1 | (* ************************************************************************* *)
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2 | (* FeynRules Model file for a Zee-Babu extension of the Standard Model. *)
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3 | (* Contains two new scalar fields: k--(Y=-2) and h-(Y=-1) that couple *)
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4 | (* to all SM leptons through Yukawa couplings, Z/A bosons through gauge *)
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5 | (* couplings, and the SM Higgs through dimensionless couplings. *)
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6 | (* Neutrinos are massless and aligned with flavor states in this model file. *)
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7 | (* The Lagrangian is written with Goldstone bosons. *)
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8 | (* *)
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9 | (* Contact author: R. Ruiz [rruiz [at] ifj.edu.pl] *)
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10 | (* *)
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11 | (* The original Zee-Babu papers are: *)
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12 | (* 1. Zee, PLB ('85) [Zee:1985rj] *)
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13 | (* 2. Zee, NPB ('86) [Zee:1985id] *)
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14 | (* 3. Babu, PLB ('88) [Babu:1988ki] *)
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15 | (* At LO and NLO in QCD, this model was implemented in: *)
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16 | (* 1. R. Ruiz [arXiv:2206.14833], *)
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17 | (* and extends the default FeynRules SM model file. *)
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18 | (* Please cite accordingly. *)
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19 | (* *)
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20 | (* ************************************************************************* *)
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21 |
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22 | (* ************************** *)
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23 | (* ***** Information ***** *)
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24 | (* ************************** *)
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25 | M$ModelName = "SM_ZeeBabu";
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26 |
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27 | M$Information = {
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28 | Authors -> {"R. Ruiz"},
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29 | Version -> "1.0",
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30 | Date -> "2022 June 30",
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31 | Institutions -> {"IFJ PAN"},
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32 | Emails -> {"rruiz@ifj.edu.pl"},
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33 | References -> {"R. Ruiz [arXiv:2206.14833];",
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34 | "Zee, PLB ('85) [Zee:1985rj];",
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35 | "Zee, NPB ('86) [Zee:1985id];",
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36 | "Babu, PLB ('88) [Babu:1988ki]"
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37 | },
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38 | URLs -> {"https://feynrules.irmp.ucl.ac.be/wiki/ZeeBabu"}
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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 NLO model file *)
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47 |
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48 | (* ************************** *)
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49 | (* ***** Parameters ***** *)
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50 | (* ************************** *)
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51 | M$Parameters = {
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52 | (* External Parameters *)
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53 |
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54 | (* ***** Scalar Sector ***** *)
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55 |
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56 | muZB == {
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57 | ParameterType -> External,
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58 | BlockName -> ZeeBabuPotential,
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59 | OrderBlock -> 1,
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60 | Value -> 1000.0,
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61 | ComplexParameter -> False,
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62 | InteractionOrder -> {NP,1},
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63 | TeX -> Subscript[mu,ZB],
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64 | Description -> "LNV mass scale; h-h-k ZB coupling"
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65 | },
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66 |
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67 | lamhZB == {
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68 | ParameterType -> External,
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69 | BlockName -> ZeeBabuPotential,
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70 | OrderBlock -> 2,
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71 | Value -> 1.0,
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72 | ComplexParameter -> False,
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73 | InteractionOrder -> {NP,1},
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74 | TeX -> Subscript[lambda,hZB],
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75 | Description -> "h-h-h-h ZB coupling"
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76 | },
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77 |
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78 | lamkZB == {
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79 | ParameterType -> External,
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80 | BlockName -> ZeeBabuPotential,
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81 | OrderBlock -> 3,
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82 | Value -> 1.000000001,
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83 | ComplexParameter -> False,
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84 | InteractionOrder -> {NP,1},
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85 | TeX -> Subscript[lambda,kZB],
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86 | Description -> "k-k-k-k ZB coupling"
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87 | },
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88 |
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89 | lamhZBkZB == {
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90 | ParameterType -> External,
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91 | BlockName -> ZeeBabuPotential,
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92 | OrderBlock -> 4,
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93 | Value -> 1.000000002,
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94 | ComplexParameter -> False,
