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 | (****** Adapted by A. Alloul for mass diagonalization ******)
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6 | (****** ******)
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7 | (****** Choose whether Feynman gauge is desired. ******)
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8 | (****** If set to False, unitary gauge is assumed. ****)
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9 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
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10 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
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11 | (***************************************************************************************************************)
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12 |
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13 | (* ************************** *)
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14 | (* ***** Information ***** *)
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15 | (* ************************** *)
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16 | M$ModelName = "2HDM_mix";
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17 |
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18 | M$Information = {
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19 | Authors -> "K. De Causmaecker",
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20 | Version -> "1.0.0",
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21 | Date -> "11. 01. 2013",
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22 | Institutions -> "IIHE - Vrije Universiteit Brussel",
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23 | Emails -> "Karen.De.Causmaecker@vub.ac.be"
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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 | (* ***** Change log ***** *)
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30 | (* ************************** *)
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31 |
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32 | (* v1.0.0: 2HDM adapted for the mass diagonalization routine*)
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33 |
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34 | (* ************************** *)
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35 | (* ***** vevs & mixings ***** *)
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36 | (* ************************** *)
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37 | M$vevs = { {phi1[2],vev1} };
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38 |
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39 | M$MixingsDescription = {
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40 | Mix["1u"] == {
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41 | MassBasis -> {A, Z},
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42 | GaugeBasis -> {B, Wi[3]},
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43 | MixingMatrix -> UG,
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44 | BlockName -> WEAKMIX
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45 | },
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46 |
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47 | Mix["2"] == {
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48 | MassBasis -> {W, Wbar},
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49 | GaugeBasis -> {Wi[1], Wi[2]},
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50 | Value -> {{1/Sqrt[2], -I/Sqrt[2]}, {1/Sqrt[2], I/Sqrt[2]}}
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51 | },
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52 |
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53 | Mix["1p"] == {
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54 | MassBasis -> {{H0}, {G0}},
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55 | GaugeBasis -> {phi1[2]},
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56 | Value -> {{{1}}, {{1}}}
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57 | },
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58 |
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59 | Mix["2p"] == {
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60 | MassBasis -> {{R0}, {I0}},
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61 | GaugeBasis -> {phi2[2]},
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62 | Value -> {{{1}}, {{1}}}
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63 | },
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64 |
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65 | Mix["1s"] == {
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66 | MassBasis -> {h1, h2, h3},
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67 | GaugeBasis -> {H0, R0, I0},
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68 | MixingMatrix -> NH,
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69 | BlockName -> NHMIX
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70 | },
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71 |
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72 | Mix["2s"] == {
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73 | MassBasis -> {HP1},
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74 | GaugeBasis -> {phi1[1]},
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75 | MixingMatrix -> CH1,
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76 | BlockName -> CH1MIX
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77 | },
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78 |
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79 | Mix["3s"] == {
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80 | MassBasis -> {HP2},
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81 | GaugeBasis -> {phi2[1]},
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82 | MixingMatrix -> CH2,
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83 | BlockName -> CH2MIX
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84 | },
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85 |
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86 | Mix["4a"] == {
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87 | MassBasis -> {dq[1, _], dq[2, _], dq[3, _]},
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88 | GaugeBasis -> {{QL[2, 1, _], QL[2, 2, _], QL[2, 3, _]}, {dR[1, _], dR[2, _], dR[3, _]}},
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89 | MixingMatrix -> {CKM, _},
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90 | Inverse -> {True, _},
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91 | Value -> {_, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}
