1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file for the Standard model ******)
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3 | (****** extended with a fermionic SU(2) triplet which give mass ******)
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4 | (****** to one neutrino via a type III seesaw mechanism ******)
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5 | (****** ******)
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6 | (****** Authors: C. Biggio, F. Bonnet ******)
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7 | (****** ******)
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8 | (****** Choose whether Feynman gauge is desired. ******)
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9 | (****** If set to False, unitary gauge is assumed. ****)
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10 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
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11 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
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12 | (***************************************************************************************************************)
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13 |
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14 | M$ModelName = "typeIIIseesaw1";
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15 |
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16 |
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17 | M$Information = {Authors -> {"C.Biggio", "F. Bonnet"},
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18 | Version -> "1.1",
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19 | Date -> "16. 03. 2011",
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20 | Institutions -> {"IFAE/UAB", "INFN Padova"},
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21 | Emails -> {"biggio@ifae.es", "bonnet@pd.infn.it"},
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22 | URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/TypeIIIseesaw"};
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23 |
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24 | FeynmanGauge = False;
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25 |
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26 |
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27 | (******* Index definitions ********)
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28 |
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29 | IndexRange[ Index[Generation] ] = Range[3]
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30 |
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31 | IndexRange[ Index[LeptonGeneration] ] = Range[4]
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32 |
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33 | IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
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34 |
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35 | IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
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36 |
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37 | IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
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38 |
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39 |
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40 | IndexStyle[Colour, i]
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41 |
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42 | IndexStyle[Generation, f]
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43 |
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44 | IndexStyle[LeptonGeneration, fl]
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45 |
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46 | IndexStyle[Gluon ,a]
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47 |
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48 | IndexStyle[SU2W ,k]
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49 |
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50 |
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51 | (******* Gauge parameters (for FeynArts) ********)
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52 |
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53 | GaugeXi[ V[1] ] = GaugeXi[A];
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54 | GaugeXi[ V[2] ] = GaugeXi[Z];
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55 | GaugeXi[ V[3] ] = GaugeXi[W];
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56 | GaugeXi[ V[4] ] = GaugeXi[G];
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57 | GaugeXi[ S[1] ] = 1;
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58 | GaugeXi[ S[2] ] = GaugeXi[Z];
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59 | GaugeXi[ S[3] ] = GaugeXi[W];
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60 | GaugeXi[ U[1] ] = GaugeXi[A];
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61 | GaugeXi[ U[2] ] = GaugeXi[Z];
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62 | GaugeXi[ U[31] ] = GaugeXi[W];
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63 | GaugeXi[ U[32] ] = GaugeXi[W];
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64 | GaugeXi[ U[4] ] = GaugeXi[G];
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65 |
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66 |
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67 | (**************** Parameters *************)
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68 |
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69 | M$Parameters = {
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70 |
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71 | (* External parameters *)
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72 |
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73 | \[Alpha]EWM1== {
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74 | ParameterType -> External,
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75 | BlockName -> SMINPUTS,
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76 | ParameterName -> aEWM1,
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77 | InteractionOrder -> {QED, -2},
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78 | Value -> 127.9,
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79 | Description -> "Inverse of the electroweak coupling constant"},
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80 |
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81 | Gf == {
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82 | ParameterType -> External,
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83 | BlockName -> SMINPUTS,
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84 | TeX -> Subscript[G, f],
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85 | InteractionOrder -> {QED, 2},
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86 | Value -> 1.16639 * 10^(-5),
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87 | Description -> "Fermi constant"},
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88 |
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89 | \[Alpha]S == {
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90 | ParameterType -> External,
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91 | BlockName -> SMINPUTS,
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92 | TeX -> Subscript[\[Alpha], s],
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93 | ParameterName -> aS,
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94 | InteractionOrder -> {QCD, 2},
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95 | Value -> 0.118,
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96 | Description -> "Strong coupling constant at the Z pole."},
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97 |
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98 | ymc == {
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99 | ParameterType -> External,
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100 | BlockName -> YUKAWA,
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101 | Value -> 1.42,
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102 | OrderBlock -> {4},
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103 | Description -> "Charm Yukawa mass"},
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104 |
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105 | ymb == {
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106 | ParameterType -> External,
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107 | BlockName -> YUKAWA,
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108 | Value -> 4.7,
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109 | OrderBlock -> {5},
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110 | Description -> "Bottom Yukawa mass"},
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111 |
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112 | ymt == {
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113 | ParameterType -> External,
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114 | BlockName -> YUKAWA,
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115 | Value -> 174.3,
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116 | OrderBlock -> {6},
