ALRM_general: ALRM_BF_uni_v2.fr

File ALRM_BF_uni_v2.fr, 36.7 KB (added by BenjF, 9 days ago)
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1(**************************************************************************************************)
2(******     Alternative FR model file for an alternative left-right symmetric model          ******)
3(******                                                                                      ******)
4(******     Author: Benjamin Fuks                                                            ******)
5(******                                                                                      ******)
6(**************************************************************************************************)
7
8(* ************************** *)
9(* *****  Information   ***** *)
10(* ************************** *)
11M$ModelName = "ALRSM_BF";
12M$Information = { Authors->{"Benjamin Fuks"}, Emails->{"fuks@lpthe.jussieu.fr"},
13                  Institutions->{"LPTHE / Sorbonne U."},
14                  Date->"29.05.19", Version->"1.1"};
15
16
17(* ************************** *)
18(* *****  Gauge groups  ***** *)
19(* ************************** *)
20M$GaugeGroups = {
21  U1BL == { Abelian->True,  CouplingConstant->gBL, GaugeBoson->B,   Charge->YBL},
22  SU2L == { Abelian->False, CouplingConstant->gL,  GaugeBoson->WLi,
23            StructureConstant->epL, Representations->{TL,SU2DL},
24            Definitions->{TL[a_,b__]-> PauliSigma[Index[SU2WL,a],b  ]/2, epL->Eps}},
25  SU2R == { Abelian->False, CouplingConstant->gR,  GaugeBoson->WRi,
26            StructureConstant->epR, Representations->{{TR, SU2DR}, {TRs,SU2DRs}},
27            Definitions->{TR[a_,b__]-> PauliSigma[Index[SU2WR,a],b]/2,
28              TRs[a_,i_,j_]->-PauliSigma[Index[SU2WR,a],j,i]/2, epR->Eps}},
29  SU3C == { Abelian->False, CouplingConstant->gs,  GaugeBoson->G,
30            StructureConstant->f,  Representations->{{T,Colour}, {Tb,Colourb}}, DTerm->dSUN }
31};
32
33
34(* ************************** *)
35(* *** Interaction orders *** *)
36(* ************************** *)
37M$InteractionOrderHierarchy = { {QCD, 1},  {QED, 2},  {HIG, 2}, {HIW, 2} };
38M$InteractionOrderLimit     = { {QCD, 99}, {QED, 99}, {HIG, 1}, {HIW, 1} };
39
40
41(* ************************** *)
42(* *****    Indices     ***** *)
43(* ************************** *)
44IndexRange[Index[SU2WL  ]] = Unfold[Range[3]];   IndexStyle[SU2WL,   j];
45IndexRange[Index[SU2DL  ]] = Unfold[Range[2]];   IndexStyle[SU2DL,   k];
46IndexRange[Index[SU2WR  ]] = Unfold[Range[3]];   IndexStyle[SU2WR,   j];
47IndexRange[Index[SU2DR  ]] = Unfold[Range[2]];   IndexStyle[SU2DR,   k];
48IndexRange[Index[SU2DRs ]] = Unfold[Range[2]];   IndexStyle[SU2DRs,  k];
49IndexRange[Index[Gluon  ]] = NoUnfold[Range[8]]; IndexStyle[Gluon,   a];
50IndexRange[Index[Colour ]] = NoUnfold[Range[3]]; IndexStyle[Colour,  m];
51IndexRange[Index[Colourb]] = NoUnfold[Range[3]]; IndexStyle[Colourb, m];
52IndexRange[Index[GEN    ]] = Range[3];           IndexStyle[GEN,     f];
53IndexRange[Index[SHIGGS ]] = Range[4];           IndexStyle[SHIGGS,  n];
54IndexRange[Index[PHIGGS ]] = Range[2];           IndexStyle[PHIGGS,  n];
55
56
57(* ************************** *)
58(* *****     Fields     ***** *)
59(* ************************** *)
60M$ClassesDescription = {
61(* Gauge bosons: unphysical vector fields *)
62  V[11] == { ClassName->B, Unphysical->True, SelfConjugate->True,
63             Definitions -> { B[mu_] -> cph*cw*A[mu] - (sph*st+cph*sw*ct)*Z[mu] + (cph*sw*st-sph*ct)*Zp[mu]}},
64  V[12] == { ClassName->WLi, Unphysical->True, SelfConjugate->True,
65             Indices->{Index[SU2WL]}, FlavorIndex->SU2WL,
66             Definitions-> {WLi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2],
67                            WLi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]),
68                            WLi[mu_,3] -> sw*A[mu] + cw*ct*Z[mu] - cw*st*Zp[mu]}},
69  V[13] == { ClassName->WRi, Unphysical->True, SelfConjugate->True,
70             Indices->{Index[SU2WR]}, FlavorIndex->SU2WR,
71             Definitions-> {WRi[mu_,1] -> (Wpbar[mu]+Wp[mu])/Sqrt[2],
72                            WRi[mu_,2] -> (Wpbar[mu]-Wp[mu])/(I*Sqrt[2]),
73                            WRi[mu_,3] -> sph*cw*A[mu] + (cph*st-sph*sw*ct)*Z[mu] + (sph*sw*st+cph*ct)*Zp[mu]}},
74
75(* Gauge bosons: physical vector fields *)
76  V[1] == { ClassName->A,  SelfConjugate->True,  Mass->0,              Width->0,           PDG->22},
77  V[2] == { ClassName->Z , SelfConjugate->True,  Mass->{MZ,91.1876},   Width->{WZ,2.4952}, PDG->23},
78  V[3] == { ClassName->Zp, SelfConjugate->True,  Mass->{MZp,Internal}, Width->{WZp, 13.2}, PDG->32},
79  V[4] == { ClassName->W , SelfConjugate->False, Mass->{MW, Internal}, Width->{WW,2.085},  PDG->24,
80            QuantumNumbers->{Q->1}},
