1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file for the Minimal Dilaton Model(MDM) ******)
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3 | (****** ******)
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4 | (****** Authors: Junjie Cao, XiQing Hao, Zhaoxia Heng, Liangliang Shang, Yang Zhang ******)
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5 | (****** ******)
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6 | (****** Choose whether Feynman gauge is desired. ******)
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7 | (****** If set to False, unitary gauge is assumed. ****)
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8 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
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9 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
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10 | (***************************************************************************************************************)
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11 |
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12 | (* ************************** *)
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13 | (* ***** Information ***** *)
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14 | (* ************************** *)
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15 | M$ModelName = "Minimal Dilaton Model";
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16 |
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17 | M$Information = {
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18 | Authors -> {"Junjie Cao", "XiQing Hao", "Zhaoxia Heng", "Liangliang Shang", "Yang Zhang"},
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19 | Version -> "1.0.0",
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20 | Date -> "19. 6. 2014",
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21 | Institutions -> {"Henan Normal University, Center for High Energy Physics, Peking University", "Henan Normal University", "Henan Normal University", "Henan Normal University", "Institute of Theoretical Physics, Academia Sinica"},
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22 | Emails -> {"junjiec@itp.ac.cn", "haoxq@ihep.ac.cn", "zhaoxiaheng@gmail.com", "shlwell1988@gmail.com", "phyzhangyang@gmail.com"},
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23 | URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/SimpleExtensions"
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24 | };
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25 |
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26 | FeynmanGauge = True;
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27 |
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28 | (* ************************** *)
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29 | (* ***** vevs ***** *)
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30 | (* ************************** *)
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31 | M$vevs = { {Phi[2],vev}, {S, vevf} };
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32 |
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33 | (* ************************** *)
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34 | (* ***** Gauge groups ***** *)
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35 | (* ************************** *)
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36 | M$GaugeGroups = {
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37 | U1Y == {
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38 | Abelian -> True,
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39 | CouplingConstant -> g1,
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40 | GaugeBoson -> B,
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41 | Charge -> Y
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42 | },
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43 | SU2L == {
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44 | Abelian -> False,
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45 | CouplingConstant -> gw,
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46 | GaugeBoson -> Wi,
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47 | StructureConstant -> Eps,
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48 | Representations -> {Ta,SU2D},
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49 | Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
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50 | },
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51 | SU3C == {
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52 | Abelian -> False,
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53 | CouplingConstant -> gs,
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54 | GaugeBoson -> G,
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55 | StructureConstant -> f,
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56 | Representations -> {T,Colour},
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57 | SymmetricTensor -> dSUN
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58 | }
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59 | };
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60 |
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61 |
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62 | (* ************************** *)
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63 | (* ***** Indices ***** *)
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64 | (* ************************** *)
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65 |
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66 | IndexRange[Index[SU2W ]] = Unfold[Range[3]];
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67 | IndexRange[Index[SU2D ]] = Unfold[Range[2]];
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68 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
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69 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
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70 | IndexRange[Index[Generation]] = Range[3];
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71 |
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72 | IndexStyle[SU2W, j];
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73 | IndexStyle[SU2D, k];
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74 | IndexStyle[Gluon, a];
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75 | IndexStyle[Colour, m];
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76 | IndexStyle[Generation, f];
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77 |
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78 |
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79 | (* ************************** *)
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80 | (* *** Interaction orders *** *)
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81 | (* *** (as used by mg5) *** *)
