On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

More documents

Recommendations

Info

16 Chapter 1. Introduction: Problems beyond the Standard Model Any Yukawa coupling can thus be generated with a fundamental parameter λ = O(1), based on the choice of the mixing angles sin ϕL = d Λγ TC Λ mχ 1−γ ETC and sin ϕR = ˜ d Λ˜γ TC Λ m˜χ 1−˜γ ETC , (1.30) and therefore, ultimatively on the anomalous dimensions of B and B c . Here, in contrast to WTC, even for very large values of ΛETC ∼ MPlanck, also the top mass can be explained, given that the corresponding anomalous dimension is γ < 2. Another virtue of partial compositeness becomes evident if one generalizes to 3 generations of SM quarks. In that case each SM quark has a set of composite partners Bi, Bc i , i = 1 . . . 3. The composites have different anomalous dimensions, so that the corresponding effective Yukawa matrices (shown here for the up-type quarks) read ⎛ sin ϕuL 0 0 Y = ⎝ 0 sin ϕcL 0 0 0 sin ϕtL ⎞ ⎛ sin ϕuR 0 0 ⎠ λ ⎝ 0 sin ϕcR 0 0 0 sin ϕtR ⎞ ⎠ , (1.31) where λ is assumed to be an anarchic order one matrix in straight generalization of λ in (1.29). In analogy to the Yukawa couplings in (1.27), there might be further bosonic technicolor resonances, which couple to the composite fermions, for example L ∋ g � Bi γµρ µ Bi + B c i γµρ µ B c� i , (1.32) which, after diagonalization of the mass mixings, leads to the couplings of the SM fermions with ⎛ sin ϕ gL = g ⎝ 2 uL 0 0 L ∋ (gL) ij ψ i L γµρ µ ψ j L + (gR) ij ψ i R γµρ µ ψ j R , (1.33) 0 sin ϕ 2 cL 0 0 0 sin ϕ 2 tL ⎞ ⎛ sin ϕ ⎠ , gR = g ⎝ 2 uR 0 0 0 sin ϕ2 cR 0 0 0 sin ϕ2 ⎞ ⎠ . tR (1.34) and although these couplings are flavor diagonal, they will have off-diagonal entries in the basis in which the Yukawas are diagonal, because only matrices proportional to the identity commute with the unitary change of basis matrices. This leads to FCNCs. However, the corresponding FCNCs are always suppressed by the same small mixing angles which generate the Yukawa couplings. Therefore, as long as the top does not participate, FCNCs are generically small in models with partial compositeness. Since Randall-Sundrum models with bulk fermions do have this feature, we will examine it in more detail in Section 2.5.
Composite Higgs 1.1. Solutions to the Gauge Hierarchy Problem 17 TC models are higgsless theories, because they do not have a scalar Higgs doublet. QCD-like theories do not predict a sharp scalar resonance at all. 14 There are candidates, for example the TC analogue of the σ/f0(550), but as in QCD it is very broad. In WTC, it may be narrow and even lighter than assumed from scaled up QCD [33], but still heavier than preferred by the LHC measurements. 15 Also, in walking TC theories, there is a Pseudo Nambu-Goldstone boson (PNGB) connected to the breaking of approximate scale invariance, if one is close enough to the conformal window, the so called dilaton, which shares the quantum numbers with the neutral SM scalar Higgs component, but has different self-couplings [34]. Composite Higgs models were first proposed and worked out by Kaplan and Georgi in the early eighties [36]. They are philosophically different from TC, because they implement electroweak symmetry breaking in two steps. A global symmetry breaks at some scale f > v, which leaves the electroweak symmetry intact but generates four composite Pseudo Nambu-Goldstone bosons. These PNGBs correspond to the degrees of freedom of the Higgs doublet. One can imagine them as being a set of technikaons, if one wants to push further the analogy with QCD. In practice, models without additional Goldstone bosons are preferable, and so the minimal composite Higgs model proposes a global symmetry breaking SO(5)/SO(4), which gives exactly four GBs [37]. The problem of fermion mass generation persists, and is usually solved by introducing partially composite fermions. After integrating out the heavy composite states, one ends up with an effective Yukawa coupling as in (1.31). A potential for the Higgs is then generated at loop level by Yukawa and gauge boson couplings which induce a negative mass squared and force the composite Higgs to take on its vev. However, it is not self-evident, that this loop-induced potential results in a vacuum which breaks the electroweak symmetry. This can be illustrated in terms of the ratio between the EWSB component of the vev, v, and the scale at which the global symmetry is broken, f, given by the angle sin θ = v/f, see Figure 1.5. Gauge boson loops “like” to preserve the gauge symmetry, i.e. they tend to induce a potential with a symmetry preserving minimum, θ = 0. On the other hand, Yukawa couplings generate contributions to the Higgs potential which point in the direction of EWSB and prefer θ = π/2. 16 Although very challenging for TC models, the heavy top is therefore a blessing for composite Higgs models, since it allows for a symmetry breaking minimum of the potential. Thus, in an interesting analogy, composite Higgs models and SUSY share a fondness for the large top Yukawa, which is crucial in both scenarios to achieve EWSB. It is however a matter of fine-tuning to get an angle which is still in agreement with electroweak and flavor bounds, which prefer a large scale f, i.e. sin 2 θ ∼ 0.1. Thus, even though it does not pose a problem to write down the top Yukawa itself, its large 14 Unitarization of W W scattering is achieved by the exchange of heavier TC vector composites. 15 It should be noted that this might not be true for theories with technifermions in higher representations [35] 16 This was known at the time when Georgi and Kaplan proposed their model, but the top quark was assumed to be lighter than ∼ 50 GeV and its contributions negligible. Therefore, new dynamics were necessary and they introduced an additional axial U(1)A.
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
Page 76 and 77:
66 Chapter 2. The Randall Sundrum M
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
92 Chapter 3. Solving the Flavor Pr
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
100 Chapter 3. Solving the Flavor P
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
146 Chapter 4. The Asymmetry in Top
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
176 Chapter 5. Conclusions describe
Page 188 and 189:
178 Appendix A. Generating Paramete
Page 190 and 191:
180 Appendix A. Generating Paramete
Page 192 and 193:
182 Appendix B. Neutral Meson Mixin
Page 194 and 195:
184 Appendix B. Neutral Meson Mixin
Page 197 and 198:
C Input Parameters This appendix is
Page 199:
Parameter Value ± Error Reference
Page 202 and 203:
192 Appendix D. Higgs Potential for
Page 204 and 205:
194 Bibliography [13] S. Dimopoulos
Page 206 and 207:
196 Bibliography [43] G. Nordström
Page 208 and 209:
198 Bibliography [72] K. S. Babu,
Page 210 and 211:
200 Bibliography [104] R. Contino a
Page 212 and 213:
202 Bibliography [133] M. Baak, M.
Page 214 and 215:
204 Bibliography [160] J. Charles,
Page 216 and 217:
206 Bibliography [185] C. Csaki, G.
Page 218 and 219:
208 Bibliography [213] E. Thomson e
Page 220:
210 Bibliography [239] V. Ahrens, A
show all

On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?