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117 | Description -> "Top Yukawa mass"},
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118 |
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119 | mv1 == {
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120 | ParameterType -> External,
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121 | BlockName -> NEWMASSES,
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122 | Value -> 0,
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123 | OrderBlock -> {1},
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124 | Description -> "nu1 mass"},
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125 |
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126 | mv2 == {
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127 | ParameterType -> External,
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128 | BlockName -> NEWMASSES,
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129 | Value -> 0,
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130 | OrderBlock -> {2},
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131 | Description -> "nu2 mass"},
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132 |
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133 | mv3 == {
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134 | ParameterType -> External,
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135 | BlockName -> NEWMASSES,
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136 | Value -> 0,
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137 | OrderBlock -> {3},
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138 | Description -> "nu3 mass"},
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139 |
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140 | yme == {
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141 | ParameterType -> External,
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142 | BlockName -> YUKAWA,
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143 | Value -> 0,
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144 | OrderBlock -> {13},
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145 | Description -> "Electron Yukawa mass"},
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146 |
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147 | ymm == {
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148 | ParameterType -> External,
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149 | BlockName -> YUKAWA,
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150 | Value -> 0,
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151 | OrderBlock -> {14},
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152 | Description -> "Muon Yukawa mass"},
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153 |
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154 | ymtau == {
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155 | ParameterType -> External,
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156 | BlockName -> YUKAWA,
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157 | Value -> 1.777,
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158 | OrderBlock -> {15},
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159 | Description -> "Tau Yukawa mass"},
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160 |
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161 | cabi == {
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162 | TeX -> Subscript[\[Theta], c],
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163 | ParameterType -> External,
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164 | BlockName -> CKMBLOCK,
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165 | Value -> 0.227736,
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166 | OrderBlock -> {1},
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167 | Description -> "Cabibbo angle"},
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168 |
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169 | mtr == {
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170 | ParameterType -> External,
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171 | BlockName -> NEWMASSES,
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172 | Value -> 100.8,
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173 | OrderBlock -> {4},
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174 | Description -> "Neutral triplet Majorana mass"},
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175 |
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176 | mtrm == {
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177 | ParameterType -> External,
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178 | BlockName -> NEWMASSES,
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179 | Value -> 101,
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180 | OrderBlock -> {5},
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181 | Description -> "Charged triplet Majorana mass"},
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182 |
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183 | Ve == {
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184 | ParameterType -> External,
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185 | BlockName -> MIXING,
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186 | Value -> 0,
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187 | OrderBlock -> {1},
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188 | Description -> "Electron mixing"},
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189 |
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190 | Vm == {
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191 | ParameterType -> External,
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192 | BlockName -> MIXING,
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193 | Value -> 0.063,
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194 | OrderBlock -> {2},
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195 | Description -> "Muon mixing"},
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196 |
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197 | Vtt == {
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198 | ParameterType -> External,
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199 | BlockName -> MIXING,
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200 | Value -> 0,
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201 | OrderBlock -> {3},
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202 | Description -> "Tau mixing"},
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203 |
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204 | theta13 == {
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205 | TeX -> Subscript[\[Theta], 13],
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206 | ParameterType -> External,
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207 | BlockName -> CKMBLOCK,
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208 | Value -> 0.1,
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209 | OrderBlock -> {2},
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210 | Description -> "PMNS theta13"},
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211 |
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212 | theta12 == {
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213 | TeX -> Subscript[\[Theta], 12],
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214 | ParameterType -> External,
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215 | BlockName -> CKMBLOCK,
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216 | Value -> 0.60,
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217 | OrderBlock -> {3},
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218 | Description -> "PMNS solar angle"},
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219 |
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220 | theta23 == {
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221 | TeX -> Subscript[\[Theta], 23],
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222 | ParameterType -> External,
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223 | BlockName -> CKMBLOCK,
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224 | Value -> 0.75,
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225 | OrderBlock -> {4},
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226 | Description -> "PMNS athmospheric angle"},
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227 |
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228 |
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229 |
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230 | (* Internal Parameters *)
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231 |
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232 | \[Alpha]EW == {
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233 | ParameterType -> Internal,
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234 | Value -> 1/\[Alpha]EWM1,
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235 | TeX -> Subscript[\[Alpha], EW],
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236 | ParameterName -> aEW,
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237 | InteractionOrder -> {QED, 2},