81  V[5] == { ClassName->Wp, SelfConjugate->False, Mass->{MWp,Internal}, Width->{WWp,3.04},  PDG->34,
82            QuantumNumbers->{Q->1}},
83  V[6] == { ClassName->G, SelfConjugate->True, Indices->{Index[Gluon]}, Mass->0, Width->0, PDG->21,
84            PropagatorType->C},
85
86(* Ghost: related to physical gauge bosons *)
87  U[1] == { ClassName->ghG,  SelfConjugate->False, Mass->0,            Width->0,
88            Ghost->G,    QuantumNumbers->{GhostNumber->1}, Indices->{Index[Gluon]} },
89
90(* Higgs: unphysical scalars *)
91  S[11] == { ClassName->Phi,  Unphysical->True, SelfConjugate->False,
92             Indices->{Index[SU2DL],Index[SU2DRs]}, FlavorIndex->SU2DRs,
93             QuantumNumbers->{LNumber->-1/2},
94             Definitions->{
95               Phi[1,1]-> (H1 +I A1)/Sqrt[2],
96               Phi[1,2]-> Cos[beta] Hp[1],
97               Phi[2,1]-> Cos[zeta] Hpbar[2],
98               Phi[2,2]:> Module[{ff}, (kk + TH[1,ff] h0[ff] + I/Sqrt[1+tb^2+tz^2] A2)/Sqrt[2]]}},
99  S[12] == { ClassName->chiL,  Unphysical->True, SelfConjugate->False,
100             Indices->{Index[SU2DL]}, FlavorIndex->SU2DL,
101             QuantumNumbers->{YBL->1/2},
102             Definitions->{
103               chiL[1]-> -Sin[beta] Hp[1],
104               chiL[2]:> Module[{ff}, (vL + TH[3,ff] h0[ff] + -I tb/Sqrt[1+tb^2+tz^2] A2)/Sqrt[2]]}},
105  S[13] == { ClassName->chiR,  Unphysical->True, SelfConjugate->False,
106             Indices->{Index[SU2DR]}, FlavorIndex->SU2DR,
107             QuantumNumbers->{YBL->1/2,LNumber-> 1/2},
108             Definitions->{
109               chiR[1]-> -Sin[zeta] Hp[2],
110               chiR[2]:> Module[{ff}, (vR + TH[4,ff] h0[ff] + I tz/Sqrt[1+tb^2+tz^2] A2 )/Sqrt[2]]}},
111
112(* Higgs: physical fields *)
113  S[1] == { ClassName->h0, SelfConjugate->True, Indices->{Index[SHIGGS]}, FlavorIndex->SHIGGS,
114            ClassMembers->{H0,H1,H2,H3},
115            Mass -> {MH, {MH0,125.},  {MH1,Internal}, {MH2,Internal}, {MH3,Internal}},
116            Width-> {WH, {WH0,0.0176},{WH1,0.95},     {WH2, 3.18},    {WH3,781.}},
117            PDG->{25,35,45,55}},
118  S[2] == { ClassName->A0, SelfConjugate->True, Indices->{Index[PHIGGS]}, FlavorIndex->PHIGGS,
119            ClassMembers->{A1,A2},
120            Mass -> {MA0, {MA1,Internal}, {MA2, Internal}},
121            Width-> {WA0, {WA1,0.95},     {WA2,3.18}},
122            PDG->{36,46}},
123  S[3] == { ClassName->Hp, SelfConjugate->False, Indices->{Index[PHIGGS]}, FlavorIndex->PHIGGS,
124            QuantumNumbers->{Q->1},
125            ClassMembers->{Hp1,Hp2},
126            Mass -> {MHp,{MHp1,Internal}, {MHp2,Internal}},
127            Width-> {WHp,{WHp1,2.83}, {WHp2,0.423}},
128            PDG->{37,47}},
129
130(* Fermions: unphysical fields *)
131  F[11] == { ClassName->LL, Unphysical->True, SelfConjugate->False,
132             Indices->{Index[SU2DL],Index[GEN]}, FlavorIndex->SU2DL,
133             QuantumNumbers->{YBL->-1/2, LNumber->1},
134             Definitions->{
135               LL[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNS[ff, ff2] ProjM[sp1,sp2] vl[sp2,ff2]],
136               LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }},
137  F[12] == { ClassName->LR, Unphysical->True, SelfConjugate->False,
138             Indices->{Index[SU2DR],Index[GEN]}, FlavorIndex->SU2DR,
139             QuantumNumbers->{YBL-> -1/2, LNumber->3/2},
140             Definitions->{
141               LR[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNSp[ff, ff2] ProjP[sp1,sp2] nl[sp2,ff2]],
142               LR[sp1_,2,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }},
143  F[13] == { ClassName->NL, Unphysical->True, SelfConjugate->False,
144             Indices->{Index[GEN]}, FlavorIndex->GEN,
145             QuantumNumbers->{LNumber->2},
146             Definitions->{ NL[sp1_,ff_] :>  Module[{sp2}, ProjM[sp1,sp2] nl[sp2,ff]]}},
147  F[14] == { ClassName->VR, Unphysical->True, SelfConjugate->False,
148             Indices->{Index[GEN]}, FlavorIndex->GEN,
149             QuantumNumbers->{LNumber->1},
150             Definitions->{ VR[sp1_,ff_] :>  Module[{sp2}, ProjP[sp1,sp2] vl[sp2,ff]]}},
151  F[21] == { ClassName->QL, Unphysical->True, SelfConjugate->False,
152             Indices->{Index[SU2DL],Index[GEN],Index[Colour]}, FlavorIndex->SU2DL,
153             QuantumNumbers->{YBL->1/6},
154             Definitions-> {
155               QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
156               QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] } },
157  F[22] == { ClassName->QR, Unphysical->True, SelfConjugate->False,
158             Indices->{Index[SU2DR],Index[GEN],Index[Colour]}, FlavorIndex->SU2DR,
159             QuantumNumbers->{YBL->1/6, LNumber->-1/2},
160             Definitions->{
161               QR[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]],
