1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file for the Large Extra Dimensions ******)
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3 | (****** ******)
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4 | (****** Author: Priscila de Aquino ******)
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5 | (****** ******)
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6 | (****** Choose whether Feynman gauge is desired. ******)
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7 | (****** If set to False, unitary gauge is assumed. ****)
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8 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
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9 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
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10 | (***************************************************************************************************************)
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11 |
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12 | M$ModelName = "LED";
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13 |
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14 | M$Information = {Authors -> {"Priscila de Aquino"},
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15 | Date -> "15.06.2009",
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16 | Institute -> {"Katholieke Universiteit Leuven & Universite Catholique Louvain - CP3"},
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17 | Emails -> {"priscila@itf.kuleuven.be"},
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18 | References -> {"Phys. Rev. D59: 105006 (1999), hep-ph/9811350", "Nucl. Phys. B544 (1999), hep-ph/9811291", "Eur. Phys. J. C56 (2008), hep-ph/0805.2554"},
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19 | URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/LED",
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20 | Version -> "1.0"};
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21 |
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22 | FeynmanGauge = False;
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23 |
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24 |
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25 | (*****************************************************************************************)
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26 | (****************************** Index definitions ****************************************)
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27 | (*****************************************************************************************)
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28 |
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29 | IndexRange[ Index[Generation] ] = Range[3]
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30 |
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31 | IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
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32 |
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33 | IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
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34 |
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35 | IndexRange[ Index[SU2W] ] = Range[3]
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36 |
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37 |
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38 | IndexStyle[Colour, i]
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39 |
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40 | IndexStyle[Generation, f]
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41 |
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42 | IndexStyle[Gluon ,a]
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43 |
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44 | IndexStyle[SU2W ,k]
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45 |
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46 | (*****************************************************************************************)
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47 | (************************************* Parameters ***************************************)
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48 | (*****************************************************************************************)
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49 |
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50 | M$Parameters = {
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51 |
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52 | (* External parameters *)
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53 |
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54 | \[Alpha]EWM1== {
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55 | ParameterType -> External,
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56 | BlockName -> SMINPUTS,
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57 | ParameterName -> aEWM1,
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58 | InteractionOrder -> {QED, -2},
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59 | Value -> 127.9,
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60 | Description -> "Inverse of the electroweak coupling constant"},
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61 |
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62 | Gf == {
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63 | ParameterType -> External,
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64 | BlockName -> SMINPUTS,
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65 | InteractionOrder -> {QED, 2},
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66 | Value -> 1.16639 * 10^(-5),
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67 | Description -> "Fermi constant"},
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68 |
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69 | \[Alpha]S == {
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70 | ParameterType -> External,
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71 | BlockName -> SMINPUTS,
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72 | ParameterName -> aS,
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73 | InteractionOrder -> {QCD, 2},
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74 | Value -> 0.118,
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75 | Description -> "Strong coupling constant at the Z pole."},
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76 |
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77 |
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78 | ZM == {
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79 | ParameterType -> External,
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80 | BlockName -> SMINPUTS,
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81 | Value -> 91.188,
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82 | Description -> "Z mass"},
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83 |
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84 |
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85 | ymc == {
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86 | ParameterType -> External,
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87 | BlockName -> YUKAWA,
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88 | Value -> 1.42,
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89 | OrderBlock -> {4},
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90 | Description -> "Charm Yukawa mass"},
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91 |
