On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

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64 Chapter 2. The Randall Sundrum Model and its Holographic Interpretation We can concentrate on the vector component, as the EOM for the scalar can again be derived by the replacement c 2 A → c2 a/ξ − 1 and x 2 n → ξx 2 n. A solution to (2.91) can be guessed by comparison with (2.64), which has the same form, � � χn(t) = t J∆−2(txn) + αnY∆−2(txn) , (2.92) where again ∆ = 2 + � 1 + c2 A . The coefficient αn is fixed by the UV BC and the IR BC gives the mass eigenvalues. In general, they read � � ∂tχn(t) � t=ɛ + = vUVχn(ɛ + ) , � � ∂tχn(t) � t=1− = −vIRχn(1 − ) . (2.93) One can infer, that the mass eigenvalues have a splitting dictated by the zeros of Bessel functions, which means the mass splitting approaches δmn = πMKK for large n. The mass of the first excitation is controlled by both BCs as shown in Figure 2.8. The plots show the mass of the lightest mode depending on one BC, while the other one is kept fixed. In all cases, x1, which denotes the mass of the lightest KK mode in units of MKK approaches a limit and the units on the x-axis are chosen in a way that this limit is shown in the respective plot. In the upper left panel the UV BC is Neumann and the IR BC varies, showing the transition from the (NN) to the (ND) scenario. From the dual picture, we expect the lightest mode to correspond to a massless gauge boson if vIR = 0, and to become massive due to spontaneous symmetry breaking once a vev is turned on on the IR brane. Its mass will therefore not grow arbitrarily, but will always be a fraction of the symmetry breaking scale, which does agree with the plot. The limit is at mn ∼ 0.235 MKK and is more or less satisfied at vIR ∼ 10. For the reverse situation, Dirichlet BCs in the UV and Neumann BCs in the IR, the dual theory predicts no elementary gauge boson and no Higgs contribution to the masses of the KK modes. This scenario should yield a straight line in the vUV − x1 plane at the mass of the first composite, unless vUV becomes so small, that Dirichlet BCs are not a good approximation. This happens only for extremely small values of vUV = O(10 ɛ), as shown in the upper right panel of Figure 2.8. In this plot, the values of vUV are unnaturally small in order to show the region in which the mass approaches zero. That corresponds to a situation, in which the breaking on the UV brane is so small, that the dual theory has an approximate massless gauge boson. For all other values, the limit is reached. From (2.93), it is evident that this limit is given by the first zero of J0(xn), x1 ≈ 2.4. Therefore the plot shows the rapid transition from the (NN) to the (DN) scenario. The last panel (in the second row) shows the plot for the situation where vUV is of O(1) and vIR is free to vary. It illustrates the transition from (DN) to (DD) BCs. The lowest mass in this plot is consequentially the limit from the upper right plot. Turning on the Higgs vev in the IR seems to have a considerable effect on the first KK mass, the limiting value is shifted to the first zero of J1(xn) at x1 ≈ 3.8. This can again easily be extracted from the equations (2.93). In the dual theory one can argue that stronger couplings between the composites may allow for larger corrections to the masses compared to the (ND) scenario, in which the contributions
x1 0.20 0.15 0.10 0.05 �NN� �ND� 0.00 0 2 4 6 8 vIR x1 3.6 3.4 3.2 3.0 2.8 2.6 vUV � 0 x1 2.0 1.5 1.0 0.5 2.4 0 10 20 30 40 2.3. Profiles of Gauge Bosons 65 �NN� �DN� 0.0 0 50 100 150 200 250 300 �DN� �DD� vIR vUV � 0 vUV� Ε vIR � 0 Figure 2.8: Mass of the lightest excitation for different BCs. See text for details. from symmetry breaking are given by a marginal mixing operator. Note, that we also found a substantial effect from the Higgs in the discussion of the (DD) propagator limit, in contrast to the (ND) scenario, which is in line with our findings here. It should be stressed, that the behavior can change significantly once one allows for a non-zero bulk mass parameter. The Electroweak Gauge Sector of the SM The electroweak gauge sector of the SM is is completely shifted into the bulk in the minimal RS model. Following the above analysis, one would expect gauge boson masses of the order of the electroweak scale, as given in the upper left panel of Figure 2.8, if we start with (NN) BCs and couple to a IR localized Higgs. It will turn out, that this proves true and the zero mode masses agree with the SM up to small
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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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12 Chapter 1. Introduction: Problem
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114 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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