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 Priscila de Aquino (paquino@vub.ac.be) for bugs and/or further information *) |
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10 | (* *) |
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11 | (* THE UFO FILE HAS BEEN MODIFIED BY HAND: COUPLINGS OF THE X2 TO THE PHOTONS MODIFIED TO *) |
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12 | (* Ka AND INTERACTIONS BETWEEN RESONANCES REMOVED. *) |
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13 | (* *) |
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14 | (*****************************************************************************************************) |
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15 | FeynmanGauge = False; |
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16 | |
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17 | M$ModelName = "Higgs_Characterization"; |
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18 | M$Information = { |
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19 | Authors -> "P. de Aquino, K. Mawatari", |
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20 | Version -> "2.0", |
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21 | Date -> "15. 04. 2013" |
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22 | }; |
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23 | |
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24 | (* ************************** *) |
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25 | (* ***** Gauge groups ***** *) |
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26 | (* ************************** *) |
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27 | M$GaugeGroups = { |
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28 | U11Y == { |
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29 | Abelian -> True, |
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30 | CouplingConstant -> g1, |
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31 | GaugeBoson -> X1, |
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32 | Charge -> Y} |
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33 | }; |
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34 | |
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35 | (* The loop coefficient from the HEFT model *) |
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36 | |
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37 | sert[x_] := 1+ 7/30 x + 2/21 x^2 + 26/525 x^3; |
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38 | |
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39 | serw[xw_, xt_] := 1 + xw * 66/235 +xw^2 * 228/1645 + xw^3 * 696/8225 + |
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40 | xw^4 * 5248/90475 +xw^5 * 1280/29939+ xw^6 * 54528/1646645- |
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41 | xt * 56/705 - xt^2 * 32/987; |
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42 | |
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43 | serp[x_] := 1 + x/3 + x^2 * 8/45 + x^3 * 4/35; |
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44 | |
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45 | (***** Setting for interaction order (as e.g. used by MadGraph 5) ******) |
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46 | |
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47 | M$InteractionOrderLimit = { |
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48 | {QNP, 99} |
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49 | }; |
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50 | |
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51 | (***** Parameter list ******) |
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52 | |
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53 | M$Parameters = { |
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54 | |
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55 | kq == { |
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56 | ParameterType -> External, |
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57 | Value -> 1, |
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58 | InteractionOrder -> {QNP, 1}, |
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59 | Description -> "Coupling with light quarks"}, |
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60 | |
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61 | kg == { |
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62 | ParameterType -> External, |
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63 | Value -> 1, |
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64 | InteractionOrder -> {QNP, 1}, |
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65 | Description -> "Coupling with gluons"}, |
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66 | |
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67 | ka == { |
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68 | ParameterType -> External, |
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69 | Value -> 1, |
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70 | InteractionOrder -> {QNP, 1}, |
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71 | Description -> "Coupling with photons"}, |
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72 | |
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73 | kv == { |
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74 | ParameterType -> External, |
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75 | Value -> 1, |
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76 | InteractionOrder -> {QNP, 1}, |
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77 | Description -> "Coupling with vector boson"}, |
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78 | |
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79 | kl == { |
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80 | ParameterType -> External, |
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81 | Value -> 1, |
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82 | InteractionOrder -> {QNP, 1}, |
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83 | Description -> "Coupling with leptons"}, |
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84 | |
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85 | ka1 == { |
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86 | ParameterType -> External, |
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87 | Value -> 0, |
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88 | InteractionOrder -> {QNP, 1}, |
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89 | Description -> "Coupling with photons"}, |
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90 | |
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91 | |
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92 | kg1 == { |
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93 | ParameterType -> External, |
