M$ModelName = "DEWSB"; M$Information = {Authors -> {"H.Cai","D. B. Franzosi"}, Version -> "1.1", Institutions -> {"IPNL", "CP3-Origins"}, Emails -> {"hcai@ipnl.in2p3.fr", "frandsen@cp3-origins.net"} }; FeynmanGauge = False; (******* Index definitions ********) IndexRange[ Index[Generation] ] = Range[3] IndexRange[ Index[Colour] ] = NoUnfold[Range[3]] IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]] IndexRange[ Index[SU2Adjoint] ] = Range[3] IndexRange[ Index[SU2D]] = Range[2] IndexRange[ Index[ChargedVector] ] = Range[5] IndexRange[ Index[NeutralVector] ] = Range[7] IndexRange[ Index[Charged]] = Range[4] IndexRange[ Index[Neutral]] = Range[5] IndexFormat[ChargedVector, f] IndexFormat[NeutralVector, f] IndexFormat[Charged, f] IndexFormat[Neutral, f] IndexFormat[SU2Adjoint, k] IndexFormat[SU2D, k] IndexStyle[Colour, i] IndexStyle[Generation, f] IndexStyle[Gluon ,a] (************** Gauge Groups ******************) M$GaugeGroups = { U1Y == { Abelian -> True, GaugeBoson -> B, Charge -> Y, CouplingConstant -> g1}, SU2L == { Abelian -> False, GaugeBoson -> Wi, StructureConstant -> Eps, CouplingConstant -> g2}, SU3C == { Abelian -> False, GaugeBoson -> G, StructureConstant -> f, SymmetricTensor -> dSUN, Representations -> {T, Colour}, CouplingConstant -> gs} } (**************** Parameters *************) M$Parameters = { (**** DEWSB external Parameters ****) MA == { ParameterType -> External, Value -> 600., BlockName -> DEWSB, Description -> "Axial mass"}, MV == { ParameterType -> External, Value -> 600., BlockName -> DEWSB, Description -> "Vector mass"}, r == { ParameterType -> External, Value -> 0.1, BlockName -> DEWSB, Description -> "The r parameter"}, th == { ParameterType -> External, Value -> 0.1, BlockName -> DEWSB, Description -> "Theta angle"}, gt == { ParameterType -> External, Value -> 2.1, InteractionOrder -> {SD,1}, BlockName -> DEWSB, Description -> "gt"}, (**** SM External Parameters ****) aEWM1== { ParameterType -> External, BlockName -> SMINPUTS, ParameterName -> aEWM1, Value -> 127.9, Description -> "Inverse of the electroweak coupling constant"}, Gf == { ParameterType -> External, BlockName -> SMINPUTS, ParameterName -> Gf, Value -> 0.0000116639, Description -> "Fermi constant"}, aS == { ParameterType -> External, BlockName -> SMINPUTS, TeX -> Subscript[a, S], ParameterName -> aS, InteractionOrder -> {QCD, 2}, Value -> 0.118, Description -> "Strong coupling constant at the Z pole."}, cabi == { TeX -> Subscript[\[Theta], c], ParameterType -> External, BlockName -> CKM, Value -> 0.227736, Description -> "Cabibbo angle"}, (**** DEWSB Internal Parameters ****) st == { TeX -> Sin[th], ParameterType -> Internal, Value -> Sin[th], BlockName -> DEWSB, Description -> "Sin(th)"}, ct == { TeX -> Cos[th], ParameterType -> Internal, Value -> Sqrt[1-st^2], BlockName -> DEWSB, Description -> "Cos(th)"}, Meta == { TeX -> Subscript[M,\[Eta]], ParameterType -> Internal, Value -> 125.0/st, BlockName -> DEWSB, Description -> "Mass of eta" }, vev == { ParameterType -> Internal, Value -> 1/Sqrt[Sqrt[2]*Gf], BlockName -> DEWSB, Description -> "Higgs VEV"}, FP1 == { ParameterType -> Internal, Value -> Sqrt[2]MA/gt , Description -> "Site one constant"}, FP0 == { ParameterType -> Internal, Value -> Sqrt[vev^2/st^2+FP1^2 r^2], Description -> "sigma decay constant"}, FU == { ParameterType -> Internal, Value -> Sqrt[2] MV/gt, Description -> "link field constant"}, FP == { ParameterType -> Internal, Value -> Sqrt[FP0^2 - r^2 FP1^2], Description -> "pion constant" }, w == { ParameterType -> Internal, Value -> (FP0^2/FU^2-1)/2, Description -> "Sigma decay constant"}, MX0 == { ParameterType -> Internal, Value -> MA, Description -> "X0 mass"}, MXt0 == { ParameterType -> Internal, Value -> MA, Description -> "Xt0 mass"}, MSt0 == { ParameterType -> Internal, Value -> MV, Description -> "St0 mass"}, MVt0 == { ParameterType -> Internal, Value -> MV, Description -> "Vt0 mass"}, MSt1 == { ParameterType -> Internal, Value -> MV, Description -> "St1 mass"}, (**** SM Internal Parameters ****) aEW == { ParameterType -> Internal, Value -> 1/aEWM1, TeX -> alphaEW, ParameterName -> aEW, Description -> "Electroweak coupling contant"}, ee == { TeX -> e, ParameterType -> Internal, Value -> Sqrt[4 Pi aEW], InteractionOrder -> {EW,1}, Description -> "Electric coupling constant"}, gs == { TeX -> Subscript[g, s], ParameterType -> Internal, Value -> Sqrt[4 Pi aS], InteractionOrder -> {QCD, 1}, ParameterName -> G, Description -> "Strong coupling constant"}, gg1g2 == { ParameterType -> Internal, Value -> -(2 gt^2 (-2 ee^2+gt^2) (MV^2-MZ^2)^2 MZ^2 (-MA^2+MZ^2))/(gt^2 (MV^2-MZ^2) (MA^4 (-MV^2+MZ^2) r^2+MA^2 MV^2 (-2 MZ^2 (2+w)+MV^2 (1+2 w))-MV^2 MZ^2 (-2 MZ^2 (2+w)+MV^2 (1+2 w)))+2 ee^2 MZ^2 (MA^4 (-MV^2+MZ^2) r^2+MV^2 MZ^2 (2 MZ^2 (2+w)-MV^2 (3+2 w))+MA^2 MV^2 (-2 MZ^2 (2+w)+MV^2 (3+2 w)))+(gt^2 (MV^2-MZ^2)+2 ee^2 MZ^2) (-MA^2 MV^4+MV^4 MZ^2+MA^4 MV^2 r^2-MA^4 MZ^2 r^2+2 MV^2 (MV^2-MZ^2) (-MA^2+MZ^2) w) Cos[2 th]), Description -> "gg1g2"}, deltag1g2 == { ParameterType -> Internal, Value -> ((gt^2 (MV^2-MZ^2)+2 ee^2 MZ^2) (gt^2 (MA^2-MZ^2) MZ^2 (-MV^2+MZ^2)+ee^2 (MA^4 (-MV^2+MZ^2) r^2+MZ^2 (2 MZ^4+2 MV^2 MZ^2 w-MV^4 (1+2 w))+MA^2 (-2 MZ^4-2 MV^2 MZ^2 w+MV^4 (1+2 w)))+ee^2 (-MA^2 MV^4+MV^4 MZ^2+MA^4 MV^2 r^2-MA^4 MZ^2 r^2+2 MV^2 (MV^2-MZ^2) (-MA^2+MZ^2) w) Cos[2 th]))/((-2 ee^2+gt^2)^2 (MV^2-MZ^2)^2 MZ^2 (-MA^2+MZ^2)), Description -> "deltag1g2"}, g2 == { TeX -> Subscript[g, 2], ParameterType -> Internal, Value -> Sqrt[gg1g2(1+Sqrt[deltag1g2])], InteractionOrder -> {EW,1}, Description -> "Weak coupling constant "}, g1 == { ParameterType -> Internal, Value -> Sqrt[gg1g2(1-Sqrt[deltag1g2])], InteractionOrder -> {EW,1}, Description -> "g1"}, (* N. B. : only Cabibbo mixing! *) CKM == { Indices -> {Index[Generation], Index[Generation]}, TensorClass -> CKM, Unitary -> True, Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0, CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0, CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1}, Description -> "CKM-Matrix"}, (* Mass matrix and mixing *) VVC11 == { ParameterType -> Internal, Value -> MV^2 g2^2/gt^2 (1+w*st^2) , Description -> "Mass matrix" }, VVC12 == { ParameterType -> Internal, Value -> - g2 r MA^2 st / Sqrt[2] / gt, Description -> "Mass matrix" }, VVC13 == { ParameterType -> Internal, Value -> - g2 MV^2 / Sqrt[2] / gt, Description -> "Mass matrix" }, VVC14 == { ParameterType -> Internal, Value -> - g2 MV^2 ct / Sqrt[2] / gt, Description -> "Mass matrix" }, VVC22 == { ParameterType -> Internal, Value -> MA^2, Description -> "Mass matrix" }, VVC23 == { ParameterType -> Internal, Value -> 0., Description -> "Mass matrix" }, VVC24 == { ParameterType -> Internal, Value -> 0., Description -> "Mass matrix" }, VVC33 == { ParameterType -> Internal, Value -> MV^2, Description -> "Mass matrix" }, VVC34 == { ParameterType -> Internal, Value -> 0, Description -> "Mass matrix" }, VVC44 == { ParameterType -> Internal, Value -> MV^2, Description -> "Mass matrix" }, VVN11 == { ParameterType -> Internal, Value -> (MV^2 (1+w st^2)) g1^2 /gt^2, Description -> "Mass matrix" }, VVN12 == { ParameterType -> Internal, Value -> - MV^2 w st^2 g1 g2/ gt^2, Description -> "Mass matrix" }, VVN13 == { ParameterType -> Internal, Value -> -g1 MA^2 r st / Sqrt[2] / gt, Description -> "Mass matrix" }, VVN14 == { ParameterType -> Internal, Value -> - g1 MV^2 / Sqrt[2] / gt, Description -> "Mass matrix" }, VVN15 == { ParameterType -> Internal, Value -> - g1 MV^2 ct / Sqrt[2] / gt, Description -> "Mass matrix" }, VVN22 == { ParameterType -> Internal, Value -> (MV^2 (1+w st^2)) g2^2 /gt^2, Description -> "Mass matrix" }, VVN23 == { ParameterType -> Internal, Value -> g2 r MA^2 st / Sqrt[2] / gt, Description -> "Mass matrix" }, VVN24 == { ParameterType -> Internal, Value -> - g2 MV^2 / Sqrt[2] / gt, Description -> "Mass matrix" }, VVN25 == { ParameterType -> Internal, Value -> g2 MV^2 ct / Sqrt[2] / gt, Description -> "Mass matrix" }, VVN33 == { ParameterType -> Internal, Value -> MA^2, Description -> "Mass matrix" }, VVN34 == { ParameterType -> Internal, Value -> 0., Description -> "Mass matrix" }, VVN35 == { ParameterType -> Internal, Value -> 0, Description -> "Mass matrix" }, VVN44 == { ParameterType -> Internal, Value -> MV^2, Description -> "Mass matrix" }, VVN45 == { ParameterType -> Internal, Value -> 0, Description -> "Mass matrix" }, VVN55 == { ParameterType -> Internal, Value -> MV^2, Description -> "Mass matrix" }, (* mixing elements computed numerically via external program *) CM =={Indices ->{Index[Charged], Index[Charged]}, ParameterType -> External, ComplexParameter -> False, Orthogonal -> True, Value -> {CM[1,1] -> 1.0, CM[2,2] -> 1.0, CM[3,3] -> 1.0, CM[4,4] -> 1.0, CM[i_, j_] :> 0 /; NumericQ[i] && NumericQ[j] && (i != j) }, BlockName ->VCMix, Description -> "mixing element" }, NM == {Indices ->{Index[Neutral], Index[Neutral]}, ParameterType -> External, ComplexParameter -> False, Orthogonal -> True, Value -> {NM[1,1] -> 1.0, NM[2,2] -> 1.0, NM[3,3] -> 1.0, NM[4,4] -> 1.0, NM[5,5] -> 1.0, NM[i_, j_] :> 0 /; NumericQ[i] && NumericQ[j] && (i != j) }, BlockName ->VNMix, Description -> "mixing element" } } (********* Particle Classes **********) Wind=1;ACind=2;VCind=3;SCind=4; STCind=5; Aind=1;Zind=2;ANind=3;VNind=4;SNind=5; M$ClassesDescription = { (********** Fermions ************) (* Leptons (neutrino): I_3 = +1/2, Q = 0 *) F[1] == { ClassName -> vl, ClassMembers -> {ve,vm,vt}, FlavorIndex -> Generation, SelfConjugate -> False, Indices -> {Index[Generation]}, Mass -> 0, Width -> 0, QuantumNumbers -> {LeptonNumber -> 1}, PropagatorLabel -> {"v", "ve", "vm", "vt"} , PropagatorType -> S, PropagatorArrow -> Forward, PDG -> {12,14,16}, FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} }, (* Leptons (electron): I_3 = -1/2, Q = -1 *) F[2] == { ClassName -> l, ClassMembers -> {e, m, tt}, FlavorIndex -> Generation, SelfConjugate -> False, Indices -> {Index[Generation]}, Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}}, Width -> 0, QuantumNumbers -> {Q -> -1, LeptonNumber -> 1}, PropagatorLabel -> {"l", "e", "m", "tt"}, PropagatorType -> Straight, ParticleName -> {"e-", "m-", "tt-"}, AntiParticleName -> {"e+", "m+", "tt+"}, PropagatorArrow -> Forward, PDG -> {11, 13, 15}, FullName -> {"Electron", "Muon", "Tau"} }, (* Quarks (u): I_3 = +1/2, Q = +2/3 *) F[3] == { ClassMembers -> {u, c, t}, ClassName -> uq, FlavorIndex -> Generation, SelfConjugate -> False, Indices -> {Index[Generation], Index[Colour]}, Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 174.3}}, Width -> {0, 0, {WT, 1.50833649}}, QuantumNumbers -> {Q -> 2/3}, PropagatorLabel -> {"uq", "u", "c", "t"}, PropagatorType -> Straight, PropagatorArrow -> Forward, PDG -> {2, 4, 6}, FullName -> {"u-quark", "c-quark", "t-quark"}}, (* Quarks (d): I_3 = -1/2, Q = -1/3 *) F[4] == { ClassMembers -> {d, s, b}, ClassName -> dq, FlavorIndex -> Generation, SelfConjugate -> False, Indices -> {Index[Generation], Index[Colour]}, Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.104}, {MB, 4.7}}, Width -> 0, QuantumNumbers -> {Q -> -1/3}, PropagatorLabel -> {"dq", "d", "s", "b"}, PropagatorType -> Straight, PropagatorArrow -> Forward, PDG -> {1,3,5}, FullName -> {"d-quark", "s-quark", "b-quark"} }, (************ Gauge Bosons ***************) (* Gauge bosons: Q = 0 *) V[1] == { ClassName -> VN, ClassMembers -> {A,Z,A0,V0,S0,St0,Vt0}, SelfConjugate -> True, Indices -> {Index[NeutralVector]}, FlavorIndex -> NeutralVector, ParticleName -> {"A","Z","A0","V0","S0","St0","Vt0"}, PropagatorType -> C, PropagatorArrow -> None, PDG -> {22,23,50,51,52,56,60}, Mass -> {Mne,0,{MZ,91.0},{MA0,604.7},{MV0,523.6},{MS0,700.0},{MSt0, Internal},{MVt0, Internal}}, Width -> {0,{WZ,2.4952},{WA0,10.},{WV0,10.},{WS0,10.},{WSt0, 10.},{WVt0, 10.