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92 | ymb == {
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93 | ParameterType -> External,
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94 | BlockName -> YUKAWA,
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95 | Value -> 4.7,
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96 | OrderBlock -> {5},
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97 | Description -> "Bottom Yukawa mass"},
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98 |
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99 | ymt == {
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100 | ParameterType -> External,
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101 | BlockName -> YUKAWA,
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102 | Value -> 174.3,
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103 | OrderBlock -> {6},
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104 | Description -> "Top Yukawa mass"},
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105 |
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106 | ymtau == {
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107 | ParameterType -> External,
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108 | BlockName -> YUKAWA,
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109 | Value -> 1.777,
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110 | OrderBlock -> {15},
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111 | Description -> "Tau Yukawa mass"},
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112 |
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113 | GN == {
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114 | ParameterType -> External,
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115 | ParameterName -> GN,
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116 | InteractionOrder -> {QCD, 2},
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117 | Value -> 10^(-16),
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118 | Description -> "Newton Constant"},
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119 |
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120 | (* Internal Parameters *)
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121 |
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122 | \[Alpha]EW == {
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123 | ParameterType -> Internal,
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124 | Value -> 1/\[Alpha]EWM1,
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125 | ParameterName -> aEW,
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126 | InteractionOrder -> {QED, 2},
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127 | Description -> "Electroweak coupling contant"},
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128 |
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129 |
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130 | MW == {
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131 | ParameterType -> Internal,
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132 | Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
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133 | Description -> "W mass"},
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134 |
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135 | sw2 == {
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136 | ParameterType -> Internal,
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137 | Value -> 1-(MW/MZ)^2,
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138 | Description -> "Squared Sin of the Weinberg angle"},
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139 |
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140 | ee == {
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141 | TeX -> e,
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142 | ParameterType -> Internal,
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143 | Value -> Sqrt[4 Pi \[Alpha]EW],
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144 | InteractionOrder -> {QED, 1},
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145 | Description -> "Electric coupling constant"},
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146 |
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147 | cw == {
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148 | TeX -> Subscript[c, w],
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149 | ParameterType -> Internal,
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150 | Value -> Sqrt[1 - sw2],
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151 | Description -> "Cos of the Weinberg angle"},
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152 |
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153 | sw == {
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154 | TeX -> Subscript[s, w],
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155 | ParameterType -> Internal,
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156 | Value -> Sqrt[sw2],
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157 | Description -> "Sin of the Weinberg angle"},
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158 |
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159 | gw == {
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160 | TeX -> Subscript[g, w],
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161 | ParameterType -> Internal,
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162 | Value -> ee / sw,
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163 | InteractionOrder -> {QED, 1},
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164 | Description -> "Weak coupling constant"},
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165 |
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166 | g1 == {
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167 | TeX -> Subscript[g, 1],
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168 | ParameterType -> Internal,
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169 | Value -> ee / cw,
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170 | InteractionOrder -> {QED, 1},
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171 | Description -> "U(1)Y coupling constant"},
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172 |
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173 | gs == {
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174 | TeX -> Subscript[g, s],
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175 | ParameterType -> Internal,
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176 | Value -> Sqrt[4 Pi \[Alpha]S],
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177 | InteractionOrder -> {QCD, 1},
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178 | ParameterName -> G,
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179 | Description -> "Strong coupling constant"},
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180 |
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181 | v == {
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182 | ParameterType -> Internal,
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183 | Value -> 2*MW*sw/ee,
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184 | InteractionOrder -> {QED, -1},
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185 | Description -> "Higgs VEV"},
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186 |
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187 | \[Lambda] == {
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188 | ParameterType -> Internal,
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189 | Value -> MH^2/(2*v^2),
