1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file for the Abelian higgs model ******)
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3 | (****** ******)
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4 | (****** Authors: C. Duhr ******)
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5 | (****** ******)
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6 | (***************************************************************************************************************)
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7 |
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8 | M$ModelName = "Abelian_Higgs_Model";
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9 |
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10 |
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11 | M$Information = {Authors -> {"C. Duhr"},
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12 | Date -> "02. 06. 2009",
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13 | Institutions -> {"Universite catholique de Louvain (CP3)"},
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14 | Emails -> {"claude.duhr@uclouvain.be"},
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15 | Version -> "1.1",
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16 | References -> " J. D. Wells, \"How to Find a Hidden World at the Large Hadron Collider,\", [arXiv:0803.1243 [hep-ph]]",
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17 | URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/HiddenAbelianHiggsModel"};
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18 |
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19 | (*
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20 | v1.1: changed name for full Lagrangian from LSM to LHAHM
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21 | v1.2: Benj: the lambda parameter had the same name as the leptons, which was making the code crashing.
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22 | *)
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23 |
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24 | (* The U(1)X charge of the abelian Higgs is a free parameter *)
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25 |
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26 | qX = 1;
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27 |
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28 |
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29 | (******* Index definitions ********)
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30 |
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31 | IndexRange[ Index[Generation] ] = Range[3]
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32 |
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33 | IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
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34 |
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35 | IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
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36 |
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37 | IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
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38 |
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39 |
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40 | IndexStyle[Colour, i]
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41 |
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42 | IndexStyle[Generation, f]
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43 |
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44 | IndexStyle[Gluon ,a]
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45 |
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46 | IndexStyle[SUW2 ,k]
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47 |
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48 |
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49 | (******* Gauge parameters (for FeynArts) ********)
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50 |
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51 | GaugeXi[ V[1] ] = GaugeXi[A];
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52 | GaugeXi[ V[2] ] = GaugeXi[Z];
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53 | GaugeXi[ V[3] ] = GaugeXi[W];
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54 | GaugeXi[ V[4] ] = GaugeXi[G];
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55 | GaugeXi[ S[1] ] = 1;
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56 | GaugeXi[ S[2] ] = GaugeXi[Z];
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57 | GaugeXi[ S[3] ] = GaugeXi[W];
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58 | GaugeXi[ U[1] ] = GaugeXi[A];
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59 | GaugeXi[ U[2] ] = GaugeXi[Z];
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60 | GaugeXi[ U[31] ] = GaugeXi[W];
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61 | GaugeXi[ U[32] ] = GaugeXi[W];
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62 | GaugeXi[ U[4] ] = GaugeXi[G];
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63 |
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64 |
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65 | (**************** Parameters *************)
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66 |
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67 | M$Parameters = {
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68 |
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69 | (* External parameters *)
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70 |
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71 | \[Alpha]EWM1== {
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72 | ParameterType -> External,
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73 | BlockName -> SMINPUTS,
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74 | ParameterName -> aEWM1,
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75 | InteractionOrder -> {QED, -2},
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76 | Value -> 127.9,
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77 | Description -> "Inverse of the electroweak coupling constant"},