}}, FullName -> {"Photon", "Z boson", "Neutral R1", "Neutral R2", "Neutral R3", "Neutral R4", "Neutral R5" } }, V[11] == { ClassName -> VX, ClassMembers -> {X0, Xt0}, SelfConjugate -> True, Indices -> {Index[SU2D]}, FlavorIndex -> SU2D, ParticleName -> {"X0","Xt0"}, PropagatorType -> C, PropagatorArrow -> None, PDG -> {58, 59}, Mass -> {Mxn,{MX0, Internal},{MXt0, Internal}}, Width -> {{WX0,10.}, {WXt0, 10.}}, FullName -> {"Neutral X1", "Neutral X2"} }, V[2] == { ClassName -> VC, ClassMembers -> {W,A1,V1,S1,St1}, SelfConjugate -> False, Indices -> {Index[ChargedVector]}, FlavorIndex -> ChargedVector, ParticleName -> {"W+","A+","V+","S+","St+"}, AntiParticleName -> {"W-","A-","V-","S-", "St-"}, QuantumNumbers -> {Q -> 1}, PropagatorType -> C, PropagatorArrow -> None, PDG -> {24,53,54,55, 57}, Mass -> {Mch,{MW,80.0},{MA1,601.1},{MV1,514.7},{MS1,700.},{MSt1, Internal}}, Width -> {{WW,2.141},{WA1,10.},{WV1,10.},{WS1,10.},{WSt1,10.}}, FullName -> {"W boson", "Charged R1", "Charged R2", "Charged R3","Charged R4" } }, V[3] == { ClassName -> B, Unphysical -> True, SelfConjugate -> True, Definitions -> {B[mu_] -> Sum[NM[Aind,f] VN[mu,f],{f,5}]}, FullName -> "U1Y B gauge field" }, V[4] == { ClassName -> VCt, Unphysical -> True, SelfConjugate -> False, Definitions -> Table[VCt[mu_,k] -> Sum[CM[k,f] VC[mu,f],{f,4}],{k,4}], Indices -> {Index[Charged]}, FlavorIndex -> Charged, FullName -> "Charged vector strong and weak eigenstates" }, V[5] == { ClassName -> Wi, Unphysical -> True, Definitions -> {Wi[mu_, 1] -> (VCt[mu,Wind] + VCtbar[mu,Wind])/Sqrt[2], Wi[mu_, 2] -> (VCt[mu,Wind] - VCtbar[mu,Wind])/Sqrt[2]/I, Wi[mu_, 3] -> Sum[NM[Zind,f] VN[mu,f],{f,5}]}, SelfConjugate -> True, Indices -> {Index[SU2Adjoint]}, FlavorIndex -> SU2Adjoint, PDG -> {1,2,3}, FullName -> "SU2L W gauge field" }, V[6] == { ClassName -> AAt, Unphysical -> True, SelfConjugate -> True, Indices -> {Index[SU2Adjoint]}, FlavorIndex -> SU2Adjoint, Definitions->{AAt[mu_,1]->(VCt[mu,ACind]+VCtbar[mu,ACind])/Sqrt[2], AAt[mu_,2]->(VCtbar[mu,ACind]-VCt[mu,ACind])/Sqrt[2]/I, AAt[mu_,3]-> Sum[(NM[ANind,f]) VN[mu,f],{f,5}]}, FullName -> "Strong vector state canonically normalized" }, V[7] == { ClassName -> VVt, Unphysical -> True, SelfConjugate -> True, Indices -> {Index[SU2Adjoint]}, FlavorIndex -> SU2Adjoint, Definitions->{VVt[mu_,1]->(VCt[mu,VCind]+VCtbar[mu,VCind])/Sqrt[2], VVt[mu_,2]->(VCt[mu,VCind]-VCtbar[mu,VCind])/Sqrt[2]/I, VVt[mu_,3]-> Sum[(NM[VNind,f]) VN[mu,f],{f,5}]}, FullName -> "Strong axial state canonically normalized" }, V[8] == { ClassName -> SSt, Unphysical -> True, SelfConjugate -> True, Indices -> {Index[SU2Adjoint]}, FlavorIndex -> SU2Adjoint, Definitions->{SSt[mu_,1]->(VCt[mu,SCind]+VCtbar[mu,SCind])/Sqrt[2], SSt[mu_,2]->(VCtbar[mu,SCind]-VCt[mu,SCind])/Sqrt[2]/I, SSt[mu_,3]-> Sum[(NM[SNind,f]) VN[mu,f],{f,5}]}, FullName -> "Strong axial state canonically normalized" }, V[9] == { ClassName -> SNt, Unphysical -> True, SelfConjugate -> True, Indices -> {Index[SU2D]}, Flavorindex -> SU2D, Definitions -> { SNt[mu_,1] -> (VCbar[mu, STCind]-VC[mu, STCind])/Sqrt[2]/I, SNt[mu_,2] -> (VCbar[mu, STCind]+VC[mu, STCind])/Sqrt[2] }, FullName -> "Strong vector state" }, V[10] == { ClassName -> G, SelfConjugate -> True, Indices -> {Index[Gluon]}, Mass -> 0, Width -> 0, PropagatorLabel -> G, PropagatorType -> C, PropagatorArrow -> None, PDG -> 21, FullName -> "G" }, (************ Scalar Fields **********) (* Higgs: physical scalars *) S[1] == { ClassName -> h, SelfConjugate -> True, Mass -> {MH,125}, Width -> {WH,0.00407}, PropagatorLabel -> "h", PropagatorType -> D, PropagatorArrow -> None, PDG -> 25, ParticleName -> "h", FullName -> "h" }, S[2] == { ClassName -> eta, SelfConjugate -> True, Mass -> {Meta, Internal}, Width -> {Weta, 2.4952}, PropagatorLabel -> "eta", PropagatorType -> D, PropagatorArrow -> None, PDG -> 26, ParticleName -> "eta", FullName -> "eta" } } (** SigmaB generators **) SS[1] = 1/2 {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}; SS[2] = 1/2 {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}; SS[3] = 1/2 {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}; SS[4] = 1/2 {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}}; SS[5] = 1/2 {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, I, 0}}; SS[6] = 1/2 {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}; SS[7] = I/(2 Sqrt[2]) {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}}; SS[8] = I/(2 Sqrt[2]) {{0, 0, 0, -I}, {0, 0, I, 0}, {0, I, 0, 0}, {-I, 0, 0, 0}}; SS[9] = I/(2 Sqrt[2]) {{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1, 0, 0}}; SS[10]=1/(2 Sqrt[2]) {{0,0,1,0},{0,0,0,1},{1,0,0,0},{0,1,0,0}}; XX[1]=1/(2Sqrt[2]) {{0,0,1,0},{0,0,0,-1},{1,0,0,0},{0,-1,0,0}}; XX[2]=1/(2Sqrt[2]) {{0,0,I,0},{0,0,0,I},{-I,0,0,0},{0,-I,0,0}}; XX[3]=1/(2Sqrt[2]) {{0,0,0,1},{0,0,1,0},{0,1,0,0},{1,0,0,0}}; XX[4]=1/(2Sqrt[2]) {{0,0,0,-I},{0,0,I,0},{0,-I,0,0},{I,0,0,0}}; XX[5]=1/(2Sqrt[2]) {{1,0,0,0},{0,1,0,0},{0,0,-1,0},{0,0,0,-1}}; (** Sigma0 generators **) Do[VV[i]=(SS[i]+SS[i+3])/Sqrt[2],{i,1,3}]; VV[4]=st XX[1]+ct (SS[1]-SS[4])/Sqrt[2]; VV[5]=st XX[2]-ct (SS[2]-SS[5])/Sqrt[2]; VV[6]=st XX[3]-ct (SS[3]-SS[6])/Sqrt[2]; VV[7]=SS[7]; VV[8]=st XX[5]+ct SS[8]; VV[9]=SS[9]; VV[10]=SS[10]; YY[1]=(ct XX[1]-st/Sqrt[2] (SS[1]-SS[4])); YY[2]=(ct XX[2]+st/Sqrt[2] (SS[2]-SS[5])); YY[3]=(ct XX[3]+st/Sqrt[2] (SS[3]-SS[6])); YY[4]=XX[4]; YY[5]=ct XX[5]-st SS[8]; Sigma0 = {{0,ct,st,0},{-ct,0,0,st},{-st,0,0,-ct},{0,-st,ct,0}}; Id = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}; R[mu_,i_] := If[i==1,B[mu], If[i<=4,Wi[mu, i-1], If[i<=7,AAt[mu, i-4], If[i<=9,VX[mu, i-7], If[i<=12,VVt[mu, i-9], If[i<=15,SSt[mu, i-12], If[i<=17,VN[mu, i-10], If[i<=19,SNt[mu, i-17],0] ]]]]]]]; BBm[mu_] := g1 R[mu, 1] SS[6]; WWm[mu_] := g2 Sum[R[mu, a+1] SS[a],{a,1,3}]; AAm[mu_] := gt Sum[R[mu, a+4] YY[a],{a,1,5}]; VVm[mu_] := gt Sum[R[mu, a+9] VV[a],{a,1,10}]; GG1m[mu_] := AAm[mu]+VVm[mu]; GG0m[mu_] := BBm[mu]+WWm[mu]; (* Field strength complete *) FTB[mu_,nu_] := del[ BBm[nu],mu] -del[BBm[mu],nu]; FTW[mu_,nu_] := del[ WWm[nu],mu] -del[WWm[mu],nu] - I WWm[mu].WWm[nu] + I WWm[nu].WWm[mu]; FTGG[mu_,nu_] := del[GG1m[nu],mu] - del[GG1m[mu],nu] - I GG1m[mu].GG1m[nu] + I GG1m[nu].GG1m[mu]; (* SM Lagrangian *) LGauge := (Normal[Series[-1/(2 g1^2) Tr[FTB[mu,nu].FTB[mu,nu]], {g1, 0, 1}]])+ (Normal[Series[-1/(2 g2^2) Tr[FTW[mu,nu].FTW[mu,nu]], {g2, 0, 1}]]); (* DEWSB *) LSGauge := (Normal[Series[-1/(2 gt^2) Tr[FTGG[mu,nu].FTGG[mu,nu]], {gt, 0, 1}]]); (********************* Fermion Lagrangian terms*************************) (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder. Fermion terms need to be checked *) LFermions := Module[{Lkin, LBright, LBleft, LWleft}, Lkin := I uqbar.Ga[mu].del[uq, mu] + I dqbar.Ga[mu].del[dq, mu] + I lbar.Ga[mu].del[l, mu] + I vlbar.Ga[mu].del[vl, mu]; LBright := -2 g1 B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) 4 g1/3 B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) 2 g1/3 B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) LBleft := - g1 B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*) g1 B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*) g1/3 B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*) g1/3 B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*) LWleft := g2/2( vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*) lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*) Sqrt[2] vlbar.Ga[mu].ProjM.l VCt[mu,Wind] + Sqrt[2] lbar.Ga[mu].ProjM.vl VCtbar[mu,Wind]+ uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*) dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*) Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq VCt[mu,Wind] + Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq VCtbar[mu,Wind] ); Lkin + LBright + LBleft + LWleft]; (******************** Scalar Lagrangian terms****************************) (* Unitary gauge eaten Goldstone=0 *) phi0 := (I Sqrt[2])/FP ( h YY[4] + eta YY[5]); phi0D := -phi0; phi1 := -(I Sqrt[2] r)/FP ( h YY[4] + eta YY[5]); phi1D := -phi1; xi0 := (Id+phi0).Sigma0; xi0D := (-Sigma0).(Id+phi0D); xi1 := (Id + phi1).Sigma0; xi1D :=-Sigma0.(Id + phi1D); Dxi0[mu_] := del[xi0, mu] - I GG0m[mu].xi0 Dxi1[mu_] := del[xi1, mu] - I GG1m[mu].xi1 ghat1[mu_] := I xi1D.Dxi1[mu] ghat0[mu_] := I xi0D.Dxi0[mu] shat1[mu_] := Sum[2 Tr[VV[i].ghat1[mu]] VV[i], {i, 1, 10}] shat0[mu_] := Sum[2 Tr[VV[i].ghat0[mu]] VV[i], {i, 1, 10}] xhat1[mu_] := Sum[2 Tr[YY[i].ghat1[mu]] YY[i], {i, 1, 5}] xhat0[mu_] := Sum[2 Tr[YY[i].ghat0[mu]] YY[i], {i, 1, 5}] LPi0 := 1/2 FP0^2 (Normal[Series[Tr[xhat0[mu].xhat0[mu]], {FP, Infinity, 1}]]) LPi1 := 1/2 FP1^2 (Normal[Series[Tr[xhat1[mu].xhat1[mu]], {FP, Infinity, 1}]]) DUU[mu_] := - I shat0[mu] + I shat1[mu]; DUUD[mu_] := I shat0[mu] - I shat1[mu]; LUU1 := 1/2 FU^2 (Normal[Series[Tr[DUU[mu].DUUD[mu]],{FP, Infinity, 1}]]) Lr := r FP1^2 (Normal[Series[Tr[xhat0[mu].xhat1[mu]], {FP, Infinity, 1}]]) (*********Total CHM Lagrangian*******) LSM := LGauge + LSGauge + LFermions + LPi0 + LPi1 + LUU1 + Lr;