RMSSM: mrssm.fr

File mrssm.fr, 54.0 KB (added by BenjF, 6 years ago)

FeynRules model file

Line 
1(* ********************************************************* *)
2(* *****                                               ***** *)
3(* *****  FeynRules model file: the MRSSM               ***** *)
4(* *****  Author: B. Fuks                              ***** *)
5(* *****                                               ***** *)
6(* ********************************************************* *)
7
8(* ************************** *)
9(* *****  Information   ***** *)
10(* ************************** *)
11M$ModelName = "MRSSM";
12M$Information = { Authors->{"Benjamin Fuks"}, Emails->{"fuks@cern.ch"}, Institutions->{"IPHC Strasbourg / University of Strasbourg"},
13                  Date->"10.02.12", Version->"1.2.5",
14                  References->{"B. Fuks, Int.J.Mod.Phys. A27 (2012) 1230007."},
15                  URLs->{"http://feynrules.phys.ucl.ac.be/view/Main/MRSSM"} };
16
17(* v1.2.5: public version.                                                               *)
18(* v1.2.2: small bug in the definition of the CKM matrix. Thanks Antonio Mariano.        *)
19(* v1.2.1: renaming of SP to SPot (variable name clashing). Thanks to Kentarou Mawatari. *)
20
21(* ************************** *)
22(* *****      Flags     ***** *)
23(* ************************** *)
24$CKMDiag = True;   (* CKM  = identity or not *)
25$MNSDiag = True;   (* PMNS = identity or not *)
26
27
28(* ************************** *)
29(* *****  Gauge groups  ***** *)
30(* ************************** *)
31M$GaugeGroups = {
32  U1Y  == { Abelian->True,  CouplingConstant->gp, Superfield->BSF, Charge->Y, GUTNormalization->3/5},
33  SU2L == { Abelian->False, CouplingConstant->gw, Superfield->WSF,
34            StructureConstant->ep, Representations->{Ta,SU2D}, Definitions->{Ta[a__]->PauliSigma[a]/2, ep->Eps}},
35  SU3C == { Abelian->False, CouplingConstant->gs, Superfield->GSF,
36            StructureConstant->f,  Representations->{{T,Colour}, {Tb,Colourb}}, SymmetricTensor->dSUN}
37};
38
39(* ************************** *)
40(* *****    Indices     ***** *)
41(* ************************** *)
42IndexRange[Index[SU2W]] =   Unfold[Range[3]]; IndexStyle[SU2W,j];  IndexRange[Index[SU2D]] =   Unfold[Range[2]]; IndexStyle[SU2D,k];
43IndexRange[Index[Gluon ]] = NoUnfold[Range[8]]; IndexStyle[Gluon, a];  IndexRange[Index[Colour ]] = NoUnfold[Range[3]]; IndexStyle[Colour, m];
44IndexRange[Index[Colourb]] = NoUnfold[Range[3]]; IndexStyle[Colourb,m];
45IndexRange[Index[INO ]] = Range[4];           IndexStyle[INO, i];
46IndexRange[Index[GEN ]] = Range[3];           IndexStyle[GEN, f];
47IndexRange[Index[SCA ]] = Range[6];           IndexStyle[SCA, i];
48IndexRange[Index[SHig]] = Range[4];           IndexStyle[SHig,n];
49IndexRange[Index[PHig]] = Range[3];           IndexStyle[PHig,n];
50IndexRange[Index[RHig]] = Range[2];           IndexStyle[RHig,n];
51IndexRange[Index[sglu]] = Range[2];           IndexStyle[sglu,n];
52
53
54(* ************************** *)
55(* *****  Superfields   ***** *)
56(* ************************** *)
57M$Superfields = {
58  VSF[1] == { ClassName->BSF, GaugeBoson->B,  Gaugino->bow},
59  VSF[2] == { ClassName->WSF, GaugeBoson->Wi, Gaugino->wow, Indices->{Index[SU2W]}},
60  VSF[3] == { ClassName->GSF, GaugeBoson->G,  Gaugino->gow, Indices->{Index[Gluon] }},
61  CSF[1] == { ClassName->HU, Chirality->Left, Weyl->huw, Scalar->hus, QuantumNumbers->{Y-> 1/2}, Indices->{Index[SU2D]}},
62  CSF[2] == { ClassName->HD, Chirality->Left, Weyl->hdw, Scalar->hds, QuantumNumbers->{Y->-1/2}, Indices->{Index[SU2D]}},
63  CSF[3] == { ClassName->LL, Chirality->Left, Weyl->LLw, Scalar->LLs, QuantumNumbers->{Y->-1/2}, Indices->{Index[SU2D], Index[GEN]}},
64  CSF[4] == { ClassName->ER, Chirality->Left, Weyl->ERw, Scalar->ERs, QuantumNumbers->{Y-> 1},   Indices->{Index[GEN]}},
65  CSF[5] == { ClassName->VR, Chirality->Left, Weyl->VRw, Scalar->VRs, Indices->{Index[GEN]}},
66  CSF[6] == { ClassName->QL, Chirality->Left, Weyl->QLw, Scalar->QLs, QuantumNumbers->{Y-> 1/6}, Indices->{Index[SU2D], Index[GEN], Index[Colour]}},
67  CSF[7] == { ClassName->UR, Chirality->Left, Weyl->URw, Scalar->URs, QuantumNumbers->{Y->-2/3}, Indices->{Index[GEN], Index[Colourb]}           },
68  CSF[8] == { ClassName->DR, Chirality->Left, Weyl->DRw, Scalar->DRs, QuantumNumbers->{Y-> 1/3}, Indices->{Index[GEN], Index[Colourb]}           },
69  CSF[9] == { ClassName->RD, Chirality->Left, Weyl->rdw, Scalar->rds, QuantumNumbers->{Y-> 1/2}, Indices->{Index[SU2D]}},
70  CSF[10]== { ClassName->RU, Chirality->Left, Weyl->ruw, Scalar->rus, QuantumNumbers->{Y->-1/2}, Indices->{Index[SU2D]}},
71  CSF[11]== { ClassName->PhiB, Chirality->Left, Weyl->bpow, Scalar->sigB},
72  CSF[12]== { ClassName->PhiW, Chirality->Left, Weyl->wpow, Scalar->sigW, Indices->{Index[SU2W]}},
73  CSF[13]== { ClassName->PhiG, Chirality->Left, Weyl->gpow, Scalar->sigG, Indices->{Index[Gluon]}}
74};
75
76(* ************************** *)
77(* *****     Fields     ***** *)
78(* ************************** *)
79M$ClassesDescription = {
80(* Gauge bosons: unphysical vector fields *)
81  V[11] == { ClassName->B, Unphysical->True, SelfConjugate->True,
82            Definitions->{B[mu_]->-sw Z[mu]+cw A[mu]} },
83  V[12] == { ClassName->Wi, Unphysical->True, SelfConjugate->True, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
84             Definitions-> {Wi[mu_,1]->(Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2]->(Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3]->cw Z[mu] + sw A[mu]} },
85
86(* Gauge bosons: physical vector fields *)
87  V[1] == { ClassName->A, SelfConjugate->True,  Mass->0,  Width->0,  ParticleName->"a",
88            PDG->22, PropagatorLabel->"A", PropagatorType->Sine, PropagatorArrow->None},
89  V[2] == { ClassName->Z, SelfConjugate->True,  Mass->MZ, Width->WZ, ParticleName->"Z",
90            PDG->23, PropagatorLabel->"Z", PropagatorType->Sine, PropagatorArrow->None},
91  V[3] == { ClassName->W, SelfConjugate->False, Mass->MW, Width->WW, ParticleName->"W+", AntiParticleName->"W-", QuantumNumbers->{Q->1},