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238 | Description -> "Electroweak coupling contant"},
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239 |
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240 |
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241 | MW == {
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242 | ParameterType -> Internal,
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243 | Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
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244 | TeX -> Subscript[M, W],
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245 | Description -> "W mass"},
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246 |
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247 | sw2 == {
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248 | ParameterType -> Internal,
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249 | Value -> 1-(MW/MZ)^2,
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250 | Description -> "Squared Sin of the Weinberg angle"},
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251 |
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252 | ee == {
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253 | TeX -> e,
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254 | ParameterType -> Internal,
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255 | Value -> Sqrt[4 Pi \[Alpha]EW],
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256 | InteractionOrder -> {QED, 1},
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257 | Description -> "Electric coupling constant"},
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258 |
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259 | cw == {
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260 | TeX -> Subscript[c, w],
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261 | ParameterType -> Internal,
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262 | Value -> Sqrt[1 - sw2],
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263 | Description -> "Cos of the Weinberg angle"},
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264 |
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265 | sw == {
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266 | TeX -> Subscript[s, w],
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267 | ParameterType -> Internal,
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268 | Value -> Sqrt[sw2],
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269 | Description -> "Sin of the Weinberg angle"},
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270 |
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271 | gw == {
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272 | TeX -> Subscript[g, w],
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273 | ParameterType -> Internal,
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274 | Value -> ee / sw,
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275 | InteractionOrder -> {QED, 1},
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276 | Description -> "Weak coupling constant"},
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277 |
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278 | g1 == {
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279 | TeX -> Subscript[g, 1],
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280 | ParameterType -> Internal,
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281 | Value -> ee / cw,
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282 | InteractionOrder -> {QED, 1},
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283 | Description -> "U(1)Y coupling constant"},
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284 |
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285 | gs == {
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286 | TeX -> Subscript[g, s],
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287 | ParameterType -> Internal,
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288 | Value -> Sqrt[4 Pi \[Alpha]S],
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289 | InteractionOrder -> {QCD, 1},
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290 | ParameterName -> G,
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291 | Description -> "Strong coupling constant"},
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292 |
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293 | v == {
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294 | ParameterType -> Internal,
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295 | Value -> 2*MW*sw/ee,
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296 | InteractionOrder -> {QED, -1},
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297 | Description -> "Higgs VEV"},
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298 |
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299 | \[Lambda] == {
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300 | ParameterType -> Internal,
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301 | Value -> MH^2/(2*v^2),
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302 | InteractionOrder -> {QED, 2},
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303 | ParameterName -> lam,
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304 | Description -> "Higgs quartic coupling"},
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305 |
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306 | muH == {
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307 | ParameterType -> Internal,
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308 | Value -> Sqrt[v^2 \[Lambda]],
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309 | TeX -> \[Mu],
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310 | Description -> "Coefficient of the quadratic piece of the Higgs potential"},
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311 |
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312 | yl == {
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313 | TeX -> Superscript[y, l],
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314 | Indices -> {Index[LeptonGeneration]},
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315 | AllowSummation -> True,
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316 | ParameterType -> Internal,
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317 | Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v, yl[4] -> 0},
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318 | ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau, yl[4] -> useless},
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319 | InteractionOrder -> {QED, 1},
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320 | ComplexParameter -> False,
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321 | Description -> "Standard Model lepton Yukawa coupling"},
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322 |
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323 | yu == {
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324 | TeX -> Superscript[y, u],
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325 | Indices -> {Index[Generation]},
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326 | AllowSummation -> True,
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327 | ParameterType -> Internal,
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328 | Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
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329 | ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
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330 | InteractionOrder -> {QED, 1},
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331 | ComplexParameter -> False,
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332 | Description -> "U-quark Yukawa coupling"},
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333 |
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334 | yd == {
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335 | TeX -> Superscript[y, d],
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336 | Indices -> {Index[Generation]},
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337 | AllowSummation -> True,
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338 | ParameterType -> Internal,
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339 | Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
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340 | ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
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341 | InteractionOrder -> {QED, 1},
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342 | ComplexParameter -> False,
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343 | Description -> "D-quark Yukawa coupling"},
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344 |
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345 | (* N. B. : only Cabibbo mixing! *)
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346 | CKM == {
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347 | Indices -> {Index[Generation], Index[Generation]},
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348 | TensorClass -> CKM,
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349 | Unitary -> True,
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350 | Value -> {CKM[1,1] -> Cos[cabi],
