On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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8 Chapter 1. Introduction: Problems beyond the Standard Model case of one generation (NF = 2), three pions. The electroweak gauge group gauges a subgroup of the full global symmetry and since qL and qR transform differently under this subgroup the electroweak symmetry is broken by the formation of the quark condensate as well. It even breaks the electroweak symmetry in the correct pattern, since the quark condensate has the same quantum numbers as a fundamental Higgs scalar. As a consequence, the coupling of the W ± to the conserved weak currents J ± µ = qLγµT ± qL results in a correction to the W propagator below ΛQCD [21], pions = � where Πµν(q) = i −i q2 − g2 Π(q2 � ηµν − )/2 qµqν q2 � d 4 x e −iq·x 〈0|T � J + µ (x)J − ν (0) � � |0〉 = ηµν − qµqν q 2 (1.7) � Π(q 2 ) . One ends up with a mass for the W ± proportional to the residue of the pole of the vacuum polarization function Π(q 2 ), which follows from pion exchange, 〈0|J + µ |π(p)〉 = i fπ � NF √2 pµ ⇒ MW = 2 gfπ 2 , (1.8) where fπ denotes the pion decay constant. electroweak gauge bosons The thereby generated masses for the � NF MW ≈ 28 2 MeV , MZ � NF ≈ 32 2 MeV , (1.9) are however to small by a factor of roughly 4000/ √ NF in order to explain the measured values. It is interesting to explore the implications of such a world without a Higgs , 10 but the important statement here is, that the confining phase of QCD would describe a viable mechanism of electroweak symmetry breaking if fπ was replaced by the electroweak scale v. In the late seventies, this observation led Weinberg [23] and Susskind [24] to propose a theory in which electroweak symmetry breaking is arranged by an upscaled version of QCD, for which the name technicolor (TC) became most established. The simplest model includes two flavors of techniquarks, 11 transforming in the fundamental representation of the TC gauge group GTC = SU(NTC) where the right-handed components transform as singlets and the left-handed components as doublet under the SM SU(2)L in order to form a techniquark condensate with the right quantum numbers. The new gauge group has a β function just like QCD, only that the coupling gTC becomes strong at the scale ΛTC = � 3 NTC f TC π fπ ΛQCD ∼ 4πf TC π , (1.10) 10 The Fermi constant for example would be larger by a factor 2v 2 /NF f 2 π and processes driven by the weak force like β−decay would occur much more rapidly. A comprehensive discussion of such a Gedankenworld can be found in [22]. 11 In the case NF > 2, additional, for now massless, technipions appear (the analog of QCD Kaons and ηs).
QTC qSM X µ ETC QTC qSM 1.1. Solutions to the Gauge Hierarchy Problem 9 QTC qSM × QTC qSM qSM × × 〈QQ〉TC Figure 1.1: Diagrammatical representation of the generation of effective Yukawa couplings for the SM fermions in extended Technicolor theories. In a first step, the heavy ET C gauge bosons are integrated out and in a second step the technicolor condesate forms. where f TC π is the analog of the pion decay constant and has a value around the electroweak scale. Thus, there is no hierarchy problem in TC theories, because the electroweak scale is dynamically generated by the confining phase of a non-abelian gauge theory. While technicolor solves the hierarchy problem and gives masses to the electroweak gauge bosons, it does not provide masses for fermions. In order to implement a Yukawa coupling, one must communicate the EWSB to the SM quarks and leptons. The solution to this problem was developed soon after the original papers, based on an enlarged technicolor gauge group GETC ⊃ GTC, in which SM and TC fermions transform under the same representation, so that the corresponding ETC gauge bosons couple the TC fermions to the SM fermions [25, 26]. These models are called extended technicolor (ETC), and after integrating out the heavy ETC gauge bosons at some scale ΛETC > ΛTC, and after Fierz transformations, there appear three different types of dimension six operators, Ld=6 = aij QT i Q QT j Q Λ 2 ETC + bij QT i Q qT j q Λ 2 ETC + cij qT i q qT j q Λ 2 ETC qSM . (1.11) where T i denote the GETC generators. The a-terms, connect TC fermions, which are denoted by Q, with each other, the b-terms couple TC fermions to SM fermions, which will from now on be denoted by q (we concentrate on the quark sector), and the c-terms couple SM fermions among each other. For the current discussion the aterms are unimportant. 12 The b-terms generate the effective Yukawa couplings after formation of the techniquark condensate at the ETC scale, as illustrated in Figure 1.1, b LYukawa ∋ Λ2 ETC q L〈QQ〉 � � ETC qR . (1.12) 12 They will give masses to additional technipions in the NF > 1 case, in the same way as the pion mass difference is generated by photon exchange, see [27, p.61] for further details.
Page 1 and 2: On the Flavor Problem in Strongly C
Page 3 and 4: UNIVERSITY OF MAINZ ABSTRACT THEORE
Page 5 and 6: Contents Acknowledgements vii Prefa
Page 7: Acknowledgements First and foremost
Page 10 and 11: x One of the most fascinating insig
Page 12 and 13: 2 Chapter 1. Introduction: Problems
Page 20 and 21: 10 Chapter 1. Introduction: Problem
Page 46 and 47: 36 Chapter 2. The Randall Sundrum M
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58 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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146 Chapter 4. The Asymmetry in Top
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176 Chapter 5. Conclusions describe
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178 Appendix A. Generating Paramete
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180 Appendix A. Generating Paramete
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182 Appendix B. Neutral Meson Mixin
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184 Appendix B. Neutral Meson Mixin
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C Input Parameters This appendix is
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Parameter Value ± Error Reference
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192 Appendix D. Higgs Potential for
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194 Bibliography [13] S. Dimopoulos
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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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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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