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94 | Value -> 0, |
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95 | InteractionOrder -> {QNP, 1}, |
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96 | Description -> "Coupling with gluons"}, |
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97 | |
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98 | ka2 == { |
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99 | ParameterType -> External, |
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100 | Value -> 0, |
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101 | InteractionOrder -> {QNP, 1}, |
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102 | Description -> "Coupling with photons"}, |
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103 | |
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104 | kg2 == { |
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105 | ParameterType -> External, |
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106 | Value -> 0, |
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107 | InteractionOrder -> {QNP, 1}, |
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108 | Description -> "Coupling with gluons"}, |
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109 | |
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110 | |
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111 | Lambda == { |
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112 | ParameterType -> External, |
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113 | Value -> 1000, |
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114 | Description -> "Spin-2 effective scale"}, |
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115 | |
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116 | ksm == { |
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117 | ParameterType -> External, |
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118 | Value -> 1, |
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119 | InteractionOrder -> {QNP, 1}, |
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120 | Description -> "Lower dimensional operator switch"}, |
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121 | |
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122 | GHaa == {TeX -> Subscript[g, Haa], |
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123 | ParameterType -> Internal, |
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124 | Value -> ee^2/4/Pi/(Pi*vev)*(47/18)*serw[(MX0/2/MW)^2, (MX0/2/MT)^2]}, |
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125 | |
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126 | GAaa == {TeX -> Subscript[g, Aaa], |
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127 | ParameterType -> Internal, |
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128 | Value -> ee^2/4/Pi/(Pi*vev)}, |
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129 | |
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130 | GHza == {TeX -> Subscript[g, Hza], |
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131 | ParameterType -> Internal, |
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132 | Value -> ee^2/4/Pi/(Pi*vev)}, |
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133 | |
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134 | GAza == {TeX -> Subscript[g, Aza], |
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135 | ParameterType -> Internal, |
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136 | Value -> ee^2/4/Pi/(Pi*vev)}, |
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137 | |
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138 | GHgg == {TeX -> Subscript[g, Hgg], |
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139 | ParameterType -> Internal, |
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140 | Value -> -gs^2/(4Pi(3Pi vev)) sert[(MX0/2/MT)^2] }, |
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141 | |
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142 | GAgg == {TeX -> Subscript[g, Agg], |
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143 | ParameterType -> Internal, |
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144 | Value -> -gs^2/4/Pi/(2*Pi*vev)*serp[(MX0/2/MT)^2]}, |
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145 | |
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146 | kHff == {TeX -> Subscript[k, Hf], |
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147 | ParameterType -> External, |
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148 | InteractionOrder -> {QNP, 1}, |
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149 | Value -> 1}, |
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150 | |
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151 | kAff == {TeX -> Subscript[k, Af], |
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152 | ParameterType -> External, |
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153 | InteractionOrder -> {QNP, 1}, |
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154 | Value -> 1}, |
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155 | |
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156 | kHaa == {TeX -> Subscript[k, Haa], |
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157 | ParameterType -> External, |
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158 | InteractionOrder -> {QNP, 1}, |
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159 | Value -> 1}, |
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160 | |
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161 | kAaa == {TeX -> Subscript[k, Aaa], |
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162 | ParameterType -> External, |
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163 | InteractionOrder -> {QNP, 1}, |
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164 | Value -> 1}, |
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165 | |
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166 | kHza == {TeX -> Subscript[k, Hza], |
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167 | ParameterType -> External, |
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168 | InteractionOrder -> {QNP, 1}, |
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169 | Value -> 1}, |
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170 | |
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171 | kAza == {TeX -> Subscript[k, Aza], |
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172 | ParameterType -> External, |
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173 | InteractionOrder -> {QNP, 1}, |
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174 | Value -> 1}, |
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175 | |
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176 | kHgg == {TeX -> Subscript[k, Hgg], |
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177 | ParameterType -> External, |
