1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file for the Standard model ******)
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3 | (****** ******)
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4 | (****** Authors: N. Christensen, C. Duhr, B. Fuks ******)
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5 | (****** ******)
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6 | (****** Choose whether Feynman gauge is desired. ******)
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7 | (****** If set to False, unitary gauge is assumed. ****)
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8 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
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9 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
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10 | (***************************************************************************************************************)
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11 |
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12 | (* ************************** *)
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13 | (* ***** Information ***** *)
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14 | (* ************************** *)
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15 | M$ModelName = "Singlet Fermion coupling to photons EFT";
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16 |
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17 | M$Information = {
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18 | Authors -> {"A.Cheek", "Luca Pagani", "Ken Mimasu", "Chiara Arina"},
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19 | Version -> "1.0.0",
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20 | Date -> "16. 10. 2019",
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21 | Institutions -> {"Universite catholique de Louvain (CP3)"},
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22 | Emails -> {"andrew.cheek@uclouvain.be", "luca.pagani7@unibo.it", "ken.mimasu@uclouvain.be", "chiara.arina@uclouvain.be"},
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23 | URLs -> "NONE"
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24 | };
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25 |
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26 | FeynmanGauge = True;
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27 |
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28 | (* ************************** *)
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29 | (* ***** NLO Variables ****** *)
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30 | (******************************)
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31 |
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32 | FR$LoopSwitches = {{Gf, MW}};
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33 | FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
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34 | ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
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35 |
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36 | (* ************************** *)
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37 | (* ***** Change log ***** *)
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38 | (* ************************** *)
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39 |
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40 | (* v1.4.6: NLO variable added. *)
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41 | (* v1.4.5: Added widths for ghosts. *)
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42 | (* v1.4.4: Changed widths of goldstone bosons to be the same as for the W and Z bosons *)
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43 | (* v1.4.3: Updated conventions for the symmetric structure constants of SU3. *)
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44 | (* v1.4.2: Set FeynmanGauge=True as default again. *)
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45 | (* v1.4: Added SU(2) representation. *)
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46 | (* -> Modification in the field declarations (doublets are added) *)
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47 | (* -> Modification in the Lagrangian (much simpler). *)
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48 | (* v1.3: Added yukawa couplings for all fermions for gauge invariance. *)
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49 | (* Added yukawa couplings for 1st generation fermions to Massless.rst. *)
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50 | (* Updated parameters to PDG 2010. *)
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51 | (* v1.2: Set FeynmanGauge=True as default. *)
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52 | (* Set Gluonic ghosts to be included in both gauges. *)
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53 | (* v1.1: Fixed yukawa couplings in Feynman gauge. *)
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54 | (* Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. *)
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55 | (* Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. *)
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56 |
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57 |
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58 | (* ************************** *)
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59 | (* ***** Gauge groups ***** *)
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60 | (* ************************** *)
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61 | M$GaugeGroups = {
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62 | U1Y == {
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63 | Abelian -> True,
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64 | CouplingConstant -> g1,
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65 | GaugeBoson -> B,
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66 | Charge -> Y
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67 | },
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68 | SU2L == {
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69 | Abelian -> False,
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70 | CouplingConstant -> gw,
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71 | GaugeBoson -> Wi,
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72 | StructureConstant -> Eps,
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73 | Representations -> {Ta,SU2D},
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74 | Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
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75 | },
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76 | SU3C == {
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77 | Abelian -> False,
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78 | CouplingConstant -> gs,
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79 | GaugeBoson -> G,