162               QR[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKMp[ff,ff2] ProjP[sp1,sp2] dqp[sp2,ff2,cc]]}},
163  F[23] == { ClassName->dLp, Unphysical->True, SelfConjugate->False,
164             Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
165             QuantumNumbers->{YBL->-1/3, LNumber->-1},
166             Definitions->{ dLp[sp1_,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] dqp[sp2,ff,cc]] }},
167  F[24] == { ClassName->dR, Unphysical->True, SelfConjugate->False,
168             Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
169             QuantumNumbers->{YBL->-1/3},
170             Definitions->{ dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }},
171
172(* Fermions: physical fields *)
173  F[1] == { ClassName->vl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
174            ClassMembers->{ve,vm,vt}, PDG->{12,14,16},
175            Mass->{Mvl,{Mve,1.0*^-12},{Mvm,0.0089*^-9},{Mvt,0.0504*^-9}}, Width->0},
176  F[2] == { ClassName->l, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
177            QuantumNumbers->{Q->-1}, ClassMembers->{e,m,ta},
178            ParticleName->{"e-","mu-","tau-"}, AntiParticleName->{"e+","mu+","tau+"}, PDG->{11,13,15},
179            Mass->{Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}}, Width->0},
180  F[3] == { ClassName->uq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
181            QuantumNumbers->{Q-> 2/3}, ClassMembers->{u,c,t}, PDG->{2,4,6},
182            Mass->{Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}}, Width->{Wuq,0,0,{WT,1.50833649}}},
183  F[4] == { ClassName->dq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
184            QuantumNumbers->{Q->-1/3}, ClassMembers->{d,s,b}, PDG->{1,3,5},
185            Mass->{Mdq, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}}, Width->0},
186  F[5] == { ClassName->nl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
187            ClassMembers->{ne,nm,nt}, PDG->{6000012,6000014,6000016},
188            ParticleName->{"~ne","~nm","~nt"}, AntiParticleName->{"~ne~","~nm~","~nt~"},
189            Mass->{Mnl,{Mne,300},{Mnm,500},{Mnt,700}},
190            Width->{Wnl,{Wne,0},{Wnm,7.09*^-4},{Wnt,1.13}}},
191  F[6] == { ClassName->dqp, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN,
192            QuantumNumbers->{Q->-1/3}, ClassMembers->{dp,sp,bp}, PDG->{6000001,6000003,6000005},
193            Mass->{Mdqp, {MDP,301}, {MSP,501}, {MBP,701}},
194            Width->{Wnl,{WDP,0},{WSP,0.262},{WBP,9.85}}}
195};
196
197
198(* ************************** *)
199(* *****   Parameters   ***** *)
200(* ************************** *)
201(* Shortcuts for Higgs mixings *)
202DENO   := (fh[MH2]^2 (1 + gh[MH0]^2) + (gh[MH0] - gh[MH2])^2 - 2 fh[MH0] fh[MH2] (1 + gh[MH0] gh[MH2]) +  fh[MH0]^2 (1 + gh[MH2]^2));
203SGN    := (#/Abs[#] &/@ {gh[MH0] (fh[MH2]-fh[MH3]) + gh[MH2] (fh[MH3]-fh[MH0]) + gh[MH3] (fh[MH0]-fh[MH2])})[[1]];
204fh[x_] := (2 x^4 vL vR + x^2 (vL^2 + vR^2) (Sqrt[2] kk kap - 4 vL vR lam3) - 2 Sqrt[2] kk (vL^2 - vR^2)^2 lam3 kap) /
205             (vR (x^2 (4 kk vL vR (alp1 + alp2) + Sqrt[2] vL^2 kap) + 2 Sqrt[2] (kk^2 (alp1 + alp2) + vL^2 lam3) (vR^2 - vL^2) kap));
206gh[x_] := (vL (x^2 (4 kk vL vR (alp1 + alp2) + Sqrt[2] vR^2 kap) + 2 Sqrt[2] (kk^2 (alp1 + alp2) + vR^2 lam3) (vL^2 - vR^2) kap)) /
207    (vR (x^2 (4 kk vL vR (alp1 + alp2) + Sqrt[2] vL^2 kap) + 2 Sqrt[2] (kk^2 (alp1 + alp2) + vL^2 lam3) (vR^2 - vL^2) kap));
208NLAM1 := Sqrt[2]*kk*MH0^6*vL*vR - 4*(alp1 + alp2)^2*kap*kk^4*(vL^2 - vR^2)^2 +
209          MH0^4*(-2*Sqrt[2]*kk*lam3*vL*vR*(vL^2 + vR^2) + kap*(vL^2*vR^2 + kk^2*(vL^2 + vR^2))) -
210          2*MH0^2*(2*Sqrt[2]*(alp1 + alp2)^2*kk^3*vL*vR*(vL^2 + vR^2) +
211          kap*(lam3*vL^2*vR^2*(vL^2 + vR^2) + kk^2*(4*(alp1 + alp2)*vL^2*vR^2 + lam3*(vL^2 - vR^2)^2)));
212DLAM1 := 2*Sqrt[2]*kk^3*MH0^4*vL*vR - 4*kap*kk^4*lam3*(vL^2 - vR^2)^2 + 2*kk^3*MH0^2*(kap*kk - 2*Sqrt[2]*lam3*vL*vR)*(vL^2 + vR^2);
213MH2AA := (vL*vR*(2*Sqrt[2]*kk^3*lam1 - kap*vL*vR) + kk*(-(kap*kk) + 2*Sqrt[2]*lam3*vL*vR)*(vL^2 + vR^2))/(Sqrt[2] kk vL vR) - MH0^2;
214MH2BB := 1/(kk vL vR)*(Sqrt[2]*kap*kk^2*(4*(alp1 + alp2)*vL^2*vR^2 + lam3*(vL^2 - vR^2)^2) +
215            (vL^2 + vR^2)*(4*kk^3*(alp1^2 + 2*alp1*alp2 + alp2^2 - lam1*lam3)*vL*vR + Sqrt[2]*kap*(kk^4*lam1 + lam3*vL^2*vR^2)));
216
217M$Parameters = {
218(* Gauge sector: external parameters *)
219  aEWM1 == { TeX->Subsuperscript[\[Alpha],w,-1], ParameterType->External, BlockName->SMINPUTS, OrderBlock->1,
220             Value->127.9,       InteractionOrder->{QED,-2},
221             Description->"Inverse of the EW coupling constant at the Z pole"},
222  Gf    == { TeX->Subscript[G,f],                ParameterType->External, BlockName->SMINPUTS, OrderBlock->2,
223             Value->1.16637*^-5, InteractionOrder->{QED,2},
224             Description->"Fermi constant"},
