(***************************************************************************************************************) (****** This is the FeynRules mod-file for the simple model with composite fermions ******) (****** ******) (****** SM + vector-like T53 and B13 interacting with gluons and W+- ******) (****** ******) (****** Choose whether Feynman gauge is desired. ******) (****** If set to False, unitary gauge is assumed. ****) (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***) (****** Feynman gauge is not supported in MadGraph and Sherpa. ****) (***************************************************************************************************************) M$ModelName = "VLF"; M$Information = {Authors -> {"O. Matsedonskyi"}, Version -> "1.1", Date -> "27. 01. 2014", Institutions -> {"SNS Pisa"}, Emails -> {"leks-m@ukr.net"}}; FeynmanGauge = False; (******* Index definitions ********) IndexRange[ Index[Generation] ] = Range[3] IndexRange[ Index[Colour] ] = NoUnfold[Range[3]] IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]] IndexRange[ Index[SU2W] ] = Unfold[Range[3]] IndexStyle[Colour, i] IndexStyle[Generation, f] IndexStyle[Gluon ,a] IndexStyle[SU2W ,k] (******* Gauge parameters (for FeynArts) ********) GaugeXi[ V[1] ] = GaugeXi[A]; GaugeXi[ V[2] ] = GaugeXi[Z]; GaugeXi[ V[3] ] = GaugeXi[W]; GaugeXi[ V[4] ] = GaugeXi[G]; GaugeXi[ S[1] ] = 1; GaugeXi[ S[2] ] = GaugeXi[Z]; GaugeXi[ S[3] ] = GaugeXi[W]; GaugeXi[ U[1] ] = GaugeXi[A]; GaugeXi[ U[2] ] = GaugeXi[Z]; GaugeXi[ U[31] ] = GaugeXi[W]; GaugeXi[ U[32] ] = GaugeXi[W]; GaugeXi[ U[4] ] = GaugeXi[G]; (**************** Parameters *************) M$Parameters = { (* Top partners couplings *) (*** T ******************) cLTW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LTW, 1}, Value -> 1, Description -> "(W bL TL)"}, cRTW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RTW, 1}, Value -> 1, Description -> "(W bR TR)"}, cLTZ == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LTZ, 1}, Value -> 1, Description -> "(Z tL TL)"}, cRTZ == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RTZ, 1}, Value -> 1, Description -> "(Z tR TR)"}, cLTh == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LTh, 1}, Value -> 1, Description -> "(h tL TR)"}, cRTh == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RTh, 1}, Value -> 1, Description -> "(h tR TL)"}, (*** B ******************) cLBW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LBW, 1}, Value -> 1, Description -> "(W tL BL)"}, cRBW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RBW, 1}, Value -> 1, Description -> "(W tR BR)"}, cLBZ == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LBZ, 1}, Value -> 1, Description -> "(Z bL BL)"}, cRBZ == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RBZ, 1}, Value -> 1, Description -> "(Z bR BR)"}, cLBh == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LBh, 1}, Value -> 1, Description -> "(h bL BR)"}, cRBh == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RBh, 1}, Value -> 1, Description -> "(h bR BL)"}, (*** X ******************) cLXW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LXW, 1}, Value -> 1, Description -> "(W tL XL)"}, cRXW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RXW, 1}, Value -> 1, Description -> "(W tR XR)"}, (*** Y ******************) cLYW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LYW, 1}, Value -> 1, Description -> "(W bL YL)"}, cRYW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RYW, 1}, Value -> 1, Description -> "(W bR YR)"}, (*** V ******************) cLVW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {LVW, 1}, Value -> 1, Description -> "(W W tL VR)"}, cRVW == { ParameterType -> External, BlockName -> BSM, InteractionOrder -> {RVW, 1}, Value -> 1, Description -> "(W W tR VL)"}, LAMBDA == { ParameterType -> External, BlockName -> BSM, Value -> 3000., Description -> "cut-off"}, (* External parameters *) \[Alpha]EWM1== { ParameterType -> External, BlockName -> SMINPUTS, ParameterName -> aEWM1, InteractionOrder -> {QED, -2}, Value -> 127.9, Description -> "Inverse of the electroweak coupling constant"}, Gf == { ParameterType -> External, BlockName -> SMINPUTS, TeX -> Subscript[G, f], InteractionOrder -> {QED, 2}, Value -> 1.16637 * 10^(-5), Description -> "Fermi constant"}, \[Alpha]S == { ParameterType -> External, BlockName -> SMINPUTS, TeX -> Subscript[\[Alpha], s], ParameterName -> aS, InteractionOrder -> {QCD, 2}, Value -> 0.1184, Description -> "Strong coupling constant at the Z pole."}, ymdo == { ParameterType -> External, BlockName -> YUKAWA, Value -> 5.04*10^(-3), OrderBlock -> {1}, Description -> "Down Yukawa mass"}, ymup == { ParameterType -> External, BlockName -> YUKAWA, Value -> 2.55*10^(-3), OrderBlock -> {2}, Description -> "Up Yukawa mass"}, yms == { ParameterType -> External, BlockName -> YUKAWA, Value -> 0.101, OrderBlock -> {3}, Description -> "Strange Yukawa mass"}, ymc == { ParameterType -> External, BlockName -> YUKAWA, Value -> 1.27, OrderBlock -> {4}, Description -> "Charm Yukawa mass"}, ymb == { ParameterType -> External, BlockName -> YUKAWA, Value -> 4.67, OrderBlock -> {5}, Description -> "Bottom Yukawa mass"}, ymt == { ParameterType -> External, BlockName -> YUKAWA, Value -> 172.5, OrderBlock -> {6}, Description -> "Top Yukawa mass"}, yme == { ParameterType -> External, BlockName -> YUKAWA, Value -> 5.11*10^(-4), OrderBlock -> {11}, Description -> "Electron Yukawa mass"}, ymm == { ParameterType -> External, BlockName -> YUKAWA, Value -> 0.10566, OrderBlock -> {13}, Description -> "Muon Yukawa mass"}, ymtau == { ParameterType -> External, BlockName -> YUKAWA, Value -> 1.777, OrderBlock -> {15}, Description -> "Tau Yukawa mass"}, cabi == { TeX -> Subscript[\[Theta], c], ParameterType -> External, BlockName -> CKMBLOCK, Value -> 0.227736, Description -> "Cabibbo angle"}, (* WIDTHS of new particles *) WT23 == { ParameterType -> Internal, Value -> ((ee/sw/2)^2)*(Sqrt[Mbot^4 + (MT23^2 - MW^2)^2 - 2*Mbot^2*(MT23^2 + MW^2)]* (-6*cLTW*cRTW*Mbot*MT23 + ((cLTW^2 + cRTW^2)*(Mbot^4 + MT23^4 + MT23^2*MW^2 - 2*MW^4 + Mbot^2*(-2*MT23^2 + MW^2)))/(2*MW^2)))/(16*MT23^3*Pi)+((ee/sw/2)^2)*(Sqrt[MT23^4 + (Mtop^2 - MZ^2)^2 - 2*MT23^2*(Mtop^2 + MZ^2)]* (-6*cLTZ*cRTZ*MT23*Mtop + ((cLTZ^2 + cRTZ^2)*(MT23^4 + Mtop^4 + Mtop^2*MZ^2 - 2*MZ^4 + MT23^2*(-2*Mtop^2 + MZ^2)))/(2*MZ^2)))/(16*MT23^3*Pi)+(Sqrt[MH^4 + (MT23^2 - Mtop^2)^2 - 2*MH^2*(MT23^2 + Mtop^2)]* (4*cLTh*cRTh*MT23*Mtop + cLTh^2*(-MH^2 + MT23^2 + Mtop^2) + cRTh^2*(-MH^2 + MT23^2 + Mtop^2)))/(32*MT23^3*Pi), Description -> "T23 width"}, WB13 == { ParameterType -> Internal, Value -> ((ee/sw/2)^2)*(Sqrt[MB13^4 + (Mtop^2 - MW^2)^2 - 2*MB13^2*(Mtop^2 + MW^2)]* (-6*cLBW*cRBW*MB13*Mtop + ((cLBW^2 + cRBW^2)*(MB13^4 + Mtop^4 + Mtop^2*MW^2 - 2*MW^4 + MB13^2*(-2*Mtop^2 + MW^2)))/(2*MW^2)))/(16*MB13^3*Pi)+((ee/sw/2)^2)*(Sqrt[MB13^4 + (Mbot^2 - MZ^2)^2 - 2*MB13^2*(Mbot^2 + MZ^2)]* (-6*cLBZ*cRBZ*MB13*Mbot + ((cLBZ^2 + cRBZ^2)*(MB13^4 + Mbot^4 + Mbot^2*MZ^2 - 2*MZ^4 + MB13^2*(-2*Mbot^2 + MZ^2)))/(2*MZ^2)))/(16*MB13^3*Pi)+((4*cLBh*cRBh*MB13*Mbot + cLBh^2*(MB13^2 + Mbot^2 - MH^2) + cRBh^2*(MB13^2 + Mbot^2 - MH^2))*Sqrt[MB13^4 + (Mbot^2 - MH^2)^2 - 2*MB13^2*(Mbot^2 + MH^2)])/(32*MB13^3*Pi), Description -> "B13 width"}, WX53 == { ParameterType -> Internal, Value -> ((ee/sw/2)^2)*(Sqrt[Mtop^4 + (MW^2 - MX53^2)^2 - 2*Mtop^2*(MW^2 + MX53^2)]* (-6*cLXW*cRXW*Mtop*MX53 + ((cLXW^2 + cRXW^2)*(Mtop^4 - 2*MW^4 + MW^2*MX53^2 + MX53^4 + Mtop^2*(MW^2 - 2*MX53^2)))/(2*MW^2)))/(16*MX53^3*Pi), Description -> "X53 width"}, WY43 == { ParameterType -> Internal, Value -> ((ee/sw/2)^2)*(Sqrt[Mbot^4 + (MW^2 - MY43^2)^2 - 2*Mbot^2*(MW^2 + MY43^2)]* (-6*cLYW*cRYW*Mbot*MY43 + ((cLYW^2 + cRYW^2)*(Mbot^4 - 2*MW^4 + MW^2*MY43^2 + MY43^4 + Mbot^2*(MW^2 - 2*MY43^2)))/(2*MW^2)))/(16*MY43^3*Pi), Description -> "Y43 width"}, (* Internal Parameters *) \[Alpha]EW == { ParameterType -> Internal, Value -> 1/\[Alpha]EWM1, TeX -> Subscript[\[Alpha], EW], ParameterName -> aEW, InteractionOrder -> {QED, 2}, Description -> "Electroweak coupling contant"}, ee == { TeX -> e, ParameterType -> Internal, Value -> Sqrt[4 Pi \[Alpha]EW], InteractionOrder -> {QED, 1}, Description -> "Electric coupling constant"}, sw2 == { ParameterType -> Internal, (* to get the correct relation between Gf(and gw) and ee *) Value -> ee^2/(8 MW^2 Gf /Sqrt[2]), Description -> "Squared Sin of the Weinberg angle"}, cw == { TeX -> Subscript[c, w], ParameterType -> Internal, Value -> Sqrt[1 - sw2], Description -> "Cos of the Weinberg angle"}, sw == { TeX -> Subscript[s, w], ParameterType -> Internal, Value -> Sqrt[sw2], Description -> "Sin of the Weinberg angle"}, gw == { TeX -> Subscript[g, w], ParameterType -> Internal, Value -> ee / sw, InteractionOrder -> {QED, 1}, Description -> "Weak coupling constant"}, g1 == { TeX -> Subscript[g, 1], ParameterType -> Internal, Value -> ee / cw, InteractionOrder -> {QED, 1}, Description -> "U(1)Y coupling constant"}, gs == { TeX -> Subscript[g, s], ParameterType -> Internal, Value -> Sqrt[4 Pi \[Alpha]S], InteractionOrder -> {QCD, 1}, ParameterName -> G, Description -> "Strong coupling constant"}, v == { ParameterType -> Internal, Value -> 2*MW*sw/ee, InteractionOrder -> {QED, -1}, Description -> "Higgs VEV"}, \[Lambda] == { ParameterType -> Internal, Value -> MH^2/(2*v^2), InteractionOrder -> {QED, 2}, ParameterName -> lam, Description -> "Higgs quartic coupling"}, muH == { ParameterType -> Internal, Value -> Sqrt[v^2 \[Lambda]], TeX -> \[Mu], Description -> "Coefficient of the quadratic piece of the Higgs potential"}, yl == { TeX -> Superscript[y, l], Indices -> {Index[Generation]}, AllowSummation -> True, ParameterType -> Internal, Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v}, ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau}, InteractionOrder -> {QED, 