1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file for the generic U(1)_X model ******)
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3 | (***************************************************************************************************************)
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4 | (****** Contains three massive Majorana neutrinos and a scalar. All the SM particles and new scalar are ********)
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5 | (***** charged under the new gauge U(1)X. Heavy neutrino masses MNi and mixing parameters VlNi between ********)
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6 | (**** heavy mass eigenstate and flavour eigenstates are considered as independent parameter. ********)
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7 | (***************************************************************************************************************)
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8 | (****** Contact Authors: Sanjoy Mandal, Arindam Das ******)
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9 | (***************************************************************************************************************)
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10 | (****** Choose whether Feynman gauge is desired. ******)
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11 | (****** If set to False, unitary gauge is assumed. ****)
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12 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
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13 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
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14 | (***************************************************************************************************************)
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15 |
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16 | (* ************************** *)
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17 | (* ***** Information ***** *)
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18 | (* ************************** *)
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19 | M$ModelName = "U1XGeneric";
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20 |
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21 | M$Information = {
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22 | Authors -> {"Sanjoy Mandal", "Arindam Das"},
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23 | Version -> "1.1.0",
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24 | Date -> "28. 01. 2022",
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25 | Institutions -> {"Korea Institute of Advanced Study, Seoul 02455â, "Hokkaido University, Sapporo 060-0817, Japan"},
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26 | Emails -> {"mandal.sanjoy10@gmail.com", "dasarindamphysics@gmail.com"},
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27 | URLs -> "http://feynrules.phys.ucl.ac.be"
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28 | };
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29 |
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30 | FeynmanGauge = True;
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31 |
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32 | (* ************************** *)
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33 | (* ***** NLO Variables ****** *)
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34 | (******************************)
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35 |
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36 | FR$LoopSwitches = {{Gf, MW}};
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37 | FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
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38 | ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
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39 |
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40 |
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41 | (* ************************** *)
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42 | (* ***** vevs ***** *)
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43 | (* ************************** *)
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44 | M$vevs = { {Phi[2],vev} };
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45 |
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46 | (* ************************** *)
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47 | (* ***** Gauge groups ***** *)
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48 | (* ************************** *)
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49 | M$GaugeGroups = {
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50 | U1BL == {
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51 | Abelian -> True,
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52 | GaugeBoson -> Bp,
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53 | Charge -> BL,
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54 | CouplingConstant -> g1p},
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55 |
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56 | U1Y == {
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57 | Abelian -> True,
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58 | CouplingConstant -> g1,
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59 | GaugeBoson -> B,
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60 | Charge -> Y
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61 | },
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62 | SU2L == {
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63 | Abelian -> False,
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64 | CouplingConstant -> gw,
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65 | GaugeBoson -> Wi,
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66 | StructureConstant -> Eps,
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67 | Representations -> {Ta,SU2D},
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68 | Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
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69 | },
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70 | SU3C == {
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71 | Abelian -> False,
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72 | CouplingConstant -> gs,
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73 | GaugeBoson -> G,
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74 | StructureConstant -> f,
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75 | Representations -> {T,Colour},
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76 | SymmetricTensor -> dSUN
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77 | }
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78 | };
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79 |
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80 |
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81 | (* ************************** *)
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82 | (* ***** Indices ***** *)
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83 | (* ************************** *)
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84 |
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85 | IndexRange[Index[SU2W ]] = Unfold[Range[3]];
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86 | IndexRange[Index[SU2D ]] = Unfold[Range[2]];
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87 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
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88 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
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89 | IndexRange[Index[Generation]] = Range[3];
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90 |
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91 | IndexStyle[SU2W, j];
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92 | IndexStyle[SU2D, k];
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93 | IndexStyle[Gluon, a];
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94 | IndexStyle[Colour, m];
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95 | IndexStyle[Generation, f];
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96 |
