| 1 | (* *********************************************************** *)
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| 2 | (* ***** ***** *)
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| 3 | (* ***** FeynRules model file: LRSM w/Higgs triplets ***** *)
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| 4 | (* ***** Authors: A. Alloul, B. 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$ModelName = "LRSM";
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| 12 |
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| 13 | M$Information = {
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| 14 | Authors -> {"Adam Alloul", "Benjamin Fuks", "Michel Rausch de Traubenberg"},
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| 15 | Emails -> {"adam.alloul@iphc.cnrs.fr", "benjamin.fuks@iphc.cnrs.fr","michel.rausch@iphc.cnrs.fr"},
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| 16 | Institutions -> {"IPHC Strasbourg / University of Strasbourg"},
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| 17 | Date -> "02.01.13", Version->"1.05", References -> "A. Alloul, K. De Causmaecker, J. D'Hondt, B. Fuks, M. Rausch de Traubenberg, EPJC (2013), arXiv: 1301.5932 [hep-ph]", URLs -> "https://feynrules.irmp.ucl.ac.be/raw-attachment/wiki/ASperGe/LRSM_mix.fr"
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| 18 | };
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| 19 |
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| 20 | (* Change log *)
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| 21 | (* v1.05 02.01.13 : Fixed mixings in neutrinos sector *)
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| 22 | (* v1.05 02.01.13 : Added yl2 and corrected a sign in the higgs potential *)
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| 23 | (* v1.04 22.01.13 : Added yq2 to the yukawa lagrangian *)
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| 24 | (* v1.03 22.01.13 : Fixed mixing relations for quarks and leptons and added the square for mu1 and mu2 in scalar pot *)
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| 25 | (* v1.02 22.11.12 : Added the minimization equations for the bilinear terms *)
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| 26 | (* v1.01 15.11.12 : minus instead of a plus in front of the kinetic terms of the higgses -> corrected *)
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| 27 | (*Remove the epsilons in the yukawa*)
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| 28 |
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| 29 | (* ************************** *)
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| 30 | (* ***** Gauge groups ***** *)
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| 31 | (* ************************** *)
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| 32 | M$GaugeGroups = {
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| 33 | U1BL == { Abelian -> True, CouplingConstant -> gBL, GaugeBoson -> B, Charge->YBL },
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| 34 | SU2L == { Abelian -> False, CouplingConstant -> gL, GaugeBoson -> WLi, StructureConstant -> epL, Representations -> {TL,SU2DL},
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| 35 | Definitions -> {TL[Index[SU2WL,a_],b__]->PauliSigma[Index[SU2WL,a],b]/2, epL->Eps} },
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| 36 | SU2R == { Abelian -> False, CouplingConstant -> gR, GaugeBoson -> WRi, StructureConstant -> epR, Representations -> {TR,SU2DR},
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| 37 | Definitions -> {TR[Index[SU2WR,a_],i_,j_]->-PauliSigma[Index[SU2WR,a],j,i]/2, epR->Eps} },
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| 38 | SU3C == { Abelian -> False, CouplingConstant -> gs, GaugeBoson -> G, StructureConstant -> f, Representations -> {T,Colour} }
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| 39 | };
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| 40 |
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| 41 |
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| 42 | (* ************************** *)
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| 43 | (* *** Interaction orders *** *)
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| 44 | (* ************************** *)
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| 45 | M$InteractionOrderHierarchy = { {QCD, 1}, {QED, 2} };
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| 46 |
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| 47 |
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| 48 | (* ************************** *)
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| 49 | (* ***** vevs & mixings ***** *)
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| 50 | (* ************************** *)
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| 51 |
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| 52 | M$vevs = { {hL[1], vL/Sqrt[2]}, {hL[2], -I vL/Sqrt[2]}, {hR[1], vR/Sqrt[2]}, {hR[2], -I*vR/Sqrt[2]}, {DeltaL0, vL}, {DeltaR0, vR}, {h1[1,1], v1}, {h1[2,2], v1p} };
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| 53 |
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| 54 |
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| 55 | M$MixingsDescription={
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| 56 |
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| 57 | (* *********************************************************** *)
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| 58 | (* **** Gauge Bosons **** *)
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| 59 | (* *********************************************************** *)
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| 60 | (* First step: from triplet to T3 eigenstates *)
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| 61 | Mix["1a"] == { MassBasis -> {WL, WLbar}, GaugeBasis -> {WLi[1], WLi[2]}, Value -> {{1/Sqrt[2], -I/Sqrt[2]}, {1/Sqrt[2], I/Sqrt[2]}} },
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| 62 | Mix["1b"] == { MassBasis -> {WR, WRbar}, GaugeBasis -> {WRi[1], WRi[2]}, Value -> {{1/Sqrt[2], -I/Sqrt[2]}, {1/Sqrt[2], I/Sqrt[2]}} },
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| 63 |
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| 64 | (* Second step: from T3 eigenstates to mass-eigenstates *)
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| 65 | Mix["1c"] == { MassBasis -> {A, Z, Zp}, GaugeBasis -> {WLi[3], WRi[3], B}, MixingMatrix->UVN, BlockName->VNMix},