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82 | (* ************************** *)
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83 |
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84 | M$InteractionOrderHierarchy = {
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85 | {QCD, 1},
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86 | {QED, 2}
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87 | };
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88 |
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89 |
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90 | (* ************************** *)
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91 | (* **** Particle classes **** *)
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92 | (* ************************** *)
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93 | M$ClassesDescription = {
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94 |
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95 | (* Gauge bosons: physical vector fields *)
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96 | V[1] == {
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97 | ClassName -> A,
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98 | SelfConjugate -> True,
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99 | Mass -> 0,
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100 | Width -> 0,
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101 | ParticleName -> "a",
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102 | PDG -> 22,
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103 | PropagatorLabel -> "a",
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104 | PropagatorType -> W,
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105 | PropagatorArrow -> None,
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106 | FullName -> "Photon"
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107 | },
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108 | V[2] == {
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109 | ClassName -> Z,
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110 | SelfConjugate -> True,
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111 | Mass -> {MZ, 91.1876},
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112 | Width -> {WZ, 2.4952},
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113 | ParticleName -> "Z",
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114 | PDG -> 23,
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115 | PropagatorLabel -> "Z",
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116 | PropagatorType -> Sine,
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117 | PropagatorArrow -> None,
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118 | FullName -> "Z"
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119 | },
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120 | V[3] == {
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121 | ClassName -> W,
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122 | SelfConjugate -> False,
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123 | Mass -> {MW, Internal},
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124 | Width -> {WW, 2.085},
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125 | ParticleName -> "W+",
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126 | AntiParticleName -> "W-",
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127 | QuantumNumbers -> {Q -> 1},
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128 | PDG -> 24,
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129 | PropagatorLabel -> "W",
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130 | PropagatorType -> Sine,
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131 | PropagatorArrow -> Forward,
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132 | FullName -> "W"
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133 | },
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134 | V[4] == {
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135 | ClassName -> G,
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136 | SelfConjugate -> True,
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137 | Indices -> {Index[Gluon]},
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138 | Mass -> 0,
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139 | Width -> 0,
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140 | ParticleName -> "g",
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141 | PDG -> 21,
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142 | PropagatorLabel -> "G",
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143 | PropagatorType -> C,
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144 | PropagatorArrow -> None,
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145 | FullName -> "G"
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146 | },
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147 |
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148 | (* Ghosts: related to physical gauge bosons *)
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149 | U[1] == {
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150 | ClassName -> ghA,
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151 | SelfConjugate -> False,
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152 | Ghost -> A,
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153 | QuantumNumbers -> {GhostNumber -> 1},
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154 | Mass -> 0,
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155 | Width -> 0,
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156 | PropagatorLabel -> "uA",
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157 | PropagatorType -> GhostDash,
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158 | PropagatorArrow -> Forward
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159 | },
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160 | U[2] == {
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161 | ClassName -> ghZ,
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162 | SelfConjugate -> False,
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163 | Ghost -> Z,
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164 | QuantumNumbers -> {GhostNumber -> 1},
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165 | Mass -> {MZ,91.1876},
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166 | Width -> {WZ, 2.4952},
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167 | PropagatorLabel -> "uZ",
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168 | PropagatorType -> GhostDash,
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169 | PropagatorArrow -> Forward
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170 | },
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171 | U[31] == {
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172 | ClassName -> ghWp,
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173 | SelfConjugate -> False,
