1 | (*****************************************************************************************************)
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2 | (* This is the FeynRules model file for the Higgs characterisation project *)
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3 | (* *)
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4 | (* It contains parts of existing FR model files: *)
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5 | (* 1) HEFT, author: C. Duhr (https://feynrules.irmp.ucl.ac.be/wiki/HiggsEffectiveTheory) *)
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6 | (* 2) Minimal Zprime, author: L. Basso (https://feynrules.irmp.ucl.ac.be/wiki/B-L-SM) *)
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7 | (* 3) RS, author: P. de Aquino (https://feynrules.irmp.ucl.ac.be/wiki/RSmodel) *)
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8 | (* *)
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9 | (* Please contact K. Mawatari (kentarou.mawatari@vub.ac.be) for bugs and/or further information. *)
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10 | (* *)
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11 | (*****************************************************************************************************)
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12 |
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13 |
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14 | (* ************************** *)
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15 | (* ***** Information ***** *)
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16 | (* ************************** *)
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17 |
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18 | M$ModelName = "HiggsCharac";
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19 |
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20 | M$Information = {
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21 | Authors -> {"P. de Aquino, K. Mawatari"},
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22 | Version -> "3.4",
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23 | Date -> "17. 10. 2013",
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24 | Institutions -> {"Vrije Universiteit Brussel"},
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25 | Emails -> {"kentarou.mawatari@vub.ac.be"},
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26 | URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/HiggsCharacterisation/",
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27 | References -> {"P. Artoisenet et al., arXiv:1306.6464"}
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28 | };
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29 |
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30 | (* ************************** *)
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31 | (* ***** Change log ***** *)
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32 | (* ************************** *)
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33 |
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34 | (* 16.01.2013 v1.0 - released version. *)
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35 | (* 04.04.2013 v1.1 - added the CP-odd Yukawa terms in the X0 Lagrangian. *)
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36 | (* modified the X2 HD lagrangian to be proportional to 1/Lambda3. *)
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37 | (* 15.04.2013 v2.0 - fixed a bug for the X2 lowest dimensional interactions with massive gauge bosons. *)
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38 | (* parametrisation for X0 modified. *)
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39 | (* 28.05.2013 v2.1 - fixed a bug for the X0 coupling to the massive vector bosons (SM couplings recovered). *)
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40 | (* 27.06.2013 v3.0 - major update and version for the paper [arXiv:1306.6464]. *)
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41 | (* 04.07.2013 v3.1 - fixed a bug in the gluon/photon gauge fixing term for X2. *)
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42 | (* 20.07.2013 v3.2 - put the X width = 0.00407 GeV by HXSWG. *)
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43 | (* introduced kqa, kqb, kla, and klb, instead of kfa and kfb. *)
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44 | (* 24.07.2013 v3.3 - added the SM X0 self-interactions and the effective g-g-X0-X0 intereaction. *)
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45 | (* 17.10.2013 v3.4 - redefined 'kHdw' as a complex. *)
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46 |
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47 |
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48 | FeynmanGauge = False;
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49 |
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50 | (***** Setting for interaction order (as e.g. used by MadGraph 5) ******)
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51 |
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52 | M$InteractionOrderLimit = {
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53 | {QNP, 2}
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54 | };
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55 |
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56 | M$InteractionOrderHierarchy = {
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57 | {QNP, 2}
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58 | };
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59 |
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60 |
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61 | (***** Particle classes list ******)
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62 |