1}, ComplexParameter -> False, Description -> "Lepton Yukawa coupling"}, yu == { TeX -> Superscript[y, u], Indices -> {Index[Generation]}, AllowSummation -> True, ParameterType -> Internal, Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v}, ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt}, InteractionOrder -> {QED, 1}, ComplexParameter -> False, Description -> "U-quark Yukawa coupling"}, yd == { TeX -> Superscript[y, d], Indices -> {Index[Generation]}, AllowSummation -> True, ParameterType -> Internal, Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v}, ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb}, InteractionOrder -> {QED, 1}, ComplexParameter -> False, Description -> "D-quark Yukawa coupling"}, (* 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"} } (************** Gauge Groups ******************) M$GaugeGroups = { U1Y == { Abelian -> True, GaugeBoson -> B, Charge -> Y, CouplingConstant -> g1}, SU2L == { Abelian -> False, GaugeBoson -> Wi, StructureConstant -> Eps, CouplingConstant -> gw}, SU3C == { Abelian -> False, GaugeBoson -> G, StructureConstant -> f, SymmetricTensor -> dSUN, Representations -> {T, Colour}, CouplingConstant -> gs} } (********* Particle Classes **********) M$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, mu, ta}, 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", "mu", "ta"}, PropagatorType -> Straight, ParticleName -> {"e-", "mu-", "ta-"}, AntiParticleName -> {"e+", "mu+", "ta+"}, PropagatorArrow -> Forward, PDG -> {11, 13, 15}, FullName -> {"Electron", "Muon", "Taon"} }, (* 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, 1.27}, {Mtop, 172.5}}, Width -> {0, 0, {Wtop, 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, 0.101}, {Mbot, 4.67}}, 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"} }, (* COMPOSITE FERMIONS *) F[5] == { ClassName -> T23, SelfConjugate -> False, Indices -> {Index[Colour]}, Mass -> {MT23, 700}, Width -> {WT23, Internal}, QuantumNumbers -> {Q -> 2/3}, PropagatorLabel -> {"T23"}, PropagatorType -> Straight, PropagatorArrow -> Forward, PDG -> {8000001}, FullName -> {"T 2/3"} }, F[6] == { ClassName -> B13, SelfConjugate -> False, Indices -> {Index[Colour]}, Mass -> {MB13, 700}, Width -> {WB13, Internal}, QuantumNumbers -> {Q -> -1/3}, PropagatorLabel -> {"B13"}, PropagatorType -> Straight, PropagatorArrow -> Forward, PDG -> {8000002}, FullName -> {"B -1/3"} }, F[7] == { ClassName -> X53, SelfConjugate -> False, Indices -> {Index[Colour]}, Mass -> {MX53, 700}, Width -> {WX53, Internal}, QuantumNumbers -> {Q -> 5/3}, PropagatorLabel -> {"X53"}, PropagatorType -> Straight, PropagatorArrow -> Forward, PDG -> {8000003}, FullName -> {"X 5/3"} }, F[8] == { ClassName -> Y43, SelfConjugate -> False, Indices -> {Index[Colour]}, Mass -> {MY43, 700}, Width -> {WY43, Internal}, QuantumNumbers -> {Q -> -4/3}, PropagatorLabel -> {"Y43"}, PropagatorType -> Straight, PropagatorArrow -> Forward, PDG -> {8000004}, FullName -> {"Y -4/3"} }, F[9] == { ClassName -> V83, SelfConjugate -> False, Indices -> {Index[Colour]}, Mass -> {MV83, 700}, Width -> {WV83, 1}, QuantumNumbers -> {Q -> 8/3}, PropagatorLabel -> {"V83"}, PropagatorType -> Straight, PropagatorArrow -> Forward, PDG -> {8000005}, FullName -> {"V 8/3"} }, (********** Ghosts **********) U[1] == { ClassName -> ghA, SelfConjugate -> False, Indices -> {}, Ghost -> A, Mass -> 0, QuantumNumbers -> {GhostNumber -> 1}, PropagatorLabel -> uA, PropagatorType -> GhostDash, PropagatorArrow -> Forward}, U[2] == { ClassName -> ghZ, SelfConjugate -> False, Indices -> {}, Mass -> {MZ, 91.1876}, Ghost -> Z, QuantumNumbers -> {GhostNumber -> 1}, PropagatorLabel -> uZ, PropagatorType -> GhostDash, PropagatorArrow -> Forward}, U[31] == { ClassName -> ghWp, SelfConjugate -> False, Indices -> {}, Mass -> {MW, 80.399}, Ghost -> W, QuantumNumbers -> {Q-> 1, GhostNumber -> 1}, PropagatorLabel -> uWp, PropagatorType -> GhostDash, PropagatorArrow -> Forward}, U[32] == { ClassName -> ghWm, SelfConjugate -> False, Indices -> {}, Mass -> {MW, 80.399}, Ghost -> Wbar, QuantumNumbers -> {Q-> -1, GhostNumber -> 1}, PropagatorLabel -> uWm, PropagatorType -> GhostDash, PropagatorArrow -> Forward}, U[4] == { ClassName -> ghG, SelfConjugate -> False, Indices -> {Index[Gluon]}, Ghost -> G, Mass -> 0, QuantumNumbers -> {GhostNumber -> 1}, PropagatorLabel -> uG, PropagatorType -> GhostDash, PropagatorArrow -> Forward}, U[5] == { ClassName -> ghWi, Unphysical -> True, Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2], ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I, ghWi[3] -> cw ghZ + sw ghA}, SelfConjugate -> False, Ghost -> Wi, Indices -> {Index[SU2W]}, FlavorIndex -> SU2W}, U[6] == { ClassName -> ghB, SelfConjugate -> False, Definitions -> {ghB -> -sw ghZ + cw ghA}, Indices -> {}, Ghost -> B, Unphysical -> True}, (************ Gauge Bosons ***************) (* Gauge bosons: Q = 0 *) V[1] == { ClassName -> A, SelfConjugate -> True, Indices -> {}, Mass -> 0, Width -> 0, PropagatorLabel -> "a", PropagatorType -> W, PropagatorArrow -> None, PDG -> 22, FullName -> "Photon" }, V[2] == { ClassName -> Z, SelfConjugate -> True, Indices -> {}, Mass -> {MZ, 91.1876}, Width -> {WZ, 2.4952}, PropagatorLabel -> "Z", PropagatorType -> Sine, PropagatorArrow -> None, PDG -> 23, FullName -> "Z" }, (* Gauge bosons: Q = -1 *) V[3] == { ClassName -> W, SelfConjugate -> False, Indices -> {}, Mass -> {MW, 80.399}, Width -> {WW, 2.085}, QuantumNumbers -> {Q -> 1}, PropagatorLabel -> "W", PropagatorType -> Sine, PropagatorArrow -> Forward, ParticleName ->"W+", AntiParticleName ->"W-", PDG -> 24, FullName -> "W" }, V[4] == { ClassName -> G, SelfConjugate -> True, Indices -> {Index[Gluon]}, Mass -> 0, Width -> 0, PropagatorLabel -> G, PropagatorType -> C, PropagatorArrow -> None, PDG -> 21, FullName -> "G" }, V[5] == { ClassName -> Wi, Unphysical -> True, Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2], Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I, Wi[mu_, 3] -> cw Z[mu] + sw A[mu]}, SelfConjugate -> True, Indices -> {Index[SU2W]}, FlavorIndex -> SU2W, Mass -> 0, PDG -> {1,2,3}}, V[6] == { ClassName -> B, SelfConjugate -> True, Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]}, Indices -> {}, Mass -> 0, Unphysical -> True}, (************ Scalar Fields **********) (* physical Higgs: Q = 0 *) S[1] == { ClassName -> H, SelfConjugate -> True, Mass -> {MH, 125}, Width -> {WH, 0.00575308848}, PropagatorLabel -> "H", PropagatorType -> D, PropagatorArrow -> None, PDG -> 25, TeXParticleName -> "\\phi", TeXClassName -> "\\phi", FullName -> "H" }, S[2] == { ClassName -> phi, SelfConjugate -> True, Mass -> {MZ, 91.1876}, Width -> Wphi, PropagatorLabel -> "Phi", PropagatorType -> D, PropagatorArrow -> None, ParticleName ->"phi0", PDG -> 250, FullName -> "Phi", Goldstone -> Z }, S[3] == { ClassName -> phi2, SelfConjugate -> False, Mass -> {MW, 80.399}, Width -> Wphi2, PropagatorLabel -> "Phi2", PropagatorType -> D, PropagatorArrow -> None, ParticleName ->"phi+", AntiParticleName ->"phi-", PDG -> 251, FullName -> "Phi2", TeXClassName -> "\\phi^+", TeXParticleName -> "\\phi^+", TeXAntiParticleName -> "\\phi^-", Goldstone -> W, QuantumNumbers -> {Q -> 1}} } (*****************************************************************************************) (* SM Lagrangian *) (******************** Gauge F^2 Lagrangian terms*************************) (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*) LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])* (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) - 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]); (********************* Fermion Lagrangian terms*************************) (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*) LFermions = Module[{Lkin, LQCD, LEWleft, LEWright, LWpart, LZpart, Lhpart, LApart}, 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] + I T23bar.Ga[mu].del[T23, mu]+ I B13bar.Ga[mu].del[B13, mu]+ I X53bar.Ga[mu].del[X53, mu]+ I Y43bar.Ga[mu].del[Y43, mu]+ I V83bar.Ga[mu].del[V83, mu]; LQCD = gs (uqbar.Ga[mu].T[a].uq + dqbar.Ga[mu].T[a].dq + T23bar.Ga[mu].T[a].T23 + B13bar.Ga[mu].T[a].B13 + X53bar.Ga[mu].T[a].X53 + Y43bar.Ga[mu].T[a].Y43 + V83bar.Ga[mu].T[a].V83 )G[mu, a]; LBright = -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) LBleft = -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*) ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*) ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*) ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq; (*Y_QL=1/3*) LWleft = ee/sw/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 W[mu] + Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+ 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 W[mu] + Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]); LWpart= ee/sw/2( cLTW T23bar.Ga[mu].ProjM.b W[mu] + cRTW T23bar.Ga[mu].ProjP.b W[mu] + cLTW bbar.Ga[mu].ProjM.T23 Wbar[mu] + cRTW bbar.Ga[mu].ProjP.T23 Wbar[mu] + cLBW tbar.Ga[mu].ProjM.B13 W[mu] + cRBW tbar.Ga[mu].ProjP.B13 W[mu] + cLBW B13bar.Ga[mu].ProjM.t Wbar[mu] + cRBW B13bar.Ga[mu].ProjP.t Wbar[mu]+ cLXW X53bar.Ga[mu].ProjM.t W[mu] + cRXW X53bar.Ga[mu].ProjP.t W[mu] + cLXW tbar.Ga[mu].ProjM.X53 Wbar[mu] + cRXW tbar.Ga[mu].ProjP.X53 Wbar[mu]+ cLYW bbar.Ga[mu].ProjM.Y43 W[mu] + cRYW bbar.Ga[mu].ProjP.Y43 W[mu] + cLYW Y43bar.Ga[mu].ProjM.b Wbar[mu] + cRYW Y43bar.Ga[mu].ProjP.b Wbar[mu]+ (ee/sw/2) cLVW/LAMBDA V83bar.ProjM.t W[mu] W[mu] + (ee/sw/2) cRVW/LAMBDA V83bar.ProjP.t W[mu] W[mu] + (ee/sw/2) cLVW/LAMBDA tbar.ProjP.V83 Wbar[mu] Wbar[mu] + (ee/sw/2) cRVW/LAMBDA tbar.ProjM.V83 Wbar[mu] Wbar[mu]); LZpart= ee/sw/2( cLTZ tbar.Ga[mu].ProjM.T23 Z[mu] + cRTZ tbar.Ga[mu].ProjP.T23 Z[mu] + cLTZ T23bar.Ga[mu].ProjM.t Z[mu] + cRTZ T23bar.Ga[mu].ProjP.t Z[mu] + cLBZ bbar.Ga[mu].ProjM.B13 Z[mu] + cRBZ bbar.Ga[mu].ProjP.B13 Z[mu] + cLBZ B13bar.Ga[mu].ProjM.b Z[mu] + cRBZ B13bar.Ga[mu].ProjP.b Z[mu]); Lhpart= cLTh tbar.ProjP.T23 H + cRTh tbar.ProjM.T23 H + cLTh T23bar.ProjM.t H + cRTh T23bar.ProjP.t H + cLBh bbar.ProjP.B13 H + cRBh bbar.ProjM.B13 H + cLBh B13bar.ProjM.b H + cRBh B13bar.ProjP.b H; LApart= ee (2/3 T23bar.Ga[mu].T23 - 1/3 B13bar.Ga[mu].B13 + 5/3 X53bar.Ga[mu].X53 - 4/3 Y43bar.Ga[mu].Y43 + 8/3 V83bar.Ga[mu].V83) A[mu]; Lkin + LQCD + LBright + LBleft + LWleft + LWpart + LZpart + Lhpart + LApart]; (******************** Higgs Lagrangian terms****************************) Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}]; Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}]; LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi}, PMVec = Table[PauliSigma[i], {i, 3}]; Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; (*Y_phi=1*) Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f; Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec); Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2; (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]]; (*************** Yukawa Lagrangian***********************) LYuk := If[FeynmanGauge, Module[{s,r,n,m,i}, - yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) - yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] - yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*) yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) - yl[n] vlbar[s,n].ProjP[s,r].l[r,n] (-I phi2) - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H +I phi)/Sqrt[2] ], Module[{s,r,n,m,i}, - yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] - yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2] ] ]; LYukawa := LYuk + HC[LYuk]; (**************Ghost terms**************************) (* Now we need the ghost terms which are of the form: *) (* - g * antighost * d_BRST G *) (* where d_BRST G is BRST transform of the gauge fixing function. *) LGhost := If[FeynmanGauge, Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB}, (***********First the pure gauge piece.**********************) dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]]; LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu]; dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ]; LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu]; dBRSTB[mu_] := cw/ee del[ghB, mu]; LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu]; (***********Next the piece from the scalar field.************) LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) + I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) - ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) - I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) - ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ; (***********Now add the pieces together.********************) LGhostG + LGhostWi + LGhostB + LGhostphi] , (*If unitary gauge, only include the gluonic ghost.*) Block[{dBRSTG,LGhostG}, (***********First the pure gauge piece.**********************) dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]]; LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu]; (***********Now add the pieces together.********************) LGhostG] ]; (*********Total SM Lagrangian*******) LSM := LGauge + LHiggs + LFermions + LYukawa + LGhost;