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178 | InteractionOrder -> {QNP, 1}, |
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179 | Value -> 1}, |
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180 | |
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181 | kAgg == {TeX -> Subscript[k, Agg], |
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182 | ParameterType -> External, |
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183 | InteractionOrder -> {QNP, 1}, |
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184 | Value -> 1}, |
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185 | |
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186 | kHvv == {TeX -> Subscript[k, Hvv], |
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187 | ParameterType -> External, |
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188 | InteractionOrder -> {QNP, 1}, |
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189 | Value -> 0}, |
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190 | |
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191 | kAvv == {TeX -> Subscript[k, Avv], |
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192 | ParameterType -> External, |
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193 | InteractionOrder -> {QNP, 1}, |
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194 | Value -> 0}, |
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195 | |
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196 | afu == { |
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197 | ParameterType -> Internal, |
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198 | Value -> -gs/(2 cw)(1/2-4*sw2/3)}, |
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199 | |
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200 | bfu == { |
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201 | ParameterType -> Internal, |
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202 | Value -> -gs/(2 cw)(1/2)}, |
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203 | |
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204 | kfau == { |
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205 | ParameterType -> External, |
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206 | Value -> 1, |
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207 | InteractionOrder -> {QNP, 1}}, |
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208 | |
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209 | kfbu == { |
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210 | ParameterType -> External, |
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211 | Value -> 1, |
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212 | InteractionOrder -> {QNP, 1}}, |
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213 | |
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214 | afd == { |
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215 | ParameterType -> Internal, |
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216 | Value -> -gs/(2 cw)(-1/2+2*sw2/3)}, |
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217 | |
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218 | bfd == { |
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219 | ParameterType -> Internal, |
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220 | Value -> -gs/(2 cw)(-1/2)}, |
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221 | |
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222 | kfad == { |
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223 | ParameterType -> External, |
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224 | Value -> 1, |
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225 | InteractionOrder -> {QNP, 1}}, |
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226 | |
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227 | kfbd == { |
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228 | ParameterType -> External, |
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229 | Value -> 1, |
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230 | InteractionOrder -> {QNP, 1}}, |
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231 | |
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232 | gwwz == { |
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233 | ParameterType -> Internal, |
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234 | Value -> -ee cw/sw, |
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235 | Description -> "SM coupling"}, |
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236 | |
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237 | kv1 == { |
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238 | ParameterType -> External, |
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239 | Value -> 0, |
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240 | InteractionOrder -> {QNP, 1}, |
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241 | Description -> "Couplings of spin-1 to X"}, |
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242 | |
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243 | kv2 == { |
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244 | ParameterType -> External, |
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245 | Value -> 0, |
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246 | InteractionOrder -> {QNP, 1}, |
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247 | Description -> "Couplings of spin-1 to X"}, |
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248 | |
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249 | kv3 == { |
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250 | ParameterType -> External, |
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251 | Value -> 0, |
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252 | InteractionOrder -> {QNP, 1}, |
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253 | Description -> "Couplings of spin-1 to X"}, |
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254 | |
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255 | kv4 == { |
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256 | ParameterType -> External, |
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257 | Value -> 0, |
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258 | InteractionOrder -> {QNP, 1}, |
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259 | Description -> "Couplings of spin-1 to X"}, |
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260 | |
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261 | kv5 == { |
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262 | ParameterType -> External, |
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263 | Value -> 0, |
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264 | InteractionOrder -> {QNP, 1}, |
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265 | Description -> "Couplings of spin-1 to X"}, |
