1 | (**************************************************************************************************)
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2 | (****** Alternative FR model file for an alternative left-right symmetric model ******)
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3 | (****** ******)
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4 | (****** Author: Benjamin Fuks ******)
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5 | (****** ******)
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6 | (**************************************************************************************************)
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7 |
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8 | (* ************************** *)
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9 | (* ***** Information ***** *)
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10 | (* ************************** *)
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11 | M$ModelName = "ALRSM_BF";
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12 | M$Information = { Authors->{"Benjamin Fuks"}, Emails->{"fuks@lpthe.jussieu.fr"},
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13 | Institutions->{"LPTHE / Sorbonne U."},
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14 | Date->"29.05.19", Version->"1.1"};
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15 |
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16 |
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17 | (* ************************** *)
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18 | (* ***** Gauge groups ***** *)
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19 | (* ************************** *)
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20 | M$GaugeGroups = {
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21 | U1BL == { Abelian->True, CouplingConstant->gBL, GaugeBoson->B, Charge->YBL},
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22 | SU2L == { Abelian->False, CouplingConstant->gL, GaugeBoson->WLi,
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23 | StructureConstant->epL, Representations->{TL,SU2DL},
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24 | Definitions->{TL[a_,b__]-> PauliSigma[Index[SU2WL,a],b ]/2, epL->Eps}},
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25 | SU2R == { Abelian->False, CouplingConstant->gR, GaugeBoson->WRi,
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26 | StructureConstant->epR, Representations->{{TR, SU2DR}, {TRs,SU2DRs}},
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27 | Definitions->{TR[a_,b__]-> PauliSigma[Index[SU2WR,a],b]/2,
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28 | TRs[a_,i_,j_]->-PauliSigma[Index[SU2WR,a],j,i]/2, epR->Eps}},
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29 | SU3C == { Abelian->False, CouplingConstant->gs, GaugeBoson->G,
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30 | StructureConstant->f, Representations->{{T,Colour}, {Tb,Colourb}}, DTerm->dSUN }
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31 | };
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32 |
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33 |
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34 | (* ************************** *)
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35 | (* *** Interaction orders *** *)
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36 | (* ************************** *)
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37 | M$InteractionOrderHierarchy = { {QCD, 1}, {QED, 2}, {HIG, 2}, {HIW, 2} };
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38 | M$InteractionOrderLimit = { {QCD, 99}, {QED, 99}, {HIG, 1}, {HIW, 1} };
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39 |
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40 |
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41 | (* ************************** *)
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42 | (* ***** Indices ***** *)
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43 | (* ************************** *)
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44 | IndexRange[Index[SU2WL ]] = Unfold[Range[3]]; IndexStyle[SU2WL, j];
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45 | IndexRange[Index[SU2DL ]] = Unfold[Range[2]]; IndexStyle[SU2DL, k];
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46 | IndexRange[Index[SU2WR ]] = Unfold[Range[3]]; IndexStyle[SU2WR, j];
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47 | IndexRange[Index[SU2DR ]] = Unfold[Range[2]]; IndexStyle[SU2DR, k];
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48 | IndexRange[Index[SU2DRs ]] = Unfold[Range[2]]; IndexStyle[SU2DRs, k];
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49 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]]; IndexStyle[Gluon, a];
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50 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]]; IndexStyle[Colour, m];
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51 | IndexRange[Index[Colourb]] = NoUnfold[Range[3]]; IndexStyle[Colourb, m];
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52 | IndexRange[Index[GEN ]] = Range[3]; IndexStyle[GEN, f];
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53 | IndexRange[Index[SHIGGS ]] = Range[4]; IndexStyle[SHIGGS, n];
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54 | IndexRange[Index[PHIGGS ]] = Range[2]; IndexStyle[PHIGGS, n];
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55 |
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56 |
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57 | (* ************************** *)
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58 | (* ***** Fields ***** *)
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59 | (* ************************** *)
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60 | M$ClassesDescription = {
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61 | (* Gauge bosons: unphysical vector fields *)
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62 | V[11] == { ClassName->B, Unphysical->True, SelfConjugate->True,
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63 | Definitions -> { B[mu_] -> cph*cw*A[mu] - (sph*st+cph*sw*ct)*Z[mu] + (cph*sw*st-sph*ct)*Zp[mu]}},
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64 | V[12] == { ClassName->WLi, Unphysical->True, SelfConjugate->True,
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65 | Indices->{Index[SU2WL]}, FlavorIndex->SU2WL,
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66 | Definitions-> {WLi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2],
