On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

More documents

Recommendations

Info

192 Appendix D. Higgs Potential for the Extended Scalar Sector structure only appears in the terms which mix all three fields, Q ijkl ABCD (x) ≡ xiTr � � � � TATB Tr TCTD + xjTr � � TATDTCTB (D.3) +xkTr � � � � TATD Tr TBTC + xlTr � � TATBTCTD , P ij ABCD (y) ≡ yiTr � � � � TATB Tr TCTD + yjTr � � TATDTBTC , � �2 Nc RABC ≡ δA0δB0δC0 − 2 Nc � � � Tr TATB δC0 + Tr 2 � � TATC δB0 + Tr � � � TCTB δA0 + Tr � � � � TATBTC + Tr TBTATC . The Higgs sector comprises 3 mass terms, 2 × 4 real parameters describing selfcouplings of the bitriplets (the P structures), one parameter describing the selfcouplings of the color singlet, 6 real and 3 complex parameters from mixing between the color singlet and one of the bitriplets as well as 12 f-terms which describe mixing between the colored scalars (the Q structures). This makes for a total of 36 real parameters. It is straightforward to solve the extremal conditions, which are given by ∂V (vℓ, vu, vd) = 0 , ∂vu ∂V (vℓ, vu, vd) = 0 , ∂vd ∂V (vℓ, vu, vd) = 0 , (D.4) ∂vℓ and can be used to eliminate three parameters. For a general Higgs potential, it is however not possible to analytically proof that this extremum is a minimum. The reason is, that a minmum is only obtained if the Hessian of the potential is positive definite. The potential will however give rise to 8 + 4 Goldstone bosons, which correspond to zeros on the diagonal of the Hessian (in blockdiagonal form). As a consequence it is a numerical problem to minimize the potential. One can further constrain the parameter space by the condition that all masses are positive, and that the vacuum value of the potential signals a local minimum, V (vℓ, vu, vd) > V (0, 0, 0) [243].
Bibliography [1] V. F. Weisskopf, “On the Self-Energy and the Electromagnetic Field of the Electron,” Phys. Rev. 56, 72 (1939). Cited on page 1. [2] M. Tegmark et al. [SDSS Collaboration], “Cosmological parameters from SDSS and WMAP,” Phys. Rev. D 69, 103501 (2004) [arXiv:astro-ph/0310723]. Cited on page 2. [3] G. ’t Hooft, (ed.), C. Itzykson, (ed.), A. Jaffe, (ed.), H. Lehmann, (ed.), P. K. Mitter, (ed.), I. M. Singer, (ed.) and R. Stora, (ed.), “Recent Developments in Gauge Theories. Proceedings, Nato Advanced Study Institute, Cargese, France, August 26 - September 8, 1979,” NATO Adv. Study Inst. Ser. B Phys. 59, 1 (1980). Cited on page 2. [4] P. F. Bedaque and U. van Kolck, “Effective field theory for few nucleon systems,” Ann. Rev. Nucl. Part. Sci. 52, 339 (2002) [arXiv:nucl-th/0203055]. Cited on page 3. [5] S. P. Martin, “A Supersymmetry primer,” In *Kane, G.L. (ed.): Perspectives on supersymmetry II* 1-153 [arXiv:hep-ph/9709356]. Cited on page 6. [6] L. E. Ibanez and G. G. Ross, “SU(2)L ×U(1) Symmetry Breaking as a Radiative Effect of Supersymmetry Breaking in Guts,” Phys. Lett. B 110, 215 (1982). Cited on page 6. [7] R. Kitano and Y. Nomura, “Supersymmetry, naturalness, and signatures at the LHC,” Phys. Rev. D 73, 095004 (2006) [arXiv:hep-ph/0602096]. Cited on page 6. [8] S. R. Coleman and J. Mandula, “All Possible Symmetries Of The S Matrix,” Phys. Rev. 159, 1251 (1967). Cited on page 5. [9] B. Sakita, “Supermultiplets of elementary particles,” Phys. Rev. 136, B1756 (1964). Cited on page 5. [10] H. Miyazawa, “Baryon Number Changing Currents,” Progress of Theoretical Physics 36, 1266 (1966). Cited on page 5. [11] J. Wess and B. Zumino, “A Lagrangian Model Invariant Under Supergauge Transformations,” Phys. Lett. B 49, 52 (1974). Cited on page 5. [12] R. Haag, J. T. Lopuszanski and M. Sohnius, “All Possible Generators of Supersymmetries of the S Matrix,” Nucl. Phys. B 88, 257 (1975). Cited on page 5.
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 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
10 Chapter 1. Introduction: Problem
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
36 Chapter 2. The Randall Sundrum M
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
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: 142 Chapter 3. Solving the Flavor P
Page 154 and 155: 144 Chapter 3. Solving the Flavor P
Page 156 and 157: 146 Chapter 4. The Asymmetry in Top
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 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

Create successful ePaper yourself

Delete template?

Save as template?