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78 |
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79 | Gf == {
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80 | ParameterType -> External,
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81 | BlockName -> SMINPUTS,
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82 | InteractionOrder -> {QED, 2},
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83 | Value -> 1.16639 * 10^(-5),
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84 | Description -> "Fermi constant"},
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85 |
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86 | \[Alpha]S == {
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87 | ParameterType -> External,
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88 | BlockName -> SMINPUTS,
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89 | ParameterName -> aS,
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90 | InteractionOrder -> {QCD, 2},
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91 | Value -> 0.118,
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92 | Description -> "Strong coupling constant at the Z pole."},
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93 |
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94 |
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95 | ymc == {
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96 | ParameterType -> External,
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97 | BlockName -> YUKAWA,
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98 | Value -> 1.42,
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99 | OrderBlock -> {4},
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100 | Description -> "Charm Yukawa mass"},
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101 |
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102 | ymb == {
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103 | ParameterType -> External,
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104 | BlockName -> YUKAWA,
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105 | Value -> 4.7,
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106 | OrderBlock -> {5},
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107 | Description -> "Bottom Yukawa mass"},
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108 |
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109 | ymt == {
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110 | ParameterType -> External,
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111 | BlockName -> YUKAWA,
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112 | Value -> 174.3,
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113 | OrderBlock -> {6},
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114 | Description -> "Top Yukawa mass"},
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115 |
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116 | ymtau == {
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117 | ParameterType -> External,
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118 | BlockName -> YUKAWA,
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119 | Value -> 1.777,
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120 | OrderBlock -> {15},
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121 | Description -> "Tau Yukawa mass"},
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122 |
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123 | \[Lambda] == {
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124 | ParameterType -> External,
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125 | BlockName -> HIGGS,
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126 | ParameterName -> lam,
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127 | Value -> 0.42568,
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128 | InteractionOrder -> {QED, 2},
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129 | Description -> "SM Higgs self-coupling"},
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130 |
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131 | cabi == {
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132 | TeX -> Subscript[\[Theta], c],
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133 | ParameterType -> External,
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134 | BlockName -> CKMBLOCK,
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135 | OrderBlock -> {1},
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136 | Value -> 0.488,
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137 | Description -> "Cabibbo angle"},
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138 |
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139 |
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140 | (* New hidden external parameters *)
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141 |
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142 | \[Alpha]XM1 == {
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143 | ParameterType -> External,
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144 | BlockName -> HIDDEN,
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145 | ParameterName -> aXM1,
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146 | InteractionOrder -> {QED, -2},
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147 | Value -> 127.9,
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148 | Description -> "Inverse of the U(1)X coupling constant"},
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149 |
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150 | \[Eta] == {
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151 | ParameterType -> External,
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152 | BlockName -> HIDDEN,
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153 | ParameterName -> eta,
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154 | Value -> 0.01,
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155 | Description -> "U(1)X - U(1)Y mixing parameter"},
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156 |