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92 | },
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93 |
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94 | Mix["4b"] == {
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95 | MassBasis -> {uq[1, _], uq[2, _], uq[3, _]},
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96 | GaugeBasis -> {{QL[1, 1, _], QL[1, 2, _], QL[1, 3, _]}, {uR[1, _], uR[2, _], uR[3, _]}}, Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}
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97 | },
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98 |
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99 | Mix["5a"] == {
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100 | MassBasis -> {l[1], l[2], l[3]},
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101 | GaugeBasis -> {{LL[2, 1], LL[2, 2], LL[2, 3]}, {lR[1], lR[2], lR[3]}}, Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}
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102 | },
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103 |
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104 | Mix["5b"] == {
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105 | MassBasis -> {vl[1], vl[2], vl[3]},
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106 | GaugeBasis -> {LL[1, 1], LL[1, 2], LL[1, 3]},
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107 | Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}}
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108 | }
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109 | };
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110 |
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111 |
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112 | (* ************************** *)
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113 | (* ***** Gauge groups ***** *)
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114 | (* ************************** *)
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115 | M$GaugeGroups = {
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116 | U1Y == {
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117 | Abelian -> True,
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118 | CouplingConstant -> g1,
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119 | GaugeBoson -> B,
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120 | Charge -> Y
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121 | },
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122 |
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123 | SU2L == {
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124 | Abelian -> False,
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125 | CouplingConstant -> gw,
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126 | GaugeBoson -> Wi,
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127 | StructureConstant -> Eps,
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128 | Representations -> {Ta,SU2D},
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129 | Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
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130 | },
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131 |
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132 | SU3C == {
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133 | Abelian -> False,
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134 | CouplingConstant -> gs,
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135 | GaugeBoson -> G,
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136 | StructureConstant -> f,
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137 | Representations -> {T,Colour},
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138 | DTerm -> dSUN
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139 | }
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140 | };
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141 |
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142 |
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143 | (* ************************** *)
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144 | (* ***** Indices ***** *)
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145 | (* ************************** *)
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146 |
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147 | IndexRange[Index[SU2W ]] = Unfold[Range[3]];
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148 | IndexRange[Index[SU2D ]] = Unfold[Range[2]];
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149 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
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150 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
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151 | IndexRange[Index[Generation]] = Range[3];
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152 | IndexRange[Index[Higgs ]] = Unfold[Range[3]];
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153 |
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154 | IndexStyle[SU2W, j];
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155 | IndexStyle[SU2D, k];
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156 | IndexStyle[Gluon, a];
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157 | IndexStyle[Colour, m];
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158 | IndexStyle[Generation, f];
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159 | IndexStyle[Higgs, h];
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160 |
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161 |
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162 | (* ************************** *)
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163 | (* *** Interaction orders *** *)
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164 | (* *** (as used by mg5) *** *)
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165 | (* ************************** *)
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166 |
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167 | M$InteractionOrderHierarchy = {
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168 | {QCD, 1},
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169 | {QED, 2}
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170 | };
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171 |
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172 |
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173 | (* ************************** *)
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174 | (* **** Particle classes **** *)
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175 | (* ************************** *)
