1 | (********************************************************************************)
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2 | (****** FeynRules mod-file for Vector-like Leptons *)
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3 | (****** *)
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4 | (****** Authors: B. Fuks *)
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5 | (********************************************************************************)
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6 |
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7 | M$ModelName = "VLL";
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8 |
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9 | M$Information = {
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10 | Authors -> {"B. Fuks"},
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11 | Institutions -> {"LPTHE / Sorbonne U."},
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12 | Emails -> {"fuks@lpthe.jussieu.fr"},
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13 | Version -> "1.0",
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14 | Date -> "13.10.2022"
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15 | };
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16 |
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17 | FeynmanGauge = False;
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18 | M$InteractionOrderHierarchy = { {QCD, 1}, {QED, 2}, {VLL,1}};
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19 | M$InteractionOrderLimit = { {QCD, 99}, {QED, 99}, {VLL,99}};
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20 |
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21 | (* ************************** *)
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22 | (* ***** Fields ***** *)
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23 | (* ************************** *)
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24 |
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25 | M$ClassesDescription = {
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26 | (* VLL doublet [gauge eigenstates] *)
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27 | F[21] == { ClassName -> VLL0, Unphysical->True, SelfConjugate->False, Indices -> {Index[SU2D]}, FlavorIndex -> SU2D, QuantumNumbers -> {Y ->-1/2},
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28 | Definitions -> { VLL0[sp1_,1] :> VLLN[sp1], VLL0[sp1_,2] :> VLLE[sp1] } },
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29 |
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30 | (* VLL doublet [mass eigenstates] *)
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31 | F[31] == { ClassName -> VLLE, SelfConjugate->False, Mass->{MVLLE,601}, Width -> {WVLLE,5.}, QuantumNumbers -> {Q->-1, LeptonNumber->1}, PDG -> 9000001, FullName -> "VLL doublet - charged component"},
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32 | F[32] == { ClassName -> VLLN, SelfConjugate->False, Mass->{MVLLN,602}, Width -> {WVLLN,5.}, QuantumNumbers -> {LeptonNumber->1}, PDG -> 9000002, FullName -> "VLL doublet - neutral component"},
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33 |
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34 | (* VLL singlets [gauge eigenstates] *)
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35 | F[22] == { ClassName -> VLE0, Unphysical->True, SelfConjugate->False, QuantumNumbers -> {Y->-1}, Definitions->{VLE0[sp_]->VLE[sp]} },
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36 | F[23] == { ClassName -> VLN0, Unphysical->True, SelfConjugate->False, Definitions->{VLN0[sp_]->VLN[sp]} },
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37 |
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38 | (* VLL singlets [mass eigenstates] *)
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39 | F[33] == { ClassName -> VLE, SelfConjugate->False, Mass->{MVLE,603}, Width -> {WVLE,5.}, QuantumNumbers -> {Q->-1, LeptonNumber->1}, PDG -> 9000003, FullName -> "Charged VLL singlet"},
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40 | F[34] == { ClassName -> VLN, SelfConjugate->False, Mass->{MVLN,604}, Width -> {WVLN,5.}, QuantumNumbers -> {LeptonNumber->1}, PDG -> 9000004, FullName -> "Neutral VLL singlet"}
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41 | };
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42 |
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43 | (* ************************** *)
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44 | (* ***** Parameters ***** *)
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45 | (* ************************** *)
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46 |
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47 | M$Parameters = {
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48 |
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49 | (* Higgs boson interactions *)
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50 | KLLEH == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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51 | Description->"Doublet charged VLL - Higgs coupling (left-handed)" ,