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157 | \[Rho] == {
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158 | ParameterType -> External,
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159 | BlockName -> HIDDEN,
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160 | ParameterName -> rho,
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161 | Value -> 0.010142,
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162 | InteractionOrder -> {QED, 2},
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163 | Description -> "Abelian Higgs self-coupling"},
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164 |
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165 | \[Kappa] == {
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166 | ParameterType -> External,
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167 | BlockName -> HIDDEN,
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168 | ParameterName -> kap,
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169 | Value -> 0.0977392,
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170 | InteractionOrder -> {QED, 2},
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171 | Description -> "Coupling between the abelian and the SM Higgs"},
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172 |
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173 |
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174 | (* Internal Parameters *)
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175 |
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176 | (* Weak Mixing *)
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177 |
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178 | cw == {
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179 | TeX -> Subscript[c, w],
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180 | ParameterType -> Internal,
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181 | Value -> MW/MZ,
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182 | Description -> "Cos of the Weinberg angle"},
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183 |
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184 | sw == {
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185 | TeX -> Subscript[s, w],
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186 | ParameterType -> Internal,
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187 | Value -> Sqrt[1-cw^2],
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188 | Description -> "Sin of the Weinberg angle"},
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189 |
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190 | (* Gauge couplings *)
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191 |
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192 | \[Alpha]EW == {
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193 | ParameterType -> Internal,
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194 | Value -> 1/\[Alpha]EWM1,
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195 | ParameterName -> aEW,
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196 | InteractionOrder -> {QED, 2},
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197 | Description -> "Electroweak coupling constant"},
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198 |
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199 | ee == {
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200 | TeX -> e,
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201 | ParameterType -> Internal,
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202 | Value -> Sqrt[4 Pi \[Alpha]EW],
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203 | InteractionOrder -> {QED, 1},
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204 | Description -> "Electric coupling constant"},
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205 |
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206 | gw == {
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207 | TeX -> Subscript[g, w],
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208 | ParameterType -> Internal,
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209 | Value -> ee / sw,
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210 | InteractionOrder -> {QED, 1},
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211 | Description -> "Weak coupling constant"},
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212 |
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213 | g1 == {
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214 | TeX -> Subscript[g, 1],
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215 | ParameterType -> Internal,
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216 | Value -> ee / cw,
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217 | InteractionOrder -> {QED, 1},
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218 | Description -> "U(1)Y coupling constant"},
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219 |
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220 | gs == {
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221 | TeX -> Subscript[g, s],
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222 | ParameterType -> Internal,
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223 | Value -> Sqrt[4 Pi \[Alpha]S],
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224 | InteractionOrder -> {QCD, 1},
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225 | ParameterName -> G,
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226 | Description -> "Strong coupling constant"},
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227 |
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228 | \[Alpha]X == {
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229 | ParameterType -> Internal,
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230 | Value -> 1/\[Alpha]XM1,
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231 | ParameterName -> aX,
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232 | InteractionOrder -> {QED, 2},
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233 | Description -> "U(1)X coupling contant"},
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234 |