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174 | Ghost -> W,
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175 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
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176 | Mass -> {MW,Internal},
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177 | Width -> {WW, 2.085},
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178 | PropagatorLabel -> "uWp",
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179 | PropagatorType -> GhostDash,
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180 | PropagatorArrow -> Forward
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181 | },
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182 | U[32] == {
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183 | ClassName -> ghWm,
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184 | SelfConjugate -> False,
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185 | Ghost -> Wbar,
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186 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
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187 | Mass -> {MW,Internal},
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188 | Width -> {WW, 2.085},
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189 | PropagatorLabel -> "uWm",
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190 | PropagatorType -> GhostDash,
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191 | PropagatorArrow -> Forward
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192 | },
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193 | U[4] == {
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194 | ClassName -> ghG,
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195 | SelfConjugate -> False,
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196 | Indices -> {Index[Gluon]},
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197 | Ghost -> G,
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198 | QuantumNumbers ->{GhostNumber -> 1},
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199 | Mass -> 0,
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200 | Width -> 0,
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201 | PropagatorLabel -> "uG",
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202 | PropagatorType -> GhostDash,
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203 | PropagatorArrow -> Forward
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204 | },
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205 |
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206 | (* Gauge bosons: unphysical vector fields *)
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207 | V[11] == {
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208 | ClassName -> B,
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209 | Unphysical -> True,
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210 | SelfConjugate -> True,
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211 | Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
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212 | },
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213 | V[12] == {
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214 | ClassName -> Wi,
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215 | Unphysical -> True,
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216 | SelfConjugate -> True,
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217 | Indices -> {Index[SU2W]},
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218 | FlavorIndex -> SU2W,
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219 | Definitions -> { Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3] -> cw Z[mu] + sw A[mu]}
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220 | },
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221 |
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222 | (* Ghosts: related to unphysical gauge bosons *)
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223 | U[11] == {
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224 | ClassName -> ghB,
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225 | Unphysical -> True,
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226 | SelfConjugate -> False,
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227 | Ghost -> B,
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228 | Definitions -> { ghB -> -sw ghZ + cw ghA}
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229 | },
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230 | U[12] == {
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231 | ClassName -> ghWi,
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232 | Unphysical -> True,
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233 | SelfConjugate -> False,
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234 | Ghost -> Wi,
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235 | Indices -> {Index[SU2W]},
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236 | FlavorIndex -> SU2W,
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237 | Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
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238 | } ,
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239 |
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240 | (* Fermions: physical fields *)
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241 | F[1] == {
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242 | ClassName -> vl,
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243 | ClassMembers -> {ve,vm,vt},
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244 | Indices -> {Index[Generation]},
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245 | FlavorIndex -> Generation,
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246 | SelfConjugate -> False,
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247 | Mass -> 0,
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248 | Width -> 0,
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249 | QuantumNumbers -> {LeptonNumber -> 1},
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250 | PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
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251 | PropagatorType -> S,
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252 | PropagatorArrow -> Forward,
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253 | PDG -> {12,14,16},
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254 | ParticleName -> {"ve","vm","vt"},
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255 | AntiParticleName -> {"ve~","vm~","vt~"},
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256 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
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257 | },
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258 | F[2] == {
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259 | ClassName -> l,
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260 | ClassMembers -> {e, mu, ta},