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63 | M$ClassesDescription = {
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64 |
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65 | S[1] == { ClassName -> X0,
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66 | SelfConjugate -> True,
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67 | Mass -> {MX0, 125.0},
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68 | Width -> {WX0, 0.00407},
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69 | ParticleName -> "X0",
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70 | PDG -> 5000000,
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71 | PropagatorLabel -> "X0",
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72 | PropagatorType -> D,
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73 | PropagatorArrow -> None,
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74 | FullName -> "X0"},
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75 |
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76 | V[5] == { ClassName -> X1,
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77 | SelfConjugate -> True,
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78 | Mass -> {MX1, 125.0},
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79 | Width -> {WX1, 0.00407},
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80 | ParticleName -> "X1",
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81 | PDG -> 5000001,
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82 | PropagatorLabel -> "X1",
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83 | PropagatorType -> Sine,
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84 | PropagatorArrow -> None,
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85 | FullName -> "X1"},
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86 |
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87 | T[1] == { ClassName -> X2,
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88 | SelfConjugate -> True,
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89 | Symmetric -> True,
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90 | Mass -> {MX2, 125.0},
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91 | Width -> {WX2,0.00407},
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92 | ParticleName -> "X2",
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93 | PDG -> 5000002,
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94 | PropagatorLabel -> "X2",
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95 | PropagatorArrow -> None,
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96 | FullName -> "X2"}
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97 |
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98 | };
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99 |
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100 |
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101 | (* The loop coefficient from the HEFT model *)
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102 |
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103 | sert[x_] := 1+ 7/30 x + 2/21 x^2 + 26/525 x^3;
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104 | serw[xw_, xt_] := 1 + xw * 66/235 +xw^2 * 228/1645 + xw^3 * 696/8225 +
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105 | xw^4 * 5248/90475 +xw^5 * 1280/29939+ xw^6 * 54528/1646645-
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106 | xt * 56/705 - xt^2 * 32/987;
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107 | serp[x_] := 1 + x/3 + x^2 * 8/45 + x^3 * 4/35;
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108 |
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109 |
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110 | (***** Parameter list ******)
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111 |
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112 | M$Parameters = {
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113 |
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114 | Lambda == { ParameterType -> External,
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115 | Value -> 1000,
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116 | TeX -> \[CapitalLambda],
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117 | Description -> "cut-off scale"},
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118 |
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119 | ca == { ParameterType -> External,
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120 | Value -> 1,
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121 | TeX -> Subscript[c,a],
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122 | Description -> "cosine of the scalar mixing between 0+ and 0-"},
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123 |
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124 | sa == { ParameterType -> Internal,
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125 | Value -> Sqrt[1-ca^2],
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126 | TeX -> Subscript[s,a],
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127 | Description -> "sine of the scalar mixing between 0+ and 0-"},
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128 |
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129 | kSM == { ParameterType -> External,
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130 | Value -> 1,
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131 | TeX -> Subscript[\[Kappa],SM],
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132 | Description -> "Hzz/Hww SM coupling parameter"},
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133 |
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134 | kHtt == { ParameterType -> External,
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135 | Value -> 1,
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136 | TeX -> Subscript[\[Kappa],Htt],