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176 | M$ClassesDescription = {
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177 |
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178 | (* Gauge bosons: physical vector fields *)
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179 |
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180 | V[1] == {
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181 | ClassName -> A,
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182 | SelfConjugate -> True,
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183 | Mass -> 0,
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184 | Width -> 0,
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185 | ParticleName -> "a",
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186 | PDG -> 22,
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187 | PropagatorLabel -> "a",
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188 | PropagatorType -> W,
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189 | PropagatorArrow -> None,
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190 | FullName -> "Photon"
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191 | },
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192 |
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193 | V[2] == {
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194 | ClassName -> Z,
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195 | SelfConjugate -> True,
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196 | Mass -> MZ,
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197 | Width -> {WZ, 2.4952},
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198 | ParticleName -> "Z",
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199 | PDG -> 23,
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200 | PropagatorLabel -> "Z",
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201 | PropagatorType -> Sine,
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202 | PropagatorArrow -> None,
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203 | FullName -> "Z"
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204 | },
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205 |
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206 | V[3] == {
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207 | ClassName -> W,
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208 | SelfConjugate -> False,
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209 | Mass -> MW,
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210 | Width -> {WW, 2.085},
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211 | ParticleName -> "W+",
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212 | AntiParticleName -> "W-",
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213 | QuantumNumbers -> {Q -> 1},
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214 | PDG -> 24,
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215 | PropagatorLabel -> "W",
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216 | PropagatorType -> Sine,
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217 | PropagatorArrow -> Forward,
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218 | FullName -> "W"
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219 | },
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220 |
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221 | V[4] == {
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222 | ClassName -> G,
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223 | SelfConjugate -> True,
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224 | Indices -> {Index[Gluon]},
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225 | Mass -> 0,
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226 | Width -> 0,
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227 | ParticleName -> "g",
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228 | PDG -> 21,
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229 | PropagatorLabel -> "G",
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230 | PropagatorType -> C,
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231 | PropagatorArrow -> None,
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232 | FullName -> "G"
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233 | },
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234 |
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235 | (* Ghosts: related to physical gauge bosons *)
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236 |
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237 | U[1] == {
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238 | ClassName -> ghA,
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239 | SelfConjugate -> False,
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240 | Ghost -> A,
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241 | QuantumNumbers -> {GhostNumber -> 1},
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242 | Mass -> 0,
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243 | PropagatorLabel -> "uA",
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244 | PropagatorType -> GhostDash,
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245 | PropagatorArrow -> Forward
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246 | },
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247 |
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248 | U[2] == {
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249 | ClassName -> ghZ,
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250 | SelfConjugate -> False,
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251 | Ghost -> Z,
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252 | QuantumNumbers -> {GhostNumber -> 1},
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253 | Mass -> MZ,
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254 | PropagatorLabel -> "uZ",
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255 | PropagatorType -> GhostDash,
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256 | PropagatorArrow -> Forward
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257 | },
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258 |
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259 | U[31] == {
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260 | ClassName -> ghWp,
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261 | SelfConjugate -> False,
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262 | Ghost -> W,
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263 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
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264 | Mass -> {MW,Internal},
