1 | (***************************************************************************************************************)
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2 | (****** FeynRules model-file for the Standard Model + some dim 6 operators for composite top quark ******)
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3 | (****** ******)
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4 | (****** Authors: J. Dror, E. Salvioni ******)
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5 | (****** ******)
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6 | (****** Model is based on Standard Model FeynRules model-file ******)
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7 | (***************************************************************************************************************)
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8 |
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9 | (* ************************** *)
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10 | (* ***** Information ***** *)
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11 | (* ************************** *)
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12 | M$ModelName = "HiggsTopCurrents";
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13 |
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14 | M$Information = {
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15 | Authors -> {"J. Dror", "E. Salvioni"},
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16 | Version -> "1.0.0",
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17 | Date -> "02.06.2016",
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18 | Institutions -> {"Cornell University", "University of California, Davis"},
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19 | Emails -> {"ajd268@cornell.edu", "esalvioni@ucdavid.edu"}
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20 | };
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21 |
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22 | FeynmanGauge = True;
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23 |
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24 | (* ************************** *)
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25 | (* ***** vevs ***** *)
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26 | (* ************************** *)
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27 | M$vevs = { {Phi[2],vev} };
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28 |
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29 | (* ************************** *)
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30 | (* ***** Gauge groups ***** *)
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31 | (* ************************** *)
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32 | M$GaugeGroups = {
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33 | U1Y == {
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34 | Abelian -> True,
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35 | CouplingConstant -> g1,
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36 | GaugeBoson -> B,
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37 | Charge -> Y
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38 | },
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39 | SU2L == {
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40 | Abelian -> False,
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41 | CouplingConstant -> gw,
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42 | GaugeBoson -> Wi,
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43 | StructureConstant -> Eps,
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44 | Representations -> {Ta,SU2D},
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45 | Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
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46 | },
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47 | SU3C == {
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48 | Abelian -> False,
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49 | CouplingConstant -> gs,
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50 | GaugeBoson -> G,
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51 | StructureConstant -> f,
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52 | Representations -> {T,Colour},
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53 | SymmetricTensor -> dSUN
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54 | }
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55 | };
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56 |
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57 |
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58 | (* ************************** *)
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59 | (* ***** Indices ***** *)
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60 | (* ************************** *)
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61 |
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62 | IndexRange[Index[SU2W ]] = Unfold[Range[3]];
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63 | IndexRange[Index[SU2D ]] = Unfold[Range[2]];
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64 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
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65 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
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66 | IndexRange[Index[Generation]] = Range[3];
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67 |
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68 | IndexStyle[SU2W, j];
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69 | IndexStyle[SU2D, k];
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70 | IndexStyle[Gluon, a];
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71 | IndexStyle[Colour, m];
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72 | IndexStyle[Generation, f];