92            PDG->24, PropagatorLabel->"W", PropagatorType->Sine, PropagatorArrow->Forward},
93  V[4] == { ClassName->G, SelfConjugate->True, Indices->{Index[Gluon]}, Mass->0, Width->0, ParticleName->"g",
94            PDG->21, PropagatorLabel->"G", PropagatorType->C,    PropagatorArrow->None },
95
96(* Gauginos: unphysical Weyls *)
97  W[20] == { ClassName->bow, Unphysical->True, Chirality->Left, SelfConjugate->False,
98             Definitions->{bow[s_]:>Module[{i}, -I*Conjugate[NNL[i,1]]*new1[s,i]]}},
99  W[21] == { ClassName->wow, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
100             Definitions->{
101               wow[s_,1]:>Module[{i},(Conjugate[UU[i,3]]*chmw[s,i]+Conjugate[VV[i,1]]*chpw[s,i])/(I*Sqrt[2])],
102               wow[s_,2]:>Module[{i},(Conjugate[UU[i,3]]*chmw[s,i]-Conjugate[VV[i,1]]*chpw[s,i])/(-Sqrt[2])],
103               wow[s_,3]:>Module[{i},-I*Conjugate[NNL[i,2]]*new1[s,i]]} },
104  W[22] == { ClassName->gow,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[Gluon]},  Definitions->{gow[inds__]->-I*goww[inds]} },
105
106(* Gaugino': unphysical Weyls *)
107  W[40] == { ClassName->bpow, Unphysical->True, Chirality->Left, SelfConjugate->False,
108             Definitions->{bpow[s_]:>Module[{i}, Conjugate[NNR[i,1]]*new2[s,i]]}},
109  W[41] == { ClassName->wpow, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
110             Definitions->{
111               wpow[s_,1]:>Module[{i},(Conjugate[UU[i,1]]*chmw[s,i]+Conjugate[VV[i,3]]*chpw[s,i])/(Sqrt[2])],
112               wpow[s_,2]:>Module[{i},(Conjugate[UU[i,1]]*chmw[s,i]-Conjugate[VV[i,3]]*chpw[s,i])/(I Sqrt[2])],
113               wpow[s_,3]:>Module[{i},Conjugate[NNR[i,2]]*new2[s,i]]} },
114
115(* Higgsinos: unphysical Weyls *)
116  W[23] == { ClassName->huw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
117             Definitions->{
118               huw[s_,1]:> Module[{i}, Conjugate[VV[i,4]]*chpw[s,i]],
119               huw[s_,2]:> Module[{i}, Conjugate[NNR[i,4]]*new2[s,i]] } },
120  W[24] == { ClassName->hdw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
121             Definitions->{
122               hdw[s_,1]:> Module[{i}, Conjugate[NNR[i,3]]*new2[s,i]],
123               hdw[s_,2]:> Module[{i}, Conjugate[UU[i,2]]*chmw[s,i]]} },
124
125(* R-Higgsinos: unphysical Weyls *)
126  W[30] == { ClassName->rdw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
127             Definitions->{
128               rdw[s_,1]:> Module[{i}, Conjugate[VV[i,2]]*chpw[s,i]],
129               rdw[s_,2]:> Module[{i}, Conjugate[NNL[i,4]]*new1[s,i]] } },
130  W[31] == { ClassName->ruw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
131             Definitions->{
132               ruw[s_,1]:> Module[{i}, Conjugate[NNL[i,3]]*new1[s,i]],
133               ruw[s_,2]:> Module[{i}, Conjugate[UU[i,4]]*chmw[s,i]]} },
134
135(* Gauginos/Higgsinos: physical Weyls *)
136  W[0] == { ClassName->new1, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[INO]}, FlavorIndex->INO },
137  W[1] == { ClassName->new2, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[INO]}, FlavorIndex->INO },
138  W[2] == { ClassName->chpw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[INO]}, FlavorIndex->INO, QuantumNumbers->{Q-> 1} } ,
139  W[3] == { ClassName->chmw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[INO]}, FlavorIndex->INO, QuantumNumbers->{Q->-1} } ,
140  W[4] == { ClassName->goww, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[Gluon]} },
141  W[42]== { ClassName->gpow, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[Gluon]} },
142
143(* Gauginos/Higgsinos: physical Diracs *)
144  F[1] == { ClassName->neu, SelfConjugate->False,  Indices->{Index[INO]}, FlavorIndex->INO, WeylComponents->{new1,new2bar},
145            ParticleName->{"n1","n2","n3","n4"},
146            ClassMembers->{neu1,neu2,neu3,neu4}, Mass->{Mneu,Mneu1,Mneu2,Mneu3,Mneu4}, Width->{Wneu,Wneu1,Wneu2,Wneu3,Wneu4},
147            PDG->{1000022,1000023,1000025,1000035}, PropagatorLabel->{"neu","neu1","neu2","neu3","neu4"}, PropagatorType->Straight, PropagatorArrow->None },
148  F[2] == { ClassName->ch,  SelfConjugate->False, Indices->{Index[INO]}, FlavorIndex->INO, WeylComponents->{chpw,chmwbar},
149            ParticleName->{"x1+","x2+","x3+","x4+"}, AntiParticleName->{"x1-","x2-","x3-","x4-"}, QuantumNumbers->{Q ->1},
150            ClassMembers->{ch1,ch2,ch3,ch4}, Mass->{Mch,Mch1,Mch2,Mch3,Mch4}, Width->{Wch,Wch1,Wch2,Wch3,Wch4},
151            PDG->{1000024,1000037,9000024,9000037}, PropagatorLabel->{"ch","ch1","ch2","ch3","ch4"}, PropagatorType->Straight, PropagatorArrow->Forward },
152  F[3] == { ClassName->go,  SelfConjugate->False, Indices->{Index[Gluon]}, WeylComponents->{goww,gpowbar}, Mass->Mgo, Width->Wgo, ParticleName->"go",
153            PDG->1000021, PropagatorLabel->"go", PropagatorType->Straight, PropagatorArrow->None },
154
155(* Higgs: unphysical scalars  *)
156 S[21] == { ClassName->hus,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
157            Definitions->{
158              hus[1] :> Module[{mm}, Conjugate[UC[mm,1]]*H[mm]],
159              hus[2] :> Module[{mm}, (vu + Conjugate[US[mm,2]]*h0[mm] + I*Conjugate[UP[mm,2]]*A0[mm])/Sqrt[2]]}},
160 S[22] == { ClassName->hds,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
161            Definitions->{
162              hds[1] :> Module[{mm}, (vd + Conjugate[US[mm,1]]*h0[mm] + I*Conjugate[UP[mm,1]]*A0[mm])/Sqrt[2]],
163              hds[2] :> Module[{mm}, UC[mm,2]*Hbar[mm]]} },
164
165(* Scalar adjoints: unphysical scalars  *)
166 S[32] == { ClassName->sigB, Unphysical->True, SelfConjugate->False,
167            Definitions->{sigB:> Module[{mm},(vB + Conjugate[US[mm,3]]*h0[mm] + I*Conjugate[UP[mm,3]]*A0[mm])/Sqrt[2]]} },
168 S[33] == { ClassName->sigW, Unphysical->True, SelfConjugate->False, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
169            Definitions->{
170              sigW[1] :> Module[{mm},(UC[mm,3]*Hbar[mm]+Conjugate[UC[mm,4]]*H[mm])/(Sqrt[2])],