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137 | Description -> "Htt coupling parameter"},
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138 |
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139 | kAtt == { ParameterType -> External,
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140 | Value -> 1,
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141 | TeX -> Subscript[\[Kappa],Att],
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142 | Description -> "Att coupling parameter"},
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143 |
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144 | kHbb == { ParameterType -> External,
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145 | Value -> 1,
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146 | TeX -> Subscript[\[Kappa],Hbb],
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147 | Description -> "Hbb coupling parameter"},
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148 |
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149 | kAbb == { ParameterType -> External,
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150 | Value -> 1,
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151 | TeX -> Subscript[\[Kappa],Abb],
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152 | Description -> "Abb coupling parameter"},
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153 |
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154 | kHll == { ParameterType -> External,
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155 | Value -> 1,
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156 | TeX -> Subscript[\[Kappa],Hll],
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157 | Description -> "Hll coupling parameter"},
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158 |
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159 | kAll == { ParameterType -> External,
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160 | Value -> 1,
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161 | TeX -> Subscript[\[Kappa],All],
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162 | Description -> "All coupling parameter"},
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163 |
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164 | kHaa == { ParameterType -> External,
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165 | Value -> 1,
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166 | InteractionOrder -> {QNP, 1},
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167 | TeX -> Subscript[\[Kappa],Haa],
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168 | Description -> "Haa coupling parameter"},
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169 |
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170 | kAaa == { ParameterType -> External,
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171 | Value -> 1,
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172 | InteractionOrder -> {QNP, 1},
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173 | TeX -> Subscript[\[Kappa],Aaa],
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174 | Description -> "Aaa coupling parameter"},
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175 |
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176 | kHza == { ParameterType -> External,
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177 | Value -> 1,
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178 | InteractionOrder -> {QNP, 1},
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179 | TeX -> Subscript[\[Kappa],Hza],
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180 | Description -> "Hza coupling parameter"},
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181 |
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182 | kAza == { ParameterType -> External,
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183 | Value -> 1,
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184 | InteractionOrder -> {QNP, 1},
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185 | TeX -> Subscript[\[Kappa],Aza],
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186 | Description -> "Aza coupling parameter"},
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187 |
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188 | kHgg == { ParameterType -> External,
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189 | Value -> 1,
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190 | InteractionOrder -> {QNP, 1},
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191 | TeX -> Subscript[\[Kappa],Hgg],
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192 | Description -> "Hgg coupling parameter"},
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193 |
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194 | kAgg == { ParameterType -> External,
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195 | Value -> 1,
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196 | InteractionOrder -> {QNP, 1},
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197 | TeX -> Subscript[\[Kappa],Agg],
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198 | Description -> "Agg coupling parameter"},
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199 |
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200 | kHzz == { ParameterType -> External,
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201 | Value -> 0,
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202 | InteractionOrder -> {QNP, 1},
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203 | TeX -> Subscript[\[Kappa],Hzz],
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204 | Description -> "Hzz coupling parameter"},
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205 |
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206 | kAzz == { ParameterType -> External,