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73 |
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74 |
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75 | (* ************************** *)
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76 | (* *** Interaction orders *** *)
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77 | (* *** (as used by mg5) *** *)
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78 | (* ************************** *)
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79 |
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80 | M$InteractionOrderHierarchy = {
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81 | {QCD, 1},
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82 | {QED, 2}
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83 | };
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84 |
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85 |
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86 | (* ************************** *)
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87 | (* **** Particle classes **** *)
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88 | (* ************************** *)
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89 | M$ClassesDescription = {
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90 |
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91 | (* Gauge bosons: physical vector fields *)
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92 | V[1] == {
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93 | ClassName -> A,
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94 | SelfConjugate -> True,
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95 | Mass -> 0,
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96 | Width -> 0,
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97 | ParticleName -> "a",
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98 | PDG -> 22,
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99 | PropagatorLabel -> "a",
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100 | PropagatorType -> W,
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101 | PropagatorArrow -> None,
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102 | FullName -> "Photon"
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103 | },
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104 | V[2] == {
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105 | ClassName -> Z,
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106 | SelfConjugate -> True,
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107 | Mass -> {MZ, 91.1876},
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108 | Width -> {WZ, 2.4952},
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109 | ParticleName -> "Z",
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110 | PDG -> 23,
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111 | PropagatorLabel -> "Z",
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112 | PropagatorType -> Sine,
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113 | PropagatorArrow -> None,
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114 | FullName -> "Z"
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115 | },
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116 | V[3] == {
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117 | ClassName -> W,
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118 | SelfConjugate -> False,
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119 | Mass -> {MW, Internal},
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120 | Width -> {WW, 2.085},
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121 | ParticleName -> "W+",
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122 | AntiParticleName -> "W-",
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123 | QuantumNumbers -> {Q -> 1},
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124 | PDG -> 24,
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125 | PropagatorLabel -> "W",
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126 | PropagatorType -> Sine,
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127 | PropagatorArrow -> Forward,
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128 | FullName -> "W"
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129 | },
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130 | V[4] == {
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131 | ClassName -> G,
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132 | SelfConjugate -> True,
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133 | Indices -> {Index[Gluon]},
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134 | Mass -> 0,
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135 | Width -> 0,
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136 | ParticleName -> "g",
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137 | PDG -> 21,
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138 | PropagatorLabel -> "G",
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139 | PropagatorType -> C,
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140 | PropagatorArrow -> None,
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141 | FullName -> "G"
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142 | },
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143 |
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144 | (* Ghosts: related to physical gauge bosons *)
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145 | U[1] == {
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146 | ClassName -> ghA,
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147 | SelfConjugate -> False,
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148 | Ghost -> A,
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149 | QuantumNumbers -> {GhostNumber -> 1},
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150 | Mass -> 0,
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151 | Width -> 0,