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265 | PropagatorLabel -> "uWp",
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266 | PropagatorType -> GhostDash,
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267 | PropagatorArrow -> Forward
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268 | },
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269 |
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270 | U[32] == {
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271 | ClassName -> ghWm,
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272 | SelfConjugate -> False,
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273 | Ghost -> Wbar,
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274 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
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275 | Mass -> MW,
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276 | PropagatorLabel -> "uWm",
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277 | PropagatorType -> GhostDash,
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278 | PropagatorArrow -> Forward
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279 | },
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280 |
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281 | U[4] == {
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282 | ClassName -> ghG,
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283 | SelfConjugate -> False,
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284 | Indices -> {Index[Gluon]},
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285 | Ghost -> G,
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286 | QuantumNumbers ->{GhostNumber -> 1},
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287 | Mass -> 0,
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288 | PropagatorLabel -> "uG",
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289 | PropagatorType -> GhostDash,
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290 | PropagatorArrow -> Forward
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291 | },
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292 |
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293 | (* Gauge bosons: unphysical vector fields *)
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294 |
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295 | V[11] == {
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296 | ClassName -> B,
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297 | Unphysical -> True,
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298 | SelfConjugate -> True
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299 | },
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300 |
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301 | V[12] == {
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302 | ClassName -> Wi,
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303 | Unphysical -> True,
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304 | SelfConjugate -> True,
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305 | Indices -> {Index[SU2W]},
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306 | FlavorIndex -> SU2W
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307 | },
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308 |
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309 | (* Ghosts: related to unphysical gauge bosons *)
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310 |
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311 | U[11] == {
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312 | ClassName -> ghB,
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313 | Unphysical -> True,
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314 | SelfConjugate -> False,
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315 | Ghost -> B,
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316 | Definitions -> { ghB -> -(ee/gw) ghZ + (ee/g1) ghA}
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317 | },
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318 |
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319 | U[12] == {
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320 | ClassName -> ghWi,
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321 | Unphysical -> True,
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322 | SelfConjugate -> False,
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323 | Ghost -> Wi,
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324 | Indices -> {Index[SU2W]},
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325 | FlavorIndex -> SU2W,
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326 | Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> (ee/g1) ghZ+(ee/gw) ghA}
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327 | },
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328 |
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329 | (* Fermions: physical fields *)
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330 |
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331 | F[1] == {
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332 | ClassName -> vl,
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333 | ClassMembers -> {ve,vm,vt},
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334 | Indices -> {Index[Generation]},
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335 | FlavorIndex -> Generation,
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336 | SelfConjugate -> False,
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337 | Mass -> 0,
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338 | Width -> 0,
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339 | QuantumNumbers -> {LeptonNumber -> 1},
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340 | PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
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341 | PropagatorType -> S,
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342 | PropagatorArrow -> Forward,
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343 | PDG -> {12,14,16},
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344 | ParticleName -> {"ve","vm","vt"},
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345 | AntiParticleName -> {"ve~","vm~","vt~"},
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346 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
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347 | },
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348 |
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349 | F[2] == {
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350 | ClassName -> l,