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97 |
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98 | (* ************************** *)
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99 | (* *** Interaction orders *** *)
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100 | (* *** (as used by mg5) *** *)
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101 | (* ************************** *)
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102 |
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103 | M$InteractionOrderHierarchy = {
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104 | {QCD, 1},
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105 | {QED, 2}
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106 | };
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107 |
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108 |
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109 | (* ************************** *)
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110 | (* **** Particle classes **** *)
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111 | (* ************************** *)
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112 | M$ClassesDescription = {
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113 |
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114 | (* Gauge bosons: physical vector fields *)
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115 | V[1] == {
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116 | ClassName -> A,
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117 | SelfConjugate -> True,
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118 | Mass -> 0,
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119 | Width -> 0,
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120 | ParticleName -> "a",
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121 | PDG -> 22,
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122 | PropagatorLabel -> "a",
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123 | PropagatorType -> W,
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124 | PropagatorArrow -> None,
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125 | FullName -> "Photon"
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126 | },
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127 | V[2] == {
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128 | ClassName -> Z,
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129 | SelfConjugate -> True,
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130 | Mass -> {MZ, 91.1876},
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131 | Width -> {WZ, 2.4952},
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132 | ParticleName -> "Z",
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133 | PDG -> 23,
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134 | PropagatorLabel -> "Z",
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135 | PropagatorType -> Sine,
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136 | PropagatorArrow -> None,
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137 | FullName -> "Z"
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138 | },
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139 | V[3] == {
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140 | ClassName -> W,
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141 | SelfConjugate -> False,
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142 | Mass -> {MW, 80.379},
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143 | Width -> {WW, 2.085},
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144 | ParticleName -> "W+",
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145 | AntiParticleName -> "W-",
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146 | QuantumNumbers -> {Q -> 1},
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147 | PDG -> 24,
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148 | PropagatorLabel -> "W",
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149 | PropagatorType -> Sine,
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150 | PropagatorArrow -> Forward,
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151 | FullName -> "W"
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152 | },
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153 | V[4] == {
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154 | ClassName -> G,
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155 | SelfConjugate -> True,
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156 | Indices -> {Index[Gluon]},
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157 | Mass -> 0,
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158 | Width -> 0,
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159 | ParticleName -> "g",
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160 | PDG -> 21,
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161 | PropagatorLabel -> "G",
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162 | PropagatorType -> C,
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163 | PropagatorArrow -> None,
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164 | FullName -> "G"
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165 | },
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166 | V[5] == {
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167 | ClassName -> Zp,
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168 | SelfConjugate -> True,
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169 | Indices -> {},
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170 | Mass -> {MZp, 3000},
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171 | Width -> {WZp, 1.0},
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172 | PropagatorLabel -> "Zp",
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173 | PropagatorType -> Sine,
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174 | PropagatorArrow -> None,
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175 | PDG -> 9900032,
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176 | FullName -> "Zp" },
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177 |
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178 | (* Ghosts: related to physical gauge bosons *)
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179 | U[1] == {
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180 | ClassName -> ghA,
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181 | SelfConjugate -> False,
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182 | Ghost -> A,
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183 | QuantumNumbers -> {GhostNumber -> 1},
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184 | Mass -> 0,
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185 | Width -> 0,
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186 | PropagatorLabel -> "uA",
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187 | PropagatorType -> GhostDash,
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188 | PropagatorArrow -> Forward
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189 | },
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190 | U[2] == {
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191 | ClassName -> ghZ,
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192 | SelfConjugate -> False,
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193 | Ghost -> Z,
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194 | QuantumNumbers -> {GhostNumber -> 1},
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195 | Mass -> {MZ,91.1876},
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196 | Width -> {WZ, 2.4952},
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197 | PropagatorLabel -> "uZ",
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198 | PropagatorType -> GhostDash,
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199 | PropagatorArrow -> Forward
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200 | },
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201 | U[31] == {
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202 | ClassName -> ghWp,
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203 | SelfConjugate -> False,
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204 | Ghost -> W,
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205 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