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190 | InteractionOrder -> {QED, 2},
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191 | ParameterName -> lam,
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192 | Description -> "Higgs quartic coupling"},
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193 |
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194 | muH == {
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195 | ParameterType -> Internal,
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196 | Value -> Sqrt[v^2 \[Lambda]],
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197 | TeX -> \[Mu],
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198 | Description -> "Coefficient of the quadratic piece of the Higgs potential"},
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199 |
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200 |
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201 | yl == {
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202 | Indices -> {Index[Generation]},
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203 | AllowSummation -> True,
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204 | ParameterType -> Internal,
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205 | Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v},
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206 | ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
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207 | InteractionOrder -> {QED, 1},
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208 | ComplexParameter -> False,
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209 | Description -> "Lepton Yukawa coupling"},
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210 |
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211 | yu == {
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212 | Indices -> {Index[Generation]},
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213 | AllowSummation -> True,
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214 | ParameterType -> Internal,
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215 | Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
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216 | ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
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217 | InteractionOrder -> {QED, 1},
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218 | ComplexParameter -> False,
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219 | Description -> "U-quark Yukawa coupling"},
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220 |
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221 | yd == {
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222 | Indices -> {Index[Generation]},
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223 | AllowSummation -> True,
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224 | ParameterType -> Internal,
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225 | Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
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226 | ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
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227 | InteractionOrder -> {QED, 1},
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228 | ComplexParameter -> False,
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229 | Description -> "D-quark Yukawa coupling"},
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230 |
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231 | cabi == {
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232 | TeX -> Subscript[\[Theta], c],
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233 | ParameterType -> External,
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234 | BlockName -> CKMBLOCK,
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235 | OrderBlock -> {1},
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236 | Value -> 0.488,
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237 | Description -> "Cabibbo angle"},
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238 |
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239 | CKM == {
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240 | Indices -> {Index[Generation], Index[Generation]},
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241 | TensorClass -> CKM,
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242 | Unitary -> True,
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243 | Value -> {CKM[1,2] -> Sin[cabi],
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244 | CKM[1,1] -> Cos[cabi],
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245 | CKM[2,1] -> -Sin[cabi],
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246 | CKM[2,2] -> Cos[cabi]},
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247 | Description -> "CKM-Matrix"},
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248 |
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249 | kappa == {
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250 | TeX -> \[Kappa],
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251 | ParameterType -> Internal,
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252 | Value -> Sqrt[16 Pi GN]}
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253 |
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254 | }
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255 |
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256 | TeXFormat[mphi, Subscript[m, phi]]
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257 | TeXFormat[mpsi, Subscript[m, psi]]
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258 | TeXFormat[mG, Subscript[m, G]]
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259 |
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260 | (*****************************************************************************************)
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261 | (********************************* Gauge Groups ******************************************)
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262 | (*****************************************************************************************)
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263 |
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264 | M$GaugeGroups = {
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265 |
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266 | U1Y == {
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267 | Abelian -> True,
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268 | GaugeBoson -> B,
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269 | Charge -> Y,
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270 | CouplingConstant -> g1},
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271 |
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272 | SU2L == {
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273 | Abelian -> False,
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274 | GaugeBoson -> Wi,
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275 | StructureConstant -> Eps,
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276 | CouplingConstant -> gw},
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277 |
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278 | SU3C == {
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279 | Abelian -> False,
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280 | GaugeBoson -> G,
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281 | StructureConstant -> f,
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282 | SymmetricTensor -> dSUN,
