1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file used for Majorana neutrinos in: ******)
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3 | (****** GeV-scale neutrinos: interactions with mesons and DUNE sensitivity, arXiv:2007.03701 ******)
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4 | (****** ******)
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5 | (****** Authors: "P. Coloma", "E. Fernandez-Martinez", "M. Gonzalez-Lopez", "J. Hernandez-Garcia" ******)
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6 | (****** ******)
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7 | (****** Note: Unitary gauge is assumed (FeynmanGauge = False) ******)
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8 | (****** since Feynman gauge is not supported in MadGraph. ******)
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9 | (***************************************************************************************************************)
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10 |
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11 | (* ************************** *)
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12 | (* ***** Information ***** *)
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13 | (* ************************** *)
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14 | M$ModelName = "effective_HeavyN_Dirac_v103";
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15 |
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16 | M$Information = {
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17 | Authors -> {"P. Coloma", "E. Fernandez-Martinez", "M. Gonzalez-Lopez", "J. Hernandez-Garcia"},
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18 | Version -> "1.0.0",
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19 | Date -> "06. 06. 2020",
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20 | Institutions -> {"Instituto de Fisica Corpuscular, Universidad de Valencia & CSIC, and Instituto de Fisica Teorica UAM/CSIC", "Departamento de Fisica Teorica & Instituto de Fisica Teorica, Universidad Autonoma de Madrid & CSIC", "Departamento de Fisica Teorica & Instituto de Fisica Teorica, Universidad Autonoma de Madrid & CSIC", "Institute for Theoretical Physics, ELTE Eotvos Lorand University"},
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21 | Emails -> {"pilar.coloma@ift.csic.es", "enrique.fernandez-martinez@uam.es", "manuel.gonzalezl@uam.es", "josu.hernandez@ttk.elte.hu"},
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22 | URLs -> "https://arxiv.org/abs/2007.03701"
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23 | };
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24 |
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25 | FeynmanGauge = False;
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26 |
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27 | (* Add mesons and remove quarks from the Lagrangian. Change to False for a high-energy description in terms of quarks and without mesons. *)
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28 | Mesons = True;
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29 |
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30 | (* ************************** *)
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31 | (* ***** NLO Variables ****** *)
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32 | (******************************)
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33 |
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34 | FR$LoopSwitches = {{Gf, MW}};
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35 | FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
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36 | ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU, MN4 -> MassN4};
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37 |
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38 |
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39 | (* ************************** *)
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40 | (* ***** vevs ***** *)
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41 | (* ************************** *)
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42 | M$vevs = { {Phi[2],vev} };
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43 |
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44 | (* ************************** *)
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45 | (* ***** Gauge groups ***** *)
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46 | (* ************************** *)
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47 | M$GaugeGroups = {
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48 | U1Y == {
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49 | Abelian -> True,
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50 | CouplingConstant -> g1,
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51 | GaugeBoson -> B,
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52 | Charge -> Y
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53 | },
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54 | SU2L == {
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55 | Abelian -> False,
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56 | CouplingConstant -> gw,
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57 | GaugeBoson -> Wi,
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58 | StructureConstant -> Eps,
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59 | Representations -> {Ta,SU2D},
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60 | Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
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61 | },
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62 | SU3C == {
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63 | Abelian -> False,
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64 | CouplingConstant -> gs,
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65 | GaugeBoson -> G,
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66 | StructureConstant -> f,
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67 | Representations -> {T,Colour},
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68 | SymmetricTensor -> dSUN
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69 | }
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70 | };
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71 |
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72 |
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73 | (* ************************** *)
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74 | (* ***** Indices ***** *)
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75 | (* ************************** *)
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76 |
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77 | IndexRange[Index[SU2W ]] = Unfold[Range[3]];
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78 | IndexRange[Index[SU2D ]] = Unfold[Range[2]];
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79 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
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80 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
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81 | IndexRange[Index[Generation]] = Range[3];
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82 | IndexRange[Index[Neutrinos ]] = Range[4];
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83 | IndexRange[Index[Heavynus ]] = Range[1];
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84 |
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85 |
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86 | IndexStyle[SU2W, j];
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87 | IndexStyle[SU2D, k];
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88 | IndexStyle[Gluon, a];
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89 | IndexStyle[Colour, m];
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90 | IndexStyle[Generation, f];
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91 | IndexStyle[Neutrinos, n];
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92 | IndexStyle[Heavynus, r];
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93 |
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94 |
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95 | (* ************************** *)
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96 | (* *** Interaction orders *** *)
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97 | (* *** (as used by mg5) *** *)
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98 | (* ************************** *)
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99 |
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100 | M$InteractionOrderHierarchy = {
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101 | {QCD, 1},
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102 | {QED, 2}
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103 | };
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104 |
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105 |
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106 | (* ************************** *)
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107 | (* **** Particle classes **** *)
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108 | (* ************************** *)
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109 | M$ClassesDescription = {
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110 |
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111 | (* Gauge bosons: physical vector fields *)
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112 | V[1] == {
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113 | ClassName -> A,
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114 | SelfConjugate -> True,
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115 | Mass -> 0,
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116 | Width -> 0,
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117 | ParticleName -> "a",
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118 | PDG -> 22,
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119 | PropagatorLabel -> "a",
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120 | PropagatorType -> W,
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121 | PropagatorArrow -> None,
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122 | FullName -> "Photon"
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123 | },
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124 | V[2] == {
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125 | ClassName -> Z,
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126 | SelfConjugate -> True,
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127 | Mass -> {MZ, 91.1876},
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128 | Width -> {WZ, 2.4952},
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129 | ParticleName -> "Z",
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130 | PDG -> 23,
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131 | PropagatorLabel -> "Z",
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132 | PropagatorType -> Sine,
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133 | PropagatorArrow -> None,
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134 | FullName -> "Z"
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135 | },
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136 | V[3] == {
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137 | ClassName -> W,
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138 | SelfConjugate -> False,
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139 | Mass -> {MW, Internal},
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140 | Width -> {WW, 2.085},
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141 | ParticleName -> "W+",
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142 | AntiParticleName -> "W-",
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143 | QuantumNumbers -> {Q -> 1},
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144 | PDG -> 24,
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145 | PropagatorLabel -> "W",
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146 | PropagatorType -> Sine,
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147 | PropagatorArrow -> Forward,
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148 | FullName -> "W"
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149 | },
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150 | V[4] == {
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151 | ClassName -> G,
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152 | SelfConjugate -> True,