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351 | ClassMembers -> {e, mu, ta},
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352 | Indices -> {Index[Generation]},
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353 | FlavorIndex -> Generation,
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354 | SelfConjugate -> False,
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355 | Mass -> {Ml, {Me,5.11*^-4}, {MM,0.10566}, {MTA,1.777}},
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356 | Width -> 0,
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357 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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358 | PropagatorLabel -> {"l", "e", "mu", "ta"},
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359 | PropagatorType -> Straight,
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360 | PropagatorArrow -> Forward,
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361 | PDG -> {11, 13, 15},
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362 | ParticleName -> {"e-", "mu-", "ta-"},
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363 | AntiParticleName -> {"e+", "mu+", "ta+"},
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364 | FullName -> {"Electron", "Muon", "Tau"}
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365 | },
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366 |
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367 | F[3] == {
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368 | ClassName -> uq,
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369 | ClassMembers -> {u, c, t},
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370 | Indices -> {Index[Generation], Index[Colour]},
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371 | FlavorIndex -> Generation,
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372 | SelfConjugate -> False,
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373 | Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
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374 | Width -> {0, 0, {WT,1.50833649}},
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375 | QuantumNumbers -> {Q -> 2/3},
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376 | PropagatorLabel -> {"uq", "u", "c", "t"},
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377 | PropagatorType -> Straight,
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378 | PropagatorArrow -> Forward,
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379 | PDG -> {2, 4, 6},
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380 | ParticleName -> {"u", "c", "t" },
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381 | AntiParticleName -> {"u~", "c~", "t~"},
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382 | FullName -> {"u-quark", "c-quark", "t-quark"}
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383 | },
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384 |
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385 | F[4] == {
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386 | ClassName -> dq,
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387 | ClassMembers -> {d, s, b},
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388 | Indices -> {Index[Generation], Index[Colour]},
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389 | FlavorIndex -> Generation,
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390 | SelfConjugate -> False,
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391 | Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
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392 | Width -> 0,
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393 | QuantumNumbers -> {Q -> -1/3},
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394 | PropagatorLabel -> {"dq", "d", "s", "b"},
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395 | PropagatorType -> Straight,
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396 | PropagatorArrow -> Forward,
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397 | PDG -> {1,3,5},
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398 | ParticleName -> {"d", "s", "b" },
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399 | AntiParticleName -> {"d~", "s~", "b~"},
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400 | FullName -> {"d-quark", "s-quark", "b-quark"}
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401 | },
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402 |
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403 | (* Fermions: unphysical fields *)
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404 |
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405 | F[11] == {
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406 | ClassName -> LL,
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407 | Unphysical -> True,
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408 | Indices -> {Index[SU2D], Index[Generation]},
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409 | FlavorIndex -> SU2D,
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410 | SelfConjugate -> False,
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411 | QuantumNumbers -> {Y -> -1/2}
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412 | },
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413 |
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414 | F[12] == {
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415 | ClassName -> lR,
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416 | Unphysical -> True,
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417 | Indices -> {Index[Generation]},
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418 | FlavorIndex -> Generation,
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419 | SelfConjugate -> False,
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420 | QuantumNumbers -> {Y -> -1}
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421 | },
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422 |
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423 | F[13] == {
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424 | ClassName -> QL,
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425 | Unphysical -> True,
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426 | Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
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427 | FlavorIndex -> SU2D,
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428 | SelfConjugate -> False,
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429 | QuantumNumbers -> {Y -> 1/6}
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430 | },
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431 |