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283 | Representations -> {T, Colour},
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284 | CouplingConstant -> gs}
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285 | }
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286 | (*****************************************************************************************)
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287 | (******************************* Particle Classes ****************************************)
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288 | (*****************************************************************************************)
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289 |
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290 | M$ClassesDescription = {
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291 |
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292 | (************************************ Fermions *******************************************)
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293 |
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294 | (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
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295 | F[1] == {
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296 | ClassName -> vl,
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297 | ClassMembers -> {ve,vm,vt},
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298 | FlavorIndex -> Generation,
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299 | SelfConjugate -> False,
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300 | Indices -> {Index[Generation]},
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301 | Mass -> 0,
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302 | Width -> 0,
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303 | QuantumNumbers -> {LeptonNumber -> 1},
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304 | PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
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305 | PropagatorType -> S,
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306 | PropagatorArrow -> Forward,
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307 | PDG -> {12,14,16},
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308 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
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309 |
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310 | (* Leptons (electron): I_3 = -1/2, Q = -1 *)
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311 | F[2] == {
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312 | ClassName -> l,
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313 | ClassMembers -> {e, m, tt},
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314 | FlavorIndex -> Generation,
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315 | SelfConjugate -> False,
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316 | Indices -> {Index[Generation]},
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317 | Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
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318 | Width -> 0,
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319 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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320 | PropagatorLabel -> {"l", "e", "m", "tt"},
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321 | PropagatorType -> Straight,
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322 | ParticleName -> {"e-", "m-", "tt-"},
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323 | AntiParticleName -> {"e+", "m+", "tt+"},
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324 | PropagatorArrow -> Forward,
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325 | PDG -> {11, 13, 15},
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326 | FullName -> {"Electron", "Muon", "Tau"} },
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327 |
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328 | (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
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329 | F[3] == {
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330 | ClassMembers -> {u, c, t},
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331 | ClassName -> uq,
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332 | FlavorIndex -> Generation,
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333 | SelfConjugate -> False,
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334 | Indices -> {Index[Generation], Index[Colour]},
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335 | Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
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336 | Width -> {0, 0, {WT, 1.50833649}},
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337 | QuantumNumbers -> {Q -> 2/3},
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338 | PropagatorLabel -> {"uq", "u", "c", "t"},
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339 | PropagatorType -> Straight,
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340 | PropagatorArrow -> Forward,
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341 | PDG -> {2, 4, 6},
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342 | FullName -> {"u-quark", "c-quark", "t-quark"}},
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343 |
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344 | (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
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345 | F[4] == {
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346 | ClassMembers -> {d, s, b},
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347 | ClassName -> dq,
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348 | FlavorIndex -> Generation,
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349 | SelfConjugate -> False,
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350 | Indices -> {Index[Generation], Index[Colour]},
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351 | Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
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352 | Width -> 0,
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353 | QuantumNumbers -> {Q -> -1/3},
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354 | PropagatorLabel -> {"dq", "d", "s", "b"},
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355 | PropagatorType -> Straight,
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356 | PropagatorArrow -> Forward,
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357 | PDG -> {1,3,5},
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358 | FullName -> {"d-quark", "s-quark", "b-quark"} },
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359 |
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360 | (************************************ Gauge Bosons ***************************************)
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361 |
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362 | (* Gauge bosons: Q = 0 *)
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363 | V[1] == {
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364 | ClassName -> A,
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365 | SelfConjugate -> True,
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366 | Indices -> {},
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367 | Mass -> 0,
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368 | Width -> 0,
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369 | PropagatorLabel -> "a",