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153 | Indices -> {Index[Gluon]},
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154 | Mass -> 0,
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155 | Width -> 0,
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156 | ParticleName -> "g",
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157 | PDG -> 21,
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158 | PropagatorLabel -> "G",
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159 | PropagatorType -> C,
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160 | PropagatorArrow -> None,
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161 | FullName -> "G"
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162 | },
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163 |
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164 | (* Ghosts: related to physical gauge bosons *)
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165 | U[1] == {
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166 | ClassName -> ghA,
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167 | SelfConjugate -> False,
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168 | Ghost -> A,
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169 | QuantumNumbers -> {GhostNumber -> 1},
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170 | Mass -> 0,
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171 | Width -> 0,
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172 | PropagatorLabel -> "uA",
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173 | PropagatorType -> GhostDash,
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174 | PropagatorArrow -> Forward
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175 | },
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176 | U[2] == {
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177 | ClassName -> ghZ,
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178 | SelfConjugate -> False,
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179 | Ghost -> Z,
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180 | QuantumNumbers -> {GhostNumber -> 1},
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181 | Mass -> {MZ,91.1876},
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182 | Width -> {WZ, 2.4952},
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183 | PropagatorLabel -> "uZ",
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184 | PropagatorType -> GhostDash,
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185 | PropagatorArrow -> Forward
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186 | },
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187 | U[31] == {
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188 | ClassName -> ghWp,
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189 | SelfConjugate -> False,
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190 | Ghost -> W,
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191 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
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192 | Mass -> {MW,Internal},
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193 | Width -> {WW, 2.085},
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194 | PropagatorLabel -> "uWp",
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195 | PropagatorType -> GhostDash,
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196 | PropagatorArrow -> Forward
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197 | },
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198 | U[32] == {
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199 | ClassName -> ghWm,
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200 | SelfConjugate -> False,
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201 | Ghost -> Wbar,
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202 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
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203 | Mass -> {MW,Internal},
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204 | Width -> {WW, 2.085},
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205 | PropagatorLabel -> "uWm",
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206 | PropagatorType -> GhostDash,
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207 | PropagatorArrow -> Forward
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208 | },
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209 | U[4] == {
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210 | ClassName -> ghG,
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211 | SelfConjugate -> False,
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212 | Indices -> {Index[Gluon]},
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213 | Ghost -> G,
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214 | PDG -> 82,
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215 | QuantumNumbers ->{GhostNumber -> 1},
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216 | Mass -> 0,
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217 | Width -> 0,
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218 | PropagatorLabel -> "uG",
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219 | PropagatorType -> GhostDash,
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220 | PropagatorArrow -> Forward
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221 | },
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222 |
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223 | (* Gauge bosons: unphysical vector fields *)
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224 | V[11] == {
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225 | ClassName -> B,
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226 | Unphysical -> True,
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227 | SelfConjugate -> True,
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228 | Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
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229 | },
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230 | V[12] == {
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231 | ClassName -> Wi,
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232 | Unphysical -> True,
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233 | SelfConjugate -> True,
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234 | Indices -> {Index[SU2W]},
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235 | FlavorIndex -> SU2W,
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236 | Definitions -> { Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3] -> cw Z[mu] + sw A[mu]}
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237 | },
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238 |
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239 | (* Ghosts: related to unphysical gauge bosons *)
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240 | U[11] == {
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241 | ClassName -> ghB,
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242 | Unphysical -> True,
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243 | SelfConjugate -> False,
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244 | Ghost -> B,
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245 | Definitions -> { ghB -> -sw ghZ + cw ghA}
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246 | },
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247 | U[12] == {
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248 | ClassName -> ghWi,
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249 | Unphysical -> True,
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250 | SelfConjugate -> False,
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251 | Ghost -> Wi,
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252 | Indices -> {Index[SU2W]},
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253 | FlavorIndex -> SU2W,
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254 | Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
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255 | } ,
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256 |
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257 | (* Fermions: physical fields *)
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258 | (* Note that technically these are neutrino mass eigenstates and as such we gave them different labels and codes than to the flavour eigenstates. *)
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259 | F[1] == {
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260 | ClassName -> vl,
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261 | ClassMembers -> {v1,v2,v3,N4},
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262 | Indices -> {Index[Neutrinos]},
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263 | FlavorIndex -> Neutrinos,
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264 | SelfConjugate -> False,
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265 | Mass -> {Mnu, 0,0,0, {MassN4, Internal}},
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266 | Width -> {0, 0, 0, {WN, 0}},
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267 | QuantumNumbers -> {LeptonNumber -> 1},
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268 | PropagatorLabel -> {"v", "v1", "v2", "v3","N4"} ,
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269 | PropagatorType -> S,
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270 | PropagatorArrow -> Forward,
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271 | PDG -> {12000,14000,16000,18000},
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272 | ParticleName -> {"v1","v2","v3","N4"},
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273 | AntiParticleName -> {"v1~","v2~","v3~","N4~"},
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274 | FullName -> {"neutrino1", "neutrino2", "neutrino3","Heavy-neutrino"}
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275 | },
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276 |
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277 | F[2] == {
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278 | ClassName -> l,
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279 | ClassMembers -> {e, mu, ta},
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280 | Indices -> {Index[Generation]},
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281 | FlavorIndex -> Generation,
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282 | SelfConjugate -> False,
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283 | Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
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284 | Width -> 0,
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285 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
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286 | PropagatorLabel -> {"l", "e", "mu", "ta"},
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287 | PropagatorType -> Straight,
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288 | PropagatorArrow -> Forward,
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289 | PDG -> {11, 13, 15},
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290 | ParticleName -> {"e-", "mu-", "ta-"},
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291 | AntiParticleName -> {"e+", "mu+", "ta+"},
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292 | FullName -> {"Electron", "Muon", "Tau"}
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293 | },
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294 | F[3] == {
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295 | ClassName -> uq,
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296 | ClassMembers -> {u, c, t},
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297 | Indices -> {Index[Generation], Index[Colour]},
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298 | FlavorIndex -> Generation,
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299 | SelfConjugate -> False,
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300 | Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
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301 | Width -> {0, 0, {WT,1.50833649}},
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302 | QuantumNumbers -> {Q -> 2/3},
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303 | PropagatorLabel -> {"uq", "u", "c", "t"},
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304 | PropagatorType -> Straight,
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305 | PropagatorArrow -> Forward,
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306 | PDG -> {2, 4, 6},
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307 | ParticleName -> {"u", "c", "t" },
