1 | (* ********************************************************************************* *)
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2 | (* FeynRules Model file for a heavy neutrino extension of the Standard Model. *)
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3 | (* Contains three massive Majorana neutrinos that couples to all SM leptons through *)
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4 | (* mixing between the active (flavor) eigenstates and mass eigenstates. *)
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5 | (* The Lagrangian is written in the Feynman Gauge. *)
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6 | (* *)
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7 | (* Contact author: R. Ruiz [richard.ruiz [at] durham.ac.uk] *)
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8 | (* *)
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9 | (* The Lagrangian is based on Atre, et. al. [arXiv:0901.3589]. *)
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10 | (* At LO, the model was implemented in Alva, et. al. [arXiv:1411.7305]. *)
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11 | (* At NLO, the model was implemented in Degrande, et al. [arXiv:1602.06957]. *)
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12 | (* Both model files are extensions of default FeynRules SM model file. *)
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13 | (* Please cite accordingly. *)
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14 | (* *)
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15 | (* Neutrino mass (mN) and mixing parameters (VlN) between heavy mass eigenstate and *)
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16 | (* flavor eigenstates are taken to be independent, phenomenological parameters. *)
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17 | (* Mixing parameters (VeN, VmuN, VtaN) are taken to be real. *)
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18 | (* This allows for maximum flexibility and model independence when calculating *)
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19 | (* rates. *)
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20 | (* *)
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21 | (* Feynman gauge is set to true. *)
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22 | (* ********************************************************************************* *)
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23 |
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24 | (* ************************** *)
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25 | (* ***** Information ***** *)
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26 | (* ************************** *)
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27 | M$ModelName = "SM_HeavyN";
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28 |
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29 | M$Information = {
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30 | Authors -> {"R. Ruiz"},
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31 | Version -> "2.2",
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32 | Date -> "27 June 2016",
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33 | Institutions -> {"IPPP / University of Durham"},
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34 | Emails -> {"richard.ruiz@durham.ac.uk"},
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35 | References -> {"Atre, et al, JHEP0905, 030 (2009) [arXiv:0901.3589]",
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36 | "Alva, et al, JHEP1502, 072 (2015) [arXiv:1411.7305]",
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37 | "Degrande, et al, [arXiv:1602.06957]"},
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38 | URLs -> {"https://feynrules.irmp.ucl.ac.be/wiki/HeavyN"}
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39 | };
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40 | FeynmanGauge = True;
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41 |
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42 |
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43 | (* ************************** *)
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44 | (* ***** Change log ***** *)
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45 | (* ************************** *)
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46 | (* v1.1: Public release of LO model file *)
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47 | (* v2.1: Added Goldstone couplings for Feynman Gauge and NLO implementation *)
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48 | (* v2.2: Corrected relative sign between Yukawa and gauge couplings. *)
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49 |
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50 | (* ************************** *)
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51 | (* ***** Parameters ***** *)
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52 | (* ************************** *)
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53 | M$Parameters = {
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54 | (* External Parameters *)
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55 |
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56 | VeN1 == {
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57 | ParameterType -> External,
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58 | BlockName -> NUMIXING,
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59 | OrderBlock -> 1,
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60 | Value -> 1.0,
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61 | ComplexParameter -> False,
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62 | TeX -> Subscript[V,eN1],
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63 | Description -> "Mixing between ve flavor/gauge state and N1 mass state"
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64 | },
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65 |
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66 | VeN2 == {
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67 | ParameterType -> External,
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68 | BlockName -> NUMIXING,
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69 | OrderBlock -> 2,
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70 | Value -> 0.0,
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71 | ComplexParameter -> False,
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72 | TeX -> Subscript[V,eN2],
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73 | Description -> "Mixing between ve flavor/gauge state and N2 mass state"
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74 | },
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75 |
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76 | VeN3 == {
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77 | ParameterType -> External,
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78 | BlockName -> NUMIXING,
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79 | OrderBlock -> 3,
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80 | Value -> 0.0,
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81 | ComplexParameter -> False,
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82 | TeX -> Subscript[V,eN3],
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83 | Description -> "Mixing between ve flavor/gauge state and N3 mass state"
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84 | },
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85 |
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86 | VmuN1 == {
