1 | (* **************************************************************************** *)
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2 | (* ***** ***** *)
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3 | (* ***** FeynRules model file: Simplified DM models ***** *)
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4 | (* ***** with an s-channel spin-2 mediator ***** *)
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5 | (* ***** Author: G. Das, C. Degrande, V. Hirschi, F. Maltoni and H. Shao ***** *)
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6 | (* ***** K. Mawatari ***** *)
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7 | (* ***** ***** *)
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8 | (* **************************************************************************** *)
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9 |
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10 |
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11 | (* ************************** *)
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12 | (* ***** Information ***** *)
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13 | (* ************************** *)
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14 | M$ModelName = "DMsimp_s_spin2";
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15 |
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16 | M$Information = {
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17 | Authors -> {"G. Das, C. Degrande, V. Hirschi, F. Maltoni, H. Shao, K. Mawatari"},
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18 | Institutions -> {"Saha Institute of Nuclear Physics, Durham University, Universite catholique de Louvain, CERN, LPSC Grenoble"},
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19 | Emails -> {"celine.degrande@durham.ac.uk","goutam.das@saha.ac.in", "kentarou.mawatari@lpsc.in2p3.fr"},
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20 | URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/DMsimp/",
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21 | References -> {"G. Das et al., arXiv:1605.09359","S. Kraml et al., arXiv:1701.07008"},
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22 | Version -> "1.1",
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23 | Date -> "01.02.2017"
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24 | };
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25 |
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26 | (* ************************** *)
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27 | (* ***** Change log ***** *)
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28 | (* ************************** *)
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29 |
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30 | (* 01.06.2016 v1.0 - release version. *)
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31 | (* 01.02.2017 v1.1 - added Xc and Xv. *)
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32 |
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33 |
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34 | (***** Setting for interaction order (as e.g. used by MadGraph 5) ******)
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35 |
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36 | M$InteractionOrderLimit = {
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37 | {DMT, 2}
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38 | };
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39 |
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40 | M$InteractionOrderHierarchy = {
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41 | {QCD, 1}, {DMT, 2}, {QED, 2}
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42 | };
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43 |
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44 |
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45 | (* ************************** *)
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46 | (* ***** Fields ***** *)
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47 | (* ************************** *)
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48 | M$ClassesDescription = {
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49 |
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50 | S[7] == { ClassName -> Xr,
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51 | SelfConjugate -> True,
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52 | Mass -> {MXr, 10.},
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53 | Width -> 0,
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54 | PDG -> 5000511,
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55 | Tex -> Subscript[X,r],
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56 | FullName -> "Real scalar DM" },
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57 |
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58 | F[7] == { ClassName -> Xd,
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59 | SelfConjugate -> False,
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60 | Mass -> {MXd, 10.},
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61 | Width -> 0,
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62 | PDG -> 5000521,
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63 | TeX -> Subscript[X,d],
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64 | FullName -> "Dirac DM" },
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65 |
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66 | V[7] == { ClassName -> Xv,
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67 | SelfConjugate -> True,
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68 | Mass -> {MXv, 10.},
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69 | Width -> 0,
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70 | PDG -> 5000531,
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71 | Tex -> Subscript[X,v],
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72 | FullNme -> "Vector DM" },
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73 |
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74 | T[1] == { ClassName -> Y2,
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75 | SelfConjugate -> True,
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76 | Symmetric -> True,
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77 | Mass -> {MY2, 1000.},
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78 | Width -> {WY2, 10.},
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79 | PDG -> 5000002,