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432 | F[14] == {
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433 | ClassName -> uR,
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434 | Unphysical -> True,
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435 | Indices -> {Index[Generation], Index[Colour]},
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436 | FlavorIndex -> Generation,
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437 | SelfConjugate -> False,
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438 | QuantumNumbers -> {Y -> 2/3}
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439 | },
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440 |
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441 | F[15] == {
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442 | ClassName -> dR,
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443 | Unphysical -> True,
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444 | Indices -> {Index[Generation], Index[Colour]},
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445 | FlavorIndex -> Generation,
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446 | SelfConjugate -> False,
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447 | QuantumNumbers -> {Y -> -1/3}
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448 | },
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449 |
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450 | (* Higgs unphysical scalars *)
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451 | (* Unphysical scalar fields *)
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452 |
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453 | S[100] == {
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454 | ClassName -> phi1,
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455 | Unphysical -> True,
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456 | SelfConjugate -> False,
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457 | Indices -> {Index[SU2D]},
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458 | FlavorIndex -> SU2D,
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459 | QuantumNumbers-> {Y -> 1/2}
|
---|
460 | },
|
---|
461 |
|
---|
462 | S[101] == {
|
---|
463 | ClassName -> phi2,
|
---|
464 | Unphysical -> True,
|
---|
465 | SelfConjugate -> False,
|
---|
466 | Indices -> {Index[SU2D]},
|
---|
467 | FlavorIndex -> SU2D,
|
---|
468 | QuantumNumbers-> {Y -> 1/2}
|
---|
469 | },
|
---|
470 |
|
---|
471 | S[110] == {
|
---|
472 | ClassName -> H0,
|
---|
473 | Unphysical -> True,
|
---|
474 | SelfConjugate -> True
|
---|
475 | },
|
---|
476 |
|
---|
477 | S[111] == {
|
---|
478 | ClassName -> R0,
|
---|
479 | Unphysical -> True,
|
---|
480 | SelfConjugate -> True
|
---|
481 | },
|
---|
482 |
|
---|
483 | S[112] == {
|
---|
484 | ClassName -> I0,
|
---|
485 | Unphysical -> True,
|
---|
486 | SelfConjugate -> True
|
---|
487 | },
|
---|
488 |
|
---|
489 |
|
---|
490 | (* Higgs physical scalars *)
|
---|
491 |
|
---|
492 | S[103] == {
|
---|
493 | ClassName -> G0,
|
---|
494 | SelfConjugate -> True,
|
---|
495 | ParticleName -> "G0"
|
---|
496 | },
|
---|
497 |
|
---|
498 | S[104] == {
|
---|
499 | ClassName -> H,
|
---|
500 | SelfConjugate -> True,
|
---|
501 | Indices -> {Index[Higgs]},
|
---|
502 | FlavorIndex -> Higgs,
|
---|
503 | ClassMembers -> {h1, h2, h3},
|
---|
504 | PDG -> {25, 35, 36}
|
---|
505 |
|
---|
506 | },
|
---|
507 |
|
---|
508 | S[105] == {
|
---|
509 | ClassName -> HP1,
|
---|
510 | SelfConjugate -> False,
|
---|
511 | QuantumNumbers -> {Q -> 1},
|
---|
512 | ParticleName -> "h1+",
|
---|
513 | AntiParticleName -> "h1-",
|
---|
514 | PDG -> 100004
|
---|
515 |
|
---|
516 | },
|
---|
517 |
|
---|
518 | S[106] == {
|
---|
519 | ClassName -> HP2,
|
---|
520 | SelfConjugate -> False,
|
---|
521 | QuantumNumbers -> {Q -> 1},
|
---|
522 | ParticleName -> "h2+",
|
---|
523 | AntiParticleName -> "h2-",
|
---|
524 | PDG -> 100005
|
---|
525 | }
|
---|
526 | };
|
---|
527 |
|
---|
528 |
|
---|
529 | (* ************************** *)
|
---|
530 | (* ***** Parameters ***** *)
|
---|
531 | (* ************************** *)
|
---|
532 | M$Parameters = {
|
---|
533 |
|
---|
534 | (* External parameters *)
|
---|
535 | aEWM1 == {
|
---|
536 | ParameterType -> External,
|
---|
537 | BlockName -> SMINPUTS,
|
---|
538 | OrderBlock -> 1,
|
---|
539 | Value -> 127.9,
|
---|
540 | InteractionOrder -> {QED,-2},
|
---|
541 | Description -> "Inverse of the EW coupling constant at the Z pole"
|
---|
542 | },
|
---|
543 |
|
---|
544 | Gf == {
|
---|
545 | ParameterType -> External,
|
---|
546 | BlockName -> SMINPUTS,
|
---|
547 | OrderBlock -> 2,
|
---|
548 | Value -> 1.16637*^-5,
|
---|
549 | InteractionOrder -> {QED,2},
|
---|
550 | TeX -> Subscript[G,f],
|
---|
551 | Description -> "Fermi constant"
|
---|
552 | },
|
---|
553 |
|
---|
554 | aS == {
|
---|
555 | ParameterType -> External,
|
---|
556 | BlockName -> SMINPUTS,
|
---|
557 | OrderBlock -> 3,
|
---|
558 | Value -> 0.1184,
|
---|
559 | InteractionOrder -> {QCD,2},
|
---|
560 | TeX -> Subscript[\[Alpha],s],
|
---|
561 | Description -> "Strong coupling constant at the Z pole"
|
---|
562 | },
|
---|
563 |
|
---|
564 | ymdo == {
|
---|
565 | ParameterType -> External,
|
---|
566 | BlockName -> YUKAWA,
|
---|
567 | OrderBlock -> 1,
|
---|
568 | Value -> 5.04*^-3,
|
---|
569 | Description -> "Down Yukawa mass"
|
---|
570 | },
|
---|
571 |
|
---|
572 | ymup == {
|
---|
573 | ParameterType -> External,
|
---|
574 | BlockName -> YUKAWA,
|
---|
575 | OrderBlock -> 2,
|
---|
576 | Value -> 2.55*^-3,
|
---|
577 | Description -> "Up Yukawa mass"
|
---|
578 | },
|
---|
579 |
|
---|
580 | yms == {
|
---|
581 | ParameterType -> External,
|
---|
582 | BlockName -> YUKAWA,
|
---|
583 | OrderBlock -> 3,
|
---|
584 | Value -> 0.101,
|
---|
585 | Description -> "Strange Yukawa mass"
|
---|
586 | },
|
---|
587 |
|
---|
588 | ymc == {
|
---|
589 | ParameterType -> External,
|
---|
590 | BlockName -> YUKAWA,
|
---|
591 | OrderBlock -> 4,
|
---|
592 | Value -> 1.27,
|
---|
593 | Description -> "Charm Yukawa mass"
|
---|
594 | },
|
---|
595 |
|
---|
596 | ymb == {
|
---|
597 | ParameterType -> External,
|
---|
598 | BlockName -> YUKAWA,
|
---|
599 | OrderBlock -> 5,
|
---|
600 | Value -> 4.7,
|
---|
601 | Description -> "Bottom Yukawa mass"
|
---|
602 | },
|
---|
603 |
|
---|
604 | ymt == {
|
---|
605 | ParameterType -> External,
|
---|
606 | BlockName -> YUKAWA,
|
---|
607 | OrderBlock -> 6,
|
---|
608 | Value -> 172,
|
---|
609 | Description -> "Top Yukawa mass"
|
---|
610 | },
|
---|
611 |
|
---|
612 | yme == {
|
---|
613 | ParameterType -> External,
|
---|
614 | BlockName -> YUKAWA,
|
---|
615 | OrderBlock -> 11,
|
---|
616 | Value -> 5.11*^-4,
|
---|