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235 | gX == {
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236 | TeX -> Subscript[g, X],
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237 | ParameterType -> Internal,
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238 | Value -> Sqrt[4 Pi \[Alpha]X],
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239 | InteractionOrder -> {QED, 1},
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240 | Description -> "U(1)X coupling constant"},
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241 |
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242 | (* New scales *)
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243 |
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244 | MZ0 == {
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245 | ParameterType -> Internal,
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246 | Value -> MZ,
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247 | Description -> "Z mass before mixing"},
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248 |
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249 | MX =={
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250 | ParameterType -> Internal,
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251 | Value -> MZp,
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252 | Description -> "X mass before mixing"},
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253 |
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254 | \[CapitalDelta]Z =={
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255 | ParameterType -> Internal,
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256 | Value -> MX^2/MZ0^2,
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257 | ParameterName -> DZ,
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258 | Description -> "Ratio of scales"},
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259 |
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260 |
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261 | (* Higgs sector *)
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262 |
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263 |
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264 |
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265 | v == {
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266 | ParameterType -> Internal,
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267 | Value -> 1/Sqrt[Gf* Sqrt[2]],
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268 | InteractionOrder -> {QED, -1},
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269 | Description -> "SM Higgs VEV"},
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270 |
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271 | \[Xi] == {
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272 | ParameterType -> Internal,
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273 | Value -> MX/qX/gX,
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274 | InteractionOrder -> {QED, -1},
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275 | ParameterName -> xi,
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276 | Description -> "Abelian Higgs VEV"},
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277 |
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278 | MH1 == {
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279 | ParameterType -> Internal,
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280 | Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 - Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]],
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281 | Description -> "Mass of H1"},
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282 |
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283 | MH2 == {
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284 | ParameterType -> Internal,
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285 | Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 + Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]],
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286 | Description -> "Mass of H2"},
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287 |
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288 | \[Mu]SM2 =={
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289 | TeX -> Subsuperscript[\[Mu], SM, 2],
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290 | ParameterType -> Internal,
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291 | Value -> (\[Rho] v^2 + \[Kappa] \[Xi]^2)/2,
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292 | ParameterName -> muSM2,
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293 | Description -> "Quadratic SM potential term"},
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294 |
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295 | \[Mu]H2 =={
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296 | TeX -> Subsuperscript[\[Mu], H, 2],
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297 | ParameterType -> Internal,
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298 | Value -> (\[Kappa] v^2 + \[Lambda] \[Xi]^2)/2,
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299 | ParameterName -> muH2,
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300 | Description -> "Quadratic abelian potential term"},
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301 |
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302 | (* Mixing parameters *)
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303 |
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304 |
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305 | \[Theta]a == {
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306 | TeX -> Subscript[\[Theta], \[Alpha]],
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307 | ParameterType -> Internal,
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308 | Value -> ArcTan[-2 sw \[Eta]/(1-sw^2 \[Eta]^2 -\[CapitalDelta]Z)]/2,
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309 | ParameterName -> alp,
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310 | Description -> "Mixing in the weak sector"},
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311 |