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67 | WLi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]),
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68 | WLi[mu_,3] -> sw*A[mu] + cw*ct*Z[mu] - cw*st*Zp[mu]}},
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69 | V[13] == { ClassName->WRi, Unphysical->True, SelfConjugate->True,
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70 | Indices->{Index[SU2WR]}, FlavorIndex->SU2WR,
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71 | Definitions-> {WRi[mu_,1] -> (Wpbar[mu]+Wp[mu])/Sqrt[2],
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72 | WRi[mu_,2] -> (Wpbar[mu]-Wp[mu])/(I*Sqrt[2]),
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73 | WRi[mu_,3] -> sph*cw*A[mu] + (cph*st-sph*sw*ct)*Z[mu] + (sph*sw*st+cph*ct)*Zp[mu]}},
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74 |
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75 | (* Gauge bosons: physical vector fields *)
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76 | V[1] == { ClassName->A, SelfConjugate->True, Mass->0, Width->0, PDG->22},
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77 | V[2] == { ClassName->Z , SelfConjugate->True, Mass->{MZ,91.1876}, Width->{WZ,2.4952}, PDG->23},
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78 | V[3] == { ClassName->Zp, SelfConjugate->True, Mass->{MZp,Internal}, Width->{WZp, 13.2}, PDG->32},
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79 | V[4] == { ClassName->W , SelfConjugate->False, Mass->{MW, Internal}, Width->{WW,2.085}, PDG->24,
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80 | QuantumNumbers->{Q->1}},
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81 | V[5] == { ClassName->Wp, SelfConjugate->False, Mass->{MWp,Internal}, Width->{WWp,3.04}, PDG->34,
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82 | QuantumNumbers->{Q->1}},
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83 | V[6] == { ClassName->G, SelfConjugate->True, Indices->{Index[Gluon]}, Mass->0, Width->0, PDG->21,
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84 | PropagatorType->C},
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85 |
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86 | (* Ghost: related to physical gauge bosons *)
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87 | U[1] == { ClassName->ghG, SelfConjugate->False, Mass->0, Width->0,
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88 | Ghost->G, QuantumNumbers->{GhostNumber->1}, Indices->{Index[Gluon]} },
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89 |
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90 | (* Higgs: unphysical scalars *)
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91 | S[11] == { ClassName->Phi, Unphysical->True, SelfConjugate->False,
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92 | Indices->{Index[SU2DL],Index[SU2DRs]}, FlavorIndex->SU2DRs,
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93 | QuantumNumbers->{LNumber->-1/2},
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94 | Definitions->{
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95 | Phi[1,1]-> (H1 +I A1)/Sqrt[2],
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96 | Phi[1,2]-> Cos[beta] Hp[1],
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97 | Phi[2,1]-> Cos[zeta] Hpbar[2],
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98 | Phi[2,2]:> Module[{ff}, (kk + TH[1,ff] h0[ff] + I/Sqrt[1+tb^2+tz^2] A2)/Sqrt[2]]}},
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99 | S[12] == { ClassName->chiL, Unphysical->True, SelfConjugate->False,
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100 | Indices->{Index[SU2DL]}, FlavorIndex->SU2DL,
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101 | QuantumNumbers->{YBL->1/2},
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102 | Definitions->{
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103 | chiL[1]-> -Sin[beta] Hp[1],
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104 | chiL[2]:> Module[{ff}, (vL + TH[3,ff] h0[ff] + -I tb/Sqrt[1+tb^2+tz^2] A2)/Sqrt[2]]}},
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105 | S[13] == { ClassName->chiR, Unphysical->True, SelfConjugate->False,
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106 | Indices->{Index[SU2DR]}, FlavorIndex->SU2DR,
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107 | QuantumNumbers->{YBL->1/2,LNumber-> 1/2},
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108 | Definitions->{
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109 | chiR[1]-> -Sin[zeta] Hp[2],
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110 | chiR[2]:> Module[{ff}, (vR + TH[4,ff] h0[ff] + I tz/Sqrt[1+tb^2+tz^2] A2 )/Sqrt[2]]}},
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111 |
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112 | (* Higgs: physical fields *)
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113 | S[1] == { ClassName->h0, SelfConjugate->True, Indices->{Index[SHIGGS]}, FlavorIndex->SHIGGS,
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114 | ClassMembers->{H0,H1,H2,H3},
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115 | Mass -> {MH, {MH0,125.}, {MH1,Internal}, {MH2,Internal}, {MH3,Internal}},
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116 | Width-> {WH, {WH0,0.0176},{WH1,0.95}, {WH2, 3.18}, {WH3,781.}},
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117 | PDG->{25,35,45,55}},
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118 | S[2] == { ClassName->A0, SelfConjugate->True, Indices->{Index[PHIGGS]}, FlavorIndex->PHIGGS,
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119 | ClassMembers->{A1,A2},
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120 | Mass -> {MA0, {MA1,Internal}, {MA2, Internal}},
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121 | Width-> {WA0, {WA1,0.95}, {WA2,3.18}},
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122 | PDG->{36,46}},
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123 | S[3] == { ClassName->Hp, SelfConjugate->False, Indices->{Index[PHIGGS]}, FlavorIndex->PHIGGS,
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124 | QuantumNumbers->{Q->1},
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125 | ClassMembers->{Hp1,Hp2},
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126 | Mass -> {MHp,{MHp1,Internal}, {MHp2,Internal}},
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127 | Width-> {WHp,{WHp1,2.83}, {WHp2,0.423}},
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128 | PDG->{37,47}},
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129 |