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206 | Mass -> {MW,80.379},
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207 | Width -> {WW, 2.085},
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208 | PropagatorLabel -> "uWp",
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209 | PropagatorType -> GhostDash,
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210 | PropagatorArrow -> Forward
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211 | },
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212 | U[32] == {
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213 | ClassName -> ghWm,
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214 | SelfConjugate -> False,
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215 | Ghost -> Wbar,
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216 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
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217 | Mass -> {MW,80.379},
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218 | Width -> {WW, 2.085},
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219 | PropagatorLabel -> "uWm",
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220 | PropagatorType -> GhostDash,
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221 | PropagatorArrow -> Forward
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222 | },
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223 | U[4] == {
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224 | ClassName -> ghG,
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225 | SelfConjugate -> False,
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226 | Indices -> {Index[Gluon]},
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227 | Ghost -> G,
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228 | PDG -> 82,
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229 | QuantumNumbers ->{GhostNumber -> 1},
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230 | Mass -> 0,
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231 | Width -> 0,
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232 | PropagatorLabel -> "uG",
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233 | PropagatorType -> GhostDash,
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234 | PropagatorArrow -> Forward
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235 | },
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236 | U[5] == {
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237 | ClassName -> ghZp,
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238 | SelfConjugate -> False,
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239 | Indices -> {},
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240 | Mass -> {MZp, 3000},
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241 | Width -> {WZp, 1.0},
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242 | Ghost -> Zp,
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243 | QuantumNumbers -> {GhostNumber -> 1},
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244 | PropagatorLabel -> uZp,
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245 | PropagatorType -> GhostDash,
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246 | PropagatorArrow -> Forward},
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247 |
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248 |
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249 | (* Gauge bosons: unphysical vector fields *)
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250 | V[11] == {
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251 | ClassName -> B,
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252 | Unphysical -> True,
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253 | SelfConjugate -> True,
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254 | Definitions -> { B[mu_] -> cw A[mu] - sw*Cp Z[mu] + sw*Sp Zp[mu]}
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255 | },
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256 | V[12] == {
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257 | ClassName -> Wi,
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258 | Unphysical -> True,
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259 | SelfConjugate -> True,
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260 | Indices -> {Index[SU2W]},
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261 | FlavorIndex -> SU2W,
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262 | Definitions -> { Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3] -> sw A[mu] + cw*Cp Z[mu] - cw*Sp Zp[mu]}
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263 | },
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264 | V[13] == {
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265 | ClassName -> Bp,
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266 | SelfConjugate -> True,
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267 | Definitions -> {Bp[mu_] -> Sp Z[mu] + Cp Zp[mu]},
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268 | Indices -> {},
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269 | Unphysical -> True},
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270 |
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271 | (* Ghosts: related to unphysical gauge bosons *)
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272 | U[11] == {
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273 | ClassName -> ghB,
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274 | Unphysical -> True,
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275 | SelfConjugate -> False,
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276 | Ghost -> B,
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277 | Definitions -> { ghB -> -sw*Cp ghZ + cw ghA + sw*Sp ghZp }
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278 | },
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279 | U[12] == {
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280 | ClassName -> ghWi,
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281 | Unphysical -> True,
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282 | SelfConjugate -> False,
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283 | Ghost -> Wi,
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284 | Indices -> {Index[SU2W]},
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285 | FlavorIndex -> SU2W,
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286 | Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw*Cp ghZ + sw ghA - cw*Sp ghZp }
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287 | } ,
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288 | U[13] == {
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289 | ClassName -> ghBp,
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290 | SelfConjugate -> False,
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291 | Definitions -> {ghBp -> Sp ghZ + Cp ghZp },
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292 | Indices -> {},
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293 | Unphysical -> True,
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294 | Ghost -> Bp},
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295 |
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296 | (* Fermions: physical fields *)
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297 | F[1] == {
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298 | ClassName -> nL,
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299 | ClassMembers -> {nL1,nL2,nL3},
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300 | Indices -> {Index[Generation]},
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301 | FlavorIndex -> Generation,
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302 | SelfConjugate -> True,
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303 | QuantumNumbers -> {},
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304 | Mass -> {MnL,{MnL1, 0},{MnL2, 0},{MnL3, 0}},
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305 | Width -> 0,
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306 | PropagatorLabel -> {"nL", "nul1", "nul2", "nul3"} ,
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307 | PropagatorType -> S,
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308 | PropagatorArrow -> Forward,