225  aS    == { TeX->Subscript[\[Alpha],s],         ParameterType->External, BlockName->SMINPUTS, OrderBlock->3,
226             Value->0.1184,      InteractionOrder->{QCD, 2},
227             Description->"Strong coupling constant at the Z pole."},
228  gR    == { TeX->Subscript[g,R],                ParameterType->External, BlockName->SMINPUTS, OrderBlock->6,
229             Value->0.646482210, InteractionOrder->{QED, 1},
230             Description->"SU(2)_R coupling constant at the Z pole"},
231
232(* Symmetry breaking; external parameters *)
233  tb   == { ParameterType->External, BlockName->SMINPUTS, OrderBlock->5, Value->10.,
234            Description->"Ratio of the bidoublet-to-left Higgs vevs", TeX->Subscript[t,\[Beta]]},
235  vevp == { ParameterType->External, BlockName->SMINPUTS, OrderBlock->7,
236            Value->6500, InteractionOrder->{QED,-1},
237            Description->"SU(2)_R x U(1)BL breaking scale", TeX-> v'},
238
239(* Symmetry breaking: internal parameters *)
240  beta == { ParameterType->Internal, Value->ArcTan[tb],
241            Description->"Arctan of the ratio of the bidoublet-to-left Higgs vevs", TeX->\[Beta]},
242  vev  == { ParameterType->Internal, Value->1/Sqrt[Sqrt[2] Gf], InteractionOrder->{QED,-1},
243            Description -> "SM Higgs vacuum expectation value", TeX ->v},
244  kk   == { ParameterType->Internal, Value->vev*Sin[beta],      InteractionOrder->{QED,-1},
245            Description -> "Higgs bidoublet vacuum expectation value", TeX -> k},
246  vL   == { ParameterType->Internal, Value->vev*Cos[beta],      InteractionOrder->{QED,-1},
247            Description -> "SU(2)L Higgs doublet vacuum expectation value", TeX->Subscript[v,L]},
248  vR   == { ParameterType->Internal, Value->Sqrt[vevp^2-kk^2],  InteractionOrder->{QED,-1},
249            Description -> "SU(2)R Higgs doublet vacuum expectation value", TeX->Subscript[v,R]},
250  tz   == { ParameterType->Internal, Value->kk/vR,
251            Description->"Ratio of the bidoublet-to-right Higgs vevs", TeX->Subscript[t,\[Zeta]]},
252  zeta == { ParameterType->Internal, Value->ArcTan[tz],
253            Description->"Arctan of the ratio of the bidoublet-to-right Higgs vevs", TeX->\[Zeta]},
254
255(* Gauge sector: internal parameters *)
256  MW == { ParameterType->Internal, Value->Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]/aEWM1/Gf*MZ^2]],
257          Description->"W-boson mass", TeX-> Subscript[M,W]},
258  ee == { ParameterType->Internal, Value->Sqrt[4 Pi/aEWM1], InteractionOrder->{QED,1},
259          Description->"Electromagnetic coupling", TeX->e},
260  gs == { ParameterType->Internal, Value->Sqrt[4 Pi aS],    InteractionOrder->{QCD,1},
261          Description->"Strong coupling at the Z pole", TeX->Subscript[g,s], ParameterName->G},
262  gL == { ParameterType->Internal, Value->2/vev MW,         InteractionOrder->{QED,1},
263          Description->"SU(2)_L coupling constant at the Z pole", TeX->Subscript[g,L]  },
264  sw == { ParameterType->Internal, Value->ee/gL,
265          Description->"Sine of the weak angle", TeX->Subscript[s,w]},
266  cw == { ParameterType->Internal, Value->Sqrt[1-sw^2],
267          Description->"Sine of the weak angle", TeX->Subscript[c,w]},
268  gY == { ParameterType->Internal, Value->ee/cw, InteractionOrder->{QED,1},
269          Description->"U(1)Y coupling constant at the Z pole", TeX->Subscript[g,Y]},
270  gBL== { ParameterType->Internal, Value->gY gR/Sqrt[gR^2-gY^2], InteractionOrder->{QED,1},
271          Description->"U(1)_{B-L} coupling constant at the Z pole", TeX->Subscript[g,B-L]},
272  sph == { ParameterType->Internal, Value->gY/gR,
273          Description->"Sine of the weak angle", TeX->Subscript[s,p]},
274  cph == { ParameterType->Internal, Value->Sqrt[1-sph^2],
275          Description->"Sine of the weak angle", TeX->Subscript[c,p]},
276  t2t== { ParameterType->Internal, Description->"Z/Z'-Mixing", TeX-> Subscript[t,2\[Theta]],
277          Value->(2*cph*cw*gL*gR*(cph^2*kk^2-sph^2*vL^2))/(-cph^2*kk^2*(gL^2-cph^2*cw^2*gR^2) - cph^2*gL^2*(gL^2-cw^2*gBL^2*sph^2) + cw^2*gR^2*vR^2)},
278  st == { ParameterType->Internal, Value->Sin[ArcTan[t2t]/2],
279          Description->"Sine of the weak angle", TeX->Subscript[s,t]},
280  ct == { ParameterType->Internal, Value->Sqrt[1-st^2],
281          Description->"Sine of the weak angle", TeX->Subscript[c,t]},
282  MWp== { ParameterType->Internal, Value->1/2 vevp gR,
283          Description->"W'-boson mass", TeX-> Subscript[M,W']},
284  MZp== { ParameterType->Internal, Value->1/2 Sqrt[ gBL^2 sph^2 vL^2 + gR^2/cph^2 (cph^4 kk^2 + vR^2)  ],
285          Description->"Z'-boson mass", TeX-> Subscript[M,Z']},
286
287(* Higgs potential: external parameters *)
288  lam2 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 1, Value -> 0.5,
289            InteractionOrder -> {QED,2},