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130 | (* Fermions: unphysical fields *)
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131 | F[11] == { ClassName->LL, Unphysical->True, SelfConjugate->False,
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132 | Indices->{Index[SU2DL],Index[GEN]}, FlavorIndex->SU2DL,
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133 | QuantumNumbers->{YBL->-1/2, LNumber->1},
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134 | Definitions->{
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135 | LL[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNS[ff, ff2] ProjM[sp1,sp2] vl[sp2,ff2]],
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136 | LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }},
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137 | F[12] == { ClassName->LR, Unphysical->True, SelfConjugate->False,
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138 | Indices->{Index[SU2DR],Index[GEN]}, FlavorIndex->SU2DR,
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139 | QuantumNumbers->{YBL-> -1/2, LNumber->3/2},
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140 | Definitions->{
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141 | LR[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNSp[ff, ff2] ProjP[sp1,sp2] nl[sp2,ff2]],
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142 | LR[sp1_,2,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }},
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143 | F[13] == { ClassName->NL, Unphysical->True, SelfConjugate->False,
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144 | Indices->{Index[GEN]}, FlavorIndex->GEN,
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145 | QuantumNumbers->{LNumber->2},
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146 | Definitions->{ NL[sp1_,ff_] :> Module[{sp2}, ProjM[sp1,sp2] nl[sp2,ff]]}},
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147 | F[14] == { ClassName->VR, Unphysical->True, SelfConjugate->False,
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148 | Indices->{Index[GEN]}, FlavorIndex->GEN,
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149 | QuantumNumbers->{LNumber->1},
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150 | Definitions->{ VR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] vl[sp2,ff]]}},
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151 | F[21] == { ClassName->QL, Unphysical->True, SelfConjugate->False,
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152 | Indices->{Index[SU2DL],Index[GEN],Index[Colour]}, FlavorIndex->SU2DL,
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153 | QuantumNumbers->{YBL->1/6},
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154 | Definitions-> {
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155 | QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
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156 | QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] } },
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157 | F[22] == { ClassName->QR, Unphysical->True, SelfConjugate->False,
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158 | Indices->{Index[SU2DR],Index[GEN],Index[Colour]}, FlavorIndex->SU2DR,
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159 | QuantumNumbers->{YBL->1/6, LNumber->-1/2},
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160 | Definitions->{
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161 | QR[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]],
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162 | QR[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKMp[ff,ff2] ProjP[sp1,sp2] dqp[sp2,ff2,cc]]}},
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163 | F[23] == { ClassName->dLp, Unphysical->True, SelfConjugate->False,
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164 | Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
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165 | QuantumNumbers->{YBL->-1/3, LNumber->-1},
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166 | Definitions->{ dLp[sp1_,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] dqp[sp2,ff,cc]] }},
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167 | F[24] == { ClassName->dR, Unphysical->True, SelfConjugate->False,
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168 | Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
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169 | QuantumNumbers->{YBL->-1/3},
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170 | Definitions->{ dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }},
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171 |
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172 | (* Fermions: physical fields *)
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173 | F[1] == { ClassName->vl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
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174 | ClassMembers->{ve,vm,vt}, PDG->{12,14,16},
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175 | Mass->{Mvl,{Mve,1.0*^-12},{Mvm,0.0089*^-9},{Mvt,0.0504*^-9}}, Width->0},
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176 | F[2] == { ClassName->l, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
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177 | QuantumNumbers->{Q->-1}, ClassMembers->{e,m,ta},
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178 | ParticleName->{"e-","mu-","tau-"}, AntiParticleName->{"e+","mu+","tau+"}, PDG->{11,13,15},
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179 | Mass->{Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}}, Width->0},
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180 | F[3] == { ClassName->uq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
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181 | QuantumNumbers->{Q-> 2/3}, ClassMembers->{u,c,t}, PDG->{2,4,6},
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182 | Mass->{Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}}, Width->{Wuq,0,0,{WT,1.50833649}}},
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183 | F[4] == { ClassName->dq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
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184 | QuantumNumbers->{Q->-1/3}, ClassMembers->{d,s,b}, PDG->{1,3,5},
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185 | Mass->{Mdq, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}}, Width->0},
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186 | F[5] == { ClassName->nl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