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309 | PDG -> {1200,1400,1600},
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310 | ParticleName -> {"v1","v2","v3"},
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311 | FullName -> {"Light neutrino 1", "Light neutrino 2", "Light neutrino 3"}
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312 | },
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313 | F[16] == {
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314 | ClassName -> nH,
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315 | ClassMembers -> {N1, N2, N3},
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316 | Indices -> {Index[Generation]},
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317 | FlavorIndex -> Generation,
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318 | SelfConjugate -> True,
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319 | QuantumNumbers -> {},
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320 | Mass -> {MnH,{MN1, 200.00},{MN2, 400.00},{MN3, 600.00}},
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321 | Width -> {{WN1,1},{WN2,1},{WN3,1}},
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322 | PropagatorLabel -> {"nH","nuh1","nuh2","nuh3"},
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323 | PropagatorType -> Straight,
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324 | PropagatorArrow -> Forward,
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325 | PDG -> {9910012, 9910014, 9910016},
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326 | ParticleName -> {"N1","N2","N3"},
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327 | FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"}
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328 | },
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329 | (* unphysical *)
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330 | F[17] == {
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331 | ClassName -> nuF,
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332 | ClassMembers -> {nuF1,nuF2,nuF3},
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333 | Indices -> {Index[Generation]},
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334 | FlavorIndex -> Generation,
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335 | SelfConjugate -> True,
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336 | Unphysical -> True,
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337 | Definitions -> {nuF[sp_,ff_] -> Module[{ff2}, UPMNS[ff,ff2] nL[sp,ff2] + Sm[ff,ff2] nH[sp,ff2]]}
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338 | },
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339 | (* unphysical *)
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340 | F[18] == {
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341 | ClassName -> nuH,
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342 | ClassMembers -> {nuH1,nuH2,nuH3},
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343 | Indices -> {Index[Generation]},
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344 | FlavorIndex -> Generation,
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345 | SelfConjugate -> True,
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346 | Unphysical -> True,
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347 | Definitions -> {nuH[sp_,ff_] -> Module[{ff2}, Conjugate[Tm[ff,ff2]] nL[sp,ff2] + Conjugate[VV[ff,ff2]] nH[sp,ff2]]}
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348 | },
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349 |
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350 | F[19] == {
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351 | ClassName -> nuHp,
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352 | ClassMembers -> {nuHp1,nuHp2,nuHp3},
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353 | Indices -> {Index[Generation]},
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354 | FlavorIndex -> Generation,
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355 | SelfConjugate -> True,
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356 | Unphysical -> True,
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357 | Definitions -> {nuHp[sp_,ff_] -> Module[{ff2}, Tm[ff,ff2] nL[sp,ff2] + VV[ff,ff2] nH[sp,ff2]]}
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358 | },
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359 |
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360 | (* Flavour-eigenstate neutrino: unphysical *)
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361 | (* Righthanded flavor neutrino: unphysical *)
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362 | F[20] == {
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363 | ClassName -> NR,
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364 | Unphysical -> True,
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365 | Indices -> {Index[Generation]},
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366 | QuantumNumbers -> {Y -> 0, BL -> -xPhi},
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367 | FlavorIndex -> Generation,
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368 | SelfConjugate -> False,
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369 | Definitions -> { NR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] nuH[sp2,ff]]}
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370 | },
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371 |
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372 | F[21] == {
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373 | ClassName -> NRc,
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374 | Unphysical -> True,
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375 | Indices -> {Index[Generation]},
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376 | QuantumNumbers -> {Y -> 0, BL -> xPhi},
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377 | FlavorIndex -> Generation,
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378 | SelfConjugate -> False,
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379 | Definitions -> { NRc[sp1_,ff_] :> Module[{sp2}, ProjM[sp1,sp2] nuHp[sp2,ff]]}
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380 | },
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381 |
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382 | F[2] == {
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383 | ClassName -> l,
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384 | ClassMembers -> {e, mu, ta},
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385 | Indices -> {Index[Generation]},
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386 | FlavorIndex -> Generation,
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387 | SelfConjugate -> False,
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388 | Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
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389 | Width -> 0,
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390 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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391 | PropagatorLabel -> {"l", "e", "mu", "ta"},
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392 | PropagatorType -> Straight,
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393 | PropagatorArrow -> Forward,
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394 | PDG -> {11, 13, 15},
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395 | ParticleName -> {"e-", "mu-", "ta-"},
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396 | AntiParticleName -> {"e+", "mu+", "ta+"},
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397 | FullName -> {"Electron", "Muon", "Tau"}
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398 | },
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399 | F[3] == {
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400 | ClassName -> uq,
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401 | ClassMembers -> {u, c, t},
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402 | Indices -> {Index[Generation], Index[Colour]},
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403 | FlavorIndex -> Generation,
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404 | SelfConjugate -> False,
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405 | Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