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308 | AntiParticleName -> {"u~", "c~", "t~"},
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309 | FullName -> {"u-quark", "c-quark", "t-quark"}
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310 | },
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311 | F[4] == {
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312 | ClassName -> dq,
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313 | ClassMembers -> {d, s, b},
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314 | Indices -> {Index[Generation], Index[Colour]},
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315 | FlavorIndex -> Generation,
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316 | SelfConjugate -> False,
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317 | Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
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318 | Width -> 0,
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319 | QuantumNumbers -> {Q -> -1/3},
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320 | PropagatorLabel -> {"dq", "d", "s", "b"},
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321 | PropagatorType -> Straight,
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322 | PropagatorArrow -> Forward,
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323 | PDG -> {1,3,5},
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324 | ParticleName -> {"d", "s", "b" },
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325 | AntiParticleName -> {"d~", "s~", "b~"},
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326 | FullName -> {"d-quark", "s-quark", "b-quark"}
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327 | },
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328 |
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329 | (* Fermions: unphysical fields *)
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330 | F[11] == {
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331 | ClassName -> LL,
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332 | Unphysical -> True,
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333 | Indices -> {Index[SU2D], Index[Generation]},
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334 | FlavorIndex -> SU2D,
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335 | SelfConjugate -> False,
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336 | QuantumNumbers -> {Y -> -1/2},
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337 | Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNS[ff,ff2] ProjM[sp1,sp2] vl[sp2,ff2]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
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338 | },
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339 | F[12] == {
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340 | ClassName -> lR,
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341 | Unphysical -> True,
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342 | Indices -> {Index[Generation]},
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343 | FlavorIndex -> Generation,
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344 | SelfConjugate -> False,
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345 | QuantumNumbers -> {Y -> -1},
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346 | Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
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347 | },
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348 | F[13] == {
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349 | ClassName -> QL,
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350 | Unphysical -> True,
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351 | Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
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352 | FlavorIndex -> SU2D,
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353 | SelfConjugate -> False,
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354 | QuantumNumbers -> {Y -> 1/6},
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355 | Definitions -> {
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356 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
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357 | QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
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358 | },
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359 | F[14] == {
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360 | ClassName -> uR,
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361 | Unphysical -> True,
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362 | Indices -> {Index[Generation], Index[Colour]},
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363 | FlavorIndex -> Generation,
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364 | SelfConjugate -> False,
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365 | QuantumNumbers -> {Y -> 2/3},
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366 | Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
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367 | },
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368 | F[15] == {
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369 | ClassName -> dR,
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370 | Unphysical -> True,
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371 | Indices -> {Index[Generation], Index[Colour]},
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372 | FlavorIndex -> Generation,
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373 | SelfConjugate -> False,
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374 | QuantumNumbers -> {Y -> -1/3},
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375 | Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
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376 | },
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377 | F[16] == {
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378 | ClassName -> NR,
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379 | Unphysical -> True,
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380 | Indices -> {Index[Heavynus]},
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381 | FlavorIndex -> Heavynus,
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382 | SelfConjugate -> False,
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383 | Definitions -> { NR[sp1_,ff_] :> Module[{sp2,ff2}, HEAVR[ff,ff2] ProjP[sp1,sp2] vl[sp2,ff2]] }
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384 | },
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385 | F[17] == {
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386 | ClassName -> NL,
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387 | Unphysical -> True,
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388 | Indices -> {Index[Heavynus]},
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389 | FlavorIndex -> Heavynus,
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390 | SelfConjugate -> False,
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391 | Definitions -> { NL[sp1_,ff_] :> Module[{sp2,ff2}, HEAV[ff,ff2] ProjM[sp1,sp2] vl[sp2,ff2]] }
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392 | },
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393 |
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394 |
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395 | (* Higgs: physical scalars *)
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396 | S[1] == {
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397 | ClassName -> H,
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398 | SelfConjugate -> True,
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399 | Mass -> {MH,125.1},
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400 | Width -> {WH,0.00407},
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401 | PropagatorLabel -> "H",
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402 | PropagatorType -> D,
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403 | PropagatorArrow -> None,
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404 | PDG -> 25,
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405 | ParticleName -> "H",
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406 | FullName -> "H"
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407 | },
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408 |
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409 | (* Higgs: physical scalars *)
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410 | S[2] == {
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411 | ClassName -> G0,
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412 | SelfConjugate -> True,
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413 | Goldstone -> Z,
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414 | Mass -> {MZ, 91.1876},
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415 | Width -> {WZ, 2.4952},
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416 | PropagatorLabel -> "Go",
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417 | PropagatorType -> D,
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418 | PropagatorArrow -> None,
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419 | PDG -> 250,
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420 | ParticleName -> "G0",
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421 | FullName -> "G0"
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422 | },
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423 | S[3] == {
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424 | ClassName -> GP,
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425 | SelfConjugate -> False,
|
---|
426 | Goldstone -> W,
|
---|
427 | Mass -> {MW, Internal},
|
---|
428 | QuantumNumbers -> {Q -> 1},
|
---|
429 | Width -> {WW, 2.085},
|
---|
430 | PropagatorLabel -> "GP",
|
---|
431 | PropagatorType -> D,
|
---|
432 | PropagatorArrow -> None,
|
---|
433 | PDG -> 251,
|
---|
434 | ParticleName -> "G+",
|
---|
435 | AntiParticleName -> "G-",
|
---|
436 | FullName -> "GP"
|
---|
437 | },
|
---|
438 |
|
---|
439 |
|
---|
440 | (* Pseudoscalar mesons *)
|
---|
441 | S[4] == {
|
---|
442 | ClassName -> K,
|
---|
443 | SelfConjugate -> False,
|
---|
444 | Mass -> {MK,0.493677},
|
---|
445 | QuantumNumbers -> {Q -> 1},
|
---|
446 | Width -> {WK,0},
|
---|
447 | PropagatorLabel -> "K",
|
---|
448 | PropagatorType -> D,
|
---|
449 | PropagatorArrow -> None,
|
---|
450 | PDG -> 321,
|
---|
451 | ParticleName -> "K+",
|
---|
452 | AntiParticleName -> "K-",
|
---|
453 | FullName -> "Charged Kaon"
|
---|
454 | },
|
---|
455 |
|
---|
456 | S[5] == {
|
---|
457 | ClassName -> Pip,
|
---|
458 | SelfConjugate -> False,
|
---|
459 | Mass -> {MPip,0.13957},
|
---|
460 | QuantumNumbers -> {Q -> 1},
|
---|
461 | Width -> {WPip, 0},
|
---|
462 | PropagatorLabel -> "Pi",
|
---|
463 | PropagatorType -> D,
|
---|
464 | PropagatorArrow -> None,
|
---|
465 | PDG -> 211,
|
---|
466 | ParticleName -> "Pi+",
|
---|
467 | AntiParticleName -> "Pi-",
|
---|
468 | FullName -> "Charged Pion"
|
---|
469 | },
|
---|
470 |
|
---|
471 | S[6] == {
|
---|
472 | ClassName -> Dd,
|
---|
473 | SelfConjugate -> False,
|
---|
474 | Mass -> {MDd,1.869},
|
---|
475 | QuantumNumbers -> {Q -> 1},
|
---|
476 | Width -> {WD, 0},
|
---|
477 | PropagatorLabel -> "Dd",
|
---|
478 | PropagatorType -> D,
|
---|
479 | PropagatorArrow -> None,
|
---|
480 | PDG -> 411,
|
---|
481 | ParticleName -> "D+",
|
---|
482 | AntiParticleName -> "D-",
|
---|
483 | FullName -> "Charged D"
|
---|
484 | },
|
---|
485 |
|
---|
486 | S[13] == {
|
---|
487 | ClassName -> D0,
|
---|
488 | SelfConjugate -> False,
|
---|
489 | Mass -> {MD0,1.865},
|
---|
490 | QuantumNumbers -> {Q -> 0},
|
---|
491 | Width -> {WD0,0},
|
---|
492 | PropagatorLabel -> "D0",
|
---|
493 | PropagatorType -> D,
|
---|
494 | PropagatorArrow -> None,
|
---|
495 | PDG -> 421,
|
---|
496 | ParticleName -> "D0",
|
---|
497 | AntiParticleName -> "D0bar",
|
---|
498 | FullName -> "Neutral D"
|
---|
499 | },
|
---|
500 |
|
---|
501 | S[7] == {
|
---|
502 | ClassName -> Pi0,
|
---|
503 | SelfConjugate -> True,
|
---|
504 | Mass -> {MPi0,0.13498},
|
---|
505 | Width -> {WPi0, 0},
|
---|
506 | PropagatorLabel -> "Pi0",
|
---|
507 | PropagatorType -> D,
|
---|
508 | PropagatorArrow -> None,
|
---|
509 | PDG -> 111,
|
---|
510 | ParticleName -> "Pi0",
|
---|
511 | FullName -> "Neutral Pion"
|
---|
512 | },
|
---|
513 |
|
---|
514 | S[12] == {
|
---|
515 | ClassName -> K0,
|
---|
516 | SelfConjugate -> False,
|
---|
517 | Mass -> {MK0,0.497611},
|
---|
518 | QuantumNumbers -> {Q -> 0},
|
---|
519 | Width -> {WK0,0},
|
---|
520 | PropagatorLabel -> "K0",
|
---|
521 | PropagatorType -> D,
|
---|
522 | PropagatorArrow -> None,
|
---|