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95 | InteractionOrder -> {NP,1},
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96 | TeX -> Subscript[lambda,hZBkZB],
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97 | Description -> "h-h-k-k ZB coupling"
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98 | },
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99 |
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100 | lamhZBH == {
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101 | ParameterType -> External,
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102 | BlockName -> ZeeBabuPotential,
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103 | OrderBlock -> 5,
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104 | Value -> 1.000000003,
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105 | ComplexParameter -> False,
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106 | InteractionOrder -> {{NP,1},{QED,1}},
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107 | TeX -> Subscript[lambda,hZBH],
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108 | Description -> "h-h-H(-H) ZB-SM coupling"
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109 | },
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110 |
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111 | lamkZBH == {
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112 | ParameterType -> External,
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113 | BlockName -> ZeeBabuPotential,
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114 | OrderBlock -> 6,
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115 | Value -> 1.000000004,
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116 | ComplexParameter -> False,
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117 | InteractionOrder -> {{NP,1},{QED,1}},
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118 | TeX -> Subscript[lambda,kZBH],
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119 | Description -> "k-k-H(-H) ZB-SM coupling"
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120 | },
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121 |
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122 | (* ***** Symmetric Couplings ***** *)
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123 |
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124 | gee == {
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125 | ParameterType -> External,
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126 | BlockName -> ZeeBabuSymmetric,
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127 | OrderBlock -> 1,
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128 | Value -> 1.000000010,
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129 | ComplexParameter -> False,
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130 | InteractionOrder -> {NP,1},
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131 | TeX -> Subscript[g,ee],
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132 | Description -> "ee coupling to k--"
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133 | },
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134 |
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135 | gemu == {
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136 | ParameterType -> External,
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137 | BlockName -> ZeeBabuSymmetric,
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138 | OrderBlock -> 2,
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139 | Value -> 1.000000011,
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140 | ComplexParameter -> False,
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141 | InteractionOrder -> {NP,1},
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142 | TeX -> Subscript[g,emu],
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143 | Description -> "emu coupling to k--"
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144 | },
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145 |
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146 | getau == {
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147 | ParameterType -> External,
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148 | BlockName -> ZeeBabuSymmetric,
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149 | OrderBlock -> 3,
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150 | Value -> 1.000000012,
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151 | ComplexParameter -> False,
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152 | InteractionOrder -> {NP,1},
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153 | TeX -> Subscript[g,etau],
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154 | Description -> "etau coupling to k--"
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155 | },
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156 |
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157 | gmumu == {
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158 | ParameterType -> External,
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159 | BlockName -> ZeeBabuSymmetric,
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160 | OrderBlock -> 4,
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161 | Value -> 1.000000013,
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162 | ComplexParameter -> False,
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163 | InteractionOrder -> {NP,1},
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164 | TeX -> Subscript[g,mumu],
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165 | Description -> "mumu coupling to k--"
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166 | },
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167 |
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168 | gmutau == {
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169 | ParameterType -> External,
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170 | BlockName -> ZeeBabuSymmetric,
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171 | OrderBlock -> 5,
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172 | Value -> 1.000000014,
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173 | ComplexParameter -> False,
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174 | InteractionOrder -> {NP,1},
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175 | TeX -> Subscript[g,mutau],
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176 | Description -> "mutau coupling to k--"
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177 | },
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178 |
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179 | gtautau == {
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180 | ParameterType -> External,
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181 | BlockName -> ZeeBabuSymmetric,
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182 | OrderBlock -> 6,
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183 | Value -> 1.000000015,
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184 | ComplexParameter -> False,
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185 | InteractionOrder -> {NP,1},
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186 | TeX -> Subscript[g,tautau],
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187 | Description -> "tautau coupling to k--"