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406 | Width -> {0, 0, {WT,1.50833649}},
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407 | QuantumNumbers -> {Q -> 2/3},
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408 | PropagatorLabel -> {"uq", "u", "c", "t"},
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409 | PropagatorType -> Straight,
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410 | PropagatorArrow -> Forward,
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411 | PDG -> {2, 4, 6},
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412 | ParticleName -> {"u", "c", "t" },
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413 | AntiParticleName -> {"u~", "c~", "t~"},
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414 | FullName -> {"u-quark", "c-quark", "t-quark"}
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415 | },
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416 | F[4] == {
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417 | ClassName -> dq,
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418 | ClassMembers -> {d, s, b},
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419 | Indices -> {Index[Generation], Index[Colour]},
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420 | FlavorIndex -> Generation,
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421 | SelfConjugate -> False,
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422 | Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
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423 | Width -> 0,
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424 | QuantumNumbers -> {Q -> -1/3},
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425 | PropagatorLabel -> {"dq", "d", "s", "b"},
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426 | PropagatorType -> Straight,
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427 | PropagatorArrow -> Forward,
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428 | PDG -> {1,3,5},
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429 | ParticleName -> {"d", "s", "b" },
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430 | AntiParticleName -> {"d~", "s~", "b~"},
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431 | FullName -> {"d-quark", "s-quark", "b-quark"}
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432 | },
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433 |
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434 | (* Fermions: unphysical fields *)
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435 | F[11] == {
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436 | ClassName -> LL,
|
---|
437 | Unphysical -> True,
|
---|
438 | Indices -> {Index[SU2D], Index[Generation]},
|
---|
439 | FlavorIndex -> SU2D,
|
---|
440 | SelfConjugate -> False,
|
---|
441 | QuantumNumbers -> {Y -> -1/2, BL -> -(1/2)*xH-xPhi },
|
---|
442 | Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] nuF[sp2,ff]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
|
---|
443 | },
|
---|
444 |
|
---|
445 | F[12] == {
|
---|
446 | ClassName -> lR,
|
---|
447 | Unphysical -> True,
|
---|
448 | Indices -> {Index[Generation]},
|
---|
449 | FlavorIndex -> Generation,
|
---|
450 | SelfConjugate -> False,
|
---|
451 | QuantumNumbers -> {Y -> -1, BL -> -xH-xPhi},
|
---|
452 | Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
|
---|
453 | },
|
---|
454 | F[13] == {
|
---|
455 | ClassName -> QL,
|
---|
456 | Unphysical -> True,
|
---|
457 | Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
|
---|
458 | FlavorIndex -> SU2D,
|
---|
459 | SelfConjugate -> False,
|
---|
460 | QuantumNumbers -> {Y -> 1/6, BL -> (1/6)*xH+(1/3)*xPhi},
|
---|
461 | Definitions -> {
|
---|
462 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
|
---|
463 | QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
|
---|
464 | },
|
---|
465 | F[14] == {
|
---|
466 | ClassName -> uR,
|
---|
467 | Unphysical -> True,
|
---|
468 | Indices -> {Index[Generation], Index[Colour]},
|
---|
469 | FlavorIndex -> Generation,
|
---|
470 | SelfConjugate -> False,
|
---|
471 | QuantumNumbers -> {Y -> 2/3, BL -> (2/3)*xH+(1/3)*xPhi},
|
---|
472 | Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
|
---|
473 | },
|
---|
474 | F[15] == {
|
---|
475 | ClassName -> dR,
|
---|
476 | Unphysical -> True,
|
---|
477 | Indices -> {Index[Generation], Index[Colour]},
|
---|
478 | FlavorIndex -> Generation,
|
---|
479 | SelfConjugate -> False,
|
---|
480 | QuantumNumbers -> {Y -> -1/3, BL -> -(1/3)*xH+(1/3)*xPhi},
|
---|
481 | Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
|
---|
482 | },
|
---|
483 |
|
---|
484 |
|
---|
485 |
|
---|
486 | (* Higgs: physical scalars *)
|
---|
487 | S[1] == {
|
---|
488 | ClassName -> H1,
|
---|
489 | SelfConjugate -> True,
|
---|
490 | Mass -> {MH1,125.18},
|
---|
491 | Width -> {WH1,0.00407},
|
---|
492 | PropagatorLabel -> "H1",
|
---|
493 | PropagatorType -> D,
|
---|
494 | PropagatorArrow -> None,
|
---|
495 | PDG -> 25,
|
---|
496 | ParticleName -> "H1",
|
---|
497 | FullName -> "H1"
|
---|
498 | },
|
---|
499 |
|
---|
500 | (* Higgs: physical scalars *)
|
---|
501 | S[2] == {
|
---|
502 | ClassName -> G0,
|
---|
503 | SelfConjugate -> True,
|
---|
504 | Goldstone -> Z,
|
---|
505 | Mass -> {MZ, 91.1876},
|
---|
506 | Width -> {WZ, 2.4952},
|
---|
507 | PropagatorLabel -> "Go",
|
---|
508 | PropagatorType -> D,
|
---|
509 | PropagatorArrow -> None,
|
---|
510 | PDG -> 250,
|
---|
511 | ParticleName -> "G0",
|
---|
512 | FullName -> "G0"
|
---|
513 | },
|
---|
514 | S[3] == {
|
---|
515 | ClassName -> GP,
|
---|
516 | SelfConjugate -> False,
|
---|
517 | Goldstone -> W,
|
---|
518 | Mass -> {MW, 80.379},
|
---|
519 | QuantumNumbers -> {Q -> 1},
|
---|
520 | Width -> {WW, 2.085},
|
---|
521 | PropagatorLabel -> "GP",
|
---|
522 | PropagatorType -> D,
|
---|
523 | PropagatorArrow -> None,
|
---|
524 | PDG -> 251,
|
---|
525 | ParticleName -> "G+",
|
---|
526 | AntiParticleName -> "G-",
|
---|
527 | FullName -> "GP"
|
---|
528 | },
|
---|
529 | S[4] == {
|
---|
530 | ClassName -> H2,
|
---|
531 | SelfConjugate -> True,
|
---|
532 | Mass -> {MH2, 450},
|
---|
533 | Width -> {WH2, 1.0},
|
---|
534 | PropagatorLabel -> "H2",
|
---|
535 | PropagatorType -> D,
|
---|
536 | PropagatorArrow -> None,
|
---|
537 | PDG -> 9900035,
|
---|
538 | FullName -> "H2" },
|
---|
539 | S[5] == {
|
---|
540 | ClassName -> phiZp,
|
---|
541 | SelfConjugate -> True,
|
---|
542 | Mass -> {MZp, 3000},
|
---|
543 | Width -> {WZp, 1.0},
|
---|
544 | PropagatorLabel -> "phiZp",
|
---|
545 | PropagatorType -> D,
|
---|
546 | PropagatorArrow -> None,
|
---|
547 | ParticleName ->"phiZp",
|
---|
548 | PDG -> 9900252,
|
---|
549 | FullName -> "PhiZp",
|
---|
550 | Goldstone -> Zp },
|
---|
551 |
|
---|
552 | S[6] == {
|
---|
553 | ClassName -> GZ,
|
---|
554 | Unphysical -> True,
|
---|
555 | Definitions -> {GZ -> cg G0 - sg phiZp},
|
---|
556 | SelfConjugate -> True},
|
---|
557 |
|
---|
558 | S[7] == {
|
---|
559 | ClassName -> GZp,
|
---|
560 | Unphysical -> True,
|
---|
561 | Definitions -> {GZp -> sg G0 + cg phiZp},
|
---|
562 | SelfConjugate -> True},
|
---|
563 |
|
---|
564 | (* Higgs: unphysical scalars *)
|
---|
565 | S[11] == {
|
---|
566 | ClassName -> Phi,
|
---|
567 | Unphysical -> True,
|
---|
568 | Indices -> {Index[SU2D]},
|
---|
569 | FlavorIndex -> SU2D,
|
---|
570 | SelfConjugate -> False,
|
---|
571 | QuantumNumbers -> {Y -> 1/2, BL -> xH/2},
|
---|
572 | Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + Ca*H1+Sa*H2 + I GZ)/Sqrt[2] }
|
---|
573 | },
|
---|
574 | S[12] == {
|
---|
575 | ClassName -> Chi,
|
---|
576 | Unphysical -> True,
|
---|
577 | Indices -> {},
|
---|
578 | SelfConjugate -> False,
|
---|
579 | QuantumNumbers -> {Y -> 0, BL -> 2*xPhi},
|
---|
580 | Definitions -> { Chi -> (x -Sa*H1+Ca*H2 + I GZp)/Sqrt[2] }
|
---|
581 | }
|
---|
582 | };
|
---|
583 |
|
---|
584 |
|
---|
585 | (* ************************** *)
|
---|
586 | (* ***** Gauge ***** *)
|
---|
587 | (* ***** Parameters ***** *)
|
---|
588 | (* ***** (FeynArts) ***** *)
|
---|
589 | (* ************************** *)
|
---|
590 |
|
---|
591 | GaugeXi[ V[1] ] = GaugeXi[A];
|
---|
592 | GaugeXi[ V[2] ] = GaugeXi[Z];
|
---|
593 | GaugeXi[ V[3] ] = GaugeXi[W];
|
---|
594 | GaugeXi[ V[4] ] = GaugeXi[G];
|
---|
595 | GaugeXi[ V[5] ] = GaugeXi[Zp];
|
---|
596 | GaugeXi[ S[1] ] = 1;
|
---|
597 | GaugeXi[ S[2] ] = GaugeXi[Z];
|
---|
598 | GaugeXi[ S[3] ] = GaugeXi[W];
