On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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18 Chapter 1. Introduction: Problems beyond the Standard Model SU(2)L × U(1)Y breaking vacuum v θ R = f SU(2)L × U(1)Y preserving vacuum Figure 1.5: Circle of a priori degenerate minima in Composite Higgs models with radius R = f, the scale at which the global theory is broken and the Higgs emerges as a pseudo Nambu-Goldstone boson. The angle θ measures the (mis-)alignment with the EWSB vacuum. contribution to the potential reintroduces a tension comparable to the situation of higgsless TC models, consult [61, Sec.3.4] for details. In terms of the angle sin θ, it also becomes clear how composite Higgs models can be seen as a link between the SM with an elementary Higgs scalar and TC theories. If f → ∞, sin θ → 0 and all composite states besides the Higgs decouple, so that the theory effectively has an elementary Higgs. For v → f however, sin θ → 1 and the model predicts only a single characteristic scale, at which the composites form and EWSB occurs, just like TC. Collective Symmetry Breaking In composite Higgs models one can achieve a natural separation of scales v < f, but the Higgs mass does still encounter quadratically divergent corrections up to the compositeness scale, because gauge and Yukawa interactions explicitly break the shift symmetry which protects it. Therefore, a large separation v ≪ f is unnatural. Loosely speaking, one could say that the Higgs does not profit from being a Nambu Goldstone boson. This was the inspiration for the mechanism of collective symmetry breaking, which is realized in a class of models called little Higgs [38]. 17 The idea is, that the global symmetry, which breaks dynamically in the composite Higgs model is larger than necessary in order to accommodate the four Goldstone bosons which are identified with the degrees of freedom of the Higgs, and the electroweak gauge group is enlarged as well, so that there is at least another copy of W ± s and the Z, which becomes heavy by eating the additional GBs. 17 The name is motivated, because the Higgs in these models is naturally light = little. See Section 1.3 in [38].
F gauging I G SSB H 1.1. Solutions to the Gauge Hierarchy Problem 19 Simplest Little Higgs: G = SU(3) × SU(3) × U(1) H = SU(2) × SU(2) × U(1) F = SU(3) × U(1) I = SU(2) × U(1) Figure 1.6: Diagram illustrating the relations between the different symmetry groups in a Little Higgs theory. Ignoring gauge interactions and spontaneous symmetry breaking (SSB), G is the global symmetry of the Lagrangian. A subgroup F – larger than the SM gauge group I– is gauged, which breaks the global symmetry. Another global subgroup H is left after SSB. A number of GBs make some of the F gauge bosons heavy, while the ones from I remain massless. The remaining GBs form the Higgs. If either the SM electroweak gauge bosons or the new gauge bosons couple to the Higgs, there will still be a leftover global symmetry, which makes the Higgs a Goldstone boson, i.e. massless, but if both gauge degrees of freedom couple to the Higgs a mass term is generated, which will then only be logarithmically divergent. This is illustrated best on the basis of a model introduced by Schmaltz, which he called the Simplest Little Higgs [39]. It will be even more simplified here, because we will ignore the U(1) gauge groups. Consider a Lagrangian with two scalar fields, invariant under the global symmetry G = SU(3)1 × SU(3)2 (ignoring additional U(1) factors), L = (∂µφ1) † (∂ µ φ1) + (∂µφ2) † (∂ µ φ2) + V (|φ1| 2 , |φ2| 2 ) . (1.35) Both scalar fields will take on a vev f, so that the symmetry breaks down to H = SU(2)1 × SU(2)2 at that scale. A scheme of the symmetry breaking is provided in Figure 1.6. We adopt the parametrization � i φ1 = exp f � i φ2 = exp f � 02×2 κ κ † � + 0 �κ � � i √ �3×3 exp 2f f � 02×2 κ κ † � + 0 �κ � � √ �3×3 exp − 2f i f � 02×2 h h † � + 0 η � √ �3×3 2f ⎛ ⎞ 0 ⎝0⎠ , f � 02×2 h (1.36) h † � − 0 η � √ �3×3 2f ⎛ ⎞ 0 ⎝0⎠ . f
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
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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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