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80 | TeX -> Subscript[Y,2],
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81 | FullName -> "Spin-2 mediator" }
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82 |
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83 | };
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84 |
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85 |
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86 | (* ************************** *)
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87 | (* ***** Parameters ***** *)
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88 | (* ************************** *)
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89 | M$Parameters = {
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90 |
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91 | Lambda == { ParameterType -> External,
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92 | BlockName -> DMINPUTS,
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93 | TeX -> \[CapitalLambda],
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94 | Description -> "cut-off scale",
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95 | Value -> 1000.0},
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96 |
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97 | gTg == {
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98 | ParameterType -> External,
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99 | InteractionOrder -> {DMT, 1},
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100 | BlockName -> DMINPUTS,
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101 | TeX -> Subscript[gT,g],
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102 | Description -> "g-Y2 coupling",
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103 | Value -> 1. },
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104 |
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105 | gTw == {
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106 | ParameterType -> External,
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107 | InteractionOrder -> {DMT, 1},
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108 | BlockName -> DMINPUTS,
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109 | TeX -> Subscript[gT,W],
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110 | Description -> "W-Y2 coupling",
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111 | Value -> 1. },
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112 |
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113 | gTb == {
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114 | ParameterType -> External,
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115 | InteractionOrder -> {DMT, 1},
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116 | BlockName -> DMINPUTS,
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117 | TeX -> Subscript[gT,B],
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118 | Description -> "B-Y2 coupling",
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119 | Value -> 1. },
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120 |
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121 | gTq == {
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122 | ParameterType -> External,
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123 | InteractionOrder -> {DMT, 1},
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124 | BlockName -> DMINPUTS,
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125 | TeX -> Subscript[gT,q],
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126 | Description -> "q-Y2 coupling",
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127 | Value -> 1. },
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128 |
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129 | gTq3 == {
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130 | ParameterType -> External,
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131 | InteractionOrder -> {DMT, 1},
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132 | BlockName -> DMINPUTS,
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133 | TeX -> Subscript[gT,q3],
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134 | Description -> "t-Y2 coupling",
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135 | Value -> 1. },
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136 |
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137 | gTl == {
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138 | ParameterType -> External,
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139 | InteractionOrder -> {DMT, 1},
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140 | BlockName -> DMINPUTS,
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141 | TeX -> Subscript[gT,l],
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142 | Description -> "l-Y2 coupling",
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143 | Value -> 1. },
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144 |
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145 | gTh == {
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146 | ParameterType -> External,
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147 | InteractionOrder -> {DMT, 1},
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148 | BlockName -> DMINPUTS,
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149 | TeX -> Subscript[gT,h],
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150 | Description -> "h-Y2 coupling",
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151 | Value -> 1. },
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152 |
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153 | gTXr == {
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154 | ParameterType -> External,
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155 | InteractionOrder -> {DMT, 1},
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156 | BlockName -> DMINPUTS,
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157 | TeX -> Subscript[gT,Xr],
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158 | Description -> "Xr-Y2 coupling",
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159 | Value -> 0. },
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160 |
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161 | gTXd == {
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162 | ParameterType -> External,
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163 | InteractionOrder -> {DMT, 1},
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164 | BlockName -> DMINPUTS,