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80 | StructureConstant -> f,
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81 | Representations -> {T,Colour},
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82 | SymmetricTensor -> dSUN
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83 | }
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84 | };
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85 |
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86 |
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87 | (* ************************** *)
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88 | (* ***** Indices ***** *)
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89 | (* ************************** *)
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90 |
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91 | IndexRange[Index[SU2W ]] = Unfold[Range[3]];
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92 | IndexRange[Index[SU2D ]] = Unfold[Range[2]];
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93 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
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94 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
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95 | IndexRange[Index[Generation]] = Range[3];
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96 |
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97 | IndexStyle[SU2W, j];
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98 | IndexStyle[SU2D, k];
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99 | IndexStyle[Gluon, a];
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100 | IndexStyle[Colour, m];
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101 | IndexStyle[Generation, f];
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102 |
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103 |
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104 | (* ************************** *)
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105 | (* *** Interaction orders *** *)
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106 | (* *** (as used by mg5) *** *)
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107 | (* ************************** *)
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108 |
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109 | M$InteractionOrderHierarchy = {
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110 | {NP, 1},
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111 | {QCD, 2},
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112 | {QED, 4}
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113 | };
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114 |
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115 | (* ************************** *)
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116 | (* **** Particle classes **** *)
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117 | (* ************************** *)
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118 | M$ClassesDescription = {
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119 |
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120 | (* Gauge bosons: physical vector fields *)
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121 | V[1] == {
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122 | ClassName -> A,
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123 | SelfConjugate -> True,
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124 | Mass -> 0,
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125 | Width -> 0,
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126 | ParticleName -> "a",
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127 | PDG -> 22,
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128 | PropagatorLabel -> "a",
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129 | PropagatorType -> W,
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130 | PropagatorArrow -> None,
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131 | FullName -> "Photon"
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132 | },
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133 | V[2] == {
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134 | ClassName -> Z,
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135 | SelfConjugate -> True,
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136 | Mass -> {MZ, 91.1876},
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137 | Width -> {WZ, 2.4952},
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138 | ParticleName -> "Z",
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139 | PDG -> 23,
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140 | PropagatorLabel -> "Z",
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141 | PropagatorType -> Sine,
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142 | PropagatorArrow -> None,
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143 | FullName -> "Z"
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144 | },
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145 | V[3] == {
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146 | ClassName -> W,
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147 | SelfConjugate -> False,
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148 | Mass -> {MW, 79.8244},
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149 | Width -> {WW, 2.085},
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150 | ParticleName -> "W+",
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151 | AntiParticleName -> "W-",
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152 | QuantumNumbers -> {Q -> 1},
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153 | PDG -> 24,
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154 | PropagatorLabel -> "W",
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155 | PropagatorType -> Sine,
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156 | PropagatorArrow -> Forward,
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157 | FullName -> "W"
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158 | },
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159 | V[4] == {
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160 | ClassName -> G,
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161 | SelfConjugate -> True,
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162 | Indices -> {Index[Gluon]},
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163 | Mass -> 0,
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164 | Width -> 0,
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165 | ParticleName -> "g",
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166 | PDG -> 21,
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167 | PropagatorLabel -> "G",
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168 | PropagatorType -> C,
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169 | PropagatorArrow -> None,
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170 | FullName -> "G"
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171 | },