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351 | CKM[1,2] -> Sin[cabi],
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352 | CKM[1,3] -> 0,
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353 | CKM[2,1] -> -Sin[cabi],
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354 | CKM[2,2] -> Cos[cabi],
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355 | CKM[2,3] -> 0,
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356 | CKM[3,1] -> 0,
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357 | CKM[3,2] -> 0,
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358 | CKM[3,3] -> 1},
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359 | Description -> "CKM-Matrix"},
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360 |
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361 | (* N. B. : no phases! *)
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362 | PMNS == {
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363 | Indices -> {Index[Generation], Index[Generation]},
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364 | TensorClass -> CKM,
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365 | Unitary -> True,
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366 | Value -> {PMNS[1,1] -> Cos[theta13] Cos[theta12],
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367 | PMNS[1,2] -> Cos[theta13] Sin[theta12],
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368 | PMNS[1,3] -> Sin[theta13],
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369 | PMNS[2,1] -> -Cos[theta23]*Sin[theta12] - Sin[theta23]*Sin[theta13]*Cos[theta12],
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370 | PMNS[2,2] -> Cos[theta23]*Cos[theta12] - Sin[theta23]*Sin[theta13]*Sin[theta12],
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371 | PMNS[2,3] -> Sin[theta23]*Cos[theta13],
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372 | PMNS[3,1] -> Sin[theta23]*Sin[theta12] - Cos[theta23]*Sin[theta13]*Cos[theta12],
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373 | PMNS[3,2] -> -Sin[theta23]*Cos[theta12] - Cos[theta23]*Sin[theta13]*Sin[theta12],
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374 | PMNS[3,3] -> Cos[theta23]*Cos[theta13]},
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375 | Description -> "PMNS-Matrix"},
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376 |
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377 |
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378 | (***********************************************)
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379 | (********** COUPLINGS **********)
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380 | (***********************************************)
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381 |
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382 | gCCL == {
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383 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
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384 | TensorClass -> CKM,
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385 | ComplexParameter -> False,
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386 | Value -> {gCCL[1,1] -> Cos[theta12] Cos[theta13] + 1/2 (Ve^2 Cos[theta12] Cos[theta13] +
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387 | Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
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388 | Ve Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
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389 | gCCL[1,2] -> Cos[theta13] Sin[theta12] + 1/2 (Ve^2 Cos[theta13] Sin[theta12] +
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390 | Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
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391 | Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
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392 | gCCL[1,3] -> Sin[theta13] + 1/2 (Ve Vtt Cos[theta13] Cos[theta23] + Ve^2 Sin[theta13] + Ve Vm Cos[theta13] Sin[theta23]),
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393 | gCCL[1,4] -> - Ve,
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394 | gCCL[2,1] -> -Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23] +
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395 | 1/2 (Ve Vm Cos[theta12] Cos[theta13] + Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
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396 | Sin[theta12] Sin[theta23]) + Vm^2 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
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397 | gCCL[2,2] -> Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23] +
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398 | 1/2 (Ve Vm Cos[theta13] Sin[theta12] + Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
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399 | Vm^2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
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400 | gCCL[2,3] -> Cos[theta13] Sin[theta23] + 1/2 (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] + Vm^2 Cos[theta13] Sin[theta23]),
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401 | gCCL[2,4] -> - Vm,
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402 | gCCL[3,1] -> -Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23] + 1/2 (Ve Vtt Cos[theta12] Cos[theta13] +
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403 | Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
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404 | Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
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405 | gCCL[3,2] -> -Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23] + 1/2 (Ve Vtt Cos[theta13] Sin[theta12] +
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406 | Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
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407 | Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
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408 | gCCL[3,3] -> Cos[theta13] Cos[theta23] + 1/2 (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] + Vm Vtt Cos[theta13] Sin[theta23]),
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409 | gCCL[3,4] -> - Vtt,
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410 | gCCL[4,1] -> 0,
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411 | gCCL[4,2] -> 0,
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412 | gCCL[4,3] -> 0,
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413 | gCCL[4,4] -> Sqrt[2] (1 + 1/2 (-Ve^2 - Vm^2 - Vtt^2))},
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414 | Description -> "gCCL-Matrix"},
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415 |
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416 |
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417 |
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418 |
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419 | gCCR == {
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420 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
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421 | TensorClass -> CKM,
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422 | ComplexParameter -> False,
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423 | Value -> {gCCR[1,1] -> 0,
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424 | gCCR[1,2] -> 0,
|
---|
425 | gCCR[1,3] -> 0,
|
---|
426 | gCCR[1,4] -> -Sqrt[2]*yme/mtr*Ve,
|
---|
427 | gCCR[2,1] -> 0,
|
---|
428 | gCCR[2,2] -> 0,
|
---|
429 | gCCR[2,3] -> 0,
|
---|
430 | gCCR[2,4] -> -Sqrt[2]*ymm/mtr*Vm,
|
---|
431 | gCCR[3,1] -> 0,
|
---|
432 | gCCR[3,2] -> 0,
|
---|
433 | gCCR[3,3] -> 0,
|
---|
434 | gCCR[3,4] -> -Sqrt[2]*ymtau/mtr*Vtt,
|
---|
435 | gCCR[4,1] -> -( Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
436 | Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
437 | gCCR[4,2] -> - (Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
438 | Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
439 | gCCR[4,3] -> - (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]),
|
---|
440 | gCCR[4,4] -> 1 + 1/2 (-Ve^2 - Vm^2 - Vtt^2)},
|
---|
441 | Description -> "gCCR-Matrix"},
|
---|
442 |
|
---|
443 |
|
---|
444 |
|
---|
445 |
|
---|
446 |
|
---|
447 | gNCL == {
|
---|
448 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
449 | TensorClass -> CKM,
|
---|
450 | Hermitian -> True,
|
---|
451 | Value -> {gNCL[1,1] -> 1/2-cw^2-Ve^2,
|
---|
452 | gNCL[1,2] -> Ve*Vm,
|
---|
453 | gNCL[1,3] -> Ve*Vtt,
|
---|
454 | gNCL[1,4] -> Ve/Sqrt[2],
|
---|
455 | gNCL[2,1] -> Ve*Vm,
|
---|
456 | gNCL[2,2] -> 1/2-cw^2-Vm^2,
|
---|
457 | gNCL[2,3] -> Vm*Vtt,
|
---|
458 | gNCL[2,4] -> Vm/Sqrt[2],
|
---|
459 | gNCL[3,1] -> Ve*Vtt,
|
---|
460 | gNCL[3,2] -> Vm*Vtt,
|
---|
461 | gNCL[3,3] -> 1/2-cw^2-Vtt^2,
|
---|
462 | gNCL[3,4] -> Vtt/Sqrt[2],
|
---|
463 | gNCL[4,1] -> Ve/Sqrt[2],
|
---|
464 | gNCL[4,2] -> Vm/Sqrt[2],
|
---|
465 | gNCL[4,3] -> Vtt/Sqrt[2],
|
---|
466 | gNCL[4,4] -> Ve^2+Vm^2+Vtt^2-cw^2},
|
---|
467 | Description -> "gNCL-Matrix"},
|
---|
468 |
|
---|
469 |
|
---|
470 |
|
---|
471 | gNCR == {
|
---|
472 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
473 | TensorClass -> CKM,
|
---|
474 | Hermitian -> True,
|
---|
475 | Value -> {gNCR[1,1] -> 1-cw^2,
|
---|
476 | gNCR[1,2] -> 0,
|
---|