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| 66 | Mix["1d"] == { MassBasis -> {W, Wp}, GaugeBasis -> {WL, WR}, MixingMatrix->UVC, BlockName->VCMix},
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| 67 |
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| 68 | (* *********************************************************** *)
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| 69 | (* **** Higgses **** *)
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| 70 | (* *********************************************************** *)
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| 71 | (* First step: from triplet to T3 eigenstates *)
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| 72 | Mix["2a"] == { MassBasis -> {DeltaLpp,DeltaL0}, GaugeBasis -> {hL[1],hL[2]}, Value -> { {1/Sqrt[2],-I/Sqrt[2]},{1/Sqrt[2],I/Sqrt[2]} }},
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| 73 | Mix["2b"] == { MassBasis -> {DeltaRpp,DeltaR0}, GaugeBasis -> {hR[1],hR[2]}, Value -> { {1/Sqrt[2],-I/Sqrt[2]},{1/Sqrt[2],I/Sqrt[2]} }},
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| 74 |
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| 75 | (* Second step: from T3 eigenstates to mass-eigenstates *)
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| 76 | Mix["2c"] == { MassBasis -> {DH1,DH2}, GaugeBasis -> {DeltaLpp,DeltaRpp}, MixingMatrix->UHD, BlockName->HDMix},
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| 77 | Mix["2d"] == { MassBasis -> {GP1,GP2,H1,H2}, GaugeBasis -> {hL[3],hR[3],h1[1,2], h1bar[2,1]}, MixingMatrix->UHC, BlockName -> HCMix},
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| 78 | Mix["2e"] == { MassBasis -> {{h01,h02,h03,h04},{G01,G02,a01,a02}}, GaugeBasis->{DeltaL0,DeltaR0,h1[1,1],h1[2,2]}, MixingMatrix->{UHN,UAN}, BlockName->{HMix,AMix}},
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| 79 |
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| 80 | (* *********************************************************** *)
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| 81 | (* **** Fermions **** *)
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| 82 | (* *********************************************************** *)
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| 83 |
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| 84 | Mix["4a"] == {MassBasis -> {dq[1, _], dq[2, _], dq[3, _]}, GaugeBasis -> {{QL[2, 1, _], QL[2, 2, _], QL[2, 3, _]}, {CC[QR][2,1, _], CC[QR][2,2, _], CC[QR][2,3, _]}},
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| 85 | MixingMatrix -> {CKML, CKMR}, BlockName->{VCKML,VCKMR}, Inverse -> {True,True} },
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| 86 |
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| 87 | Mix["4b"] == {MassBasis -> {uq[1, _], uq[2, _], uq[3, _]}, GaugeBasis -> {{QL[1, 1, _], QL[1, 2, _], QL[1, 3, _]}, {CC[QR][1,1, _], CC[QR][1,2, _], CC[QR][1,3, _]}},
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| 88 | Value -> {{{1,0,0},{0,1,0},{0,0,1}},{{1,0,0},{0,1,0},{0,0,1}}}},
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| 89 |
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| 90 | Mix["5a"] == {MassBasis -> {l[1], l[2], l[3]}, GaugeBasis -> {{LL[2, 1], LL[2, 2], LL[2, 3]}, {CC[LR][2,1], CC[LR][2,2], CC[LR][2,3]}},
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| 91 | Value -> {{{1,0,0},{0,1,0},{0,0,1}},{{1,0,0},{0,1,0},{0,0,1}}}},
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| 92 |
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| 93 | Mix["5b"] == {MassBasis -> {vl[1], vl[2], vl[3],Nl[1], Nl[2],Nl[3]},
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| 94 | GaugeBasis -> {{LL[1, 1], LL[1, 2], LL[1, 3],LR[1,1],LR[1,2],LR[1,3]},
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| 95 | {CC[LL][1, 1], CC[LL][1, 2], CC[LL][1, 3],CC[LR][1, 1], CC[LR][1, 2], CC[LR][1, 3]} },
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| 96 | MixingMatrix -> {PMNSL, PMNSR}, BlockName -> {PMNSMIX, PMNSRMIX}}
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| 97 |
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| 98 | };
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| 99 |
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| 100 |
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| 101 |
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| 102 | (* ************************** *)
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| 103 | (* ***** Indices ***** *)
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| 104 | (* ************************** *)
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| 105 | (* Gauge indices *)
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| 106 | IndexRange[Index[SU2WL]] = Unfold[Range[3]]; IndexStyle[SU2WL,j];
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| 107 | IndexRange[Index[SU2WR]] = Unfold[Range[3]]; IndexStyle[SU2WR,j];
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| 108 | IndexRange[Index[SU2DL]] = Unfold[Range[2]]; IndexStyle[SU2DL,k];
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| 109 | IndexRange[Index[SU2DR]] = Unfold[Range[2]]; IndexStyle[SU2DR,k];
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| 110 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]]; IndexStyle[Gluon, a];
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| 111 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]]; IndexStyle[Colour, m];
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| 112 |
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| 113 | (* "Generation" indices *)
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| 114 | IndexRange[Index[GEN ]] = Range[3]; IndexStyle[GEN, f];
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| 115 | IndexRange[Index[SHIG]] = Range[4]; IndexStyle[SHIG,n];
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| 116 | IndexRange[Index[PHIG]] = Range[2]; IndexStyle[PHIG,n];
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| 117 | IndexRange[Index[CHIG]] = Range[2]; IndexStyle[CHIG,n];
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| 118 | IndexRange[Index[DHIG]] = Range[2]; IndexStyle[DHIG,n];
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| 119 |
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| 120 |
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| 121 | (* ************************** *)
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| 122 | (* ***** Fields ***** *)
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| 123 | (* ************************** *)
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| 124 | M$ClassesDescription = {