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172 | (* Ghosts: related to physical gauge bosons *)
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173 | U[1] == {
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174 | ClassName -> ghA,
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175 | SelfConjugate -> False,
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176 | Ghost -> A,
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177 | QuantumNumbers -> {GhostNumber -> 1},
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178 | Mass -> 0,
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179 | Width -> 0,
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180 | PropagatorLabel -> "uA",
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181 | PropagatorType -> GhostDash,
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182 | PropagatorArrow -> Forward
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183 | },
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184 | U[2] == {
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185 | ClassName -> ghZ,
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186 | SelfConjugate -> False,
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187 | Ghost -> Z,
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188 | QuantumNumbers -> {GhostNumber -> 1},
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189 | Mass -> {MZ, 91.1876},
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190 | Width -> {WZ, 2.4952},
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191 | PropagatorLabel -> "uZ",
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192 | PropagatorType -> GhostDash,
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193 | PropagatorArrow -> Forward
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194 | },
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195 | U[31] == {
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196 | ClassName -> ghWp,
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197 | SelfConjugate -> False,
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198 | Ghost -> W,
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199 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
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200 | Mass -> {MW, 79.8244},
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201 | Width -> {WW, 2.085},
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202 | PropagatorLabel -> "uWp",
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203 | PropagatorType -> GhostDash,
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204 | PropagatorArrow -> Forward
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205 | },
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206 | U[32] == {
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207 | ClassName -> ghWm,
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208 | SelfConjugate -> False,
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209 | Ghost -> Wbar,
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210 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
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211 | Mass -> {MW, 79.8244},
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212 | Width -> {WW, 2.085},
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213 | PropagatorLabel -> "uWm",
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214 | PropagatorType -> GhostDash,
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215 | PropagatorArrow -> Forward
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216 | },
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217 | U[4] == {
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218 | ClassName -> ghG,
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219 | SelfConjugate -> False,
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220 | Indices -> {Index[Gluon]},
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221 | Ghost -> G,
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222 | QuantumNumbers ->{GhostNumber -> 1},
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223 | Mass -> 0,
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224 | Width -> 0,
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225 | PropagatorLabel -> "uG",
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226 | PropagatorType -> GhostDash,
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227 | PropagatorArrow -> Forward
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228 | },
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229 |
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230 | (* Gauge bosons: unphysical vector fields *)
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231 | V[11] == {
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232 | ClassName -> B,
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233 | Unphysical -> True,
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234 | SelfConjugate -> True,
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235 | Definitions -> {
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236 | B[mu_] ->(cw*A[mu] + sw*Z[mu])
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237 | }
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238 | },
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239 | V[12] == {
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240 | ClassName -> Wi,
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241 | Unphysical -> True,
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242 | SelfConjugate -> True,
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243 | Indices -> {Index[SU2W]},
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244 | FlavorIndex -> SU2W,
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245 | Definitions -> {
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246 | Wi[mu_,1] -> ( Wbar[mu] + W[mu] )/Sqrt[2],
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247 | Wi[mu_,2] -> ( Wbar[mu] - W[mu] )/(I*Sqrt[2]),
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248 | Wi[mu_,3] -> ( sw*A[mu] - cw*Z[mu] )
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249 | }
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250 | },
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251 |
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252 | (* Ghosts: related to unphysical gauge bosons *)
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253 | U[11] == {
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254 | ClassName -> ghB,
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255 | Unphysical -> True,
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256 | SelfConjugate -> False,
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257 | Ghost -> B,
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258 | Definitions -> { ghB -> -sw ghZ + cw ghA }
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259 | },
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260 | U[12] == {
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261 | ClassName -> ghWi,