477 | gNCR[1,3] -> 0,
|
---|
478 | gNCR[1,4] -> Sqrt[2]*yme/mtr*Ve,
|
---|
479 | gNCR[2,1] -> 0,
|
---|
480 | gNCR[2,2] -> 1-cw^2,
|
---|
481 | gNCR[2,3] -> 0,
|
---|
482 | gNCR[2,4] -> Sqrt[2]*ymm/mtr*Vm,
|
---|
483 | gNCR[3,1] -> 0,
|
---|
484 | gNCR[3,2] -> 0,
|
---|
485 | gNCR[3,3] -> 1-cw^2,
|
---|
486 | gNCR[3,4] -> Sqrt[2]*ymtau/mtr*Vtt,
|
---|
487 | gNCR[4,1] -> Sqrt[2]*yme/mtr*Ve,
|
---|
488 | gNCR[4,2] -> Sqrt[2]*ymm/mtr*Vm,
|
---|
489 | gNCR[4,3] -> Sqrt[2]*ymtau/mtr*Vtt,
|
---|
490 | gNCR[4,4] -> -cw^2},
|
---|
491 | Description -> "gNCR-Matrix"},
|
---|
492 |
|
---|
493 |
|
---|
494 |
|
---|
495 |
|
---|
496 |
|
---|
497 |
|
---|
498 | gNCnu == {
|
---|
499 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
500 | TensorClass -> CKM,
|
---|
501 | Hermitian -> True,
|
---|
502 | Value -> {gNCnu[1,1] -> 1 - Cos[theta12] Cos[theta13] (Ve^2 Cos[theta12] Cos[theta13] +
|
---|
503 | Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
504 | Ve Vm (-Cos[theta23] Sin[theta12] -
|
---|
505 | Cos[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] -
|
---|
506 | Cos[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta12] Cos[theta13] +
|
---|
507 | Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
508 | Sin[theta12] Sin[theta23]) + Vm^2 (-Cos[theta23] Sin[theta12] -
|
---|
509 | Cos[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
510 | Sin[theta12] Sin[theta23]) (Ve Vtt Cos[theta12] Cos[theta13] +
|
---|
511 | Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
512 | Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
513 | gNCnu[1,2] -> -Cos[theta13] Sin[theta12] (Ve^2 Cos[theta12] Cos[theta13] +
|
---|
514 | Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
515 | Ve Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) - (Cos[theta12] Cos[theta23] -
|
---|
516 | Sin[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta12] Cos[theta13] +
|
---|
517 | Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
518 | Vm^2 (-Cos[theta23] Sin[theta12] -
|
---|
519 | Cos[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
520 | Cos[theta12] Sin[theta23]) (Ve Vtt Cos[theta12] Cos[theta13] +
|
---|
521 | Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
522 | Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
523 | gNCnu[1,3] -> -Sin[theta13] (Ve^2 Cos[theta12] Cos[theta13] + Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
524 | Sin[theta12] Sin[theta23]) + Ve Vm (-Cos[theta23] Sin[theta12] -
|
---|
525 | Cos[theta12] Sin[theta13] Sin[theta23])) - Cos[theta13] Sin[theta23] (Ve Vm Cos[theta12] Cos[theta13] +
|
---|
526 | Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
527 | Vm^2 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) -
|
---|
528 | Cos[theta13] Cos[theta23] (Ve Vtt Cos[theta12] Cos[theta13] +
|
---|
529 | Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
530 | Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
531 | gNCnu[1,4] -> Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
532 | Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]),
|
---|
533 | gNCnu[2,1] -> -Cos[theta12] Cos[theta13] (Ve^2 Cos[theta13] Sin[theta12] +
|
---|
534 | Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
535 | Ve Vm (Cos[theta12] Cos[theta23] -
|
---|
536 | Sin[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] -
|
---|
537 | Cos[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta13] Sin[theta12] +
|
---|
538 | Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
539 | Vm^2 (Cos[theta12] Cos[theta23] -
|
---|
540 | Sin[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
541 | Sin[theta12] Sin[theta23]) (Ve Vtt Cos[theta13] Sin[theta12] +
|
---|
542 | Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
543 | Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
544 | gNCnu[2,2] -> 1 - Cos[theta13] Sin[theta12] (Ve^2 Cos[theta13] Sin[theta12] +
|
---|
545 | Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
546 | Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])) - (Cos[theta12] Cos[theta23] -
|
---|
547 | Sin[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta13] Sin[theta12] +
|
---|
548 | Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
549 | Vm^2 (Cos[theta12] Cos[theta23] -
|
---|
550 | Sin[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
551 | Cos[theta12] Sin[theta23]) (Ve Vtt Cos[theta13] Sin[theta12] +
|
---|
552 | Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
553 | Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
554 | gNCnu[2,3] -> -Sin[theta13] (Ve^2 Cos[theta13] Sin[theta12] +
|
---|
555 | Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
556 | Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])) -
|
---|
557 | Cos[theta13] Sin[theta23] (Ve Vm Cos[theta13] Sin[theta12] +
|
---|
558 | Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
559 | Vm^2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])) -
|
---|
560 | Cos[theta13] Cos[theta23] (Ve Vtt Cos[theta13] Sin[theta12] +
|
---|
561 | Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
562 | Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
563 | gNCnu[2,4] -> Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
564 | Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]),
|
---|
565 | gNCnu[3,1] -> -Cos[theta12] Cos[theta13] (Ve Vtt Cos[theta13] Cos[theta23] + Ve^2 Sin[theta13] +
|
---|
566 | Ve Vm Cos[theta13] Sin[theta23]) - (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] +
|
---|
567 | Vm Vtt Cos[theta13] Sin[theta23]) (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
568 | Sin[theta12] Sin[theta23]) - (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] +
|
---|
569 | Vm^2 Cos[theta13] Sin[theta23]) (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]),
|
---|
570 | gNCnu[3,2] -> -Cos[theta13] Sin[theta12] (Ve Vtt Cos[theta13] Cos[theta23] + Ve^2 Sin[theta13] +
|
---|
571 | Ve Vm Cos[theta13] Sin[theta23]) - (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
572 | Cos[theta12] Sin[theta23]) (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] +
|
---|
573 | Vm Vtt Cos[theta13] Sin[theta23]) - (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] +
|
---|
574 | Vm^2 Cos[theta13] Sin[theta23]) (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]),
|
---|
575 | gNCnu[3,3] -> 1 - Sin[theta13] (Ve Vtt Cos[theta13] Cos[theta23] +
|
---|
576 | Ve^2 Sin[theta13] + Ve Vm Cos[theta13] Sin[theta23]) -
|
---|
577 | Cos[theta13] Sin[theta23] (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] +
|
---|
578 | Vm^2 Cos[theta13] Sin[theta23]) -
|
---|
579 | Cos[theta13] Cos[theta23] (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] +
|
---|
580 | Vm Vtt Cos[theta13] Sin[theta23]),
|
---|
581 | gNCnu[3,4] -> Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23],
|
---|
582 | gNCnu[4,1] -> Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
583 | Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]),
|
---|
584 | gNCnu[4,2] -> Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
585 | Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]),
|
---|
586 | gNCnu[4,3] -> Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23],
|
---|
587 | gNCnu[4,4] -> Ve^2 + Vm^2 + Vtt^2},
|
---|
588 | Description -> "gNCnu-Matrix"},
|
---|
589 |
|
---|
590 |
|
---|
591 |
|
---|
592 |
|
---|
593 | gHlR == {
|
---|
594 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
595 | TensorClass -> CKM,
|
---|
596 | ComplexParameter -> False,
|
---|
597 | Value -> {gHlR[1,1] -> yme/v*(1-3*Ve^2),
|
---|
598 | gHlR[2,1] -> -3*yme/v*Ve*Vm,
|
---|
599 | gHlR[3,1] -> -3*yme/v*Ve*Vtt,
|
---|
600 | gHlR[4,1] -> Sqrt[2]*yme/v*Ve,
|
---|
601 | gHlR[1,2] -> -3*ymm/v*Ve*Vm,
|
---|
602 | gHlR[2,2] -> ymm/v*(1-3*Vm^2),
|
---|
603 | gHlR[3,2] -> -3*ymm/v*Vm*Vtt,
|
---|
604 | gHlR[4,2] -> Sqrt[2]*ymm/v*Vm,
|
---|
605 | gHlR[1,3] -> -3*ymtau/v*Ve*Vtt,
|
---|
606 | gHlR[2,3] -> -3*ymtau/v*Vm*Vtt,
|
---|
607 | gHlR[3,3] -> ymtau/v*(1-3*Vtt^2),
|
---|
608 | gHlR[4,3] -> Sqrt[2]*ymtau/v*Vtt,
|
---|
609 | gHlR[1,4] -> Sqrt[2]*mtr/v*Ve*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*yme^2/v/mtr*Ve,
|
---|
610 | gHlR[2,4] -> Sqrt[2]*mtr/v*Vm*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymm^2/v/mtr*Vm,
|
---|
611 | gHlR[3,4] -> Sqrt[2]*mtr/v*Vtt*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymtau^2/v/mtr*Vtt,
|
---|
612 | gHlR[4,4] -> 2*mtr/v*(Ve^2+Vm^2+Vtt^2)},
|
---|
613 | InteractionOrder -> {QED, 1},
|
---|
614 | Description -> "gHlR-Matrix"},
|
---|
615 |
|
---|
616 |
|
---|
617 |
|
---|
618 |
|
---|
619 | getalR == {
|
---|
620 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
621 | TensorClass -> CKM,
|
---|
622 | ComplexParameter -> False,
|
---|
623 | Value -> {getalR[1,1] -> yme/v*(1+Ve^2),
|
---|
624 | getalR[2,1] -> yme/v*Ve*Vm,
|
---|
625 | getalR[3,1] -> yme/v*Ve*Vtt,
|
---|
626 | getalR[4,1] -> Sqrt[2]*yme/v*Ve,
|
---|
627 | getalR[1,2] -> ymm/v*Ve*Vm,
|
---|
628 | getalR[2,2] -> ymm/v*(1+Vm^2),
|
---|
629 | getalR[3,2] -> ymm/v*Vm*Vtt,
|
---|
630 | getalR[4,2] -> Sqrt[2]*ymm/v*Vm,
|
---|
631 | getalR[1,3] -> ymtau/v*Ve*Vtt,
|
---|
632 | getalR[2,3] -> ymtau/v*Vm*Vtt,
|
---|
633 | getalR[3,3] -> ymtau/v*(1+Vtt^2),
|
---|
634 | getalR[4,3] -> Sqrt[2]*ymtau/v*Vtt,
|
---|
635 | getalR[1,4] -> -Sqrt[2]*mtr/v*Ve*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*yme^2/v/mtr*Ve,
|
---|
636 | getalR[2,4] -> -Sqrt[2]*mtr/v*Vm*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymm^2/v/mtr*Vm,