523 | PDG -> 311,
|
---|
524 | ParticleName -> "K0",
|
---|
525 | AntiParticleName -> "K0bar",
|
---|
526 | FullName -> "Neutral Kaon"
|
---|
527 | },
|
---|
528 |
|
---|
529 | S[8] == {
|
---|
530 | ClassName -> Eta,
|
---|
531 | SelfConjugate -> True,
|
---|
532 | Mass -> {Meta,0.54786},
|
---|
533 | Width -> {Weta, 0},
|
---|
534 | PropagatorLabel -> "eta",
|
---|
535 | PropagatorType -> D,
|
---|
536 | PropagatorArrow -> None,
|
---|
537 | PDG -> 221,
|
---|
538 | ParticleName -> "Eta",
|
---|
539 | FullName -> "Eta"
|
---|
540 | },
|
---|
541 |
|
---|
542 | S[9] == {
|
---|
543 | ClassName -> Etap,
|
---|
544 | SelfConjugate -> True,
|
---|
545 | Mass -> {Metap,0.9578},
|
---|
546 | Width -> {Wetap, 0},
|
---|
547 | PropagatorLabel -> "etap",
|
---|
548 | PropagatorType -> D,
|
---|
549 | PropagatorArrow -> None,
|
---|
550 | PDG -> 331,
|
---|
551 | ParticleName -> "Etap",
|
---|
552 | FullName -> "Eta Prime"
|
---|
553 | },
|
---|
554 |
|
---|
555 | S[10] == {
|
---|
556 | ClassName -> Ds,
|
---|
557 | SelfConjugate -> False,
|
---|
558 | Mass -> {MDs,1.9683},
|
---|
559 | QuantumNumbers -> {Q -> 1},
|
---|
560 | Width -> {WDs, 0},
|
---|
561 | PropagatorLabel -> "Ds",
|
---|
562 | PropagatorType -> D,
|
---|
563 | PropagatorArrow -> None,
|
---|
564 | PDG -> 431,
|
---|
565 | ParticleName -> "Ds+",
|
---|
566 | AntiParticleName -> "Ds-",
|
---|
567 | FullName -> "Charged Ds"
|
---|
568 | },
|
---|
569 |
|
---|
570 | S[15] == {
|
---|
571 | ClassName -> Bu,
|
---|
572 | SelfConjugate -> False,
|
---|
573 | Mass -> {MBu,5.279},
|
---|
574 | QuantumNumbers -> {Q -> 1},
|
---|
575 | Width -> {WBu, 0},
|
---|
576 | PropagatorLabel -> "Bu",
|
---|
577 | PropagatorType -> D,
|
---|
578 | PropagatorArrow -> None,
|
---|
579 | PDG -> 521,
|
---|
580 | ParticleName -> "B+",
|
---|
581 | AntiParticleName -> "B-",
|
---|
582 | FullName -> "Charged B"
|
---|
583 | },
|
---|
584 |
|
---|
585 | S[16] == {
|
---|
586 | ClassName -> Bc,
|
---|
587 | SelfConjugate -> False,
|
---|
588 | Mass -> {MBc,6.275},
|
---|
589 | QuantumNumbers -> {Q -> 1},
|
---|
590 | Width -> {WBc, 0},
|
---|
591 | PropagatorLabel -> "Bc",
|
---|
592 | PropagatorType -> D,
|
---|
593 | PropagatorArrow -> None,
|
---|
594 | PDG -> 541,
|
---|
595 | ParticleName -> "Bc+",
|
---|
596 | AntiParticleName -> "Bc-",
|
---|
597 | FullName -> "Charged Bc"
|
---|
598 | },
|
---|
599 |
|
---|
600 | S[17] == {
|
---|
601 | ClassName -> B0,
|
---|
602 | SelfConjugate -> False,
|
---|
603 | Mass -> {MB0,5.280},
|
---|
604 | QuantumNumbers -> {Q -> 0},
|
---|
605 | Width -> {WB0,0},
|
---|
606 | PropagatorLabel -> "B0",
|
---|
607 | PropagatorType -> D,
|
---|
608 | PropagatorArrow -> None,
|
---|
609 | PDG -> 511,
|
---|
610 | ParticleName -> "B0",
|
---|
611 | AntiParticleName -> "B0bar",
|
---|
612 | FullName -> "Neutral B"
|
---|
613 | },
|
---|
614 |
|
---|
615 | S[18] == {
|
---|
616 | ClassName -> B0s,
|
---|
617 | SelfConjugate -> False,
|
---|
618 | Mass -> {MB0s,5.367},
|
---|
619 | QuantumNumbers -> {Q -> 0},
|
---|
620 | Width -> {WB0s,0},
|
---|
621 | PropagatorLabel -> "B0s",
|
---|
622 | PropagatorType -> D,
|
---|
623 | PropagatorArrow -> None,
|
---|
624 | PDG -> 531,
|
---|
625 | ParticleName -> "B0s",
|
---|
626 | AntiParticleName -> "B0sbar",
|
---|
627 | FullName -> "Neutral Bs"
|
---|
628 | },
|
---|
629 |
|
---|
630 | (* Higgs: unphysical scalars *)
|
---|
631 | S[11] == {
|
---|
632 | ClassName -> Phi,
|
---|
633 | Unphysical -> True,
|
---|
634 | Indices -> {Index[SU2D]},
|
---|
635 | FlavorIndex -> SU2D,
|
---|
636 | SelfConjugate -> False,
|
---|
637 | QuantumNumbers -> {Y -> 1/2},
|
---|
638 | Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
|
---|
639 | },
|
---|
640 |
|
---|
641 | (* Vector mesons *)
|
---|
642 |
|
---|
643 |
|
---|
644 | V[21] == {
|
---|
645 | ClassName -> rho0,
|
---|
646 | SelfConjugate -> True,
|
---|
647 | Mass -> {Mrho0, 0.77526},
|
---|
648 | Width -> {Wrho0, 0.1478},
|
---|
649 | ParticleName -> "rho0",
|
---|
650 | PDG -> 113,
|
---|
651 | PropagatorLabel -> "rho0",
|
---|
652 | PropagatorType -> Sine,
|
---|
653 | PropagatorArrow -> None,
|
---|
654 | FullName -> "rho 0"
|
---|
655 | },
|
---|
656 |
|
---|
657 | V[22] == {
|
---|
658 | ClassName -> rho,
|
---|
659 | SelfConjugate -> False,
|
---|
660 | Mass -> {Mrho, 0.77511},
|
---|
661 | Width -> {Wrho, 0.1491},
|
---|
662 | ParticleName -> "rho+",
|
---|
663 | AntiParticleName -> "rho-",
|
---|
664 | QuantumNumbers -> {Q -> 1},
|
---|
665 | PDG -> 213,
|
---|
666 | PropagatorLabel -> "rho",
|
---|
667 | PropagatorType -> Sine,
|
---|
668 | PropagatorArrow -> Forward,
|
---|
669 | FullName -> "charged rho"
|
---|
670 | },
|
---|
671 |
|
---|
672 |
|
---|
673 | V[23] == {
|
---|
674 | ClassName -> omega,
|
---|
675 | SelfConjugate -> True,
|
---|
676 | Mass -> {Mom, 0.78265},
|
---|
677 | Width -> {Wom, 0.00849},
|
---|
678 | ParticleName -> "omega",
|
---|
679 | PDG -> 223,
|
---|
680 | PropagatorLabel -> "omega",
|
---|
681 | PropagatorType -> Sine,
|
---|
682 | PropagatorArrow -> None,
|
---|
683 | FullName -> "Omega"
|
---|
684 | },
|
---|
685 |
|
---|
686 | V[24] == {
|
---|
687 | ClassName -> Kstar,
|
---|
688 | SelfConjugate -> False,
|
---|
689 | Mass -> {MKstar, 0.8917},
|
---|
690 | Width -> {WKstar, 0.0508},
|
---|
691 | ParticleName -> "Kstar+",
|
---|
692 | AntiParticleName -> "Kstar-",
|
---|
693 | QuantumNumbers -> {Q -> 1},
|
---|
694 | PDG -> 323,
|
---|
695 | PropagatorLabel -> "Kstar",
|
---|
696 | PropagatorType -> Sine,
|
---|
697 | PropagatorArrow -> Forward,
|
---|
698 | FullName -> "Charged Kstar"
|
---|
699 | },
|
---|
700 |
|
---|
701 | V[25] == {
|
---|
702 | ClassName -> phimeson,
|
---|
703 | SelfConjugate -> True,
|
---|
704 | Mass -> {Mphi, 1.019461},
|
---|
705 | Width -> {Wphi, 0.004249},
|
---|
706 | ParticleName -> "phimeson",
|
---|
707 | PDG -> 333,
|
---|
708 | PropagatorLabel -> "phi",
|
---|
709 | PropagatorType -> Sine,
|
---|
710 | PropagatorArrow -> Forward,
|
---|
711 | FullName -> "phi meson"
|
---|
712 | },
|
---|
713 |
|
---|
714 | V[26] == {
|
---|
715 | ClassName -> Bstar,
|
---|
716 | SelfConjugate -> False,
|
---|
717 | Mass -> {MBstar, 5.3247},
|
---|
718 | Width -> {WBstar, 0},
|
---|
719 | ParticleName -> "Bstar+",
|
---|
720 | AntiParticleName -> "Bstar-",
|
---|
721 | QuantumNumbers -> {Q -> 1},
|
---|
722 | PDG -> 523,
|
---|
723 | PropagatorLabel -> "Bstar",
|
---|
724 | PropagatorType -> Sine,
|
---|
725 | PropagatorArrow -> Forward,
|
---|
726 | FullName -> "Charged Bstar"
|
---|
727 | }
|
---|
728 |
|
---|
729 | };
|
---|
730 |
|
---|
731 |
|
---|
732 |
|
---|
733 | (* ************************** *)
|
---|
734 | (* ***** Gauge ***** *)
|
---|
735 | (* ***** Parameters ***** *)
|
---|
736 | (* ***** (FeynArts) ***** *)
|
---|
737 | (* ************************** *)
|
---|
738 |
|
---|
739 | GaugeXi[ V[1] ] = GaugeXi[A];
|
---|
740 | GaugeXi[ V[2] ] = GaugeXi[Z];
|
---|
741 | GaugeXi[ V[3] ] = GaugeXi[W];
|
---|
742 | GaugeXi[ V[4] ] = GaugeXi[G];
|
---|
743 | GaugeXi[ S[1] ] = 1;
|
---|
744 | GaugeXi[ S[2] ] = GaugeXi[Z];
|
---|
745 | GaugeXi[ S[3] ] = GaugeXi[W];
|
---|
746 | GaugeXi[ U[1] ] = GaugeXi[A];
|
---|
747 | GaugeXi[ U[2] ] = GaugeXi[Z];
|
---|
748 | GaugeXi[ U[31] ] = GaugeXi[W];
|
---|
749 | GaugeXi[ U[32] ] = GaugeXi[W];
|
---|
750 | GaugeXi[ U[4] ] = GaugeXi[G];
|
---|
751 |
|
---|
752 |
|
---|
753 | (* ************************** *)
|
---|
754 | (* ***** Parameters ***** *)
|
---|
755 | (* ************************** *)
|
---|
756 | M$Parameters = {
|
---|
757 |
|
---|
758 | (* External parameters *)
|
---|
759 | aEWM1 == {
|
---|
760 | ParameterType -> External,
|
---|
761 | BlockName -> SMINPUTS,
|
---|
762 | OrderBlock -> 1,
|
---|
763 | Value -> 127.9,
|
---|
764 | InteractionOrder -> {QED,-2},
|
---|
765 | Description -> "Inverse of the EW coupling constant at the Z pole"
|
---|
766 | },
|
---|
767 | Gf == {
|
---|
768 | ParameterType -> External,
|
---|
769 | BlockName -> SMINPUTS,
|
---|
770 | OrderBlock -> 2,
|
---|
771 | Value -> 1.16637*^-5,
|
---|
772 | InteractionOrder -> {QED,2},
|
---|
773 | TeX -> Subscript[G,f],
|
---|
774 | Description -> "Fermi constant"
|
---|
775 | },
|
---|
776 | aS == {
|
---|
777 | ParameterType -> External,
|
---|
778 | BlockName -> SMINPUTS,
|
---|
779 | OrderBlock -> 3,
|
---|
780 | Value -> 0.1184,
|
---|
781 | InteractionOrder -> {QCD,2},
|
---|
782 | TeX -> Subscript[\[Alpha],s],
|
---|
783 | Description -> "Strong coupling constant at the Z pole"
|
---|
784 | },
|
---|
785 | ymdo == {
|
---|
786 | ParameterType -> External,
|
---|
787 | BlockName -> YUKAWA,
|
---|
788 | OrderBlock -> 1,
|
---|
789 | Value -> 5.04*^-3,
|
---|
790 | Description -> "Down Yukawa mass"
|
---|
791 | },
|
---|
792 | ymup == {
|
---|
793 | ParameterType -> External,
|
---|
794 | BlockName -> YUKAWA,
|
---|
795 | OrderBlock -> 2,
|
---|
796 | Value -> 2.55*^-3,
|
---|
797 | Description -> "Up Yukawa mass"
|
---|
798 | },
|
---|
799 | yms == {
|
---|
800 | ParameterType -> External,
|
---|
801 | BlockName -> YUKAWA,
|
---|
802 | OrderBlock -> 3,
|
---|
803 | Value -> 0.101,
|
---|
804 | Description -> "Strange Yukawa mass"
|
---|
805 | },
|
---|
806 | ymc == {
|
---|
807 | ParameterType -> External,
|
---|
808 | BlockName -> YUKAWA,
|
---|
809 | OrderBlock -> 4,
|
---|
810 | Value -> 1.27,
|
---|
811 | Description -> "Charm Yukawa mass"
|
---|
812 | },
|
---|
813 | ymb == {
|
---|
814 | ParameterType -> External,
|
---|
815 | BlockName -> YUKAWA,
|
---|
816 | OrderBlock -> 5,
|
---|
817 | Value -> 4.7,
|
---|
818 | Description -> "Bottom Yukawa mass"
|
---|
819 | },
|
---|
820 | ymt == {
|
---|
821 | ParameterType -> External,
|
---|
822 | BlockName -> YUKAWA,
|
---|
823 | OrderBlock -> 6,
|
---|
824 | Value -> 172,
|
---|
825 | Description -> "Top Yukawa mass"
|
---|
826 | },
|
---|
827 | yme == {
|
---|
828 | ParameterType -> External,
|
---|
829 | BlockName -> YUKAWA,
|
---|
830 | OrderBlock -> 11,
|
---|
831 | Value -> 5.11*^-4,
|
---|
832 | Description -> "Electron Yukawa mass"
|
---|
833 | },
|
---|
834 | ymm == {
|
---|
835 | ParameterType -> External,
|
---|
836 | BlockName -> YUKAWA,
|
---|
837 | OrderBlock -> 13,
|
---|
838 | Value -> 0.10566,
|
---|
839 | Description -> "Muon Yukawa mass"
|
---|
840 | },
|
---|
841 | ymtau == {
|
---|
842 | ParameterType -> External,
|
---|
843 | BlockName -> YUKAWA,
|
---|
844 | OrderBlock -> 15,
|
---|
845 | Value -> 1.777,
|
---|
846 | Description -> "Tau Yukawa mass"
|
---|
847 | },
|
---|
848 | modthetae == {
|
---|
849 | ParameterType -> External,
|
---|
850 | BlockName -> YUKAWA,
|
---|
851 | OrderBlock -> 16,
|
---|
852 | Value -> 0.00001,
|
---|
853 | Description -> "Heavy-nu-electron mixing modulus"
|
---|
854 | },
|
---|
855 | argthetae == {
|
---|
856 | ParameterType -> External,
|
---|
857 | BlockName -> YUKAWA,
|
---|
858 | OrderBlock -> 17,
|
---|
859 | Value -> 0,
|
---|
860 | Description -> "Heavy-nu-electron mixing argument (degrees)"
|
---|
861 | },
|
---|
862 | thetae == {
|
---|
863 | ParameterType -> Internal,
|
---|
864 | BlockName -> YUKAWA,
|
---|
865 | Value -> modthetae*Exp[I*Pi/180*argthetae],
|
---|
866 | Description -> "Heavy-nu-electron mixing"
|
---|
867 | },
|
---|
868 | modthetamu == {
|
---|
869 | ParameterType -> External,
|
---|
870 | BlockName -> YUKAWA,
|
---|
871 | OrderBlock -> 18,
|
---|
872 | Value -> 0.00001,
|
---|
873 | Description -> "Heavy-nu-muon mixing modulus"
|
---|
874 | },
|
---|
875 | argthetamu == {
|
---|
876 | ParameterType -> External,
|
---|
877 | BlockName -> YUKAWA,
|
---|
878 | OrderBlock -> 19,
|
---|
879 | Value -> 0,
|
---|
880 | Description -> "Heavy-nu-muon mixing argument (degrees)"
|
---|
881 | },
|
---|
882 | thetamu == {
|
---|
883 | ParameterType -> Internal,
|
---|
884 | BlockName -> YUKAWA,
|
---|
885 | Value -> modthetamu*Exp[I*Pi/180*argthetamu],
|
---|
886 | Description -> "Heavy-nu-muon mixing"
|
---|
887 | },
|
---|
888 | modthetatau == {
|
---|
889 | ParameterType -> External,
|
---|
890 | BlockName -> YUKAWA,
|
---|
891 | OrderBlock -> 20,
|
---|
892 | Value -> 0.00001,
|
---|
893 | Description -> "Heavy-nu-tau mixing modulus"
|
---|
894 | },
|
---|
895 | argthetatau == {
|
---|
896 | ParameterType -> External,
|
---|
897 | BlockName -> YUKAWA,
|
---|
898 | OrderBlock -> 21,
|
---|
899 | Value -> 0,
|
---|
900 | Description -> "Heavy-nu-tau mixing argument (degrees)"
|
---|
901 | },
|
---|
902 | thetatau == {
|
---|
903 | ParameterType -> Internal,
|
---|
904 | BlockName -> YUKAWA,
|
---|
905 | Value -> modthetatau*Exp[I*Pi/180*argthetatau],
|
---|
906 | Description -> "Heavy-nu-tau mixing"
|
---|
907 | },
|
---|
908 | MN4 == {
|
---|
909 | ParameterType -> External,
|
---|
910 | BlockName -> YUKAWA,
|
---|
911 | OrderBlock -> 22,
|
---|
912 | Value -> 1.0,
|
---|
913 | Description -> "Majorana mass for N4 in GeV"
|
---|
914 | },
|
---|
915 |
|
---|
916 | cabi == {
|
---|
917 | ParameterType -> External,
|
---|
918 | BlockName -> CKMBLOCK,