171              sigW[2] :> Module[{mm},(UC[mm,3]*Hbar[mm]-Conjugate[UC[mm,4]]*H[mm])/(I Sqrt[2])],
172              sigW[3] :> Module[{mm},(vW + Conjugate[US[mm,4]]*h0[mm] + I*Conjugate[UP[mm,4]]*A0[mm])/Sqrt[2]]}  },
173 S[34] == { ClassName->sigG, Unphysical->True, SelfConjugate->False, Indices->{Index[Gluon]},
174            Definitions -> { sigG[aa_]:> Module[{mm}, (Conjugate[UG[mm,1]] sgl[mm,aa] + I*Conjugate[UG[mm,2]] sgl[mm,aa])/Sqrt[2] ] }  },
175
176(* Higgs and scalar adjoints: physical fields and Goldstones *)
177  S[1] == { ClassName->h0, SelfConjugate->True, Indices->{Index[SHig]}, FlavorIndex->SHig,
178            ParticleName->{"h01","h02","h03","h04"}, ClassMembers->{h01,h02,h03,h04}, Mass->{MH0,MH01,MH02,MH03,MH04}, Width->{WH0,WH01,WH02,WH03,WH04},
179            PDG->{25,35,45,9000025}, PropagatorLabel->{"h0","h01","h02","h03","h04"}, PropagatorType->ScalarDash, PropagatorArrow->None},
180  S[2] == { ClassName->A0, SelfConjugate->True, Indices->{Index[PHig]}, FlavorIndex->PHig,
181            ParticleName->{"a01","a02","a03"}, ClassMembers->{a01,a02,a03}, Mass->{MA0,MA01,MA02,MA03}, Width->{WA0,WA01,WA02,WA03},
182            PDG->{36,46,9000036}, PropagatorLabel->{"a0","a01","a02","a03"}, PropagatorType->ScalarDash, PropagatorArrow->None},
183  S[3] == { ClassName->H,  SelfConjugate->False, Indices->{Index[PHig]}, FlavorIndex->PHig, QuantumNumbers->{Q-> 1},
184            ParticleName->{"H1+","H2+","H3+"}, AntiParticleName->{"H1-","H2-","H3-"}, ClassMembers->{H1,H2,H3},
185            Mass->{MH,MH1,MH2,MH3}, Width->{WH,WH1,WH2,WH3},
186            PDG->{37,9000137,9000237}, PropagatorLabel->{"H","H1","H2","H3"}, PropagatorType->ScalarDash, PropagatorArrow->Forward},
187  S[6] == { ClassName->sgl, SelfConjugate->True, Indices->{Index[sglu],Index[Gluon]}, FlavorIndex->sglu,
188            ParticleName->{"sgl1","sgl2"}, ClassMembers->{sgl1,sgl2}, Mass->{Msgl,Msgl1,Msgl2}, Width->{Wsgl,Wsgl1,Wsgl2},
189            PDG->{9000001,9000002}, PropagatorLabel->{"sgl","sgl1","sgl2"}, PropagatorType->ScalarDash, PropagatorArrow->None},
190
191(* R-Higgs: unphysical scalars *)
192 S[40] == { ClassName->rds,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
193            Definitions->{
194              rds[1] -> RH[1],
195              rds[2] :> Module[{mm}, Conjugate[URH[mm,1]]*RH0[mm] ]}},
196 S[41] == { ClassName->rus,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
197            Definitions->{
198              rus[1] :> Module[{mm}, Conjugate[URH[mm,2]]*RH0[mm]],
199              rus[2] -> HC[RH[2]]} }, 
200
201(* R-Higgs: physical scalars *)
202 S[42] == {ClassName->RH, SelfConjugate->False, Indices->{Index[RHig]}, FlavorIndex->RHig, QuantumNumbers->{Q->1},
203           ParticleName->{"Rd+","Ru+"}, AntiParticleName->{"Rd-","Ru-"}, ClassMembers->{RHd,RHu},
204           Mass->{MRH,MRHd,MRHu}, Width->{WRH,WRHd,WRHu},
205           PDG->{9000051,9000052}, PropagatorLabel->{"RH","Rd","Ru"}, PropagatorType->ScalarDash, PropagatorArrow->Forward},
206 S[43] == {ClassName->RH0, SelfConjugate->False, Indices->{Index[RHig]}, FlavorIndex->RHig,
207           ParticleName->{"Rh01","Rh02"}, AntiParticleName->{"Rh01~","Rh02~"}, ClassMembers->{Rh01,Rh02},           
208           Mass->{MRH0,MRH01,MRH02}, Width->{WRH0,WRH01,WRH02},
209           PDG->{9000003,9000004}, PropagatorLabel->{"Rh0","Rh01","Rh02"}, PropagatorType->ScalarDash, PropagatorArrow->Forward},
210
211(* Fermions: unphysical Weyls *)
212 W[25] == { ClassName->LLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D],Index[GEN]},              FlavorIndex->SU2D,
213            QuantumNumbers->{Y->-1/2},
214            Definitions->{LLw[s_,1,ff_]:>Module[{ff2}, PMNS[ff,ff2]*vLw[s,ff2]], LLw[s_,2,ff_]->eLw[s,ff]}},
215 W[26] == { ClassName->QLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D],Index[GEN],Index[Colour]},FlavorIndex->SU2D,
216            QuantumNumbers->{Y->1/6},
217            Definitions->{QLw[s_,1,ff_,cc_]->uLw[s,ff,cc], QLw[s_,2,ff_,cc_]:>Module[{ff2}, CKM[ff,ff2] dLw[s,ff2,cc]]}},
218
219(* Fermions: physical Weyls *)
220  W[5] == { ClassName->vLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
221  W[6] == { ClassName->eLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
222  W[7] == { ClassName->VRw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
223  W[8] == { ClassName->ERw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1} },
224  W[9] == { ClassName->uLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]},  FlavorIndex->GEN },
225  W[10]== { ClassName->dLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]},  FlavorIndex->GEN },
226  W[11]== { ClassName->URw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y->-2/3} },
227  W[12]== { ClassName->DRw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1/3} },
228
229(* Fermions: physical Dirac *)
230  F[4] == { ClassName->vl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, WeylComponents->{vLw,VRwbar},
231            ParticleName->{"ve","vm","vt"}, AntiParticleName->{"ve~","vm~","vt~"},
232            ClassMembers->{ve,vm,vt}, Mass->{Mvl,Mve,Mvm,Mvt}, Width->0,
233            PDG->{12,14,16}, PropagatorLabel->{"v","ve","vm","vt"}, PropagatorType->Straight, PropagatorArrow->Forward},
234  F[5] == { ClassName->l, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, WeylComponents->{eLw,ERwbar}, QuantumNumbers->{Q->-1},
235            ParticleName->{"e-","mu-","tau-"}, AntiParticleName->{"e+","mu+","tau+"},
236            ClassMembers->{e,m,ta}, Mass->{Ml,Me,Mm,Mta}, Width->0,
237            PDG->{11,13,15}, PropagatorLabel->{"l","e","mu","tau"}, PropagatorType->Straight, PropagatorArrow->Forward},
238  F[6] == { ClassName->uq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, WeylComponents->{uLw,URwbar}, QuantumNumbers->{Q-> 2/3},
239            ParticleName->{"u","c","t"}, AntiParticleName->{"u~","c~","t~"},
240            ClassMembers->{u,c,t}, Mass->{Muq,MU,MC,MT}, Width->{Wuq,0,0,WT},
241            PDG->{2,4,6}, PropagatorLabel->{"uq","u","c","t"}, PropagatorType->Straight, PropagatorArrow->Forward},