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207 | Value -> 0,
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208 | InteractionOrder -> {QNP, 1},
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209 | TeX -> Subscript[\[Kappa],Azz],
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210 | Description -> "Azz coupling parameter"},
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211 |
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212 | kHww == { ParameterType -> External,
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213 | Value -> 0,
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214 | InteractionOrder -> {QNP, 1},
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215 | TeX -> Subscript[\[Kappa],Hww],
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216 | Description -> "Hww coupling parameter"},
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217 |
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218 | kAww == { ParameterType -> External,
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219 | Value -> 0,
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220 | InteractionOrder -> {QNP, 1},
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221 | TeX -> Subscript[\[Kappa],Aww],
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222 | Description -> "Aww coupling parameter"},
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223 |
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224 | kHda == { ParameterType -> External,
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225 | Value -> 0,
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226 | InteractionOrder -> {QNP, 1},
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227 | TeX -> Subscript[\[Kappa],Hda],
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228 | Description -> "Hda coupling parameter"},
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229 |
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230 | kHdz == { ParameterType -> External,
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231 | Value -> 0,
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232 | InteractionOrder -> {QNP, 1},
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233 | TeX -> Subscript[\[Kappa],Hdz],
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234 | Description -> "Hdz coupling parameter"},
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235 |
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236 | kHdwR == { ParameterType -> External,
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237 | ComplexParameter -> False,
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238 | Value -> 0,
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239 | TeX -> Subscript[\[Kappa],HdwR],
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240 | Description -> "Hdw coupling parameter (real part)"},
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241 |
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242 | kHdwI == { ParameterType -> External,
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243 | ComplexParameter -> False,
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244 | Value -> 0,
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245 | TeX -> Subscript[\[Kappa],HdwI],
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246 | Description -> "Hdw coupling parameter (imaginary part)"},
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247 |
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248 | kHdw == { ParameterType -> Internal,
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249 | ComplexParameter -> True,
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250 | Value -> {kHdwR+I*kHdwI},
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251 | InteractionOrder -> {QNP, 1},
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252 | TeX -> Subscript[\[Kappa],Hdw],
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253 | Description -> "Hdw coupling parameter"},
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254 |
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255 | kHHgg == { ParameterType -> External,
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256 | Value -> 1,
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257 | InteractionOrder -> {QNP, 1},
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258 | TeX -> Subscript[\[Kappa],HHgg],
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259 | Description -> "HHgg coupling parameter"},
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260 |
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261 | kAAgg == { ParameterType -> External,
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262 | Value -> 1,
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263 | InteractionOrder -> {QNP, 1},
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264 | TeX -> Subscript[\[Kappa],AAgg],
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265 | Description -> "AAgg coupling parameter"},
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266 |
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267 | kqa == { ParameterType -> External,
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268 | Value -> 1,
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269 | InteractionOrder -> {QNP, 1},
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270 | TeX -> Subscript[\[Kappa],qqa],
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271 | Description -> "X1-qq vector coupling parameter"},
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272 |
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273 | kqb == { ParameterType -> External,
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274 | Value -> 1,
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275 | InteractionOrder -> {QNP, 1},
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276 | TeX -> Subscript[\[Kappa],qqb],