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262 | Unphysical -> True,
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263 | SelfConjugate -> False,
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264 | Ghost -> Wi,
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265 | Indices -> {Index[SU2W]},
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266 | FlavorIndex -> SU2W,
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267 | Definitions -> { ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
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268 | ghWi[2] -> (ghWm - ghWp)/(I*Sqrt[2]),
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269 | ghWi[3] -> cw ghZ + sw ghA }
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270 | } ,
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271 |
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272 | (* Fermions: physical fields *)
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273 | F[1] == {
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274 | ClassName -> vl,
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275 | ClassMembers -> {ve, vm, vt},
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276 | Indices -> {Index[Generation]},
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277 | FlavorIndex -> Generation,
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278 | SelfConjugate -> False,
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279 | Mass -> 0,
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280 | Width -> 0,
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281 | QuantumNumbers -> {LeptonNumber -> 1},
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282 | PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
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283 | PropagatorType -> S,
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284 | PropagatorArrow -> Forward,
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285 | PDG -> {12,14,16},
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286 | ParticleName -> {"ve","vm","vt"},
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287 | AntiParticleName -> {"ve~","vm~","vt~"},
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288 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
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289 | },
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290 | F[2] == {
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291 | ClassName -> l,
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292 | ClassMembers -> {e, mu, ta},
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293 | Indices -> {Index[Generation]},
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294 | FlavorIndex -> Generation,
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295 | SelfConjugate -> False,
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296 | Mass -> {Ml, {Me,5.11*^-4}, {MM,0.10566}, {MTA,1.777}},
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297 | Width -> 0,
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298 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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299 | PropagatorLabel -> {"l", "e", "mu", "ta"},
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300 | PropagatorType -> Straight,
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301 | PropagatorArrow -> Forward,
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302 | PDG -> {11, 13, 15},
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303 | ParticleName -> {"e-", "mu-", "ta-"},
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304 | AntiParticleName -> {"e+", "mu+", "ta+"},
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305 | FullName -> {"Electron", "Muon", "Tau"}
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306 | },
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307 | F[3] == {
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308 | ClassName -> uq,
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309 | ClassMembers -> {u, c, t},
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310 | Indices -> {Index[Generation], Index[Colour]},
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311 | FlavorIndex -> Generation,
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312 | SelfConjugate -> False,
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313 | Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
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314 | Width -> {0, 0, {WT,1.50833649}},
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315 | QuantumNumbers -> {Q -> 2/3},
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316 | PropagatorLabel -> {"uq", "u", "c", "t"},
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317 | PropagatorType -> Straight,
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318 | PropagatorArrow -> Forward,
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319 | PDG -> {2, 4, 6},
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320 | ParticleName -> {"u", "c", "t" },
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321 | AntiParticleName -> {"u~", "c~", "t~"},
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322 | FullName -> {"u-quark", "c-quark", "t-quark"}
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323 | },
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324 | F[4] == {
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325 | ClassName -> dq,
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326 | ClassMembers -> {d, s, b},
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327 | Indices -> {Index[Generation], Index[Colour]},
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328 | FlavorIndex -> Generation,
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329 | SelfConjugate -> False,
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330 | Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
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331 | Width -> 0,
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332 | QuantumNumbers -> {Q -> -1/3},
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333 | PropagatorLabel -> {"dq", "d", "s", "b"},
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334 | PropagatorType -> Straight,
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335 | PropagatorArrow -> Forward,
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336 | PDG -> {1,3,5},
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337 | ParticleName -> {"d", "s", "b" },
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338 | AntiParticleName -> {"d~", "s~", "b~"},
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339 | FullName -> {"d-quark", "s-quark", "b-quark"}
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340 | },
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341 |
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342 | (* Fermions: unphysical fields *)
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343 | F[11] == {
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344 | ClassName -> LL,
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345 | Unphysical -> True,