242  F[7] == { ClassName->dq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, WeylComponents->{dLw,DRwbar}, QuantumNumbers->{Q->-1/3},
243            ParticleName->{"d","s","b"}, AntiParticleName->{"d~","s~","b~"},
244            ClassMembers->{d,s,b}, Mass->{Mdq,MD,MS,MB}, Width->0,
245            PDG->{1,3,5}, PropagatorLabel->{"dq","d","s","b"}, PropagatorType->Straight, PropagatorArrow->Forward},
246
247(* Sfermion: unphysical scalars *)
248 S[23] == { ClassName->LLs,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D], Index[GEN]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
249            Definitions->{ LLs[1,ff_] :> Module[{ff2,ff3}, Conjugate[Rn[ff3,ff2]]*PMNS[ff,ff2]*sn[ff3]], LLs[2,ff_]:> Module[{ff2}, Conjugate[RlL[ff2,ff]]*sl[ff2]] } },
250 S[24] == { ClassName->ERs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1},
251            Definitions->{ ERs[ff_] :> Module[{ff2}, slbar[ff2]*RlR[ff2,ff]]} },
252 S[25] == { ClassName->VRs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
253            Definitions->{ VRs[_] -> 0 } },
254 S[26] == { ClassName->QLs,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D], Index[GEN],Index[Colour]}, FlavorIndex->SU2D, QuantumNumbers->{Y->1/6},
255            Definitions->{
256              QLs[1,ff_,cc_]:>Module[{ff2},Conjugate[RuL[ff2,ff]]*su[ff2,cc]],
257              QLs[2,ff_,cc_]:>Module[{ff2,ff3},Conjugate[RdL[ff2,ff3]]*CKM[ff,ff3]*sd[ff2,cc]]}},
258 S[27] == { ClassName->URs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y->-2/3},
259            Definitions->{ URs[ff_,cc_]:>Module[{ff2}, subar[ff2,cc]*RuR[ff2,ff]]} },
260 S[28] == { ClassName->DRs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1/3},
261            Definitions->{ DRs[ff_,cc_]:>Module[{ff2}, sdbar[ff2,cc]*RdR[ff2,ff]]} },
262
263(* Sfermion: physical scalars *)
264 S[7] == {  ClassName->sn, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
265            ParticleName->{"sv1","sv2","sv3"}, AntiParticleName->{"sv1~","sv2~","sv3~"},
266            ClassMembers-> {sn1, sn2, sn3}, Mass->{Msn,Msn1,Msn2,Msn3}, Width->{Wsn,Wsn1,Wsn2,Wsn3},
267            PDG->{1000012,1000014,1000016}, PropagatorLabel->{"sn","sn1","sn2","sn3"}, PropagatorType->ScalarDash, PropagatorArrow->Forward },
268 S[8] == {  ClassName->sl, SelfConjugate->False, Indices->{Index[SCA]}, FlavorIndex->SCA, QuantumNumbers->{Q->-1},
269            ParticleName->{"sl1-","sl2-","sl3-","sl4-","sl5-","sl6-"}, AntiParticleName->{"sl1+","sl2+","sl3+","sl4+","sl5+","sl6+"},
270            ClassMembers->{sl1,sl2,sl3,sl4,sl5,sl6}, Mass->{Msl,Msl1,Msl2,Msl3,Msl4,Msl5,Msl6}, Width->{Wsl,Wsl1,Wsl2,Wsl3,Wsl4,Wsl5,Wsl6},
271            PDG->{1000011,1000013,1000015,2000011,2000013,2000015}, PropagatorLabel->{"sl","sl1","sl2","sl3","sl4","sl5","sl6"},
272            PropagatorType->ScalarDash, PropagatorArrow->Forward},
273 S[9] == {  ClassName->su, SelfConjugate->False, Indices->{Index[SCA],Index[Colour]}, FlavorIndex->SCA, QuantumNumbers->{Q-> 2/3},
274            ParticleName->{"su1","su2","su3","su4","su5","su6"}, AntiParticleName->{"su1~","su2~","su3~","su4~","su5~","su6~"},
275            ClassMembers->{su1,su2,su3,su4,su5,su6}, Mass->{Msu,Msu1,Msu2,Msu3,Msu4,Msu5,Msu6}, Width->{Wsu,Wsu1,Wsu2,Wsu3,Wsu4,Wsu5,Wsu6},
276            PDG->{1000002,1000004,1000006,2000002,2000004,2000006}, PropagatorLabel->{"su","su1","su2","su3","su4","su5","su6"},
277            PropagatorType->ScalarDash, PropagatorArrow->Forward},
278 S[10]== {  ClassName->sd, SelfConjugate->False, Indices->{Index[SCA],Index[Colour]}, FlavorIndex->SCA, QuantumNumbers->{Q->-1/3},
279            ParticleName->{"sd1","sd2","sd3","sd4","sd5","sd6"}, AntiParticleName->{"sd1~","sd2~","sd3~","sd4~","sd5~","sd6~"},
280            ClassMembers->{sd1,sd2,sd3,sd4,sd5,sd6}, Mass->{Msd,Msd1,Msd2,Msd3,Msd4,Msd5,Msd6}, Width->{Wsd,Wsd1,Wsd2,Wsd3,Wsd4,Wsd5,Wsd6},
281            PDG->{1000001,1000003,1000005,2000001,2000003,2000005}, PropagatorLabel->{"sd","sd1","sd2","sd3","sd4","sd5","sd6"},
282            PropagatorType->ScalarDash, PropagatorArrow->Forward}
283};
284
285
286(* ************************** *)
287(* *****   Parameters   ***** *)
288(* ************************** *)
289M$Parameters = {
290(* Mixing: external parameters *)
291  RMNS== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->UPMNS,
292           Description->"Neutrino PMNS mixing matrix (real part)"},
293  IMNS== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMUPMNS,
294           Description->"Neutrino PMNS mixing matrix (imaginary part)"},
295  RCKM== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->VCKM,
296           Description->"CKM mixing matrix (real part)"},
297  ICKM== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMVCKM,
298           Description->"CKM mixing matrix (imaginary part)"},
299  RNNL== { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->NLMIX,
300           Description->"Left-neutralino mixing matrix (real part)"},
301  INNL== { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->IMNLMIX,
302           Description->"Left-neutralino mixing matrix (imaginary part)"},
303  RNNR== { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->NRMIX,
304           Description->"Right-neutralino mixing matrix (real part)"},
305  INNR== { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->IMNRMIX,
306           Description->"Right-neutralino mixing matrix (imaginary part)"},
307  RUU == { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->UMIX,
308           Description->"Chargino mixing matrix U (real part)"},
309  IUU == { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->IMUMIX,
310           Description->"Chargino mixing matrix U (imaginary part)"},
311  RVV == { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->VMIX,
312           Description->"Chargino mixing matrix V (real part)"},
313  IVV == { ParameterType->External, ComplexParameter->False, Indices->{Index[INO],Index[INO]}, BlockName->IMVMIX,
314           Description->"Chargino mixing matrix V (imaginary part)"},
315  RRn == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->SNUMIX,