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| 125 |
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| 126 | (* *********************************************************** *)
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| 127 | (* **** Unphysical Gauge Bosons **** *)
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| 128 | (* *********************************************************** *)
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| 129 | (* SU(2) triplets and U(1) *)
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| 130 | V[11] == { ClassName->B, Unphysical->True, SelfConjugate->True },
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| 131 | V[12] == { ClassName->WLi, Unphysical->True, SelfConjugate->True, Indices->{Index[SU2WL]}, FlavorIndex->SU2WL},
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| 132 | V[13] == { ClassName->WRi, Unphysical->True, SelfConjugate->True, Indices->{Index[SU2WR]}, FlavorIndex->SU2WR},
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| 133 | (* T3 eigenstates *)
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| 134 | V[22] == { ClassName->WL, Unphysical->True, SelfConjugate->False},
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| 135 | V[23] == { ClassName->WR, Unphysical->True, SelfConjugate->False},
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| 136 |
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| 137 | (* *********************************************************** *)
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| 138 | (* **** Physical Gauge Bosons **** *)
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| 139 | (* *********************************************************** *)
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| 140 | (* Neutral weak bosons *)
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| 141 | V[1] == { ClassName->A, SelfConjugate->True, Mass->0, Width->0, ParticleName->"a", PDG->22, PropagatorLabel->"A", PropagatorType->Sine, PropagatorArrow->None},
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| 142 | V[2] == { ClassName->Z, SelfConjugate->True, Mass->MZ, Width->WZ, ParticleName->"Z", PDG->23, PropagatorLabel->"Z", PropagatorType->Sine, PropagatorArrow->None},
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| 143 | V[3] == { ClassName->Zp, SelfConjugate->True, Mass->MZp, Width->WZp, ParticleName->"Zp", PDG->32, PropagatorLabel->"Zp", PropagatorType->Sine, PropagatorArrow->None},
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| 144 | (* Charge weak bosons *)
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| 145 | V[4] == { ClassName->W, SelfConjugate->False, Mass->MW, Width->WW, ParticleName->"W+", PDG->24, PropagatorLabel->"W", PropagatorType->Sine,
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| 146 | PropagatorArrow->Forward, AntiParticleName->"W-", QuantumNumbers->{Q->1} },
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| 147 | V[5] == { ClassName->Wp, SelfConjugate->False, Mass->MWp, Width->WWp, ParticleName->"Wp+", PDG->34, PropagatorLabel->"Wp", PropagatorType->Sine,
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| 148 | PropagatorArrow->Forward, AntiParticleName->"Wp-", QuantumNumbers->{Q->1} },
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| 149 | (* QCD *)
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| 150 | V[6] == { ClassName->G, SelfConjugate->True, Mass->0, Width->0, ParticleName->"g", PDG->21, PropagatorLabel->"G", PropagatorType->C, PropagatorArrow->None,
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| 151 | Indices->{Index[Gluon]} },
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| 152 |
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| 153 | (* *********************************************************** *)
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| 154 | (* **** Unphysical higgses **** *)
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| 155 | (* *********************************************************** *)
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| 156 | (* Bidoublets, triplets, singlet *)
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| 157 | S[21] == { ClassName->h1, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2DL],Index[SU2DR]}, FlavorIndex->SU2DL},
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| 158 | S[22] == { ClassName->hL, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2WL]}, FlavorIndex->SU2WL, QuantumNumbers->{YBL->1} },
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| 159 | S[23] == { ClassName->hR, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2WR]}, FlavorIndex->SU2WR, QuantumNumbers->{YBL->1} },
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| 160 |
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| 161 | (* T3 eigenstates for the triplets *)
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| 162 | S[221] == { ClassName -> DeltaL0, Unphysical -> True, SelfConjugate -> False},
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| 163 | S[222] == { ClassName -> DeltaLpp, Unphysical -> True, SelfConjugate -> False},
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| 164 | S[231] == { ClassName -> DeltaR0, Unphysical -> True, SelfConjugate -> False},
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| 165 | S[232] == { ClassName -> DeltaRpp, Unphysical -> True, SelfConjugate -> False},
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| 166 |
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| 167 | (* *********************************************************** *)
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| 168 | (* **** Physical higgses **** *)
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| 169 | (* *********************************************************** *)
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| 170 | (* Four neutral scalars*)
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| 171 | S[1] == { ClassName->h0, SelfConjugate->True, Indices->{Index[SHIG]}, FlavorIndex->SHIG, ClassMembers->{h01,h02,h03,h04},
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| 172 | Mass->{Mh0,Mh01,Mh02,Mh03,Mh04}, Width->{Wh01,Wh02,Wh03,Wh04,Wh05}, PDG->{25,35,45,9000025},
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| 173 | ParticleName->{"h01","h02","h03","h04"}, PropagatorLabel->{"h0","h01","h02","h03","h04"}, PropagatorType->ScalarDash, PropagatorArrow->None},
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| 174 |
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| 175 | (*Two neutral pseudoscalars*)