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312 | ca == {
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313 | TeX -> Subscript[c, \[Alpha]],
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314 | ParameterType -> Internal,
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315 | Value -> Cos[\[Theta]a],
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316 | Description -> "Cosine of alp"},
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317 |
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318 | sa == {
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319 | TeX -> Subscript[s, \[Alpha]],
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320 | ParameterType -> Internal,
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321 | Value -> Sin[\[Theta]a],
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322 | Description -> "Sine of alp"},
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323 |
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324 | \[Chi] == {
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325 | ParameterType -> Internal,
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326 | Value -> (Sqrt[1+4\[Eta]^2] - 1)/2/\[Eta],
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327 | ParameterName -> chi,
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328 | Description -> "kinetic mixing parameter"},
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329 |
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330 | (* Higgs *)
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331 |
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332 | \[Theta]h == {
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333 | TeX -> Subscript[\[Theta], h],
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334 | ParameterType -> Internal,
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335 | Value -> ArcTan[\[Kappa] v \[Xi]/(\[Rho] \[Xi]^2 - \[Lambda] v^2)]/2,
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336 | ParameterName -> th,
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337 | Description -> "Mixing in the Higgs sector"},
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338 |
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339 | ch == {
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340 | TeX -> Subscript[c, h],
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341 | ParameterType -> Internal,
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342 | Value -> Cos[\[Theta]h],
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343 | Description -> "Cosine of th"},
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344 |
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345 | sh == {
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346 | TeX -> Subscript[s, h],
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347 | ParameterType -> Internal,
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348 | Value -> Sin[\[Theta]h],
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349 | Description -> "Sine of th"},
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350 |
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351 | (* Yukawa sector *)
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352 |
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353 | yl == {
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354 | Indices -> {Index[Generation]},
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355 | AllowSummation -> True,
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356 | ParameterType -> Internal,
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357 | Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v},
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358 | ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
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359 | InteractionOrder -> {QED, 1},
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360 | ComplexParameter -> False,
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361 | Definitions -> {yl[1] -> 0, yl[2] ->0},
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362 | Description -> "Lepton Yukawa coupling"},
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363 |
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364 | yu == {
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365 | Indices -> {Index[Generation]},
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366 | AllowSummation -> True,
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367 | ParameterType -> Internal,
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368 | Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
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369 | ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
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370 | InteractionOrder -> {QED, 1},
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371 | ComplexParameter -> False,
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372 | Definitions -> {yu[1] -> 0},
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373 | Description -> "U-quark Yukawa coupling"},
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374 |
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375 | yd == {
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376 | Indices -> {Index[Generation]},
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377 | AllowSummation -> True,
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378 | ParameterType -> Internal,
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379 | Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
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380 | ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
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381 | InteractionOrder -> {QED, 1},
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382 | ComplexParameter -> False,
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383 | Definitions -> {yd[1] -> 0, yd[2] -> 0},
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384 | Description -> "D-quark Yukawa coupling"},
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385 |