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152 | PropagatorLabel -> "uA",
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153 | PropagatorType -> GhostDash,
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154 | PropagatorArrow -> Forward
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155 | },
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156 | U[2] == {
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157 | ClassName -> ghZ,
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158 | SelfConjugate -> False,
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159 | Ghost -> Z,
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160 | QuantumNumbers -> {GhostNumber -> 1},
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161 | Mass -> {MZ,91.1876},
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162 | Width -> {WZ, 2.4952},
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163 | PropagatorLabel -> "uZ",
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164 | PropagatorType -> GhostDash,
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165 | PropagatorArrow -> Forward
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166 | },
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167 | U[31] == {
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168 | ClassName -> ghWp,
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169 | SelfConjugate -> False,
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170 | Ghost -> W,
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171 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
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172 | Mass -> {MW,Internal},
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173 | Width -> {WW, 2.085},
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174 | PropagatorLabel -> "uWp",
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175 | PropagatorType -> GhostDash,
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176 | PropagatorArrow -> Forward
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177 | },
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178 | U[32] == {
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179 | ClassName -> ghWm,
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180 | SelfConjugate -> False,
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181 | Ghost -> Wbar,
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182 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
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183 | Mass -> {MW,Internal},
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184 | Width -> {WW, 2.085},
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185 | PropagatorLabel -> "uWm",
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186 | PropagatorType -> GhostDash,
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187 | PropagatorArrow -> Forward
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188 | },
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189 | U[4] == {
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190 | ClassName -> ghG,
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191 | SelfConjugate -> False,
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192 | Indices -> {Index[Gluon]},
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193 | Ghost -> G,
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194 | QuantumNumbers ->{GhostNumber -> 1},
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195 | Mass -> 0,
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196 | Width -> 0,
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197 | PropagatorLabel -> "uG",
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198 | PropagatorType -> GhostDash,
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199 | PropagatorArrow -> Forward
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200 | },
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201 |
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202 | (* Gauge bosons: unphysical vector fields *)
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203 | V[11] == {
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204 | ClassName -> B,
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205 | Unphysical -> True,
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206 | SelfConjugate -> True,
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207 | Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
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208 | },
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209 | V[12] == {
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210 | ClassName -> Wi,
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211 | Unphysical -> True,
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212 | SelfConjugate -> True,
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213 | Indices -> {Index[SU2W]},
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214 | FlavorIndex -> SU2W,
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215 | 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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216 | },
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217 |
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218 | (* Ghosts: related to unphysical gauge bosons *)
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219 | U[11] == {
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220 | ClassName -> ghB,
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221 | Unphysical -> True,
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222 | SelfConjugate -> False,
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223 | Ghost -> B,
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224 | Definitions -> { ghB -> -sw ghZ + cw ghA}
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225 | },
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226 | U[12] == {
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227 | ClassName -> ghWi,