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| 176 | S[2] == { ClassName->a0, SelfConjugate->True, Indices->{Index[PHIG]}, FlavorIndex->PHIG, ClassMembers->{a01,a02},
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| 177 | Mass->{MA0,MA01}, Width->{WA01,WA02}, PDG->{36,46},
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| 178 | ParticleName->{"a01","a02"}, PropagatorLabel->{"a0","a01","a02"}, PropagatorType->ScalarDash, PropagatorArrow->None},
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| 179 |
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| 180 | (*Two singly charged*)
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| 181 | S[3] == { ClassName->H, SelfConjugate->False, Indices->{Index[CHIG]}, FlavorIndex->CHIG, ClassMembers->{H1,H2},
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| 182 | Mass->{MH,MH1,MH2}, Width->{WH1,WH2}, PDG->{37,9000037}, QuantumNumbers->{Q-> 1},
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| 183 | ParticleName->{"H1+","H2+"}, AntiParticleName->{"H1-","H2-"}, PropagatorLabel->{"H","H1","H2"}, PropagatorType->ScalarDash, PropagatorArrow->Forward },
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| 184 |
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| 185 | (*Two doubly charged*)
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| 186 | S[4] == { ClassName->DH, SelfConjugate->False, Indices->{Index[DHIG]}, FlavorIndex->DHIG, ClassMembers->{DH1,DH2},
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| 187 | Mass->{MDH,MDH1,MDH2}, Width->{WDH1,WDH2}, PDG->{9000055,9000056}, QuantumNumbers->{Q-> 2},
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| 188 | ParticleName->{"H1++","H2++"}, AntiParticleName->{"H1--","H2--"}, PropagatorLabel->{"DH","DH1","DH2"}, PropagatorType->ScalarDash, PropagatorArrow->Forward},
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| 189 |
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| 190 | (* Goldstones *)
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| 191 | S[10] == { ClassName->G01, SelfConjugate->True, Goldstone->Z, Mass->MZ, Width->WG01, PDG->250,
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| 192 | ParticleName->"G01", PropagatorLabel->"G01", PropagatorType->D, PropagatorArrow->None },
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| 193 | S[11] == { ClassName->G02, SelfConjugate->True, Goldstone->Zp, Mass->MZp, Width->WG02, PDG->251,
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| 194 | ParticleName->"G02", PropagatorLabel->"G02", PropagatorType->D, PropagatorArrow->None },
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| 195 | S[12] == { ClassName->GP1, SelfConjugate->False, Goldstone->W, Mass->MW, Width->WGP1, PDG->252, QuantumNumbers->{Q->1},
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| 196 | ParticleName -> "G1+", AntiParticleName->"G1-", PropagatorLabel->"GP1", PropagatorType->D, PropagatorArrow->None },
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| 197 | S[13] == { ClassName->GP2, SelfConjugate->False, Goldstone->Wp, Mass->MWp, Width->WGP2, PDG->253, QuantumNumbers->{Q->1},
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| 198 | ParticleName -> "G2+", AntiParticleName->"G2-", PropagatorLabel->"GP2", PropagatorType->D, PropagatorArrow->None },
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| 199 |
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| 200 |
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| 201 |
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| 202 | (* *********************************************************** *)
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| 203 | (* **** Unphysical Dirac Fermions **** *)
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| 204 | (* *********************************************************** *)
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| 205 | F[31] == { ClassName->LL, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2DL],Index[GEN]}, FlavorIndex->SU2DL, QuantumNumbers->{YBL->-1/2} },
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| 206 | F[32] == { ClassName->LR, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2DR],Index[GEN]}, FlavorIndex->SU2DR, QuantumNumbers->{YBL-> 1/2} },
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| 207 | F[13] == { ClassName->QL, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2DL],Index[GEN],Index[Colour ]}, FlavorIndex->SU2DL, QuantumNumbers->{YBL -> 1/6}},
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| 208 | F[34] == { ClassName->QR, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2DR],Index[GEN],Index[Colour]}, FlavorIndex->SU2DR, QuantumNumbers->{YBL-> -1/6}},
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| 209 |
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| 210 |
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| 211 |
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| 212 | (* *********************************************************** *)
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| 213 | (* **** Physical Dirac Fermions **** *)
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| 214 | (* *********************************************************** *)
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| 215 |
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| 216 | F[5] == { ClassName->vl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, ParticleName->{"ve","vm","vt"}, AntiParticleName->{"ve~","vm~","vt~"},
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| 217 | ClassMembers->{ve,vm,vt}, Mass->{Mvl,Mve,Mvm,Mvt}, Width->0, PDG->{12,14,16}, PropagatorLabel->{"v","ve","vm","vt"}, PropagatorType->Straight, PropagatorArrow->Forward},
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| 218 |
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| 219 | F[6] == { ClassName->Nl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, ParticleName->{"Ne","Nm","Nt"}, AntiParticleName->{"Ne~","Nm~","Nt~"},
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| 220 | ClassMembers->{Ne,Nm,Nt}, Mass->{MNl,MNe,MNm,MNt}, Width->{WNl,WNe,WNm,WNt}, PDG->{6000012,6000014,6000016}, PropagatorLabel->{"Nl","Ne","Nm","Nt"}, PropagatorType->Straight, PropagatorArrow->Forward},
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| 221 |
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| 222 | F[7] == { ClassName->l, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, QuantumNumbers->{Q->-1}, ParticleName->{"e-","mu-","tau-"}, AntiParticleName->{"e+","mu+","tau+"},