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87 | ParameterType -> External,
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88 | BlockName -> NUMIXING,
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89 | OrderBlock -> 4,
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90 | Value -> 0.0,
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91 | ComplexParameter -> False,
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92 | TeX -> Subscript[V,muN1],
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93 | Description -> "Mixing between vm flavor/gauge state and N1 mass state"
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94 | },
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95 |
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96 | VmuN2 == {
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97 | ParameterType -> External,
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98 | BlockName -> NUMIXING,
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99 | OrderBlock -> 5,
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100 | Value -> 1.0,
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101 | ComplexParameter -> False,
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102 | TeX -> Subscript[V,muN2],
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103 | Description -> "Mixing between vm flavor/gauge state and N2 mass state"
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104 | },
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105 |
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106 | VmuN3 == {
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107 | ParameterType -> External,
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108 | BlockName -> NUMIXING,
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109 | OrderBlock -> 6,
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110 | Value -> 0.0,
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111 | ComplexParameter -> False,
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112 | TeX -> Subscript[V,muN3],
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113 | Description -> "Mixing between vm flavor/gauge state and N3 mass state"
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114 | },
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115 |
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116 | VtaN1 == {
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117 | ParameterType -> External,
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118 | BlockName -> NUMIXING,
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119 | OrderBlock -> 7,
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120 | Value -> 0.0,
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121 | ComplexParameter -> False,
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122 | TeX -> Subscript[V,taN1],
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123 | Description -> "Mixing between vt flavor/gauge state and N1 mass state"
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124 | },
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125 |
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126 | VtaN2 == {
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127 | ParameterType -> External,
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128 | BlockName -> NUMIXING,
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129 | OrderBlock -> 8,
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130 | Value -> 0.0,
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131 | ComplexParameter -> False,
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132 | TeX -> Subscript[V,taN2],
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133 | Description -> "Mixing between vt flavor/gauge state and N2 mass state"
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134 | },
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135 |
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136 | VtaN3 == {
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137 | ParameterType -> External,
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138 | BlockName -> NUMIXING,
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139 | OrderBlock -> 9,
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140 | Value -> 1.0,
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141 | ComplexParameter -> False,
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142 | TeX -> Subscript[V,taN3],
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143 | Description -> "Mixing between vt flavor/gauge state and N3 mass state"
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144 | },
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145 |
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146 | (* Internal Parameters *)
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147 | gN == {
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148 | ParameterType -> Internal,
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149 | Definitions -> {gN->ee/sw},
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150 | InteractionOrder -> {NP,1},
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151 | TeX -> Subscript[g,N]}
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152 | };
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153 |
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154 | M$InteractionOrderHierarchy = {
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155 | {QCD,1},
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156 | {QED,2}
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157 | };
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158 |
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159 | (* ************************** *)
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160 | (* **** Particle classes **** *)
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161 | (* ************************** *)
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162 | M$ClassesDescription = {
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163 | (*Majorana Neutrino*)
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164 | F[131] == {
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165 | ClassName -> N1,
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166 | SelfConjugate -> True,
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167 | Mass -> {mN1,300.},
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168 | Width -> {WN1,0.303},
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169 | PropagatorLabel -> "N1",
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170 | PropagatorType -> Straight,
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171 | PropagatorArrow -> False,
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172 | ParticleName -> "N1",
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173 | PDG -> {9900012},
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174 | FullName -> "N1"},
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175 |
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176 | F[132] == {
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177 | ClassName -> N2,
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178 | SelfConjugate -> True,
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179 | Mass -> {mN2,500.},
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180 | Width -> {WN2,1.50},
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181 | PropagatorLabel -> "N2",
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182 | PropagatorType -> Straight,
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183 | PropagatorArrow -> False,
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184 | ParticleName -> "N2",