|
---|
599 | GaugeXi[ S[4] ] = 1;
|
---|
600 | GaugeXi[ S[5] ] = GaugeXi[Zp];
|
---|
601 | GaugeXi[ U[1] ] = GaugeXi[A];
|
---|
602 | GaugeXi[ U[2] ] = GaugeXi[Z];
|
---|
603 | GaugeXi[ U[31] ] = GaugeXi[W];
|
---|
604 | GaugeXi[ U[32] ] = GaugeXi[W];
|
---|
605 | GaugeXi[ U[4] ] = GaugeXi[G];
|
---|
606 | GaugeXi[ U[5] ] = GaugeXi[Zp];
|
---|
607 |
|
---|
608 |
|
---|
609 | (* ************************** *)
|
---|
610 | (* ***** Parameters ***** *)
|
---|
611 | (* ************************** *)
|
---|
612 | M$Parameters = {
|
---|
613 |
|
---|
614 | (* External parameters *)
|
---|
615 | aEWM1 == {
|
---|
616 | ParameterType -> External,
|
---|
617 | BlockName -> SMINPUTS,
|
---|
618 | OrderBlock -> 1,
|
---|
619 | Value -> 127.9,
|
---|
620 | InteractionOrder -> {QED,-2},
|
---|
621 | Description -> "Inverse of the EW coupling constant at the Z pole"
|
---|
622 | },
|
---|
623 | Gf == {
|
---|
624 | ParameterType -> External,
|
---|
625 | BlockName -> SMINPUTS,
|
---|
626 | OrderBlock -> 2,
|
---|
627 | Value -> 1.16637*^-5,
|
---|
628 | InteractionOrder -> {QED,2},
|
---|
629 | TeX -> Subscript[G,f],
|
---|
630 | Description -> "Fermi constant"
|
---|
631 | },
|
---|
632 | aS == {
|
---|
633 | ParameterType -> External,
|
---|
634 | BlockName -> SMINPUTS,
|
---|
635 | OrderBlock -> 3,
|
---|
636 | Value -> 0.1184,
|
---|
637 | InteractionOrder -> {QCD,2},
|
---|
638 | TeX -> Subscript[\[Alpha],s],
|
---|
639 | Description -> "Strong coupling constant at the Z pole"
|
---|
640 | },
|
---|
641 |
|
---|
642 |
|
---|
643 | xH == {
|
---|
644 | ParameterType -> External,
|
---|
645 | BlockName -> BLINPUTS,
|
---|
646 | Value -> 1,
|
---|
647 | Description -> "xH parameter"},
|
---|
648 |
|
---|
649 | xPhi == {
|
---|
650 | ParameterType -> External,
|
---|
651 | BlockName -> BLINPUTS,
|
---|
652 | Value -> 1,
|
---|
653 | Description -> "xPhi parameter"},
|
---|
654 |
|
---|
655 |
|
---|
656 | g1p == {
|
---|
657 | ParameterType -> External,
|
---|
658 | BlockName -> BLINPUTS,
|
---|
659 | InteractionOrder -> {QED, 1},
|
---|
660 | Value -> 0.2,
|
---|
661 | Description -> "Zp coupling"},
|
---|
662 |
|
---|
663 | g1pp == {
|
---|
664 | ParameterType -> Internal,
|
---|
665 | BlockName -> BLINPUTS,
|
---|
666 | InteractionOrder -> {QED, 1},
|
---|
667 | Value -> g1p*xPhi,
|
---|
668 | Description -> "effective-Zp coupling"},
|
---|
669 |
|
---|
670 |
|
---|
671 | gt == {
|
---|
672 | ParameterType -> Internal,
|
---|
673 | BlockName -> BLINPUTS,
|
---|
674 | InteractionOrder -> {QED, 1},
|
---|
675 | Value -> g1p*xH,
|
---|
676 | Description -> "Z-Zp mixing coupling"},
|
---|
677 |
|
---|
678 |
|
---|
679 | Sa == {
|
---|
680 | ParameterType -> External,
|
---|
681 | BlockName -> BLINPUTS,
|
---|
682 | Value -> 0.01,
|
---|
683 | Description -> "Sine of Higgses mixing angle"},
|
---|
684 |
|
---|
685 | Ca == {
|
---|
686 | ParameterType -> Internal,
|
---|
687 | Value -> Sqrt[1-Sa^2],
|
---|
688 | ParameterName -> Ca,
|
---|
689 | Description -> "Cosine of Higgses mixing angle"},
|
---|
690 |
|
---|
691 | ymdo == {
|
---|
692 | ParameterType -> External,
|
---|
693 | BlockName -> YUKAWA,
|
---|
694 | OrderBlock -> 1,
|
---|
695 | Value -> 5.04*^-3,
|
---|
696 | Description -> "Down Yukawa mass"
|
---|
697 | },
|
---|
698 | ymup == {
|
---|
699 | ParameterType -> External,
|
---|
700 | BlockName -> YUKAWA,
|
---|
701 | OrderBlock -> 2,
|
---|
702 | Value -> 2.55*^-3,
|
---|
703 | Description -> "Up Yukawa mass"
|
---|
704 | },
|
---|
705 | yms == {
|
---|
706 | ParameterType -> External,
|
---|
707 | BlockName -> YUKAWA,
|
---|
708 | OrderBlock -> 3,
|
---|
709 | Value -> 0.101,
|
---|
710 | Description -> "Strange Yukawa mass"
|
---|
711 | },
|
---|
712 | ymc == {
|
---|
713 | ParameterType -> External,
|
---|
714 | BlockName -> YUKAWA,
|
---|
715 | OrderBlock -> 4,
|
---|
716 | Value -> 1.27,
|
---|
717 | Description -> "Charm Yukawa mass"
|
---|
718 | },
|
---|
719 | ymb == {
|
---|
720 | ParameterType -> External,
|
---|
721 | BlockName -> YUKAWA,
|
---|
722 | OrderBlock -> 5,
|
---|
723 | Value -> 4.7,
|
---|
724 | Description -> "Bottom Yukawa mass"
|
---|
725 | },
|
---|
726 | ymt == {
|
---|
727 | ParameterType -> External,
|
---|
728 | BlockName -> YUKAWA,
|
---|
729 | OrderBlock -> 6,
|
---|
730 | Value -> 172,
|
---|
731 | Description -> "Top Yukawa mass"
|
---|
732 | },
|
---|
733 | yme == {
|
---|
734 | ParameterType -> External,
|
---|
735 | BlockName -> YUKAWA,
|
---|
736 | OrderBlock -> 11,
|
---|
737 | Value -> 5.11*^-4,
|
---|
738 | Description -> "Electron Yukawa mass"
|
---|
739 | },
|
---|
740 | ymm == {
|
---|
741 | ParameterType -> External,
|
---|
742 | BlockName -> YUKAWA,
|
---|
743 | OrderBlock -> 13,
|
---|
744 | Value -> 0.10566,
|
---|
745 | Description -> "Muon Yukawa mass"
|
---|
746 | },
|
---|
747 | ymtau == {
|
---|
748 | ParameterType -> External,
|
---|
749 | BlockName -> YUKAWA,
|
---|
750 | OrderBlock -> 15,
|
---|
751 | Value -> 1.777,
|
---|
752 | Description -> "Tau Yukawa mass"
|
---|
753 | },
|
---|
754 | cabi == {
|
---|
755 | ParameterType -> External,
|
---|
756 | BlockName -> CKMBLOCK,
|
---|
757 | OrderBlock -> 1,
|
---|
758 | Value -> 0.227736,
|
---|
759 | TeX -> Subscript[\[Theta], c],
|
---|
760 | Description -> "Cabibbo angle"
|
---|
761 | },
|
---|
762 |
|
---|
763 | (* Internal Parameters *)
|
---|
764 | aEW == {
|
---|
765 | ParameterType -> Internal,
|
---|
766 | Value -> 1/aEWM1,
|
---|
767 | InteractionOrder -> {QED,2},
|
---|
768 | TeX -> Subscript[\[Alpha], EW],
|
---|
769 | Description -> "Electroweak coupling contant"
|
---|
770 | },
|
---|
771 |
|
---|
772 | sw2 == {
|
---|
773 | ParameterType -> Internal,
|
---|
774 | Value -> 0.231,
|
---|
775 | Description -> "Squared Sin of the Weinberg angle"
|
---|
776 | },
|
---|
777 | ee == {
|
---|
778 | ParameterType -> Internal,
|
---|
779 | Value -> Sqrt[4 Pi aEW],
|
---|
780 | InteractionOrder -> {QED,1},
|
---|
781 | TeX -> e,
|
---|
782 | Description -> "Electric coupling constant"
|
---|
783 | },
|
---|
784 | cw == {
|
---|
785 | ParameterType -> Internal,
|
---|
786 | Value -> Sqrt[1-sw2],
|
---|
787 | TeX -> Subscript[c,w],
|
---|
788 | Description -> "Cosine of the Weinberg angle"
|
---|
789 | },
|
---|
790 | sw == {
|
---|
791 | ParameterType -> Internal,
|
---|
792 | Value -> Sqrt[sw2],
|
---|
793 | TeX -> Subscript[s,w],
|
---|
794 | Description -> "Sine of the Weinberg angle"
|
---|
795 | },
|
---|
796 | gw == {
|
---|
797 | ParameterType -> Internal,
|
---|
798 | Definitions -> {gw->ee/sw},
|
---|
799 | InteractionOrder -> {QED,1},
|
---|
800 | TeX -> Subscript[g,w],
|
---|
801 | Description -> "Weak coupling constant at the Z pole"
|
---|
802 | },
|
---|
803 | g1 == {
|
---|
804 | ParameterType -> Internal,
|
---|
805 | Definitions -> {g1->ee/cw},
|
---|
806 | InteractionOrder -> {QED,1},
|
---|
807 | TeX -> Subscript[g,1],
|
---|
808 | Description -> "U(1)Y coupling constant at the Z pole"
|
---|
809 | },
|
---|
810 | gs == {
|
---|
811 | ParameterType -> Internal,
|
---|
812 | Value -> Sqrt[4 Pi aS],
|
---|
813 | InteractionOrder -> {QCD,1},
|
---|
814 | TeX -> Subscript[g,s],
|
---|
815 | ParameterName -> G,
|
---|
816 | Description -> "Strong coupling constant at the Z pole"
|
---|
817 | },
|
---|
818 |
|
---|
819 | vev == {
|
---|
820 | ParameterType -> Internal,
|
---|
821 | BlockName -> VEV,
|
---|
822 | Value -> 2*MW*sw/ee,
|
---|
823 | InteractionOrder -> {QED,-1},
|
---|
824 | Description -> "SM Higgs vacuum expectation value"
|
---|
825 | },
|
---|
826 |
|
---|
827 | x == {
|
---|
828 | ParameterType -> Internal,
|
---|
829 | BlockName -> VEV,
|
---|
830 | Value -> MZp/(2*g1pp)*Sqrt[1-gt^2*vev^2/(4*MZp^2-vev^2*(gw^2+g1^2))],
|
---|
831 | InteractionOrder -> {QED, -1},
|
---|
832 | Description -> "Non SM Higgs VEV"},
|
---|
833 |
|
---|
834 |
|
---|
835 | \[Lambda]1 == {
|
---|
836 | ParameterType -> Internal,
|
---|
837 | Value -> MH1^2 /(2*vev^2)*Ca^2 + MH2^2 /(2*vev^2)*Sa^2,
|
---|
838 | ParameterName -> lam1,
|
---|
839 | InteractionOrder -> {QED, 2},
|
---|
840 | Description -> "Lambda 1"},
|
---|
841 |
|
---|
842 | \[Lambda]2 == {
|
---|
843 | ParameterType -> Internal,
|
---|
844 | Value -> MH1^2 /(2*x^2)*Sa^2 + MH2^2 /(2*x^2)*Ca^2,
|
---|
845 | ParameterName -> lam2,
|
---|
846 | InteractionOrder -> {QED, 2},
|
---|
847 | Description -> "Lambda 2"},
|
---|
848 |
|
---|
849 | \[Lambda]3 == {
|
---|
850 | ParameterType -> Internal,
|
---|
851 | Value -> (MH2^2 - MH1^2)/(x*vev)*Sa*Ca,
|