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228 | Unphysical -> True,
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229 | SelfConjugate -> False,
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230 | Ghost -> Wi,
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231 | Indices -> {Index[SU2W]},
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232 | FlavorIndex -> SU2W,
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233 | Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
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234 | } ,
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235 |
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236 | (* Fermions: physical fields *)
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237 | F[1] == {
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238 | ClassName -> vl,
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239 | ClassMembers -> {ve,vm,vt},
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240 | Indices -> {Index[Generation]},
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241 | FlavorIndex -> Generation,
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242 | SelfConjugate -> False,
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243 | Mass -> 0,
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244 | Width -> 0,
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245 | QuantumNumbers -> {LeptonNumber -> 1},
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246 | PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
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247 | PropagatorType -> S,
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248 | PropagatorArrow -> Forward,
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249 | PDG -> {12,14,16},
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250 | ParticleName -> {"ve","vm","vt"},
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251 | AntiParticleName -> {"ve~","vm~","vt~"},
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252 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
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253 | },
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254 | F[2] == {
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255 | ClassName -> l,
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256 | ClassMembers -> {e, mu, ta},
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257 | Indices -> {Index[Generation]},
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258 | FlavorIndex -> Generation,
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259 | SelfConjugate -> False,
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260 | Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
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261 | Width -> 0,
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262 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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263 | PropagatorLabel -> {"l", "e", "mu", "ta"},
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264 | PropagatorType -> Straight,
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265 | PropagatorArrow -> Forward,
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266 | PDG -> {11, 13, 15},
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267 | ParticleName -> {"e-", "mu-", "ta-"},
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268 | AntiParticleName -> {"e+", "mu+", "ta+"},
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269 | FullName -> {"Electron", "Muon", "Tau"}
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270 | },
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271 | F[3] == {
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272 | ClassName -> uq,
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273 | ClassMembers -> {u, c, t},
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274 | Indices -> {Index[Generation], Index[Colour]},
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275 | FlavorIndex -> Generation,
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276 | SelfConjugate -> False,
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277 | Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
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278 | Width -> {0, 0, {WT,1.50833649}},
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279 | QuantumNumbers -> {Q -> 2/3},
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280 | PropagatorLabel -> {"uq", "u", "c", "t"},
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281 | PropagatorType -> Straight,
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282 | PropagatorArrow -> Forward,
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283 | PDG -> {2, 4, 6},
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284 | ParticleName -> {"u", "c", "t" },
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285 | AntiParticleName -> {"u~", "c~", "t~"},
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286 | FullName -> {"u-quark", "c-quark", "t-quark"}
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287 | },
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288 | F[4] == {
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289 | ClassName -> dq,
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290 | ClassMembers -> {d, s, b},
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291 | Indices -> {Index[Generation], Index[Colour]},
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292 | FlavorIndex -> Generation,
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293 | SelfConjugate -> False,
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294 | Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
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295 | Width -> 0,
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296 | QuantumNumbers -> {Q -> -1/3},
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297 | PropagatorLabel -> {"dq", "d", "s", "b"},