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370 | PropagatorType -> W,
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371 | PropagatorArrow -> None,
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372 | PDG -> 22,
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373 | FullName -> "Photon" },
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374 |
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375 | V[2] == {
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376 | ClassName -> Z,
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377 | SelfConjugate -> True,
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378 | Indices -> {},
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379 | Mass -> {MZ, 91.188},
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380 | Width -> {WZ, 2.44140351},
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381 | PropagatorLabel -> "Z",
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382 | PropagatorType -> Sine,
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383 | PropagatorArrow -> None,
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384 | PDG -> 23,
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385 | FullName -> "Z" },
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386 |
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387 | (* Gauge bosons: Q = -1 *)
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388 | V[3] == {
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389 | ClassName -> W,
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390 | SelfConjugate -> False,
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391 | Indices -> {},
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392 | Mass -> {MW, Internal},
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393 | Width -> {WW, 2.04759951},
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394 | QuantumNumbers -> {Q -> 1},
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395 | PropagatorLabel -> "W",
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396 | PropagatorType -> Sine,
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397 | PropagatorArrow -> Forward,
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398 | ParticleName ->"W+",
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399 | AntiParticleName ->"W-",
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400 | PDG -> 24,
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401 | FullName -> "W" },
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402 |
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403 | V[4] == {
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404 | ClassName -> G,
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405 | SelfConjugate -> True,
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406 | Indices -> {Index[Gluon]},
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407 | Mass -> {mG,0},
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408 | Width -> 0,
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409 | PropagatorLabel -> G,
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410 | PropagatorType -> C,
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411 | PropagatorArrow -> None,
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412 | PDG -> 21,
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413 | FullName -> "G" },
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414 |
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415 | V[5] == {
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416 | ClassName -> Wi,
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417 | Unphysical -> True,
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418 | Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
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419 | Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
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420 | Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
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421 | SelfConjugate -> True,
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422 | Indices -> {Index[SU2W]},
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423 | FlavorIndex -> SU2W,
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424 | Mass -> 0,
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425 | PDG -> {1,2,3}},
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426 |
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427 | V[6] == {
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428 | ClassName -> B,
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429 | SelfConjugate -> True,
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430 | Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
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431 | Indices -> {},
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432 | Mass -> 0,
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433 | Unphysical -> True},
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434 |
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435 | (****************************** Scalar Fields *********************************************)
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436 |
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437 | (* physical Higgs: Q = 0 *)
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438 | S[1] == {
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439 | ClassName -> H,
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440 | SelfConjugate -> True,
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441 | Mass -> {MH, 120},
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442 | Width -> {WH, 0.00575308848},
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443 | PropagatorLabel -> "H",
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444 | PropagatorType -> D,
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445 | PropagatorArrow -> None,
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446 | PDG -> 25,
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447 | TeXParticleName -> "\\phi",
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448 | TeXClassName -> "\\phi",
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449 | FullName -> "H" },
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450 |
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451 | S[2] == {
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452 | ClassName -> phi,
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453 | SelfConjugate -> True,
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454 | Mass -> {MZ, 91.188},
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455 | Width -> Wphi,
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456 | PropagatorLabel -> "Phi",
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457 | PropagatorType -> D,
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458 | PropagatorArrow -> None,
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459 | ParticleName ->"phi0",
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460 | PDG -> 250,
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461 | FullName -> "Phi",
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462 | Goldstone -> Z },
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463 |
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464 | S[3] == {
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465 | ClassName -> phi2,
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466 | SelfConjugate -> False,
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467 | Mass -> {MW, Internal},
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468 | Width -> Wphi2,