|
---|
637 | getalR[3,4] -> -Sqrt[2]*mtr/v*Vtt*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymtau^2/v/mtr*Vtt,
|
---|
638 | getalR[4,4] -> -2*mtr/v*(Ve^2+Vm^2+Vtt^2)},
|
---|
639 | InteractionOrder -> {QED, 1},
|
---|
640 | Description -> "getalR-Matrix"},
|
---|
641 |
|
---|
642 |
|
---|
643 |
|
---|
644 |
|
---|
645 | gHnuR == {
|
---|
646 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
647 | TensorClass -> CKM,
|
---|
648 | ComplexParameter -> False,
|
---|
649 | Value -> {gHnuR[1,1] -> Sqrt[2]/v*mv1,
|
---|
650 | gHnuR[2,1] -> 0,
|
---|
651 | gHnuR[3,1] -> 0,
|
---|
652 | gHnuR[4,1] -> Sqrt[2]/v*mv1*(Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
653 | Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
654 | gHnuR[1,2] -> 0,
|
---|
655 | gHnuR[2,2] -> Sqrt[2]/v*mv2,
|
---|
656 | gHnuR[3,2] -> 0,
|
---|
657 | gHnuR[4,2] -> Sqrt[2]/v*mv2*(Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
658 | Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
659 | gHnuR[1,3] -> 0,
|
---|
660 | gHnuR[2,3] -> 0,
|
---|
661 | gHnuR[3,3] -> Sqrt[2]/v*mv3,
|
---|
662 | gHnuR[4,3] -> Sqrt[2]/v*mv3*(Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]),
|
---|
663 | gHnuR[1,4] -> Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Sin[theta12] (-Vm Cos[theta23] + Vtt Sin[theta23]) +
|
---|
664 | Cos[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
|
---|
665 | gHnuR[2,4] -> Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Cos[theta12] (Vm Cos[theta23] - Vtt Sin[theta23]) +
|
---|
666 | Sin[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
|
---|
667 | gHnuR[3,4] -> Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Ve Sin[theta13] + Cos[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))),
|
---|
668 | gHnuR[4,4] -> Sqrt[2]*mtr/v*(Ve^2+Vm^2+Vtt^2)},
|
---|
669 | InteractionOrder -> {QED, 1},
|
---|
670 | Description -> "gHnuR-Matrix"},
|
---|
671 |
|
---|
672 |
|
---|
673 |
|
---|
674 |
|
---|
675 |
|
---|
676 | getanuR == {
|
---|
677 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
678 | TensorClass -> CKM,
|
---|
679 | ComplexParameter -> False,
|
---|
680 | Value -> {getanuR[1,1] -> -Sqrt[2]/v*mv1,
|
---|
681 | getanuR[2,1] -> 0,
|
---|
682 | getanuR[3,1] -> 0,
|
---|
683 | getanuR[4,1] -> -(Sqrt[2]/v*mv1*(Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
684 | Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]))),
|
---|
685 | getanuR[1,2] -> 0,
|
---|
686 | getanuR[2,2] -> -Sqrt[2]/v*mv2,
|
---|
687 | getanuR[3,2] -> 0,
|
---|
688 | getanuR[4,2] -> -(Sqrt[2]/v*mv2*(Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
689 | Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
|
---|
690 | getanuR[1,3] -> 0,
|
---|
691 | getanuR[2,3] -> 0,
|
---|
692 | getanuR[3,3] -> -Sqrt[2]/v*mv3,
|
---|
693 | getanuR[4,3] -> -(Sqrt[2]/v*mv3*(Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23])),
|
---|
694 | getanuR[1,4] -> -(Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Sin[theta12] (-Vm Cos[theta23] + Vtt Sin[theta23]) +
|
---|
695 | Cos[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))))),
|
---|
696 | getanuR[2,4] -> -(Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Cos[theta12] (Vm Cos[theta23] - Vtt Sin[theta23]) +
|
---|
697 | Sin[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))))),
|
---|
698 | getanuR[3,4] -> -(Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Ve Sin[theta13] + Cos[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
|
---|
699 | getanuR[4,4] -> -(Sqrt[2]*mtr/v*(Ve^2+Vm^2+Vtt^2))},
|
---|
700 | InteractionOrder -> {QED, 1},
|
---|
701 | Description -> "getanuR-Matrix"},
|
---|
702 |
|
---|
703 |
|
---|
704 |
|
---|
705 | gPhiL == {
|
---|
706 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
707 | TensorClass -> CKM,
|
---|
708 | ComplexParameter -> False,
|
---|
709 | Value -> {gPhiL[1,1] -> Sqrt[2]/v*yme*((1 - Ve^2/2) Cos[theta12] Cos[theta13] -
|
---|
710 | 1/2 Ve Vtt (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13]) -
|
---|
711 | 1/2 Ve Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
712 | gPhiL[1,2] -> Sqrt[2]/v*yme*((1 - Ve^2/2) Cos[theta13] Sin[theta12] -
|
---|
713 | 1/2 Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) -
|
---|
714 | 1/2 Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
715 | gPhiL[1,3] -> Sqrt[2]/v*yme*( (1 - Ve^2/2) Sin[theta13] -
|
---|
716 | 1/2 Ve Vtt Cos[theta13] Cos[theta23] - 1/2 Ve Vm Cos[theta13] Sin[theta23] ),
|
---|
717 | gPhiL[1,4] -> Sqrt[2]/v*yme Ve,
|
---|
718 | gPhiL[2,1] -> Sqrt[2]/v*ymm*( (1 - Vm^2/2) (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]) -
|
---|
719 | 1/2 Ve Vm Cos[theta12] Cos[theta13] -
|
---|
720 | 1/2 Vm Vtt (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13])),
|
---|
721 | gPhiL[2,2] -> Sqrt[2]/v*ymm*( (1 - Vm^2/2) (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]) -
|
---|
722 | 1/2 Ve Vm Cos[theta13] Sin[theta12] -
|
---|
723 | 1/2 Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23])),
|
---|
724 | gPhiL[2,3] -> Sqrt[2]/v*ymm*( (1 - Vm^2/2) Cos[theta13] Sin[theta23] -
|
---|
725 | 1/2 Vm Vtt Cos[theta13] Cos[theta23] - 1/2 Ve Vm Sin[theta13]),
|
---|
726 | gPhiL[2,4] -> Sqrt[2]/v* ymm Vm,
|
---|
727 | gPhiL[3,1] -> Sqrt[2]/v*ymtau*( (1 - Vtt^2/2) (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13]) -
|
---|
728 | 1/2 Ve Vtt Cos[theta12] Cos[theta13] -
|
---|
729 | 1/2 Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
730 | gPhiL[3,2] -> Sqrt[2]/v*ymtau*( (1 - Vtt^2/2) (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) -
|
---|
731 | 1/2 Ve Vtt Cos[theta13] Sin[theta12] -
|
---|
732 | 1/2 Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
733 | gPhiL[3,3] -> Sqrt[2]/v*ymtau*( (1 - Vtt^2/2) Cos[theta13] Cos[theta23] -
|
---|
734 | 1/2 Ve Vtt Sin[theta13] - 1/2 Vm Vtt Cos[theta13] Sin[theta23]),
|
---|
735 | gPhiL[3,4] -> Sqrt[2]/v* ymtau Vtt,
|
---|
736 | gPhiL[4,1] -> 2/(mtr*v)*(Ve Cos[theta12] Cos[theta13] yme^2 +
|
---|
737 | ymtau^2 Vtt (Sin[theta12] Sin[theta23]-Cos[theta12] Cos[theta23] Sin[theta13]) +
|
---|
738 | ymm^2 Vm (-Cos[theta23] Sin[theta12]-Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
739 | gPhiL[4,2] -> 2/(mtr*v)*(Ve Cos[theta13] Sin[theta12] yme^2 +
|
---|
740 | ymtau^2 Vtt (-Cos[theta23] Sin[theta12] Sin[theta13]-Cos[theta12] Sin[theta23]) +
|
---|
741 | ymm^2 Vm (Cos[theta12] Cos[theta23]-Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
742 | gPhiL[4,3] -> 2/(mtr*v)*(Ve Sin[theta13] yme^2 + ymtau^2 Vtt Cos[theta13] Cos[theta23] + ymm^2 Vm Cos[theta13] Sin[theta23]),
|
---|
743 | gPhiL[4,4] -> 0 },
|
---|
744 | Description -> "gPhiL-Matrix"},
|
---|
745 |
|
---|
746 |
|
---|
747 |
|
---|
748 | gPhiR == {
|
---|
749 | Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
|
---|
750 | TensorClass -> CKM,
|
---|
751 | ComplexParameter -> False,
|
---|
752 | Value -> {gPhiR[1,1] -> -Sqrt[2]/v*(mv1 Cos[theta12] Cos[theta13]),
|
---|
753 | gPhiR[1,2] -> -Sqrt[2]/v*(mv2 Cos[theta13] Sin[theta12]),
|
---|
754 | gPhiR[1,3] -> -Sqrt[2]/v*(mv3 Sin[theta13]),
|
---|
755 | gPhiR[1,4] -> (mtr/v*Sqrt[2])*(-1/2 Ve (3 Ve^2 + 3 Vm^2 + 3 Vtt^2 - 2)) -
|
---|
756 | 2/v*Sqrt[2]( mv3 Sin[theta13] (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]) +
|
---|
757 | mv1 Cos[theta12] Cos[theta13] (Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
|
---|
758 | Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) +
|
---|
759 | mv2 Cos[theta13] Sin[theta12] (Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
|
---|
760 | Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
|
---|
761 | gPhiR[2,1] -> -Sqrt[2]/v*(mv1 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
|
---|
762 | gPhiR[2,2] -> -Sqrt[2]/v*(mv2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
|
---|
763 | gPhiR[2,3] -> -Sqrt[2]/v*(mv3 Cos[theta13] Sin[theta23]),
|
---|
764 | gPhiR[2,4] -> (mtr/v*Sqrt[2])*(-1/2 Vm (3 Ve^2 + 3 Vm^2 + 3 Vtt^2 - 2)) -
|
---|
765 | 2/v*Sqrt[2] (
|
---|
766 | mv3 Cos[theta13] Sin[theta23] (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]) +
|
---|
767 | mv1 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]) (Ve Cos[theta12] Cos[theta13] +
|
---|
768 | Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
769 | Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) +
|
---|
770 | mv2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]) (Ve Cos[theta13] Sin[theta12] +
|
---|
771 | Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
772 | Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
|
---|
773 | gPhiR[3,1] -> -Sqrt[2]/v*(mv1 (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13])),
|
---|
774 | gPhiR[3,2] -> -Sqrt[2]/v*(mv2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23])),
|
---|
775 | gPhiR[3,3] -> -Sqrt[2]/v*(mv3 Cos[theta13] Cos[theta23]),
|
---|
776 | gPhiR[3,4] -> (mtr/v*Sqrt[2])*(-1/2 Vtt (3 Ve^2 + 3 Vm^2 + 3 Vtt^2 - 2)) -
|
---|
777 | 2/v*Sqrt[2] (
|
---|
778 | mv3 Cos[theta13] Cos[theta23] (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]) +
|
---|
779 | mv1 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) (Ve Cos[theta12] Cos[theta13] +
|
---|
780 | Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
|
---|
781 | Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) +
|
---|
782 | mv2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) (Ve Cos[theta13] Sin[theta12] +
|
---|
783 | Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
|
---|