|
---|
919 | OrderBlock -> 1,
|
---|
920 | Value -> 0.227736,
|
---|
921 | TeX -> Subscript[\[Theta], c],
|
---|
922 | Description -> "Cabibbo angle"
|
---|
923 | },
|
---|
924 |
|
---|
925 | th13 == {
|
---|
926 | ParameterType -> External,
|
---|
927 | ComplexParameter -> False,
|
---|
928 | BlockName -> CKMBLOCK,
|
---|
929 | OrderBlock -> 2,
|
---|
930 | Value -> 0.003508,
|
---|
931 | TeX -> Subscript[\[Theta], 13],
|
---|
932 | Description -> "CKM Theta 13"
|
---|
933 | },
|
---|
934 |
|
---|
935 | th23 == {
|
---|
936 | ParameterType -> External,
|
---|
937 | ComplexParameter -> False,
|
---|
938 | BlockName -> CKMBLOCK,
|
---|
939 | OrderBlock -> 3,
|
---|
940 | Value -> 0.041539,
|
---|
941 | TeX -> Subscript[\[Theta], 23],
|
---|
942 | Description -> "CKM theta 23"
|
---|
943 | },
|
---|
944 |
|
---|
945 | del13 == {
|
---|
946 | ParameterType -> External,
|
---|
947 | ComplexParameter -> False,
|
---|
948 | BlockName -> CKMBLOCK,
|
---|
949 | OrderBlock -> 4,
|
---|
950 | Value -> 1.20,
|
---|
951 | TeX -> Subscript[\[Delta], 13],
|
---|
952 | Description -> "CKM delta 13"
|
---|
953 | },
|
---|
954 |
|
---|
955 | MassN4 == {
|
---|
956 | ParameterType -> Internal,
|
---|
957 | Value -> MN4,
|
---|
958 | Description -> "Heavy mass"
|
---|
959 | },
|
---|
960 |
|
---|
961 | fK == {
|
---|
962 | ParameterType -> External,
|
---|
963 | BlockName -> MESONBLOCK,
|
---|
964 | OrderBlock -> 2,
|
---|
965 | Value -> 0.1556,
|
---|
966 | Description -> "Kaon decay constant"
|
---|
967 | },
|
---|
968 |
|
---|
969 | fpi == {
|
---|
970 | ParameterType -> External,
|
---|
971 | BlockName -> MESONBLOCK,
|
---|
972 | OrderBlock -> 3,
|
---|
973 | Value -> 0.1302,
|
---|
974 | Description -> "Pion decay constant"
|
---|
975 | },
|
---|
976 |
|
---|
977 | feta == {
|
---|
978 | ParameterType -> External,
|
---|
979 | BlockName -> MESONBLOCK,
|
---|
980 | OrderBlock -> 4,
|
---|
981 | Value -> 0.08159,
|
---|
982 | Description -> "Eta decay constant"
|
---|
983 | },
|
---|
984 |
|
---|
985 | fetap == {
|
---|
986 | ParameterType -> External,
|
---|
987 | BlockName -> MESONBLOCK,
|
---|
988 | OrderBlock -> 5,
|
---|
989 | Value -> -0.0946,
|
---|
990 | Description -> "Eta prime decay constant"
|
---|
991 | },
|
---|
992 |
|
---|
993 | fD == {
|
---|
994 | ParameterType -> External,
|
---|
995 | BlockName -> MESONBLOCK,
|
---|
996 | OrderBlock -> 6,
|
---|
997 | Value -> 0.212,
|
---|
998 | Description -> "D decay constant"
|
---|
999 | },
|
---|
1000 |
|
---|
1001 | frho == {
|
---|
1002 | ParameterType -> External,
|
---|
1003 | BlockName -> MESONBLOCK,
|
---|
1004 | OrderBlock -> 7,
|
---|
1005 | Value -> 0.17,
|
---|
1006 | Description -> "rho decay constant"
|
---|
1007 | },
|
---|
1008 |
|
---|
1009 | fKstar == {
|
---|
1010 | ParameterType -> External,
|
---|
1011 | BlockName -> MESONBLOCK,
|
---|
1012 | OrderBlock -> 34,
|
---|
1013 | Value -> 0.177,
|
---|
1014 | Description -> "Kstar decay constant"
|
---|
1015 | },
|
---|
1016 |
|
---|
1017 | fDs == {
|
---|
1018 | ParameterType -> External,
|
---|
1019 | BlockName -> MESONBLOCK,
|
---|
1020 | OrderBlock -> 8,
|
---|
1021 | Value -> 0.249,
|
---|
1022 | Description -> "Ds decay constant"
|
---|
1023 | },
|
---|
1024 |
|
---|
1025 | fomega == {
|
---|
1026 | ParameterType -> External,
|
---|
1027 | BlockName -> MESONBLOCK,
|
---|
1028 | OrderBlock -> 9,
|
---|
1029 | Value -> 0.155,
|
---|
1030 | Description -> "omega decay constant"
|
---|
1031 | },
|
---|
1032 |
|
---|
1033 | fphi == {
|
---|
1034 | ParameterType -> External,
|
---|
1035 | BlockName -> MESONBLOCK,
|
---|
1036 | OrderBlock -> 10,
|
---|
1037 | Value -> 0.232,
|
---|
1038 | Description -> "phi decay constant"
|
---|
1039 | },
|
---|
1040 |
|
---|
1041 | fB == {
|
---|
1042 | ParameterType -> External,
|
---|
1043 | BlockName -> MESONBLOCK,
|
---|
1044 | OrderBlock -> 11,
|
---|
1045 | Value -> 0.190,
|
---|
1046 | ComplexParameter -> False,
|
---|
1047 | Description -> "B decay constant"
|
---|
1048 | },
|
---|
1049 |
|
---|
1050 | fBs == {
|
---|
1051 | ParameterType -> External,
|
---|
1052 | BlockName -> MESONBLOCK,
|
---|
1053 | OrderBlock -> 12,
|
---|
1054 | Value -> 0.230,
|
---|
1055 | ComplexParameter -> False,
|
---|
1056 | Description -> "Bs decay constant"
|
---|
1057 | },
|
---|
1058 |
|
---|
1059 | fBc == {
|
---|
1060 | ParameterType -> External,
|
---|
1061 | BlockName -> MESONBLOCK,
|
---|
1062 | OrderBlock -> 13,
|
---|
1063 | Value -> 0.190,
|
---|
1064 | ComplexParameter -> False,
|
---|
1065 | Description -> "Bc decay constant"
|
---|
1066 | },
|
---|
1067 |
|
---|
1068 |
|
---|
1069 | (* Internal Parameters *)
|
---|
1070 | aEW == {
|
---|
1071 | ParameterType -> Internal,
|
---|
1072 | Value -> 1/aEWM1,
|
---|
1073 | InteractionOrder -> {QED,2},
|
---|
1074 | TeX -> Subscript[\[Alpha], EW],
|
---|
1075 | Description -> "Electroweak coupling contant"
|
---|
1076 | },
|
---|
1077 | MW == {
|
---|
1078 | ParameterType -> Internal,
|
---|
1079 | Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-3.14/Sqrt[2]*aEW/Gf*MZ^2]],
|
---|
1080 | TeX -> Subscript[M,W],
|
---|
1081 | Description -> "W mass"
|
---|
1082 | },
|
---|
1083 | sw2 == {
|
---|
1084 | ParameterType -> Internal,
|
---|
1085 | Value -> 1-(MW/MZ)^2,
|
---|
1086 | Description -> "Squared Sin of the Weinberg angle"
|
---|
1087 | },
|
---|
1088 | ee == {
|
---|
1089 | ParameterType -> Internal,
|
---|
1090 | Value -> Sqrt[4 3.14 aEW],
|
---|
1091 | InteractionOrder -> {QED,1},
|
---|
1092 | TeX -> e,
|
---|
1093 | Description -> "Electric coupling constant"
|
---|
1094 | },
|
---|
1095 | cw == {
|
---|
1096 | ParameterType -> Internal,
|
---|
1097 | Value -> Sqrt[1-sw2],
|
---|
1098 | TeX -> Subscript[c,w],
|
---|
1099 | Description -> "Cosine of the Weinberg angle"
|
---|
1100 | },
|
---|
1101 | sw == {
|
---|
1102 | ParameterType -> Internal,
|
---|
1103 | Value -> Sqrt[sw2],
|
---|
1104 | TeX -> Subscript[s,w],
|
---|
1105 | Description -> "Sine of the Weinberg angle"
|
---|
1106 | },
|
---|
1107 | gw == {
|
---|
1108 | ParameterType -> Internal,
|
---|
1109 | Definitions -> {gw->ee/sw},
|
---|
1110 | InteractionOrder -> {QED,1},
|
---|
1111 | TeX -> Subscript[g,w],
|
---|
1112 | Description -> "Weak coupling constant at the Z pole"
|
---|
1113 | },
|
---|
1114 | g1 == {
|
---|
1115 | ParameterType -> Internal,
|
---|
1116 | Definitions -> {g1->ee/cw},
|
---|
1117 | InteractionOrder -> {QED,1},
|
---|
1118 | TeX -> Subscript[g,1],
|
---|
1119 | Description -> "U(1)Y coupling constant at the Z pole"
|
---|
1120 | },
|
---|
1121 | gs == {
|
---|
1122 | ParameterType -> Internal,
|
---|
1123 | Value -> Sqrt[4 3.14 aS],
|
---|
1124 | InteractionOrder -> {QCD,1},
|
---|
1125 | TeX -> Subscript[g,s],
|
---|
1126 | ParameterName -> G,
|
---|
1127 | Description -> "Strong coupling constant at the Z pole"
|
---|
1128 | },
|
---|
1129 | vev == {
|
---|
1130 | ParameterType -> Internal,
|
---|
1131 | Value -> 2*MW*sw/ee,
|
---|
1132 | InteractionOrder -> {QED,-1},
|
---|
1133 | Description -> "Higgs vacuum expectation value"
|
---|
1134 | },
|
---|
1135 | lam == {
|
---|
1136 | ParameterType -> Internal,
|
---|
1137 | Value -> MH^2/(2*vev^2),
|
---|
1138 | InteractionOrder -> {QED, 2},
|
---|
1139 | Description -> "Higgs quartic coupling"
|
---|
1140 | },
|
---|
1141 | muH == {
|
---|
1142 | ParameterType -> Internal,
|
---|
1143 | Value -> Sqrt[vev^2 lam],
|
---|
1144 | TeX -> \[Mu],
|
---|
1145 | Description -> "Coefficient of the quadratic piece of the Higgs potential"
|
---|
1146 | },
|
---|
1147 | thetatot == {
|
---|
1148 | ParameterType -> Internal,
|
---|
1149 | Value -> Sqrt[thetae*Conjugate[thetae]+thetamu*Conjugate[thetamu]+thetatau*Conjugate[thetatau]],
|
---|
1150 | TeX -> \[Theta],
|
---|
1151 | Description -> "Heavy-active mixing"
|
---|
1152 | },
|
---|
1153 | thetas == {
|
---|
1154 | ParameterType -> Internal,
|
---|
1155 | Value -> thetae+thetamu+thetatau,
|
---|
1156 | TeX -> Subscript[\[Theta],s],
|
---|
1157 | Description -> "Heavy-active mixing sum"
|
---|
1158 | },
|
---|
1159 | r == {
|
---|
1160 | ParameterType -> Internal,
|
---|
1161 | Value -> 1/Sqrt[1+thetatot^2],
|
---|
1162 | Description -> "useful ratio"
|
---|
1163 | },
|
---|
1164 | yN == {
|
---|
1165 | ParameterType -> Internal,
|
---|
1166 | Indices -> {Index[Generation], Index[Heavynus]},
|
---|
1167 | Value -> {yN[1,1] -> Sqrt[2] Conjugate[thetae] MN4 /vev, yN[2,1] -> Sqrt[2] Conjugate[thetamu] MN4 /vev, yN[3,1] -> Sqrt[2] Conjugate[thetatau] MN4 /vev},
|
---|
1168 | InteractionOrder -> {QED, 1},
|
---|
1169 | ParameterName -> {yN[1,1] -> yNe, yN[2,1] -> yNmu, yN[3,1] -> yNtau},
|
---|
1170 | TeX -> Superscript[y, N],
|
---|
1171 | Description -> "Heavy nu Yukawa couplings"
|
---|
1172 | },
|
---|
1173 | numass == {
|
---|
1174 | ParameterType -> Internal,
|
---|
1175 | Indices -> {Index[Neutrinos], Index[Neutrinos]},
|
---|
1176 | Value -> {numass[4,4] :> MN4, numass[ii_,jj_] :> 0},
|
---|
1177 | InteractionOrder -> {QED, 0},
|
---|
1178 | ParameterName -> {numass[1,1] :> mnu1, numass[2,2] :> mnu2, numass[3,3] :> mnu3, numass[4,4] :> mnu4},
|
---|
1179 | TeX -> Superscript[m, nu],
|
---|
1180 | Description -> "Neutrino mass"
|
---|
1181 | },
|
---|
1182 |
|
---|
1183 | (** Form factors for K0 to Pi+ decays: linear parametrization **)
|
---|
1184 |
|
---|
1185 | avq2K0Pi == {
|
---|
1186 | ParameterType -> Internal,
|
---|
1187 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1188 | Value -> {avq2K0Pi[ii_,ll_] ->
|
---|
1189 | If[ll==1, -1.7232*numass[ii,ii]^3 + 1.08186*numass[ii,ii]^2 + 0.0973741*numass[ii,ii] + 0.0331474*KroneckerDelta[ii,ii],
|
---|
1190 | If[ll==2, -3.15565*numass[ii,ii]^3 + 1.70749*numass[ii,ii]^2 + 0.0668773*numass[ii,ii] + 0.052815*KroneckerDelta[ii,ii], 10^-90]]},
|
---|
1191 | Description -> "Average momentum transfer in K0 to Pi decays"
|
---|
1192 | },
|
---|
1193 |
|
---|
1194 | fplusK0Pi == {
|
---|
1195 | ParameterType -> Internal,
|
---|
1196 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1197 | Value -> {fplusK0Pi[ii_,ll_] -> 0.9749*(1+0.0282*avq2K0Pi[ii,ll]/MPip^2)},
|
---|
1198 | Description -> "Average f+ form factor in K0 to Pi+ decays"
|
---|
1199 | },
|
---|
1200 |
|
---|
1201 | f0K0Pi == {
|
---|
1202 | ParameterType -> Internal,
|
---|
1203 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1204 | Value -> {f0K0Pi[ii_,ll_] -> 0.9749*(1+0.0138*avq2K0Pi[ii,ll]/MPip^2)},
|
---|
1205 | Description -> "Average f0 form factor in K0 to Pi+ decays"
|
---|
1206 | },
|
---|
1207 |
|
---|
1208 | fminusK0Pi == {
|
---|
1209 | ParameterType -> Internal,
|
---|
1210 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1211 | Value -> {fminusK0Pi[ii_,ll_] -> (MPip^2-MK0^2)*(f0K0Pi[ii,ll]-fplusK0Pi[ii,ll])/avq2K0Pi[ii,ll]},
|
---|
1212 | Description -> "Average f- form factor in K0 to Pi+ decays"
|
---|
1213 | },
|
---|
1214 |
|
---|
1215 | (** Form factors for K+ to Pi0 decays: linear parametrization **)
|
---|
1216 |
|
---|
1217 | avq2KPi0 == {
|
---|
1218 | ParameterType -> Internal,
|
---|
1219 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1220 | Value -> {avq2KPi0[ii_,ll_] ->
|
---|
1221 | If[ll==1, -1.80782*numass[ii,ii]^3 + 1.10701*numass[ii,ii]^2 + 0.0998414*numass[ii,ii] + 0.0329829*KroneckerDelta[ii,ii],
|
---|
1222 | If[ll==2, -3.22495*numass[ii,ii]^3 + 1.71265*numass[ii,ii]^2 + 0.0698265*numass[ii,ii] + 0.052995*KroneckerDelta[ii,ii], 10^-90]]},
|
---|
1223 | Description -> "Average momentum transfer in K+ to Pi0 decays"
|
---|
1224 | },
|
---|
1225 |
|
---|
1226 | fplusKPi0 == {
|
---|
1227 | ParameterType -> Internal,
|
---|
1228 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1229 | Value -> {fplusKPi0[ii_,ll_] -> 0.9749*(1+0.0297*avq2KPi0[ii,ll]/MPip^2)},
|
---|
1230 | Description -> "Average f+ form factor in K+ to Pi0 decays"
|
---|
1231 | },
|
---|
1232 |
|
---|
1233 | f0KPi0 == {
|
---|
1234 | ParameterType -> Internal,
|
---|
1235 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1236 | Value -> {f0KPi0[ii_,ll_] -> 0.9749*(1+0.0195*avq2KPi0[ii,ll]/MPip^2)},
|
---|
1237 | Description -> "Average f0 form factor in K+ to Pi0 decays"
|
---|
1238 | },
|
---|
1239 |
|
---|
1240 | fminusKPi0 == {
|
---|
1241 | ParameterType -> Internal,
|
---|
1242 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1243 | Value -> {fminusKPi0[ii_,ll_] -> (MPi0^2-MK^2)*(f0KPi0[ii,ll]-fplusKPi0[ii,ll])/avq2KPi0[ii,ll]},
|
---|
1244 | Description -> "Average f- form factor in K+ to Pi0 decays"
|
---|
1245 | },
|
---|
1246 |
|
---|
1247 | (** Form factors for D to K decays: pole parametrization **)
|
---|
1248 |
|
---|
1249 | avq2DK == {
|
---|
1250 | ParameterType -> Internal,
|
---|
1251 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1252 | Value -> {avq2DK[ii_,ll_] ->
|
---|
1253 | If[ll==1, -0.364268*numass[ii,ii]^3 + 0.932086*numass[ii,ii]^2 + 0.381641*numass[ii,ii] + 0.538848*KroneckerDelta[ii,ii],
|
---|