617 | Description -> "Electron Yukawa mass"
|
---|
618 | },
|
---|
619 |
|
---|
620 | ymm == {
|
---|
621 | ParameterType -> External,
|
---|
622 | BlockName -> YUKAWA,
|
---|
623 | OrderBlock -> 13,
|
---|
624 | Value -> 0.10566,
|
---|
625 | Description -> "Muon Yukawa mass"
|
---|
626 | },
|
---|
627 |
|
---|
628 | ymtau == {
|
---|
629 | ParameterType -> External,
|
---|
630 | BlockName -> YUKAWA,
|
---|
631 | OrderBlock -> 15,
|
---|
632 | Value -> 1.777,
|
---|
633 | Description -> "Tau Yukawa mass"
|
---|
634 | },
|
---|
635 |
|
---|
636 | cabi == {
|
---|
637 | ParameterType -> External,
|
---|
638 | BlockName -> CKMBLOCK,
|
---|
639 | OrderBlock -> 1,
|
---|
640 | Value -> 0.227736,
|
---|
641 | TeX -> Subscript[\[Theta], c],
|
---|
642 | Description -> "Cabibbo angle"
|
---|
643 | },
|
---|
644 |
|
---|
645 | (*Adam Modifs: 09/17/12*)
|
---|
646 |
|
---|
647 | gw == {
|
---|
648 | ParameterType -> External,
|
---|
649 | BlockName -> Gauge,
|
---|
650 | OrderBlock -> 2,
|
---|
651 | Value -> 0.663922,
|
---|
652 | InteractionOrder -> {QED,1},
|
---|
653 | TeX -> Subscript[g,w],
|
---|
654 | Description -> "Weak coupling constant at the Z pole"
|
---|
655 | },
|
---|
656 |
|
---|
657 | g1 == {
|
---|
658 | ParameterType -> External,
|
---|
659 | BlockName -> Gauge,
|
---|
660 | OrderBlock -> 1,
|
---|
661 | Value -> 0.355574,
|
---|
662 | InteractionOrder -> {QED,1},
|
---|
663 | TeX -> Subscript[g,1],
|
---|
664 | Description -> "U(1)Y coupling constant at the Z pole"
|
---|
665 | },
|
---|
666 |
|
---|
667 | vev1 == {
|
---|
668 | ParameterType -> External,
|
---|
669 | BlockName -> HMIX,
|
---|
670 | OrderBlock -> 1,
|
---|
671 | InteractionOrder -> {QED,-1},
|
---|
672 | Description -> "vacuum expectation value of the first doublet"
|
---|
673 | },
|
---|
674 |
|
---|
675 |
|
---|
676 |
|
---|
677 | (* Internal Parameters *)
|
---|
678 |
|
---|
679 | aEW == {
|
---|
680 | ParameterType -> Internal,
|
---|
681 | Value -> 1/aEWM1,
|
---|
682 | InteractionOrder -> {QED,2},
|
---|
683 | TeX -> Subscript[\[Alpha], EW],
|
---|
684 | Description -> "Electroweak coupling contant"
|
---|
685 | },
|
---|
686 |
|
---|
687 | ee == {
|
---|
688 | ParameterType -> Internal,
|
---|
689 | Value -> Sqrt[4 Pi aEW],
|
---|
690 | InteractionOrder -> {QED,1},
|
---|
691 | TeX -> e,
|
---|
692 | Description -> "Electric coupling constant"
|
---|
693 | },
|
---|
694 |
|
---|
695 | gs == {
|
---|
696 | ParameterType -> Internal,
|
---|
697 | Value -> Sqrt[4*Pi*aS],
|
---|
698 | InteractionOrder -> {QCD,1},
|
---|
699 | TeX -> Subscript[g,s],
|
---|
700 | ParameterName -> G,
|
---|
701 | Description -> "Strong coupling constant at the Z pole"
|
---|
702 | },
|
---|
703 |
|
---|
704 | (*Internal parameters: Yukawa's*)
|
---|
705 |
|
---|
706 | yl1 == {
|
---|
707 | ParameterType -> Internal,
|
---|
708 | Indices -> {Index[Generation], Index[Generation]},
|
---|
709 | Definitions -> {yl1[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
|
---|
710 | Value -> {yl1[1,1] -> Sqrt[2] yme/vev1, yl1[2,2] -> Sqrt[2] ymm/vev1, yl1[3,3] -> Sqrt[2] ymtau/vev1},
|
---|
711 | InteractionOrder -> {QED, 1},
|
---|
712 | ParameterName -> {yl1[1,1] -> ye, yl1[2,2] -> ym, yl1[3,3] -> ytau},
|
---|
713 | TeX -> Superscript[y, l1],
|
---|
714 | Description -> "Lepton Yukawa couplings"
|
---|
715 | },
|
---|
716 |
|
---|
717 | yu1 == {
|
---|
718 | ParameterType -> Internal,
|
---|
719 | Indices -> {Index[Generation], Index[Generation]},
|
---|
720 | Definitions -> {yu1[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
|
---|
721 | Value -> {yu1[1,1] -> Sqrt[2] ymup/vev1, yu1[2,2] -> Sqrt[2] ymc/vev1, yu1[3,3] -> Sqrt[2] ymt/vev1},
|
---|
722 | InteractionOrder -> {QED, 1},
|
---|
723 | ParameterName -> {yu1[1,1] -> yup, yu1[2,2] -> yc, yu1[3,3] -> yt},
|
---|
724 | TeX -> Superscript[y, u1],
|
---|
725 | Description -> "Up-type Yukawa couplings"
|
---|
726 | },
|
---|
727 |
|
---|
728 | yd1 == {
|
---|
729 | ParameterType -> Internal,
|
---|
730 | Indices -> {Index[Generation], Index[Generation]},
|
---|
731 | Definitions -> {yd1[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
|
---|
732 | Value -> {yd1[1,1] -> Sqrt[2] ymdo/vev1, yd1[2,2] -> Sqrt[2] yms/vev1, yd1[3,3] -> Sqrt[2] ymb/vev1},
|
---|
733 | InteractionOrder -> {QED, 1},
|
---|
734 | ParameterName -> {yd1[1,1] -> ydo, yd1[2,2] -> ys, yd1[3,3] -> yb},
|
---|
735 | TeX -> Superscript[y, d1],
|
---|
736 | Description -> "Down-type Yukawa couplings"
|
---|
737 | },
|
---|
738 |
|
---|
739 | yl2 == {
|
---|
740 | ParameterType -> Internal,
|
---|
741 | Indices -> {Index[Generation], Index[Generation]},
|
---|
742 | Definitions -> {yl2[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
|
---|
743 | Value -> {yl2[1,1] -> Sqrt[2] yme/vev1, yl2[2,2] -> Sqrt[2] ymm/vev1, yl2[3,3] -> Sqrt[2] ymtau/vev1},
|
---|
744 | InteractionOrder -> {QED, 1},
|
---|
745 | ParameterName -> {yl2[1,1] -> ye, yl2[2,2] -> ym, yl2[3,3] -> ytau},
|
---|
746 | TeX -> Superscript[y, l2],
|
---|
747 | Description -> "Lepton Yukawa couplings"
|
---|
748 | },
|
---|
749 |
|
---|
750 | yu2 == {
|
---|
751 | ParameterType -> Internal,
|
---|
752 | Indices -> {Index[Generation], Index[Generation]},
|
---|
753 | Definitions -> {yu2[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
|
---|
754 | Value -> {yu2[1,1] -> Sqrt[2] ymup/vev1, yu2[2,2] -> Sqrt[2] ymc/vev1, yu2[3,3] -> Sqrt[2] ymt/vev1},
|
---|
755 | InteractionOrder -> {QED, 1},
|
---|
756 | ParameterName -> {yu2[1,1] -> yup, yu2[2,2] -> yc, yu2[3,3] -> yt},
|
---|
757 | TeX -> Superscript[y, u2],
|
---|
758 | Description -> "Up-type Yukawa couplings"
|
---|
759 | },
|
---|
760 |
|
---|
761 | yd2 == {
|
---|
762 | ParameterType -> Internal,
|
---|
763 | Indices -> {Index[Generation], Index[Generation]},
|
---|
764 | Definitions -> {yd2[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
|
---|
765 | Value -> {yd2[1,1] -> Sqrt[2] ymdo/vev1, yd2[2,2] -> Sqrt[2] yms/vev1, yd2[3,3] -> Sqrt[2] ymb/vev1},
|
---|
766 | InteractionOrder -> {QED, 1},
|
---|
767 | ParameterName -> {yd2[1,1] -> ydo, yd2[2,2] -> ys, yd2[3,3] -> yb},
|
---|
768 | TeX -> Superscript[y, d2],
|
---|
769 | Description -> "Down-type Yukawa couplings"
|
---|
770 | },
|
---|
771 |
|
---|
772 |
|
---|
773 | (* Higgs potential parameters *)
|
---|
774 |
|
---|
775 | lambda1 == {
|
---|
776 | BlockName -> Higgs,
|
---|
777 | OrderBlock -> 1,
|
---|
778 | ComplexParameter -> False,
|
---|
779 | Value -> 1,
|
---|
780 | ParameterType -> External
|
---|
781 | },
|
---|
782 |
|
---|
783 | lambda2 == {
|
---|
784 | BlockName -> Higgs,
|
---|
785 | OrderBlock -> 2,
|
---|
786 | ComplexParameter -> False,
|
---|
787 | Value -> 1,
|
---|
788 | ParameterType -> External
|
---|
789 | },
|
---|
790 |
|
---|
791 | lambda3 == {
|
---|
792 | BlockName -> Higgs,