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261 | Indices -> {Index[Generation]},
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262 | FlavorIndex -> Generation,
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263 | SelfConjugate -> False,
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264 | Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
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265 | Width -> 0,
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266 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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267 | PropagatorLabel -> {"l", "e", "mu", "ta"},
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268 | PropagatorType -> Straight,
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269 | PropagatorArrow -> Forward,
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270 | PDG -> {11, 13, 15},
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271 | ParticleName -> {"e-", "mu-", "ta-"},
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272 | AntiParticleName -> {"e+", "mu+", "ta+"},
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273 | FullName -> {"Electron", "Muon", "Tau"}
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274 | },
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275 | F[3] == {
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276 | ClassName -> dq,
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277 | ClassMembers -> {d, s, b},
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278 | Indices -> {Index[Generation], Index[Colour]},
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279 | FlavorIndex -> Generation,
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280 | SelfConjugate -> False,
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281 | Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
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282 | Width -> 0,
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283 | QuantumNumbers -> {Q -> -1/3},
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284 | PropagatorLabel -> {"dq", "d", "s", "b"},
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285 | PropagatorType -> Straight,
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286 | PropagatorArrow -> Forward,
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287 | PDG -> {1,3,5},
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288 | ParticleName -> {"d", "s", "b" },
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289 | AntiParticleName -> {"d~", "s~", "b~"},
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290 | FullName -> {"d-quark", "s-quark", "b-quark"}
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291 | },
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292 |
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293 | (* new adding *)
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294 | F[4] == {
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295 | ClassName -> u,
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296 | Indices -> {Index[Colour]},
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297 | SelfConjugate -> False,
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298 | Mass -> {MU,2.55*^-3},
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299 | Width -> 0,
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300 | QuantumNumbers -> {Q -> 2/3},
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301 | PropagatorLabel -> {"u"},
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302 | PropagatorType -> Straight,
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303 | PropagatorArrow -> Forward,
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304 | PDG -> {2},
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305 | ParticleName -> {"u" },
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306 | AntiParticleName -> {"u~"},
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307 | FullName -> {"u-quark"}
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308 | },
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309 | F[5] == {
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310 | ClassName -> c,
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311 | Indices -> {Index[Colour]},
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312 | SelfConjugate -> False,
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313 | Mass -> {MC,1.27},
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314 | Width -> 0,
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315 | QuantumNumbers -> {Q -> 2/3},
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316 | PropagatorLabel -> {"c"},
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317 | PropagatorType -> Straight,
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318 | PropagatorArrow -> Forward,
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319 | PDG -> {4},
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320 | ParticleName -> {"c" },
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321 | AntiParticleName -> {"c~"},
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322 | FullName -> {"c-quark"}
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323 | },
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324 | F[6] == {
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325 | ClassName -> t,
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326 | Indices -> {Index[Colour]},
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327 | SelfConjugate -> False,
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328 | Mass -> {MT,172},
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329 | Width -> {WT,1.50833649},
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330 | QuantumNumbers -> {Q -> 2/3},
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331 | PropagatorLabel -> {"t"},
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332 | PropagatorType -> Straight,
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333 | PropagatorArrow -> Forward,
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334 | PDG -> {6},
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335 | ParticleName -> {"t" },
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336 | AntiParticleName -> {"t~"},
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337 | FullName -> {"t-quark"}
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338 | },
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339 | F[7] == {
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340 | ClassName -> tp,
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341 | Indices -> {Index[Colour]},
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342 | SelfConjugate -> False,
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343 | Mass -> {MTP,1670.3},
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344 | Width -> {WTP,37.8},
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345 | QuantumNumbers -> {Q -> 2/3},