1254 | If[ll==2, -0.337128*numass[ii,ii]^3 + 0.94568*numass[ii,ii]^2 + 0.368498*numass[ii,ii] + 0.568881*KroneckerDelta[ii,ii], 10^-90]]},
|
---|
1255 | Description -> "Average momentum transfer in D to K decays"
|
---|
1256 | },
|
---|
1257 |
|
---|
1258 | tplusDK == {
|
---|
1259 | ParameterType -> Internal,
|
---|
1260 | Value -> (MDd+MK)^2,
|
---|
1261 | Description -> "t+ factor in the pole parametrization"
|
---|
1262 | },
|
---|
1263 |
|
---|
1264 | t0DK == {
|
---|
1265 | ParameterType -> Internal,
|
---|
1266 | Value -> (MDd+MK)*(Sqrt[MK]-Sqrt[MDd])^2,
|
---|
1267 | Description -> "t0 factor in the pole parametrization"
|
---|
1268 | },
|
---|
1269 |
|
---|
1270 | zDK == {
|
---|
1271 | ParameterType -> Internal,
|
---|
1272 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1273 | Value -> {zDK[ii_,ll_] -> (Sqrt[tplusDK-avq2DK[ii,ll]]-Sqrt[tplusDK-t0DK])/(Sqrt[tplusDK-avq2DK[ii,ll]]+Sqrt[tplusDK-t0DK])},
|
---|
1274 | Description -> "z factor in the pole parametrization"
|
---|
1275 | },
|
---|
1276 |
|
---|
1277 | z0DK == {
|
---|
1278 | ParameterType -> Internal,
|
---|
1279 | Value -> (Sqrt[tplusDK]-Sqrt[tplusDK-t0DK])/(Sqrt[tplusDK]+Sqrt[tplusDK-t0DK]),
|
---|
1280 | Description -> "z0 factor in the pole parametrization"
|
---|
1281 | },
|
---|
1282 |
|
---|
1283 | fplusDK == {
|
---|
1284 | ParameterType -> Internal,
|
---|
1285 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1286 | Value -> {fplusDK[ii_,ll_] -> (0.7647-0.066*(zDK[ii,ll]-z0DK)*(1+0.5*(zDK[ii,ll]+z0DK)))/(1-0.22*avq2DK[ii,ll])},
|
---|
1287 | Description -> "Average f+ form factor in D to K decays"
|
---|
1288 | },
|
---|
1289 |
|
---|
1290 | f0DK == {
|
---|
1291 | ParameterType -> Internal,
|
---|
1292 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1293 | Value -> {f0DK[ii_,ll_] -> (0.7647-2.084*(zDK[ii,ll]-z0DK)*(1+0.5*(zDK[ii,ll]+z0DK)))},
|
---|
1294 | Description -> "Average f0 form factor in D to K decays"
|
---|
1295 | },
|
---|
1296 |
|
---|
1297 | fminusDK == {
|
---|
1298 | ParameterType -> Internal,
|
---|
1299 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1300 | Value -> {fminusDK[ii_,ll_] -> (MK^2-MDd^2)/avq2DK[ii,ll]*(f0DK[ii,ll]-fplusDK[ii,ll])},
|
---|
1301 | Description -> "Average f- form factor in D to K decays"
|
---|
1302 | },
|
---|
1303 |
|
---|
1304 | (** Form factors for B+ to Pi0 decays: FLAG review **)
|
---|
1305 |
|
---|
1306 | avq2BPi0 == {
|
---|
1307 | ParameterType -> Internal,
|
---|
1308 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1309 | Value -> {avq2BPi0[ii_,ll_] ->
|
---|
1310 | If[ll==1, -0.0747182*numass[ii,ii]^3 + 0.757551*numass[ii,ii]^2 + 1.43992*numass[ii,ii] + 9.05607*KroneckerDelta[ii,ii],
|
---|
1311 | If[ll==2, -0.0692688*numass[ii,ii]^3 + 0.731411*numass[ii,ii]^2 + 1.47166*numass[ii,ii] + 9.08105*KroneckerDelta[ii,ii],
|
---|
1312 | If[ll==3, -0.163478*numass[ii,ii]^3 + 1.45186*numass[ii,ii]^2 + 0.790463*numass[ii,ii] + 13.5051*KroneckerDelta[ii,ii],10^-90]]]},
|
---|
1313 | Description -> "Average momentum transfer in B+ to Pi0 decays"
|
---|
1314 | },
|
---|
1315 |
|
---|
1316 | tplusBPi0 == {
|
---|
1317 | ParameterType -> Internal,
|
---|
1318 | Value -> (MBu + MPi0)^2,
|
---|
1319 | Description -> "t+ factor"
|
---|
1320 | },
|
---|
1321 |
|
---|
1322 | t0BPi0 == {
|
---|
1323 | ParameterType -> Internal,
|
---|
1324 | Value -> (MBu + MPi0)*(Sqrt[MPi0]-Sqrt[MBu])^2,
|
---|
1325 | Description -> "t0 factor"
|
---|
1326 | },
|
---|
1327 |
|
---|
1328 | zBPi0 == {
|
---|
1329 | ParameterType -> Internal,
|
---|
1330 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1331 | Value -> {zBPi0[ii_,ll_] -> (Sqrt[tplusBPi0-avq2BPi0[ii,ll]]-Sqrt[tplusBPi0-t0BPi0])/(Sqrt[tplusBPi0-avq2BPi0[ii,ll]]+Sqrt[tplusBPi0-t0BPi0])},
|
---|
1332 | Description -> "z factor"
|
---|
1333 | },
|
---|
1334 |
|
---|
1335 | z0BPi0 == {
|
---|
1336 | ParameterType -> Internal,
|
---|
1337 | Value -> (Sqrt[tplusBPi0]-Sqrt[tplusBPi0-t0BPi0])/(Sqrt[tplusBPi0]+Sqrt[tplusBPi0-t0BPi0]),
|
---|
1338 | Description -> "z0 factor"
|
---|
1339 | },
|
---|
1340 |
|
---|
1341 | fplusBPi0 == {
|
---|
1342 | ParameterType -> Internal,
|
---|
1343 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1344 | Value -> {fplusBPi0[ii_,ll_] -> (1/(1-avq2BPi0[ii,ll]/MBstar^2))*(-0.68*(zBPi0[ii,ll]-1/3(zBPi0[ii,ll]^3))-0.86*((zBPi0[ii,ll]^3)2/3 + zBPi0[ii,ll]^2) + 0.404)},
|
---|
1345 | Description -> "Average f+ form factor in B+ to Pi0 decays"
|
---|
1346 | },
|
---|
1347 |
|
---|
1348 | f0BPi0 == {
|
---|
1349 | ParameterType -> Internal,
|
---|
1350 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1351 | Value -> {f0BPi0[ii_,ll_] -> (1.2527548*zBPi0[ii,ll]^2 - 1.61*zBPi0[ii,ll] + 0.490)},
|
---|
1352 | Description -> "Average f0 form factor in B+ to Pi0 decays"
|
---|
1353 | },
|
---|
1354 |
|
---|
1355 | fminusBPi0 == {
|
---|
1356 | ParameterType -> Internal,
|
---|
1357 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1358 | Value -> {fminusBPi0[ii_,ll_] -> (MPi0^2-MBu^2)/avq2BPi0[ii,ll]*(f0BPi0[ii,ll]-fplusBPi0[ii,ll])},
|
---|
1359 | Description -> "Average f- form factor in B+ to Pi0 decays"
|
---|
1360 | },
|
---|
1361 |
|
---|
1362 | (** Form factors for B0 to Pi+ decays: FLAG review **)
|
---|
1363 |
|
---|
1364 | avq2B0Pi == {
|
---|
1365 | ParameterType -> Internal,
|
---|
1366 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1367 | Value -> {avq2B0Pi[ii_,ll_] ->
|
---|
1368 | If[ll==1, -0.0738527*numass[ii,ii]^3 + 0.750683*numass[ii,ii]^2 + 1.45882*numass[ii,ii] + 9.01069*KroneckerDelta[ii,ii],
|
---|
1369 | If[ll==2, -0.0695186*numass[ii,ii]^3 + 0.731836*numass[ii,ii]^2 + 1.47827*numass[ii,ii] + 9.0398*KroneckerDelta[ii,ii],
|
---|
1370 | If[ll==3, -0.164163*numass[ii,ii]^3 + 1.45367*numass[ii,ii]^2 + 0.794287*numass[ii,ii] + 13.4752*KroneckerDelta[ii,ii], 10^-90]]]},
|
---|
1371 | Description -> "Average momentum transfer in B0 to Pi+ decays"
|
---|
1372 | },
|
---|
1373 |
|
---|
1374 | tplusB0Pi == {
|
---|
1375 | ParameterType -> Internal,
|
---|
1376 | Value -> (MB0 + MPip)^2,
|
---|
1377 | Description -> "t+ factor"
|
---|
1378 | },
|
---|
1379 |
|
---|
1380 | t0B0Pi == {
|
---|
1381 | ParameterType -> Internal,
|
---|
1382 | Value -> (MB0 + MPip)*(Sqrt[MPip]-Sqrt[MB0])^2,
|
---|
1383 | Description -> "t0 factor"
|
---|
1384 | },
|
---|
1385 |
|
---|
1386 | zB0Pi == {
|
---|
1387 | ParameterType -> Internal,
|
---|
1388 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1389 | Value -> {zB0Pi[ii_,ll_] -> (Sqrt[tplusB0Pi-avq2B0Pi[ii,ll]]-Sqrt[tplusB0Pi-t0B0Pi])/(Sqrt[tplusB0Pi-avq2B0Pi[ii,ll]]+Sqrt[tplusB0Pi-t0B0Pi])},
|
---|
1390 | Description -> "z factor"
|
---|
1391 | },
|
---|
1392 |
|
---|
1393 | z0B0Pi == {
|
---|
1394 | ParameterType -> Internal,
|
---|
1395 | Value -> (Sqrt[tplusB0Pi]-Sqrt[tplusB0Pi-t0B0Pi])/(Sqrt[tplusB0Pi]+Sqrt[tplusB0Pi-t0B0Pi]),
|
---|
1396 | Description -> "z0 factor"
|
---|
1397 | },
|
---|
1398 |
|
---|
1399 | fplusB0Pi == {
|
---|
1400 | ParameterType -> Internal,
|
---|
1401 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1402 | Value -> {fplusB0Pi[ii_,ll_] -> (1/(1-avq2B0Pi[ii,ll]/MBstar^2))*(-0.68*(zB0Pi[ii,ll]-zB0Pi[ii,ll]^3/3)-0.86*((2 zB0Pi[ii,ll]^3)/3 + zB0Pi[ii,ll]^2) + 0.404)},
|
---|
1403 | Description -> "Average f+ form factor in B0 to Pi+ decays"
|
---|
1404 | },
|
---|
1405 |
|
---|
1406 | f0B0Pi == {
|
---|
1407 | ParameterType -> Internal,
|
---|
1408 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1409 | Value -> {f0B0Pi[ii_,ll_] -> (1.268691923*zB0Pi[ii,ll]^2 - 1.61*zB0Pi[ii,ll] + 0.490)},
|
---|
1410 | Description -> "Average f0 form factor in B0 to Pi+ decays"
|
---|
1411 | },
|
---|
1412 |
|
---|
1413 | fminusB0Pi == {
|
---|
1414 | ParameterType -> Internal,
|
---|
1415 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1416 | Value -> {fminusB0Pi[ii_,ll_] -> (MPip^2-MB0^2)/avq2B0Pi[ii,ll]*(f0B0Pi[ii,ll]-fplusB0Pi[ii,ll])},
|
---|
1417 | Description -> "Average f- form factor in B0 to Pi+ decays"
|
---|
1418 | },
|
---|
1419 |
|
---|
1420 | (** Form factors for B+ to D0 decays: FLAG review **)
|
---|
1421 |
|
---|
1422 | avq2BD0 == {
|
---|
1423 | ParameterType -> Internal,
|
---|
1424 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1425 | Value -> {avq2BD0[ii_,ll_] ->
|
---|
1426 | If[ll==1, -0.0756751*numass[ii,ii]^3 + 0.619874*numass[ii,ii]^2 + 1.06348*numass[ii,ii] + 3.82403*KroneckerDelta[ii,ii],
|
---|
1427 | If[ll==2, -0.0614*numass[ii,ii]^3 + 0.580972*numass[ii,ii]^2 + 1.08624*numass[ii,ii] + 3.85694*KroneckerDelta[ii,ii],
|
---|
1428 | If[ll==3, -0.49004*numass[ii,ii]^3 + 2.19813*numass[ii,ii]^2 + 0.420447*numass[ii,ii] + 7.22909*KroneckerDelta[ii,ii],10^-90]]]},
|
---|
1429 | Description -> "Average momentum transfer in B+ to D0 decays"
|
---|
1430 | },
|
---|
1431 |
|
---|
1432 | tplusBD0 == {
|
---|
1433 | ParameterType -> Internal,
|
---|
1434 | Value -> (MBu + MD0)^2,
|
---|
1435 | Description -> "t+ factor"
|
---|
1436 | },
|
---|
1437 |
|
---|
1438 | t0BD0 == {
|
---|
1439 | ParameterType -> Internal,
|
---|
1440 | Value -> (MBu + MD0)*(Sqrt[MD0]-Sqrt[MBu])^2,
|
---|
1441 | Description -> "t0 factor"
|
---|
1442 | },
|
---|
1443 |
|
---|
1444 | zBD0 == {
|
---|
1445 | ParameterType -> Internal,
|
---|
1446 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1447 | Value -> {zBD0[ii_,ll_] -> (Sqrt[tplusBD0-avq2BD0[ii,ll]]-Sqrt[tplusBD0-t0BD0])/(Sqrt[tplusBD0-avq2BD0[ii,ll]]+Sqrt[tplusBD0-t0BD0])},
|
---|
1448 | Description -> "z factor"
|
---|
1449 | },
|
---|
1450 |
|
---|
1451 | z0BD0 == {
|
---|
1452 | ParameterType -> Internal,
|
---|
1453 | Value -> (Sqrt[tplusBD0]-Sqrt[tplusBD0-t0BD0])/(Sqrt[tplusBD0]+Sqrt[tplusBD0-t0BD0]),
|
---|
1454 | Description -> "z0 factor"
|
---|
1455 | },
|
---|
1456 |
|
---|
1457 | fplusBD0 == {
|
---|
1458 | ParameterType -> Internal,
|
---|
1459 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1460 | Value -> {fplusBD0[ii_,ll_] -> (1/(1-avq2BD0[ii,ll]/MBstar^2))*(-7.11*(zBD0[ii,ll]-1/3(zBD0[ii,ll]^3)) + 66*((zBD0[ii,ll]^3)2/3 + zBD0[ii,ll]^2) + 0.909)},
|
---|
1461 | Description -> "Average f+ form factor in B+ to D0 decays"
|
---|
1462 | },
|
---|
1463 |
|
---|
1464 | f0BD0 == {
|
---|
1465 | ParameterType -> Internal,
|
---|
1466 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1467 | Value -> {f0BD0[ii_,ll_] -> (33.2166*zBD0[ii,ll]^2 - 2.45*zBD0[ii,ll] + 0.794)},
|
---|
1468 | Description -> "Average f0 form factor in B+ to D0 decays"
|
---|
1469 | },
|
---|
1470 |
|
---|
1471 | fminusBD0 == {
|
---|
1472 | ParameterType -> Internal,
|
---|
1473 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1474 | Value -> {fminusBD0[ii_,ll_] -> (MD0^2-MBu^2)/avq2BD0[ii,ll]*(f0BD0[ii,ll]-fplusBD0[ii,ll])},
|
---|
1475 | Description -> "Average f- form factor in B+ to D0 decays"
|
---|
1476 | },
|
---|
1477 |
|
---|
1478 | (** Form factors for B0 to D+ decays: FLAG review **)
|
---|
1479 |
|
---|
1480 | avq2B0D == {
|
---|
1481 | ParameterType -> Internal,
|
---|
1482 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1483 | Value -> {avq2B0D[ii_,ll_] ->
|
---|
1484 | If[ll==1, -0.0759024*numass[ii,ii]^3 + 0.620479*numass[ii,ii]^2 + 1.06255*numass[ii,ii] + 3.81359*KroneckerDelta[ii,ii],
|
---|
1485 | If[ll==2, -0.0616034*numass[ii,ii]^3 + 0.58158*numass[ii,ii]^2 + 1.08525*numass[ii,ii] + 3.84654*KroneckerDelta[ii,ii],
|
---|
1486 | If[ll==3, -0.492883*numass[ii,ii]^3 + 2.20311*numass[ii,ii]^2 + 0.419677*numass[ii,ii] + 7.2176*KroneckerDelta[ii,ii],10^-90]]]},
|
---|
1487 | Description -> "Average momentum transfer in B0 to D+ decays"
|
---|
1488 | },
|
---|
1489 |
|
---|
1490 | tplusB0D == {
|
---|
1491 | ParameterType -> Internal,
|
---|
1492 | Value -> (MB0 + MDd)^2,
|
---|
1493 | Description -> "t+ factor"
|
---|
1494 | },
|
---|
1495 |
|
---|
1496 | t0B0D == {
|
---|
1497 | ParameterType -> Internal,
|
---|
1498 | Value -> (MB0 + MDd)*(Sqrt[MDd]-Sqrt[MB0])^2,
|
---|
1499 | Description -> "t0 factor"
|
---|
1500 | },
|
---|
1501 |
|
---|
1502 | zB0D == {
|
---|
1503 | ParameterType -> Internal,
|
---|
1504 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1505 | Value -> {zB0D[ii_,ll_] -> (Sqrt[tplusB0D-avq2B0D[ii,ll]]-Sqrt[tplusB0D-t0B0D])/(Sqrt[tplusB0D-avq2B0D[ii,ll]]+Sqrt[tplusB0D-t0B0D])},
|
---|
1506 | Description -> "z factor"
|
---|
1507 | },
|
---|
1508 |
|
---|
1509 | z0B0D == {
|
---|
1510 | ParameterType -> Internal,
|
---|
1511 | Value -> (Sqrt[tplusB0D]-Sqrt[tplusB0D-t0B0D])/(Sqrt[tplusB0D]+Sqrt[tplusB0D-t0B0D]),
|
---|
1512 | Description -> "z0 factor"
|
---|
1513 | },
|
---|
1514 |
|
---|
1515 | fplusB0D == {
|
---|
1516 | ParameterType -> Internal,
|
---|
1517 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1518 | Value -> {fplusB0D[ii_,ll_] -> (1/(1-avq2B0D[ii,ll]/MBstar^2))*(-7.11*(zB0D[ii,ll]-1/3(zB0D[ii,ll]^3)) + 66*((zB0D[ii,ll]^3)2/3 + zB0D[ii,ll]^2) + 0.909)},
|
---|
1519 | Description -> "Average f+ form factor in B0 to D+ decays"
|
---|
1520 | },
|
---|
1521 |
|
---|
1522 | f0B0D == {
|
---|
1523 | ParameterType -> Internal,
|
---|