784 | Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
|
---|
785 | gPhiR[4,1] -> mtr/v*( (Ve^2 + Vm^2 + Vtt^2 - 2) (Sin[theta12] (Vtt Sin[theta23] - Vm Cos[theta23]) +
|
---|
786 | Cos[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
|
---|
787 | gPhiR[4,2] -> mtr/v*( (Ve^2 + Vm^2 + Vtt^2 - 2) (Cos[theta12] (Vm Cos[theta23] - Vtt Sin[theta23]) +
|
---|
788 | Sin[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
|
---|
789 | gPhiR[4,3] -> mtr/v*( (Ve^2 + Vm^2 + Vtt^2 - 2) (Ve Sin[theta13] + Cos[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))),
|
---|
790 | gPhiR[4,4] -> 0 },
|
---|
791 | Description -> "gPhiR-Matrix"}
|
---|
792 |
|
---|
793 |
|
---|
794 |
|
---|
795 |
|
---|
796 | }
|
---|
797 |
|
---|
798 |
|
---|
799 | (************** Gauge Groups ******************)
|
---|
800 |
|
---|
801 | M$GaugeGroups = {
|
---|
802 |
|
---|
803 | U1Y == {
|
---|
804 | Abelian -> True,
|
---|
805 | GaugeBoson -> B,
|
---|
806 | Charge -> Y,
|
---|
807 | CouplingConstant -> g1},
|
---|
808 |
|
---|
809 | SU2L == {
|
---|
810 | Abelian -> False,
|
---|
811 | GaugeBoson -> Wi,
|
---|
812 | StructureConstant -> Eps,
|
---|
813 | CouplingConstant -> gw},
|
---|
814 |
|
---|
815 | SU3C == {
|
---|
816 | Abelian -> False,
|
---|
817 | GaugeBoson -> G,
|
---|
818 | StructureConstant -> f,
|
---|
819 | SymmetricTensor -> dSUN,
|
---|
820 | Representations -> {T, Colour},
|
---|
821 | CouplingConstant -> gs}
|
---|
822 | }
|
---|
823 |
|
---|
824 | (********* Particle Classes **********)
|
---|
825 |
|
---|
826 | M$ClassesDescription = {
|
---|
827 |
|
---|
828 | (********** Fermions ************)
|
---|
829 | (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
|
---|
830 | F[1] == {
|
---|
831 | ClassName -> vl,
|
---|
832 | ClassMembers -> {v1,v2,v3,tr0},
|
---|
833 | FlavorIndex -> LeptonGeneration,
|
---|
834 | SelfConjugate -> True,
|
---|
835 | Indices -> {Index[LeptonGeneration]},
|
---|
836 | Mass -> {Mv, {Mv1, 0}, {Mv2, 0}, {Mv3, 0}, {Mtr0, 100.8}},
|
---|
837 | Width -> {0, 0, 0, {Wtr0, 0.1}},
|
---|
838 | PropagatorLabel -> {"v", "v1", "v2", "v3","tr0"} ,
|
---|
839 | PropagatorType -> S,
|
---|
840 | PropagatorArrow -> Forward,
|
---|
841 | PDG -> {8000012,8000014,8000016,8000018},
|
---|
842 | FullName -> {"nu1", "nu2", "nu3", "Sigma0"} },
|
---|
843 |
|
---|
844 | (* Leptons (electron): I_3 = -1/2, Q = -1 *)
|
---|
845 | F[2] == {
|
---|
846 | ClassName -> l,
|
---|
847 | ClassMembers -> {e, m, tt,trm},
|
---|
848 | FlavorIndex -> LeptonGeneration,
|
---|
849 | SelfConjugate -> False,
|
---|
850 | Indices -> {Index[LeptonGeneration]},
|
---|
851 | Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}, {Mtrch, 101}},
|
---|
852 | Width -> {0, 0, {Wtau, 0.1}, {Wtrch, 0.1}},
|
---|
853 | QuantumNumbers -> {Q -> -1},
|
---|
854 | PropagatorLabel -> {"l", "e", "m", "tt", "tr-"},
|
---|
855 | PropagatorType -> Straight,
|
---|
856 | ParticleName -> {"e-", "m-", "tt-", "tr-"},
|
---|
857 | AntiParticleName -> {"e+", "m+", "tt+", "tr+"},
|
---|
858 | PropagatorArrow -> Forward,
|
---|
859 | PDG -> {11, 13, 15,8000020},
|
---|
860 | FullName -> {"Electron", "Muon", "Tau", "Sigma-"} },
|
---|
861 |
|
---|
862 | (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
|
---|
863 | F[3] == {
|
---|
864 | ClassMembers -> {u, c, t},
|
---|
865 | ClassName -> uq,
|
---|
866 | FlavorIndex -> Generation,
|
---|
867 | SelfConjugate -> False,
|
---|
868 | Indices -> {Index[Generation], Index[Colour]},
|
---|
869 | Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 174.3}},
|
---|
870 | Width -> {0, {WC, 0.1}, {WT, 1.50833649}},
|
---|
871 | QuantumNumbers -> {Q -> 2/3},
|
---|
872 | PropagatorLabel -> {"uq", "u", "c", "t"},
|
---|
873 | PropagatorType -> Straight,
|
---|
874 | PropagatorArrow -> Forward,
|
---|
875 | PDG -> {2, 4, 6},
|
---|
876 | FullName -> {"u-quark", "c-quark", "t-quark"}},
|
---|
877 |
|
---|
878 | (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
|
---|
879 | F[4] == {
|
---|
880 | ClassMembers -> {d, s, b},
|
---|
881 | ClassName -> dq,
|
---|
882 | FlavorIndex -> Generation,
|
---|
883 | SelfConjugate -> False,
|
---|
884 | Indices -> {Index[Generation], Index[Colour]},
|
---|
885 | Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.104}, {MB, 4.7}},
|
---|
886 | Width -> {0, 0, {WB, 0.1}},
|
---|
887 | QuantumNumbers -> {Q -> -1/3},
|
---|
888 | PropagatorLabel -> {"dq", "d", "s", "b"},
|
---|
889 | PropagatorType -> Straight,
|
---|
890 | PropagatorArrow -> Forward,
|
---|
891 | PDG -> {1,3,5},
|
---|
892 | FullName -> {"d-quark", "s-quark", "b-quark"} },
|
---|
893 |
|
---|
894 | (********** Ghosts **********)
|
---|
895 | U[1] == {
|
---|
896 | ClassName -> ghA,
|
---|
897 | SelfConjugate -> False,
|
---|
898 | Indices -> {},
|
---|
899 | Ghost -> A,
|
---|
900 | Mass -> 0,
|
---|
901 | QuantumNumbers -> {GhostNumber -> 1},
|
---|
902 | PropagatorLabel -> uA,
|
---|
903 | PropagatorType -> GhostDash,
|
---|
904 | PropagatorArrow -> Forward},
|
---|
905 |
|
---|
906 | U[2] == {
|
---|
907 | ClassName -> ghZ,
|
---|
908 | SelfConjugate -> False,
|
---|
909 | Indices -> {},
|
---|
910 | Mass -> {MZ, 91.188},
|
---|
911 | Ghost -> Z,
|
---|
912 | QuantumNumbers -> {GhostNumber -> 1},
|
---|
913 | PropagatorLabel -> uZ,
|
---|
914 | PropagatorType -> GhostDash,
|
---|
915 | PropagatorArrow -> Forward},
|
---|
916 |
|
---|
917 | U[31] == {
|
---|
918 | ClassName -> ghWp,
|
---|
919 | SelfConjugate -> False,
|
---|
920 | Indices -> {},
|
---|
921 | Mass -> {MW, Internal},
|
---|
922 | Ghost -> W,
|
---|
923 | QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
|
---|
924 | PropagatorLabel -> uWp,
|
---|
925 | PropagatorType -> GhostDash,
|
---|
926 | PropagatorArrow -> Forward},
|
---|
927 |
|
---|
928 | U[32] == {
|
---|
929 | ClassName -> ghWm,
|
---|
930 | SelfConjugate -> False,
|
---|
931 | Indices -> {},
|
---|
932 | Mass -> {MW, Internal},
|
---|
933 | Ghost -> Wbar,
|
---|
934 | QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
|
---|
935 | PropagatorLabel -> uWm,
|
---|
936 | PropagatorType -> GhostDash,
|
---|
937 | PropagatorArrow -> Forward},
|
---|
938 |
|
---|
939 | U[4] == {
|
---|
940 | ClassName -> ghG,
|
---|
941 | SelfConjugate -> False,
|
---|
942 | Indices -> {Index[Gluon]},
|
---|
943 | Ghost -> G,
|
---|
944 | Mass -> 0,
|
---|
945 | QuantumNumbers -> {GhostNumber -> 1},
|
---|
946 | PropagatorLabel -> uG,
|
---|
947 | PropagatorType -> GhostDash,
|
---|
948 | PropagatorArrow -> Forward},
|
---|
949 |
|
---|
950 | U[5] == {
|
---|
951 | ClassName -> ghWi,
|
---|
952 | Unphysical -> True,
|
---|
953 | Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
|
---|
954 | ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
|
---|
955 | ghWi[3] -> cw ghZ + sw ghA},
|
---|
956 | SelfConjugate -> False,
|
---|
957 | Ghost -> Wi,
|
---|
958 | Indices -> {Index[SU2W]},
|
---|
959 | FlavorIndex -> SU2W},
|
---|
960 |
|
---|
961 | U[6] == {
|
---|
962 | ClassName -> ghB,
|
---|
963 | SelfConjugate -> False,
|
---|
964 | Definitions -> {ghB -> -sw ghZ + cw ghA},
|
---|
965 | Indices -> {},
|
---|
966 | Ghost -> B,
|
---|
967 | Unphysical -> True},
|
---|
968 |
|
---|
969 | (************ Gauge Bosons ***************)
|
---|
970 | (* Gauge bosons: Q = 0 *)
|
---|
971 | V[1] == {
|
---|
972 | ClassName -> A,
|
---|
973 | SelfConjugate -> True,
|
---|
974 | Indices -> {},
|
---|
975 | Mass -> 0,
|
---|
976 | Width -> 0,
|
---|
977 | PropagatorLabel -> "a",
|
---|
978 | PropagatorType -> W,
|
---|
979 | PropagatorArrow -> None,
|
---|
980 | PDG -> 22,
|
---|
981 | FullName -> "Photon" },
|
---|
982 |
|
---|
983 | V[2] == {
|
---|
984 | ClassName -> Z,
|
---|
985 | SelfConjugate -> True,
|
---|
986 | Indices -> {},
|
---|
987 | Mass -> {MZ, 91.188},
|
---|
988 | Width -> {WZ, 2.44140351},
|
---|
989 | PropagatorLabel -> "Z",
|
---|
990 | PropagatorType -> Sine,
|
---|
991 | PropagatorArrow -> None,
|
---|
992 | PDG -> 23,
|
---|
993 | FullName -> "Z" },
|
---|
994 |
|
---|
995 | (* Gauge bosons: Q = -1 *)
|
---|
996 | V[3] == {
|
---|
997 | ClassName -> W,
|
---|
998 | SelfConjugate -> False,
|
---|
999 | Indices -> {},
|
---|
1000 | Mass -> {MW, Internal},
|
---|
1001 | Width -> {WW, 2.04759951},
|
---|
1002 | QuantumNumbers -> {Q -> 1},
|
---|
1003 | PropagatorLabel -> "W",
|
---|
1004 | PropagatorType -> Sine,
|
---|
1005 | PropagatorArrow -> Forward,
|
---|
1006 | ParticleName ->"W+",
|
---|
1007 | AntiParticleName ->"W-",
|
---|
1008 | PDG -> 24,
|
---|
1009 | FullName -> "W" },
|
---|
1010 |
|
---|
1011 | V[4] == {
|
---|
1012 | ClassName -> G,
|
---|
1013 | SelfConjugate -> True,
|
---|
1014 | Indices -> {Index[Gluon]},
|
---|
1015 | Mass -> 0,
|
---|
1016 | Width -> 0,
|
---|
1017 | PropagatorLabel -> G,
|
---|
1018 | PropagatorType -> C,
|
---|
1019 | PropagatorArrow -> None,
|
---|
1020 | PDG -> 21,
|
---|
1021 | FullName -> "G" },
|
---|
1022 |
|
---|
1023 | V[5] == {
|
---|
1024 | ClassName -> Wi,
|
---|
1025 | Unphysical -> True,
|
---|
1026 | Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
|
---|
1027 | Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
|
---|
1028 | Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
|
---|
1029 | SelfConjugate -> True,
|
---|
1030 | Indices -> {Index[SU2W]},
|
---|
1031 | FlavorIndex -> SU2W,
|
---|
1032 | Mass -> 0,
|
---|
1033 | PDG -> {1,2,3}},
|
---|
1034 |
|
---|
1035 | V[6] == {
|
---|
1036 | ClassName -> B,
|
---|
1037 | SelfConjugate -> True,
|
---|