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| 223 | ClassMembers->{e,m,ta}, Mass->{Ml,Me,Mm,Mta}, Width->0, PDG->{11,13,15}, PropagatorLabel->{"l","e","mu","tau"}, PropagatorType->Straight, PropagatorArrow->Forward},
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| 224 |
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| 225 | F[8] == { ClassName->uq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, QuantumNumbers->{Q-> 2/3}, ParticleName->{"u","c","t"}, AntiParticleName->{"u~","c~","t~"},
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| 226 | ClassMembers->{u,c,t}, Mass->{Muq,MU,MC,MT}, Width->{Wuq,0,0,WT}, PDG->{2,4,6}, PropagatorLabel->{"uq","u","c","t"}, PropagatorType->Straight, PropagatorArrow->Forward},
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| 227 |
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| 228 | F[9] == { ClassName->dq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, QuantumNumbers->{Q->-1/3}, ParticleName->{"d","s","b"}, AntiParticleName->{"d~","s~","b~"},
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| 229 | ClassMembers->{d,s,b}, Mass->{Mdq,MD,MS,MB}, Width->0, PDG->{1,3,5}, PropagatorLabel->{"dq","d","s","b"}, PropagatorType->Straight, PropagatorArrow->Forward}
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| 230 | };
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| 231 |
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| 232 |
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| 233 | (* ************************** *)
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| 234 | (* ***** Parameters ***** *)
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| 235 | (* ************************** *)
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| 236 | M$Parameters = {
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| 237 |
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| 238 | (* *********************************************************** *)
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| 239 | (* **** Higgses vevs **** *)
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| 240 | (* *********************************************************** *)
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| 241 | (* *)
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| 242 | vR == { TeX->Subscript[v,"R"], ParameterType->External, ComplexParameter->False, BlockName->FRVevs, OrderBlock->1, Value -> 1000, InteractionOrder->{QED,-1}, Description->"SU(2)_R Higgs triplet vacuum expectation value"},
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| 243 |
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| 244 | vL == { TeX->Subscript[v,"L"], ParameterType->External, ComplexParameter->False, InteractionOrder->{QED,-1}, BlockName -> FRVevs, OrderBlock -> 2, Value -> 0, Description->"SU(2)_L Higgs triplet vacuum expectation value"},
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| 245 |
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| 246 | v1 == { TeX->Subscript[v,1], ParameterType->External, ComplexParameter->False, InteractionOrder->{QED,-1},BlockName -> FRVevs, OrderBlock -> 3, Value -> 248, Description->"Higgs bidoublet vacuum expectation value"},
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| 247 |
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| 248 | v1p == { TeX->Subsuperscript[v,1,"'"], ParameterType->External, ComplexParameter->False, InteractionOrder->{QED,-1}, BlockName -> FRVevs, OrderBlock -> 4, Value -> 0,Description->"Higgs bidoublet second vacuum expectation value"},
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| 249 |
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| 250 |
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| 251 | (* *********************************************************** *)
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| 252 | (* **** Coupling constants **** *)
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| 253 | (* *********************************************************** *)
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| 254 | (* External parameters *)
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| 255 | aEWM1 == { TeX->Subsuperscript[\[Alpha],w,-1], ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->1, Value->127.9, InteractionOrder->{QED,-2}, Description->"Inverse of the EW coupling constant at the Z pole"},
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| 256 | aS == { TeX->Subscript[\[Alpha],s], ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->5, InteractionOrder->{QCD, 2}, Description->"Strong coupling constant at the Z pole."},
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| 257 | gR == { TeX->Subscript[g,R], ParameterType->External, ComplexParameter->False, BlockName->Gauge, OrderBlock->4, Value -> 0.646482210, InteractionOrder->{QED, 1}, Description->"SU(2)_R coupling constant at the Z pole"},
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| 258 |
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| 259 | gL == { TeX->Subscript[g,L], ParameterType->External, ComplexParameter->False, BlockName -> Gauge, OrderBlock -> 2, Value->0.646482210, InteractionOrder->{QED,1}, Description->"SU(2)_L coupling constant at the Z pole"},
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| 260 | gY == { TeX->Subscript[g,Y], ParameterType->External, ComplexParameter->False, BlockName -> Gauge, OrderBlock -> 1, Value-> 0.360966847, InteractionOrder->{QED,1}, Description->"U(1)Y coupling constant at the Z pole"},
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| 261 |
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| 262 | (* *********************************************************** *)
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| 263 | (* **** Electroweak mixings **** *)
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| 264 | (* *********************************************************** *)
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| 265 | (* Internal parameters *)
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| 266 | gBL== { TeX->Subscript[g,B-L],ParameterType->Internal, ComplexParameter->False, Value->gY gR/Sqrt[gR^2-gY^2], InteractionOrder->{QED,1}, Description->"U(1)_{B-L} coupling constant at the Z pole"},
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| 267 |
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| 268 | gs == { TeX->Subscript[g,s], ParameterType->Internal, ComplexParameter->False, Value->Sqrt[4 Pi aS], InteractionOrder->{QCD,1}, ParameterName->G, Description->"Strong coupling constant"},
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| 269 |