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52 | BlockName -> KLLEH, Value -> {KLLEH[1] -> 0.001, KLLEH[2] -> 0.002, KLLEH[3] -> 0.003} },
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53 | KRLEH == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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54 | Description->"Doublet charged VLL - Higgs coupling (right-handed)" ,
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55 | BlockName -> KRLEH, Value -> {KRLEH[1] -> 0.004, KRLEH[2] -> 0.005, KRLEH[3] -> 0.006} },
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56 | KLEH == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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57 | Description->"Singlet charged VLL - Higgs coupling (left-handed)" ,
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58 | BlockName -> KLEH, Value -> {KLEH[1] -> 0.007, KLEH[2] -> 0.008, KLEH[3] -> 0.009} },
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59 | KREH == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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60 | Description->"Singlet charged VLL - Higgs coupling (right-handed)" ,
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61 | BlockName -> KREH, Value -> {KREH[1] -> 0.010, KREH[2] -> 0.011, KREH[3] -> 0.012} },
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62 | KLLNH == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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63 | Description->"Doublet neutral VLL - Higgs coupling (left-handed)" ,
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64 | BlockName -> KLLNH, Value -> {KLLNH[1] -> 0.013, KLLNH[2] -> 0.014, KLLNH[3] -> 0.015} },
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65 | KLNH == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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66 | Description->"Singlet neutral VLL - Higgs coupling (left-handed)" ,
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67 | BlockName -> KLNH, Value -> {KLNH[1] -> 0.016, KLNH[2] -> 0.017, KLNH[3] -> 0.018} },
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68 |
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69 | (* Z boson interactions *)
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70 | KLLEZ == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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71 | Description->"Doublet charged VLL - Z coupling (left-handed)" ,
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72 | BlockName -> KLLEZ, Value -> {KLLEZ[1] -> 0.021, KLLEZ[2] -> 0.022, KLLEZ[3] -> 0.023} },
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73 | KRLEZ == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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74 | Description->"Doublet charged VLL - Z coupling (right-handed)" ,
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75 | BlockName -> KRLEZ, Value -> {KRLEZ[1] -> 0.024, KRLEZ[2] -> 0.025, KRLEZ[3] -> 0.026} },
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76 | KLEZ == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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77 | Description->"Singlet charged VLL - Z coupling (left-handed)" ,
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78 | BlockName -> KLEZ, Value -> {KLEZ[1] -> 0.027, KLEZ[2] -> 0.028, KLEZ[3] -> 0.029} },
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79 | KREZ == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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80 | Description->"Singlet charged VLL - Z coupling (right-handed)" ,
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81 | BlockName -> KREZ, Value -> {KREZ[1] -> 0.030, KREZ[2] -> 0.031, KREZ[3] -> 0.032} },
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82 | KLLNZ == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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83 | Description->"Doublet neutral VLL - Z coupling (left-handed)" ,
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84 | BlockName -> KLLNZ, Value -> {KLLNZ[1] -> 0.033, KLLNZ[2] -> 0.034, KLLNZ[3] -> 0.035} },
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85 | KLNZ == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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86 | Description->"Singlet neutral VLL - Z coupling (left-handed)" ,
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87 | BlockName -> KLNZ, Value -> {KLNZ[1] -> 0.036, KLNZ[2] -> 0.037, KLNZ[3] -> 0.038} },
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88 |
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89 | (* W boson interactions *)
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90 | KLLEW == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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91 | Description->"Doublet charged VLL - W coupling (left-handed)" ,
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92 | BlockName -> KLLEW, Value -> {KLLEW[1] -> 0.041, KLLEW[2] -> 0.042, KLLEW[3] -> 0.043} },
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93 | KLEW == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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94 | Description->"Singlet charged VLL - W coupling (left-handed)" ,