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346 | Indices -> {Index[SU2D], Index[Generation]},
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347 | FlavorIndex -> SU2D,
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348 | SelfConjugate -> False,
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349 | QuantumNumbers -> {Y -> -1/2},
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350 | Definitions -> {
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351 | LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] vl[sp2,ff]],
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352 | LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]]
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353 | }
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354 | },
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355 | F[12] == {
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356 | ClassName -> lR,
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357 | Unphysical -> True,
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358 | Indices -> {Index[Generation]},
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359 | FlavorIndex -> Generation,
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360 | SelfConjugate -> False,
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361 | QuantumNumbers -> {Y -> -1},
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362 | Definitions -> {
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363 | lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]]
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364 | }
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365 | },
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366 | F[13] == {
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367 | ClassName -> QL,
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368 | Unphysical -> True,
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369 | Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
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370 | FlavorIndex -> SU2D,
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371 | SelfConjugate -> False,
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372 | QuantumNumbers -> {Y -> 1/6},
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373 | Definitions -> {
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374 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
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375 | QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2},
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376 | CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]
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377 | ]
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378 | }
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379 | },
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380 | F[14] == {
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381 | ClassName -> uR,
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382 | Unphysical -> True,
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383 | Indices -> {Index[Generation], Index[Colour]},
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384 | FlavorIndex -> Generation,
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385 | SelfConjugate -> False,
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386 | QuantumNumbers -> {Y -> 2/3},
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387 | Definitions -> {
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388 | uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]]
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389 | }
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390 | },
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391 | F[15] == {
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392 | ClassName -> dR,
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393 | Unphysical -> True,
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394 | Indices -> {Index[Generation], Index[Colour]},
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395 | FlavorIndex -> Generation,
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396 | SelfConjugate -> False,
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397 | QuantumNumbers -> {Y -> -1/3},
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398 | Definitions -> {
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399 | dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]]
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400 | }
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401 | },
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402 |
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403 | (* Fermionic DM candidates *)
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404 | F[16] == {
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405 | ClassName -> Chi,
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406 | SelfConjugate -> True,
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407 | Mass -> {MChi, 10.},
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408 | PropagatorLabel -> "X" ,
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409 | PropagatorType -> Straight,
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410 | PDG -> {9990},
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411 | Width -> 0,
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412 | ParticleName -> {"Chi"},
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413 | FullName -> {"Dark Majorana fermion singlet"}
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414 | },
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415 |
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416 | F[17] == {
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417 | ClassName -> Psi,
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418 | SelfConjugate -> False,
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419 | Mass -> {MPsi, 10.},
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420 | PropagatorLabel -> "Psi" ,
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421 | PropagatorType -> Straight,
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422 | PDG -> {9991},
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423 | Width -> 0,
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424 | ParticleName -> {"Psi"},
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425 | FullName -> {"Dark Dirac fermion singlet"}
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426 | },
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427 |
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428 | (* Higgs: physical scalars *)
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429 | S[1] == {
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430 | ClassName -> H,
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431 | SelfConjugate -> True,
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432 | Mass -> {MH,125},
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433 | Width -> {WH,0.00575308848},