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188 | },
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189 |
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190 | (* ***** Anti-symmetric Couplings ***** *)
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191 |
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192 | femu == {
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193 | ParameterType -> External,
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194 | BlockName -> ZeeBabuAntisymmetric,
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195 | OrderBlock -> 1,
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196 | Value -> 1.000000020,
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197 | ComplexParameter -> False,
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198 | InteractionOrder -> {NP,1},
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199 | TeX -> Subscript[f,emu],
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200 | Description -> "emu coupling to h-"
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201 | },
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202 |
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203 | fetau == {
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204 | ParameterType -> External,
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205 | BlockName -> ZeeBabuAntisymmetric,
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206 | OrderBlock -> 2,
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207 | Value -> 1.000000021,
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208 | ComplexParameter -> False,
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209 | InteractionOrder -> {NP,1},
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210 | TeX -> Subscript[f,etau],
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211 | Description -> "etau coupling to h-"
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212 | },
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213 |
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214 | fmutau == {
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215 | ParameterType -> External,
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216 | BlockName -> ZeeBabuAntisymmetric,
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217 | OrderBlock -> 3,
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218 | Value -> 1.000000022,
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219 | ComplexParameter -> False,
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220 | InteractionOrder -> {NP,1},
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221 | TeX -> Subscript[f,mutau],
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222 | Description -> "mutau coupling to h-"
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223 | },
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224 |
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225 |
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226 | (* Internal Parameters *)
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227 | mhZBTree == {
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228 | ParameterType -> Internal,
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229 | Value -> Sqrt[mhZB^2 - lamhZBH*vev^2 /2],
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230 | ComplexParameter -> False,
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231 | Description -> "tree-level mass of h- before EWSB"
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232 | },
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233 |
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234 | mkZBTree == {
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235 | ParameterType -> Internal,
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236 | Value -> Sqrt[mkZB^2 - lamhZBH*vev^2 /2],
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237 | ComplexParameter -> False,
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238 | Description -> "tree-level mass of k-- before EWSB"
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239 | },
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240 |
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241 |
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242 | (* ************************** *)
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243 | (* ***** Containers ***** *)
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244 | (* ************************** *)
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245 |
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246 | gll == {
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247 | ParameterType ->Internal,
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248 | Indices ->{Index[Generation],Index[Generation]},
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249 | ComplexParameter->False,
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250 | Unitary ->False,
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251 | InteractionOrder->{NP,1},
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252 | Value ->{
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253 | gll[1,1]->gee, gll[1,2]->gemu, gll[1,3]->getau,
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254 | gll[2,1]->gemu, gll[2,2]->gmumu, gll[2,3]->gmutau,
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255 | gll[3,1]->getau, gll[3,2]->gmutau, gll[3,3]->gtautau},
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256 | TeX ->Subscript[g,ll],
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257 | Description ->"symmetric ll coupling matrix to k--"
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258 | },
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259 |
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260 | fll == {
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261 | ParameterType ->Internal,
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262 | Indices ->{Index[Generation],Index[Generation]},
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263 | ComplexParameter->False,
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264 | Unitary ->False,
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265 | InteractionOrder->{NP,1},
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266 | Value ->{
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267 | fll[1,1]->0, fll[1,2]->femu, fll[1,3]->fetau,
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268 | fll[2,1]->-femu, fll[2,2]->0, fll[2,3]->fmutau,
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269 | fll[3,1]->-fetau, fll[3,2]->-fmutau, fll[3,3]->0},
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270 | TeX ->Subscript[f,ll],
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271 | Description ->"anti-symmetric ll coupling matrix to h-"
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272 | }
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273 |
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274 | };
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275 |
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276 |
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277 | M$InteractionOrderHierarchy = {
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278 | {QCD,1},
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279 | {QED,2},
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280 | {NP,1}