---|
852 | ParameterName -> lam3,
|
---|
853 | InteractionOrder -> {QED, 2},
|
---|
854 | Description -> "Lambda 3, mixing parameter"},
|
---|
855 |
|
---|
856 | mu2H1 == {
|
---|
857 | ParameterType -> Internal,
|
---|
858 | Value -> \[Lambda]1 * vev^2 + \[Lambda]3 /2 * x^2,
|
---|
859 | TeX -> m^2,
|
---|
860 | Description -> "Coefficient of the quadratic piece of the H1 potential"},
|
---|
861 |
|
---|
862 | mu2H2 == {
|
---|
863 | ParameterType -> Internal,
|
---|
864 | Value -> \[Lambda]3 /2 * vev^2 + \[Lambda]2 * x^2,
|
---|
865 | TeX -> \[Mu]^2,
|
---|
866 | Description -> "Coefficient of the quadratic piece of the H2 potential"},
|
---|
867 |
|
---|
868 | Sp2num == {
|
---|
869 | ParameterType -> Internal,
|
---|
870 | Value -> 2*gt*Sqrt[(ee/sw)^2+(ee/cw)^2]},
|
---|
871 |
|
---|
872 | Cp2num == {
|
---|
873 | ParameterType -> Internal,
|
---|
874 | Value -> gt^2+16*(x/vev)^2*(g1pp)^2-(ee/sw)^2-(ee/cw)^2},
|
---|
875 |
|
---|
876 | Sp == {
|
---|
877 | ParameterType -> Internal,
|
---|
878 | Value -> Sin[ArcSin[Sp2num/Sqrt[Sp2num^2+Cp2num^2]]/2],
|
---|
879 | ComplexParameter -> False,
|
---|
880 | Description -> "sine mixing Zp-Z"},
|
---|
881 |
|
---|
882 | Cp == {
|
---|
883 | ParameterType -> Internal,
|
---|
884 | Value -> Sqrt[1-Sp^2],
|
---|
885 | ComplexParameter -> False,
|
---|
886 | Description -> "cosine mixing Zp-Z"},
|
---|
887 |
|
---|
888 | Cn == {
|
---|
889 | ParameterType -> Internal,
|
---|
890 | ComplexParameter -> False,
|
---|
891 | Value -> (ee/sw)^2+(ee/cw)^2+gt^2+16*(x/vev)^2*(g1pp)^2},
|
---|
892 |
|
---|
893 | Dn == {
|
---|
894 | ParameterType -> Internal,
|
---|
895 | ComplexParameter -> False,
|
---|
896 | Value -> 64*((ee/sw)^2+(ee/cw)^2)*(g1pp)^2*vev^2*x^2},
|
---|
897 |
|
---|
898 |
|
---|
899 | (* MZ == {
|
---|
900 | ParameterType -> Internal,
|
---|
901 | Value -> Sqrt[(Cn*vev^2-Sqrt[-Dn+vev^4*Cn^2])/8],
|
---|
902 | Description -> "Z mass"}, *)
|
---|
903 |
|
---|
904 | S2gNum == {
|
---|
905 | ParameterType -> Internal,
|
---|
906 | ComplexParameter -> False,
|
---|
907 | Value -> 8*x/vev*gt*(g1pp)},
|
---|
908 |
|
---|
909 | C2gNum == {
|
---|
910 | ParameterType -> Internal,
|
---|
911 | ComplexParameter -> False,
|
---|
912 | Value -> (ee/sw)^2+(ee/cw)^2+gt^2-16*(x/vev)^2*(g1pp)^2},
|
---|
913 |
|
---|
914 |
|
---|
915 | sg == {
|
---|
916 | ParameterType -> Internal,
|
---|
917 | ComplexParameter -> False,
|
---|
918 | Value -> Sin[ArcSin[-S2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2],
|
---|
919 | Description -> "cosine of Z-Zp goldostone mixing angle"},
|
---|
920 | cg == {
|
---|
921 | ParameterType -> Internal,
|
---|
922 | ComplexParameter -> False,
|
---|
923 | Value -> Sqrt[1-sg^2],
|
---|
924 | Description -> "sine of Z-Zp goldstone mixing angle"},
|
---|
925 |
|
---|
926 |
|
---|
927 | yl == {
|
---|
928 | ParameterType -> Internal,
|
---|
929 | Indices -> {Index[Generation], Index[Generation]},
|
---|
930 | Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
931 | Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
|
---|
932 | InteractionOrder -> {QED, 1},
|
---|
933 | ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
|
---|
934 | TeX -> Superscript[y, l],
|
---|
935 | Description -> "Lepton Yukawa couplings"
|
---|
936 | },
|
---|
937 | yu == {
|
---|
938 | ParameterType -> Internal,
|
---|
939 | Indices -> {Index[Generation], Index[Generation]},
|
---|
940 | Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
941 | Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
|
---|
942 | InteractionOrder -> {QED, 1},
|
---|
943 | ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
|
---|
944 | TeX -> Superscript[y, u],
|
---|
945 | Description -> "Up-type Yukawa couplings"
|
---|
946 | },
|
---|
947 | yd == {
|
---|
948 | ParameterType -> Internal,
|
---|
949 | Indices -> {Index[Generation], Index[Generation]},
|
---|
950 | Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
951 | Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
|
---|
952 | InteractionOrder -> {QED, 1},
|
---|
953 | ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
|
---|
954 | TeX -> Superscript[y, d],
|
---|
955 | Description -> "Down-type Yukawa couplings"
|
---|
956 | },
|
---|
957 |
|
---|
958 | (* Cabibbo mixing! *)
|
---|
959 | CKM == {
|
---|
960 | ParameterType -> Internal,
|
---|
961 | Indices -> {Index[Generation], Index[Generation]},
|
---|
962 | Unitary -> True,
|
---|
963 | Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
|
---|
964 | CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
|
---|
965 | CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
|
---|
966 | TeX -> Superscript[V,CKM],
|
---|
967 | Description -> "CKM-Matrix"},
|
---|
968 |
|
---|
969 | (* ***** RHN parameters ***** *)
|
---|
970 |
|
---|
971 | VeN1 == {
|
---|
972 | ParameterType -> External,
|
---|
973 | BlockName -> NUMIXING,
|
---|
974 | OrderBlock -> 1,
|
---|
975 | Value -> 0.001,
|
---|
976 | ComplexParameter -> False,
|
---|
977 | TeX -> Subscript[V,eN1],
|
---|
978 | Description -> "Mixing between ve flavor/gauge state and N1 mass state"
|
---|
979 | },
|
---|
980 |
|
---|
981 | VeN2 == {
|
---|
982 | ParameterType -> External,
|
---|
983 | BlockName -> NUMIXING,
|
---|
984 | OrderBlock -> 2,
|
---|
985 | Value -> 0.0,
|
---|
986 | ComplexParameter -> False,
|
---|
987 | TeX -> Subscript[V,eN2],
|
---|
988 | Description -> "Mixing between ve flavor/gauge state and N2 mass state"
|
---|
989 | },
|
---|
990 |
|
---|
991 | VeN3 == {
|
---|
992 | ParameterType -> External,
|
---|
993 | BlockName -> NUMIXING,
|
---|
994 | OrderBlock -> 3,
|
---|
995 | Value -> 0.0,
|
---|
996 | ComplexParameter -> False,
|
---|
997 | TeX -> Subscript[V,eN3],
|
---|
998 | Description -> "Mixing between ve flavor/gauge state and N3 mass state"
|
---|
999 | },
|
---|
1000 |
|
---|
1001 | VmuN1 == {
|
---|
1002 | ParameterType -> External,
|
---|
1003 | BlockName -> NUMIXING,
|
---|
1004 | OrderBlock -> 4,
|
---|
1005 | Value -> 0.0,
|
---|
1006 | ComplexParameter -> False,
|
---|
1007 | TeX -> Subscript[V,muN1],
|
---|
1008 | Description -> "Mixing between vm flavor/gauge state and N1 mass state"
|
---|
1009 | },
|
---|
1010 |
|
---|
1011 | VmuN2 == {
|
---|
1012 | ParameterType -> External,
|
---|
1013 | BlockName -> NUMIXING,
|
---|
1014 | OrderBlock -> 5,
|
---|
1015 | Value -> 0.001,
|
---|
1016 | ComplexParameter -> False,
|
---|
1017 | TeX -> Subscript[V,muN2],
|
---|
1018 | Description -> "Mixing between vm flavor/gauge state and N2 mass state"
|
---|
1019 | },
|
---|
1020 |
|
---|
1021 | VmuN3 == {
|
---|
1022 | ParameterType -> External,
|
---|
1023 | BlockName -> NUMIXING,
|
---|
1024 | OrderBlock -> 6,
|
---|
1025 | Value -> 0.0,
|
---|
1026 | ComplexParameter -> False,
|
---|
1027 | TeX -> Subscript[V,muN3],
|
---|
1028 | Description -> "Mixing between vm flavor/gauge state and N3 mass state"
|
---|
1029 | },
|
---|
1030 |
|
---|
1031 | VtaN1 == {
|
---|
1032 | ParameterType -> External,
|
---|
1033 | BlockName -> NUMIXING,
|
---|
1034 | OrderBlock -> 7,
|
---|
1035 | Value -> 0.0,
|
---|
1036 | ComplexParameter -> False,
|
---|
1037 | TeX -> Subscript[V,taN1],
|
---|
1038 | Description -> "Mixing between vt flavor/gauge state and N1 mass state"
|
---|
1039 | },
|
---|
1040 |
|
---|
1041 | VtaN2 == {
|
---|
1042 | ParameterType -> External,
|
---|
1043 | BlockName -> NUMIXING,
|
---|
1044 | OrderBlock -> 8,
|
---|
1045 | Value -> 0.0,
|
---|
1046 | ComplexParameter -> False,
|
---|
1047 | TeX -> Subscript[V,taN2],
|
---|
1048 | Description -> "Mixing between vt flavor/gauge state and N2 mass state"
|
---|
1049 | },
|
---|
1050 |
|
---|
1051 | VtaN3 == {
|
---|
1052 | ParameterType -> External,
|
---|
1053 | BlockName -> NUMIXING,
|
---|
1054 | OrderBlock -> 9,
|
---|
1055 | Value -> 0.001,
|
---|
1056 | ComplexParameter -> False,
|
---|
1057 | TeX -> Subscript[V,taN3],
|
---|
1058 | Description -> "Mixing between vt flavor/gauge state and N3 mass state"
|
---|
1059 | },
|
---|
1060 |
|
---|
1061 | Sm == {
|
---|
1062 | ParameterType -> Internal,
|
---|
1063 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1064 | Value -> {Sm[1,1] -> VeN1, Sm[1,2] -> VeN2, Sm[1,3] -> VeN3,
|
---|
1065 | Sm[2,1] -> VmuN1, Sm[2,2] -> VmuN2, Sm[2,3] -> VmuN3,
|
---|
1066 | Sm[3,1] -> VtaN1, Sm[3,2] -> VtaN2, Sm[3,3] -> VtaN3},
|
---|
1067 | TeX -> Superscript[S,m],
|
---|
1068 | Description -> "S-Matrix"},
|
---|
1069 |
|
---|
1070 |
|
---|
1071 | UPMNS == {
|
---|
1072 | ParameterType -> Internal,