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386 |
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387 | CKM == {
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388 | Indices -> {Index[Generation], Index[Generation]},
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389 | TensorClass -> CKM,
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390 | Unitary -> True,
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391 | Definitions -> {CKM[3, 3] -> 1,
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392 | CKM[i_, 3] :> 0 /; i != 3,
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393 | CKM[3, i_] :> 0 /; i != 3},
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394 | Value -> {CKM[1,2] -> Sin[cabi],
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395 | CKM[1,1] -> Cos[cabi],
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396 | CKM[2,1] -> -Sin[cabi],
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397 | CKM[2,2] -> Cos[cabi]},
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398 | Description -> "CKM-Matrix"}
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399 |
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400 |
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401 |
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402 | }
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403 |
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404 |
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405 | (************** Gauge Groups ******************)
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406 |
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407 | M$GaugeGroups = {
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408 |
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409 | U1Y == {
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410 | Abelian -> True,
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411 | GaugeBoson -> B,
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412 | Charge -> Y,
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413 | CouplingConstant -> g1},
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414 |
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415 | U1X == {
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416 | Abelian -> True,
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417 | GaugeBoson -> X,
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418 | Charge -> QX,
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419 | CouplingConstant -> ee},
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420 |
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421 | SU2L == {
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422 | Abelian -> False,
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423 | GaugeBoson -> Wi,
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424 | StructureConstant -> Eps,
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425 | CouplingConstant -> gw},
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426 |
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427 | SU3C == {
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428 | Abelian -> False,
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429 | GaugeBoson -> G,
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430 | StructureConstant -> f,
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431 | SymmetricTensor -> dSUN,
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432 | Representations -> {T, Colour},
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433 | CouplingConstant -> gs}
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434 | }
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435 |
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436 | (********* Particle Classes **********)
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437 |
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438 | M$ClassesDescription = {
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439 |
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440 | (********** Fermions ************)
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441 | (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
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442 | F[1] == {
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443 | ClassName -> vl,
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444 | ClassMembers -> {ve,vm,vt},
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445 | FlavorIndex -> Generation,
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446 | SelfConjugate -> False,
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447 | Indices -> {Index[Generation]},
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448 | Mass -> 0,
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449 | Width -> 0,
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450 | QuantumNumbers -> {LeptonNumber -> 1},
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451 | PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
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452 | PropagatorType -> S,
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453 | PropagatorArrow -> Forward,
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454 | PDG -> {12,14,16},
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455 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
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456 |
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457 | (* Leptons (electron): I_3 = -1/2, Q = -1 *)
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458 | F[2] == {
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459 | ClassName -> l,
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460 | ClassMembers -> {e, m, tt},
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461 | FlavorIndex -> Generation,
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462 | SelfConjugate -> False,
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463 | Indices -> {Index[Generation]},
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464 | Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
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465 | Width -> 0,