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298 | PropagatorType -> Straight,
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299 | PropagatorArrow -> Forward,
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300 | PDG -> {1,3,5},
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301 | ParticleName -> {"d", "s", "b" },
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302 | AntiParticleName -> {"d~", "s~", "b~"},
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303 | FullName -> {"d-quark", "s-quark", "b-quark"}
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304 | },
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305 |
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306 | (* Fermions: unphysical fields *)
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307 | F[11] == {
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308 | ClassName -> LL,
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309 | Unphysical -> True,
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310 | Indices -> {Index[SU2D], Index[Generation]},
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311 | FlavorIndex -> SU2D,
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312 | SelfConjugate -> False,
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313 | QuantumNumbers -> {Y -> -1/2},
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314 | 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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315 | },
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316 | F[12] == {
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317 | ClassName -> lR,
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318 | Unphysical -> True,
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319 | Indices -> {Index[Generation]},
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320 | FlavorIndex -> Generation,
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321 | SelfConjugate -> False,
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322 | QuantumNumbers -> {Y -> -1},
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323 | Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
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324 | },
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325 | F[13] == {
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326 | ClassName -> QL,
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327 | Unphysical -> True,
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328 | Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
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329 | FlavorIndex -> SU2D,
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330 | SelfConjugate -> False,
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331 | QuantumNumbers -> {Y -> 1/6},
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332 | Definitions -> {
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333 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
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334 | QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
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335 | },
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336 | F[14] == {
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337 | ClassName -> uR,
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338 | Unphysical -> True,
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339 | Indices -> {Index[Generation], Index[Colour]},
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340 | FlavorIndex -> Generation,
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341 | SelfConjugate -> False,
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342 | QuantumNumbers -> {Y -> 2/3},
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343 | Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
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344 | },
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345 | F[15] == {
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346 | ClassName -> dR,
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347 | Unphysical -> True,
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348 | Indices -> {Index[Generation], Index[Colour]},
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349 | FlavorIndex -> Generation,
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350 | SelfConjugate -> False,
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351 | QuantumNumbers -> {Y -> -1/3},
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352 | Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
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353 | },
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354 |
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355 | (* Higgs: physical scalars *)
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356 | S[1] == {
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357 | ClassName -> H,
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358 | SelfConjugate -> True,
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359 | Mass -> {MH,125},
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360 | Width -> {WH,0.00407},
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361 | PropagatorLabel -> "H",
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362 | PropagatorType -> D,
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363 | PropagatorArrow -> None,
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364 | PDG -> 25,
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365 | ParticleName -> "H",
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366 | FullName -> "H"
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367 | },
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368 |
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369 | (* Higgs: physical scalars *)
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370 | S[2] == {