316           Description->"Sneutrino mixing matrix (real part)"},
317  IRn == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMSNUMIX,
318           Description->"Sneutrino mixing matrix (imaginary part)"},
319  RRl == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->SELMIX,
320           Description->"Slepton mixing matrix (real part)"},
321  IRl == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMSELMIX,
322           Description->"Slepton mixing matrix (imaginary part)"},
323  RRu == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->USQMIX,
324           Description->"Up squark mixing matrix (real part)"},
325  IRu == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMUSQMIX,
326           Description->"Up squark mixing matrix (imaginary part)"},
327  RRd == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->DSQMIX,
328           Description->"Down squark mixing matrix (real part)"},
329  IRd == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMDSQMIX,
330           Description->"Down squark mixing matrix (imaginary part)"},
331  RUS == { ParameterType->External, ComplexParameter->False, Indices->{Index[SHig],Index[SHig]}, BlockName->MRHMIX,
332            Description->"Scalar Higgses mixing matrix (real part)"},
333  IUS == { ParameterType->External, ComplexParameter->False, Indices->{Index[SHig],Index[SHig]}, BlockName->IMMRHMIX,
334            Description->"Scalar Higgses mixing matrix (imaginary part)"},
335  RUP == { ParameterType->External, ComplexParameter->False, Indices->{Index[PHig],Index[SHig]}, BlockName->MRAMIX,
336            Description->"Pseudoscalar Higgses mixing matrix (real part)"},
337  IUP == { ParameterType->External, ComplexParameter->False, Indices->{Index[PHig],Index[SHig]}, BlockName->IMMRAMIX,
338            Description->"Pseudoscalar Higgses mixing matrix (imaginary part)"},
339  RUC == { ParameterType->External, ComplexParameter->False, Indices->{Index[PHig],Index[SHig]}, BlockName->MRCHMIX,
340            Description->"Charged Higgses mixing matrix (real part)"},
341  IUC == { ParameterType->External, ComplexParameter->False, Indices->{Index[PHig],Index[SHig]}, BlockName->IMMRCHMIX,
342            Description->"Charged Higgses mixing matrix (imaginary part)"},
343  RUG == { ParameterType->External, ComplexParameter->False, Indices->{Index[sglu],Index[sglu]}, BlockName->MRSGMIX,
344            Description->"Sgluon mixing matrix (real part)"},
345  IUG == { ParameterType->External, ComplexParameter->False, Indices->{Index[sglu],Index[sglu]}, BlockName->IMMRSGMIX,
346            Description->"Sgluon mixing matrix (imaginary part)"},
347  RURH == { ParameterType->External, ComplexParameter->False, Indices->{Index[RHig],Index[RHig]}, BlockName->MRRMIX,
348            Description->"Neutral R-Higgses mixing matrix (real part)"},
349  IURH == { ParameterType->External, ComplexParameter->False, Indices->{Index[RHig],Index[RHig]}, BlockName->IMMRMIX,
350            Description->"Neutral R-Higgses mixing matrix (imaginary part)"},
351
352(* Mixing: internal parameters *)
353  cw  == { TeX->Subscript[c,w],        ParameterType->Internal, ComplexParameter->False, Value->MW/MZ,        Description->"Cosine of the weak angle"}, 
354  sw  == { TeX->Subscript[s,w],        ParameterType->Internal, ComplexParameter->False, Value->Sqrt[1-cw^2], Description->"Sine of the weak angle"},
355  PMNS== { TeX->Superscript[U,pmns], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
356           If[$MNSDiag, Definitions:>{PMNS[i_,j_]:>0 /;(i!=j), PMNS[i_,j_]:>1/;(i==j)}, Value->{PMNS[i_,j_]:>RMNS[i,j]+I*IMNS[i,j]}],
357           Description-> "Neutrino PMNS mixing matrix"},
358  CKM == { TeX->Superscript[V,ckm], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
359           If[$CKMDiag, Definitions:>{CKM[i_,j_]:>0 /;(i!=j), CKM[i_,j_]:>1/;(i==j)}, Value->{CKM[i_,j_]:>RCKM[i,j]+I*ICKM[i,j]}],
360           Description-> "CKM mixing matrix"},
361  NNL == { TeX->Subscript[N,L], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[INO],Index[INO]}, Unitary->True,
362           Value->{NNL[i_,j_]:>RNNL[i,j]+I*INNL[i,j]}, Description-> "Left-neutralino mixing matrix"},
363  NNR == { TeX->Subscript[N,R], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[INO],Index[INO]}, Unitary->True,
364           Value->{NNR[i_,j_]:>RNNR[i,j]+I*INNR[i,j]}, Description-> "Right-neutralino mixing matrix"},
365  UU  == { TeX->U, ParameterType->Internal, ComplexParameter->True, Indices->{Index[INO],Index[INO]}, Unitary->True,
366           Value->{UU[i_,j_]:>RUU[i,j]+I*IUU[i,j]}, Description-> "Chargino mixing matrix U"},
367  VV  == { TeX->V, ParameterType->Internal, ComplexParameter->True, Indices->{Index[INO],Index[INO]}, Unitary->True,
368           Value->{VV[i_,j_]:>RVV[i,j]+I*IVV[i,j]}, Description-> "Chargino mixing matrix V"},
369  Rl  == { TeX->Superscript[R,l], ParameterType->Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
370           Value->{Rl[i_,j_]:>RRl[i,j]+I*IRl[i,j]}, Description-> "Slepton mixing matrix"},
371  Rn  == { TeX->Superscript[R,n], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
372           Value->{Rn[i_,j_]:>RRn[i,j]+I*IRn[i,j]}, Description-> "Sneutrino mixing matrix"},
373  Ru  == { TeX->Superscript[R,u], ParameterType->Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
374           Value->{Ru[i_,j_]:>RRu[i,j]+I*IRu[i,j]}, Description-> "Up squark mixing matrix"},
375  Rd  == { TeX->Superscript[R,d], ParameterType->Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
376           Value->{Rd[i_,j_]:>RRd[i,j]+I*IRd[i,j]}, Description-> "Down squark mixing matrix"},
377  US  == { TeX->Superscript[U,S], ParameterType->Internal, ComplexParameter->True, Indices->{Index[SHig],Index[SHig]}, Unitary->True,
378           Value->{US[i_,j_]:>RUS[i,j]+I*IUS[i,j]}, Description->"Scalar Higgs mixing matrix"},
379  UP  == { TeX->Superscript[U,P], ParameterType->Internal, ComplexParameter->True, Indices->{Index[PHig],Index[SHig]},
380           Value->{UP[i_,j_]:>RUP[i,j]+I*IUP[i,j]}, Description->"Pseudoscalar Higgs mixing matrix"},