290            Description -> "Higgs bidoublet quartic coupling", TeX -> Subscript[\[Lambda],2]},
291  lam3 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 2, Value -> 1.6,
292            InteractionOrder -> {QED,2},
293            Description -> "Higgs doublet quartic coupling", TeX -> Subscript[\[Lambda],3]},
294  alp1 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 3, Value -> 0.3,
295            InteractionOrder -> {QED,2},
296            Description -> "Higgs doublet-bidoublet quartic coupling", TeX -> Subscript[\[Alpha],1]},
297  alp2 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 4, Value -> 0.1,
298            InteractionOrder -> {QED,2},
299            Description -> "Higgs doublet-bidoublet quartic coupling", TeX -> Subscript[\[Alpha],2]},
300  alp3 == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 5, Value -> 0.3,
301            InteractionOrder -> {QED,2},
302            Description -> "Higgs doublet-bidoublet quartic coupling", TeX -> Subscript[\[Alpha],3]},
303  kap  == { ParameterType -> External, BlockName -> HPOTINPUTS, OrderBlock -> 6, Value -> -10.,
304            InteractionOrder -> {QED,1},
305            Description -> "Higgs doublet-bidoublet trilinear coupling", TeX -> \[Kappa]},
306
307(* Higgs potential: internal parameters *)
308  IDLT == { ParameterType->Internal, ComplexParameter->False,
309            Indices -> {Index[SU2DR], Index[SU2DRs]},
310            Definitions -> { IDLT[1,1]->1, IDLT[1,2]->0, IDLT[2,1]->0, IDLT[2,2]->1 },
311            Description -> "Delta contracting SU2DR and SU2DRs indices", TeX->\[Delta]},
312  UEpsRs== { ParameterType->Internal, ComplexParameter->False,
313            Indices -> {Index[SU2DRs], Index[SU2DRs]},
314            Definitions -> { UEpsRs[1,1]->0, UEpsRs[1,2]->-1, UEpsRs[2,1]-> 1, UEpsRs[2,2]->0 },
315            Description -> "Epsilon in SU2R space (with upper indices)", TeX->Subscript[\[Epsilon],u]},
316  UEpsR== { ParameterType->Internal, ComplexParameter->False,
317            Indices -> {Index[SU2DR], Index[SU2DR]},
318            Definitions -> { UEpsR[1,1]->0, UEpsR[1,2]->-1, UEpsR[2,1]-> 1, UEpsR[2,2]->0 },
319            Description -> "Epsilon in SU2R space (with upper indices)", TeX->Subscript[\[Epsilon],u]},
320  UEpsL== { ParameterType->Internal, ComplexParameter->False,
321            Indices -> {Index[SU2DL], Index[SU2DL]},
322            Definitions -> { UEpsL[1,1]->0, UEpsL[1,2]->-1, UEpsL[2,1]-> 1, UEpsL[2,2]->0 },
323            Description -> "Epsilon in SU2L space (with upper indices)", TeX->Subscript[\[Epsilon],u]},
324  DEps== { ParameterType->Internal, ComplexParameter->False,
325            Indices -> {Index[SU2DL], Index[SU2DL]},
326            Definitions -> { DEps[1,1]->0, DEps[1,2]-> 1, DEps[2,1]->-1, DEps[2,2]->0 },
327            Description -> "Epsilon in SU2L space (with lower indices)", TeX->Subscript[\[Epsilon],d]},
328  lam1 == { ParameterType->Internal,  Value -> NLAM1/DLAM1,
329            InteractionOrder -> {QED,2},
330            Description   -> "Higgs bidoublet quartic term", TeX->Subscript[\[Lambda],1]},
331  MU12 == { ParameterType->Internal, Value -> (vL^2+vR^2)(alp1+alp2) + kk^2 lam1 + vL vR kap/(Sqrt[2] kk),
332            Description   -> "Higgs bidoublet quadratic term", TeX->Subsuperscript[\[Mu],1,2]},
333  MU22 == { ParameterType->Internal, Value -> kk^2(alp1+alp2) + (vL^2+vR^2)*lam3,
334            Description   -> "Higgs doublet quadratic term", TeX->Subsuperscript[\[Mu],2,2]},
335  lam4 == { ParameterType->Internal, Value -> lam3 - kk kap/(Sqrt[2]vL vR),
336            InteractionOrder -> {QED,2},
337            Description   -> "Higgs doublet-bidoublet quartic term", TeX->Subscript[\[Lambda],4]},
338
339(* Higgs masses and mixings: internal parameters *)
340  MHp1 == { ParameterType->Internal,  Value -> Sqrt[-(2 kk vL (alp2-alp3) + Sqrt[2] kap vR)*(kk^2+vL^2)/(2 kk vL)],
341            Description   -> "Lightest charged Higgs mass"},
342  MHp2 == { ParameterType->Internal,  Value -> Sqrt[-(2 kk vR (alp2-alp3) + Sqrt[2] kap vL)*(kk^2+vR^2)/(2 kk vR)],
343            Description   -> "Heaviest charged Higgs mass"},
344  MH1  == { ParameterType->Internal,  Value -> Sqrt[2*kk^2*lam2 - kap*vL*vR/(Sqrt[2]*kk) - (alp2-alp3)*(vL^2+vR^2)],
345            Description   -> "Next-to-lightest scalar Higgs mass"},
346  MH2  == { ParameterType->Internal,  Value -> 1/Sqrt[2] Sqrt[MH2AA - Sqrt[MH2AA^2 + 4(MH2BB + MH0^2 MH2AA)]],
347            Description   -> "Second scalar Higgs mass", TeX->Subscript[M,H2]},
348  MH3  == { ParameterType->Internal,  Value -> 1/Sqrt[2] Sqrt[MH2AA + Sqrt[MH2AA^2 + 4(MH2BB + MH0^2 MH2AA)]],
349            Description   -> "Third scalar Higgs mass", TeX->Subscript[M,H3]},
350  MA1  == { ParameterType->Internal,  Value -> Sqrt[2*kk^2*lam2 - kap*vL*vR/(Sqrt[2]*kk) - (alp2-alp3)*(vL^2+vR^2)],