1524 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1525 | Value -> {f0B0D[ii_,ll_] -> (33.5115*zB0D[ii,ll]^2 - 2.45*zB0D[ii,ll] + 0.794)},
|
---|
1526 | Description -> "Average f0 form factor in B0 to D+ decays"
|
---|
1527 | },
|
---|
1528 |
|
---|
1529 | fminusB0D == {
|
---|
1530 | ParameterType -> Internal,
|
---|
1531 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1532 | Value -> {fminusB0D[ii_,ll_] -> (MDd^2-MB0^2)/avq2B0D[ii,ll]*(f0B0D[ii,ll]-fplusB0D[ii,ll])},
|
---|
1533 | Description -> "Average f- form factor in B0 to D+ decays"
|
---|
1534 | },
|
---|
1535 |
|
---|
1536 | (** Form factors for B0s to Ds+ decays: FLAG review **)
|
---|
1537 |
|
---|
1538 | avq2B0sDs == {
|
---|
1539 | ParameterType -> Internal,
|
---|
1540 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1541 | Value -> {avq2B0sDs[ii_,ll_] ->
|
---|
1542 | If[ll==1, -0.0767788*numass[ii,ii]^3 + 0.621995*numass[ii,ii]^2 + 1.06724*numass[ii,ii] + 3.76534*KroneckerDelta[ii,ii],
|
---|
1543 | If[ll==2, -0.0624231*numass[ii,ii]^3 + 0.583268*numass[ii,ii]^2 + 1.08928*numass[ii,ii] + 3.79888*KroneckerDelta[ii,ii],
|
---|
1544 | If[ll==3, -0.505219*numass[ii,ii]^3 + 2.2248*numass[ii,ii]^2 + 0.418473*numass[ii,ii] + 7.17705*KroneckerDelta[ii,ii],10^-90]]]},
|
---|
1545 | Description -> "Average momentum transfer in B0s to Ds+ decays"
|
---|
1546 | },
|
---|
1547 |
|
---|
1548 | tplusB0sDs == {
|
---|
1549 | ParameterType -> Internal,
|
---|
1550 | Value -> (MB0s + MDs)^2,
|
---|
1551 | Description -> "t+ factor"
|
---|
1552 | },
|
---|
1553 |
|
---|
1554 | t0B0sDs == {
|
---|
1555 | ParameterType -> Internal,
|
---|
1556 | Value -> (MB0s + MDs)*(Sqrt[MDs]-Sqrt[MB0s])^2,
|
---|
1557 | Description -> "t0 factor"
|
---|
1558 | },
|
---|
1559 |
|
---|
1560 | zB0sDs == {
|
---|
1561 | ParameterType -> Internal,
|
---|
1562 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1563 | Value -> {zB0sDs[ii_,ll_] -> (Sqrt[tplusB0sDs-avq2B0sDs[ii,ll]]-Sqrt[tplusB0sDs-t0B0sDs])/(Sqrt[tplusB0sDs-avq2B0sDs[ii,ll]]+Sqrt[tplusB0sDs-t0B0sDs])},
|
---|
1564 | Description -> "z factor"
|
---|
1565 | },
|
---|
1566 |
|
---|
1567 | z0B0sDs == {
|
---|
1568 | ParameterType -> Internal,
|
---|
1569 | Value -> (Sqrt[tplusB0sDs]-Sqrt[tplusB0sDs-t0B0sDs])/(Sqrt[tplusB0sDs]+Sqrt[tplusB0sDs-t0B0sDs]),
|
---|
1570 | Description -> "z0 factor"
|
---|
1571 | },
|
---|
1572 |
|
---|
1573 | fplusB0sDs == {
|
---|
1574 | ParameterType -> Internal,
|
---|
1575 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1576 | Value -> {fplusB0sDs[ii_,ll_] -> (1/(1-avq2B0sDs[ii,ll]/MBstar^2))*(-7.11*(zB0sDs[ii,ll]-1/3(zB0sDs[ii,ll]^3)) + 66*((zB0sDs[ii,ll]^3)2/3 + zB0sDs[ii,ll]^2) + 0.909)},
|
---|
1577 | Description -> "Average f+ form factor in B0s to Ds+ decays"
|
---|
1578 | },
|
---|
1579 |
|
---|
1580 | f0B0sDs == {
|
---|
1581 | ParameterType -> Internal,
|
---|
1582 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1583 | Value -> {f0B0sDs[ii_,ll_] -> (39.1988*zB0sDs[ii,ll]^2 - 2.45*zB0sDs[ii,ll] + 0.794)},
|
---|
1584 | Description -> "Average f0 form factor in B0s to Ds+ decays"
|
---|
1585 | },
|
---|
1586 |
|
---|
1587 | fminusB0sDs == {
|
---|
1588 | ParameterType -> Internal,
|
---|
1589 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1590 | Value -> {fminusB0sDs[ii_,ll_] -> (MDs^2-MB0s^2)/avq2B0sDs[ii,ll]*(f0B0sDs[ii,ll]-fplusB0sDs[ii,ll])},
|
---|
1591 | Description -> "Average f- form factor in B0s to Ds+ decays"
|
---|
1592 | },
|
---|
1593 |
|
---|
1594 | (** Form factors for B0s to K+ decays: FLAG review **)
|
---|
1595 |
|
---|
1596 | avq2B0sK == {
|
---|
1597 | ParameterType -> Internal,
|
---|
1598 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1599 | Value -> {avq2B0sK[ii_,ll_] ->
|
---|
1600 | If[ll==1, -0.0305836*numass[ii,ii]^3 + 0.431928*numass[ii,ii]^2 + 1.84666*numass[ii,ii] + 7.82438*KroneckerDelta[ii,ii],
|
---|
1601 | If[ll==2, -0.0223321*numass[ii,ii]^3 + 0.3961*numass[ii,ii]^2 + 1.87998*numass[ii,ii] + 7.86105*KroneckerDelta[ii,ii],
|
---|
1602 | If[ll==3, -0.111798*numass[ii,ii]^3 + 1.23898*numass[ii,ii]^2 + 0.905063*numass[ii,ii] + 12.2134*KroneckerDelta[ii,ii],10^-90]]]},
|
---|
1603 | Description -> "Average momentum transfer in B0s to K+ decays"
|
---|
1604 | },
|
---|
1605 |
|
---|
1606 | tplusB0sK == {
|
---|
1607 | ParameterType -> Internal,
|
---|
1608 | Value -> (MB0s + MK)^2,
|
---|
1609 | Description -> "t+ factor"
|
---|
1610 | },
|
---|
1611 |
|
---|
1612 | t0B0sK == {
|
---|
1613 | ParameterType -> Internal,
|
---|
1614 | Value -> (MB0s + MK)*(Sqrt[MK]-Sqrt[MB0s])^2,
|
---|
1615 | Description -> "t0 factor"
|
---|
1616 | },
|
---|
1617 |
|
---|
1618 | zB0sK == {
|
---|
1619 | ParameterType -> Internal,
|
---|
1620 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1621 | Value -> {zB0sK[ii_,ll_] -> (Sqrt[tplusB0sK-avq2B0sK[ii,ll]]-Sqrt[tplusB0sK-t0B0sK])/(Sqrt[tplusB0sK-avq2B0sK[ii,ll]]+Sqrt[tplusB0sK-t0B0sK])},
|
---|
1622 | Description -> "z factor"
|
---|
1623 | },
|
---|
1624 |
|
---|
1625 | z0B0sK == {
|
---|
1626 | ParameterType -> Internal,
|
---|
1627 | Value -> (Sqrt[tplusB0sK]-Sqrt[tplusB0sK-t0B0sK])/(Sqrt[tplusB0sK]+Sqrt[tplusB0sK-t0B0sK]),
|
---|
1628 | Description -> "z0 factor"
|
---|
1629 | },
|
---|
1630 |
|
---|
1631 | fplusB0sK == {
|
---|
1632 | ParameterType -> Internal,
|
---|
1633 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1634 | Value -> {fplusB0sK[ii_,ll_] -> (1/(1-avq2B0sK[ii,ll]/MBstar^2))*(-0.672*(zB0sK[ii,ll]+1/4*zB0sK[ii,ll]^4) + 0.07*(zB0sK[ii,ll]^2 - 1/2*zB0sK[ii,ll]^4) + 1.34*(3/4*zB0sK[ii,ll]^4 + zB0sK[ii,ll]^3) + 0.374)},
|
---|
1635 | Description -> "Average f+ form factor in B0s to K+ decays"
|
---|
1636 | },
|
---|
1637 |
|
---|
1638 | f0B0sK == {
|
---|
1639 | ParameterType -> Internal,
|
---|
1640 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1641 | Value -> {f0B0sK[ii_,ll_] -> (14.0162*zB0sK[ii,ll]^3 + 0.24*zB0sK[ii,ll]^2 + 0.089*zB0sK[ii,ll] + 0.2203)},
|
---|
1642 | Description -> "Average f0 form factor in B0s to K+ decays"
|
---|
1643 | },
|
---|
1644 |
|
---|
1645 | fminusB0sK == {
|
---|
1646 | ParameterType -> Internal,
|
---|
1647 | Indices -> {Index[Neutrinos], Index[Generation]},
|
---|
1648 | Value -> {fminusB0sK[ii_,ll_] -> (MK^2-MB0s^2)/avq2B0sK[ii,ll]*(f0B0sK[ii,ll]-fplusB0sK[ii,ll])},
|
---|
1649 | Description -> "Average f- form factor in B0s to K+ decays"
|
---|
1650 | },
|
---|
1651 |
|
---|
1652 | yl == {
|
---|
1653 | ParameterType -> Internal,
|
---|
1654 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1655 | Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1656 | Value -> {yl[1,1] -> Sqrt[2] yme /vev, yl[2,2] -> Sqrt[2] ymm /vev, yl[3,3] -> Sqrt[2] ymtau /vev},
|
---|
1657 | InteractionOrder -> {QED, 1},
|
---|
1658 | ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
|
---|
1659 | TeX -> Superscript[y, l],
|
---|
1660 | Description -> "Lepton Yukawa couplings"
|
---|
1661 | },
|
---|
1662 | yu == {
|
---|
1663 | ParameterType -> Internal,
|
---|
1664 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1665 | Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1666 | Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
|
---|
1667 | InteractionOrder -> {QED, 1},
|
---|
1668 | ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
|
---|
1669 | TeX -> Superscript[y, u],
|
---|
1670 | Description -> "Up-type Yukawa couplings"
|
---|
1671 | },
|
---|
1672 | yd == {
|
---|
1673 | ParameterType -> Internal,
|
---|
1674 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1675 | Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1676 | Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
|
---|
1677 | InteractionOrder -> {QED, 1},
|
---|
1678 | ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
|
---|
1679 | TeX -> Superscript[y, d],
|
---|
1680 | Description -> "Down-type Yukawa couplings"
|
---|
1681 | },
|
---|
1682 |
|
---|
1683 | CKM == {
|
---|
1684 | ParameterType -> Internal,
|
---|
1685 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1686 | Unitary -> True,
|
---|
1687 | Value -> {CKM[1,1] -> Cos[cabi] Cos[th13], CKM[1,2] -> Sin[cabi] Cos[th13], CKM[1,3] -> Sin[th13] Exp[-I del13],
|
---|
1688 | CKM[2,1] -> -Sin[cabi] Cos[th23] - Cos[cabi] Sin[th23] Sin[th13] Exp[I del13], CKM[2,2] -> Cos[cabi] Cos[th23] - Sin[cabi] Sin[th23] Sin[th13] Exp[I del13], CKM[2,3] -> Sin[th23] Cos[th13],
|
---|
1689 | CKM[3,1] -> Sin[cabi] Sin[th23] - Cos[cabi] Cos[th23] Sin[th13] Exp[I del13], CKM[3,2] -> -Cos[cabi] Sin[th23] - Sin[cabi] Cos[th23] Sin[th13] Exp[I del13], CKM[3,3] -> Cos[th23] Cos[th13]},
|
---|
1690 | TeX -> Superscript[V,CKM],
|
---|
1691 | Description -> "CKM-Matrix"},
|
---|
1692 |
|
---|
1693 | HEAV == {
|
---|
1694 | ParameterType -> Internal,
|
---|
1695 | Indices -> {Index[Heavynus],Index[Neutrinos]},
|
---|
1696 | Value -> {HEAV[1,1] -> -Conjugate[thetae]/r,
|
---|
1697 | HEAV[1,2] -> -Conjugate[thetamu]/r,
|
---|
1698 | HEAV[1,3] -> -Conjugate[thetatau]/r,
|
---|
1699 | HEAV[1,4] -> 1/r},
|
---|
1700 | TeX -> Superscript[UL,n],
|
---|
1701 | ComplexParameter -> True,
|
---|
1702 | Description -> "Mass eigenstate component of right-handed nu"},
|
---|
1703 |
|
---|
1704 | HEAVR == {
|
---|
1705 | ParameterType -> Internal,
|
---|
1706 | Indices -> {Index[Heavynus],Index[Neutrinos]},
|
---|
1707 | Value -> {HEAVR[1,1] -> 0,
|
---|
1708 | HEAVR[1,2] -> 0,
|
---|
1709 | HEAVR[1,3] -> 0,
|
---|
1710 | HEAVR[1,4] -> 1},
|
---|
1711 | TeX -> Superscript[UR,n],
|
---|
1712 | ComplexParameter -> True,
|
---|
1713 | Description -> "Mass eigenstate component of right-handed nu"},
|
---|
1714 |
|
---|
1715 |
|
---|
1716 | PMNS == {
|
---|
1717 | ParameterType -> Internal,
|
---|
1718 | Indices -> {Index[Generation], Index[Neutrinos]},
|
---|
1719 | Unitary -> False,
|
---|
1720 | Value -> {PMNS[1,1] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 1, 1-thetae*Conjugate[thetae]*(r-1)/r/thetatot^2],
|
---|
1721 | PMNS[1,2] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -thetae*Conjugate[thetamu]*(r-1)/r/thetatot^2],
|
---|
1722 | PMNS[1,3] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -thetae*Conjugate[thetatau]*(r-1)/r/thetatot^2],
|
---|
1723 | PMNS[1,4] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, thetae/r],
|
---|
1724 | PMNS[2,1] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -Conjugate[thetae]*thetamu*(r-1)/r/thetatot^2],
|
---|
1725 | PMNS[2,2] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 1, 1-thetamu*Conjugate[thetamu]*(r-1)/r/thetatot^2],
|
---|
1726 | PMNS[2,3] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -thetamu*Conjugate[thetatau]*(r-1)/r/thetatot^2],
|
---|
1727 | PMNS[2,4] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, thetamu/r],
|
---|
1728 | PMNS[3,1] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -Conjugate[thetae]*thetatau*(r-1)/r/thetatot^2],
|
---|
1729 | PMNS[3,2] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -Conjugate[thetamu]*thetatau*(r-1)/r/thetatot^2],
|
---|
1730 | PMNS[3,3] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 1, 1-thetatau*Conjugate[thetatau]*(r-1)/r/thetatot^2],
|
---|
1731 | PMNS[3,4] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, thetatau/r]},
|
---|
1732 | TeX -> Superscript[U,PMNS],
|
---|
1733 | TeX -> Superscript[U,PMNS],
|
---|
1734 | ComplexParameter -> True,
|
---|
1735 | Description -> "PMNS-Matrix"}
|
---|
1736 | };
|
---|
1737 |
|
---|
1738 |
|
---|
1739 |
|
---|
1740 | (* ************************** *)
|
---|
1741 | (* ***** Lagrangian ***** *)
|
---|
1742 | (* For consistency we do not *)
|
---|
1743 | (* add quarks with mesons *)
|
---|
1744 | (* ************************** *)
|
---|
1745 |
|
---|
1746 | LGauge := Block[{mu,nu,ii,aa},
|
---|
1747 | ExpandIndices[-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], FlavorExpand->SU2W]];
|
---|
1748 |
|
---|
1749 | LQuarks := Block[{mu},
|
---|
1750 | ExpandIndices[I*(
|
---|
1751 | QLbar.Ga[mu].DC[QL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu]),
|
---|
1752 | FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c], PMNS[b_,a_] Conjugate[PMNS[c_,a_]]->IndexDelta[b,c], HEAV[b_,a_] Conjugate[HEAV[c_,a_]]->IndexDelta[b,c], PMNS[a_,b_] Conjugate[PMNS[a_,c_]] ->IndexDelta[b,c] - HEAV[1,b] Conjugate[HEAV[1,c]]}];
|
---|
1753 |
|
---|
1754 | LFermions := Block[{mu},
|
---|
1755 | ExpandIndices[I*(
|
---|
1756 | LLbar.Ga[mu].DC[LL, mu] + lRbar.Ga[mu].DC[lR, mu] + NLbar.Ga[mu].DC[NL, mu] + NRbar.Ga[mu].DC[NR, mu] ),
|
---|
1757 | FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c], PMNS[b_,a_] Conjugate[PMNS[c_,a_]]->IndexDelta[b,c], HEAV[b_,a_] Conjugate[HEAV[c_,a_]]->IndexDelta[b,c], PMNS[a_,b_] Conjugate[PMNS[a_,c_]] ->IndexDelta[b,c] - HEAV[1,b] Conjugate[HEAV[1,c]]}];
|
---|
1758 |
|
---|
1759 | LHiggs := Block[{ii,mu, feynmangaugerules},
|
---|
1760 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
1761 | ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
|
---|
1762 | ];
|
---|
1763 |
|
---|
1764 | LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
