3 in the respective ranges, we express t1 and u1 in terms of θ and the top-quark velocity β, t1 = − ˆs 2 (1 − β cos θ) , u1 = − ˆs (1 + β cos θ) , 2 β = � 1 − ρ , ρ = 4m2 t ˆs The hadronic differential cross section may then be written as dσ p¯p→t¯tX d cos θ = αs m 2 t � i,j � s 4m 2 t . (4.18) dˆs s ffij � � � � 4m2 t ˆs/s, µf Kij , cos θ, µf , (4.19) ˆs where µf denotes the factorization scale and ffij denote the parton luminosity functions introduced in (3.113). The luminosities for ij = q¯q, ¯qq are understood to be summed over all species of light quarks, and the functions f i/p(x, µf ) (f i/¯p(x, µf )) are the universal non-perturbative PDFs, which describe the probability of finding the parton i in the proton (antiproton) with longitudinal momentum fraction x. The hard-scattering kernels Kij(ρ, cos θ, µf ) are related to the partonic cross sections and can be expanded in αs, Kij(ρ, cos θ, µf ) = ∞� n=0 � � αs n K 4π (n) ij (ρ, cos θ, µf ) . (4.20) At leading order, only the diagrams in (4.16) contribute, and one finds K (0) πβρ CF q¯q = αs 8 Nc = αs πβρ 16 CF Nc K (0) πβρ gg = αs 8(N 2 c − 1) πβρ = αs 8(N 2 c − 1) � t2 1 + u2 1 ˆs 2 + 2m2 � t ˆs � 1 + β 2 cos 2 θ + 4m2 � t , (4.21) ˆs � ˆs CF 2 � � t2 1 + u − Nc t1u1 2 1 ˆs 2 + 4m2t ˆs − 4m4 � t t1u1 � 4CF 1 − β2 cos2 � − Nc (4.22) θ � 1� � 2 2 4m × 1 − β cos θ + 2 2 t ˆs − 16m4 t ˆs 2�1 − β2 cos2 θ � � . The factors Nc = 3 and CF = 4/3 are the usual color factors and K (0) ¯qq = K (0) q¯q in the SM, because they are related by replacing cos θ with − cos θ the coefficients.
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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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Page 188 and 189: 178 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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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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210 Bibliography [239] V. Ahrens, A
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On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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