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346 | PropagatorLabel -> {"tp"},
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347 | PropagatorType -> Straight,
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348 | PropagatorArrow -> Forward,
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349 | PDG -> {6000001},
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350 | ParticleName -> {"tp" },
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351 | AntiParticleName -> {"tp~"},
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352 | FullName -> {"tp-quark"}
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353 | },
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354 |
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355 | (* Fermions: unphysical fields *)
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356 | F[21] == {
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357 | ClassName -> LL,
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358 | Unphysical -> True,
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359 | Indices -> {Index[SU2D], Index[Generation]},
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360 | FlavorIndex -> SU2D,
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361 | SelfConjugate -> False,
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362 | QuantumNumbers -> {Y -> -1/2},
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363 | Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] vl[sp2,ff]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
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364 | },
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365 | F[22] == {
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366 | ClassName -> lR,
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367 | Unphysical -> True,
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368 | Indices -> {Index[Generation]},
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369 | FlavorIndex -> Generation,
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370 | SelfConjugate -> False,
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371 | QuantumNumbers -> {Y -> -1},
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372 | Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
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373 | },
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374 | (* QL modified *)
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375 | F[23] == {
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376 | ClassName -> QL,
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377 | Unphysical -> True,
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378 | Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
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379 | FlavorIndex -> SU2D,
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380 | SelfConjugate -> False,
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381 | QuantumNumbers -> {Y -> 1/6},
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382 | Definitions -> {
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383 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] u[sp2,cc] /; ff==1],
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384 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] c[sp2,cc] /; ff==2],
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385 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] ( cl t[sp2,cc] + sl tp[sp2,cc] ) /; ff==3],
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386 | QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
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387 | },
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388 | F[31] == {
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389 | ClassName -> QLb,
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390 | Unphysical -> True,
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391 | Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
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392 | FlavorIndex -> SU2D,
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393 | SelfConjugate -> False,
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394 | QuantumNumbers -> {Y -> 1/6},
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395 | Definitions -> {
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396 | QLb[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp2,sp1] ubar[sp2,cc] /; ff==1],
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397 | QLb[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp2,sp1] cbar[sp2,cc] /; ff==2],
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398 | QLb[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp2,sp1] ( cl tbar[sp2,cc] + sl tpbar[sp2,cc] ) /; ff==3],
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399 | QLb[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, Conjugate[ CKM[ff,ff2] ] ProjP[sp2,sp1] dqbar[sp2,ff2,cc]] }
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400 | },
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401 | (* uR modified *)
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402 | F[24] == {
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403 | ClassName -> uR,
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404 | Unphysical -> True,
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405 | Indices -> {Index[Generation], Index[Colour]},
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406 | FlavorIndex -> Generation,
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407 | SelfConjugate -> False,
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408 | QuantumNumbers -> {Y -> 2/3},
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409 | Definitions -> {
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410 | uR[sp1_,1,cc_] :> Module [ {sp2}, ProjP[sp1,sp2] u[sp2,cc]],
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411 | uR[sp1_,2,cc_] :> Module [ {sp2}, ProjP[sp1,sp2] c[sp2,cc]],
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412 | uR[sp1_,3,cc_] :> Module [ {sp2}, ProjP[sp1,sp2] ( cr t[sp2,cc] + sr tp[sp2,cc] )] }
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413 | },
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414 | F[32] == {
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415 | ClassName -> uRb,
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416 | Unphysical -> True,
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417 | Indices -> {Index[Generation], Index[Colour]},
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418 | FlavorIndex -> Generation,
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419 | SelfConjugate -> False,
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420 | QuantumNumbers -> {Y -> 2/3},
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421 | Definitions -> {
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422 | uRb[sp1_,1,cc_] :> Module [ {sp2}, ProjM[sp2,sp1] ubar[sp2,cc]],
|
---|
423 | uRb[sp1_,2,cc_] :> Module [ {sp2}, ProjM[sp2,sp1] cbar[sp2,cc]],