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281 | };
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282 |
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283 |
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284 | (* ************************** *)
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285 | (* **** Particle classes **** *)
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286 | (* ************************** *)
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287 | M$ClassesDescription = {
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288 | (*Zee-Babu Scalars*)
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289 | S[138] == {
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290 | ClassName -> hZB,
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291 | SelfConjugate -> False,
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292 | Mass -> {mhZB,300.},
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293 | Width -> {whZB,1},
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294 | QuantumNumbers -> {Q->-1,LeptonNumber -> 2},
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295 | PropagatorLabel -> "h-",
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296 | PropagatorType -> ScalarDash,
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297 | PropagatorArrow -> True,
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298 | ParticleName -> "h-",
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299 | AntiParticleName-> "h+",
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300 | PDG -> 38,
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301 | FullName -> "h-"
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302 | },
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303 |
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304 | S[161] == {
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305 | ClassName -> kZB,
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306 | SelfConjugate -> False,
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307 | Mass -> {mkZB,500.},
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308 | Width -> {wkZB,1},
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309 | QuantumNumbers -> {Q->-2,LeptonNumber -> 2},
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310 | PropagatorLabel -> "k--",
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311 | PropagatorType -> ScalarDash,
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312 | PropagatorArrow -> True,
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313 | ParticleName -> "k--",
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314 | AntiParticleName-> "k++",
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315 | PDG -> 61,
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316 | FullName -> "k--"
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317 | },
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318 |
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319 | S[238] == {
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320 | ClassName -> hGauge,
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321 | Unphysical -> True,
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322 | SelfConjugate -> False,
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323 | QuantumNumbers-> {Y->-1,LeptonNumber -> 2},
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324 | Definitions -> { hGauge -> hZB }
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325 | },
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326 |
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327 | S[261] == {
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328 | ClassName -> kGauge,
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329 | Unphysical -> True,
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330 | SelfConjugate -> False,
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331 | QuantumNumbers-> {Y->-2,LeptonNumber -> 2},
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332 | Definitions -> { kGauge -> kZB }
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333 | }
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334 |
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335 | };
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336 |
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337 | (* ************************** *)
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338 | (* ***** Lagrangian ***** *)
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339 | (* ************************** *)
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340 |
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341 | (* hZB and kZB covariant derivatives and masses before EWSB *)
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342 | LZBKin := DC[hGaugebar,mu] DC[hGauge,mu] + DC[kGaugebar,mu] DC[kGauge,mu] - mhZBTree^2 hGaugebar hGauge - mkZBTree^2 kGaugebar kGauge;
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343 |
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344 | (* hZB and kZB self-couplings *)
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345 | LZBScalarSelf := lamhZB * (hGaugebar hGauge)^2 + lamkZB * (kGaugebar kGauge)^2 + lamhZBkZB * (hGaugebar hGauge) (kGaugebar kGauge);
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346 |
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347 | (* hZB and kZB couplings to SM Higgs *)
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348 | LZBHiggs := lamhZBH (hGaugebar hGauge) * Phibar[ii] * Phi[ii] + lamkZBH (kGaugebar kGauge) * Phibar[ii] * Phi[ii];
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349 |
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350 | (* hZB and kZB LNV coupling *)
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351 | LlnvBare := muZB hGauge hGauge kGaugebar;
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352 | Llnv := LlnvBare + HC[LlnvBare];
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353 |
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354 | (* kZB couplings to leptons *)
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355 | LkllBare := kGaugebar * CC[lRbar][sp1,ff1].gll[ff1,ff2].lR[sp1,ff2];
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356 | Lkll := LkllBare + HC[LkllBare];
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357 |
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358 | (* hZB couplings to leptons *)
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359 | (* ii,jj = isospin; ff1,ff2 = flavor; sp = spin *)
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360 | LhllBare := hGaugebar * CC[LLbar][sp, ii, ff1].fll[ff1,ff2].Eps[ii, jj].LL[sp, jj, ff2];
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361 | Lhll := LhllBare + HC[LhllBare];
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362 |
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363 | (* Full ZB Lagrangian *)
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364 | LScalar := LZBScalarSelf + LZBHiggs + Llnv;
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365 | LZB:= LZBKin + Lkll + Lhll - LScalar;
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366 |
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367 | (* Full SM+ZB Lagrangian *)
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368 | LFull := LSM + LZB;
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