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266 | |
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267 | |
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268 | (*tha == {Value -> 2.88, |
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269 | TeX -> Subscript[\[Theta], a], |
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270 | Description -> "Scalar mixing angle"},*) |
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271 | |
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272 | ca == {ParameterType -> External, |
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273 | Value -> 1, |
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274 | TeX -> Subscript[c,a], |
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275 | InteractionOrder -> {QNP, 0}, |
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276 | Description -> "Cos of the scalar mixing angle"}, |
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277 | |
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278 | sa == {ParameterType -> Internal, |
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279 | Value -> Sqrt[1-ca^2], |
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280 | TeX -> Subscript[s,a], |
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281 | InteractionOrder -> {QNP, 0}, |
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282 | Description -> "Sin of the scalar mixing angle"} |
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283 | }; |
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284 | |
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285 | |
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286 | (***** Particle classes list ******) |
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287 | |
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288 | M$ClassesDescription = { |
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289 | V[7] == { |
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290 | ClassName -> X1, |
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291 | SelfConjugate -> True, |
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292 | Indices -> {}, |
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293 | Mass -> {MX1, 125.0}, |
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294 | Width -> {WX1, 0.07567860}, |
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295 | PropagatorLabel -> "X1", |
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296 | ParticleName -> "X1", |
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297 | PropagatorType -> Sine, |
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298 | PropagatorArrow -> None, |
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299 | PDG -> 5000002, |
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300 | FullName -> "X1"}, |
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301 | |
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302 | (*V[8] == { |
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303 | ClassName -> X1p, |
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304 | SelfConjugate -> True, |
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305 | Indices -> {}, |
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306 | Mass -> {MX1p, 125.0}, |
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307 | Width -> {WX1p, 0.07567860}, |
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308 | PropagatorLabel -> "X1p", |
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309 | ParticleName -> "X1p", |
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310 | PropagatorType -> Sine, |
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311 | PropagatorArrow -> None, |
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312 | PDG -> 5000003, |
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313 | FullName -> "X1m"},*) |
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314 | |
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315 | S[3] == { |
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316 | ClassName -> X0x, |
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317 | SelfConjugate -> True, |
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318 | Mass -> {MX0,125}, |
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319 | Width -> {WX0, 0.07567860}, |
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320 | PDG -> 5000001, |
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321 | ParticleName -> "X0"}, |
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322 | |
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323 | |
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324 | T[1] == { |
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325 | ClassName -> X2, |
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326 | SelfConjugate -> True, |
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327 | ParticleName ->"X2", |
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328 | PDG -> 5000004, |
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329 | Symmetric -> True, |
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330 | Mass -> {MX2, 125.0}, |
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331 | Width -> {WX2,0.07567860}} |
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332 | |
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333 | }; |
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334 | |
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335 | (**************************************** Lagrangian *************************************) |
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336 | (*****************************************************************************************) |
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337 | |
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338 | (* Spin-0 ********************************************************************************) |
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339 | (*****************************************************************************************) |
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340 | |
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341 | LG0:= - 1/4 ( ca kHgg GHgg FS[G, mu, nu, b] FS[G, mu, nu, b] + |
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342 | sa kAgg GAgg FS[G, mu, nu, b] Dual[FS][G, mu, nu, b]) X0x - |
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343 | 1/4 ( ca kHaa GHaa (del[A[nu], mu] - del[A[mu], nu])(del[A[nu], mu] - del[A[mu], nu]) + |
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344 | sa kAaa GAaa (del[A[nu], mu] - del[A[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[A[sig], rho]-del[A[rho], sig])) X0x - |
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345 | 1/4 ( ca kHza GHza (del[Z[nu], mu] - del[Z[mu], nu])(del[A[nu], mu] - del[A[mu], nu]) + |