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187 | ClassMembers->{ne,nm,nt}, PDG->{6000012,6000014,6000016},
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188 | ParticleName->{"~ne","~nm","~nt"}, AntiParticleName->{"~ne~","~nm~","~nt~"},
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189 | Mass->{Mnl,{Mne,300},{Mnm,500},{Mnt,700}},
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190 | Width->{Wnl,{Wne,0},{Wnm,7.09*^-4},{Wnt,1.13}}},
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191 | F[6] == { ClassName->dqp, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
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192 | QuantumNumbers->{Q->-1/3}, ClassMembers->{dp,sp,bp}, PDG->{6000001,6000003,6000005},
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193 | Mass->{Mdqp, {MDP,301}, {MSP,501}, {MBP,701}},
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194 | Width->{Wnl,{WDP,0},{WSP,0.262},{WBP,9.85}}}
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195 | };
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196 |
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197 |
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198 | (* ************************** *)
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199 | (* ***** Parameters ***** *)
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200 | (* ************************** *)
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201 | (* Shortcuts for Higgs mixings *)
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202 | DENO := (fh[MH2]^2 (1 + gh[MH0]^2) + (gh[MH0] - gh[MH2])^2 - 2 fh[MH0] fh[MH2] (1 + gh[MH0] gh[MH2]) + fh[MH0]^2 (1 + gh[MH2]^2));
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203 | SGN := (#/Abs[#] &/@ {gh[MH0] (fh[MH2]-fh[MH3]) + gh[MH2] (fh[MH3]-fh[MH0]) + gh[MH3] (fh[MH0]-fh[MH2])})[[1]];
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204 | fh[x_] := (2 x^4 vL vR + x^2 (vL^2 + vR^2) (Sqrt[2] kk kap - 4 vL vR lam3) - 2 Sqrt[2] kk (vL^2 - vR^2)^2 lam3 kap) /
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205 | (vR (x^2 (4 kk vL vR (alp1 + alp2) + Sqrt[2] vL^2 kap) + 2 Sqrt[2] (kk^2 (alp1 + alp2) + vL^2 lam3) (vR^2 - vL^2) kap));
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206 | gh[x_] := (vL (x^2 (4 kk vL vR (alp1 + alp2) + Sqrt[2] vR^2 kap) + 2 Sqrt[2] (kk^2 (alp1 + alp2) + vR^2 lam3) (vL^2 - vR^2) kap)) /
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207 | (vR (x^2 (4 kk vL vR (alp1 + alp2) + Sqrt[2] vL^2 kap) + 2 Sqrt[2] (kk^2 (alp1 + alp2) + vL^2 lam3) (vR^2 - vL^2) kap));
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208 | NLAM1 := Sqrt[2]*kk*MH0^6*vL*vR - 4*(alp1 + alp2)^2*kap*kk^4*(vL^2 - vR^2)^2 +
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209 | MH0^4*(-2*Sqrt[2]*kk*lam3*vL*vR*(vL^2 + vR^2) + kap*(vL^2*vR^2 + kk^2*(vL^2 + vR^2))) -
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210 | 2*MH0^2*(2*Sqrt[2]*(alp1 + alp2)^2*kk^3*vL*vR*(vL^2 + vR^2) +
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211 | kap*(lam3*vL^2*vR^2*(vL^2 + vR^2) + kk^2*(4*(alp1 + alp2)*vL^2*vR^2 + lam3*(vL^2 - vR^2)^2)));
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212 | DLAM1 := 2*Sqrt[2]*kk^3*MH0^4*vL*vR - 4*kap*kk^4*lam3*(vL^2 - vR^2)^2 + 2*kk^3*MH0^2*(kap*kk - 2*Sqrt[2]*lam3*vL*vR)*(vL^2 + vR^2);
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213 | MH2AA := (vL*vR*(2*Sqrt[2]*kk^3*lam1 - kap*vL*vR) + kk*(-(kap*kk) + 2*Sqrt[2]*lam3*vL*vR)*(vL^2 + vR^2))/(Sqrt[2] kk vL vR) - MH0^2;
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214 | MH2BB := 1/(kk vL vR)*(Sqrt[2]*kap*kk^2*(4*(alp1 + alp2)*vL^2*vR^2 + lam3*(vL^2 - vR^2)^2) +
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215 | (vL^2 + vR^2)*(4*kk^3*(alp1^2 + 2*alp1*alp2 + alp2^2 - lam1*lam3)*vL*vR + Sqrt[2]*kap*(kk^4*lam1 + lam3*vL^2*vR^2)));
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216 |
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217 | M$Parameters = {
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218 | (* Gauge sector: external parameters *)
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219 | aEWM1 == { TeX->Subsuperscript[\[Alpha],w,-1], ParameterType->External, BlockName->SMINPUTS, OrderBlock->1,
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220 | Value->127.9, InteractionOrder->{QED,-2},
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221 | Description->"Inverse of the EW coupling constant at the Z pole"},
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222 | Gf == { TeX->Subscript[G,f], ParameterType->External, BlockName->SMINPUTS, OrderBlock->2,
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223 | Value->1.16637*^-5, InteractionOrder->{QED,2},
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224 | Description->"Fermi constant"},
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225 | aS == { TeX->Subscript[\[Alpha],s], ParameterType->External, BlockName->SMINPUTS, OrderBlock->3,
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226 | Value->0.1184, InteractionOrder->{QCD, 2},
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227 | Description->"Strong coupling constant at the Z pole."},
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228 | gR == { TeX->Subscript[g,R], ParameterType->External, BlockName->SMINPUTS, OrderBlock->6,
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229 | Value->0.646482210, InteractionOrder->{QED, 1},
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230 | Description->"SU(2)_R coupling constant at the Z pole"},
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231 |
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232 | (* Symmetry breaking; external parameters *)
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233 | tb == { ParameterType->External, BlockName->SMINPUTS, OrderBlock->5, Value->10.,
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234 | Description->"Ratio of the bidoublet-to-left Higgs vevs", TeX->Subscript[t,\[Beta]]},
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235 | vevp == { ParameterType->External, BlockName->SMINPUTS, OrderBlock->7,
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236 | Value->6500, InteractionOrder->{QED,-1},
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237 | Description->"SU(2)_R x U(1)BL breaking scale", TeX-> v'},
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238 |
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239 | (* Symmetry breaking: internal parameters *)
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240 | beta == { ParameterType->Internal, Value->ArcTan[tb],
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241 | Description->"Arctan of the ratio of the bidoublet-to-left Higgs vevs", TeX->\[Beta]},