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277 | Description -> "X1-qq axial-vector coupling parameter"},
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278 |
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279 | kla == { ParameterType -> External,
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280 | Value -> 1,
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281 | InteractionOrder -> {QNP, 1},
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282 | TeX -> Subscript[\[Kappa],lla],
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283 | Description -> "X1-ll vector coupling parameter"},
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284 |
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285 | klb == { ParameterType -> External,
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286 | Value -> 1,
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287 | InteractionOrder -> {QNP, 1},
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288 | TeX -> Subscript[\[Kappa],llb],
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289 | Description -> "X1-ll axial-vector coupling parameter"},
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290 |
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291 | kw1 == { ParameterType -> External,
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292 | Value -> 1,
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293 | InteractionOrder -> {QNP, 1},
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294 | TeX -> Subscript[\[Kappa],w1],
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295 | Description -> "X1-WW coupling parameter 1"},
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296 |
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297 | kw2 == { ParameterType -> External,
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298 | Value -> 1,
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299 | InteractionOrder -> {QNP, 1},
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300 | TeX -> Subscript[\[Kappa],w2],
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301 | Description -> "X1-WW coupling parameter 2"},
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302 |
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303 | kw3 == { ParameterType -> External,
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304 | Value -> 0,
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305 | InteractionOrder -> {QNP, 1},
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306 | TeX -> Subscript[\[Kappa],w3],
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307 | Description -> "X1-WW coupling parameter 3"},
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308 |
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309 | kw4 == { ParameterType -> External,
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310 | Value -> 0,
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311 | InteractionOrder -> {QNP, 1},
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312 | TeX -> Subscript[\[Kappa],w4],
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313 | Description -> "X1-WW coupling parameter 4"},
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314 |
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315 | kw5 == { ParameterType -> External,
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316 | Value -> 0,
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317 | InteractionOrder -> {QNP, 1},
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318 | TeX -> Subscript[\[Kappa],w5],
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319 | Description -> "X1-WW coupling parameter 5"},
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320 |
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321 | kz1 == { ParameterType -> External,
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322 | Value -> 0,
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323 | InteractionOrder -> {QNP, 1},
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324 | TeX -> Subscript[\[Kappa],z1],
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325 | Description -> "X1-ZZ coupling parameter 1"},
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326 |
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327 | kz3 == { ParameterType -> External,
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328 | Value -> 1,
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329 | InteractionOrder -> {QNP, 1},
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330 | TeX -> Subscript[\[Kappa],z3],
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331 | Description -> "X1-ZZ coupling parameter 3"},
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332 |
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333 | kz5 == { ParameterType -> External,
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334 | Value -> 0,
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335 | InteractionOrder -> {QNP, 1},
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336 | TeX -> Subscript[\[Kappa],z5],
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337 | Description -> "X1-ZZ coupling parameter 5"},
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338 |
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339 | kq == { ParameterType -> External,
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340 | Value -> 1,
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341 | InteractionOrder -> {QNP, 1},
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342 | TeX -> Subscript[\[Kappa],q],
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343 | Description -> "X2-quark coupling parameter"},
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344 |
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345 | kl == { ParameterType -> External,
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346 | Value -> 1,
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347 | InteractionOrder -> {QNP, 1},
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348 | TeX -> Subscript[\[Kappa],l],
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349 | Description -> "X2-lepton coupling parameter"},
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350 |
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351 | kg == { ParameterType -> External,
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352 | Value -> 1,
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353 | InteractionOrder -> {QNP, 1},
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354 | TeX -> Subscript[\[Kappa],g],
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355 | Description -> "X2-gluon coupling parameter"},
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356 |
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357 | ka == { ParameterType -> External,
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358 | Value -> 1,
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359 | InteractionOrder -> {QNP, 1},
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360 | TeX -> Subscript[\[Kappa],a],
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361 | Description -> "X2-photon coupling parameter"},
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362 |
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363 | kz == { ParameterType -> External,
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364 | Value -> 1,
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365 | InteractionOrder -> {QNP, 1},
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366 | TeX -> Subscript[\[Kappa],z],
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367 | Description -> "X2-Z coupling parameter"},
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368 |
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369 | kw == { ParameterType -> External,
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370 | Value -> 1,
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371 | InteractionOrder -> {QNP, 1},
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372 | TeX -> Subscript[\[Kappa],w],
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373 | Description -> "X2-W coupling parameter"},
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374 |
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375 |
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376 | gHaa == { ParameterType -> Internal,
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377 | Value -> -ee^2/(4*Pi)/(Pi*vev)*(-47/18), (* *serw[(MX0/2/MW)^2, (MX0/2/MT)^2], *)
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378 | TeX -> Subscript[g,Haa],
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379 | Description -> "Haa coupling"},
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380 |
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381 | gAaa == { ParameterType -> Internal,
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382 | Value -> -ee^2/(4*Pi)/(Pi*vev)*(4/3),
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383 | TeX -> Subscript[g,Aaa],
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384 | Description -> "Aaa coupling"},
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385 |
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386 | gHza == { ParameterType -> Internal,
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387 | Value -> Sqrt[ee^2/(4*Pi)*Gf*MZ^2/(8*Sqrt[2]*Pi)]*(94*cw^2-13)/(9*Pi*vev),
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388 | TeX -> Subscript[g,Hza],
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389 | Description -> "Hza coupling"},
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390 |
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391 | gAza == { ParameterType -> Internal,
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392 | Value -> -2*Sqrt[ee^2/(4*Pi)*Gf*MZ^2/(8*Sqrt[2]*Pi)]*(8*cw^2-5)/(3*Pi*vev),
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393 | TeX -> Subscript[g,Aza],
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394 | Description -> "Aza coupling"},
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395 |
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396 | gHgg == { ParameterType -> Internal,
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397 | Value -> -gs^2/(4*Pi)/(3*Pi*vev), (* *sert[(MX0/2/MT)^2], *)
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398 | TeX -> Subscript[g,Hgg],
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399 | Description -> "Hgg coupling"},
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400 |
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401 | gAgg == { ParameterType -> Internal,
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402 | Value -> -gs^2/(4*Pi)/(2*Pi*vev), (* *serp[(MX0/2/MT)^2], *)
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403 | TeX -> Subscript[g,Agg],
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404 | Description -> "Agg coupling"},
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405 |
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406 | gHHgg == { ParameterType -> Internal,
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407 | Value -> gs^2/(4*Pi)/(3*Pi*vev^2),
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408 | TeX -> Subscript[g,HHgg],
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409 | Description -> "HHgg coupling"},
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410 |
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411 | gAAgg == { ParameterType -> Internal,
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412 | Value -> gs^2/(4*Pi)/(2*Pi*vev^2),
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413 | TeX -> Subscript[g,AAgg],