381  UC  == { TeX->Superscript[U,C], ParameterType->Internal, ComplexParameter->True, Indices->{Index[PHig],Index[SHig]},
382           Value->{UC[i_,j_]:>RUC[i,j]+I*IUC[i,j]}, Description->"Charged Higgs mixing matrix"},
383  URH == { TeX->Superscript[U,R], ParameterType->Internal, ComplexParameter->True, Indices->{Index[RHig],Index[RHig]}, Unitary->True,
384           Value->{URH[i_,j_]:>RURH[i,j]+I*IURH[i,j]}, Description->"neutral R-Higgses mixing matrix"},
385  UG  == { TeX->Superscript[U,G], ParameterType->Internal, ComplexParameter->True, Indices->{Index[sglu],Index[sglu]},
386           Value->{UG[i_,j_]:>RUG[i,j]+I*IUG[i,j]}, Description->"Sgluon mixing matrix"},
387
388(* Left and right parts of the sfermion mixing matrices *)
389  RlL == { TeX->Superscript[RL,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
390            Definitions->{RlL[i_,j_]:>Rl[i,j]/;NumericQ[j]},  Description-> "Slepton mixing matrix - first three columns"},
391  RlR == { TeX->Superscript[RR,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
392            Definitions->{RlR[i_,j_]:>Rl[i,j+3]/;NumericQ[j]},Description-> "Slepton mixing matrix - last three columns"},
393  RuL == { TeX->Superscript[RL,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
394            Definitions->{RuL[i_,j_]:>Ru[i,j]/;NumericQ[j]},  Description-> "Up squark mixing matrix - first three columns"},
395  RuR == { TeX->Superscript[RR,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
396            Definitions->{RuR[i_,j_]:>Ru[i,j+3]/;NumericQ[j]},Description-> "Up squark mixing matrix - last three columns"},
397  RdL == { TeX->Superscript[RL,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
398            Definitions->{RdL[i_,j_]:>Rd[i,j]/;NumericQ[j]},  Description-> "Down squark mixing matrix - first three columns"},
399  RdR == { TeX->Superscript[RR,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
400            Definitions->{RdR[i_,j_]:>Rd[i,j+3]/;NumericQ[j]},Description-> "Down squark mixing matrix - last three columns"},
401
402(* Couplings constants: external parameters *)
403  aEWM1 == { TeX->Subsuperscript[\[Alpha],w,-1], ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->1, InteractionOrder->{QED,-2},
404             Description->"Inverse of the EW coupling constant at the Z pole"},
405  aS    == { TeX->Subscript[\[Alpha],s],         ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->3, InteractionOrder->{QCD, 2},
406             Description->"Strong coupling constant at the Z pole."},
407
408(* Couplings constants: internal parameters *)
409  ee == { TeX->e,              ParameterType->Internal, ComplexParameter->False, Value->Sqrt[4 Pi / aEWM1], InteractionOrder->{QED,1},
410          Description->"Electric coupling constant"},
411  gs == { TeX->Subscript[g,s], ParameterType->Internal, ComplexParameter->False, Value->Sqrt[4 Pi aS],      InteractionOrder->{QCD,1}, ParameterName->G,
412          Description->"Strong coupling constant"},
413  gp == { TeX->g',             ParameterType->Internal, ComplexParameter->False, Definitions-> {gp->ee/cw}, InteractionOrder->{QED,1},
414          Description->"Hypercharge coupling constant at the Z pole"},
415  gw == { TeX->Subscript[g,w], ParameterType->Internal, ComplexParameter->False, Definitions-> {gw->ee/sw}, InteractionOrder->{QED,1},
416          Description->"Weak coupling constant at the Z pole"},
417
418(* Higgs sector: external parameters *)
419  tb == { TeX->Subscript[t,b], ParameterType->External, ComplexParameter->False, BlockName->HMIX, OrderBlock->1, Description->"Ratio of the two Higgs vevs"},
420  vB   == { TeX->Subscript[v,B], ParameterType->External, ComplexParameter->False, InteractionOrder->{QED,-1}, BlockName->HMIX, OrderBlock->2,
421            Description->"B-scalar adjoint vacuum expectation value"},
422  vW   == { TeX->Subscript[v,W], ParameterType->External, ComplexParameter->False, InteractionOrder->{QED,-1}, BlockName->HMIX, OrderBlock->3,
423            Description->"W3-scalar adjoint vacuum expectation value"},
424
425(* Higgs sector: internal parameters *)
426  beta == { TeX->\[Beta], ParameterType->Internal, ComplexParameter->False, Value->ArcTan[tb], Description->"Arctan of the ratio of the two Higgs vevs"},
427  vev  == { TeX->v,              ParameterType->Internal, ComplexParameter->False, Value->2*MZ*sw*cw/ee, InteractionOrder->{QED,-1},
428            Description->"Higgs vacuum expectation value"},
429  vd   == { TeX->Subscript[v,d], ParameterType->Internal, ComplexParameter->False, Value->vev*Cos[beta],    InteractionOrder->{QED,-1},
430            Description->"Down-type Higgs vacuum expectation value"},
431  vu   == { TeX->Subscript[v,u], ParameterType->Internal, ComplexParameter->False, Value->vev*Sin[beta],    InteractionOrder->{QED,-1},
432            Description->"Up-type Higgs vacuum expectation value"},
433
434(* Superpotential: external parameters *)
435  Ryu  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YU,
436            Description->"Up-type quark Yukawa matrix (real part)"},
437  Iyu  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYU,
438            Description->"Up-type quark Yukawa matrix (imaginary part)"},
439  Ryd  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YD,
440            Description->"Down-type quark Yukawa matrix (real part)"},
441  Iyd  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYD,
442            Description->"Down-type quark Yukawa matrix (imaginary part)"},
443  Rye  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YE,
444            Description->"Charged lepton Yukawa matrix (real part)"},
445  Iye  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYE,
446            Description->"Charged lepton Yukawa matrix (imaginary part)"},
447  RMUu == { ParameterType->External, ComplexParameter->False, BlockName->HMIX,   OrderBlock->4, Description->"Uptype Higgs/R-Higgs mixing parameter (real part)"},
448  IMUu == { ParameterType->External, ComplexParameter->False, BlockName->IMHMIX, OrderBlock->4, Description->"Uptype Higgs/R-Higgs mixing parameter (imaginary part)"},