|
---|
424 | uRb[sp1_,3,cc_] :> Module [ {sp2}, ProjM[sp2,sp1] ( cr tbar[sp2,cc] + sr tpbar[sp2,cc] )] }
|
---|
425 | },
|
---|
426 | F[25] == {
|
---|
427 | ClassName -> dR,
|
---|
428 | Unphysical -> True,
|
---|
429 | Indices -> {Index[Generation], Index[Colour]},
|
---|
430 | FlavorIndex -> Generation,
|
---|
431 | SelfConjugate -> False,
|
---|
432 | QuantumNumbers -> {Y -> -1/3},
|
---|
433 | Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
|
---|
434 | },
|
---|
435 |
|
---|
436 | (* new adding *)
|
---|
437 | F[26] == {
|
---|
438 | ClassName -> TR,
|
---|
439 | Unphysical -> True,
|
---|
440 | Indices -> {Index[Colour]},
|
---|
441 | SelfConjugate -> False,
|
---|
442 | QuantumNumbers -> {Y -> 2/3},
|
---|
443 | Definitions -> { TR[sp1_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] ( -sr t[sp2,cc] + cr tp[sp2,cc] )] }
|
---|
444 | },
|
---|
445 | F[27] == {
|
---|
446 | ClassName -> TL,
|
---|
447 | Unphysical -> True,
|
---|
448 | Indices -> {Index[Colour]},
|
---|
449 | SelfConjugate -> False,
|
---|
450 | QuantumNumbers -> {Y -> 2/3},
|
---|
451 | Definitions -> { TL[sp1_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] ( -sl t[sp2,cc] + cl tp[sp2,cc] )] }
|
---|
452 | },
|
---|
453 |
|
---|
454 | (* Higgs: physical scalars *)
|
---|
455 | S[1] == {
|
---|
456 | ClassName -> h,
|
---|
457 | SelfConjugate -> True,
|
---|
458 | Mass -> {Mh,125},
|
---|
459 | Width -> {Wh,0.00407},
|
---|
460 | PropagatorLabel -> "h",
|
---|
461 | PropagatorType -> D,
|
---|
462 | PropagatorArrow -> None,
|
---|
463 | PDG -> 25,
|
---|
464 | ParticleName -> "h",
|
---|
465 | FullName -> "h"
|
---|
466 | },
|
---|
467 |
|
---|
468 | (* Higgs: physical scalars *)
|
---|
469 | S[2] == {
|
---|
470 | ClassName -> G0,
|
---|
471 | SelfConjugate -> True,
|
---|
472 | Goldstone -> Z,
|
---|
473 | Mass -> {MZ, 91.1876},
|
---|
474 | Width -> {WZ, 2.4952},
|
---|
475 | PropagatorLabel -> "Go",
|
---|
476 | PropagatorType -> D,
|
---|
477 | PropagatorArrow -> None,
|
---|
478 | PDG -> 250,
|
---|
479 | ParticleName -> "G0",
|
---|
480 | FullName -> "G0"
|
---|
481 | },
|
---|
482 | S[3] == {
|
---|
483 | ClassName -> GP,
|
---|
484 | SelfConjugate -> False,
|
---|
485 | Goldstone -> W,
|
---|
486 | Mass -> {MW, Internal},
|
---|
487 | QuantumNumbers -> {Q -> 1},
|
---|
488 | Width -> {WW, 2.085},
|
---|
489 | PropagatorLabel -> "GP",
|
---|
490 | PropagatorType -> D,
|
---|
491 | PropagatorArrow -> None,
|
---|
492 | PDG -> 251,
|
---|
493 | ParticleName -> "G+",
|
---|
494 | AntiParticleName -> "G-",
|
---|
495 | FullName -> "GP"
|
---|
496 | },
|
---|
497 | (* new adding *)
|
---|
498 | S[21] == {
|
---|
499 | ClassName -> sDM,
|
---|
500 | SelfConjugate -> True,
|
---|
501 | Mass -> {MsDM, 173.2},
|
---|
502 | Width -> {WsDM,1},
|
---|
503 | PropagatorLabel -> "sDM",
|
---|
504 | PropagatorType -> D,
|
---|
505 | PropagatorArrow -> None,
|
---|
506 | PDG -> 6000011,
|
---|
507 | ParticleName -> "sDM",
|
---|
508 | FullName -> "the dilaton particle"
|
---|
509 | },
|
---|
510 |
|
---|
511 | (* Higgs part: unphysical scalars *)
|
---|
512 | (* new adding *)
|
---|
513 | S[31] == {
|
---|
514 | ClassName -> S,
|
---|
515 | Unphysical -> True,
|
---|
516 | SelfConjugate -> True,
|
---|
517 | Definitions -> { S -> vevf + h ss + sDM cs}
|
---|
518 | },
|
---|
519 | (* Phi modified *)
|
---|
520 | S[11] == {
|
---|
521 | ClassName -> Phi,
|
---|
522 | Unphysical -> True,
|
---|
523 | Indices -> {Index[SU2D]},
|
---|
524 | FlavorIndex -> SU2D,
|
---|
525 | SelfConjugate -> False,
|
---|
526 | QuantumNumbers -> {Y -> 1/2},
|
---|
527 | Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + h cs - sDM ss + I G0)/Sqrt[2] }
|
---|
528 | }
|
---|
529 | };
|
---|
530 |
|
---|
531 |
|
---|
532 | (* ************************** *)
|
---|
533 | (* ***** Gauge ***** *)
|
---|
534 | (* ***** Parameters ***** *)
|
---|
535 | (* ***** (FeynArts) ***** *)
|
---|
536 | (* ************************** *)
|
---|
537 |
|
---|
538 | GaugeXi[ V[1] ] = GaugeXi[A];
|
---|
539 | GaugeXi[ V[2] ] = GaugeXi[Z];
|
---|
540 | GaugeXi[ V[3] ] = GaugeXi[W];
|
---|
541 | GaugeXi[ V[4] ] = GaugeXi[G];
|
---|
542 | GaugeXi[ S[1] ] = 1;
|
---|
543 | GaugeXi[ S[2] ] = GaugeXi[Z];
|
---|
544 | GaugeXi[ S[3] ] = GaugeXi[W];
|
---|
545 | GaugeXi[ U[1] ] = GaugeXi[A];
|
---|
546 | GaugeXi[ U[2] ] = GaugeXi[Z];
|
---|
547 | GaugeXi[ U[31] ] = GaugeXi[W];
|
---|
548 | GaugeXi[ U[32] ] = GaugeXi[W];
|
---|
549 | GaugeXi[ U[4] ] = GaugeXi[G];
|
---|
550 |
|
---|
551 |
|
---|
552 | (* ************************** *)
|
---|
553 | (* ***** Parameters ***** *)
|
---|
554 | (* ************************** *)
|
---|
555 | M$Parameters = {
|
---|
556 |
|
---|
557 | (* External parameters *)
|
---|
558 | aEWM1 == {
|
---|
559 | ParameterType -> External,
|
---|
560 | BlockName -> SMINPUTS,
|
---|
561 | OrderBlock -> 1,
|
---|
562 | Value -> 127.9,
|
---|
563 | InteractionOrder -> {QED,-2},
|
---|
564 | Description -> "Inverse of the EW coupling constant at the Z pole"
|
---|
565 | },
|
---|
566 | Gf == {
|
---|
567 | ParameterType -> External,
|
---|
568 | BlockName -> SMINPUTS,
|
---|
569 | OrderBlock -> 2,
|
---|
570 | Value -> 1.16637*^-5,
|
---|
571 | InteractionOrder -> {QED,2},
|
---|
572 | TeX -> Subscript[G,f],
|
---|
573 | Description -> "Fermi constant"
|
---|
574 | },
|
---|
575 | aS == {
|
---|
576 | ParameterType -> External,
|
---|
577 | BlockName -> SMINPUTS,
|
---|
578 | OrderBlock -> 3,
|
---|
579 | Value -> 0.1184,
|
---|
580 | InteractionOrder -> {QCD,2},
|
---|
581 | TeX -> Subscript[\[Alpha],s],
|
---|
582 | Description -> "Strong coupling constant at the Z pole"
|
---|
583 | },
|
---|
584 | ymdo == {
|
---|
585 | ParameterType -> External,
|
---|
586 | BlockName -> YUKAWA,
|
---|
587 | OrderBlock -> 1,
|
---|
588 | Value -> 5.04*^-3,
|
---|
589 | Description -> "Down Yukawa mass"
|
---|
590 | },
|
---|
591 | ymup == {
|
---|
592 | ParameterType -> External,
|
---|
593 | BlockName -> YUKAWA,
|
---|
594 | OrderBlock -> 2,
|
---|
595 | Value -> 2.55*^-3,
|
---|
596 | Description -> "Up Yukawa mass"
|
---|
597 | },
|
---|
598 | yms == {
|
---|
599 | ParameterType -> External,
|
---|
600 | BlockName -> YUKAWA,
|
---|
601 | OrderBlock -> 3,
|
---|
602 | Value -> 0.101,
|
---|
603 | Description -> "Strange Yukawa mass"
|
---|
604 | },
|
---|
605 | ymc == {
|
---|
606 | ParameterType -> External,
|
---|
607 | BlockName -> YUKAWA,
|
---|
608 | OrderBlock -> 4,
|
---|
609 | Value -> 1.27,
|
---|
610 | Description -> "Charm Yukawa mass"
|
---|
611 | },
|
---|
612 | ymb == {
|
---|
613 | ParameterType -> External,
|
---|
614 | BlockName -> YUKAWA,
|
---|
615 | OrderBlock -> 5,
|
---|
616 | Value -> 4.7,
|
---|
617 | Description -> "Bottom Yukawa mass"
|
---|
618 | },
|
---|
619 | yme == {
|
---|
620 | ParameterType -> External,
|
---|
621 | BlockName -> YUKAWA,
|
---|
622 | OrderBlock -> 11,
|
---|
623 | Value -> 5.11*^-4,
|
---|
624 | Description -> "Electron Yukawa mass"
|
---|
625 | },
|
---|
626 | ymm == {
|
---|
627 | ParameterType -> External,
|
---|
628 | BlockName -> YUKAWA,
|
---|
629 | OrderBlock -> 13,