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434 | PropagatorLabel -> "H",
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435 | PropagatorType -> D,
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436 | PropagatorArrow -> None,
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437 | PDG -> 25,
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438 | ParticleName -> "H",
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439 | FullName -> "H"
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440 | },
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441 |
|
---|
442 | (* Higgs: physical scalars *)
|
---|
443 | S[2] == {
|
---|
444 | ClassName -> G0,
|
---|
445 | SelfConjugate -> True,
|
---|
446 | Goldstone -> Z,
|
---|
447 | Mass -> {MZ, 91.1876},
|
---|
448 | Width -> {WZ, 2.4952},
|
---|
449 | PropagatorLabel -> "Go",
|
---|
450 | PropagatorType -> D,
|
---|
451 | PropagatorArrow -> None,
|
---|
452 | PDG -> 250,
|
---|
453 | ParticleName -> "G0",
|
---|
454 | FullName -> "G0"
|
---|
455 | },
|
---|
456 | S[3] == {
|
---|
457 | ClassName -> GP,
|
---|
458 | SelfConjugate -> False,
|
---|
459 | Goldstone -> W,
|
---|
460 | Mass -> {MW, 79.8244},
|
---|
461 | QuantumNumbers -> {Q -> 1},
|
---|
462 | Width -> {WW, 2.085},
|
---|
463 | PropagatorLabel -> "GP",
|
---|
464 | PropagatorType -> D,
|
---|
465 | PropagatorArrow -> None,
|
---|
466 | PDG -> 251,
|
---|
467 | ParticleName -> "G+",
|
---|
468 | AntiParticleName -> "G-",
|
---|
469 | FullName -> "GP"
|
---|
470 | },
|
---|
471 |
|
---|
472 | (* Higgs: unphysical scalars *)
|
---|
473 | S[11] == {
|
---|
474 | ClassName -> Phi,
|
---|
475 | Unphysical -> True,
|
---|
476 | Indices -> {Index[SU2D]},
|
---|
477 | FlavorIndex -> SU2D,
|
---|
478 | SelfConjugate -> False,
|
---|
479 | QuantumNumbers -> {Y -> 1/2},
|
---|
480 | Definitions -> {
|
---|
481 | Phi[1] -> -I GP,
|
---|
482 | (* Canonical normalisation of Higgs and G0 fields *)
|
---|
483 | Phi[2] -> ( vev + H + I G0 )/Sqrt[2]
|
---|
484 | }
|
---|
485 | }
|
---|
486 | };
|
---|
487 |
|
---|
488 |
|
---|
489 | (* ************************** *)
|
---|
490 | (* ***** Gauge ***** *)
|
---|
491 | (* ***** Parameters ***** *)
|
---|
492 | (* ***** (FeynArts) ***** *)
|
---|
493 | (* ************************** *)
|
---|
494 |
|
---|
495 | GaugeXi[ V[1] ] = GaugeXi[A];
|
---|
496 | GaugeXi[ V[2] ] = GaugeXi[Z];
|
---|
497 | GaugeXi[ V[3] ] = GaugeXi[W];
|
---|
498 | GaugeXi[ V[4] ] = GaugeXi[G];
|
---|
499 | GaugeXi[ S[1] ] = 1;
|
---|
500 | GaugeXi[ S[2] ] = GaugeXi[Z];
|
---|
501 | GaugeXi[ S[3] ] = GaugeXi[W];
|
---|
502 | GaugeXi[ U[1] ] = GaugeXi[A];
|
---|
503 | GaugeXi[ U[2] ] = GaugeXi[Z];
|
---|
504 | GaugeXi[ U[31] ] = GaugeXi[W];
|
---|
505 | GaugeXi[ U[32] ] = GaugeXi[W];
|
---|
506 | GaugeXi[ U[4] ] = GaugeXi[G];
|
---|
507 |
|
---|
508 |
|
---|
509 | (* ************************** *)
|
---|
510 | (* ***** Parameters ***** *)
|
---|
511 | (* ************************** *)
|
---|
512 | M$Parameters = {
|
---|
513 |
|
---|
514 | (* External parameters *)
|
---|
515 | Gf == {
|
---|
516 | ParameterType -> External,
|
---|
517 | BlockName -> SMINPUTS,
|
---|
518 | OrderBlock -> 2,
|
---|
519 | Value -> 1.16637*^-5,
|
---|
520 | InteractionOrder -> {QED,2},
|
---|
521 | TeX -> Subscript[G,f],
|
---|
522 | Description -> "Fermi constant"
|
---|
523 | },
|
---|
524 | Mreno == {
|
---|
525 | ParameterType -> External,
|
---|
526 | BlockName -> Renor,
|
---|
527 | Value -> 555,
|
---|
528 | TeX -> Subscript[M,reno],
|
---|
529 | Description -> "scale for the renormalisation of dim6 op"
|
---|
530 | },
|
---|
531 | aS == {
|
---|
532 | ParameterType -> External,
|
---|
533 | BlockName -> SMINPUTS,
|
---|
534 | OrderBlock -> 3,
|
---|
535 | Value -> 0.1184,
|
---|
536 | InteractionOrder -> {QCD,2},
|
---|
537 | TeX -> Subscript[\[Alpha],s],
|
---|
538 | Description -> "Strong coupling constant at the Z pole"
|
---|
539 | },
|
---|
540 | ymdo == {
|
---|
541 | ParameterType -> External,
|
---|
542 | BlockName -> YUKAWA,
|
---|
543 | OrderBlock -> 1,
|
---|
544 | Value -> 5.04*^-3,
|
---|
545 | Description -> "Down Yukawa mass"
|
---|
546 | },
|
---|
547 | ymup == {
|
---|
548 | ParameterType -> External,
|
---|
549 | BlockName -> YUKAWA,
|
---|
550 | OrderBlock -> 2,
|
---|
551 | Value -> 2.55*^-3,
|
---|
552 | Description -> "Up Yukawa mass"
|
---|
553 | },
|
---|
554 | yms == {
|
---|
555 | ParameterType -> External,
|
---|
556 | BlockName -> YUKAWA,
|
---|
557 | OrderBlock -> 3,
|
---|
558 | Value -> 0.101,
|
---|
559 | Description -> "Strange Yukawa mass"
|
---|
560 | },
|
---|
561 | ymc == {
|
---|
562 | ParameterType -> External,
|
---|
563 | BlockName -> YUKAWA,
|
---|
564 | OrderBlock -> 4,
|
---|
565 | Value -> 1.27,
|
---|
566 | Description -> "Charm Yukawa mass"
|
---|
567 | },
|
---|
568 | ymb == {
|
---|
569 | ParameterType -> External,
|
---|
570 | BlockName -> YUKAWA,
|
---|
571 | OrderBlock -> 5,
|
---|
572 | Value -> 4.7,
|
---|
573 | Description -> "Bottom Yukawa mass"
|
---|
574 | },
|
---|
575 | ymt == {
|
---|
576 | ParameterType -> External,
|
---|
577 | BlockName -> YUKAWA,
|
---|
578 | OrderBlock -> 6,
|
---|
579 | Value -> 172,
|
---|
580 | Description -> "Top Yukawa mass"
|
---|
581 | },
|
---|
582 | yme == {
|
---|
583 | ParameterType -> External,
|
---|
584 | BlockName -> YUKAWA,
|
---|
585 | OrderBlock -> 11,
|
---|
586 | Value -> 5.11*^-4,
|
---|
587 | Description -> "Electron Yukawa mass"
|
---|
588 | },
|
---|
589 | ymm == {
|
---|
590 | ParameterType -> External,
|
---|
591 | BlockName -> YUKAWA,
|
---|
592 | OrderBlock -> 13,
|
---|
593 | Value -> 0.10566,
|
---|
594 | Description -> "Muon Yukawa mass"
|
---|
595 | },
|
---|
596 | ymtau == {
|
---|
597 | ParameterType -> External,
|
---|
598 | BlockName -> YUKAWA,
|
---|
599 | OrderBlock -> 15,
|
---|
600 | Value -> 1.777,
|
---|
601 | Description -> "Tau Yukawa mass"
|
---|
602 | },
|
---|
603 | cabi == {
|
---|
604 | ParameterType -> External,
|
---|
605 | BlockName -> CKMBLOCK,
|
---|
606 | OrderBlock -> 1,
|
---|
607 | Value -> 0.227736,
|
---|
608 | TeX -> Subscript[\[Theta], c],
|
---|
609 | Description -> "Cabibbo angle"
|
---|
610 | },
|
---|
611 | (* External parameters *)
|
---|
612 | Lambda == {
|
---|
613 | ParameterType -> External,
|
---|
614 | BlockName -> LDARK,
|
---|
615 | OrderBlock -> 1,
|
---|
616 | Value -> 100000.,
|
---|
617 | InteractionOrder -> {NP, -1},
|
---|
618 | TeX -> \[CapitalLambda],
|
---|
619 | Description -> "EFT cutoff"
|
---|
620 | },
|
---|
621 |
|
---|
622 | CAn == {
|
---|
623 | ParameterType -> External,
|
---|
624 | BlockName -> LDARK,
|
---|
625 | OrderBlock -> 2,
|
---|
626 | InteractionOrder -> {QED,1},
|
---|
627 | Value -> 1.,
|
---|
628 | TeX -> Subscript[C,An],
|
---|
629 | Description -> "Anapole coupling"
|
---|
630 | },
|
---|
631 | CBan == {
|
---|
632 | ParameterType -> External,
|
---|
633 | BlockName -> LDARK,
|
---|
634 | OrderBlock -> 3,
|
---|
635 | InteractionOrder -> {QED,1},
|
---|
636 | Value -> 1.,
|
---|
637 | TeX -> Subscript[C,Ban],
|
---|
638 | Description -> "Banapole coupling"
|
---|
639 | },
|
---|
640 |
|
---|
641 | CMag == {
|
---|
642 | ParameterType -> External,