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242 | vev == { ParameterType->Internal, Value->1/Sqrt[Sqrt[2] Gf], InteractionOrder->{QED,-1},
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243 | Description -> "SM Higgs vacuum expectation value", TeX ->v},
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244 | kk == { ParameterType->Internal, Value->vev*Sin[beta], InteractionOrder->{QED,-1},
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245 | Description -> "Higgs bidoublet vacuum expectation value", TeX -> k},
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246 | vL == { ParameterType->Internal, Value->vev*Cos[beta], InteractionOrder->{QED,-1},
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247 | Description -> "SU(2)L Higgs doublet vacuum expectation value", TeX->Subscript[v,L]},
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248 | vR == { ParameterType->Internal, Value->Sqrt[vevp^2-kk^2], InteractionOrder->{QED,-1},
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249 | Description -> "SU(2)R Higgs doublet vacuum expectation value", TeX->Subscript[v,R]},
|
---|
250 | tz == { ParameterType->Internal, Value->kk/vR,
|
---|
251 | Description->"Ratio of the bidoublet-to-right Higgs vevs", TeX->Subscript[t,\[Zeta]]},
|
---|
252 | zeta == { ParameterType->Internal, Value->ArcTan[tz],
|
---|
253 | Description->"Arctan of the ratio of the bidoublet-to-right Higgs vevs", TeX->\[Zeta]},
|
---|
254 |
|
---|
255 | (* Gauge sector: internal parameters *)
|
---|
256 | MW == { ParameterType->Internal, Value->Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]/aEWM1/Gf*MZ^2]],
|
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257 | Description->"W-boson mass", TeX-> Subscript[M,W]},
|
---|
258 | ee == { ParameterType->Internal, Value->Sqrt[4 Pi/aEWM1], InteractionOrder->{QED,1},
|
---|
259 | Description->"Electromagnetic coupling", TeX->e},
|
---|
260 | gs == { ParameterType->Internal, Value->Sqrt[4 Pi aS], InteractionOrder->{QCD,1},
|
---|
261 | Description->"Strong coupling at the Z pole", TeX->Subscript[g,s], ParameterName->G},
|
---|
262 | gL == { ParameterType->Internal, Value->2/vev MW, InteractionOrder->{QED,1},
|
---|
263 | Description->"SU(2)_L coupling constant at the Z pole", TeX->Subscript[g,L] },
|
---|
264 | sw == { ParameterType->Internal, Value->ee/gL,
|
---|
265 | Description->"Sine of the weak angle", TeX->Subscript[s,w]},
|
---|
266 | cw == { ParameterType->Internal, Value->Sqrt[1-sw^2],
|
---|
267 | Description->"Sine of the weak angle", TeX->Subscript[c,w]},
|
---|
268 | gY == { ParameterType->Internal, Value->ee/cw, InteractionOrder->{QED,1},
|
---|
269 | Description->"U(1)Y coupling constant at the Z pole", TeX->Subscript[g,Y]},
|
---|
270 | gBL== { ParameterType->Internal, Value->gY gR/Sqrt[gR^2-gY^2], InteractionOrder->{QED,1},
|
---|
271 | Description->"U(1)_{B-L} coupling constant at the Z pole", TeX->Subscript[g,B-L]},
|
---|
272 | sph == { ParameterType->Internal, Value->gY/gR,
|
---|
273 | Description->"Sine of the weak angle", TeX->Subscript[s,p]},
|
---|
274 | cph == { ParameterType->Internal, Value->Sqrt[1-sph^2],
|
---|
275 | Description->"Sine of the weak angle", TeX->Subscript[c,p]},
|
---|
276 | t2t== { ParameterType->Internal, Description->"Z/Z'-Mixing", TeX-> Subscript[t,2\[Theta]],
|
---|
277 | Value->(2*cph*cw*gL*gR*(cph^2*kk^2-sph^2*vL^2))/(-cph^2*kk^2*(gL^2-cph^2*cw^2*gR^2) - cph^2*gL^2*(gL^2-cw^2*gBL^2*sph^2) + cw^2*gR^2*vR^2)},
|
---|
278 | st == { ParameterType->Internal, Value->Sin[ArcTan[t2t]/2],
|
---|
279 | Description->"Sine of the weak angle", TeX->Subscript[s,t]},
|
---|
280 | ct == { ParameterType->Internal, Value->Sqrt[1-st^2],
|
---|
281 | Description->"Sine of the weak angle", TeX->Subscript[c,t]},
|
---|
282 | MWp== { ParameterType->Internal, Value->1/2 vevp gR,
|
---|
283 | Description->"W'-boson mass", TeX-> Subscript[M,W']},
|
---|
284 | MZp== { ParameterType->Internal, Value->1/2 Sqrt[ gBL^2 sph^2 vL^2 + gR^2/cph^2 (cph^4 kk^2 + vR^2) ],
|
---|
285 | Description->"Z'-boson mass", TeX-> Subscript[M,Z']},
|
---|
286 |
|
---|
287 | (* Higgs potential: external parameters *)
|
---|
288 | lam2 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 1, Value -> 0.5,
|
---|
289 | InteractionOrder -> {QED,2},
|
---|
290 | Description -> "Higgs bidoublet quartic coupling", TeX -> Subscript[\[Lambda],2]},
|
---|
291 | lam3 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 2, Value -> 1.6,
|
---|
292 | InteractionOrder -> {QED,2},
|
---|
293 | Description -> "Higgs doublet quartic coupling", TeX -> Subscript[\[Lambda],3]},
|
---|
294 | alp1 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 3, Value -> 0.3,
|
---|
295 | InteractionOrder -> {QED,2},
|
---|
296 | Description -> "Higgs doublet-bidoublet quartic coupling", TeX -> Subscript[\[Alpha],1]},
|
---|
297 | alp2 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 4, Value -> 0.1,
|
---|
298 | InteractionOrder -> {QED,2},
|
---|
299 | Description -> "Higgs doublet-bidoublet quartic coupling", TeX -> Subscript[\[Alpha],2]},
|
---|
300 | alp3 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 5, Value -> 0.3,
|
---|
301 | InteractionOrder -> {QED,2},
|
---|
302 | Description -> "Higgs doublet-bidoublet quartic coupling", TeX -> Subscript[\[Alpha],3]},
|
---|
303 | kap == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 6, Value -> -10.,
|
---|
304 | InteractionOrder -> {QED,1},
|
---|
305 | Description -> "Higgs doublet-bidoublet trilinear coupling", TeX -> \[Kappa]},
|
---|
306 |
|
---|
307 | (* Higgs potential: internal parameters *)
|
---|
308 | IDLT == { ParameterType->Internal, ComplexParameter->False,
|
---|
309 | Indices -> {Index[SU2DR], Index[SU2DRs]},
|
---|
310 | Definitions -> { IDLT[1,1]->1, IDLT[1,2]->0, IDLT[2,1]->0, IDLT[2,2]->1 },
|
---|
311 | Description -> "Delta contracting SU2DR and SU2DRs indices", TeX->\[Delta]},
|
---|
312 | UEpsRs== { ParameterType->Internal, ComplexParameter->False,
|
---|
313 | Indices -> {Index[SU2DRs], Index[SU2DRs]},
|
---|
314 | Definitions -> { UEpsRs[1,1]->0, UEpsRs[1,2]->-1, UEpsRs[2,1]-> 1, UEpsRs[2,2]->0 },
|
---|
315 | Description -> "Epsilon in SU2R space (with upper indices)", TeX->Subscript[\[Epsilon],u]},
|
---|
316 | UEpsR== { ParameterType->Internal, ComplexParameter->False,
|
---|
317 | Indices -> {Index[SU2DR], Index[SU2DR]},
|
---|
318 | Definitions -> { UEpsR[1,1]->0, UEpsR[1,2]->-1, UEpsR[2,1]-> 1, UEpsR[2,2]->0 },
|
---|
319 | Description -> "Epsilon in SU2R space (with upper indices)", TeX->Subscript[\[Epsilon],u]},
|
---|
320 | UEpsL== { ParameterType->Internal, ComplexParameter->False,
|
---|
321 | Indices -> {Index[SU2DL], Index[SU2DL]},
|
---|