449  RMUd == { ParameterType->External, ComplexParameter->False, BlockName->HMIX,   OrderBlock->5, Description->"Downtype Higgs/R-Higgs mixing parameter (real part)"},
450  IMUd == { ParameterType->External, ComplexParameter->False, BlockName->IMHMIX, OrderBlock->5, Description->"Downtype Higgs/R-Higgs mixing parameter (imaginary part)"},
451  RluB == { ParameterType->External, ComplexParameter->False, BlockName->HMIX,   OrderBlock->6, Description->"Uptype Higgs/R-Higgs/chiral-B coupling (real part)"},
452  IluB == { ParameterType->External, ComplexParameter->False, BlockName->IMHMIX, OrderBlock->6, Description->"Uptype Higgs/R-Higgs/chiral-B coupling (imaginary part)"},
453  RluW == { ParameterType->External, ComplexParameter->False, BlockName->HMIX,   OrderBlock->7, Description->"Uptype Higgs/R-Higgs/chiral-W coupling (real part)"},
454  IluW == { ParameterType->External, ComplexParameter->False, BlockName->IMHMIX, OrderBlock->7, Description->"Uptype Higgs/R-Higgs/chiral-W coupling (imaginary part)"},
455  RldB == { ParameterType->External, ComplexParameter->False, BlockName->HMIX,   OrderBlock->8, Description->"Downtype Higgs/R-Higgs/chiral-B coupling (real part)"},
456  IldB == { ParameterType->External, ComplexParameter->False, BlockName->IMHMIX, OrderBlock->8, Description->"Downtype Higgs/R-Higgs/chiral-B coupling (imaginary part)"},
457  RldW == { ParameterType->External, ComplexParameter->False, BlockName->HMIX,   OrderBlock->9, Description->"Downtype Higgs/R-Higgs/chiral-W coupling (real part)"},
458  IldW == { ParameterType->External, ComplexParameter->False, BlockName->IMHMIX, OrderBlock->9, Description->"Downtype Higgs/R-Higgs/chiral-W coupling (imaginary part)"},
459
460(* Superpotential: internal parameters *)
461  yu  == { TeX->Superscript[y,u], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
462           Definitions:>{yu[i_,j_]:>0 /;(i!=j)}, Value->{yu[i_,j_]:>If[i==j,Ryu[i,j]+I*Iyu[i,j]]}, InteractionOrder->{QED,1}, Description-> "Up-type quark Yukawa matrix"},
463  yd  == { TeX->Superscript[y,d], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
464           Definitions:>{yd[i_,j_]:>0 /;(i!=j)}, Value->{yd[i_,j_]:>If[i==j,Ryd[i,j]+I*Iyd[i,j]]}, InteractionOrder->{QED,1}, Description-> "Down-type quark Yukawa matrix"},
465  ye  == { TeX->Superscript[y,e], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
466           Definitions:>{ye[i_,j_]:>0 /;(i!=j)}, Value->{ye[i_,j_]:>If[i==j,Rye[i,j]+I*Iye[i,j]]}, InteractionOrder->{QED,1}, Description-> "Charged lepton Yukawa matrix"},
467  MUu == { TeX->Subscript[\[Mu],u], ParameterType->Internal, ComplexParameter->True, Value->RMUu+I*IMUu, Description->"Uptype Higgs/R-Higgs mixing parameter"},
468  MUd == { TeX->Subscript[\[Mu],d], ParameterType->Internal, ComplexParameter->True, Value->RMUd+I*IMUd, Description->"Downtype Higgs/R-Higgs mixing parameter"},
469  luB == { TeX->Subsuperscript[\[Lambda],u,B], ParameterType->Internal, ComplexParameter->True, Value->RluB+I*IluB, Description->"Uptype Higgs/R-Higgs/chiral-B coupling"},
470  ldB == { TeX->Subsuperscript[\[Lambda],d,B], ParameterType->Internal, ComplexParameter->True, Value->RldB+I*IldB, Description->"Downtype Higgs/R-Higgs/chiral-B coupling"},
471  luW == { TeX->Subsuperscript[\[Lambda],u,W], ParameterType->Internal, ComplexParameter->True, Value->RluW+I*IluW, Description->"Uptype Higgs/R-Higgs/chiral-W coupling"},
472  ldW == { TeX->Subsuperscript[\[Lambda],d,W], ParameterType->Internal, ComplexParameter->True, Value->RldW+I*IldW, Description->"Downtype Higgs/R-Higgs/chiral-W coupling"},
473
474(* Soft terms: external parameters *)
475  RMx1 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->1, Description->"Bino mass (real part)"},
476  RMx2 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->2, Description->"Wino mass (real part)"},
477  RMx3 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->3, Description->"Gluino mass (real part)"},
478  IMx1 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->1, Description->"Bino mass (imaginary part)"},
479  IMx2 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->2, Description->"Wino mass (imaginary part)"},
480  IMx3 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->3, Description->"Gluino mass (imaginary part)"},
481  Rbb == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT,   OrderBlock->8, Description->"Higgs bilinear soft term (real part)"},
482  Ibb == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->8, Description->"Higgs bilinear soft term (imaginary part)"},
483  m1G2 == { TeX->Subsuperscript[m,"1G",2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->9,
484            Description->"SU(3) scalar adjoint squared mass"},
485  m1W2 == { TeX->Subsuperscript[m,"1W",2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->10,
486            Description->"SU(2) scalar adjoint squared mass"},
487  m1B2 == { TeX->Subsuperscript[m,"1B",2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->11,
488            Description->"U(1) scalar adjoint squared mass"},
489  Rm2G2 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->12, Description->"SU(3) scalar adjoint squared mass (real part)"},
490  Rm2W2 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->13, Description->"SU(2) scalar adjoint squared mass (real part)"},
491  Rm2B2 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->14, Description->"U(1)  scalar adjoint squared mass (real part)"},
492  Im2G2 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->12, Description->"SU(3) scalar adjoint squared mass (imaginary part)"},
493  Im2W2 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->13, Description->"SU(2) scalar adjoint squared mass (imaginary part)"},
494  Im2B2 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->14, Description->"U(1)  scalar adjoint squared mass (imaginary part)"},
495  mHu2 == { TeX->Subsuperscript[m,Subscript[H,u],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->4,