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466 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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467 | PropagatorLabel -> {"l", "e", "m", "tt"},
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468 | PropagatorType -> Straight,
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469 | ParticleName -> {"e-", "m-", "tt-"},
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470 | AntiParticleName -> {"e+", "m+", "tt+"},
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471 | PropagatorArrow -> Forward,
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472 | PDG -> {11, 13, 15},
|
---|
473 | FullName -> {"Electron", "Muon", "Tau"} },
|
---|
474 |
|
---|
475 | (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
|
---|
476 | F[3] == {
|
---|
477 | ClassMembers -> {u, c, t},
|
---|
478 | ClassName -> uq,
|
---|
479 | FlavorIndex -> Generation,
|
---|
480 | SelfConjugate -> False,
|
---|
481 | Indices -> {Index[Generation], Index[Colour]},
|
---|
482 | Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
|
---|
483 | Width -> {0, 0, {WT, 1.50833649}},
|
---|
484 | QuantumNumbers -> {Q -> 2/3},
|
---|
485 | PropagatorLabel -> {"uq", "u", "c", "t"},
|
---|
486 | PropagatorType -> Straight,
|
---|
487 | PropagatorArrow -> Forward,
|
---|
488 | PDG -> {2, 4, 6},
|
---|
489 | FullName -> {"u-quark", "c-quark", "t-quark"}},
|
---|
490 |
|
---|
491 | (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
|
---|
492 | F[4] == {
|
---|
493 | ClassMembers -> {d, s, b},
|
---|
494 | ClassName -> dq,
|
---|
495 | FlavorIndex -> Generation,
|
---|
496 | SelfConjugate -> False,
|
---|
497 | Indices -> {Index[Generation], Index[Colour]},
|
---|
498 | Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
|
---|
499 | Width -> 0,
|
---|
500 | QuantumNumbers -> {Q -> -1/3},
|
---|
501 | PropagatorLabel -> {"dq", "d", "s", "b"},
|
---|
502 | PropagatorType -> Straight,
|
---|
503 | PropagatorArrow -> Forward,
|
---|
504 | PDG -> {1,3,5},
|
---|
505 | FullName -> {"d-quark", "s-quark", "b-quark"} },
|
---|
506 |
|
---|
507 | (********** Ghosts **********)
|
---|
508 |
|
---|
509 | U[1] == {
|
---|
510 | ClassName -> ghG,
|
---|
511 | SelfConjugate -> False,
|
---|
512 | Indices -> {Index[Gluon]},
|
---|
513 | Ghost -> G,
|
---|
514 | Mass -> 0,
|
---|
515 | Width -> 0,
|
---|
516 | QuantumNumbers -> {GhostNumber -> 1},
|
---|
517 | PropagatorLabel -> uG,
|
---|
518 | PropagatorType -> GhostDash,
|
---|
519 | PropagatorArrow -> Forward},
|
---|
520 |
|
---|
521 |
|
---|
522 | (************ Gauge Bosons ***************)
|
---|
523 | (* Gauge bosons: Q = 0 *)
|
---|
524 | V[1] == {
|
---|
525 | ClassName -> A,
|
---|
526 | SelfConjugate -> True,
|
---|
527 | Indices -> {},
|
---|
528 | Mass -> 0,
|
---|
529 | Width -> 0,
|
---|
530 | PropagatorLabel -> "a",
|
---|
531 | PropagatorType -> W,
|
---|
532 | PropagatorArrow -> None,
|
---|
533 | PDG -> 22,
|
---|
534 | FullName -> "Photon" },
|
---|
535 |
|
---|
536 | V[21] == {
|
---|
537 | ClassName -> Z,
|
---|
538 | SelfConjugate -> True,
|
---|
539 | Indices -> {},
|
---|
540 | Mass -> {MZ, 91.188},
|
---|
541 | Width -> {WZ, 2.44140351},
|
---|
542 | PropagatorLabel -> "Z",
|
---|
543 | PropagatorType -> Sine,
|
---|
544 | PropagatorArrow -> None,
|
---|
545 | PDG -> 23,
|
---|
546 | FullName -> "Z" },
|
---|
547 |
|
---|
548 | V[22] == {
|
---|
549 | ClassName -> Zp,
|
---|
550 | SelfConjugate -> True,
|
---|
551 | Indices -> {},
|
---|
552 | Mass -> {MZp, 500},
|
---|
553 | Width -> {WZp, 0.0008252},
|
---|
554 | PropagatorLabel -> "Zp",
|
---|
555 | PropagatorType -> Sine,
|
---|
556 | PropagatorArrow -> None,
|
---|
557 | PDG -> 1023,
|
---|
558 | FullName -> "Zp" },
|
---|
559 |
|
---|
560 | V[210] == {
|
---|
561 | ClassName -> Bp,
|
---|
562 | SelfConjugate -> True,
|
---|
563 | Unphysical -> True,
|
---|
564 | Indices -> {},
|
---|
565 | Mass -> 0,
|
---|
566 | Width -> 0,
|
---|
567 | Definitions -> {Bp[mu_] :> cw A[mu] -sw ca Z[mu] + sw sa Zp[mu]}},
|
---|
568 |
|
---|
569 | V[220] == {
|
---|
570 | ClassName -> Xp,
|
---|
571 | SelfConjugate -> True,
|
---|
572 | Unphysical -> True,
|
---|
573 | Indices -> {},
|
---|
574 | Mass -> 0,
|
---|
575 | Width -> 0,
|
---|
576 | Definitions -> {Xp[mu_] :> sa Z[mu] + ca Zp[mu]}},
|
---|
577 |
|
---|
578 |
|
---|
579 | (* Gauge bosons: Q = -1 *)
|
---|
580 | V[3] == {
|
---|
581 | ClassName -> W,
|
---|
582 | SelfConjugate -> False,
|
---|
583 | Indices -> {},
|
---|
584 | Mass -> {MW, 80.419},
|
---|
585 | Width -> {WW, 2.04759951},
|
---|
586 | QuantumNumbers -> {Q -> 1},
|
---|
587 | PropagatorLabel -> "W",
|
---|
588 | PropagatorType -> Sine,
|
---|
589 | PropagatorArrow -> Forward,
|
---|
590 | ParticleName ->"W+",
|
---|
591 | AntiParticleName ->"W-",
|
---|
592 | PDG -> 24,
|
---|
593 | FullName -> "W" },
|
---|
594 |
|
---|
595 | V[4] == {
|
---|
596 | ClassName -> G,
|
---|
597 | SelfConjugate -> True,
|
---|
598 | Indices -> {Index[Gluon]},
|
---|
599 | Mass -> 0,
|
---|
600 | Width -> 0,
|
---|
601 | PropagatorLabel -> G,
|
---|
602 | PropagatorType -> C,
|
---|
603 | PropagatorArrow -> None,
|
---|
604 | PDG -> 21,
|
---|
605 | FullName -> "G" },
|
---|
606 |
|
---|
607 | V[5] == {
|
---|
608 | ClassName -> Wi,
|
---|
609 | Unphysical -> True,
|
---|
610 | Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
|
---|
611 | Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
|
---|
612 | Wi[mu_, 3] -> -cw sa Zp[mu] + cw ca Z[mu] + sw A[mu]},
|
---|
613 | SelfConjugate -> True,
|
---|
614 | Indices -> {Index[SU2W]},
|
---|
615 | FlavorIndex -> SU2W,
|
---|
616 | Mass -> 0,
|
---|
617 | PDG -> {1,2,3}},
|
---|
618 |
|
---|
619 | V[6] == {
|
---|
620 | ClassName -> B,
|
---|
621 | SelfConjugate -> True,
|
---|
622 | Definitions -> {B[mu_] -> Bp[mu] + \[Eta] Xp[mu]},
|
---|
623 | Indices -> {},
|
---|
624 | Mass -> 0,
|
---|
625 | Unphysical -> True},
|
---|
626 |
|
---|
627 | V[61] == {
|
---|
628 | ClassName -> X,
|
---|
629 | SelfConjugate -> True,
|
---|
630 | Definitions -> {X[mu_] -> \[Chi] \[Eta] Xp[mu]},
|
---|
631 | Indices -> {},
|
---|
632 | Mass -> 0,
|
---|
633 | Unphysical -> True},
|
---|
634 |
|
---|
635 |
|
---|
636 |
|
---|