322 | Definitions -> { UEpsL[1,1]->0, UEpsL[1,2]->-1, UEpsL[2,1]-> 1, UEpsL[2,2]->0 },
|
---|
323 | Description -> "Epsilon in SU2L space (with upper indices)", TeX->Subscript[\[Epsilon],u]},
|
---|
324 | DEps== { ParameterType->Internal, ComplexParameter->False,
|
---|
325 | Indices -> {Index[SU2DL], Index[SU2DL]},
|
---|
326 | Definitions -> { DEps[1,1]->0, DEps[1,2]-> 1, DEps[2,1]->-1, DEps[2,2]->0 },
|
---|
327 | Description -> "Epsilon in SU2L space (with lower indices)", TeX->Subscript[\[Epsilon],d]},
|
---|
328 | lam1 == { ParameterType->Internal, Value -> NLAM1/DLAM1,
|
---|
329 | InteractionOrder -> {QED,2},
|
---|
330 | Description -> "Higgs bidoublet quartic term", TeX->Subscript[\[Lambda],1]},
|
---|
331 | MU12 == { ParameterType->Internal, Value -> (vL^2+vR^2)(alp1+alp2) + kk^2 lam1 + vL vR kap/(Sqrt[2] kk),
|
---|
332 | Description -> "Higgs bidoublet quadratic term", TeX->Subsuperscript[\[Mu],1,2]},
|
---|
333 | MU22 == { ParameterType->Internal, Value -> kk^2(alp1+alp2) + (vL^2+vR^2)*lam3,
|
---|
334 | Description -> "Higgs doublet quadratic term", TeX->Subsuperscript[\[Mu],2,2]},
|
---|
335 | lam4 == { ParameterType->Internal, Value -> lam3 - kk kap/(Sqrt[2]vL vR),
|
---|
336 | InteractionOrder -> {QED,2},
|
---|
337 | Description -> "Higgs doublet-bidoublet quartic term", TeX->Subscript[\[Lambda],4]},
|
---|
338 |
|
---|
339 | (* Higgs masses and mixings: internal parameters *)
|
---|
340 | MHp1 == { ParameterType->Internal, Value -> Sqrt[-(2 kk vL (alp2-alp3) + Sqrt[2] kap vR)*(kk^2+vL^2)/(2 kk vL)],
|
---|
341 | Description -> "Lightest charged Higgs mass"},
|
---|
342 | MHp2 == { ParameterType->Internal, Value -> Sqrt[-(2 kk vR (alp2-alp3) + Sqrt[2] kap vL)*(kk^2+vR^2)/(2 kk vR)],
|
---|
343 | Description -> "Heaviest charged Higgs mass"},
|
---|
344 | MH1 == { ParameterType->Internal, Value -> Sqrt[2*kk^2*lam2 - kap*vL*vR/(Sqrt[2]*kk) - (alp2-alp3)*(vL^2+vR^2)],
|
---|
345 | Description -> "Next-to-lightest scalar Higgs mass"},
|
---|
346 | MH2 == { ParameterType->Internal, Value -> 1/Sqrt[2] Sqrt[MH2AA - Sqrt[MH2AA^2 + 4(MH2BB + MH0^2 MH2AA)]],
|
---|
347 | Description -> "Second scalar Higgs mass", TeX->Subscript[M,H2]},
|
---|
348 | MH3 == { ParameterType->Internal, Value -> 1/Sqrt[2] Sqrt[MH2AA + Sqrt[MH2AA^2 + 4(MH2BB + MH0^2 MH2AA)]],
|
---|
349 | Description -> "Third scalar Higgs mass", TeX->Subscript[M,H3]},
|
---|
350 | MA1 == { ParameterType->Internal, Value -> Sqrt[2*kk^2*lam2 - kap*vL*vR/(Sqrt[2]*kk) - (alp2-alp3)*(vL^2+vR^2)],
|
---|
351 | Description -> "Lightest pseudoscalar Higgs mass"},
|
---|
352 | MA2 == { ParameterType->Internal, Value -> Sqrt[ -kap/(Sqrt[2] kk vL vR) ( vL^2 vR^2 + kk^2(vL^2+vR^2)) ],
|
---|
353 | Description -> "Lightest pseudoscalar Higgs mass"},
|
---|
354 | TH == { ParameterType-> Internal, ComplexParameter->False,
|
---|
355 | Indices->{Index[SHIGGS],Index[SHIGGS]}, Unitary->True,
|
---|
356 | Value -> {
|
---|
357 | TH[1,2]-> 0, TH[2,1]-> 0, TH[2,2]-> 1, TH[2,3]-> 0, TH[2,4]-> 0, TH[3,2]-> 0, TH[4,2]-> 0,
|
---|
358 | TH[1,1]-> fh[MH0]/Sqrt[1 + fh[MH0]^2 + gh[MH0]^2],
|
---|
359 | TH[1,3]-> (fh[MH2] (1 + gh[MH0]^2) - fh[MH0] (1 + gh[MH0] gh[MH2]))/Sqrt[(1 + fh[MH0]^2 + gh[MH0]^2) DENO],
|
---|
360 | TH[1,4]-> SGN (gh[MH2] - gh[MH0])/Sqrt[DENO],
|
---|
361 | TH[3,1]-> gh[MH0]/Sqrt[1 + fh[MH0]^2 + gh[MH0]^2],
|
---|
362 | TH[3,3]-> (gh[MH2]*(1 + fh[MH0]^2) - gh[MH0]*(1 + fh[MH0]*fh[MH2]))/Sqrt[(1 + fh[MH0]^2 + gh[MH0]^2) DENO],
|
---|
363 | TH[3,4]-> SGN (fh[MH0] - fh[MH2])/Sqrt[DENO],
|
---|
364 | TH[4,1]-> 1/Sqrt[1 + fh[MH0]^2 + gh[MH0]^2],
|
---|
365 | TH[4,3]-> (fh[MH0]^2 + gh[MH0]^2 - fh[MH0]*fh[MH2] - gh[MH0]*gh[MH2])/Sqrt[(1 + fh[MH0]^2 + gh[MH0]^2) DENO],
|
---|
366 | TH[4,4]-> SGN (gh[MH0] fh[MH2] - gh[MH2] fh[MH0])/Sqrt[DENO]
|
---|
367 | }, Description-> "Scalar Higgs mixing matrix TH", TeX->Subscript[T,H]},
|
---|
368 |
|
---|
369 | (* Fermion masses: internal parameters *)
|
---|
370 | yu == { ParameterType->Internal, ComplexParameter->False,
|
---|
371 | Indices->{Index[GEN], Index[GEN]},
|
---|
372 | InteractionOrder->{QED, 1},
|
---|
373 | Definitions-> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
374 | Value -> {yu[1,1] -> Sqrt[2] MU/kk, yu[2,2] -> Sqrt[2] MC/kk, yu[3,3] -> Sqrt[2] MT/kk},
|
---|
375 | Description->"Up-type quark Yukawa couplings", TeX->Superscript[y,u]},
|
---|
376 | yd == { ParameterType->Internal, ComplexParameter->False,
|
---|
377 | Indices->{Index[GEN], Index[GEN]},
|
---|
378 | InteractionOrder->{QED, 1},
|
---|
379 | Definitions-> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
380 | Value -> {yd[1,1] -> Sqrt[2] MD/vL, yd[2,2] -> Sqrt[2] MS/vL, yd[3,3] -> Sqrt[2] MB/vL},
|
---|
381 | Description->"Down-type quark Yukawa couplings", TeX->Superscript[y,d]},
|
---|
382 | ydp== { ParameterType->Internal, ComplexParameter->False,
|
---|
383 | Indices->{Index[GEN], Index[GEN]},
|
---|
384 | InteractionOrder->{QED, 1},
|
---|
385 | Definitions-> {ydp[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
386 | Value -> {ydp[1,1] -> Sqrt[2] MDP/vR, ydp[2,2] -> Sqrt[2] MSP/vR, ydp[3,3] -> Sqrt[2] MBP/vR},
|
---|
387 | Description->"Exotic down-type quark Yukawa couplings", TeX->Superscript[y,d']},
|
---|
388 | ye == { ParameterType->Internal, ComplexParameter->False,
|
---|
389 | Indices->{Index[GEN], Index[GEN]},
|
---|
390 | InteractionOrder->{QED, 1},
|
---|
391 | Definitions-> {ye[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
392 | Value -> {ye[1,1] -> Sqrt[2] Me/kk, ye[2,2] -> Sqrt[2] MMU/kk, ye[3,3] -> Sqrt[2] MTA/kk},
|
---|
393 | Description->"Charged lepton Yukawa couplings", TeX->Superscript[y,e]},
|
---|
394 | ynu== { ParameterType->Internal, ComplexParameter->False,
|
---|
395 | Indices->{Index[GEN], Index[GEN]},
|
---|
396 | InteractionOrder->{QED, 1},
|
---|
397 | Definitions-> {ynu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
398 | Value -> {ynu[1,1] -> Sqrt[2] Mve/vL, ynu[2,2] -> Sqrt[2] Mvm/vL, ynu[3,3] -> Sqrt[2] Mvt/vL},
|
---|
399 | Description->"Neutrino Yukawa couplings", TeX->Superscript[y,\[Nu]]},
|
---|
400 | yn == { ParameterType->Internal, ComplexParameter->False,
|
---|
401 | Indices->{Index[GEN], Index[GEN]},
|
---|
402 | InteractionOrder->{QED, 1},
|
---|
403 | Definitions-> {yn[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
404 | Value -> {yn[1,1] -> Sqrt[2] Mne/vR, yn[2,2] -> Sqrt[2] Mnm/vR, yn[3,3] -> Sqrt[2] Mnt/vR},
|
---|
405 | Description->"Scotino Yukawa couplings", TeX->Superscript[y,n]},
|
---|
406 |
|
---|
407 | (* Fermion mixings: external parameters *)
|
---|
408 | CKMlam == { TeX->Subscript[\[Lambda],CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->1,
|
---|
409 | Value->0.22453, Description->"Wolfenstein parameter lambda (quark mixings)"},
|
---|