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165 | TeX -> Subscript[gT,Xd],
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166 | Description -> "Xd-Y2 coupling",
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167 | Value -> 1. },
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168 |
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169 | gTXv == {
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170 | ParameterType -> External,
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171 | InteractionOrder -> {DMT, 1},
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172 | BlockName -> DMINPUTS,
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173 | TeX -> Subscript[gT,Xv],
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174 | Description -> "Xv-Y2 coupling",
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175 | Value -> 0. }
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176 |
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177 | };
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178 |
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179 | (****************************************** Spin-2 ***************************************)
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180 |
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181 | (*** Defining the cov derivatives ***)
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182 |
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183 | covdelE[field_, mu_] :=
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184 | Module[{j, a}, del[field, mu]
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185 | + I ee/cw 2 B[mu]/2 ProjP.field + I ee/cw B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
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186 |
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187 | covdelN[field_, mu_] :=
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188 | Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
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189 |
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190 | (*** Defining the energy-momentum tensor T[mu,nu] ***)
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191 |
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192 | (* Fermions *)
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193 |
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194 | TFf[mu_, nu_, ff_] := QLbar[ss, ii, ff, cc].Ga[mu, ss, ss1].DC[QL[ss1, ii, ff, cc], nu] - DC[QLbar[ss, ii, ff, cc], mu].Ga[nu, ss, ss1].QL[ss1, ii, ff, cc] +
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195 | uRbar[ss, ff, cc].Ga[mu, ss, ss1].DC[uR[ss1, ff, cc], nu] - DC[uRbar[ss, ff, cc], mu].Ga[nu, ss, ss1].uR[ss1, ff, cc] +
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196 | dRbar[ss, ff, cc].Ga[mu, ss, ss1].DC[dR[ss1, ff, cc], nu] - DC[dRbar[ss, ff, cc], mu].Ga[nu, ss, ss1].dR[ss1, ff, cc];
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197 |
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198 |
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199 | TFhb[mu_, nu_] := QLbar[ss, 2, 3, cc].Ga[mu, ss, ss1].DC[QL[ss1, 2, 3, cc], nu] -
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200 | DC[QLbar[ss, 2, 3, cc], mu].Ga[nu, ss, ss1].QL[ss1, 2, 3, cc] +
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201 | dRbar[ss, 3, cc].Ga[mu, ss, ss1].DC[dR[ss1, 3, cc], nu] -
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202 | DC[dRbar[ss, 3, cc], mu].Ga[nu, ss, ss1].dR[ss1, 3, cc];
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203 |
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204 | TFht[mu_, nu_] := QLbar[ss, 1, 3, cc].Ga[mu, ss, ss1].DC[QL[ss1, 1, 3, cc], nu] -
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205 | DC[QLbar[ss, 1, 3, cc], mu].Ga[nu, ss, ss1].QL[ss1, 1, 3, cc] +
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206 | uRbar[ss, 3, cc].Ga[mu, ss, ss1].DC[uR[ss1, 3, cc], nu] -
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207 | DC[uRbar[ss, 3, cc], mu].Ga[nu, ss, ss1].uR[ss1, 3, cc];
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208 |
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209 | TFlq[mu_, nu_] := -ME[mu, nu] I/2 TFf[al, al, 1] + I/4 ( TFf[mu, nu, 1] + TFf[nu, mu, 1]) - ME[mu, nu] I/2 TFf[al, al, 2] + I/4 ( TFf[mu, nu, 2] + TFf[nu, mu, 2])-ME[mu, nu] I/2 TFhb[al, al] + I/4 ( TFhb[mu, nu] + TFhb[nu, mu]);
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210 |
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211 | TFt[mu_, nu_] := -ME[mu, nu] I/2 TFht[al, al] + I/4 ( TFht[mu, nu] + TFht[nu, mu]);
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212 |
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213 | feynmangaugerules = If[Not[FeynmanGauge], {G0 | GP | GPbar -> 0}, {}];
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214 | yuk = ExpandIndices[-yd[ff2, 3] CKM[3, ff2] QLbar[sp, ii, 3, cc].dR[sp, 3, cc] Phi[ii] - yu[3, 3] QLbar[sp, ii, 3, cc].uR[sp, 3, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
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215 | yuk = yuk /. {CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
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216 |
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217 | TYt[mu_, nu_] := -ME[mu, nu] (yuk + HC[yuk] /. feynmangaugerules)
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218 |
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219 | TFlep[mu_, nu_] := LLbar[ss, ii, ff].Ga[mu, ss, ss1].DC[LL[ss1, ii, ff], nu] - DC[LLbar[ss, ii, ff], mu].Ga[nu, ss, ss1].LL[ss1, ii, ff] +
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220 | lRbar[ss, ff].Ga[mu, ss, ss1].DC[lR[ss1, ff], nu] - DC[lRbar[ss, ff], mu].Ga[nu, ss, ss1].lR[ss1, ff] ;
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221 |
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222 | TFl[mu_, nu_] := -ME[mu, nu] I/2 TFlep[al, al] + I/4 ( TFlep[mu, nu] + TFlep[nu, mu]);
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223 |
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224 | TYl[mu_,nu_] := -ME[mu,nu] ( - MTA tabar.ta );
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225 |
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226 | (* Higgs *)
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227 |
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228 | Tscalar[mu_, nu_] := (2 DC[Phibar[ii], mu] DC[Phi[ii], nu]) - ME[mu, nu] (DC[Phibar[ii], rho] DC[Phi[ii], rho] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj])
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229 |