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346 | sa kAza GAza (del[Z[nu], mu] - del[Z[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[A[sig], rho]-del[A[rho], sig])) X0x - |
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347 | 1/4( ca kHvv ((del[Z[nu], mu] - del[Z[mu], nu])(del[Z[nu], mu] - del[Z[mu], nu]) + |
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348 | (del[Wbar[nu], mu] - del[Wbar[mu], nu])(del[W[nu], mu] - del[W[mu], nu])) + |
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349 | sa kAvv ((del[Z[nu], mu] - del[Z[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[Z[sig], rho] - del[Z[rho], sig]) + |
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350 | (del[Wbar[nu], mu] - del[Wbar[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[W[sig], rho] - del[W[rho], sig]))) X0x; |
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351 | |
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352 | |
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353 | (*****************************************************************************************) |
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354 | |
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355 | (* RS ************************************************************************************) |
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356 | (*****************************************************************************************) |
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357 | |
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358 | |
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359 | (********************** Gravitational Coupling ******************************************) |
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360 | (********************** Defining the cov derivatives *************************************) |
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361 | |
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362 | covdelU[field_, mu_] := |
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363 | Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field |
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364 | - 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]]; |
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365 | |
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366 | covdelD[field_, mu_] := |
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367 | Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field |
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368 | + 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]]; |
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369 | |
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370 | covdelE[field_, mu_] := |
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371 | Module[{j, a}, del[field, mu] |
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372 | + 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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373 | |
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374 | (* Version 2.0 => fixed a sign problem and a factor 2 missing in the above derivative *) |
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375 | |
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376 | covdelN[field_, mu_] := |
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377 | 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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378 | |
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379 | (******************** Defining the field strenght tensors:********************************) |
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380 | |
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381 | 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]; |
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382 | |
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383 | FA[mu_,nu_] := del[B[nu], mu] - del[B[mu], nu]; |
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384 | |
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385 | 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]; |
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386 | |
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387 | (******************* Defining the energy-momentum tensor T[mu,nu] ************************) |
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388 | |
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389 | (* Gauge bosons *) |
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390 | |
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391 | TG[mu_,nu_]:= ( - ME[mu,nu]. (-1/4 (-kv) FA[rho, sig] FA[rho,sig] - 1/4 (-kv)FW[rho,sig,i1,i2,i3] FW[rho,sig, i1,i4,i5] - 1/4 (-kg)FG[rho,sig,a1,a2,a3] FG[rho,sig, a1,a4,a5]) |
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392 | - (-kv)FA[mu,rho] FA[nu,rho] - (-kv)FW[mu,rho,i1,i2,i3] FW[nu,rho, i1,i4,i5] - (-kg) FG[mu,rho,a1,a2,a3] FG[nu,rho, a1,a2,a3]); |
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393 | (* Fermions *) |
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394 | |
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395 | TF[mu_,nu_] := (-ME[mu,nu] ((-kq) (I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho] |
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396 | + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho]) |
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397 | +(-kl)(+ I vlbar.(Ga[rho].covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].vl, rho] |
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398 | + I lbar.(Ga[rho].covdelE[l, rho] ) -1/2 del[I lbar.Ga[rho].l, rho]) |
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399 | |
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400 | + ee/sw/Sqrt[2] ((-kq) uqbar.Ga[rho].ProjM.CKM.dq W[rho] + (-kq) dqbar.Ga[rho].ProjM.HC[CKM].uq Wbar[rho] |
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401 | + (-kl) vlbar.Ga[rho].ProjM.l W[rho] + (-kq) lbar.Ga[rho].ProjM.vl Wbar[rho]) ) |
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402 | + ( (-kq) (I/2 uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu] |
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403 | + I/2 uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu] |
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404 | + I/2 dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu] |
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405 | + I/2 dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu])+ |
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406 | (-kl) (I/2 vlbar.Ga[mu].covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].vl, mu] |
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407 | + I/2 vlbar.Ga[nu].covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].vl, nu] |