|
---|
630 | Value -> 0.10566,
|
---|
631 | Description -> "Muon Yukawa mass"
|
---|
632 | },
|
---|
633 | ymtau == {
|
---|
634 | ParameterType -> External,
|
---|
635 | BlockName -> YUKAWA,
|
---|
636 | OrderBlock -> 15,
|
---|
637 | Value -> 1.777,
|
---|
638 | Description -> "Tau Yukawa mass"
|
---|
639 | },
|
---|
640 | cabi == {
|
---|
641 | ParameterType -> External,
|
---|
642 | BlockName -> CKMBLOCK,
|
---|
643 | OrderBlock -> 1,
|
---|
644 | Value -> 0.227736,
|
---|
645 | TeX -> Subscript[\[Theta], c],
|
---|
646 | Description -> "Cabibbo angle"
|
---|
647 | },
|
---|
648 |
|
---|
649 | (* Internal Parameters *)
|
---|
650 | aEW == {
|
---|
651 | ParameterType -> Internal,
|
---|
652 | Value -> 1/aEWM1,
|
---|
653 | InteractionOrder -> {QED,2},
|
---|
654 | TeX -> Subscript[\[Alpha], EW],
|
---|
655 | Description -> "Electroweak coupling contant"
|
---|
656 | },
|
---|
657 | MW == {
|
---|
658 | ParameterType -> Internal,
|
---|
659 | Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
|
---|
660 | TeX -> Subscript[M,W],
|
---|
661 | Description -> "W mass"
|
---|
662 | },
|
---|
663 | sw2 == {
|
---|
664 | ParameterType -> Internal,
|
---|
665 | Value -> 1-(MW/MZ)^2,
|
---|
666 | Description -> "Squared Sin of the Weinberg angle"
|
---|
667 | },
|
---|
668 | ee == {
|
---|
669 | ParameterType -> Internal,
|
---|
670 | Value -> Sqrt[4 Pi aEW],
|
---|
671 | InteractionOrder -> {QED,1},
|
---|
672 | TeX -> e,
|
---|
673 | Description -> "Electric coupling constant"
|
---|
674 | },
|
---|
675 | cw == {
|
---|
676 | ParameterType -> Internal,
|
---|
677 | Value -> Sqrt[1-sw2],
|
---|
678 | TeX -> Subscript[c,w],
|
---|
679 | Description -> "Cosine of the Weinberg angle"
|
---|
680 | },
|
---|
681 | sw == {
|
---|
682 | ParameterType -> Internal,
|
---|
683 | Value -> Sqrt[sw2],
|
---|
684 | TeX -> Subscript[s,w],
|
---|
685 | Description -> "Sine of the Weinberg angle"
|
---|
686 | },
|
---|
687 | gw == {
|
---|
688 | ParameterType -> Internal,
|
---|
689 | Definitions -> {gw->ee/sw},
|
---|
690 | InteractionOrder -> {QED,1},
|
---|
691 | TeX -> Subscript[g,w],
|
---|
692 | Description -> "Weak coupling constant at the Z pole"
|
---|
693 | },
|
---|
694 | g1 == {
|
---|
695 | ParameterType -> Internal,
|
---|
696 | Definitions -> {g1->ee/cw},
|
---|
697 | InteractionOrder -> {QED,1},
|
---|
698 | TeX -> Subscript[g,1],
|
---|
699 | Description -> "U(1)Y coupling constant at the Z pole"
|
---|
700 | },
|
---|
701 | gs == {
|
---|
702 | ParameterType -> Internal,
|
---|
703 | Value -> Sqrt[4 Pi aS],
|
---|
704 | InteractionOrder -> {QCD,1},
|
---|
705 | TeX -> Subscript[g,s],
|
---|
706 | ParameterName -> G,
|
---|
707 | Description -> "Strong coupling constant at the Z pole"
|
---|
708 | },
|
---|
709 | vev == {
|
---|
710 | ParameterType -> Internal,
|
---|
711 | Value -> 2*MW*sw/ee,
|
---|
712 | InteractionOrder -> {QED,-1},
|
---|
713 | Description -> "Higgs vacuum expectation value"
|
---|
714 | },
|
---|
715 | yl == {
|
---|
716 | ParameterType -> Internal,
|
---|
717 | Indices -> {Index[Generation], Index[Generation]},
|
---|
718 | Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
719 | Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
|
---|
720 | InteractionOrder -> {QED, 1},
|
---|
721 | ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
|
---|
722 | TeX -> Superscript[y, l],
|
---|
723 | Description -> "Lepton Yukawa couplings"
|
---|
724 | },
|
---|
725 | yd == {
|
---|
726 | ParameterType -> Internal,
|
---|
727 | Indices -> {Index[Generation], Index[Generation]},
|
---|
728 | Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
729 | Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
|
---|
730 | InteractionOrder -> {QED, 1},
|
---|
731 | ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
|
---|
732 | TeX -> Superscript[y, d],
|
---|
733 | Description -> "Down-type Yukawa couplings"
|
---|
734 | },
|
---|
735 | (* N. B. : only Cabibbo mixing! *)
|
---|
736 | CKM == {
|
---|
737 | ParameterType -> Internal,
|
---|
738 | Indices -> {Index[Generation], Index[Generation]},
|
---|
739 | Unitary -> True,
|
---|
740 | Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
|
---|
741 | CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
|
---|
742 | CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
|
---|
743 | TeX -> Superscript[V,CKM],
|
---|
744 | Description -> "CKM-Matrix"},
|
---|
745 |
|
---|
746 | (* new add *)
|
---|
747 | eta == {
|
---|
748 | ParameterType -> External,
|
---|
749 | BlockName -> MDMINPUTS,
|
---|
750 | OrderBlock -> 1,
|
---|
751 | Value -> 0.33,
|
---|
752 | TeX -> \[Eta],
|
---|
753 | Description -> "The ratio of the two scalar vacuum expectation values in the MDM"
|
---|
754 | },
|
---|
755 | ts == {
|
---|
756 | ParameterType -> External,
|
---|
757 | BlockName -> MDMINPUTS,
|
---|
758 | OrderBlock -> 2,
|
---|
759 | Value -> -0.23,
|
---|
760 | Tex -> Subscript[tan\[Theta],S],
|
---|
761 | Description -> "The tangent value of the mixing angle \[Theta]_S between the new Scalar S and the unphysical Higgs scalar Phi[2]"
|
---|
762 | },
|
---|
763 | sl == {
|
---|
764 | ParameterType -> External,
|
---|
765 | BlockName -> MDMINPUTS,
|
---|
766 | OrderBlock -> 3,
|
---|
767 | Value -> 0.12,
|
---|
768 | Tex -> Subscript[sin\[Theta],L],
|
---|
769 | Description -> "The sine value of the mixing angle \[Theta]_L between top quark and its partner"
|
---|
770 | },
|
---|
771 |
|
---|
772 | vevf == {
|
---|
773 | ParameterType -> Internal,
|
---|
774 | Value -> vev/eta,
|
---|
775 | InteractionOrder -> {QED,-1},
|
---|
776 | Description -> "The new scalar vacuum expectation value in the MDM"
|
---|
777 | },
|
---|
778 | ss == {
|
---|
779 | ParameterType -> Internal,
|
---|
780 | Value -> ts / Sqrt[1 + ts^2],
|
---|
781 | Tex -> Subscript[sin\[Theta],S],
|
---|
782 | Description -> "The sine value of \[Theta]_S"
|
---|
783 | },
|
---|
784 | cs == {
|
---|
785 | ParameterType -> Internal,
|
---|
786 | Value -> 1 / Sqrt[1 + ts^2],
|
---|
787 | Tex -> Subscript[cos\[Theta],S],
|
---|
788 | Description -> "The cosine value of \[Theta]_S"
|
---|
789 | },
|
---|
790 | cl == {
|
---|
791 | ParameterType -> Internal,
|
---|
792 | Value -> Sqrt[1 - sl^2],
|
---|
793 | Tex -> Subscript[cos\[Theta],L],
|
---|
794 | Description -> "The cosine value of \[Theta]_L"
|
---|
795 | },
|
---|
796 | sr == {
|
---|
797 | ParameterType -> Internal,
|
---|
798 | Value -> MT sl / (MTP cl),
|
---|
799 | Tex -> Subscript[sin\[Theta],R],
|
---|
800 | Description -> "The sine value of the mixing angle \[Theta]_R between top quark and its partner"
|
---|
801 | },
|
---|
802 | cr == {
|
---|
803 | ParameterType -> Internal,
|
---|
804 | Value -> 1,
|
---|
805 | Tex -> Subscript[cos\[Theta],L],
|
---|
806 | Description -> "The cosine value of \[Theta]_R fixed to 1"
|
---|
807 | },
|
---|
808 | dkappa == {
|
---|
809 | ParameterType -> Internal,
|
---|
810 | Value -> Abs[Mh^2 - MsDM^2] / vev^2 Abs[eta ts] / (1 + ts^2),
|
---|
811 | TeX -> \[Kappa],
|
---|
812 | InteractionOrder -> {QED,2},
|
---|