|
---|
793 | OrderBlock -> 3,
|
---|
794 | ComplexParameter -> False,
|
---|
795 | Value -> 1,
|
---|
796 | ParameterType -> External
|
---|
797 | },
|
---|
798 |
|
---|
799 | lambda4 == {
|
---|
800 | BlockName -> Higgs,
|
---|
801 | OrderBlock -> 4,
|
---|
802 | ComplexParameter -> False,
|
---|
803 | Value -> 1,
|
---|
804 | ParameterType -> External
|
---|
805 | },
|
---|
806 |
|
---|
807 | lambda5 == {
|
---|
808 | ComplexParameter -> False,
|
---|
809 | OrderBlock -> 5,
|
---|
810 | ParameterType -> External,
|
---|
811 | BlockName -> Higgs,
|
---|
812 | Value -> 1,
|
---|
813 | Description -> "lambda5"
|
---|
814 | },
|
---|
815 |
|
---|
816 | lambda6R == {
|
---|
817 | BlockName -> Higgs,
|
---|
818 | OrderBlock -> 6,
|
---|
819 | ComplexParameter -> False,
|
---|
820 | ParameterType -> External,
|
---|
821 | Value -> 1,
|
---|
822 | Description -> "real part of lambda6"
|
---|
823 | },
|
---|
824 |
|
---|
825 | lambda6I == {
|
---|
826 | BlockName -> Higgs,
|
---|
827 | OrderBlock -> 7,
|
---|
828 | ComplexParameter -> False,
|
---|
829 | ParameterType -> External,
|
---|
830 | Value -> 1,
|
---|
831 | Description -> "imaginary part of lambda6"
|
---|
832 | },
|
---|
833 |
|
---|
834 | lambda6 == {
|
---|
835 | ComplexParameter -> True,
|
---|
836 | ParameterType -> Internal,
|
---|
837 | Value -> lambda6R + I*lambda6I,
|
---|
838 | Description -> "lambda6"
|
---|
839 | },
|
---|
840 |
|
---|
841 | lambda7R == {
|
---|
842 | BlockName -> Higgs,
|
---|
843 | OrderBlock -> 8,
|
---|
844 | ComplexParameter -> False,
|
---|
845 | ParameterType -> External,
|
---|
846 | Value -> 1,
|
---|
847 | Description -> "real part of lambda6"
|
---|
848 | },
|
---|
849 |
|
---|
850 | lambda7I == {
|
---|
851 | BlockName -> Higgs,
|
---|
852 | OrderBlock -> 9,
|
---|
853 | ComplexParameter -> False,
|
---|
854 | ParameterType -> External,
|
---|
855 | Value -> 1,
|
---|
856 | Description -> "imaginary part of lambda6"
|
---|
857 | },
|
---|
858 |
|
---|
859 | lambda7 == {
|
---|
860 | ParameterType -> Internal,
|
---|
861 | ComplexParameter -> True,
|
---|
862 | Value -> lambda7R + I*lambda7I,
|
---|
863 | Description -> "lambda7"
|
---|
864 | },
|
---|
865 |
|
---|
866 | mu1 == {
|
---|
867 | ComplexParameter -> False,
|
---|
868 | ParameterType -> Internal,
|
---|
869 | Value -> -lambda1*vev1^2,
|
---|
870 | Description -> "mu1"
|
---|
871 | },
|
---|
872 |
|
---|
873 | mu2 == {
|
---|
874 | BlockName -> Higgs,
|
---|
875 | OrderBlock -> 10,
|
---|
876 | ComplexParameter -> False,
|
---|
877 | ParameterType -> External,
|
---|
878 | Value -> 1,
|
---|
879 | Description -> "mu2"
|
---|
880 | },
|
---|
881 |
|
---|
882 | mu3 == {
|
---|
883 | ComplexParameter -> True,
|
---|
884 | ParameterType -> Internal,
|
---|
885 | Value -> -lambda6*vev1^2/2,
|
---|
886 | Description -> "mu3"
|
---|
887 | },
|
---|
888 |
|
---|
889 | (* N. B. : only Cabibbo mixing! *)
|
---|
890 | CKM == {
|
---|
891 | ParameterType -> Internal,
|
---|
892 | Indices -> {Index[Generation], Index[Generation]},
|
---|
893 | Unitary -> True,
|
---|
894 | Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
|
---|
895 | CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
|
---|
896 | CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
|
---|
897 | TeX -> Superscript[V,CKM],
|
---|
898 | Description -> "CKM-Matrix"}
|
---|
899 |
|
---|
900 | };
|
---|
901 |
|
---|
902 | (* ************************** *)
|
---|
903 | (* ***** Lagrangian ***** *)
|
---|
904 | (* ************************** *)
|
---|
905 |
|
---|
906 |
|
---|
907 | LGauge := Block[{mu,nu,ii,aa},
|
---|
908 | -1/4 FS[B,mu,nu] FS[B,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] ];
|
---|
909 |
|
---|
910 | LFermions := Block[{mu},
|
---|
911 | I*(
|
---|
912 | 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])];
|
---|
913 |
|
---|
914 | LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk},
|
---|
915 |
|
---|
916 | yuk =
|
---|
917 | - yd1[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] phi1[ii]
|
---|
918 | - yl1[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] phi1[ii]
|
---|
919 | - yu1[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] phi1bar[jj] Eps[ii, jj];
|
---|
920 |
|
---|
921 | yuk +=
|
---|
922 | - yd2[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] phi2[ii]
|
---|
923 | - yl2[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] phi2[ii]
|
---|
924 | - yu2[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] phi2bar[jj] Eps[ii, jj];
|
---|
925 |
|
---|
926 | yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
|
---|
927 |
|
---|
928 | yuk += HC[yuk]
|
---|
929 | ];
|
---|
930 |
|
---|
931 | LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
|
---|
932 | (* Pure gauge piece *)
|
---|
933 | LGh1 = -ghBbar.del[DC[ghB,mu],mu];
|
---|
934 | LGhw = -ghWibar.del[DC[ghWi,mu],mu];
|
---|
935 | LGhs = -ghGbar.del[DC[ghG,mu],mu];
|
---|
936 |
|
---|
937 | (* Scalar pieces: see Peskin pages 739-742 *)
|
---|
938 | (* phi1 and phi2 are the real degrees of freedom of GP *)
|
---|
939 | (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
|
---|
940 |
|
---|
941 | gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
|
---|
942 | ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
|
---|
943 | generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
|
---|
944 | doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], phi2} /. MR$Definitions /. vev -> 0];
|
---|
945 | doublet0 = {0, vev/Sqrt[2]};
|
---|
946 | Vectorize[{a_, b_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]}/.{Im[_]->0, Re[num_]->num}];
|
---|
947 | togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
|
---|
948 | LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
|
---|
949 |
|
---|
950 | LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0]];
|
---|
951 |
|
---|
952 | (* 2HDM potential *)
|
---|
953 |
|
---|
954 | LHiggsKin := Block[{ii, mu},
|
---|
955 | DC[phi1bar[ii], mu] DC[phi1[ii], mu] +
|
---|
956 | DC[phi2bar[ii], mu] DC[phi2[ii], mu]
|
---|
957 | ];
|
---|
958 |
|
---|
959 | P1 = {phi1[1], phi1[2]};
|
---|
960 | P2 = {phi2[1], phi2[2]};
|
---|
961 |
|
---|
962 | P1bar = HC[P1];
|
---|
963 | P2bar = HC[P2];
|
---|
964 |
|
---|
965 | P11 = HC[P1].P1;
|
---|
966 | P12 = HC[P1].P2;
|
---|
967 | P21 = HC[P2].P1;
|
---|
968 | P22 = HC[P2].P2;
|
---|
969 |
|
---|
970 | V2HDM := mu1 P11 +mu2 P22 +mu3 P12 +HC[mu3] P21 +
|
---|
971 | lambda1 P11^2 + lambda2 P22^2 + lambda3 P11 P22 +
|
---|
972 | lambda4 P12 P21 + lambda5 P12^2 + Conjugate[lambda5] P21^2 +
|
---|
973 | P11 (lambda6 P12+ Conjugate[lambda6] P21) + P22 (lambda7 P12+ Conjugate[lambda7]P21);
|
---|
974 |
|
---|
975 | LHiggs := LHiggsKin - V2HDM;
|
---|
976 |
|
---|
977 | L2HDM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;
|
---|