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371 | ClassName -> G0,
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372 | SelfConjugate -> True,
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373 | Goldstone -> Z,
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374 | Mass -> {MZ, 91.1876},
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375 | Width -> {WZ, 2.4952},
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376 | PropagatorLabel -> "Go",
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377 | PropagatorType -> D,
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378 | PropagatorArrow -> None,
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379 | PDG -> 250,
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380 | ParticleName -> "G0",
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381 | FullName -> "G0"
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382 | },
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383 | S[3] == {
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384 | ClassName -> GP,
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385 | SelfConjugate -> False,
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386 | Goldstone -> W,
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387 | Mass -> {MW, Internal},
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388 | QuantumNumbers -> {Q -> 1},
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389 | Width -> {WW, 2.085},
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390 | PropagatorLabel -> "GP",
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391 | PropagatorType -> D,
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392 | PropagatorArrow -> None,
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393 | PDG -> 251,
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394 | ParticleName -> "G+",
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395 | AntiParticleName -> "G-",
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396 | FullName -> "GP"
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397 | },
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398 |
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399 | (* Higgs: unphysical scalars *)
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400 | S[11] == {
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401 | ClassName -> Phi,
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402 | Unphysical -> True,
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403 | Indices -> {Index[SU2D]},
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404 | FlavorIndex -> SU2D,
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405 | SelfConjugate -> False,
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406 | QuantumNumbers -> {Y -> 1/2},
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407 | Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
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408 | }
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409 | };
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410 |
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411 |
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412 | (* ************************** *)
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413 | (* ***** Gauge ***** *)
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414 | (* ***** Parameters ***** *)
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415 | (* ***** (FeynArts) ***** *)
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416 | (* ************************** *)
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417 |
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418 | GaugeXi[ V[1] ] = GaugeXi[A];
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419 | GaugeXi[ V[2] ] = GaugeXi[Z];
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420 | GaugeXi[ V[3] ] = GaugeXi[W];
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421 | GaugeXi[ V[4] ] = GaugeXi[G];
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422 | GaugeXi[ S[1] ] = 1;
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423 | GaugeXi[ S[2] ] = GaugeXi[Z];
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424 | GaugeXi[ S[3] ] = GaugeXi[W];
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425 | GaugeXi[ U[1] ] = GaugeXi[A];
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426 | GaugeXi[ U[2] ] = GaugeXi[Z];
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427 | GaugeXi[ U[31] ] = GaugeXi[W];
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428 | GaugeXi[ U[32] ] = GaugeXi[W];
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429 | GaugeXi[ U[4] ] = GaugeXi[G];
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430 |
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431 |
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432 | (* ************************** *)
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433 | (* ***** Parameters ***** *)
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434 | (* ************************** *)
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435 | M$Parameters = {
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436 |
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437 | (* External parameters *)
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438 | aEWM1 == {
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439 | ParameterType -> External,
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440 | BlockName -> SMINPUTS,
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441 | OrderBlock -> 1,
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442 | Value -> 127.9,
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443 | InteractionOrder -> {QED,-2},
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444 | Description -> "Inverse of the EW coupling constant at the Z pole"
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445 | },
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446 | Gf == {