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| 270 | (* *********************************************************** *)
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| 271 | (* **** Yukawas **** *)
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| 272 | (* *********************************************************** *)
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| 273 |
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| 274 | (* External parameters *)
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| 275 | Ryq1 == { ParameterType->External, ComplexParameter->False, BlockName->YQ1, Indices->{Index[GEN],Index[GEN]}, Description->"Quark Yukawa matrix 1 (real part)"},
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| 276 | Iyq1 == { ParameterType->External, ComplexParameter->False, BlockName->IMYQ1, Indices->{Index[GEN],Index[GEN]}, Description->"Quark Yukawa matrix 1 (imaginary part)"},
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| 277 |
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| 278 | Ryq2 == { ParameterType->External, ComplexParameter->False, BlockName->YQ2, Indices->{Index[GEN],Index[GEN]}, Description->"Quark Yukawa matrix 2 (real part)"},
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| 279 | Iyq2 == { ParameterType->External, ComplexParameter->False, BlockName->IMYQ2, Indices->{Index[GEN],Index[GEN]}, Description->"Quark Yukawa matrix 2 (imaginary part)"},
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| 280 |
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| 281 | Ryl1 == { ParameterType->External, ComplexParameter->False, BlockName->YL1, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 1 (real part)"},
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| 282 | Iyl1 == { ParameterType->External, ComplexParameter->False, BlockName->IMYL1, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 1 (imaginary part)"},
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| 283 |
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| 284 | Ryl2 == { ParameterType->External, ComplexParameter->False, BlockName->YL2, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 2 (real part)"},
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| 285 | Iyl2 == { ParameterType->External, ComplexParameter->False, BlockName->IMYL2, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 2 (imaginary part)"},
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| 286 |
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| 287 | Ryl3 == { ParameterType->External, ComplexParameter->False, BlockName->YL3, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 3 (real part)"},
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| 288 | Iyl3 == { ParameterType->External, ComplexParameter->False, BlockName->IMYL3, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 3 (imaginary part)"},
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| 289 |
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| 290 | Ryl4 == { ParameterType->External, ComplexParameter->False, BlockName->YL4, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 4 (real part)"},
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| 291 | Iyl4 == { ParameterType->External, ComplexParameter->False, BlockName->IMYL4, Indices->{Index[GEN],Index[GEN]}, Description->"Lepton Yukawa matrix 4 (imaginary part)"},
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|---|
| 292 |
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| 293 |
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|---|
| 294 | (* Quartic terms for bidoublets *)
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|---|
| 295 | RLAM1 == { ParameterType->External, ComplexParameter->False, BlockName->HLAM, OrderBlock->1, Description->"1st bidoublet quartic term (real part)"},
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| 296 | ILAM1 == { ParameterType->External, ComplexParameter->False, BlockName->IMHLAM, OrderBlock->1, Description->"1st bidoublet quartic term (imaginary part)"},
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|---|
| 297 |
|
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| 298 | RLAM2 == { ParameterType->External, ComplexParameter->False, BlockName->HLAM, OrderBlock->2, Description->"2nd bidoublet quartic term(real part)"},
|
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| 299 | ILAM2 == { ParameterType->External, ComplexParameter->False, BlockName->IMHLAM, OrderBlock->2, Description-> "2nd bidoublet quartic term (imaginary part)"},
|
|---|
| 300 |
|
|---|
| 301 | RLAM3 == { ParameterType->External, ComplexParameter->False, BlockName->HLAM, OrderBlock->3, Description->"3rd bidoublet quartic term (real part)"},
|
|---|
| 302 | ILAM3 == { ParameterType->External, ComplexParameter->False, BlockName->IMHLAM, OrderBlock->3, Description->"3rd bidoublet quartic term (imaginary part)"},
|
|---|
| 303 |
|
|---|
| 304 | RLAM4 == { ParameterType->External, ComplexParameter->False, BlockName->HLAM, OrderBlock->4, Description->"4th bidoublet quartic term (real part)"},
|
|---|
| 305 | ILAM4 == { ParameterType->External, ComplexParameter->False, BlockName->IMHLAM, OrderBlock->4, Description->"4th bidoublet quartic term (imaginary part)"},
|
|---|
| 306 |
|
|---|
| 307 | RLAM5 == { ParameterType->External, ComplexParameter->False, BlockName->HLAM, OrderBlock->5, Description->"5th bidoublet quartic term (real part)"},
|
|---|
| 308 | ILAM5 == { ParameterType->External, ComplexParameter->False, BlockName->IMHLAM, OrderBlock->5, Description->"5th bidoublet quartic term (imaginary part)"},
|
|---|
| 309 |
|
|---|
| 310 | RLAM6 == { ParameterType->External, ComplexParameter->False, BlockName->HLAM, OrderBlock->6, Description->"6th bidoublet quartic term (real part)"},
|
|---|
| 311 | ILAM6 == { ParameterType->External, ComplexParameter->False, BlockName->IMHLAM, OrderBlock->6, Description->"6th bidoublet quartic term (imaginary part)"},
|
|---|
| 312 |
|
|---|
| 313 | (* Quartic terms for triplets *)
|
|---|
| 314 | RRHO1 == { ParameterType->External, ComplexParameter->False, BlockName->HRHO, OrderBlock->1, Description->"1st triplet quartic term (real part)"},
|
|---|
| 315 | IRHO1 == { ParameterType->External, ComplexParameter->False, BlockName->IMRHO, OrderBlock->1, Description->"1st triplet quartic term (imaginary part)"},
|
|---|
| 316 |
|
|---|
| 317 | RRHO2 == { ParameterType->External, ComplexParameter->False, BlockName->HRHO, OrderBlock->2, Description->"2nd triplet quartic term (real part)"},
|
|---|
| 318 | IRHO2 == { ParameterType->External, ComplexParameter->False, BlockName->IMRHO, OrderBlock->2, Description->"2nd triplet quartic term (imaginary part)"},