410 | CKMA == { TeX->Subscript[A,CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->2,
|
---|
411 | Value->0.836, Description->"Wolfenstein parameter A (quark mixings)"},
|
---|
412 | CKMrho == { TeX->Subscript[\[Rho],CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->3,
|
---|
413 | Value->0.122, Description->"Wolfenstein parameter rhobar (quark mixings)"},
|
---|
414 | CKMeta == { TeX->Subscript[\[Eta],CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->4,
|
---|
415 | Value->0.355, Description->"Wolfenstein parameter etabar (quark mixings)"},
|
---|
416 | PMNSs12 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->1,
|
---|
417 | Value->Sqrt[.297], Description->"Sine of theta_{12} (neutrino mixings)"},
|
---|
418 | PMNSs23 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->2,
|
---|
419 | Value->Sqrt[.425], Description->"Sine of theta_{23} (neutrino mixings)"},
|
---|
420 | PMNSs13 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->3,
|
---|
421 | Value->Sqrt[.0215], Description->"Sine of theta_{13} (neutrino mixings)"},
|
---|
422 | PMNSdel == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->4,
|
---|
423 | Value->1.38 Pi, Description->"CP phase (neutrino mixings)"},
|
---|
424 | PMNSps12 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->11,
|
---|
425 | Value->Sqrt[.297], Description->"Sine of theta_{12} (scotino mixings)"},
|
---|
426 | PMNSps23 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->12,
|
---|
427 | Value->Sqrt[.425], Description->"Sine of theta_{23} (scotino mixings)"},
|
---|
428 | PMNSps13 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->13,
|
---|
429 | Value->Sqrt[.0215], Description->"Sine of theta_{13} (scotino mixings)"},
|
---|
430 | PMNSpdel == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->14,
|
---|
431 | Value->1.38 Pi, Description->"Cp phase (scotino mixings)"},
|
---|
432 | CKMps12 == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->11,
|
---|
433 | Value->0.22453, Description->"Sine of theta_{12} (exotic down-type quark mixings)"},
|
---|
434 | CKMps23 == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->12,
|
---|
435 | Value->0.0421, Description->"Sine of theta_{23} (exotic down-type quark mixings)"},
|
---|
436 | CKMps13 == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->13,
|
---|
437 | Value->0.00364, Description->"Sine of theta_{13} (exotic down-type quark mixings)"},
|
---|
438 | CKMpdel == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->14,
|
---|
439 | Value->1.24, Description->"CP phase (exotic down-type quark mixings)"},
|
---|
440 |
|
---|
441 | (* Fermion mixings: internal parameters *)
|
---|
442 | CKMs12 == { ParameterType -> Internal, Value->CKMlam, Description->"s_{12}"},
|
---|
443 | CKMs23 == { ParameterType -> Internal, Value->CKMA*CKMlam^2, Description->"s_{23}"},
|
---|
444 | CKMs13d == { ParameterType -> Internal, Value->CKMA*CKMlam^3*Sqrt[1-CKMA^2 CKMlam^4](CKMrho + I CKMeta)/
|
---|
445 | (Sqrt[1-CKMlam^2]*(1-CKMA^2 CKMlam^4 (CKMrho + I CKMeta))), Description->"s_{13} Exp[i delta]"},
|
---|
446 | CKMc12 == { ParameterType -> Internal, Value-> Sqrt[1-CKMs12^2], Description->"c_{12}"},
|
---|
447 | CKMc13 == { ParameterType -> Internal, Value-> Sqrt[1-Abs[CKMs13d]^2], Description->"c_{13}"},
|
---|
448 | CKMc23 == { ParameterType -> Internal, Value-> Sqrt[1-CKMs23^2], Description->"c_{23}"},
|
---|
449 | CKM == { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
|
---|
450 | Value->{
|
---|
451 | CKM[1,1]-> CKMc12*CKMc13, CKM[1,2]-> CKMs12*CKMc13, CKM[1,3]->Conjugate[CKMs13d],
|
---|
452 | CKM[2,1]->-CKMs12*CKMc23-CKMc12*CKMs23*CKMs13d, CKM[2,2]-> CKMc12*CKMc23-CKMs12*CKMs23*CKMs13d, CKM[2,3]->CKMs23*CKMc13,
|
---|
453 | CKM[3,1]-> CKMs12*CKMs23-CKMc12*CKMc23*CKMs13d, CKM[3,2]->-CKMc12*CKMs23-CKMs12*CKMc23*CKMs13d, CKM[3,3]->CKMc23*CKMc13},
|
---|
454 | Description -> "CKM-Matrix", TeX-> Superscript[V,CKM]},
|
---|
455 | PMNSs13d == { ParameterType -> Internal, Value-> PMNSs13*Exp[I PMNSdel], Description->"s_{13} Exp[i delta]"},
|
---|
456 | PMNSc12 == { ParameterType -> Internal, Value-> Sqrt[1-PMNSs12^2], Description->"c_{12}"},
|
---|
457 | PMNSc13 == { ParameterType -> Internal, Value-> Sqrt[1-PMNSs13^2], Description->"c_{13}"},
|
---|
458 | PMNSc23 == { ParameterType -> Internal, Value-> Sqrt[1-PMNSs23^2], Description->"c_{23}"},
|
---|
459 | PMNS == { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
|
---|
460 | Value->{
|
---|
461 | PMNS[1,1]-> PMNSc12*PMNSc13, PMNS[1,2]-> PMNSs12*PMNSc13, PMNS[1,3]->Conjugate[PMNSs13d],
|
---|
462 | PMNS[2,1]->-PMNSs12*PMNSc23-PMNSc12*PMNSs23*PMNSs13d, PMNS[2,2]-> PMNSc12*PMNSc23-PMNSs12*PMNSs23*PMNSs13d, PMNS[2,3]->PMNSs23*PMNSc13,
|
---|
463 | PMNS[3,1]-> PMNSs12*PMNSs23-PMNSc12*PMNSc23*PMNSs13d, PMNS[3,2]->-PMNSc12*PMNSs23-PMNSs12*PMNSc23*PMNSs13d, PMNS[3,3]->PMNSc23*PMNSc13},
|
---|
464 | Description -> "PMNS-Matrix", TeX-> Superscript[V,PMNS]},
|
---|
465 | PMNSps13d == { ParameterType -> Internal, Value-> PMNSps13*Exp[I PMNSpdel], Description->"s_{13} Exp[i delta]"},
|
---|
466 | PMNSpc12 == { ParameterType -> Internal, Value-> Sqrt[1-PMNSps12^2], Description->"c_{12}"},
|
---|
467 | PMNSpc13 == { ParameterType -> Internal, Value-> Sqrt[1-PMNSps13^2], Description->"c_{13}"},
|
---|
468 | PMNSpc23 == { ParameterType -> Internal, Value-> Sqrt[1-PMNSps23^2], Description->"c_{23}"},
|
---|
469 | PMNSp== { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
|
---|
470 | Value->{
|
---|
471 | PMNSp[1,1]-> PMNSpc12*PMNSpc13, PMNSp[1,2]-> PMNSps12*PMNSpc13, PMNSp[1,3]->Conjugate[PMNSps13d],
|
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472 | PMNSp[2,1]->-PMNSps12*PMNSpc23-PMNSpc12*PMNSps23*PMNSps13d, PMNSp[2,2]-> PMNSpc12*PMNSpc23-PMNSps12*PMNSps23*PMNSps13d, PMNSp[2,3]->PMNSps23*PMNSpc13,
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473 | PMNSp[3,1]-> PMNSps12*PMNSps23-PMNSpc12*PMNSpc23*PMNSps13d, PMNSp[3,2]->-PMNSpc12*PMNSps23-PMNSps12*PMNSpc23*PMNSps13d, PMNSp[3,3]->PMNSpc23*PMNSpc13},
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474 | Description -> "PMNS'-Matrix", TeX-> Superscript[V',PMNS]},
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475 | CKMps13d == { ParameterType -> Internal, Value-> CKMps13*Exp[I CKMpdel], Description->"s_{13} Exp[i delta]"},
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476 | CKMpc12 == { ParameterType -> Internal, Value-> Sqrt[1-CKMps12^2], Description->"c_{12}"},
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477 | CKMpc13 == { ParameterType -> Internal, Value-> Sqrt[1-CKMps13^2], Description->"c_{13}"},
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478 | CKMpc23 == { ParameterType -> Internal, Value-> Sqrt[1-CKMps23^2], Description->"c_{23}"},