|
---|
1073 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1074 | Value -> {UPMNS[1,1] -> 1, UPMNS[1,2] -> 0, UPMNS[1,3] -> 0,
|
---|
1075 | UPMNS[2,1] -> 0, UPMNS[2,2] -> 1, UPMNS[2,3] -> 0,
|
---|
1076 | UPMNS[3,1] -> 0, UPMNS[3,2] -> 0, UPMNS[3,3] -> 1},
|
---|
1077 | ComplexParameter -> True,
|
---|
1078 | ParameterName -> {UPMNS[1,1]->U11, UPMNS[1,2]->U12, UPMNS[1,3]->U13, UPMNS[2,1]->U21, UPMNS[2,2]->U22, UPMNS[2,3]->U23, UPMNS[3,1]->U31, UPMNS[3,2]->U32, UPMNS[3,3]->U33},
|
---|
1079 | TeX -> Superscript[U,PMNS],
|
---|
1080 | Description -> "PMNS-Matrix"},
|
---|
1081 |
|
---|
1082 |
|
---|
1083 | Tm == {
|
---|
1084 | ParameterType -> Internal,
|
---|
1085 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1086 | Value -> {Tm[1,1] -> -VeN1, Tm[1,2] -> -VmuN1, Tm[1,3] -> -VtaN1,
|
---|
1087 | Tm[2,1] -> -VeN2, Tm[2,2] -> -VmuN2, Tm[2,3] -> -VtaN2,
|
---|
1088 | Tm[3,1] -> -VeN3, Tm[3,2] -> -VmuN3, Tm[3,3] -> -VtaN3},
|
---|
1089 | TeX -> Superscript[T,m],
|
---|
1090 | Description -> "T-Matrix"},
|
---|
1091 |
|
---|
1092 |
|
---|
1093 | VV == {
|
---|
1094 | ParameterType -> External,
|
---|
1095 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1096 | BlockName -> VV,
|
---|
1097 | Value -> {VV[1,1] -> 1, VV[1,2] -> 0, VV[1,3] -> 0,
|
---|
1098 | VV[2,1] -> 0, VV[2,2] -> 1, VV[2,3] -> 0,
|
---|
1099 | VV[3,1] -> 0, VV[3,2] -> 0, VV[3,3] -> 1},
|
---|
1100 | ComplexParameter -> True,
|
---|
1101 | TeX -> Superscript[V,V],
|
---|
1102 | Description -> "V-Matrix"},
|
---|
1103 |
|
---|
1104 | ynd == {
|
---|
1105 | ParameterType -> Internal,
|
---|
1106 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1107 | Value -> {ynd[1,1] -> Sqrt[2] VeN1 MN1/(vev) , ynd[1,2] -> 0, ynd[1,3] -> 0,
|
---|
1108 | ynd[2,1] -> 0, ynd[2,2] -> Sqrt[2] VmuN2 MN2/(vev), ynd[2,3] -> 0,
|
---|
1109 | ynd[3,1] -> 0, ynd[3,2] -> 0, ynd[3,3] -> Sqrt[2] VtaN3 MN3/(vev)},
|
---|
1110 | TeX -> Superscript[y,nd],
|
---|
1111 | InteractionOrder -> {QED,1},
|
---|
1112 | Description -> "ynd-Matrix"},
|
---|
1113 |
|
---|
1114 | ynm == {
|
---|
1115 | ComplexParameter -> False,
|
---|
1116 | ParameterType -> Internal,
|
---|
1117 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1118 | Value -> {ynm[1, 1] -> MN1/(Sqrt[2]*x), ynm[1, 2] -> 0.0, ynm[1, 3] -> 0.0,
|
---|
1119 | ynm[2, 1] -> 0.0, ynm[2, 2] -> MN2/(Sqrt[2]*x), ynm[2, 3] -> 0.0,
|
---|
1120 | ynm[3, 1] -> 0.0, ynm[3, 2] -> 0.0, ynm[3, 3] -> MN3/(Sqrt[2]*x) },
|
---|
1121 | InteractionOrder -> {QED,1},
|
---|
1122 | Description -> "Majorana yukawa",
|
---|
1123 | TeX -> Subscript[y, MN]
|
---|
1124 | }
|
---|
1125 |
|
---|
1126 | };
|
---|
1127 |
|
---|
1128 | (* ************************** *)
|
---|
1129 | (* ***** Lagrangian ***** *)
|
---|
1130 | (* ************************** *)
|
---|
1131 |
|
---|
1132 | (* Kinetic terms for SM gauge fields and U(1)X gauge field Bp *)
|
---|
1133 |
|
---|
1134 | LGauge := Block[{mu,nu,ii,aa},
|
---|
1135 | ExpandIndices[-1/4 FS[B,mu,nu] FS[B,mu,nu] -1/4 FS[Bp,mu,nu] FS[Bp,mu,nu] - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa], FlavorExpand->SU2W]];
|
---|
1136 |
|
---|
1137 | (* Note that as we redefine LL in presence of light and heavy neutrino mixing, the term LLbar.Ga[mu].DC[LL, mu] contains all the new mixing dependent charged and neutral current interactions such as N-l-W, N-vl-Z, N-N-Z *)
|
---|
1138 |
|
---|
1139 | LFermions := Block[{mu},
|
---|
1140 | ExpandIndices[I*(
|
---|
1141 | QLbar.Ga[mu].DC[QL, mu] + LLbar.Ga[mu].DC[LL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu] + lRbar.Ga[mu].DC[lR, mu] ),
|
---|
1142 | FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
|
---|
1143 |
|
---|
1144 | (* Most general Higgs potential with SM Higgs doublet and new scalar Chi *)
|
---|
1145 |
|
---|
1146 | LHiggs := Block[{ii,mu, feynmangaugerules},
|
---|
1147 | feynmangaugerules = If[Not[FeynmanGauge], {GZ|GP|GPbar|GZp ->0}, {}];
|
---|
1148 |
|
---|
1149 | ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] + (DC[Chibar, mu]).DC[Chi, mu] + mu2H1 Phibar[ii] Phi[ii] + mu2H2 Chibar.Chi - \[Lambda]1 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]-\[Lambda]2 (Chibar.Chi)^2 -
|
---|
1150 | \[Lambda]3 (Phibar[ii] Phi[ii])*(Chibar.Chi), FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
|
---|
1151 | ];
|
---|
1152 |
|
---|
1153 | (* SM Yukawa *)
|
---|
1154 | LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
|
---|
1155 | feynmangaugerules = If[Not[FeynmanGauge], {GZ|GP|GPbar|GZp ->0}, {}];
|
---|
1156 |
|
---|
1157 | yuk = ExpandIndices[
|
---|
1158 | -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
|
---|
1159 | yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] - yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj] , FlavorExpand -> SU2D];
|
---|
1160 | yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
|
---|
1161 | yuk+HC[yuk]/.feynmangaugerules
|
---|
1162 | ];
|
---|
1163 |
|
---|
1164 | (* ************************** *)
|
---|
1165 | (* ***** RHN Lagrangian ***** *)
|
---|
1166 | (* ************************** *)
|
---|
1167 |
|
---|
1168 | LFermionsNR := Block[{mu},
|
---|
1169 | ExpandIndices[I*( NRbar.Ga[mu].DC[NR,mu] ),
|
---|
1170 | FlavorExpand->{SU2W,SU2D}]];
|
---|
1171 |
|
---|
1172 | (* LYukawaNR contains all the Higgs interactions such as vl-vl-H, vl-N-H, N-N-H *)
|
---|
1173 | LYukawaNR := Block[{ff1,ff2,sp,ii,yun,feynmangaugerules},
|
---|
1174 | feynmangaugerules = If[Not[FeynmanGauge], {GZ|GP|GPbar|GZp ->0}, {}];
|
---|
1175 | yun = ExpandIndices[
|
---|
1176 | -ynd[ff1,ff2] LLbar[sp,ii,ff1].NR[sp,ff2] Phibar[jj] Eps[ii, jj] - ynm[ff1,ff2]/2 NRcbar[sp,ff1].NR[sp,ff2] Chi, FlavorExpand -> SU2D];
|
---|
1177 | yun+HC[yun]/.feynmangaugerules
|
---|
1178 | ];
|
---|
1179 |
|
---|
1180 | LGhost := If[FeynmanGauge,
|
---|
1181 | Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB, dBRSTBp, LGhostBp},
|
---|
1182 |
|
---|
1183 | (***********First the pure gauge piece.**********************)
|
---|
1184 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
|
---|
1185 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
|
---|
1186 |
|
---|
1187 | dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
|
---|
1188 | LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
|
---|
1189 |
|
---|
1190 | dBRSTB[mu_] := cw/ee del[ghB, mu];
|
---|
1191 | LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
|
---|
1192 |
|
---|
1193 | dBRSTBp[mu_] := 1/g1pp del[ghBp, mu];
|
---|
1194 | LGhostBp := - g1pp ghBpbar.del[dBRSTBp[mu],mu];
|
---|
1195 |
|
---|
1196 | (***********Next the piece from the scalar field.************)
|
---|
1197 | LGhostphi :=
|
---|
1198 | (1/4*gw*vev (-gw*(vev +Ca*H1+Sa*H2) ghWibar[1].ghWi[1] + g1 phi2 ghWibar[1].ghB +gw phi2 ghWibar[1].ghWi[3] -gw GZ ghWibar[1].ghWi[2] + gt phi2 ghWibar[1].ghBp) +
|
---|
1199 | 1/4*gw*vev (-gw*(vev +Ca*H1+Sa*H2) ghWibar[2].ghWi[2] - g1 phi1 ghWibar[2].ghB -gw phi1 ghWibar[2].ghWi[3] +gw GZ ghWibar[2].ghWi[1] -gt phi1 ghWibar[2].ghBp) +
|
---|
1200 | 1/4*gw*vev (g1*(vev +Ca*H1+Sa*H2) ghWibar[3].ghB -gw*(vev +Ca*H1+Sa*H2) ghWibar[3].ghWi[3] +gw phi1 ghWibar[3].ghWi[2]
|
---|
1201 | -gw phi2 ghWibar[3].ghWi[1] +gt (vev +Ca*H1+Sa*H2) ghWibar[3].ghBp ) +
|
---|
1202 | 1/4*g1*vev (-g1*(vev +Ca*H1+Sa*H2) ghBbar.ghB +gw*(vev +Ca*H1+Sa*H2) ghBbar.ghWi[3] -gw phi1 ghBbar.ghWi[2] +gw phi2 ghBbar.ghWi[1] -gt*(vev +Ca*H1+Sa*H2) ghBbar.ghBp) +
|
---|
1203 | 1/4*gt*vev (-g1*(vev +Ca*H1+Sa*H2) ghBpbar.ghB +gw*(vev +Ca*H1+Sa*H2) ghBpbar.ghWi[3] -gw phi1 ghBpbar.ghWi[2] +gw phi2 ghBpbar.ghWi[1] -gt (vev +Ca*H1+Sa*H2) ghBpbar.ghBp) -
|
---|
1204 | 4*g1pp^2*x*(x-Sa*H1+Ca*H2) ghBpbar.ghBp) /.{phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])}
|
---|
1205 | ;
|
---|
1206 |
|
---|
1207 | (***********Now add the pieces together.********************)
|
---|
1208 | LGhostG + LGhostWi + LGhostB + LGhostphi + LGhostBp ],
|
---|
1209 | (*If unitary gauge, only include the gluonic ghost.*)
|
---|
1210 | Block[{dBRSTG,LGhostG},
|
---|
1211 | (***********First the pure gauge piece.**********************)
|
---|
1212 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
|
---|
1213 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
|
---|
1214 | (***********Now add the pieces together.********************)
|
---|
1215 | LGhostG]
|
---|
1216 | ];
|
---|
1217 |
|
---|
1218 |
|
---|
1219 | LRHN := LFermionsNR + LYukawaNR;
|
---|
1220 |
|
---|
1221 | LSM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;
|
---|
1222 | Lfull := LSM+LRHN;
|
---|