813 | Description -> "Coefficient of quartic couplings of the new scalar S and the unphical Higgs scalar Phi"
|
---|
814 | },
|
---|
815 | dlamh == {
|
---|
816 | ParameterType -> Internal,
|
---|
817 | Value -> Abs[Mh^2 - MsDM^2] / vev^2 (Abs[(Mh^2 + MsDM^2) / (Mh^2 - MsDM^2)] + Abs[2 cs ss]/(2 cs ss) (cs^2 - ss^2)),
|
---|
818 | TeX -> Subscript[\[Lambda],H],
|
---|
819 | InteractionOrder -> {QED,2},
|
---|
820 | Description -> "Coefficient of quartic self-couplings of the unphical Higgs scalar Phi"
|
---|
821 | },
|
---|
822 | dlams == {
|
---|
823 | ParameterType -> Internal,
|
---|
824 | Value -> 3 Abs[Mh^2 - MsDM^2] / (2 vevf^2) (Abs[(Mh^2 + MsDM^2) / (Mh^2 - MsDM^2)] - Abs[2 cs ss]/(2 cs ss) (cs^2 - ss^2)),
|
---|
825 | TeX -> Subscript[\[Lambda],S],
|
---|
826 | InteractionOrder -> {QED,2},
|
---|
827 | Description -> "Coefficient of quartic self-couplings of the new scalar S in the MDM"
|
---|
828 | },
|
---|
829 | muS2 == {
|
---|
830 | ParameterType -> Internal,
|
---|
831 | Value -> - dlams / 6 vevf^2 - dkappa vev^2 / 2,
|
---|
832 | Tex -> Superscript[Subscript[m, S],2],
|
---|
833 | Description -> "Coefficient of the quadratic piece of the new scalar S"
|
---|
834 | },
|
---|
835 | (* muH modified*)
|
---|
836 | muH2 == {
|
---|
837 | ParameterType -> Internal,
|
---|
838 | Value -> - dkappa vevf^2 / 2 - dlamh vev^2 / 4,
|
---|
839 | TeX -> Superscript[Subscript[m, H],2],
|
---|
840 | Description -> "Coefficient of the quadratic piece of the unphysical Higgs scalar"
|
---|
841 | },
|
---|
842 | (* modified ymt *)
|
---|
843 | ymt == {
|
---|
844 | ParameterType -> Internal,
|
---|
845 | Value -> MT / cl,
|
---|
846 | Description -> "Modified top Yukawa mass in the MDM"
|
---|
847 | },
|
---|
848 | yu == {
|
---|
849 | ParameterType -> Internal,
|
---|
850 | Indices -> {Index[Generation], Index[Generation]},
|
---|
851 | Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
852 | Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
|
---|
853 | InteractionOrder -> {QED, 1},
|
---|
854 | ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
|
---|
855 | TeX -> Superscript[y, u],
|
---|
856 | Description -> "Up-type Yukawa couplings"
|
---|
857 | },
|
---|
858 | yp == {
|
---|
859 | ParameterType -> Internal,
|
---|
860 | Value -> Sqrt[2] / vev MTP sl,
|
---|
861 | InteractionOrder -> {QED, 1},
|
---|
862 | ParameterName -> yp,
|
---|
863 | Tex -> Superscript[y, \[Prime]],
|
---|
864 | Description -> "new Yukawa Couplings of the top quark partner in the MDM"
|
---|
865 | },
|
---|
866 | Mdltn == {
|
---|
867 | ParameterType -> Internal,
|
---|
868 | Value -> MTP cl,
|
---|
869 | Description -> "Coefficient of couplings of the top quark partner and the new scalar"
|
---|
870 | }
|
---|
871 |
|
---|
872 | };
|
---|
873 |
|
---|
874 | (* ************************** *)
|
---|
875 | (* ***** Lagrangian ***** *)
|
---|
876 | (* ************************** *)
|
---|
877 |
|
---|
878 | LGauge := Block[{mu,nu,ii,aa},
|
---|
879 | ExpandIndices[-1/4 FS[B,mu,nu] FS[B,mu,nu] - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa], FlavorExpand->SU2W]];
|
---|
880 |
|
---|
881 | (* LFermions modified *)
|
---|
882 | LFermions := Block[{mu,ii,cc,sp1,sp2,ff},
|
---|
883 | ExpandIndices[I*(
|
---|
884 | Ga[mu,sp1,sp2] QLb[sp1, ii, ff, cc].DC[QL[sp2, ii, ff, cc], mu] + Ga[mu,sp1,sp2] LLbar[sp1, ii, ff].DC[LL[sp2, ii, ff], mu] + Ga[mu,sp1,sp2] uRb[sp1, ff, cc].DC[uR[sp2, ff, cc], mu] + Ga[mu,sp1,sp2] dRbar[sp1, ff, cc].DC[dR[sp2, ff, cc], mu] + Ga[mu,sp1,sp2] lRbar[sp1, ff].DC[lR[sp2, ff], mu])]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
|
---|
885 |
|
---|
886 | (* new adding *)
|
---|
887 | LFermionsDM := Block[{mu,sp,cc},
|
---|
888 | ExpandIndices[ I TLbar.Ga[mu].DC[TL, mu] + I TLbar.Ga[mu].DC[TR, mu] + I TRbar.Ga[mu].DC[TL, mu] + I TRbar.Ga[mu].DC[TR, mu] - Mdltn / vevf S ( TLbar[sp,cc].TL[sp,cc] + TLbar[sp,cc].TR[sp,cc] + TRbar[sp,cc].TL[sp,cc] + TRbar[sp,cc].TR[sp,cc] ) ,
|
---|
889 | FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
|
---|
890 |
|
---|
891 | (* LHiggs modified *)
|
---|
892 | LHiggs := Block[{ii,jj,mu, feynmangaugerules},
|
---|
893 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
894 |
|
---|
895 | ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] - 1 / 2 del[S,mu] del[S,mu] - muS2 / 2 S^2 - dlams / 24 S^4 - dkappa / 2 S^2 Phibar[ii] Phi[ii] - muH2 Phibar[ii] Phi[ii] - dlamh / 4 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
|
---|
896 | ];
|
---|
897 |
|
---|
898 | (* LYukawa modified *)
|
---|
899 | LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
|
---|
900 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
901 |
|
---|
902 | yuk = ExpandIndices[
|
---|
903 | -yd[ff2, ff3] CKM[ff1, ff2] QLb[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
|
---|
904 | yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
|
---|
905 | yu[ff1, ff2] QLb[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj]
|
---|
906 | -Conjugate[yd[ff2, ff3]] Conjugate[CKM[ff1, ff2]] dRbar [sp, ff3, cc].QL [sp, ii, ff1, cc] Phibar[ii] -
|
---|
907 | Conjugate[yl[ff1, ff3]] lRbar[sp, ff3].LL [sp, ii, ff1]. Phibar[ii] -
|
---|
908 | Conjugate[yu[ff1, ff2]] uRb[sp, ff2, cc].QL [sp, ii, ff1, cc] Phi[jj] Conjugate[Eps[ii, jj]]];
|
---|
909 | yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
|
---|
910 | yuk/.feynmangaugerules
|
---|
911 | ];
|
---|
912 |
|
---|
913 | (* new adding *)
|
---|
914 | LYukawaDM := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
|
---|
915 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
916 |
|
---|
917 | yuk = ExpandIndices[
|
---|
918 | -yp QLb[sp, ii, 3, cc].TR [sp, cc] Phibar[jj] Eps[ii, jj]
|
---|
919 | -Conjugate[yp] TRbar[sp, cc].QL [sp, ii, 3, cc] Phi[jj] Conjugate[Eps[ii, jj]], FlavorExpand -> SU2D];
|
---|
920 | yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
|
---|
921 | yuk/.feynmangaugerules
|
---|
922 | ];
|
---|
923 |
|
---|
924 | LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
|
---|
925 | (* Pure gauge piece *)
|
---|
926 | LGh1 = -ghBbar.del[DC[ghB,mu],mu];
|
---|
927 | LGhw = -ghWibar.del[DC[ghWi,mu],mu];
|
---|
928 | LGhs = -ghGbar.del[DC[ghG,mu],mu];
|
---|
929 |
|
---|
930 | (* Scalar pieces: see Peskin pages 739-742 *)
|
---|
931 | (* phi1 and phi2 are the real degrees of freedom of GP *)
|
---|
932 | (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
|
---|
933 | gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
|
---|
934 | ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
|
---|
935 | generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
|
---|
936 | doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
|
---|
937 | doublet0 = {0, vev/Sqrt[2]};
|
---|
938 | Vectorize[{a_, b_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]}/.{Im[_]->0, Re[num_]->num}];
|
---|
939 | togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
|
---|
940 | LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
|
---|
941 |
|
---|
942 | ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
|
---|
943 |
|
---|
944 | LMDM:= LGauge + LFermions + LFermionsDM + LHiggs + LYukawa + LYukawaDM + LGhost;
|
---|