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479 | CKMp== { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
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480 | Value->{
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481 | CKMp[1,1]-> CKMpc12*CKMpc13, CKMp[1,2]-> CKMps12*CKMpc13, CKMp[1,3]->Conjugate[CKMps13d],
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482 | CKMp[2,1]->-CKMps12*CKMpc23-CKMpc12*CKMps23*CKMps13d, CKMp[2,2]-> CKMpc12*CKMpc23-CKMps12*CKMps23*CKMps13d, CKMp[2,3]->CKMps23*CKMpc13,
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483 | CKMp[3,1]-> CKMps12*CKMps23-CKMpc12*CKMpc23*CKMps13d, CKMp[3,2]->-CKMpc12*CKMps23-CKMps12*CKMpc23*CKMps13d, CKMp[3,3]->CKMpc23*CKMpc13},
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484 | Description -> "CKM'-Matrix", TeX-> Superscript[V',CKM]},
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485 |
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486 | (* Effective Higgs couplings *)
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487 | Ghgg == { ParameterType -> External, InteractionOrder->{HIG,1}, TeX->Subscript[g,hgg], Description -> "Loop-induced h0-gluon coupling",
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488 | BlockName -> EffectiveHiggs, OrderBlock->1, Value -> 0.12},
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489 | Ghaa == { ParameterType -> External, InteractionOrder->{HIG,1}, TeX->Subscript[g,haa], Description -> "Loop-induced h0-photon coupling",
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490 | BlockName -> EffectiveHiggs, OrderBlock->2, Value -> 0.11}
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491 | };
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492 |
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493 | (* ************************** *)
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494 | (* ***** Lagrangian ***** *)
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495 | (* ************************** *)
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496 | (* LVector *)
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497 | LVector := Plus@@ (Block[{aa,mu,nu}, -1/4 If[Abelian, FS[GaugeBoson,mu,nu]^2, FS[GaugeBoson,mu,nu,aa]^2] /.MR$GaugeGroupRules[#]] & /@ MR$GaugeGroupList);
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498 |
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499 | (* LMatter *)
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500 | LMatter := Block[{mu}, I*(
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501 | QLbar.Ga[mu].DC[QL, mu] + QRbar.Ga[mu].DC[QR, mu] + dLpbar.Ga[mu].DC[dLp, mu] + dRbar.Ga[mu].DC[dR, mu] +
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502 | LLbar.Ga[mu].DC[LL, mu] + LRbar.Ga[mu].DC[LR, mu] + NLbar.Ga[mu].DC[NL, mu] + VRbar.Ga[mu].DC[VR, mu])];
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503 |
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504 | (* Scalar potential *)
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505 | VHiggs:= Block[{II,IIp,JJ,JJp,JJpp,KK,KKp,LL,LLp,LLpp},
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506 | - MU22 (chiLbar[II] chiL[II] + chiRbar[II] chiR[II])\
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507 | - MU12 (Phibar[II,JJ] Phi[II,JJ]) \
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508 | + lam1 (Phibar[II,JJ] Phi[II,JJ]) (Phibar[KK,LL]Phi[KK,LL]) \
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509 | + lam2 (Phi[II, JJ] UEpsRs[JJ, JJp] DEps[II, IIp] Phi[IIp, JJp]) HC[Phi[KK, LL] UEpsRs[LL, LLp] DEps[KK, KKp] Phi[KKp, LLp]] \
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510 | + lam3 ( chiLbar[II] chiL[II] chiLbar[JJ] chiL[JJ] + chiRbar[II] chiR[II] chiRbar[JJ] chiR[JJ]) \
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511 | + 2 lam4 chiLbar[II] chiL[II] chiRbar[JJ] chiR[JJ] \
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512 | + kap (chiLbar[II] Phi[II, JJ] IDLT[JJp, JJ] chiR[JJp] + chiRbar[JJp] IDLT[JJp, JJ] Phibar[II, JJ] chiL[II]) \
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513 | + 2 alp1 (Phibar[II,JJ] Phi[II,JJ]) (chiLbar[KK] chiL[KK] + chiRbar[KK] chiR[KK]) \
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514 | + 2 alp2 (chiLbar[II] Phi[II, JJ] chiL[KK] Phibar[KK, JJ] + IDLT[II, IIp] IDLT[KK, KKp] Phibar[JJ, IIp] chiRbar[II] Phi[JJ, KKp] chiR[KK]) \
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515 | + 2 alp3 HC[chiL[II] UEpsRs[JJ,JJp] DEps[II,IIp] Phi[IIp,JJp]] (chiL[KK] UEpsRs[JJ,LLp] DEps[KK,KKp] Phi[KKp,LLp]) \
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516 | + 2 alp3 chiRbar[JJpp] IDLT[JJpp,JJ] UEpsRs[JJ,JJp] DEps[II,IIp] Phi[IIp,JJp] HC[chiRbar[LLpp] IDLT[LLpp,LL] UEpsRs[LL,LLp] DEps[II,KKp] Phi[KKp,LLp]]];
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517 |
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518 | (* Higgs Lagrangian *)
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519 | LHiggs:= DC[Phibar[II,JJ],mu] DC[Phi[II,JJ],mu] + DC[chiLbar[II],mu] DC[chiL[II],mu] + DC[chiRbar[II],mu] DC[chiR[II],mu] - VHiggs;
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520 |
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521 | (* Yukawa Lagrangian *)
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522 | LYuk:= Block[{sp1,ff1,ff2,ff3,cc,ii,iip,jj,jjp,jjpp},
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523 | yu[ff1,ff2] QLbar[sp1,ii,ff1,cc].QR[sp1,jjpp,ff2,cc] IDLT[jjpp,jj] DEps[ii,iip] UEpsRs[jj,jjp] Phibar[iip, jjp] \
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524 | - yd[ff2,ff3] CKM[ff1,ff2] QLbar[sp1,ii,ff1,cc].dR[sp1,ff3,cc] chiL[ii] \
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525 | - ydp[ff2,ff3] CKMp[ff1,ff2] QRbar[sp1,ii,ff1,cc].dLp[sp1,ff3,cc] chiR[ii] \
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526 | - ye[ff1,ff2] LLbar[sp1,ii,ff1].LR[sp1,jj,ff2] IDLT[jj,jjp] Phi[ii,jjp] \
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527 | + ynu[ff2,ff3] PMNS[ff1,ff2] LLbar[sp1,ii,ff1].VR[sp1,ff3] UEpsL[ii,jj] chiLbar[jj] \
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---|
528 | + yn[ff2,ff3] PMNSp[ff1,ff2] LRbar[sp1,ii,ff1].NL[sp1,ff3] UEpsR[ii,jj] chiRbar[jj] ];
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529 |
|
---|
530 | (* Ghost Lagrangian *)
|
---|
531 | LGhost:= - ghGbar.del[DC[ghG,mu],mu];
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---|
532 |
|
---|
533 | (* Effective Higgs couplings *)
|
---|
534 | LagHEffective := Block[{mu,nu,aa}, -1/4 Ghaa H0 FS[A,mu,nu] FS[A,mu,nu] -1/4 Ghgg H0 FS[G,mu,nu,aa] FS[G,mu,nu,aa] ];
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535 |
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