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408 | + I/2 lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu] |
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409 | + I/2 lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu]) ) |
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410 | |
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411 | + ee/sw/2/Sqrt[2] ((-kq)(uqbar.Ga[mu].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[nu] |
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412 | + uqbar.Ga[nu].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].ProjM.HC[CKM].uq Wbar[mu]) |
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413 | + (-kl)(vlbar.Ga[mu].ProjM.l W[nu] + lbar.Ga[mu].ProjM.vl Wbar[nu] |
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414 | + vlbar.Ga[nu].ProjM.l W[mu] + lbar.Ga[nu].ProjM.vl Wbar[mu]))); |
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415 | |
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416 | TFAxial[mu_,nu_] := (-ME[mu,nu] ((-kq)(I uqbar.(Ga[rho].Ga[5].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].Ga[5].uq, rho] |
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417 | + I dqbar.(Ga[rho].Ga[5].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].Ga[5].dq, rho]) |
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418 | + (-kl)( I vtbar.(Ga[rho].Ga[5].covdelN[vt, rho]) -1/2 del[I vtbar.Ga[rho].Ga[5].vt, rho] |
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419 | + I lbar.(Ga[rho].Ga[5].covdelE[l, rho] ) -1/2 del[I lbar.Ga[rho].Ga[5].l, rho]) |
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420 | |
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421 | + ee/sw/Sqrt[2] (-kq uqbar.Ga[rho].Ga[5].ProjM.CKM.dq W[rho] + (-kq) dqbar.Ga[rho].Ga[5].ProjM.HC[CKM].uq Wbar[rho] |
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422 | + (-kl) vtbar.Ga[rho].Ga[5].ProjM.l W[rho] + (-kl) lbar.Ga[rho].Ga[5].ProjM.vt Wbar[rho]) ) |
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423 | + ((-kq)(I/2 uqbar.Ga[mu].Ga[5].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].Ga[5].uq, mu] |
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424 | + I/2 uqbar.Ga[nu].Ga[5].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].Ga[5].uq, nu] |
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425 | + I/2 dqbar.Ga[mu].Ga[5].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].Ga[5].dq, mu] |
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426 | + I/2 dqbar.Ga[nu].Ga[5].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].Ga[5].dq, nu]) |
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427 | + (-kl) (I/2 vtbar.Ga[mu].Ga[5].covdelN[vt, nu] - 1/4 I del[vtbar.Ga[nu].Ga[5].vt, mu] |
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428 | + I/2 vtbar.Ga[nu].Ga[5].covdelN[vt, mu] - 1/4 I del[vtbar.Ga[mu].Ga[5].vt, nu] |
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429 | + I/2 lbar.Ga[mu].Ga[5].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].Ga[5].l, mu] |
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430 | + I/2 lbar.Ga[nu].Ga[5].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].Ga[5].l, nu])) |
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431 | |
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432 | + ee/sw/2/Sqrt[2] ((-kq) (uqbar.Ga[mu].Ga[5].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].Ga[5].ProjM.HC[CKM].uq Wbar[nu] |
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433 | + uqbar.Ga[nu].Ga[5].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].Ga[5].ProjM.HC[CKM].uq Wbar[mu]) |
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434 | +(-kl) (vtbar.Ga[mu].Ga[5].ProjM.l W[nu] + lbar.Ga[mu].Ga[5].ProjM.vt Wbar[nu] |
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435 | + vtbar.Ga[nu].Ga[5].ProjM.l W[mu] + lbar.Ga[nu].Ga[5].ProjM.vt Wbar[mu]))); |
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436 | |
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437 | |
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438 | (* Definitions for Higgs and Yukawa *) |
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439 | |
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440 | TH[mu_, nu_] := Block[{ii,mu, feynmangaugerules}, |
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441 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}]; |
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442 | |
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443 | ExpandIndices[-ME[mu,nu].(DC[PhiHbar[ii],rho] DC[PhiH[ii],rho])+DC[PhiHbar[ii],mu] DC[PhiH[ii],nu]+DC[PhiHbar[ii],nu] DC[PhiH[ii],mu], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules |
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444 | ]; |
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445 | |
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446 | (* Yukawa *) |
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447 | |
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448 | TYuk := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules}, |
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449 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}]; |
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450 | |
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451 | yuk = ExpandIndices[ |
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452 | -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] PhiH[ii] - |
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453 | yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] PhiH[ii] - |
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454 | yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] PhiHbar[jj] Eps[ii, jj], FlavorExpand -> SU2D]; |
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455 | 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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456 | yuk+HC[yuk]/.feynmangaugerules |
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457 | ]; |
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458 | |
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459 | TY[mu_,nu_] := -ME[mu,nu](TYuk + HC[TYuk]); |
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460 | |
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461 | |
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462 | (* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators and unitary gauge for massive gauge boson propagators. *) |
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463 | |
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464 | TGF[mu_, nu_]:= (-ME[mu,nu].( (-kg)del[del[G[sig, a1], sig], rho].G[rho, a1] + (-ka)del[del[A[sig], sig], rho].A[rho] + |
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465 | 1/2 (-kg)del[G[rho, a1], rho].del[G[rho, a1], rho] + 1/2 (-ka)del[A[rho], rho].del[A[rho], rho]) |
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466 | + ((-kg)del[del[G[rho, a1], rho], mu].G[nu, a1] + (-ka)del[del[A[rho], rho], mu].A[nu] +(-kg) |