|
---|
1765 | feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
|
---|
1766 |
|
---|
1767 | yuk = ExpandIndices[
|
---|
1768 | -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
|
---|
1769 | yl[ff1, ff3] LLbar[sp, ii, ff1].lR[sp, ff3] Phi[ii] -
|
---|
1770 | yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj] - yN[ff1, ff2] LLbar[sp, ii, ff1].NR[sp, ff2] Phibar[jj] Eps[ii, jj] - MN4 NLbar[sp,ff1].NR[sp,ff1] , FlavorExpand -> SU2D];
|
---|
1771 | yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c], PMNS[b_,a_] Conjugate[PMNS[c_,a_]]->IndexDelta[b,c], HEAV[b_,a_] Conjugate[HEAV[c_,a_]]->IndexDelta[b,c], PMNS[a_,b_] Conjugate[PMNS[a_,c_]] ->IndexDelta[b,c] - HEAV[1,b] Conjugate[HEAV[1,c]]};
|
---|
1772 | yuk+HC[yuk]/.feynmangaugerules
|
---|
1773 | ];
|
---|
1774 |
|
---|
1775 | LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
|
---|
1776 | (* Pure gauge piece *)
|
---|
1777 | LGh1 = -ghBbar.del[DC[ghB,mu],mu];
|
---|
1778 | LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
|
---|
1779 | LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
|
---|
1780 |
|
---|
1781 | (***********************************)
|
---|
1782 | (*** Meson interactions ***)
|
---|
1783 | (***********************************)
|
---|
1784 |
|
---|
1785 | (*LHadr := Block[{mu,nu,ii,jj,kk,ff1,ff2,ff3,ff4,ff5,yhad},*)
|
---|
1786 | LHadr := Block[{mu,nu,ii,jj,kk,ff1,ff2,ff3,yhad},
|
---|
1787 | yhad = ExpandIndices[
|
---|
1788 |
|
---|
1789 | (*** Charged pseudoscalars ***)
|
---|
1790 |
|
---|
1791 | (*K*)
|
---|
1792 |
|
---|
1793 | 1/2 DC[Kbar,mu] DC[K,mu] - MK^2/2 Kbar K
|
---|
1794 | + Sum[I*Sqrt[2]*Gf*fK*CKM[1,2] Kbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1],{ff1,1,4},{ff2,1,3}]
|
---|
1795 | - Sum[I*Sqrt[2]*Gf*fK*CKM[1,2] Kbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1],{ff1,4,4},{ff2,1,3}]
|
---|
1796 |
|
---|
1797 | (* Pi *)
|
---|
1798 |
|
---|
1799 | + 1/2 DC[Pipbar,mu] DC[Pip,mu] - MPip^2/2 Pipbar Pip
|
---|
1800 | + Sum[I*Sqrt[2]*Gf*fpi*CKM[1,1] Pipbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1801 | - Sum[I*Sqrt[2]*Gf*fpi*CKM[1,1] Pipbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1802 |
|
---|
1803 | (*D*)
|
---|
1804 |
|
---|
1805 | + 1/2 DC[Ddbar,mu] DC[Dd,mu] - MDd^2/2 Ddbar Dd
|
---|
1806 | + Sum[I*Sqrt[2]*Gf*fD*CKM[2,1] Ddbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1807 | - Sum[I*Sqrt[2]*Gf*fD*CKM[2,1] Ddbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1808 |
|
---|
1809 | (*Ds*)
|
---|
1810 |
|
---|
1811 | + 1/2 DC[Dsbar,mu] DC[Ds,mu] - MDs^2/2 Dsbar Ds
|
---|
1812 | + Sum[I*Sqrt[2]*Gf*fDs*CKM[2,2] Dsbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1813 | - Sum[I*Sqrt[2]*Gf*fDs*CKM[2,2] Dsbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1814 |
|
---|
1815 | (*B*)
|
---|
1816 |
|
---|
1817 | + 1/2 DC[Bubar,mu] DC[Bu,mu] - MBu^2/2 Bubar Bu
|
---|
1818 | + Sum[I*Sqrt[2]*Gf*fB*CKM[1,3] Bubar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1819 | - Sum[I*Sqrt[2]*Gf*fB*CKM[1,3] Bubar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1820 |
|
---|
1821 | (*Bc*)
|
---|
1822 |
|
---|
1823 | + 1/2 DC[Bcbar,mu] DC[Bc,mu] - MBc^2/2 Bcbar Bc
|
---|
1824 | + Sum[I*Sqrt[2]*Gf*fBc*CKM[2,3] Bcbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1825 | - Sum[I*Sqrt[2]*Gf*fBc*CKM[2,3] Bcbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1826 |
|
---|
1827 | (*** Neutral pseudoscalars ***)
|
---|
1828 |
|
---|
1829 | (* pi0 *)
|
---|
1830 |
|
---|
1831 | - Sum[I/2*Gf*fpi Pi0 Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff2,ff2] vlbar[ii, ff1].ProjP[ii,jj].vl[jj, ff2] ,{ff1,1,4},{ff2,4,4},{ff3,1,3}]
|
---|
1832 | + 1/4 DC[Pi0,mu] DC[Pi0,mu] - MPi0^2/4 Pi0 Pi0
|
---|
1833 | + Sum[I/2*Gf*fpi Pi0 Conjugate[PMNS[ff3,ff1]] PMNS[ff3,ff2] numass[ff1,ff1] vlbar[ii, ff1].ProjM[ii,jj].vl[jj, ff2] ,{ff1,4,4},{ff2,1,4},{ff3,1,3}]
|
---|
1834 |
|
---|
1835 | (* eta *)
|
---|
1836 |
|
---|
1837 | + 1/4 DC[Etabar,mu] DC[Eta,mu] - Meta^2/4 Eta Eta
|
---|
1838 | - Sum[I/2*Gf*feta Eta Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff2,ff2] vlbar[ii, ff1].ProjP[ii,jj].vl[jj, ff2] ,{ff1,1,4},{ff2,4,4},{ff3,1,3}]
|
---|
1839 | + Sum[I/2*Gf*feta Eta Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff1,ff1] vlbar[ii, ff1].ProjM[ii,jj].vl[jj, ff2] ,{ff1,4,4},{ff2,1,4},{ff3,1,3}]
|
---|
1840 |
|
---|
1841 | (* eta^' *)
|
---|
1842 |
|
---|
1843 | + 1/4 DC[Etapbar,mu] DC[Etap,mu] - Metap^2/4 Etap Etap
|
---|
1844 | - Sum[I/2*Gf*fetap Etap Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff2,ff2] vlbar[ii, ff1].ProjP[ii,jj].vl[jj, ff2] ,{ff1,1,4},{ff2,4,4},{ff3,1,3}]
|
---|
1845 | + Sum[I/2*Gf*fetap Etap Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff1,ff1] vlbar[ii, ff1].ProjM[ii,jj].vl[jj, ff2] ,{ff1,4,4},{ff2,1,4},{ff3,1,3}]
|
---|
1846 |
|
---|
1847 | (*** Neutral vector mesons ***)
|
---|
1848 |
|
---|
1849 | (* rho0 *)
|
---|
1850 |
|
---|
1851 | -1/8 FS[rho0,mu,nu] FS[rho0,mu,nu] + Mrho0^2/4 rho0[mu] rho0[mu]
|
---|
1852 | - Sum[1/2*Gf*frho*(1-2*sw^2) rho0[mu] Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] vlbar[ii, ff1].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk, ff2] ,{ff1,1,4},{ff2,1,4},{ff3,1,3}]
|
---|
1853 |
|
---|
1854 | (* omega *)
|
---|
1855 |
|
---|
1856 | -1/8 FS[omega,mu,nu] FS[omega,mu,nu] + Mom^2/4 omega[mu] omega[mu]
|
---|
1857 | + Sum[1/2*Gf*fomega*(2/3*sw^2) omega[mu] Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] vlbar[ii,ff1].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff2] ,{ff1,1,4},{ff2,1,4},{ff3,1,3}]
|
---|
1858 |
|
---|
1859 | (* phi *)
|
---|
1860 |
|
---|
1861 | -1/8 FS[phimeson,mu,nu] FS[phimeson,mu,nu] + Mphi^2/4 phimeson[mu] phimeson[mu]
|
---|
1862 | + Sum[1/2*Sqrt[2]*Gf*fphi*(1/2 - 2/3*sw^2) phimeson[mu] Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] vlbar[ii,ff1].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff2] ,{ff1,1,4},{ff2,1,4},{ff3,1,3}]
|
---|
1863 |
|
---|
1864 | (*** Charged vector mesons ***)
|
---|
1865 |
|
---|
1866 | (* Rho *)
|
---|
1867 |
|
---|
1868 | -1/4 FS[rhobar,mu,nu] FS[rho,mu,nu] + Mrho^2/2 rhobar[mu] rho[mu]
|
---|
1869 | - Sum[Sqrt[2]*Gf*frho*CKM[1,1] PMNS[ff2,ff1] lbar[ii, ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] rhobar[mu] ,{ff1,1,4},{ff2,1,3}]
|
---|
1870 |
|
---|
1871 | (* Kstar *)
|
---|
1872 |
|
---|
1873 | -1/4 FS[Kstarbar,mu,nu] FS[Kstar,mu,nu] + MKstar^2/2 Kstarbar[mu] Kstar[mu]
|
---|
1874 | - Sum[Sqrt[2]*Gf*fKstar*CKM[1,2] PMNS[ff2,ff1] lbar[ii, ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] Kstarbar[mu] ,{ff1,1,4},{ff2,1,3}]
|
---|
1875 |
|
---|
1876 | (*** Semileptonic decays: ***)
|
---|
1877 |
|
---|
1878 | (* K -> pi0 l nu and K0 -> pip l nu *)
|
---|
1879 |
|
---|
1880 | + 1/2 DC[K0bar,mu] DC[K0,mu] - MK0^2/2 K0bar K0
|
---|
1881 |
|
---|
1882 | -Sum[2*Sqrt[2]*Gf*CKM[1,2]*fplusK0Pi[ff1,ff2]*I del[Pipbar,mu] K0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1883 | +Sum[Sqrt[2]*Gf*CKM[1,2]*(fplusK0Pi[ff1,ff2] - fminusK0Pi[ff1,ff2])*vev/Sqrt[2] Pipbar K0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1884 | -Sum[Sqrt[2]*Gf*CKM[1,2]*(fplusK0Pi[ff1,ff2] - fminusK0Pi[ff1,ff2]) Pipbar K0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,4,4},{ff2,1,2}]
|
---|
1885 |
|
---|
1886 | -Sum[2*Gf*CKM[1,2]*fplusKPi0[ff1,ff2]*I del[Pi0,mu] Kbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1887 | +Sum[Gf*CKM[1,2]*(fplusKPi0[ff1,ff2] - fminusKPi0[ff1,ff2])*vev/Sqrt[2] Pi0 Kbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1888 | -Sum[Gf*CKM[1,2]*(fplusKPi0[ff1,ff2] - fminusKPi0[ff1,ff2]) Pi0 Kbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1],{ff1,4,4},{ff2,1,2}]
|
---|
1889 |
|
---|
1890 | (* D -> K0 l nu and D0 -> K l nu *)
|
---|
1891 |
|
---|
1892 | + 1/2 DC[D0bar,mu] DC[D0,mu] - MD0^2/2 D0bar D0
|
---|
1893 |
|
---|
1894 | -Sum[2*Sqrt[2]*Gf*CKM[2,2]*fplusDK[ff1,ff2]*I del[Kbar,mu] D0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1895 | +Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2] - fminusDK[ff1,ff2])*vev/Sqrt[2] Kbar D0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1896 | -Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2] - fminusDK[ff1,ff2]) Kbar D0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1],{ff1,4,4},{ff2,1,2}]
|
---|
1897 |
|
---|
1898 | -Sum[2*Sqrt[2]*Gf*CKM[2,2]*fplusDK[ff1,ff2]*I del[K0bar,mu] Ddbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1899 | +Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2]-fminusDK[ff1,ff2])*vev/Sqrt[2] K0bar Ddbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
|
---|
1900 | -Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2]-fminusDK[ff1,ff2]) K0bar Ddbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1],{ff1,4,4},{ff2,1,2}]
|
---|
1901 |
|
---|
1902 | (* B+ -> pi0 l nu and B0 -> pi+ l nu *)
|
---|
1903 |
|
---|
1904 | + 1/2 DC[B0bar,mu] DC[B0,mu] - MB0^2/2 B0bar B0
|
---|
1905 |
|
---|
1906 | -Sum[2*Gf*CKM[1,3]*fplusBPi0[ff1,ff2]*I del[Pi0,mu] Bubar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1907 | +Sum[Gf*CKM[1,3]*(fplusBPi0[ff1,ff2] - fminusBPi0[ff1,ff2])*vev/Sqrt[2] Pi0 Bubar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1908 | -Sum[Gf*CKM[1,3]*(fplusBPi0[ff1,ff2] - fminusBPi0[ff1,ff2]) Pi0 Bubar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1909 |
|
---|
1910 | -Sum[2*Sqrt[2]*Gf*CKM[1,3]*fplusB0Pi[ff1,ff2]*I del[Pipbar,mu] B0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1911 | +Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0Pi[ff1,ff2] - fminusB0Pi[ff1,ff2])*vev/Sqrt[2] Pipbar B0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1912 | -Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0Pi[ff1,ff2] - fminusB0Pi[ff1,ff2]) Pipbar B0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1913 |
|
---|
1914 | (* B+ -> D0 l nu, B0 -> D+ l nu and B0s -> Ds+ l nu *)
|
---|
1915 |
|
---|
1916 | -Sum[2*Sqrt[2]*Gf*CKM[2,3]*fplusBD0[ff1,ff2]*I del[D0bar,mu] Bubar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1917 | +Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusBD0[ff1,ff2]-fminusBD0[ff1,ff2])*vev/Sqrt[2] D0bar Bubar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1918 | -Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusBD0[ff1,ff2]-fminusBD0[ff1,ff2]) D0bar Bubar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1919 |
|
---|
1920 | -Sum[2*Sqrt[2]*Gf*CKM[2,3]fplusB0D[ff1,ff2]*I del[Ddbar,mu] B0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1921 | +Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0D[ff1,ff2] - fminusB0D[ff1,ff2])*vev/Sqrt[2] Ddbar B0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1922 | -Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0D[ff1,ff2] - fminusB0D[ff1,ff2]) Ddbar B0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1923 |
|
---|
1924 | + 1/2 DC[B0sbar,mu] DC[B0s,mu] - MB0s^2/2 B0sbar B0s
|
---|
1925 |
|
---|
1926 | -Sum[2*Sqrt[2]*Gf*CKM[2,3]*fplusB0sDs[ff1,ff2]*I del[Dsbar,mu] B0sbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1927 | +Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0sDs[ff1,ff2] - fminusB0sDs[ff1,ff2])*vev/Sqrt[2] Dsbar B0sbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1928 | -Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0sDs[ff1,ff2] - fminusB0sDs[ff1,ff2]) Dsbar B0sbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1929 |
|
---|
1930 | (* B0s -> K+ l nu *)
|
---|
1931 |
|
---|
1932 | -Sum[2*Sqrt[2]*Gf*CKM[1,3]*fplusB0sK[ff1,ff2]*I del[Kbar,mu] B0sbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1933 | +Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0sK[ff1,ff2] - fminusB0sK[ff1,ff2])*vev/Sqrt[2] Kbar B0sbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
|
---|
1934 | -Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0sK[ff1,ff2] - fminusB0sK[ff1,ff2]) Kbar B0sbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,4,4},{ff2,1,3}]
|
---|
1935 |
|
---|
1936 |
|
---|
1937 |
|
---|
1938 | , FlavorExpand->{SU2D,SU2W}];
|
---|
1939 | yhad+HC[yhad]
|
---|
1940 | ];
|
---|
1941 |
|
---|
1942 |
|
---|
1943 | (* Scalar pieces: see Peskin pages 739-742 *)
|
---|
1944 | (* phi1 and phi2 are the real degrees of freedom of GP *)
|
---|
1945 | (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
|
---|
1946 | gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
|
---|
1947 | ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
|
---|
1948 | generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
|
---|
1949 | doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
|
---|
1950 | doublet0 = {0, vev/Sqrt[2]};
|
---|
1951 | 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}];
|
---|
1952 | togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
|
---|
1953 | LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
|
---|
1954 |
|
---|
1955 | ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
|
---|
1956 |
|
---|
1957 | LagHeavyN:= LGauge + LFermions + LHiggs + LYukawa + LGhost + If[Mesons,LHadr,LQuarks];
|
---|