351            Description   -> "Lightest pseudoscalar Higgs mass"},
352  MA2  == { ParameterType->Internal,  Value -> Sqrt[ -kap/(Sqrt[2] kk vL vR) ( vL^2 vR^2 + kk^2(vL^2+vR^2)) ],
353            Description   -> "Lightest pseudoscalar Higgs mass"},
354  TH   == { ParameterType-> Internal, ComplexParameter->False,
355            Indices->{Index[SHIGGS],Index[SHIGGS]}, Unitary->True,
356            Value -> {
357              TH[1,2]-> 0, TH[2,1]-> 0, TH[2,2]-> 1, TH[2,3]-> 0, TH[2,4]-> 0, TH[3,2]-> 0, TH[4,2]-> 0,
358              TH[1,1]-> fh[MH0]/Sqrt[1 + fh[MH0]^2 + gh[MH0]^2],
359              TH[1,3]-> (fh[MH2] (1 + gh[MH0]^2) - fh[MH0] (1 + gh[MH0] gh[MH2]))/Sqrt[(1 + fh[MH0]^2 + gh[MH0]^2) DENO],
360              TH[1,4]-> SGN (gh[MH2] - gh[MH0])/Sqrt[DENO],
361              TH[3,1]-> gh[MH0]/Sqrt[1 + fh[MH0]^2 + gh[MH0]^2],
362              TH[3,3]-> (gh[MH2]*(1 + fh[MH0]^2) - gh[MH0]*(1 + fh[MH0]*fh[MH2]))/Sqrt[(1 + fh[MH0]^2 + gh[MH0]^2) DENO],
363              TH[3,4]-> SGN (fh[MH0] - fh[MH2])/Sqrt[DENO],
364              TH[4,1]-> 1/Sqrt[1 + fh[MH0]^2 + gh[MH0]^2],
365              TH[4,3]-> (fh[MH0]^2 + gh[MH0]^2 - fh[MH0]*fh[MH2] - gh[MH0]*gh[MH2])/Sqrt[(1 + fh[MH0]^2 + gh[MH0]^2) DENO],
366              TH[4,4]-> SGN (gh[MH0] fh[MH2] - gh[MH2] fh[MH0])/Sqrt[DENO]
367            }, Description-> "Scalar Higgs mixing matrix TH",  TeX->Subscript[T,H]},
368
369(* Fermion masses: internal parameters *)
370  yu == { ParameterType->Internal, ComplexParameter->False,
371          Indices->{Index[GEN], Index[GEN]},
372          InteractionOrder->{QED, 1},
373          Definitions-> {yu[i_?NumericQ, j_?NumericQ] :> 0  /; (i =!= j)},
374          Value      -> {yu[1,1] -> Sqrt[2] MU/kk, yu[2,2] -> Sqrt[2] MC/kk, yu[3,3] -> Sqrt[2] MT/kk},
375          Description->"Up-type quark Yukawa couplings", TeX->Superscript[y,u]},
376  yd == { ParameterType->Internal, ComplexParameter->False,
377          Indices->{Index[GEN], Index[GEN]},
378          InteractionOrder->{QED, 1},
379          Definitions-> {yd[i_?NumericQ, j_?NumericQ] :> 0  /; (i =!= j)},
380          Value      -> {yd[1,1] -> Sqrt[2] MD/vL, yd[2,2] -> Sqrt[2] MS/vL, yd[3,3] -> Sqrt[2] MB/vL},
381          Description->"Down-type quark Yukawa couplings", TeX->Superscript[y,d]},
382  ydp== { ParameterType->Internal, ComplexParameter->False,
383          Indices->{Index[GEN], Index[GEN]},
384          InteractionOrder->{QED, 1},
385          Definitions-> {ydp[i_?NumericQ, j_?NumericQ] :> 0  /; (i =!= j)},
386          Value      -> {ydp[1,1] -> Sqrt[2] MDP/vR, ydp[2,2] -> Sqrt[2] MSP/vR, ydp[3,3] -> Sqrt[2] MBP/vR},
387          Description->"Exotic down-type quark Yukawa couplings", TeX->Superscript[y,d']},
388  ye == { ParameterType->Internal, ComplexParameter->False,
389          Indices->{Index[GEN], Index[GEN]},
390          InteractionOrder->{QED, 1},
391          Definitions-> {ye[i_?NumericQ, j_?NumericQ] :> 0  /; (i =!= j)},
392          Value      -> {ye[1,1] -> Sqrt[2] Me/kk, ye[2,2] -> Sqrt[2] MMU/kk, ye[3,3] -> Sqrt[2] MTA/kk},
393          Description->"Charged lepton Yukawa couplings", TeX->Superscript[y,e]},
394  ynu== { ParameterType->Internal, ComplexParameter->False,
395          Indices->{Index[GEN], Index[GEN]},
396          InteractionOrder->{QED, 1},
397          Definitions-> {ynu[i_?NumericQ, j_?NumericQ] :> 0  /; (i =!= j)},
398          Value      -> {ynu[1,1] -> Sqrt[2] Mve/vL, ynu[2,2] -> Sqrt[2] Mvm/vL, ynu[3,3] -> Sqrt[2] Mvt/vL},
399          Description->"Neutrino Yukawa couplings", TeX->Superscript[y,\[Nu]]},
400  yn == { ParameterType->Internal, ComplexParameter->False,
401          Indices->{Index[GEN], Index[GEN]},
402          InteractionOrder->{QED, 1},
403          Definitions-> {yn[i_?NumericQ, j_?NumericQ] :> 0  /; (i =!= j)},
404          Value      -> {yn[1,1] -> Sqrt[2] Mne/vR, yn[2,2] -> Sqrt[2] Mnm/vR, yn[3,3] -> Sqrt[2] Mnt/vR},
405          Description->"Scotino Yukawa couplings", TeX->Superscript[y,n]},
406
407(* Fermion mixings: external parameters *)
408  CKMlam == { TeX->Subscript[\[Lambda],CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->1,
409              Value->0.22453, Description->"Wolfenstein parameter lambda (quark mixings)"},
410  CKMA   == { TeX->Subscript[A,CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->2,
411              Value->0.836, Description->"Wolfenstein parameter A (quark mixings)"},
412  CKMrho == { TeX->Subscript[\[Rho],CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->3,
413              Value->0.122, Description->"Wolfenstein parameter rhobar (quark mixings)"},
414  CKMeta == { TeX->Subscript[\[Eta],CKM], ParameterType->External, BlockName->CKMBLOCK, OrderBlock->4,
415              Value->0.355, Description->"Wolfenstein parameter etabar (quark mixings)"},
416  PMNSs12 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->1,