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414 | Description -> "AAgg coupling"},
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415 |
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416 | au == { ParameterType -> Internal,
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417 | Value -> ee/(2 sw cw)(1/2-4/3 sw2),
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418 | Tex -> Subscript[a,u],
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419 | Description -> "vector coupling for up-type quarks"},
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420 |
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421 | bu == { ParameterType -> Internal,
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422 | Value -> ee/(2 sw cw)(1/2),
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423 | TeX -> Subscript[b,u],
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424 | Description -> "axial-vector coupling for up-type quarks"},
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425 |
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426 | ad == { ParameterType -> Internal,
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427 | Value -> ee/(2 sw cw)(-1/2+2/3 sw2),
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428 | TeX -> Subscript[a,d],
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429 | Description -> "vector coupling for down-type quarks"},
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430 |
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431 | bd == { ParameterType -> Internal,
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432 | Value -> ee/(2 sw cw)(-1/2),
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433 | TeX -> Subscript[b,d],
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434 | Description -> "axial-vector coupling for down-type quarks"},
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435 |
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436 | an == { ParameterType -> Internal,
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437 | Value -> ee/(2 sw cw)(1/2),
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438 | Tex -> Subscript[a,n],
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439 | Description -> "vector coupling for neutrinos"},
|
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440 |
|
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441 | bn == { ParameterType -> Internal,
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442 | Value -> ee/(2 sw cw)(1/2),
|
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443 | TeX -> Subscript[b,n],
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444 | Description -> "axial-vector coupling for neutrinos"},
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445 |
|
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446 | al == { ParameterType -> Internal,
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447 | Value -> ee/(2 sw cw)(-1/2+2 sw2),
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448 | TeX -> Subscript[a,l],
|
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449 | Description -> "vector coupling for charged leptons"},
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450 |
|
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451 | bl == { ParameterType -> Internal,
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452 | Value -> ee/(2 sw cw)(-1/2),
|
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453 | TeX -> Subscript[b,l],
|
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454 | Description -> "axial-vector coupling for charged leptons"},
|
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455 |
|
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456 | gwwz == { ParameterType -> Internal,
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457 | Value -> -ee cw/sw,
|
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458 | TeX -> Subscript[g,wwz],
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459 | Description -> "WWZ coupling"}
|
---|
460 |
|
---|
461 | };
|
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462 |
|
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463 |
|
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464 | (*****************************************************************************************)
|
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465 | (**************************************** Lagrangian *************************************)
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466 | (*****************************************************************************************)
|
---|
467 |
|
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468 | (****************************************** Spin-0 ***************************************)
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---|
469 |
|
---|
470 | L0v := (-1/4 ( ca kHaa gHaa FS[A,mu,nu] FS[A,mu,nu] + sa kAaa gAaa FS[A,mu,nu] Dual[FS][A,mu,nu] ) -
|
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471 | 1/2 ( ca kHza gHza FS[Z,mu,nu] FS[A,mu,nu] + sa kAza gAza FS[Z,mu,nu] Dual[FS][A,mu,nu] ) -
|
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472 | 1/4 ( ca kHgg gHgg FS[G,mu,nu,a] FS[G,mu,nu,a] + sa kAgg gAgg FS[G,mu,nu,a] Dual[FS][G,mu,nu,a] ) -
|
---|
473 | 1/4/Lambda ( ca kHzz FS[Z,mu,nu] FS[Z,mu,nu] + sa kAzz FS[Z,mu,nu] Dual[FS][Z,mu,nu] ) -
|
---|
474 | 1/2/Lambda ( ca kHww FS[Wbar,mu,nu] FS[W,mu,nu] + sa kAww FS[Wbar,mu,nu] Dual[FS][W,mu,nu] ) -
|
---|
475 | 1 /Lambda ( ca kHda Z[nu] del[FS[A,mu,nu],mu] +
|
---|
476 | ca kHdz Z[nu] del[FS[Z,mu,nu],mu] +
|
---|
477 | ca ( kHdw Wbar[nu] del[FS[W,mu,nu],mu] + HC[kHdw Wbar[nu] del[FS[W,mu,nu],mu]] ) ) ) X0;
|
---|
478 |
|
---|
479 | L0v6 := -1/8 ( ca kHHgg gHHgg FS[G,mu,nu,a] FS[G,mu,nu,a] +
|
---|
480 | +sa kAAgg gAAgg FS[G,mu,nu,a] Dual[FS][G,mu,nu,a] ) X0 X0;
|
---|
481 |
|
---|
482 |
|
---|
