On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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12 Chapter 1. Introduction: Problems beyond the Standard Model N F 40 30 20 10 0 Free electric Phase Walking Behaviour? 2 4 6 8 10 N C Conformal Window Asymptotically free Figure 1.3: Phase diagram of an SU(NC) Yang-Mills theory with NC numbers of color and NF copies of fermions in the fundamental representation. is a function of the number of flavors and colors, β(g) = − g3 (4π) 2 (11NC − 2NF ) + g5 (4π) 4 � 34 3 N 2 C − 1 2 NF � 16 3 20 − 3 NC �� + O(g 7 ) , (1.19) and those must be chosen in a certain ratio in order to end up just below the lower boundary of the conformal window (the region where the theory may evolve to an infrared fixed point), 11 2 NC > NF > 17N 2 C 4 + 5NC (1.20) which allows for walking gauge theories, see Figure 1.3. A technicolor theory is therefore constrained in the possible values of NF and NTC. Also, a larger number of flavors will give rise to additional technipions which have not been seen at colliders. It is however possible to allow for theories, which are not SU(NC), but SO(N) or Sp(N) and also the technifermions must not be in the fundamental representation, but may be in the adjoint or even higher representations of the gauge group, which changes the conformal window and therefore the possible NF , NC configurations (a
� � Q Q � ² 5.5 5.0 4.5 4.0 3.5 3.0 2.5 1.1. Solutions to the Gauge Hierarchy Problem 13 � � Q Q � ² � 2 � Q Q 2.0 1.0 1.2 1.4 1.6 1.8 � Q Q Figure 1.4: Region in the ∆QQ ¯ − ∆ ( QQ) ¯ 2 plane which is excluded using numerical methods, shown in blue. These bounds depend on the global symmetry of the technicolor condensate (and become weaker for a larger symmetry group), which is assumed to be SU(2) in this plot. The red region in the upper left corner is the preferred region by flavor bounds on the ETC scale and a natural top mass. The dashed cross indicates the lowest possible value of ∆QQ ¯ , while ∆2 = 4, and the orange line depicts the large N limit ∆¯ (QQ) 2 = 2∆ ¯ QQ . good review is [28]). Alternatively one can avoid the bound on the technicolor condensate scaling dimension ∆ ¯ QQ ≥ 2 and ask for even larger anomalous dimensions γ > 1, considering the confining gauge theory is at a strongly interacting fixed point, which means in the conformal window in Figure 1.3 or actually reaching g ∗ in the lower right panel of Figure 1.2. These theories are called conformal technicolor (CTC) and, in contrast to WTC, such a Yang-Mills theory requires an external source which breaks the conformal symmetry in order to create a mass gap and force the techniquark condensate to form. In this respect CTC is very similar to supersymmetry, where also an external breaking ultimatively triggers EWSB. Ideally, one would aim for a theory, in which the scaling dimension of the technicolor condensate is as close to ∆ ¯ QQ = 1 as possible, and the top mass is as natural as in the SM, while the “Higgs mass” operator still is at ∆ ( ¯ QQ) 2 ≡ dim〈QQQQ〉 = 4 so that the hierarchy problem can be avoided [29]. However, the limit ∆ ¯ QQ = 1 corresponds to the free noninteracting theory, in which always ∆ ( ¯ QQ) 2 = 2. Yet for slightly different values ∆ ¯ QQ = 1 + ɛ, with ɛ = 1/few, the relation ∆ ( ¯ QQ) 2 = 2∆ ¯ QQ does not hold, except in the large NC limit, in which matrix elements factorize. The question is, how small can ɛ be, while ∆ ( ¯ QQ) 2 ≥ 4? Although there is very limited knowledge about strongly interacting theories, the ( ¯ QQ)
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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62 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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