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447 | ParameterType -> External,
|
---|
448 | BlockName -> SMINPUTS,
|
---|
449 | OrderBlock -> 2,
|
---|
450 | Value -> 1.16637*^-5,
|
---|
451 | InteractionOrder -> {QED,2},
|
---|
452 | TeX -> Subscript[G,f],
|
---|
453 | Description -> "Fermi constant"
|
---|
454 | },
|
---|
455 | aS == {
|
---|
456 | ParameterType -> External,
|
---|
457 | BlockName -> SMINPUTS,
|
---|
458 | OrderBlock -> 3,
|
---|
459 | Value -> 0.1184,
|
---|
460 | InteractionOrder -> {QCD,2},
|
---|
461 | TeX -> Subscript[\[Alpha],s],
|
---|
462 | Description -> "Strong coupling constant at the Z pole"
|
---|
463 | },
|
---|
464 | cutoff == {
|
---|
465 | ParameterType -> External,
|
---|
466 | BlockName -> HDO,
|
---|
467 | OrderBlock -> 1,
|
---|
468 | Value -> 246.221,
|
---|
469 | InteractionOrder -> {QED,0},
|
---|
470 | Description -> "scale of HDO. Default is equal to Higg's VEV ."
|
---|
471 | },
|
---|
472 | cR == {
|
---|
473 | ParameterType -> External,
|
---|
474 | BlockName -> HDO,
|
---|
475 | OrderBlock -> 2,
|
---|
476 | Value -> 1,
|
---|
477 | InteractionOrder -> {QED,2},
|
---|
478 | Description -> "coefficient of tRtR operator"
|
---|
479 | },
|
---|
480 | cL1 == {
|
---|
481 | ParameterType -> External,
|
---|
482 | BlockName -> HDO,
|
---|
483 | OrderBlock -> 3,
|
---|
484 | Value -> 1,
|
---|
485 | InteractionOrder -> {QED,2},
|
---|
486 | Description -> "coefficient of qLqL1 operator"
|
---|
487 | },
|
---|
488 | cL3 == {
|
---|
489 | ParameterType -> External,
|
---|
490 | BlockName -> HDO,
|
---|
491 | OrderBlock -> 4,
|
---|
492 | Value -> 1,
|
---|
493 | InteractionOrder -> {QED,2},
|
---|
494 | Description -> "coefficient of qLqL3 operator"
|
---|
495 | },
|
---|
496 | ymdo == {
|
---|
497 | ParameterType -> External,
|
---|
498 | BlockName -> YUKAWA,
|
---|
499 | OrderBlock -> 1,
|
---|
500 | Value -> 5.04*^-3,
|
---|
501 | Description -> "Down Yukawa mass"
|
---|
502 | },
|
---|
503 | ymup == {
|
---|
504 | ParameterType -> External,
|
---|
505 | BlockName -> YUKAWA,
|
---|
506 | OrderBlock -> 2,
|
---|
507 | Value -> 2.55*^-3,
|
---|
508 | Description -> "Up Yukawa mass"
|
---|
509 | },
|
---|
510 | yms == {
|
---|
511 | ParameterType -> External,
|
---|
512 | BlockName -> YUKAWA,
|
---|
513 | OrderBlock -> 3,
|
---|
514 | Value -> 0.101,
|
---|
515 | Description -> "Strange Yukawa mass"
|
---|
516 | },
|
---|
517 | ymc == {
|
---|
518 | ParameterType -> External,
|
---|
519 | BlockName -> YUKAWA,
|
---|
520 | OrderBlock -> 4,
|
---|
521 | Value -> 1.27,
|
---|
522 | Description -> "Charm Yukawa mass"
|
---|
523 | },
|
---|
524 | ymb == {
|
---|
525 | ParameterType -> External,
|
---|
526 | BlockName -> YUKAWA,
|
---|
527 | OrderBlock -> 5,
|
---|
528 | Value -> 4.7,
|
---|
529 | Description -> "Bottom Yukawa mass"
|
---|
530 | },
|
---|
531 | ymt == {
|
---|
532 | ParameterType -> External,
|
---|
533 | BlockName -> YUKAWA,
|
---|
534 | OrderBlock -> 6,
|
---|
535 | Value -> 172,
|
---|
536 | Description -> "Top Yukawa mass"
|
---|
537 | },
|
---|
538 | yme == {
|
---|
539 | ParameterType -> External,
|
---|
540 | BlockName -> YUKAWA,
|
---|
541 | OrderBlock -> 11,
|
---|
542 | Value -> 5.11*^-4,
|
---|
543 | Description -> "Electron Yukawa mass"
|
---|
544 | },
|
---|
545 | ymm == {
|
---|
546 | ParameterType -> External,
|
---|
547 | BlockName -> YUKAWA,
|
---|
548 | OrderBlock -> 13,
|
---|
549 | Value -> 0.10566,
|
---|
550 | Description -> "Muon Yukawa mass"
|
---|
551 | },
|
---|
552 | ymtau == {
|
---|
553 | ParameterType -> External,
|
---|
554 | BlockName -> YUKAWA,
|
---|
555 | OrderBlock -> 15,
|
---|
556 | Value -> 1.777,
|
---|
557 | Description -> "Tau Yukawa mass"
|
---|
558 | },
|
---|
559 | cabi == {
|
---|
560 | ParameterType -> External,
|
---|
561 | BlockName -> CKMBLOCK,
|
---|
562 | OrderBlock -> 1,
|
---|
563 | Value -> 0.227736,
|
---|
564 | TeX -> Subscript[\[Theta], c],
|
---|
565 | Description -> "Cabibbo angle"
|
---|
566 | },
|
---|
567 |
|
---|
568 | (* Internal Parameters *)
|
---|
569 | aEW == {
|
---|
570 | ParameterType -> Internal,
|
---|
571 | Value -> 1/aEWM1,
|
---|
572 | InteractionOrder -> {QED,2},
|
---|
573 | TeX -> Subscript[\[Alpha], EW],
|
---|
574 | Description -> "Electroweak coupling contant"
|
---|
575 | },
|
---|
576 | MW == {
|
---|
577 | ParameterType -> Internal,
|
---|
578 | Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
|
---|
579 | TeX -> Subscript[M,W],
|
---|
580 | Description -> "W mass"
|
---|
581 | },
|
---|
582 | sw2 == {
|
---|
583 | ParameterType -> Internal,
|
---|
584 | Value -> 1-(MW/MZ)^2,
|
---|
585 | Description -> "Squared Sin of the Weinberg angle"
|
---|
586 | },
|
---|
587 | ee == {
|
---|
588 | ParameterType -> Internal,
|
---|
589 | Value -> Sqrt[4 Pi aEW],
|
---|
590 | InteractionOrder -> {QED,1},
|
---|
591 | TeX -> e,
|
---|
592 | Description -> "Electric coupling constant"
|
---|
593 | },
|
---|
594 | cw == {
|
---|
595 | ParameterType -> Internal,
|
---|
596 | Value -> Sqrt[1-sw2],
|
---|
597 | TeX -> Subscript[c,w],
|
---|
598 | Description -> "Cosine of the Weinberg angle"
|
---|
599 | },
|
---|
600 | sw == {
|
---|
601 | ParameterType -> Internal,
|
---|
602 | Value -> Sqrt[sw2],
|
---|
603 | TeX -> Subscript[s,w],
|
---|
604 | Description -> "Sine of the Weinberg angle"
|
---|
605 | },
|
---|
606 | gw == {
|
---|
607 | ParameterType -> Internal,
|
---|
608 | Definitions -> {gw->ee/sw},
|
---|
609 | InteractionOrder -> {QED,1},
|
---|
610 | TeX -> Subscript[g,w],
|
---|
611 | Description -> "Weak coupling constant at the Z pole"
|
---|
612 | },
|
---|
613 | g1 == {
|
---|
614 | ParameterType -> Internal,
|
---|
615 | Definitions -> {g1->ee/cw},
|
---|
616 | InteractionOrder -> {QED,1},
|
---|
617 | TeX -> Subscript[g,1],
|
---|
618 | Description -> "U(1)Y coupling constant at the Z pole"
|
---|
619 | },
|
---|
620 | gs == {
|
---|
621 | ParameterType -> Internal,
|
---|
622 | Value -> Sqrt[4 Pi aS],
|
---|
623 | InteractionOrder -> {QCD,1},
|
---|
624 | TeX -> Subscript[g,s],
|
---|
625 | ParameterName -> G,