|
|---|
| 319 |
|
|---|
| 320 | RRHO3 == { ParameterType->External, ComplexParameter->False, BlockName->HRHO, OrderBlock->3, Description->"3rd triplet quartic term (real part)"},
|
|---|
| 321 | IRHO3 == { ParameterType->External, ComplexParameter->False, BlockName->IMRHO, OrderBlock->3, Description->"3rd triplet quartic term (imaginary part)"},
|
|---|
| 322 |
|
|---|
| 323 | (* Quartic terms for bidoublets-triplets *)
|
|---|
| 324 | RAL1 == { ParameterType->External, ComplexParameter->False, BlockName->HAL, OrderBlock->1, Description->"1st bidoubet-triplets quartic term (real part)"},
|
|---|
| 325 | IAL1 == { ParameterType->External, ComplexParameter->False, BlockName->IMAL, OrderBlock->1, Description->"1st bidoubet-triplets quartic term (imaginary part)"},
|
|---|
| 326 |
|
|---|
| 327 | RAL2 == { ParameterType->External, ComplexParameter->False, BlockName->HAL, OrderBlock->2, Description->"2nd bidoubet-triplets quartic term (real part)"},
|
|---|
| 328 | IAL2 == { ParameterType->External, ComplexParameter->False, BlockName->IMAL, OrderBlock->2, Description->"2nd bidoubet-triplets quartic term (imaginary part)"},
|
|---|
| 329 |
|
|---|
| 330 | RAL3 == { ParameterType->External, ComplexParameter->False, BlockName->HAL, OrderBlock->3, Description->"3rd bidoubet-triplets quartic term (real part)"},
|
|---|
| 331 | IAL3 == { ParameterType->External, ComplexParameter->False, BlockName->IMAL, OrderBlock->3, Description->"3rd bidoubet-triplets quartic term (imaginary part)"},
|
|---|
| 332 |
|
|---|
| 333 |
|
|---|
| 334 |
|
|---|
| 335 | (* Internal parameters *)
|
|---|
| 336 | yq1 == { TeX->Superscript[y,q1], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,Value->{yq1[i_,j_]:>Ryq1[i,j]+I*Iyq1[i,j]}, InteractionOrder->{QED,1},
|
|---|
| 337 | Description-> "Quark Yukawa matrix 1"},
|
|---|
| 338 |
|
|---|
| 339 | yq2 == { TeX->Superscript[y,q2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,Value->{yq2[i_,j_]:>Ryq2[i,j]+I*Iyq2[i,j]}, InteractionOrder->{QED,1}, Description-> "Quark Yukawa matrix 2"},
|
|---|
| 340 |
|
|---|
| 341 | yl1 == { TeX->Superscript[y,l1], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,Value->{yl1[i_,j_]:>Ryl1[i,j]+I*Iyl1[i,j]}, InteractionOrder->{QED,1}, Description-> "Lepton Yukawa matrix 1"},
|
|---|
| 342 | yl2 == { TeX->Superscript[y,l2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,Value->{yl2[i_,j_]:>Ryl2[i,j]+I*Iyl2[i,j]}, InteractionOrder->{QED,1}, Description-> "Lepton Yukawa matrix 2"},
|
|---|
| 343 | yl3 == { TeX->Superscript[y,l3], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,Value->{yl3[i_,j_]:>Ryl3[i,j]+I*Iyl3[i,j]}, InteractionOrder->{QED,1}, Description-> "Lepton Yukawa matrix 3"},
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|---|
| 344 | yl4 == { TeX->Superscript[y,l4], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,Value->{yl4[i_,j_]:>Ryl4[i,j]+I*Iyl4[i,j]}, InteractionOrder->{QED,1}, Description-> "Lepton Yukawa matrix 4"},
|
|---|
| 345 |
|
|---|
| 346 | (* quartic terms for bidoublets *)
|
|---|
| 347 | lam1 == { TeX->Subscript[\[Lambda],1], ParameterType->Internal, ComplexParameter->True, Value->RLAM1+I*ILAM1, Description->"1st bidoublet quartic term"},
|
|---|
| 348 | lam2 == { TeX->Subscript[\[Lambda],2], ParameterType->Internal, ComplexParameter->True, Value->RLAM2+I*ILAM2, Description->"2md bidoublet quartic term"},
|
|---|
| 349 | lam3 == { TeX->Subscript[\[Lambda],3], ParameterType->Internal, ComplexParameter->True, Value->RLAM3+I*ILAM3, Description->"3rd bidoublet quartic term"},
|
|---|
| 350 | lam4 == { TeX->Subscript[\[Lambda],4], ParameterType->Internal, ComplexParameter->True, Value->RLAM4+I*ILAM4, Description->"4th bidoublet quartic term"},
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|---|
| 351 | lam5 == { TeX->Subscript[\[Lambda],5], ParameterType->Internal, ComplexParameter->True, Value->RLAM5+I*ILAM5, Description->"5th bidoublet quartic term"},
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|---|
| 352 | lam6 == { TeX->Subscript[\[Lambda],6], ParameterType->Internal, ComplexParameter->True, Value->RLAM6+I*ILAM6, Description->"6th bidoublet quartic term"},
|
|---|
| 353 |
|
|---|
| 354 | (* quartic terms for triplets *)
|
|---|
| 355 | rho1 == { TeX->Subscript[\[Rho],1], ParameterType->Internal, ComplexParameter->True, Value->RRHO1+I*IRHO1, Description->" 1st triplets quartic term"},
|
|---|
| 356 | rho2 == { TeX->Subscript[\[Rho],2], ParameterType->Internal, ComplexParameter->True, Value->RRHO2+I*IRHO2, Description->" 2nd triplets quartic term"},
|
|---|
| 357 | rho3 == { TeX->Subscript[\[Rho],3], ParameterType->Internal, ComplexParameter->True, Value->RRHO3+I*IRHO3, Description->" 3rd triplets quartic term"},
|
|---|
| 358 |
|
|---|
| 359 | (* quartic terms for bidoublets-triplets *)
|
|---|
| 360 | al1 == { TeX->Subscript[\[Alpha],1], ParameterType->Internal, ComplexParameter->True, Value->RAL1+I*IAL1, Description->" 1st bidoubet-triplets quartic term"},
|
|---|
| 361 | al2 == { TeX->Subscript[\[Alpha],2], ParameterType->Internal, ComplexParameter->True, Value->RAL2+I*IAL2, Description->" 2nd bidoubet-triplets quartic term"},
|
|---|
| 362 | al3 == { TeX->Subscript[\[Alpha],3], ParameterType->Internal, ComplexParameter->True, Value->RAL3+I*IAL3, Description->" 3rd bidoubet-triplets quartic term"},
|
|---|
| 363 | (* Bilinear terms *)
|
|---|
| 364 |
|
|---|
| 365 |
|
|---|
| 366 | mu12 == { TeX->Superscript[Subscript[\[Mu],1],2], ParameterType->Internal, ComplexParameter->True, Value ->(2*(lam1 + lam2)*v1^2 + 2*(lam1 + 4*lam3 + lam5 + lam6)*v1p^2 + (al1 + al3)*(vL^2 + vR^2))/2 ,Description->"Square of the bidoublet quadratic term"},
|
|---|
| 367 |
|
|---|
| 368 |
|
|---|
| 369 | mu1 == { TeX->Subscript[\[Mu],1], ParameterType->Internal, ComplexParameter->True, Value ->Sqrt[mu12] , Description->"Bidoublet quadratic term"},
|
|---|
| 370 |
|
|---|
| 371 | mu22 == { TeX->Superscript[Subscript[\[Mu],2],2], ParameterType->Internal, ComplexParameter->True, Value ->((al1 + al3)*v1^2 + (al1 + al2)*v1p^2 + rho3*vL^2 + 2*(rho1 + rho2)*vR^2)/2,Description->"Square of the triplet quadratic term"},
|
|---|
| 372 |
|
|---|
| 373 |
|
|---|
| 374 | mu2 == { TeX->Subscript[\[Mu],2], ParameterType->Internal, ComplexParameter->True, Value ->Sqrt[mu22], Description->"Triplet quadratic term"}
|
|---|
| 375 |
|
|---|
| 376 | };
|
|---|
| 377 |
|
|---|
| 378 | (* ************************** *)
|
|---|
| 379 | (* ***** Lagrangian ***** *)
|
|---|
| 380 | (* ************************** *)
|
|---|
| 381 |
|
|---|
| 382 |
|
|---|
| 383 | (*Gauge piece*)
|
|---|