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467 | del[del[G[rho, a1], rho], nu].G[mu, a1] + (-ka)del[del[A[rho], rho], nu].A[mu] )); |
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468 | |
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469 | (******************************* Writing the lagrangian *********************************) |
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470 | |
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471 | LagG := 1/Lambda (X2[mu,nu] (TG[mu,nu] + TGF[mu,nu])); (*ka,kg,kv are defined with TG[mu,nu]*) |
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472 | LagF := 1/Lambda(X2[mu,nu] TF[mu,nu]); |
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473 | LagHY := -kq/Lambda(X2[mu,nu] TY[mu,nu]) -kv/Lambda(X2[mu,nu] TH[mu,nu]); |
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474 | LagRS := LagG + LagF + LagHY; |
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475 | |
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476 | (********** Beta implementation of the 2+ (higher dimensional) and 2- resonance ***********) |
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477 | |
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478 | TA2m[mu_, nu_] := (-del[del[(-1/4 FA[rho, sig] FA[rho, sig]), mu], nu]); |
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479 | TA2mAxial[mu_, nu_] := (-del[del[(-1/8 FA[rho, sig] Eps[rho, sig, alpha, beta] FA[alpha, beta]), mu], nu]); |
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480 | |
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481 | TW2m[mu_, nu_] := (-del[del[(-1/4 FW[rho, sig, i1, i2, i3] FW[rho, sig, i1, i4, i5]), mu], nu]); |
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482 | TW2mAxial[mu_, nu_] := (-del[del[(-1/8 FW[rho, sig, i1, i2, i3] Eps[rho, sig, alpha, beta] FW[alpha, beta, i1, i4, i5]), mu], nu]); |
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483 | |
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484 | TG2m[mu_, nu_] := (-del[del[(-1/4 FG[rho, sig, a1, a2, a3] FG[rho, sig, a1, a4, a5]),mu],nu]); |
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485 | TG2mAxial[mu_, nu_] := (-del[del[(-1/8 FG[rho, sig, a1, a2, a3] Eps[rho, sig, alpha, beta] FG[alpha, beta, a1, a4, a5]), mu], nu]); |
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486 | |
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487 | LG2m := X2[mu,nu] (-ka2/Lambda^3 TA2mAxial[mu,nu] -kv2/Lambda^3 TW2mAxial[mu,nu] -kg2/Lambda^3 TG2mAxial[mu,nu]); |
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488 | LGHD := X2[mu,nu] (-ka1/Lambda^3 TA2m[mu,nu] -kv1/Lambda^3 TW2m[mu,nu] -kg1/Lambda^3 TG2m[mu,nu]); |
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489 | |
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490 | (*****************************************************************************************) |
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491 | (* Spin-1 - vector and pseudo-vector *****************************************************) |
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492 | (*****************************************************************************************) |
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493 | |
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494 | (* Defining one arbitrary coupling of the spin-1 with W+ W- *) |
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495 | |
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496 | LBprightPsVec = |
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497 | kfbu bfu X1[mu] uqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjP[x,r].uq[r,n,i] + |
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498 | kfbd bfd X1[mu] dqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjP[x,r].dq[r,n,i]; |
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499 | |
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500 | LBpleftPsVec = |
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501 | kfbu bfu X1[mu] uqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjM[x,r].uq[r,n,i] + |
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502 | kfbd bfd X1[mu] dqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjM[x,r].dq[r,n,i]; |
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503 | |
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504 | LBprightVec = |
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505 | kfau afu X1[mu] uqbar[s,n,i].Ga[mu,s,v].ProjP[v,r].uq[r,n,i] + |
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506 | kfad afd X1[mu] dqbar[s,n,i].Ga[mu,s,v].ProjP[v,r].dq[r,n,i]; |
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507 | |
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508 | LBpleftVec = |
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509 | kfau afu X1[mu] uqbar[s,n,i].Ga[mu,s,v].ProjM[v,r].uq[r,n,i] + |
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510 | kfad afd X1[mu] dqbar[s,n,i].Ga[mu,s,v].ProjM[v,r].dq[r,n,i]; |
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511 | |
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512 | |
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513 | LF= LBprightVec + LBpleftVec + LBprightPsVec + LBpleftPsVec; |
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514 | |
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515 | |
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516 | LWW=( I kv1 gwwz(del[Wbar[nu], mu] - del[Wbar[mu], nu]) W[mu] X1[nu] - I kv1 gwwz Wbar[mu] X1[nu] (del[W[nu], mu] - del[W[mu], nu]) |
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517 | +I kv2 gwwz Wbar[mu]W[nu]FS[X1,mu,nu] |
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518 | -kv3 Wbar[mu]W[nu](del[X1[nu],mu]+del[X1[mu],nu]) |
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519 | -kv5 Eps[mu,nu,rho,sig](Wbar[mu]del[W[nu],rho]-del[Wbar[mu],rho]W[nu])X1[sig] |
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520 | +I kv4 Wbar[mu]W[nu](1/2)Eps[mu,nu,rho,sig](del[X1[sig],rho]-del[X1[rho],sig]) |
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521 | ); |
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522 | LZZ= -kv3 X1[mu]del[Z[mu],nu]Z[nu]- kv5 Eps[mu,nu,rho,sig]X1[mu]Z[nu]del[Z[sig],rho]; |
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523 | |
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524 | (* LWW and LZZ based on the reference: K.Hagiwara et al, Nucl. Phys. B282 (1987) 253-307 *) |
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525 | (*****************************************************************************************) |
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526 | |
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527 | Ltot:= LSM + LF +LagRS + LG0 + LWW + LZZ + LGHD + LG2m; |
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528 | |
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