|
---|
626 | Description -> "Strong coupling constant at the Z pole"
|
---|
627 | },
|
---|
628 | vev == {
|
---|
629 | ParameterType -> Internal,
|
---|
630 | Value -> 2*MW*sw/ee,
|
---|
631 | InteractionOrder -> {QED,-1},
|
---|
632 | Description -> "Higgs vacuum expectation value"
|
---|
633 | },
|
---|
634 | lam == {
|
---|
635 | ParameterType -> Internal,
|
---|
636 | Value -> MH^2/(2*vev^2),
|
---|
637 | InteractionOrder -> {QED, 2},
|
---|
638 | Description -> "Higgs quartic coupling"
|
---|
639 | },
|
---|
640 | muH == {
|
---|
641 | ParameterType -> Internal,
|
---|
642 | Value -> Sqrt[vev^2 lam],
|
---|
643 | TeX -> \[Mu],
|
---|
644 | Description -> "Coefficient of the quadratic piece of the Higgs potential"
|
---|
645 | },
|
---|
646 | yl == {
|
---|
647 | ParameterType -> Internal,
|
---|
648 | Indices -> {Index[Generation], Index[Generation]},
|
---|
649 | Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
650 | Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
|
---|
651 | InteractionOrder -> {QED, 1},
|
---|
652 | ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
|
---|
653 | TeX -> Superscript[y, l],
|
---|
654 | Description -> "Lepton Yukawa couplings"
|
---|
655 | },
|
---|
656 | yu == {
|
---|
657 | ParameterType -> Internal,
|
---|
658 | Indices -> {Index[Generation], Index[Generation]},
|
---|
659 | Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
660 | Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
|
---|
661 | InteractionOrder -> {QED, 1},
|
---|
662 | ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
|
---|
663 | TeX -> Superscript[y, u],
|
---|
664 | Description -> "Up-type Yukawa couplings"
|
---|
665 | },
|
---|
666 | yd == {
|
---|
667 | ParameterType -> Internal,
|
---|
668 | Indices -> {Index[Generation], Index[Generation]},
|
---|
669 | Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
670 | Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
|
---|
671 | InteractionOrder -> {QED, 1},
|
---|
672 | ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
|
---|
673 | TeX -> Superscript[y, d],
|
---|
674 | Description -> "Down-type Yukawa couplings"
|
---|
675 | },
|
---|
676 | (* N. B. : only Cabibbo mixing! *)
|
---|
677 | CKM == {
|
---|
678 | ParameterType -> Internal,
|
---|
679 | Indices -> {Index[Generation], Index[Generation]},
|
---|
680 | Unitary -> True,
|
---|
681 | Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
|
---|
682 | CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
|
---|
683 | CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
|
---|
684 | TeX -> Superscript[V,CKM],
|
---|
685 | Description -> "CKM-Matrix"
|
---|
686 | }
|
---|
687 | };
|
---|
688 |
|
---|
689 | (* ************************** *)
|
---|
690 | (* ***** Lagrangian ***** *)
|
---|
691 | (* ************************** *)
|
---|
692 |
|
---|
693 | LGauge := Block[{mu,nu,ii,aa},
|
---|
694 | 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]];
|
---|
695 |
|
---|
696 | LFermions := Block[{mu},
|
---|
697 | ExpandIndices[I*(
|
---|
698 | QLbar.Ga[mu].DC[QL, mu] + LLbar.Ga[mu].DC[LL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu] + lRbar.Ga[mu].DC[lR, mu]),
|
---|
699 | FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
|
---|
700 |
|
---|
701 | LHiggs := Block[{ii,mu, feynmangaugerules},
|
---|
702 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
703 |
|
---|
704 | ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
|
---|
705 | ];
|
---|
706 |
|
---|
707 | LHDO := Block[{ii,jj,kk,tt,iso,mu,sp1,sp2,cc,feynmangaugerules,operators},
|
---|
708 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
709 |
|
---|
710 | operators = ExpandIndices[cR*I/(cutoff^2) Phibar[ii] DC[Phi[ii],mu] uRbar[sp1,3,cc].Ga[mu,sp1,sp2].uR[sp2,3,cc] + cL1*I/(cutoff^2) Phibar[ii] DC[Phi[ii],mu] QLbar[sp1,jj,3,cc].Ga[mu,sp1,sp2].QL[sp2,jj,3,cc] + 4*cL3*I/(cutoff^2) Phibar[ii] Ta[iso,ii,kk] DC[Phi[kk],mu] Ta[iso,jj,tt] QLbar[sp1,jj,3,cc].Ga[mu,sp1,sp2].QL[sp2,tt,3,cc], FlavorExpand-> {SU2W,SU2D}];
|
---|
711 |
|
---|
712 | (* neglect (1,3) and (2,3) terms in the CKM matrix: *)
|
---|
713 | operators = operators /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[3, b] IndexDelta[3, c], CKM[a_, b_] -> IndexDelta[3, b], Conjugate[CKM[a_, c_]] -> IndexDelta[3, c]};
|
---|
714 | operators+HC[operators]/.feynmangaugerules
|
---|
715 | ];
|
---|
716 |
|
---|
717 | LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
|
---|
718 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
719 |
|
---|
720 | yuk = ExpandIndices[
|
---|
721 | -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
|
---|
722 | yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
|
---|
723 | yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
|
---|
724 | yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
|
---|
725 | yuk+HC[yuk]/.feynmangaugerules
|
---|
726 | ];
|
---|
727 |
|
---|
728 | LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
|
---|
729 | (* Pure gauge piece *)
|
---|
730 | LGh1 = -ghBbar.del[DC[ghB,mu],mu];
|
---|
731 | LGhw = -ghWibar.del[DC[ghWi,mu],mu];
|
---|
732 | LGhs = -ghGbar.del[DC[ghG,mu],mu];
|
---|
733 |
|
---|
734 | (* Scalar pieces: see Peskin pages 739-742 *)
|
---|
735 | (* phi1 and phi2 are the real degrees of freedom of GP *)
|
---|
736 | (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
|
---|
737 | gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
|
---|
738 | ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
|
---|
739 | generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
|
---|
740 | doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
|
---|
741 | doublet0 = {0, vev/Sqrt[2]};
|
---|
742 | 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}];
|
---|
743 | togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
|
---|
744 | LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
|
---|
745 |
|
---|
746 | ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
|
---|
747 |
|
---|
748 | Ltot:= LGauge + LFermions + LHiggs + LYukawa + LGhost + LHDO;
|
---|
749 |
|
---|