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230 | (* Gauge bosons *)
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231 |
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232 | TGg[mu_,nu_] := -ME[mu,nu] (-1/4 FS[G,rho,sig,a] FS[G,rho,sig,a]) - FS[G,mu,rho,a] FS[G,nu,rho,a];
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233 | (*new lag for he weak sector before EWSB*)
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234 | (*Careful to check the gauge fixing term coefficient*)
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235 | TGB[mu_,nu_] := -ME[mu,nu](-1/4 FS[B,rho,sig]FS[B,rho,sig])-FS[B,mu,rho]FS[B,nu,rho];
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236 | TGW[mu_,nu_] := -ME[mu,nu](-1/4 FS[Wi,rho,sig,ii]FS[Wi,rho,sig,ii])-FS[Wi,mu,rho,ii]FS[Wi,nu,rho,ii];
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237 |
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238 |
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239 | (* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators *)
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240 | (* and unitary gauge for massive gauge boson propagators. *)
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241 |
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242 | TGFg[mu_,nu_]:= -ME[mu,nu].( del[del[G[sig, a1], sig], rho].G[rho, a1] +
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243 | 1/2 del[G[rho, a1], rho].del[G[sig, a1], sig] ) +
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244 | del[del[G[rho, a1], rho], mu].G[nu, a1] + del[del[G[rho, a1], rho], nu].G[mu, a1];
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245 |
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246 | TGFa[mu_,nu_]:= -ME[mu,nu].( del[del[A[sig], sig], rho].A[rho] +
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247 | 1/2 del[A[rho], rho].del[A[sig], sig] ) +
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248 | del[del[A[rho], rho], mu].A[nu] + del[del[A[rho], rho], nu].A[mu];
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249 |
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250 | (** Ghost **)
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251 |
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252 | (*TGhost[mu_,nu_] := ( -ME[mu,nu].(DC[ghGbar,rho] DC[ghG,rho]) +
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253 | DC[ghGbar,mu] DC[ghG,nu] + DC[ghGbar,nu] DC[ghG,mu] ); *)
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254 |
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255 | LQCDGhs = -ghGbar[ii].del[DC[ghG[ii], mu], mu];
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256 | TGhost[mu_,nu_] := -ME[mu,nu](ExpandIndices[ LQCDGhs , FlavorExpand->SU2W]) + ( del[ghGbar[a], mu].(del[ghG[a], nu] - gs f[a,b,c] G[nu,c] ghG[b] ) + del[ghGbar[a], nu].(del[ghG[a], mu] - gs f[a,b,c] G[mu,c] ghG[b] ) );
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257 |
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258 |
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259 | (*** Writing the lagrangian ***)
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260 |
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261 | L2f := -1/Lambda (gTq TFlq[mu, nu] + gTq3 (TFt[mu, nu] + TYt[mu, nu]) + gTl (TFl[mu, nu] + TYl[mu, nu])) Y2[mu, nu]
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262 | L2v := -1/Lambda ExpandIndices[ ( gTg (TGg[mu,nu]+TGFg[mu,nu]) + gTw TGW[mu,nu] + gTb TGB[mu,nu] + (gTb cw^2 + gTw sw^2) TGFa[mu,nu]) Y2[mu,nu],FlavorExpand->True];
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263 | L2gh := -1/Lambda (gTg TGhost[mu,nu] ) Y2[mu,nu];
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264 | L2H := -1/Lambda ExpandIndices[(gTh Tscalar[mu,nu] )Y2[mu,nu],FlavorExpand->True] /. feynmangaugerules;
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265 |
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266 | (*** Writing the lagrangian ***)
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267 |
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268 | L2SM := L2f + L2v + L2gh + L2H;
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269 |
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270 |
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271 | (**** DM sector ***)
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272 | (* Real Scalars: r *)
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273 | TSrX[mu_,nu_] := -1/2 ME[mu,nu] (del[Xr, rho] del[Xr, rho] - MXr MXr Xr Xr ) +
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274 | del[Xr, mu] del[Xr, nu];
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275 |
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276 | L2rX := -1/Lambda ( gTXr TSrX[mu,nu] Y2[mu,nu] );
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277 |
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278 | (* Fermions: q *)
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279 | TFqX[mu_,nu_] := -ME[mu,nu] I Xdbar.(Ga[rho].del[Xd, rho]) +
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280 | 1/2 ME[mu,nu] del[I Xdbar.Ga[rho].Xd, rho] +
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281 | I/2 Xdbar.Ga[mu].del[Xd, nu] - 1/4 I del[Xdbar.Ga[nu].Xd, mu] +
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282 | I/2 Xdbar.Ga[nu].del[Xd, mu] - 1/4 I del[Xdbar.Ga[mu].Xd, nu];
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283 | TYqX[mu_,nu_] := -ME[mu,nu] ( - MXd Xdbar.Xd );
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284 |
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285 | L2fX := -1/Lambda ( gTXd (TFqX[mu,nu] + TYqX[mu,nu]) ) Y2[mu,nu];
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286 |
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287 | (* Vectors: v *)
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288 | TVvX[mu_,nu_] := -ME[mu,nu] ( -1/4 FS[Xv,sig,rho] FS[Xv,sig,rho] +
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289 | +1/2 MXv MXv Xv[rho] Xv[rho] ) +
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290 | FS[Xv,mu,rho] FS[Xv,rho,nu] +
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291 | MXv MXv Xv[mu] Xv[nu];
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292 |
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293 | L2vX := -1/Lambda ( gTXv TVvX[mu,nu] Y2[mu,nu] );
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294 |
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295 |
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296 | L2DM := L2rX + L2fX + L2vX + L2SM;
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