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95 | BlockName -> KLEW, Value -> {KLEW[1] -> 0.044, KLEW[2] -> 0.045, KLEW[3] -> 0.046} },
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96 | KLLNW == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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97 | Description->"Doublet neutral VLL - W coupling (left-handed)" ,
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98 | BlockName -> KLLNW, Value -> {KLLNW[1] -> 0.047, KLLNW[2] -> 0.048, KLLNW[3] -> 0.049} },
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99 | KRLNW == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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100 | Description->"Doublet neutral VLL - W coupling (right-handed)" ,
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101 | BlockName -> KRLNW, Value -> {KRLNW[1] -> 0.050, KRLNW[2] -> 0.051, KRLNW[3] -> 0.052} },
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102 | KLNW == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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103 | Description->"Singlet neutral VLL - W coupling (left-handed)" ,
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104 | BlockName -> KLNW, Value -> {KLNW[1] -> 0.053, KLNW[2] -> 0.054, KLNW[3] -> 0.055} },
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105 | KRNW == { ParameterType->External, ComplexParameter->False, Indices->{Index[Generation]}, InteractionOrder->{VLL,1},
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106 | Description->"Doublet neutral VLL - W coupling (right-handed)" ,
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107 | BlockName -> KRNW, Value -> {KRNW[1] -> 0.056, KRNW[2] -> 0.057, KRNW[3] -> 0.058} }
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108 | };
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109 |
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110 |
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111 | (* ************************** *)
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112 | (* ***** Lagrangian ***** *)
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113 | (* ************************** *)
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114 |
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115 | (* Kinetic and mass terms *)
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116 | Lkin := I VLL0bar.Ga[mu].DC[VLL0,mu] - MVLLE VLLEbar.VLLE - MVLLN VLLNbar.VLLN \
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117 | + I VLE0bar.Ga[mu].DC[VLE0,mu] - MVLE VLEbar.VLE \
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118 | + I VLN0bar.Ga[mu].DC[VLN0,mu] - MVLN VLNbar.VLN;
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119 |
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120 | (* Interactions with the Higgs *)
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121 | LVLH := H VLLEbar[sp1] . l[sp3,ff] (ProjM[sp1,sp3] KLLEH[ff] + ProjP[sp1,sp3] KRLEH[ff]) \
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122 | + H VLEbar[sp1] . l[sp3,ff] (ProjM[sp1,sp3] KLEH[ff] + ProjP[sp1,sp3] KREH[ff]) \
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123 | + H VLLNbar[sp1] . vl[sp3,ff] (ProjM[sp1,sp3] KLLNH[ff] ) \
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124 | + H VLNbar[sp1] . vl[sp3,ff] (ProjM[sp1,sp3] KLNH[ff] );
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125 |
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126 | (* Interactions with the Z boson*)
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127 | LVLZ := gw/(2 cw) * Z[mu] * Ga[mu,sp1,sp2] * VLLEbar[sp1] . l[sp3,ff] (ProjM[sp2,sp3] KLLEZ[ff] + ProjP[sp2,sp3] KRLEZ[ff]) \
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128 | + gw/(2 cw) * Z[mu] * Ga[mu,sp1,sp2] * VLEbar[sp1] . l[sp3,ff] (ProjM[sp2,sp3] KLEZ[ff] + ProjP[sp2,sp3] KREZ[ff]) \
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129 | + gw/(2 cw) * Z[mu] * Ga[mu,sp1,sp2] * VLLNbar[sp1] . vl[sp3,ff] (ProjM[sp2,sp3] KLLNZ[ff] ) \
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130 | + gw/(2 cw) * Z[mu] * Ga[mu,sp1,sp2] * VLNbar[sp1] . vl[sp3,ff] (ProjM[sp2,sp3] KLNZ[ff] );
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131 |
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132 | (* Interactions with the W boson*)
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133 | LVLW := gw/Sqrt[2] * Wbar[mu] * Ga[mu,sp1,sp2] * VLLEbar[sp1] . vl[sp3,ff] (ProjM[sp2,sp3] KLLEW[ff] ) \
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134 | + gw/Sqrt[2] * Wbar[mu] * Ga[mu,sp1,sp2] * VLEbar[sp1] . vl[sp3,ff] (ProjM[sp2,sp3] KLEW[ff] ) \
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135 | + gw/Sqrt[2] * W[mu] * Ga[mu,sp1,sp2] * VLLNbar[sp1] . l[sp3,ff] (ProjM[sp2,sp3] KLLNW[ff] + ProjP[sp2,sp3] KRLNW[ff] ) \
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136 | + gw/Sqrt[2] * W[mu] * Ga[mu,sp1,sp2] * VLNbar[sp1] . l[sp3,ff] (ProjM[sp2,sp3] KLNW[ff] + ProjP[sp2,sp3] KRNW[ff] );
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137 |
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138 | LVLL := { LSM, Lkin, LVLH, LVLZ, LVLW, HC[LVLH], HC[LVLZ], HC[LVLW] };
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