|
---|
643 | BlockName -> LDARK,
|
---|
644 | OrderBlock -> 4,
|
---|
645 | InteractionOrder -> {QED,1},
|
---|
646 | Value -> 1.,
|
---|
647 | TeX -> Subscript[C,Mag],
|
---|
648 | Description -> "Magnetic dipole coupling"
|
---|
649 | },
|
---|
650 |
|
---|
651 | CBmag == {
|
---|
652 | ParameterType -> External,
|
---|
653 | BlockName -> LDARK,
|
---|
654 | OrderBlock -> 5,
|
---|
655 | InteractionOrder -> {QED,1},
|
---|
656 | Value -> 1.,
|
---|
657 | TeX -> Subscript[C,Bmag],
|
---|
658 | Description -> "B-Magnetic dipole coupling"
|
---|
659 | },
|
---|
660 |
|
---|
661 | CElec == {
|
---|
662 | ParameterType -> External,
|
---|
663 | BlockName -> LDARK,
|
---|
664 | OrderBlock -> 6,
|
---|
665 | InteractionOrder -> {QED,1},
|
---|
666 | Value -> 1.,
|
---|
667 | TeX -> Subscript[C,Elec],
|
---|
668 | Description -> "Electric dipole coupling"
|
---|
669 | },
|
---|
670 |
|
---|
671 | CBelec == {
|
---|
672 | ParameterType -> External,
|
---|
673 | BlockName -> LDARK,
|
---|
674 | OrderBlock -> 7,
|
---|
675 | InteractionOrder -> {QED,1},
|
---|
676 | Value -> 1.,
|
---|
677 | TeX -> Subscript[C,Belec],
|
---|
678 | Description -> "B-Electric dipole coupling"
|
---|
679 | },
|
---|
680 | Ccr == {
|
---|
681 | ParameterType -> External,
|
---|
682 | BlockName -> LDARK,
|
---|
683 | OrderBlock -> 8,
|
---|
684 | InteractionOrder -> {QED,1},
|
---|
685 | Value -> 1.,
|
---|
686 | TeX -> Subscript[C,CR],
|
---|
687 | Description -> "Charge-Radius coupling"
|
---|
688 | },
|
---|
689 |
|
---|
690 | CBcr == {
|
---|
691 | ParameterType -> External,
|
---|
692 | BlockName -> LDARK,
|
---|
693 | OrderBlock -> 9,
|
---|
694 | InteractionOrder -> {QED,1},
|
---|
695 | Value -> 1.,
|
---|
696 | TeX -> Subscript[C,Bcr],
|
---|
697 | Description -> "B Charge-Radius coupling"
|
---|
698 | },
|
---|
699 |
|
---|
700 | CDan == {
|
---|
701 | ParameterType -> External,
|
---|
702 | BlockName -> LDARK,
|
---|
703 | OrderBlock -> 10,
|
---|
704 | InteractionOrder -> {QED,1},
|
---|
705 | Value -> 1.,
|
---|
706 | TeX -> Subscript[C,Dan],
|
---|
707 | Description -> "Anapole coupling to Dirac DM"
|
---|
708 | },
|
---|
709 | CBdan == {
|
---|
710 | ParameterType -> External,
|
---|
711 | BlockName -> LDARK,
|
---|
712 | OrderBlock -> 11,
|
---|
713 | InteractionOrder -> {QED,1},
|
---|
714 | Value -> 1.,
|
---|
715 | TeX -> Subscript[C,Bdan],
|
---|
716 | Description -> "Banapole coupling to Dirac"
|
---|
717 | },
|
---|
718 |
|
---|
719 |
|
---|
720 | (* Internal Parameters *)
|
---|
721 | (* SM inputs *)
|
---|
722 | (* EW parameters *)
|
---|
723 | vev == {
|
---|
724 | ParameterType -> Internal,
|
---|
725 | Value -> (
|
---|
726 | Sqrt[ 1/(Sqrt[2]*Gf) ]
|
---|
727 | ),
|
---|
728 | TeX -> v,
|
---|
729 | InteractionOrder -> {QED,-1},
|
---|
730 | Description -> "Higgs vacuum expectation value in terms of Gf in the SM"
|
---|
731 | },
|
---|
732 |
|
---|
733 | cw == {
|
---|
734 | ParameterType -> Internal,
|
---|
735 | Value -> MW/MZ ,
|
---|
736 | TeX -> Subscript[c,w],
|
---|
737 | Description -> "Cosine of the Weinberg angle in terms of inputs in the SM"
|
---|
738 | },
|
---|
739 |
|
---|
740 | sw == {
|
---|
741 | ParameterType -> Internal,
|
---|
742 | Value -> ( Sqrt[1 - (MW/MZ)^2] ),
|
---|
743 | TeX -> Subscript[s,w],
|
---|
744 | Description -> "Sine of the Weinberg angle in terms of inputs in the SM"
|
---|
745 | },
|
---|
746 |
|
---|
747 | ee == {
|
---|
748 | ParameterType -> Internal,
|
---|
749 | Value -> 2*MW*sw/vev,
|
---|
750 | InteractionOrder -> {QED,1},
|
---|
751 | TeX -> e,
|
---|
752 | Description -> "Electric coupling constant in terms of inputs in the SM"
|
---|
753 | },
|
---|
754 |
|
---|
755 | gw == {
|
---|
756 | ParameterType -> Internal,
|
---|
757 | Definitions -> {
|
---|
758 | gw -> ee/sw
|
---|
759 | },
|
---|
760 | InteractionOrder -> {QED,1},
|
---|
761 | TeX -> Subscript[g,w],
|
---|
762 | Description -> "Weak coupling constant at the Z pole"
|
---|
763 | },
|
---|
764 |
|
---|
765 | g1 == {
|
---|
766 | ParameterType -> Internal,
|
---|
767 | Definitions -> {
|
---|
768 | g1 -> ee/cw
|
---|
769 | },
|
---|
770 | InteractionOrder -> {QED,1},
|
---|
771 | TeX -> Subscript[g,1],
|
---|
772 | Description -> "U(1)Y coupling constant at the Z pole"
|
---|
773 | },
|
---|
774 |
|
---|
775 | gs == {
|
---|
776 | ParameterType -> Internal,
|
---|
777 | Value -> Sqrt[4 Pi aS],
|
---|
778 | InteractionOrder -> {QCD,1},
|
---|
779 | TeX -> Subscript[g,s],
|
---|
780 | ParameterName -> G,
|
---|
781 | Description -> "Strong coupling constant at the Z pole"
|
---|
782 | },
|
---|
783 |
|
---|
784 | aEW == {
|
---|
785 | ParameterType -> Internal,
|
---|
786 | Value -> ee^2/(4*Pi),
|
---|
787 | InteractionOrder -> {QED,2},
|
---|
788 | TeX -> Subscript[\[Alpha], EW],
|
---|
789 | Description -> "Electroweak fine structure constant"
|
---|
790 | },
|
---|
791 |
|
---|
792 | aEWM1 == {
|
---|
793 | ParameterType -> Internal,
|
---|
794 | OrderBlock -> 1,
|
---|
795 | Value -> 1/aEW,
|
---|
796 | InteractionOrder -> {QED,-2},
|
---|
797 | Description -> "Inverse of the EW coupling constant at the Z pole"
|
---|
798 | },
|
---|
799 |
|
---|
800 | lam == {
|
---|
801 | ParameterType -> Internal,
|
---|
802 | Definitions -> {
|
---|
803 | lam -> (MH^2)/(2*vev^2)
|
---|
804 | },
|
---|
805 | InteractionOrder -> {QED, 2},
|
---|
806 | Description -> "Higgs quartic coupling"
|
---|
807 | },
|
---|
808 |
|
---|
809 | muH == {
|
---|
810 | ParameterType -> Internal,
|
---|
811 | Definitions -> { muH -> MH/Sqrt[2] },
|
---|
812 | TeX -> \[Mu],
|
---|
813 | Description -> "Mass parameter of the Higgs potential in terms of inputs in the SM"
|
---|
814 | },
|
---|
815 |
|
---|
816 | yl == {
|
---|
817 | ParameterType -> Internal,
|
---|
818 | Indices -> {Index[Generation], Index[Generation]},
|
---|
819 | Definitions -> {
|
---|
820 | yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j),
|
---|
821 | yl[1,1] -> Sqrt[2] yme / vev ,
|
---|
822 | yl[2,2] -> Sqrt[2] ymm / vev ,
|
---|
823 | yl[3,3] -> Sqrt[2] ymtau/ vev
|
---|
824 | },
|
---|
825 | InteractionOrder -> {QED, 1},
|
---|
826 | ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
|
---|
827 | TeX -> Superscript[y, l],
|
---|
828 | Description -> "Lepton Yukawa couplings"
|
---|
829 | },
|
---|
830 |
|
---|
831 | yu == {
|
---|
832 | ParameterType -> Internal,
|
---|
833 | Indices -> {Index[Generation], Index[Generation]},
|
---|
834 | Definitions -> {
|
---|
835 | yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j),
|
---|
836 | yu[1,1] -> Sqrt[2] ymup/ vev,
|
---|
837 | yu[2,2] -> Sqrt[2] ymc / vev,
|
---|
838 | yu[3,3] -> Sqrt[2] ymt / vev
|
---|
839 | },
|
---|
840 | InteractionOrder -> {QED, 1},
|
---|
841 | ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
|
---|
842 | TeX -> Superscript[y, u],
|
---|
843 | Description -> "Up-type Yukawa couplings"
|
---|
844 | },
|
---|
845 |
|
---|
846 | yd == {
|
---|
847 | ParameterType -> Internal,
|
---|
848 | Indices -> {Index[Generation], Index[Generation]},
|
---|
849 | Definitions -> {
|
---|
850 | yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j),
|
---|
851 | yd[1,1] -> Sqrt[2] ymdo/ vev,
|
---|
852 | yd[2,2] -> Sqrt[2] yms / vev,