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469 | PropagatorLabel -> "Phi2",
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470 | PropagatorType -> D,
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471 | PropagatorArrow -> None,
|
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472 | ParticleName ->"phi+",
|
---|
473 | AntiParticleName ->"phi-",
|
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474 | PDG -> 251,
|
---|
475 | FullName -> "Phi2",
|
---|
476 | TeXClassName -> "\\phi^+",
|
---|
477 | TeXParticleName -> "\\phi^+",
|
---|
478 | TeXAntiParticleName -> "\\phi^-",
|
---|
479 | Goldstone -> W,
|
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480 | QuantumNumbers -> {Q -> 1}},
|
---|
481 |
|
---|
482 | (******************************* Spin 2 particles: graviton *****************************)
|
---|
483 |
|
---|
484 | T[1] == {
|
---|
485 | ClassName -> h,
|
---|
486 | SelfConjugate -> True,
|
---|
487 | Symmetric -> True,
|
---|
488 | Mass -> {Mh, 500}}
|
---|
489 |
|
---|
490 | }
|
---|
491 |
|
---|
492 | (*****************************************************************************************)
|
---|
493 | (* *)
|
---|
494 | (* The Lagrangian *)
|
---|
495 | (* *)
|
---|
496 | (*****************************************************************************************)
|
---|
497 |
|
---|
498 | (* Some shorthands (for nicer printing) *)
|
---|
499 |
|
---|
500 | Format[mu, TraditionalForm] = \[Mu];
|
---|
501 | Format[nu, TraditionalForm] = \[Nu];
|
---|
502 | Format[lam, TraditionalForm] = \[Lambda];
|
---|
503 | Format[rho, TraditionalForm] = \[Rho];
|
---|
504 |
|
---|
505 | psi = \[Psi];
|
---|
506 | psibar = \[Psi]bar;
|
---|
507 | phi = \[Phi];
|
---|
508 | phibar = \[Phi]bar;
|
---|
509 | phiK = \[Sigma];
|
---|
510 |
|
---|
511 | (*****************************************************************************************)
|
---|
512 | (********************** Defining the cov derivatives ************************************)
|
---|
513 | (*****************************************************************************************)
|
---|
514 |
|
---|
515 | covdelU[field_, mu_] :=
|
---|
516 | Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
|
---|
517 | - I ee/cw 4/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
|
---|
518 |
|
---|
519 | covdelD[field_, mu_] :=
|
---|
520 | Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
|
---|
521 | + I ee/cw 2/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
|
---|
522 |
|
---|
523 | covdelE[field_, mu_] :=
|
---|
524 | Module[{j, a}, del[field, mu]
|
---|
525 | + I 2 ee/cw B[mu]/2 ProjP.field - I ee/cw B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
|
---|
526 |
|
---|
527 | covdelN[field_, mu_] :=
|
---|
528 | Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM. field Wi[mu,3]];
|
---|
529 |
|
---|
530 | (*****************************************************************************************)
|
---|
531 | (******************** Defining the field strenght tensors:********************************)
|
---|
532 | (*****************************************************************************************)
|
---|
533 |
|
---|
534 | FG[mu_,nu_,a1_,a2_,a3_] := del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3];
|
---|
535 |
|
---|
536 | FA[mu_,nu_] := del[B[nu], mu] - del[B[mu], nu];
|
---|
537 |
|
---|
538 | FW[mu_,nu_,i1_,i2_,i3_] := del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + ee/sw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3];
|
---|
539 |
|
---|
540 |
|
---|
541 |
|
---|
542 | (*****************************************************************************************)
|
---|
543 | (******************* Defining the energy-momentum tensor T[mu,nu] ************************)
|
---|
544 | (*****************************************************************************************)
|
---|
545 |
|
---|
546 | (* Gauge bosons *)
|
---|
547 |
|
---|
548 | TG[mu_,nu_]:= ( -ME[mu,nu]. (-1/4 FA[rho, sig] FA[rho,sig] - 1/4 FW[rho,sig,i1,i2,i3] FW[rho,sig, i1,i4,i5] - 1/4 FG[rho,sig,a1,a2,a3] FG[rho,sig, a1,a4,a5])
|
---|
549 | -FA[mu,rho] FA[nu,rho] - FW[mu,rho,i1,i2,i3] FW[nu,rho, i1,i4,i5] - FG[mu,rho,a1,a2,a3] FG[nu,rho, a1,a2,a3]);
|
---|
550 |
|
---|
551 | (* Fermions *)
|
---|
552 |
|
---|
553 | TF[mu_,nu_] := (-ME[mu,nu].(I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho]
|
---|
554 | + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho]
|
---|
555 | + I vlbar.(Ga[rho].covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].vl, rho]
|
---|
556 | + I lbar.(Ga[rho].covdelE[l, rho] ) -1/2 del[I lbar.Ga[rho].l, rho]
|
---|
557 |
|
---|
558 | - ee/sw/2 Sqrt[2] (CKM uqbar.Ga[rho].ProjM.dq W[rho] + HC[CKM] dqbar.Ga[rho].ProjM.uq Wbar[rho]
|
---|
559 | + vlbar.Ga[rho].ProjM.l W[rho] + lbar.Ga[rho].ProjM.vl Wbar[rho]) )
|
---|
560 | + ( I/2 uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu]
|
---|
561 | + I/2 uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu]
|
---|
562 | + I/2 dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu]
|
---|
563 | + I/2 dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu]
|
---|
564 | + I/2 vlbar.Ga[mu].covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].vl, mu]
|
---|
565 | + I/2 vlbar.Ga[nu].covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].vl, nu]
|
---|
566 | + I/2 lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu]
|
---|
567 | + I/2 lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu] )
|
---|
568 |
|
---|
569 | - ee/sw/Sqrt[2] ( CKM uqbar.Ga[mu].ProjM.dq W[nu] + HC[CKM] dqbar.Ga[mu].ProjM.uq Wbar[nu]
|
---|
570 | + CKM uqbar.Ga[nu].ProjM.dq W[mu] + HC[CKM] dqbar.Ga[nu].ProjM.uq Wbar[mu]
|
---|
571 | + vlbar.Ga[mu].ProjM.l W[nu] + lbar.Ga[mu].ProjM.vl Wbar[nu]
|
---|
572 | + vlbar.Ga[nu].ProjM.l W[mu] + lbar.Ga[nu].ProjM.vl Wbar[mu]));
|
---|
573 |
|
---|
574 | (* Definitions for Higgs and Yukawa *)
|
---|
575 |
|
---|
576 | Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
|
---|
577 | Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
|
---|
578 |
|
---|
579 | PMVec = Table[PauliSigma[i], {i, 3}];
|
---|
580 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
|
---|
581 |
|
---|
582 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
|
---|
583 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
|
---|
584 |
|
---|
585 | Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
|
---|
586 |
|
---|
587 |
|
---|
588 | (* Higgs *)
|
---|
589 |
|
---|
590 | TH[mu_, nu_] := (-ME[mu,nu].(Dcbar[Phibar, rho]).Dc[Phi, rho] - Vphi[Phi, Phibar]+
|
---|
591 | (Dcbar[Phibar, mu]).Dc[Phi, nu] + (Dcbar[Phibar, nu]).Dc[Phi, mu] );
|
---|
592 |
|
---|
593 | (* Yukawa *)
|
---|
594 |
|
---|
595 | TYuk:= Module[{s,r,n,m,i}, -
|
---|
596 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
|
---|
597 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
|
---|
598 | yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]];
|
---|
599 |
|
---|
600 | TY[mu_,nu_] := -ME[mu,nu].(TYuk + HC[TYuk]);
|
---|
601 |
|
---|
602 |
|
---|
603 | (*****************************************************************************************)
|
---|
604 | (******************************* Writing the lagrangian *********************************)
|
---|
605 | (*****************************************************************************************)
|
---|
606 |
|
---|
607 | LagH := -kappa/2 (h[mu,nu].TH[mu,nu]);
|
---|
608 |
|
---|
609 | LagG := -kappa/2 (h[mu,nu].TG[mu,nu]);
|
---|
610 |
|
---|
611 | LagF := -kappa/2 (h[mu,nu].TF[mu,nu]);
|
---|
612 |
|
---|
613 | LagY := -kappa/2 (h[mu,nu].TY[mu,nu])
|
---|
614 |
|
---|
615 |
|
---|
616 | (*****************************************************************************************)
|
---|
617 |
|
---|