| 384 | LGauge := Block[{mu,nu,ii,aa}, -1/4 FS[B,mu,nu] FS[B,mu,nu] - 1/4 FS[WLi,mu,nu,ii] FS[WLi,mu,nu,ii] - 1/4 FS[WRi,mu,nu,ii] FS[WRi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa] ];
|
|---|
| 385 |
|
|---|
| 386 | (* Fermions *)
|
|---|
| 387 | LFermions := Block[{mu}, I*( QLbar.Ga[mu].DC[QL, mu] + LLbar.Ga[mu].DC[LL, mu] + QRbar.Ga[mu].DC[QR, mu] + LRbar.Ga[mu].DC[LR, mu])];
|
|---|
| 388 |
|
|---|
| 389 | (*Higgses*)
|
|---|
| 390 | LHiggs := Block[{ii, jj, mu, UE, DE, DEL, DER, resu = 0, h1t, h1tbar, tmpp},
|
|---|
| 391 |
|
|---|
| 392 | (*Some definitions*)
|
|---|
| 393 | UE := {{0, -1}, {1, 0}};
|
|---|
| 394 | DE := {{0, 1}, {-1, 0}};
|
|---|
| 395 | DER[a_, b_] := Expand[1/Sqrt[2] (PauliSigma[1, a, b] hR[1] + PauliSigma[2, a, b] hR[2] + PauliSigma[3, a, b] hR[3])];
|
|---|
| 396 | DEL[a_, b_] := Expand[1/Sqrt[2] (PauliSigma[1, a, b] hL[1] + PauliSigma[2, a, b] hL[2] + PauliSigma[3, a, b] hL[3])];
|
|---|
| 397 | h1t[ii_, iip_] := Plus @@ Flatten[Table[UE[[ii, jj]] DE[[iip, jjp]] HC[h1[jjp, jj]], {jj, 1, 2}, {jjp, 1, 2}]];
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|---|
| 398 | h1tbar[ii_, iip_] := Plus @@ Flatten[Table[UE[[iip, jjp]] DE[[ii, jj]] h1[jjp, jj], {jj, 1, 2}, {jjp, 1, 2}]];
|
|---|
| 399 |
|
|---|
| 400 | (*kinetic terms*)
|
|---|
| 401 | resu += DC[h1bar[ii, jj], mu] DC[h1[ii, jj], mu] + DC[hLbar[ii], mu] DC[hL[ii], mu] + DC[hRbar[ii], mu] DC[hR[ii], mu];
|
|---|
| 402 | (*higgs-higgs Interactions*)
|
|---|
| 403 | tmpp = 0; Do[tmpp += mu12*h1bar[ii, jj]*h1[ii, jj], {ii, 1, 2}, {jj, 1, 2}]; resu += Expand[tmpp];
|
|---|
| 404 | tmpp = 0; Do[tmpp += mu22*(HC[DEL[ii, jj]]*DEL[ii, jj] + HC[DER[ii, jj]]*DER[ii, jj]), {ii, 1, 2}, {jj, 1, 2}]; resu += Expand[tmpp];
|
|---|
| 405 | tmpp = 0; Do[tmpp += lam1*h1bar[ii, jj]*h1[ii, jj]*h1bar[ll, kk]*h1[ll, kk], {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 406 | tmpp = 0; Do[tmpp += lam2*h1bar[ii, jj]*h1[ii, ll]*h1bar[kk, ll]*h1[kk, jj], {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 407 | tmpp = 0; Do[tmpp += (h1bar[ii, jj]*h1t[jj, ii] + h1tbar[jj, ii]*h1[ii, jj]), {ii, 1, 2}, {jj, 1, 2}]; resu -= Expand[tmpp]^2*lam3/2;
|
|---|
| 408 | tmpp = 0; Do[tmpp += (h1bar[jj, ii]*h1t[ii, jj] - h1tbar[jj, ii]*h1[ii, jj]), {ii, 1, 2}, {jj, 1, 2}]; resu -= Expand[tmpp]^2*lam4/2;
|
|---|
| 409 | tmpp = 0; Do[tmpp += lam5*h1bar[ii, jj]*h1[jj, kk]*h1tbar[kk, ll]*h1t[ll, ii], {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 410 | tmpp = 0; Do[tmpp += lam6*(h1bar[ii, jj]*h1t[jj, kk]*h1bar[kk, ll]*h1t[ll, ii] + h1tbar[ii, jj]*h1[jj, kk]*h1tbar[kk, ll]*h1[ll, ii]), {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp]/2;
|
|---|
| 411 | tmpp = 0; Do[tmpp += rho1*(HC[DEL[ii, jj]]*DEL[ii, jj]*HC[DEL[kk, ll]]*DEL[kk, ll] + HC[DER[ii, jj]]*DER[ii, jj]*HC[DER[kk, ll]]*DER[kk, ll]), {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 412 | tmpp = 0; Do[tmpp += rho2*(HC[DEL[ii, jj]]*DEL[ii, ll]*HC[DEL[kk, ll]]*DEL[kk, jj] + HC[DER[ii, jj]]*DER[ii, ll]*HC[DER[kk, ll]]*DER[kk, jj]), {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 413 | tmpp = 0; Do[tmpp += rho3*HC[DEL[ii, jj]] DEL[ii, jj]*HC[DER[kk, ll]]*DER[kk, ll], {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 414 | tmpp = 0; Do[tmpp += al1*h1bar[ii, jj]*h1[ii, jj]*(HC[DEL[kk, ll]]*DEL[kk, ll] + HC[DER[kk, ll]]*DER[kk, ll]), {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 415 | tmpp = 0; Do[tmpp += al2*(HC[DER[jj, ii]] h1bar[kk, jj] h1[kk, ll] DER[ll, ii] + HC[DEL[jj, ii]] h1bar[kk, jj] h1[kk, ll] DEL[ll, ii]), {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 416 | tmpp = 0; Do[tmpp += al3*(HC[DER[jj, ii]] h1tbar[jj, kk] h1t[ll, kk] DER[ll, ii] + HC[DEL[jj, ii]] h1tbar[jj, kk] h1t[ll, kk] DEL[ll, ii]), {ii, 1, 2}, {jj, 1, 2}, {kk, 1, 2}, {ll, 1, 2}]; resu -= Expand[tmpp];
|
|---|
| 417 |
|
|---|
| 418 | Expand[resu]];
|
|---|
| 419 |
|
|---|
| 420 |
|
|---|
| 421 | (*Yukawa piece*)
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| 422 | LYukawa := Block[{UE, DE, ii,jj,iip,jjp,ff1,ff2,cc1,sp, resu=0, DEL, DER},
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| 423 | (* some definitions *)
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| 424 | UE := {{0, -1}, {1, 0}};
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| 425 | DE := {{0, 1}, {-1, 0}};
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| 426 | DER[a_,b_] := Expand[1/Sqrt[2] (PauliSigma[1,a,b] hR[1] + PauliSigma[2,a,b] hR[2] + PauliSigma[3,a,b] hR[3])];
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| 427 | DEL[a_,b_] := Expand[1/Sqrt[2] (PauliSigma[1,a,b] hL[1] + PauliSigma[2,a,b] hL[2] + PauliSigma[3,a,b] hL[3])];
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| 428 | (* Fermion-bidoublet interactions *)
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| 429 | Do[
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| 430 | resu -= yq1[ff1,ff2] CC[QLbar[sp,jj,ff1,cc1]].QR[sp,jjp,ff2,cc1] h1[ii,iip] DE[[jj,ii]] UE[[jjp,iip]] +
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| 431 | yl1[ff1,ff2] CC[LLbar[sp,jj,ff1 ]].LR[sp,jjp,ff2 ] h1[ii,iip] DE[[jj,ii]] UE[[jjp,iip]],
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| 432 | {ii,1,2},{jj,1,2},{iip,1,2},{jjp,1,2}];
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| 433 | Do[
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| 434 | resu -= yq2[ff1,ff2] CC[QRbar[sp,ii,ff1,cc1]].QL[sp,iip,ff2,cc1] h1bar[ii,iip] +
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| 435 | yl2[ff1,ff2] CC[LRbar[sp,ii,ff1 ]].LL[sp,iip,ff2 ] h1bar[ii,iip],
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| 436 | {ii,1,2},{iip,1,2}];
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| 437 | (* Fermion-triplet interactions *)
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| 438 | Do[
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| 439 | resu -= yl3[ff1, ff2] DE[[jj, ii]] CC[ LLbar][sp, ii, ff1].LL[sp, kk, ff2] DEL[jj, kk];
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| 440 | resu -= yl4[ff1, ff2] UE[[jj, kk]] LRbar[sp, jj, ff1].CC[LR][sp, ii, ff2] DER[kk,ii],
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| 441 | {ii,1,2},{jj,1,2},{kk,1,2}];
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| 442 | resu += HC[resu];
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| 443 | Expand[resu]
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| 444 | ];
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| 445 |
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| 446 |
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| 447 | LagLRSM :=LYukawa + LFermions + LGauge + LHiggs;
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