1038 | Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
|
---|
1039 | Indices -> {},
|
---|
1040 | Mass -> 0,
|
---|
1041 | Unphysical -> True},
|
---|
1042 |
|
---|
1043 |
|
---|
1044 | (************ Scalar Fields **********)
|
---|
1045 | (* physical Higgs: Q = 0 *)
|
---|
1046 | S[1] == {
|
---|
1047 | ClassName -> H,
|
---|
1048 | SelfConjugate -> True,
|
---|
1049 | Mass -> {MH, 120},
|
---|
1050 | Width -> {WH, 0.00575308848},
|
---|
1051 | PropagatorLabel -> "H",
|
---|
1052 | PropagatorType -> D,
|
---|
1053 | PropagatorArrow -> None,
|
---|
1054 | PDG -> 25,
|
---|
1055 | TeXParticleName -> "\\phi",
|
---|
1056 | TeXClassName -> "\\phi",
|
---|
1057 | FullName -> "H" },
|
---|
1058 |
|
---|
1059 | S[2] == {
|
---|
1060 | ClassName -> phi,
|
---|
1061 | SelfConjugate -> True,
|
---|
1062 | Mass -> {MZ, 91.188},
|
---|
1063 | Width -> Wphi,
|
---|
1064 | PropagatorLabel -> "Phi",
|
---|
1065 | PropagatorType -> D,
|
---|
1066 | PropagatorArrow -> None,
|
---|
1067 | ParticleName ->"phi0",
|
---|
1068 | PDG -> 250,
|
---|
1069 | FullName -> "Phi",
|
---|
1070 | Goldstone -> Z },
|
---|
1071 |
|
---|
1072 | S[3] == {
|
---|
1073 | ClassName -> phi2,
|
---|
1074 | SelfConjugate -> False,
|
---|
1075 | Mass -> {MW, Internal},
|
---|
1076 | Width -> Wphi2,
|
---|
1077 | PropagatorLabel -> "Phi2",
|
---|
1078 | PropagatorType -> D,
|
---|
1079 | PropagatorArrow -> None,
|
---|
1080 | ParticleName ->"phi+",
|
---|
1081 | AntiParticleName ->"phi-",
|
---|
1082 | PDG -> 251,
|
---|
1083 | FullName -> "Phi2",
|
---|
1084 | TeXClassName -> "\\phi^+",
|
---|
1085 | TeXParticleName -> "\\phi^+",
|
---|
1086 | TeXAntiParticleName -> "\\phi^-",
|
---|
1087 | Goldstone -> W,
|
---|
1088 | QuantumNumbers -> {Q -> 1}}
|
---|
1089 | }
|
---|
1090 |
|
---|
1091 |
|
---|
1092 |
|
---|
1093 |
|
---|
1094 | (*****************************************************************************************)
|
---|
1095 |
|
---|
1096 | (* SM + type III seesaw Lagrangian *)
|
---|
1097 |
|
---|
1098 | (******************** Gauge F^2 Lagrangian terms*************************)
|
---|
1099 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
|
---|
1100 | LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
|
---|
1101 | (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
|
---|
1102 |
|
---|
1103 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
|
---|
1104 |
|
---|
1105 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
|
---|
1106 | (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
|
---|
1107 |
|
---|
1108 |
|
---|
1109 | (********************* Fermion Lagrangian terms*************************)
|
---|
1110 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
|
---|
1111 | LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
|
---|
1112 |
|
---|
1113 | Lkin = I uqbar.Ga[mu].del[uq, mu] +
|
---|
1114 | I dqbar.Ga[mu].del[dq, mu] +
|
---|
1115 | I lbar.Ga[mu].del[l, mu] +
|
---|
1116 | I/2 vlbar.Ga[mu].del[vl, mu];
|
---|
1117 |
|
---|
1118 | LQCD = gs (uqbar.Ga[mu].T[a].uq +
|
---|
1119 | dqbar.Ga[mu].T[a].dq)G[mu, a];
|
---|
1120 |
|
---|
1121 | LBright =
|
---|
1122 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.gNCR.l +
|
---|
1123 | -2ee*cw B[mu]/2 lbar.Ga[mu].ProjP.l +
|
---|
1124 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
|
---|
1125 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
|
---|
1126 |
|
---|
1127 | LBleft =
|
---|
1128 | -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.gNCnu.vl +
|
---|
1129 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjM.gNCL.l +
|
---|
1130 | -2ee*cw B[mu]/2 lbar.Ga[mu].ProjM.l +
|
---|
1131 | ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
|
---|
1132 | ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
|
---|
1133 |
|
---|
1134 | LWleft = Module[{s,r,p,n,m,i},
|
---|
1135 | ee/sw/2(
|
---|
1136 |
|
---|
1137 | vlbar[s,n].Ga[mu,s,p].ProjM[p,r].gNCnu[n,m].vl[r,m] Wi[mu, 3] +
|
---|
1138 | + 2 lbar[s,n].Ga[mu,s,p].ProjM[p,r].gNCL[n,m].l[r,m] Wi[mu, 3] +
|
---|
1139 | - 2*sw^2 lbar[s,n].Ga[mu,s,p].ProjM[p,r].l[r,n] Wi[mu, 3] +
|
---|
1140 | + 2 lbar[s,n].Ga[mu,s,p].ProjP[p,r].gNCR[n,m].l[r,m] Wi[mu, 3] +
|
---|
1141 | - 2*sw^2 lbar[s,n].Ga[mu,s,p].ProjP[p,r].l[r,n] Wi[mu, 3] +
|
---|
1142 |
|
---|
1143 | Sqrt[2] vlbar[s,n].Ga[mu,s,p].ProjM[p,r].gCCL[m,n].l[r,m] W[mu] +
|
---|
1144 | Sqrt[2] lbar[s,n].Ga[mu,s,p].ProjM[p,r].gCCL[n,m].vl[r,m] Wbar[mu]+
|
---|
1145 | 2 vlbar[s,n].Ga[mu,s,p].ProjP[p,r].gCCR[m,n].l[r,m] W[mu] +
|
---|
1146 | 2 lbar[s,n].Ga[mu,s,p].ProjP[p,r].gCCR[n,m].vl[r,m] Wbar[mu]+
|
---|
1147 |
|
---|
1148 | uqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].uq[r,n,i] Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
|
---|
1149 | dqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].dq[r,n,i] Wi[mu, 3] + (* ( 0 -1 )*)
|
---|
1150 |
|
---|
1151 | Sqrt[2] uqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].CKM[n,m].dq[r,m,i] W[mu] +
|
---|
1152 | Sqrt[2] dqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].Conjugate[CKM[m,n]].uq[r,m,i] Wbar[mu]
|
---|
1153 | )];
|
---|
1154 |
|
---|
1155 | Lkin + LQCD + LBright + LBleft + LWleft];
|
---|
1156 |
|
---|
1157 | (******************** Higgs Lagrangian terms****************************)
|
---|
1158 | Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
|
---|
1159 | Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
|
---|
1160 |
|
---|
1161 |
|
---|
1162 |
|
---|
1163 | LHiggs := Block[{PMvec, WVec, Dc, Dcbar, Vphi},
|
---|
1164 |
|
---|
1165 | PMvec = Table[PauliSigma[i], {i, 3}];
|
---|
1166 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
|
---|
1167 |
|
---|
1168 | (*Y_phi=1*)
|
---|
1169 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMvec).f;
|
---|
1170 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMvec);
|
---|
1171 |
|
---|
1172 | Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
|
---|
1173 |
|
---|
1174 | (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
|
---|
1175 |
|
---|
1176 |
|
---|
1177 | (*************** Yukawa Lagrangian***********************)
|
---|
1178 | LYuk := If[FeynmanGauge,
|
---|
1179 |
|
---|
1180 | Module[{s,r,n,m,i}, -
|
---|
1181 | yd[n] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
|
---|
1182 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] -
|
---|
1183 |
|
---|
1184 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*)
|
---|
1185 | yu[n] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) -
|
---|
1186 |
|
---|
1187 | yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v)/Sqrt[2] -
|
---|
1188 | gHlR[n,m] lbar[s,n].ProjP[s,r].l[r,m] (H) -
|
---|
1189 | gHnuR[n,m] vlbar[s,n].ProjP[s,r].vl[r,m] (H)/Sqrt[2] -
|
---|
1190 | getalR[n,m] lbar[s,n].ProjP[s,r].l[r,m] (I phi) -
|
---|
1191 | getanuR[n,m] vlbar[s,n].ProjP[s,r].vl[r,m] (I phi)/Sqrt[2] -
|
---|
1192 | gPhiR[n,m] lbar[s,n].ProjP[s,r].vl[r,m] (I phi2bar) - (* Different convention in phi2 definition compared to paper *)
|
---|
1193 | gPhiL[n,m] lbar[s,n].ProjM[s,r].vl[r,m] (I phi2bar) (* Different convention in phi2 definition compared to paper *)
|
---|
1194 | ],
|
---|
1195 |
|
---|
1196 | Module[{s,r,n,m,i}, -
|
---|
1197 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
|
---|
1198 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
|
---|
1199 | yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v)/Sqrt[2] -
|
---|
1200 | gHlR[n,m] lbar[s,n].ProjP[s,r].l[r,m] (H) -
|
---|
1201 | gHnuR[n,m] vlbar[s,n].ProjP[s,r].vl[r,m] (H)/Sqrt[2]
|
---|
1202 | ]
|
---|
1203 | ];
|
---|
1204 |
|
---|
1205 | LYukawa := LYuk + HC[LYuk];
|
---|
1206 |
|
---|
1207 | (****************** Majorana Masses *********************)
|
---|
1208 |
|
---|
1209 | LMasses= - mtr/2 tr0bar.tr0 - mtrm trmbar.trm
|
---|
1210 |
|
---|
1211 |
|
---|
1212 | (**************Ghost terms**************************)
|
---|
1213 | (* Now we need the ghost terms which are of the form: *)
|
---|
1214 | (* - g * antighost * d_BRST G *)
|
---|
1215 | (* where d_BRST G is BRST transform of the gauge fixing function. *)
|
---|
1216 |
|
---|
1217 | LGhost := If[FeynmanGauge,
|
---|
1218 | Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
|
---|
1219 |
|
---|
1220 | (***********First the pure gauge piece.**********************)
|
---|
1221 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
|
---|
1222 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
|
---|
1223 |
|
---|
1224 | dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
|
---|
1225 | LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
|
---|
1226 |
|
---|
1227 | dBRSTB[mu_] := cw/ee del[ghB, mu];
|
---|
1228 | LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
|
---|
1229 |
|
---|
1230 | (***********Next the piece from the scalar field.************)
|
---|
1231 | LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
|
---|
1232 | I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
|
---|
1233 | ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) -
|
---|
1234 | I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
|
---|
1235 | ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
|
---|
1236 |
|
---|
1237 |
|
---|
1238 | (***********Now add the pieces together.********************)
|
---|
1239 | LGhostG + LGhostWi + LGhostB + LGhostphi]
|
---|
1240 |
|
---|
1241 | , 0];
|
---|
1242 |
|
---|
1243 | (*********Total Lagrangian*******)
|
---|
1244 | LTypeIII := LGauge + LHiggs + LFermions + LYukawa + LGhost + LMasses
|
---|
1245 |
|
---|
1246 |
|
---|