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185 | PDG -> {9900014},
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186 | FullName -> "N2"},
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187 |
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188 | F[133] == {
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189 | ClassName -> N3,
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190 | SelfConjugate -> True,
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191 | Mass -> {mN3,1000.},
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192 | Width -> {WN3,12.3},
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193 | PropagatorLabel -> "N3",
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194 | PropagatorType -> Straight,
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195 | PropagatorArrow -> False,
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196 | ParticleName -> "N3",
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197 | PDG -> {9900016},
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198 | FullName -> "N3"}
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199 | };
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200 |
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201 |
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202 | (* ************************** *)
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203 | (* ***** Lagrangian ***** *)
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204 | (* ************************** *)
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205 | LNKin := I/2 N1bar[s1].Ga[v,s1,s2].del[N1[s2],v] - 1/2 mN1 N1bar[s1]N1[s1] \
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206 | + I/2 N2bar[s1].Ga[v,s1,s2].del[N2[s2],v] - 1/2 mN2 N2bar[s1]N2[s1] \
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207 | + I/2 N3bar[s1].Ga[v,s1,s2].del[N3[s2],v] - 1/2 mN3 N3bar[s1]N3[s1];
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208 |
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209 | (* Charge Current *)
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210 | LNCCbare := gN/Sqrt[2] *( VeN1 * N1bar.W[m].ProjM[m].e \
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211 | + VmuN1 * N1bar.W[m].ProjM[m].mu \
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212 | + VtaN1 * N1bar.W[m].ProjM[m].ta ) \
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213 | + gN/Sqrt[2] *( VeN2 * N2bar.W[m].ProjM[m].e \
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214 | + VmuN2 * N2bar.W[m].ProjM[m].mu \
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215 | + VtaN2 * N2bar.W[m].ProjM[m].ta ) \
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216 | + gN/Sqrt[2] *( VeN3 * N3bar.W[m].ProjM[m].e \
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217 | + VmuN3 * N3bar.W[m].ProjM[m].mu \
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218 | + VtaN3 * N3bar.W[m].ProjM[m].ta );
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219 | LNCC := LNCCbare + HC[LNCCbare];
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220 |
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221 | (* Neutral Current *)
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222 | LNNCBare := 1/2 * gN/cw *( VeN1 * N1bar.Z[m].ProjM[m].ve \
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223 | + VmuN1 * N1bar.Z[m].ProjM[m].vm \
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224 | + VtaN1 * N1bar.Z[m].ProjM[m].vt ) \
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225 | + 1/2 * gN/cw *( VeN2 * N2bar.Z[m].ProjM[m].ve \
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226 | + VmuN2 * N2bar.Z[m].ProjM[m].vm \
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227 | + VtaN2 * N2bar.Z[m].ProjM[m].vt ) \
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228 | + 1/2 * gN/cw *( VeN3 * N3bar.Z[m].ProjM[m].ve \
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229 | + VmuN3 * N3bar.Z[m].ProjM[m].vm \
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230 | + VtaN3 * N3bar.Z[m].ProjM[m].vt );
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231 | LNNC := LNNCBare + HC[LNNCBare];
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232 |
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233 | (* Higgs Interaction *)
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234 | LNHbare := - gN*mN1/(2*MW) *( VeN1 * N1bar.ProjM.ve H \
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235 | + VmuN1 * N1bar.ProjM.vm H \
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236 | + VtaN1 * N1bar.ProjM.vt H ) \
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237 | - gN*mN2/(2*MW) *( VeN2 * N2bar.ProjM.ve H \
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238 | + VmuN2 * N2bar.ProjM.vm H \
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239 | + VtaN2 * N2bar.ProjM.vt H ) \
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240 | - gN*mN3/(2*MW) *( VeN3 * N3bar.ProjM.ve H \
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241 | + VmuN3 * N3bar.ProjM.vm H \
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242 | + VtaN3 * N3bar.ProjM.vt H );
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243 | LNH := LNHbare + HC[LNHbare];
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244 |
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245 | (* Goldstone Interaction *)
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246 | LNGbare := I *gN*mN1/(2*MW) *( VeN1 * vebar.ProjP.N1 G0 \
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247 | + VmuN1 * vmbar.ProjP.N1 G0 \
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248 | + VtaN1 * vtbar.ProjP.N1 G0) \
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249 | + I *gN*mN2/(2*MW) *( VeN2 * vebar.ProjP.N2 G0 \
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250 | + VmuN2 * vmbar.ProjP.N2 G0 \
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251 | + VtaN2 * vtbar.ProjP.N2 G0) \
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252 | + I *gN*mN3/(2*MW) *( VeN3 * vebar.ProjP.N3 G0 \
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253 | + VmuN3 * vmbar.ProjP.N3 G0 \
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254 | + VtaN3 * vtbar.ProjP.N3 G0) \
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255 | + I *gN*mN1/(Sqrt[2]*MW) *( VeN1 * ebar.ProjP.N1 GPbar \
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256 | + VmuN1 * mubar.ProjP.N1 GPbar \
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257 | + VtaN1 * tabar.ProjP.N1 GPbar) \
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258 | + I *gN*mN2/(Sqrt[2]*MW) *( VeN2 * ebar.ProjP.N2 GPbar \
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259 | + VmuN2 * mubar.ProjP.N2 GPbar \
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260 | + VtaN2 * tabar.ProjP.N2 GPbar) \
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261 | + I *gN*mN3/(Sqrt[2]*MW) *( VeN3 * ebar.ProjP.N3 GPbar \
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262 | + VmuN3 * mubar.ProjP.N3 GPbar \
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263 | + VtaN3 * tabar.ProjP.N3 GPbar);
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264 | LNG := LNGbare + HC[LNGbare];
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265 |
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266 | (* Full N Lagrangian *)
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267 | LN:= LNKin + LNCC + LNNC + LNH + LNG;
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268 |
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269 | (* Combine Lagrangian *)
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270 | LFull := LSM + LN;
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