|
---|
853 | yd[3,3] -> Sqrt[2] ymb / vev
|
---|
854 | },
|
---|
855 | InteractionOrder -> {QED, 1},
|
---|
856 | ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
|
---|
857 | TeX -> Superscript[y, d],
|
---|
858 | Description -> "Down-type Yukawa couplings"
|
---|
859 | },
|
---|
860 |
|
---|
861 | (* N. B. : only Cabibbo mixing! *)
|
---|
862 | CKM == {
|
---|
863 | ParameterType -> Internal,
|
---|
864 | Indices -> {Index[Generation], Index[Generation]},
|
---|
865 | Unitary -> True,
|
---|
866 | Value -> {
|
---|
867 | CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
|
---|
868 | CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
|
---|
869 | CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1
|
---|
870 | },
|
---|
871 | TeX -> Superscript[V,CKM],
|
---|
872 | Description -> "CKM-Matrix"}
|
---|
873 | };
|
---|
874 |
|
---|
875 |
|
---|
876 | (* ************************** *)
|
---|
877 | (* ***** Lagrangian ***** *)
|
---|
878 | (* ************************** *)
|
---|
879 |
|
---|
880 | ckm = {Conjugate[CKM[i_, j_]] -> IndexDelta[i, j], CKM[i_, j_] -> IndexDelta[i, j]};
|
---|
881 |
|
---|
882 | ExpandFunc[a_, subs___] := (
|
---|
883 | ( ExpandIndices[a, FlavorExpand -> True] /. Flatten[List[subs]] ) // Expand
|
---|
884 | (* // ReplaceAll[#, Power[Lambda, i_Integer] :> 0 /; i < -2] &
|
---|
885 | // Series[#, {Lambda, Infinity , 2}] & // Normal *)
|
---|
886 | )
|
---|
887 |
|
---|
888 | LGauge := Module[{mu,nu,ii,aa},
|
---|
889 |
|
---|
890 | Print["--- Expanding LGauge ---"];
|
---|
891 |
|
---|
892 | Map[ExpandFunc, {
|
---|
893 | - 1/4 FS[B,mu,nu] FS[B,mu,nu],
|
---|
894 | - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii],
|
---|
895 | - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa]
|
---|
896 | }
|
---|
897 | ] // Total
|
---|
898 |
|
---|
899 | ];
|
---|
900 |
|
---|
901 |
|
---|
902 | LFermions := Module[{mu},
|
---|
903 |
|
---|
904 | Print["--- Expanding LFermions ---"];
|
---|
905 |
|
---|
906 | Map[ExpandFunc[#, {}] &, {
|
---|
907 | I*QLbar.Ga[mu].DC[QL, mu],
|
---|
908 | I*LLbar.Ga[mu].DC[LL, mu],
|
---|
909 | I*uRbar.Ga[mu].DC[uR, mu],
|
---|
910 | I*dRbar.Ga[mu].DC[dR, mu],
|
---|
911 | I*lRbar.Ga[mu].DC[lR, mu]
|
---|
912 | }
|
---|
913 | ] // Total
|
---|
914 |
|
---|
915 | ];
|
---|
916 |
|
---|
917 |
|
---|
918 | LHiggs := Module[{ii,jj,mu,feynmangaugerules},
|
---|
919 |
|
---|
920 | Print["--- Expanding LHiggs ---"];
|
---|
921 |
|
---|
922 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
923 |
|
---|
924 | Map[ExpandFunc[#, feynmangaugerules] &, {
|
---|
925 | DC[Phibar[ii],mu] DC[Phi[ii],mu] ,
|
---|
926 | muH^2 Phibar[ii] Phi[ii],
|
---|
927 | - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]
|
---|
928 | }
|
---|
929 | ] // Total
|
---|
930 |
|
---|
931 | ];
|
---|
932 |
|
---|
933 |
|
---|
934 | LYukawa := Module[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
|
---|
935 |
|
---|
936 | Print["--- Expanding LYukawa ---"];
|
---|
937 |
|
---|
938 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
939 |
|
---|
940 | yuk = Map[ExpandFunc[#, feynmangaugerules] &, {
|
---|
941 | - yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc] dR[sp, ff3, cc] Phi[ii],
|
---|
942 | - yl[ff1, ff3] LLbar[sp, ii, ff1] lR[sp, ff3] Phi[ii],
|
---|
943 | - yu[ff1, ff2] QLbar[sp, ii, ff1, cc] uR[sp, ff2, cc] Phibar[jj] Eps[ii, jj]
|
---|
944 | }
|
---|
945 | ] // Total;
|
---|
946 |
|
---|
947 | yuk+HC[yuk]
|
---|
948 |
|
---|
949 | ];
|
---|
950 |
|
---|
951 |
|
---|
952 | LGhost := Module[ {LGh1,LGhw,LGhs,LGhphi,mu,generators,gh,ghbar,
|
---|
953 | Vectorize,phi1,phi2,togoldstones,doublet,doublet0,ii},
|
---|
954 |
|
---|
955 | Print["--- Expanding LGhost ---"];
|
---|
956 |
|
---|
957 | (* Pure gauge piece *)
|
---|
958 | LGh1 = -ghBbar.del[DC[ghB,mu],mu];
|
---|
959 | LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
|
---|
960 | LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
|
---|
961 |
|
---|
962 | (* Scalar pieces: see Peskin pages 739-742 *)
|
---|
963 | (* phi1 and phi2 are the real degrees of freedom of GP *)
|
---|
964 | (* Vectorize transforms a doublet in a vector in the phi-basis, *)
|
---|
965 | (* i.e. the basis of real degrees of freedom *)
|
---|
966 | gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
|
---|
967 | ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
|
---|
968 |
|
---|
969 | generators = { -I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1],
|
---|
970 | -I/2 gw PauliSigma[2] , -I/2 gw PauliSigma[3]};
|
---|
971 |
|
---|
972 | doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
|
---|
973 | doublet0 = {0, vev/Sqrt[2]};
|
---|
974 | Vectorize[{a_, b_}]:= Simplify[
|
---|
975 | {Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]],
|
---|
976 | Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]
|
---|
977 | }/.{Im[_]->0, Re[num_]->num}
|
---|
978 | ];
|
---|
979 |
|
---|
980 | togoldstones := {phi1 -> ( GP + GPbar )/Sqrt[2],
|
---|
981 | phi2 -> (-GP + GPbar )/(I Sqrt[2])};
|
---|
982 |
|
---|
983 | LGhphi = Plus@@Flatten[Table[
|
---|
984 | - ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0]
|
---|
985 | . Vectorize[generators[[lll]].(doublet+doublet0)],
|
---|
986 | {kkk,4}, {lll,4}
|
---|
987 | ]]/.togoldstones;
|
---|
988 |
|
---|
989 | ExpandIndices[
|
---|
990 | LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi, 0]
|
---|
991 | , FlavorExpand->SU2W
|
---|
992 | ]
|
---|
993 |
|
---|
994 | ]// Expand ;
|
---|
995 |
|
---|
996 | (* Full Lagrangian *)
|
---|
997 | LSM := LGauge + LFermions + LHiggs + LYukawa + LGhost;
|
---|
998 |
|
---|
999 | Lkin := I/2 Chibar.Ga[mu].del[Chi, mu]\
|
---|
1000 | - 1/2 MChi Chibar.Chi\
|
---|
1001 | + I Psibar.Ga[mu].del[Psi,mu]\
|
---|
1002 | - MPsi Psibar.Psi;
|
---|
1003 |
|
---|
1004 | Lan := cw(CAn/Lambda^2) (1/2) Chibar.Ga[mu].Ga[5].Chi.del[FS[A, mu, nu],nu]
|
---|
1005 |
|
---|
1006 | Lban := (CBan/Lambda^2) (1/2) Chibar.Ga[mu].Ga[5].Chi.del[FS[B, mu, nu],nu]
|
---|
1007 |
|
---|
1008 | Lmag := cw(CMag/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Psi.FS[A, mu, nu] - cw(CMag/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Psi.FS[A, mu, nu]
|
---|
1009 |
|
---|
1010 | LBmag := (CBmag/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Psi.FS[B, mu, nu] - (CBmag/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Psi.FS[B, mu, nu]
|
---|
1011 |
|
---|
1012 | Lelec := cw I (CElec/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Ga[5].Psi.FS[A, mu, nu] - cw I (CElec/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Ga[5].Psi.FS[A, mu, nu]
|
---|
1013 |
|
---|
1014 | LBelec := I (CBelec/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Ga[5].Psi.FS[B, mu, nu] - I (CBelec/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Ga[5].Psi.FS[B, mu, nu]
|
---|
1015 |
|
---|
1016 | LCR := cw (Ccr/Lambda^2) Psibar.Ga[mu].Psi.del[FS[A, mu, nu], nu]
|
---|
1017 |
|
---|
1018 | LBcr := (CBcr/Lambda^2) Psibar.Ga[mu].Psi.del[FS[B, mu, nu], nu]
|
---|
1019 |
|
---|
1020 | LAndirac := cw(CDan/Lambda^2) Psibar.Ga[mu].Ga[5].Psi.del[FS[A, mu, nu],nu]
|
---|
1021 |
|
---|
1022 | LBandirac := (CBdan/Lambda^2) Psibar.Ga[mu].Ga[5].Psi.del[FS[B, mu, nu],nu]
|
---|