483 | (****************************************** Spin-1 ***************************************)
|
---|
484 |
|
---|
485 | L1f := ( kqa au uqbar[s,n,i].Ga[mu,s,t].uq[t,n,i] +
|
---|
486 | kqa ad dqbar[s,n,i].Ga[mu,s,t].dq[t,n,i] +
|
---|
487 | kla an vlbar[s,n] .Ga[mu,s,t].vl[t,n] +
|
---|
488 | kla al lbar[s,n] .Ga[mu,s,t]. l[t,n] -
|
---|
489 | kqb bu uqbar[s,n,i].Ga[mu,s,t].Ga[5,t,u].uq[u,n,i] -
|
---|
490 | kqb bd dqbar[s,n,i].Ga[mu,s,t].Ga[5,t,u].dq[u,n,i] -
|
---|
491 | klb bn vlbar[s,n] .Ga[mu,s,t].Ga[5,t,u].vl[u,n] -
|
---|
492 | klb bl lbar[s,n] .Ga[mu,s,t].Ga[5,t,u]. l[u,n] ) X1[mu];
|
---|
493 |
|
---|
494 | L1w := I kw1 gwwz ( FS[Wbar,mu,nu] W[mu] - FS[W,mu,nu] Wbar[mu] ) X1[nu] +
|
---|
495 | I kw2 gwwz Wbar[mu] W[nu] FS[X1,mu,nu] -
|
---|
496 | kw3 Wbar[mu] W[nu] ( del[X1[nu],mu] + del[X1[mu],nu] ) +
|
---|
497 | I kw4 Wbar[mu] W[nu] Dual[FS][X1,mu,nu] -
|
---|
498 | kw5 Eps[mu,nu,rho,sig] ( Wbar[mu] del[W[nu],rho] - del[Wbar[mu],rho] W[nu] ) X1[sig];
|
---|
499 |
|
---|
500 | L1z := - kz1 FS[Z,mu,nu] Z[mu] X1[nu] -
|
---|
501 | kz3 X1[mu] del[Z[mu],nu] Z[nu] -
|
---|
502 | kz5 Eps[mu,nu,rho,sig] X1[mu] Z[nu] del[Z[sig],rho];
|
---|
503 |
|
---|
504 | L1 := L1f + L1w + L1z;
|
---|
505 |
|
---|
506 |
|
---|
507 | (****************************************** Spin-2 ***************************************)
|
---|
508 |
|
---|
509 | (*** Defining the cov derivatives ***)
|
---|
510 |
|
---|
511 | covdelU[field_, mu_] :=
|
---|
512 | Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
|
---|
513 | - 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]];
|
---|
514 |
|
---|
515 | covdelD[field_, mu_] :=
|
---|
516 | Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
|
---|
517 | + 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]];
|
---|
518 |
|
---|
519 | covdelE[field_, mu_] :=
|
---|
520 | Module[{j, a}, del[field, mu]
|
---|
521 | + 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]];
|
---|
522 |
|
---|
523 | covdelN[field_, mu_] :=
|
---|
524 | Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
|
---|
525 |
|
---|
526 |
|
---|
527 | (*** Defining the energy-momentum tensor T[mu,nu] ***)
|
---|
528 |
|
---|
529 | (* Fermions *)
|
---|
530 |
|
---|
531 | TFq[mu_,nu_] := (-ME[mu,nu] (I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho]
|
---|
532 | + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho]
|
---|
533 |
|
---|
534 | + ee/sw/Sqrt[2] (uqbar.Ga[rho].ProjM.CKM.dq W[rho] + dqbar.Ga[rho].ProjM.HC[CKM].uq Wbar[rho]) )
|
---|
535 | + ( I/2 uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu]
|
---|
536 | + I/2 uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu]
|
---|
537 | + I/2 dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu]
|
---|
538 | + I/2 dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu] )
|
---|
539 |
|
---|
540 | + ee/sw/2/Sqrt[2] (uqbar.Ga[mu].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[nu]
|
---|
541 | + uqbar.Ga[nu].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].ProjM.HC[CKM].uq Wbar[mu] ));
|
---|
542 |
|
---|
543 | TFl[mu_,nu_] := (-ME[mu,nu] (I vlbar.(Ga[rho].covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].vl, rho]
|
---|
544 | + I lbar.(Ga[rho].covdelE[l, rho] ) -1/2 del[I lbar.Ga[rho].l, rho]
|
---|
545 |
|
---|
546 | + ee/sw/Sqrt[2] ( vlbar.Ga[rho].ProjM.l W[rho] + lbar.Ga[rho].ProjM.vl Wbar[rho]) )
|
---|
547 | + ( I/2 vlbar.Ga[mu].covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].vl, mu]
|
---|
548 | + I/2 vlbar.Ga[nu].covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].vl, nu]
|
---|
549 | + I/2 lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu]
|
---|
550 | + I/2 lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu] )
|
---|
551 |
|
---|
552 | + ee/sw/2/Sqrt[2] (vlbar.Ga[mu].ProjM.l W[nu] + lbar.Ga[mu].ProjM.vl Wbar[nu]
|
---|
553 | + vlbar.Ga[nu].ProjM.l W[mu] + lbar.Ga[nu].ProjM.vl Wbar[mu]));
|
---|
554 |
|
---|
555 | (* Yukawa *)
|
---|
556 |
|
---|
557 | TYq[mu_,nu_] := -ME[mu,nu] ( - MT tbar.t - MB bbar.b );
|
---|
558 | TYl[mu_,nu_] := -ME[mu,nu] ( - MTA tabar.ta );
|
---|
559 |
|
---|
560 | (* Gauge bosons *)
|
---|
561 |
|
---|
562 | 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];
|
---|
563 | TGa[mu_,nu_] := -ME[mu,nu] (-1/4 FS[A,rho,sig] FS[A,rho,sig]) - FS[A,mu,rho] FS[A,nu,rho];
|
---|
564 | TGz[mu_,nu_] := -ME[mu,nu] (-1/4 FS[Z,rho,sig] FS[Z,rho,sig] + 1/2 MZ^2 Z[rho] Z[rho]) -
|
---|
565 | (FS[Z,mu,rho] FS[Z,nu,rho] - MZ^2 Z[mu] Z[nu]);
|
---|
566 | TGw[mu_,nu_] := -ME[mu,nu] (-1/2 FS[Wbar,rho,sig] FS[W,rho,sig] + MW^2 Wbar[rho] W[rho]) -
|
---|
567 | (FS[Wbar,mu,rho] FS[W,nu,rho] - MW^2 Wbar[mu] W[nu] + FS[Wbar,nu,rho] FS[W,mu,rho] - MW^2 Wbar[nu] W[mu]);
|
---|
568 |
|
---|
569 | (* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators *)
|
---|
570 | (* and unitary gauge for massive gauge boson propagators. *)
|
---|
571 |
|
---|
572 | TGFg[mu_,nu_]:= -ME[mu,nu].( del[del[G[sig, a1], sig], rho].G[rho, a1] +
|
---|
573 | 1/2 del[G[rho, a1], rho].del[G[sig, a1], sig] ) +
|
---|
574 | del[del[G[rho, a1], rho], mu].G[nu, a1] + del[del[G[rho, a1], rho], nu].G[mu, a1];
|
---|
575 |
|
---|
576 | TGFa[mu_,nu_]:= -ME[mu,nu].( del[del[A[sig], sig], rho].A[rho] +
|
---|
577 | 1/2 del[A[rho], rho].del[A[sig], sig] ) +
|
---|
578 | del[del[A[rho], rho], mu].A[nu] + del[del[A[rho], rho], nu].A[mu];
|
---|
579 |
|
---|
580 | (*** Writing the lagrangian ***)
|
---|
581 |
|
---|
582 | L2f := -1/Lambda ( kq (TFq[mu,nu]+TYq[mu,nu]) + kl (TFl[mu,nu]+TYl[mu,nu]) ) X2[mu,nu];
|
---|
583 | L2v := -1/Lambda ( kg (TGg[mu,nu]+TGFg[mu,nu]) +
|
---|
584 | ka (TGa[mu,nu]+TGFa[mu,nu]) +
|
---|
585 | kz TGz[mu,nu] +
|
---|
586 | kw TGw[mu,nu] ) X2[mu,nu];
|
---|
587 |
|
---|
588 | L2 := L2f + L2v;
|
---|
589 |
|
---|
590 | (*****************************************************************************************)
|
---|
591 |
|
---|
592 | LagHC:= LSM + L0v + L1 + L2 + L0v6;
|
---|