On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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6 Chapter 1. Introduction: Problems beyond the Standard Model Quadratic divergences cancel and, as expected for a chirally protected mass, all remaining divergences are logarithmic and vanish in the limit where the Higgs vev goes to zero. In the limit of exact supersymmetry, mt = M˜t , all corrections vanish. Moreover, since SUSY is a symmetry of the quantum theory, no divergences will occur at any loop order, in fact, the masses are not renormalized at all, see [14, Sec. 4]. However, the MSSM does not only –in conflict with experiment– predict degenerate masses of superpartners, but it necessarily gives the Higgs boson a positive mass squared. 7 As a consequence, in order to have nondegenerate masses in the MSSM (or massive particles at all), supersymmetry needs to be broken. There is no phenomenologically viable way to incoporate SUSY breaking with only the MSSM field content and a breaking communicated at tree level (a direct couplings to the SUSY-breaking field) will also lead to inconsistencies8 , see e.g. [5, Sec. 7]. One therefore assumes a hidden sector, in which SUSY is broken and some kind of messenger fields communicate the breaking to the MSSM. In the spirit of effective field theory one writes down the relevant terms of the most general Lagrangian parametrizing the breaking. This introduces 124 new parameters to the MSSM, which are in general unrelated, and will lead to a breaking of the chiral protection of the scalar masses, because M˜t = mt + m✘ ✘ SUSY in (1.5) is now sensitive to the size of the breaking terms. They are usually given by m✘ ✘ SUSY ∼ 〈F〉 , (1.6) Λ where 〈F〉 denotes the vev of the SUSY breaking field and Λ is the SUSY breaking scale (the mass of the messenger field). These masses should clearly not exceed the TeV scale by much m✘ ✘ SUSY � TeV in a natural model. However, since the SUSY breaking sfermion masses induce radiative corrections relative to their Yukawa couplings, one can relax this bound depending on flavor. For example a 200 GeV stop contributes roughly as much to ∆m2 H as a sbottom at 3.5 TeV. Natural supersymmetric models may therefore allow for a large splitting in the superpartner mass spectrum [7]. It should be noted, that such an ansatz requires the SUSY breaking sector to generate this hierarchy in superpartner masses. The modeling of the SUSY breaking sector may accomodate further attractive features. For a large enough SUSY breaking scale, renormalization group running may eventually turn one of the scalar mass parameters negative, triggering condensation of the corresponding field. It would be a disaster, if this would be any sfermion mass, because it would induce a color- or electromagnetic breaking vacuum. However, the Higgs boson mass parameter will get the largest negative corrections by the top Yukawa and thus generically turns negative first, ultimatively triggering EWSB. This is known as radiative symmetry breaking [6] and although it depends on the values m✘ ✘ SUSY at the SUSY breaking scale, it is a step beyond the ignorace of the EWSB 7 In order to achieve EWSB in a (unbroken) supersymmetric extension of the SM, one therefore has to include additional fields, which do not have superpartners in the SM, see for example the dicsussion in [15, Sec.5.4]. 8 There is for example no scalar-gaugino-gaugino term allowed by SUSY, therefore the gauginos remain massless in such a scenario.
1.1. Solutions to the Gauge Hierarchy Problem 7 mechanism in the SM. Another interesting property of SUSY models is, that the running of the gauge couplings will lead to gauge coupling unification at a scale of about Λ ∼ 10 16 GeV, which can be understood as a strong hint at a grand unified theory (GUT), in which all MSSM gauge interactions are low energy remnants of a single large gauge symmetry (this assumes a desert of energy scales up to the GUT scale with no new physics besides the MSSM). But there are further additional concepts necessary in order to bring a supersymmetric field theory in agreement with experiment. In contrast to the SM, there are renormalizable couplings involving the new scalar superpartners, which allow for Lepton and Baryon number violation. These couplings lead to rapid proton decay and must either be forbidden or extremely small. The most established solution for this problem is called R parity, a discrete symmetry which allows only vertices with two superpartners attached, and thus eliminates the dangerous couplings, first introduced in [16]. Some interesting consequences of such an additional symmetry is that superpartners will only be pair produced at colliders and that there is a stable lightest supersymmetric particle (LSP) with a mass around the electroweak scale, which makes for an ideal dark matter candidate. Less restrictive solutions are possible, e.g. imposing Lepton-, Baryon number conservation as a global symmetry [17] or minimal flavor violation [18, 19]. The MSSM allows also for one parameter carying mass dimension, which is not from the SUSY-breaking sector and as a consequence should be sensitive to the scale where the UV-completion of the MSSM sets in, the GUT or the Planck scale. Yet, this so called µ−parameter is related to the weak scale, since it plays a fundamental role in EWSB. This is the MSSM fine-tuning problem, and although the situation is better than in the SM (because the µ−parameter does not renormalize), the scale disparity remains. Technicolor and Composite Higgs Models Technicolor In essence, the idea of Technicolor (TC) solves the gauge hierarchy problem by replacing the scalar Goldstone degrees of freedom necessary to give masses to the electroweak gauge bosons by composite bound states. It is based on the observation, that even in the absence of a Higgs boson the electroweak symmetry is broken by the quark condensate 〈 ¯qq 〉 = 〈 ¯qLqR 〉 + 〈 ¯qRqL 〉 formed at the scale at which QCD becomes strongly coupled, ΛQCD. In such a scenario, fermions are massless and the SM with NF quark flavors exhibits a global SU(NF )L × SU(NF )R × U(1)B chiral (and Baryon number) symmetry9 , which is broken down to SU(NF )V × U(1)B by the quark condensate. Due to Goldstones theorem this symmetry breaking generates N 2 F − 1 massless Goldstone bosons, in the limit. 9 The axial U(1) is broken by quantum effects and therefore the η ′ is massive even in the chiral
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
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56 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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