637 | (************ Scalar Fields **********)
|
---|
638 | (* physical Higgs: Q = 0 *)
|
---|
639 | S[11] == {
|
---|
640 | ClassName -> h1,
|
---|
641 | SelfConjugate -> True,
|
---|
642 | Mass -> {MH1, Internal},
|
---|
643 | Width -> {WH1, 0.00282299},
|
---|
644 | PropagatorLabel -> "h1",
|
---|
645 | PropagatorType -> D,
|
---|
646 | PropagatorArrow -> None,
|
---|
647 | PDG -> 25,
|
---|
648 | FullName -> "h1" },
|
---|
649 |
|
---|
650 | S[12] == {
|
---|
651 | ClassName -> h2,
|
---|
652 | SelfConjugate -> True,
|
---|
653 | Mass -> {MH2, Internal},
|
---|
654 | Width -> {WH2, 5.23795},
|
---|
655 | PropagatorLabel -> "h2",
|
---|
656 | PropagatorType -> D,
|
---|
657 | PropagatorArrow -> None,
|
---|
658 | PDG -> 35,
|
---|
659 | FullName -> "h2" },
|
---|
660 |
|
---|
661 | S[110] == {
|
---|
662 | ClassName -> H,
|
---|
663 | SelfConjugate -> True,
|
---|
664 | Unphysical -> True,
|
---|
665 | Definitions -> {H -> ch h1 + sh h2}},
|
---|
666 |
|
---|
667 | S[120] == {
|
---|
668 | ClassName -> phih,
|
---|
669 | SelfConjugate -> False,
|
---|
670 | Unphysical -> True,
|
---|
671 | Definitions -> {phih -> \[Xi]/Sqrt[2]-sh h1 + ch h2}}
|
---|
672 | }
|
---|
673 |
|
---|
674 |
|
---|
675 |
|
---|
676 | (*****************************************************************************************)
|
---|
677 |
|
---|
678 | (* SM Lagrangian *)
|
---|
679 |
|
---|
680 | (******************** Gauge F^2 Lagrangian terms*************************)
|
---|
681 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
|
---|
682 | LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
|
---|
683 | (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
|
---|
684 |
|
---|
685 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[X[nu], mu] - del[X[mu], nu])^2 +
|
---|
686 | \[Chi]/2 (del[X[nu], mu] - del[X[mu], nu]) (del[B[nu], mu] - del[B[mu], nu]) -
|
---|
687 |
|
---|
688 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
|
---|
689 | (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
|
---|
690 |
|
---|
691 |
|
---|
692 | (********************* Fermion Lagrangian terms*************************)
|
---|
693 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
|
---|
694 | LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
|
---|
695 |
|
---|
696 | Lkin = I uqbar.Ga[mu].del[uq, mu] +
|
---|
697 | I dqbar.Ga[mu].del[dq, mu] +
|
---|
698 | I lbar.Ga[mu].del[l, mu] +
|
---|
699 | I vlbar.Ga[mu].del[vl, mu];
|
---|
700 |
|
---|
701 | LQCD = gs (uqbar.Ga[mu].T[a].uq +
|
---|
702 | dqbar.Ga[mu].T[a].dq)G[mu, a];
|
---|
703 |
|
---|
704 | LBright =
|
---|
705 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
|
---|
706 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
|
---|
707 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
|
---|
708 |
|
---|
709 | LBleft =
|
---|
710 | -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
|
---|
711 | ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
|
---|
712 | ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
|
---|
713 | ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
|
---|
714 |
|
---|
715 | LWleft = ee/sw/2(
|
---|
716 | vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
|
---|
717 | lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
|
---|
718 |
|
---|
719 | Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
|
---|
720 | Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
|
---|
721 |
|
---|
722 | uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
|
---|
723 | dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
|
---|
724 |
|
---|
725 | Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
|
---|
726 | Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
|
---|
727 | );
|
---|
728 |
|
---|
729 | Lkin + LQCD + LBright + LBleft + LWleft];
|
---|
730 |
|
---|
731 | (******************** Higgs Lagrangian terms****************************)
|
---|
732 | Phi := {0, (v + H)/Sqrt[2]};
|
---|
733 | Phibar := {0, (v + H)/Sqrt[2]};
|
---|
734 |
|
---|
735 |
|
---|
736 |
|
---|
737 | LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
|
---|
738 |
|
---|
739 | PMVec = Table[PauliSigma[i], {i, 3}];
|
---|
740 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
|
---|
741 |
|
---|
742 | (*Y_phi=1*)
|
---|
743 | Dc[f_List, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
|
---|
744 | Dcbar[f_List, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
|
---|
745 |
|
---|
746 | Dc[phih, mu_] := del[phih, mu] -I gX qX X[mu] phih;
|
---|
747 | Dc[phihbar, mu_] := del[phihbar, mu] +I gX qX X[mu] phihbar;
|
---|
748 |
|
---|
749 | Vphi[Phi2SM_, Phi2H_] := -\[Mu]SM2 Phi2SM + \[Lambda] (Phi2SM)^2 -
|
---|
750 | \[Mu]H2 Phi2H + \[Rho] (Phi2H)^2 +
|
---|
751 | \[Kappa] (Phi2H) (Phi2SM) ;
|
---|
752 |
|
---|
753 | (* The value of qX is set at the beginning of the notebook *)
|
---|
754 |
|
---|
755 | (Dcbar[Phibar, mu]).Dc[Phi, mu] + Dc[phihbar,mu] Dc[phih, mu] - Vphi[Phibar.Phi, phihbar phih]];
|
---|
756 |
|
---|
757 |
|
---|
758 | (*************** Yukawa Lagrangian***********************)
|
---|
759 | LYuk := Module[{s,r,n,m,i}, -
|
---|
760 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
|
---|
761 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
|
---|
762 | yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]
|
---|
763 | ]
|
---|
764 |
|
---|
765 | LYukawa := LYuk + HC[LYuk];
|
---|
766 |
|
---|
767 |
|
---|
768 |
|
---|
769 | (**************Ghost terms**************************)
|
---|
770 | (* Now we need the ghost terms which are of the form: *)
|
---|
771 | (* - g * antighost * d_BRST G *)
|
---|
772 | (* where d_BRST G is BRST transform of the gauge fixing function. *)
|
---|
773 |
|
---|
774 | LGhost :=
|
---|
775 | Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
|
---|
776 |
|
---|
777 | (***********First the pure gauge piece.**********************)
|
---|
778 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
|
---|
779 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
|
---|
780 |
|
---|
781 | (***********Now add the pieces together.********************)
|
---|
782 | LGhostG]
|
---|
783 |
|
---|
784 |
|
---|
785 | (*********Total SM Lagrangian*******)
|
---|
786 | LHAHM := LGauge + LHiggs + LFermions + LYukawa + LGhost;
|
---|
787 |
|
---|
788 |
|
---|