417              Value->Sqrt[.297], Description->"Sine of theta_{12} (neutrino mixings)"},
418  PMNSs23 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->2,
419              Value->Sqrt[.425], Description->"Sine of theta_{23} (neutrino mixings)"},
420  PMNSs13 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->3,
421              Value->Sqrt[.0215], Description->"Sine of theta_{13} (neutrino mixings)"},
422  PMNSdel == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->4,
423              Value->1.38 Pi, Description->"CP phase (neutrino mixings)"},
424  PMNSps12 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->11,
425              Value->Sqrt[.297], Description->"Sine of theta_{12} (scotino mixings)"},
426  PMNSps23 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->12,
427              Value->Sqrt[.425], Description->"Sine of theta_{23} (scotino mixings)"},
428  PMNSps13 == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->13,
429              Value->Sqrt[.0215], Description->"Sine of theta_{13} (scotino mixings)"},
430  PMNSpdel == { ParameterType->External, BlockName->PMNSBLOCK, OrderBlock->14,
431              Value->1.38 Pi, Description->"Cp phase (scotino mixings)"},
432  CKMps12 == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->11,
433               Value->0.22453, Description->"Sine of theta_{12} (exotic down-type quark mixings)"},
434  CKMps23 == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->12,
435               Value->0.0421, Description->"Sine of theta_{23} (exotic down-type quark mixings)"},
436  CKMps13 == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->13,
437               Value->0.00364, Description->"Sine of theta_{13} (exotic down-type quark mixings)"},
438  CKMpdel == { ParameterType->External, BlockName->CKMBLOCK, OrderBlock->14,
439               Value->1.24, Description->"CP phase (exotic down-type quark mixings)"},
440
441(* Fermion mixings: internal parameters *)
442   CKMs12  == { ParameterType -> Internal, Value->CKMlam,        Description->"s_{12}"},
443   CKMs23  == { ParameterType -> Internal, Value->CKMA*CKMlam^2, Description->"s_{23}"},
444   CKMs13d == { ParameterType -> Internal, Value->CKMA*CKMlam^3*Sqrt[1-CKMA^2 CKMlam^4](CKMrho + I CKMeta)/
445                    (Sqrt[1-CKMlam^2]*(1-CKMA^2 CKMlam^4 (CKMrho + I CKMeta))), Description->"s_{13} Exp[i delta]"},
446   CKMc12  == { ParameterType -> Internal, Value-> Sqrt[1-CKMs12^2], Description->"c_{12}"},
447   CKMc13  == { ParameterType -> Internal, Value-> Sqrt[1-Abs[CKMs13d]^2], Description->"c_{13}"},
448   CKMc23  == { ParameterType -> Internal, Value-> Sqrt[1-CKMs23^2], Description->"c_{23}"},
449   CKM  == { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
450             Value->{
451               CKM[1,1]-> CKMc12*CKMc13,                       CKM[1,2]-> CKMs12*CKMc13,                       CKM[1,3]->Conjugate[CKMs13d],
452               CKM[2,1]->-CKMs12*CKMc23-CKMc12*CKMs23*CKMs13d, CKM[2,2]-> CKMc12*CKMc23-CKMs12*CKMs23*CKMs13d, CKM[2,3]->CKMs23*CKMc13,
453               CKM[3,1]-> CKMs12*CKMs23-CKMc12*CKMc23*CKMs13d, CKM[3,2]->-CKMc12*CKMs23-CKMs12*CKMc23*CKMs13d, CKM[3,3]->CKMc23*CKMc13},
454             Description -> "CKM-Matrix", TeX-> Superscript[V,CKM]},
455   PMNSs13d == { ParameterType -> Internal, Value-> PMNSs13*Exp[I PMNSdel], Description->"s_{13} Exp[i delta]"},
456   PMNSc12  == { ParameterType -> Internal, Value-> Sqrt[1-PMNSs12^2], Description->"c_{12}"},
457   PMNSc13  == { ParameterType -> Internal, Value-> Sqrt[1-PMNSs13^2], Description->"c_{13}"},
458   PMNSc23  == { ParameterType -> Internal, Value-> Sqrt[1-PMNSs23^2], Description->"c_{23}"},
459   PMNS == { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
460             Value->{
461              PMNS[1,1]-> PMNSc12*PMNSc13,                          PMNS[1,2]-> PMNSs12*PMNSc13,                          PMNS[1,3]->Conjugate[PMNSs13d],
462              PMNS[2,1]->-PMNSs12*PMNSc23-PMNSc12*PMNSs23*PMNSs13d, PMNS[2,2]-> PMNSc12*PMNSc23-PMNSs12*PMNSs23*PMNSs13d, PMNS[2,3]->PMNSs23*PMNSc13,
463              PMNS[3,1]-> PMNSs12*PMNSs23-PMNSc12*PMNSc23*PMNSs13d, PMNS[3,2]->-PMNSc12*PMNSs23-PMNSs12*PMNSc23*PMNSs13d, PMNS[3,3]->PMNSc23*PMNSc13},
464             Description -> "PMNS-Matrix", TeX-> Superscript[V,PMNS]},
465   PMNSps13d == { ParameterType -> Internal, Value-> PMNSps13*Exp[I PMNSpdel], Description->"s_{13} Exp[i delta]"},
466   PMNSpc12  == { ParameterType -> Internal, Value-> Sqrt[1-PMNSps12^2], Description->"c_{12}"},
467   PMNSpc13  == { ParameterType -> Internal, Value-> Sqrt[1-PMNSps13^2], Description->"c_{13}"},
468   PMNSpc23  == { ParameterType -> Internal, Value-> Sqrt[1-PMNSps23^2], Description->"c_{23}"},
469   PMNSp== { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
470             Value->{
471              PMNSp[1,1]-> PMNSpc12*PMNSpc13,                             PMNSp[1,2]-> PMNSps12*PMNSpc13,                             PMNSp[1,3]->Conjugate[PMNSps13d],
472              PMNSp[2,1]->-PMNSps12*PMNSpc23-PMNSpc12*PMNSps23*PMNSps13d, PMNSp[2,2]-> PMNSpc12*PMNSpc23-PMNSps12*PMNSps23*PMNSps13d, PMNSp[2,3]->PMNSps23*PMNSpc13,
473              PMNSp[3,1]-> PMNSps12*PMNSps23-PMNSpc12*PMNSpc23*PMNSps13d, PMNSp[3,2]->-PMNSpc12*PMNSps23-PMNSps12*PMNSpc23*PMNSps13d, PMNSp[3,3]->PMNSpc23*PMNSpc13},
474             Description -> "PMNS'-Matrix", TeX-> Superscript[V',PMNS]},
475   CKMps13d == { ParameterType -> Internal, Value-> CKMps13*Exp[I CKMpdel], Description->"s_{13} Exp[i delta]"},
476   CKMpc12  == { ParameterType -> Internal, Value-> Sqrt[1-CKMps12^2], Description->"c_{12}"},
477   CKMpc13  == { ParameterType -> Internal, Value-> Sqrt[1-CKMps13^2], Description->"c_{13}"},
478   CKMpc23  == { ParameterType -> Internal, Value-> Sqrt[1-CKMps23^2], Description->"c_{23}"},
479   CKMp== { ParameterType -> Internal, Indices->{Index[GEN],Index[GEN]}, Unitary-> True,
480             Value->{
481              CKMp[1,1]-> CKMpc12*CKMpc13,                          CKMp[1,2]-> CKMps12*CKMpc13,                          CKMp[1,3]->Conjugate[CKMps13d],
482              CKMp[2,1]->-CKMps12*CKMpc23-CKMpc12*CKMps23*CKMps13d, CKMp[2,2]-> CKMpc12*CKMpc23-CKMps12*CKMps23*CKMps13d, CKMp[2,3]->CKMps23*CKMpc13,
483              CKMp[3,1]-> CKMps12*CKMps23-CKMpc12*CKMpc23*CKMps13d, CKMp[3,2]->-CKMpc12*CKMps23-CKMps12*CKMpc23*CKMps13d, CKMp[3,3]->CKMpc23*CKMpc13},
484             Description -> "CKM'-Matrix", TeX-> Superscript[V',CKM]},
485
486(* Effective Higgs couplings *)
487  Ghgg == { ParameterType -> External, InteractionOrder->{HIG,1}, TeX->Subscript[g,hgg], Description -> "Loop-induced h0-gluon coupling",
488            BlockName -> EffectiveHiggs, OrderBlock->1, Value ->  0.12},
489  Ghaa == { ParameterType -> External, InteractionOrder->{HIG,1}, TeX->Subscript[g,haa], Description -> "Loop-induced h0-photon coupling",
490            BlockName -> EffectiveHiggs, OrderBlock->2, Value ->  0.11}
491};
492
493(* ************************** *)
494(* *****   Lagrangian   ***** *)
495(* ************************** *)
496(* LVector *)
497LVector := Plus@@ (Block[{aa,mu,nu}, -1/4 If[Abelian, FS[GaugeBoson,mu,nu]^2, FS[GaugeBoson,mu,nu,aa]^2] /.MR$GaugeGroupRules[#]] & /@ MR$GaugeGroupList);
498
499(* LMatter *)
500LMatter := Block[{mu}, I*(
501    QLbar.Ga[mu].DC[QL, mu] + QRbar.Ga[mu].DC[QR, mu] + dLpbar.Ga[mu].DC[dLp, mu] + dRbar.Ga[mu].DC[dR, mu] +
502    LLbar.Ga[mu].DC[LL, mu] + LRbar.Ga[mu].DC[LR, mu] + NLbar.Ga[mu].DC[NL, mu] + VRbar.Ga[mu].DC[VR, mu])];
503
504(* Scalar potential *)
505VHiggs:= Block[{II,IIp,JJ,JJp,JJpp,KK,KKp,LL,LLp,LLpp},
506     - MU22 (chiLbar[II] chiL[II] + chiRbar[II] chiR[II])\
507     - MU12 (Phibar[II,JJ] Phi[II,JJ]) \
508     + lam1 (Phibar[II,JJ] Phi[II,JJ]) (Phibar[KK,LL]Phi[KK,LL]) \
509     + lam2 (Phi[II, JJ] UEpsRs[JJ, JJp] DEps[II, IIp] Phi[IIp, JJp]) HC[Phi[KK, LL] UEpsRs[LL, LLp] DEps[KK, KKp] Phi[KKp, LLp]] \
510     + lam3 ( chiLbar[II] chiL[II] chiLbar[JJ] chiL[JJ] + chiRbar[II] chiR[II] chiRbar[JJ] chiR[JJ]) \
511     + 2 lam4 chiLbar[II] chiL[II] chiRbar[JJ] chiR[JJ] \
512     + kap (chiLbar[II] Phi[II, JJ] IDLT[JJp, JJ] chiR[JJp] + chiRbar[JJp] IDLT[JJp, JJ] Phibar[II, JJ] chiL[II]) \
513     + 2 alp1 (Phibar[II,JJ] Phi[II,JJ]) (chiLbar[KK] chiL[KK] + chiRbar[KK] chiR[KK]) \
514     + 2 alp2 (chiLbar[II] Phi[II, JJ] chiL[KK] Phibar[KK, JJ] + IDLT[II, IIp] IDLT[KK, KKp] Phibar[JJ, IIp] chiRbar[II] Phi[JJ, KKp] chiR[KK]) \
515     + 2 alp3 HC[chiL[II] UEpsRs[JJ,JJp] DEps[II,IIp] Phi[IIp,JJp]] (chiL[KK] UEpsRs[JJ,LLp] DEps[KK,KKp] Phi[KKp,LLp]) \
516     + 2 alp3 chiRbar[JJpp] IDLT[JJpp,JJ] UEpsRs[JJ,JJp] DEps[II,IIp] Phi[IIp,JJp] HC[chiRbar[LLpp] IDLT[LLpp,LL] UEpsRs[LL,LLp] DEps[II,KKp] Phi[KKp,LLp]]];
517
518(* Higgs Lagrangian *)
519LHiggs:= DC[Phibar[II,JJ],mu] DC[Phi[II,JJ],mu] + DC[chiLbar[II],mu] DC[chiL[II],mu] + DC[chiRbar[II],mu] DC[chiR[II],mu] - VHiggs;
520
521(* Yukawa Lagrangian *)
522LYuk:= Block[{sp1,ff1,ff2,ff3,cc,ii,iip,jj,jjp,jjpp},
523    yu[ff1,ff2]  QLbar[sp1,ii,ff1,cc].QR[sp1,jjpp,ff2,cc] IDLT[jjpp,jj] DEps[ii,iip] UEpsRs[jj,jjp] Phibar[iip, jjp] \
524  - yd[ff2,ff3]  CKM[ff1,ff2]  QLbar[sp1,ii,ff1,cc].dR[sp1,ff3,cc] chiL[ii] \
525  - ydp[ff2,ff3] CKMp[ff1,ff2] QRbar[sp1,ii,ff1,cc].dLp[sp1,ff3,cc] chiR[ii] \
526  - ye[ff1,ff2]  LLbar[sp1,ii,ff1].LR[sp1,jj,ff2] IDLT[jj,jjp] Phi[ii,jjp] \
527  + ynu[ff2,ff3] PMNS[ff1,ff2] LLbar[sp1,ii,ff1].VR[sp1,ff3] UEpsL[ii,jj] chiLbar[jj] \
528  + yn[ff2,ff3]  PMNSp[ff1,ff2] LRbar[sp1,ii,ff1].NL[sp1,ff3] UEpsR[ii,jj] chiRbar[jj] ];
529
530(* Ghost Lagrangian *)
531LGhost:= - ghGbar.del[DC[ghG,mu],mu];
532
533(* Effective Higgs couplings *)
534LagHEffective := Block[{mu,nu,aa}, -1/4 Ghaa H0 FS[A,mu,nu] FS[A,mu,nu] -1/4 Ghgg H0 FS[G,mu,nu,aa] FS[G,mu,nu,aa] ];
535