496            Description->"Up-type Higgs squared mass"},
497  mHd2 == { TeX->Subsuperscript[m,Subscript[H,d],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->5,
498            Description->"Down-type Higgs squared mass"},
499  mRu2 == { TeX->Subsuperscript[m,Subscript[R,u],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->6,
500            Description->"Up-type R-Higgs squared mass"},
501  mRd2 == { TeX->Subsuperscript[m,Subscript[R,d],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->7,
502            Description->"Down-type R-Higgs squared mass"},
503  RmL2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSL2,
504            Description->"Left-handed slepton squared mass matrix (real part)"},
505  ImL2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSL2,
506            Description->"Left-handed slepton squared mass matrix (imaginary part)"},
507  RmE2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSE2,
508            Description->"Right-handed slepton squared mass matrix (real part)"},
509  ImE2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSE2,
510            Description->"Right-handed slepton squared mass matrix (imaginary part)"},
511  RmQ2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSQ2,
512            Description->"Left-handed squark squared mass matrix (real part)"},
513  ImQ2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSQ2,
514            Description->"Left-handed squark squared mass matrix (imaginary part)"},
515  RmU2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSU2,
516            Description->"Right-handed up-type squark squared mass matrix (real part)"},
517  ImU2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSU2,
518            Description->"Right-handed up-type squark squared mass matrix (imaginary part)"},
519  RmD2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSD2,
520            Description->"Right-handed down-type squark squared mass matrix (real part)"},
521  ImD2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSD2,
522            Description->"Right-handed down-type squark squared mass matrix (imaginary part)"},
523
524(* Soft terms: internal parameters *)
525  Mx1 == { TeX->Subscript[M,1], ParameterType->Internal, ComplexParameter->True, Value->RMx1+I*IMx1, Description->"Bino mass"},
526  Mx2 == { TeX->Subscript[M,2], ParameterType->Internal, ComplexParameter->True, Value->RMx2+I*IMx2, Description->"Wino mass"},
527  Mx3 == { TeX->Subscript[M,3], ParameterType->Internal, ComplexParameter->True, Value->RMx3+I*IMx3, Description->"Gluino mass"},
528  bb  == { TeX->b, ParameterType->Internal, ComplexParameter->True, Value->Rbb+I*Ibb, Description->"Higgs bilinear soft term"},
529  m2G2== { TeX->Subsuperscript[m,"2G",2], ParameterType->Internal, ComplexParameter->True, Value->Rm2G2+I*Im2G2, Description->"SU(3) scalar adjoint squared mass"},
530  m2W2== { TeX->Subsuperscript[m,"2W",2], ParameterType->Internal, ComplexParameter->True, Value->Rm2W2+I*Im2W2, Description->"SU(2) scalar adjoint squared mass"},
531  m2B2== { TeX->Subsuperscript[m,"2B",2], ParameterType->Internal, ComplexParameter->True, Value->Rm2B2+I*Im2B2, Description->"U(1)  scalar adjoint squared mass"},
532  mL2 == { TeX->Subsuperscript[m,OverTilde[L],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
533           Value->{mL2[i_,j_]:>RmL2[i,j]+I*ImL2[i,j]}, Description-> "Left-handed slepton squared mass matrix"},
534  mE2 == { TeX->Subsuperscript[m,OverTilde[E],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
535           Value->{mE2[i_,j_]:>RmE2[i,j]+I*ImE2[i,j]}, Description-> "Right-handed slepton squared mass matrix"},
536  mQ2 == { TeX->Subsuperscript[m,OverTilde[Q],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
537           Value->{mQ2[i_,j_]:>RmQ2[i,j]+I*ImQ2[i,j]}, Description-> "Left-handed squark squared mass matrix"},
538  mU2 == { TeX->Subsuperscript[m,OverTilde[U],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
539           Value->{mU2[i_,j_]:>RmU2[i,j]+I*ImU2[i,j]}, Description-> "Right-handed up-type squark squared mass matrix"},
540  mD2 == { TeX->Subsuperscript[m,OverTilde[D],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
541           Value->{mD2[i_,j_]:>RmD2[i,j]+I*ImD2[i,j]}, Description-> "Right-handed down-type squark squared mass matrix"},
542  lamL == { TeX->Subscript[\[Lambda],L], ParameterType->External, ComplexParameter->False, BlockName->NEWCOUP, OrderBlock->1, Value->0.1, InteractionOrder->{SG,1},
543            Description->"Sgluon coupling to left-handed quarks"},
544  lamR == { TeX->Subscript[\[Lambda],R], ParameterType->External, ComplexParameter->False, BlockName->NEWCOUP, OrderBlock->2, Value->0.1, InteractionOrder->{SG,1},
545            Description->"Sgluon coupling to right-handed quarks"},
546  lamG == { TeX->Subscript[\[Lambda],G], ParameterType->External, ComplexParameter->False, BlockName->NEWCOUP, OrderBlock->3, Value->0.1, InteractionOrder->{SG,1},
547            Description->"Sgluon coupling to left-handed quarks"}
548
549};
550
551(* ************************** *)
552(* ****  Diracification  **** *)
553(* ************************** *)
554ToDirac[exp_]:= Module[{tmp=Expand[exp],cnt=0,prg1=0,prg2=0,prgo1=0,prgo2=0,tot},
555  Colourb=Colour;
556
557  tmp = If[Head[tmp]===Plus,List@@tmp,List[tmp]]/.Tb[a_,i_,j_]->-T[a,j,i];
558  tmp = OptimizeIndex[#] &/@ tmp;
559  tot=Length[tmp];
560  Print["Flavor expansion: ", ProgressIndicator[Dynamic[prg1]]];
561  tmp = Module[{}, cnt++; prg1=cnt/tot;
562     Expand[(ExpandIndices[#, FlavorExpand->{SU2W, SU2D}] /. {
563         gp->ee/cw,
564         gw->ee/sw,
565         cw^n_?(Mod[#,2]===0&)->(1 - sw^2)^(n/2),
566         cw^n_?(Mod[#, 2]===1 &)->(1 - sw^2)^((n - 1)/2) cw,
567         Power[PauliSigma[a_,i_?(NumericQ[#] &),j_?(NumericQ[#] &)],2]->PauliSigma[1,i,j]^2 + PauliSigma[3,i,j]^2 + PauliSigma[2,i,j]^2,
568         PauliSigma[a_,i_?(NumericQ[#] &),j_?(NumericQ[#] &)] PauliSigma[a_,k_?(NumericQ[#] &),l_?(NumericQ[#] &)]->
569           PauliSigma[1,i,j] PauliSigma[1,k,l] + PauliSigma[2,i,j] PauliSigma[2,k,l] + PauliSigma[3,i,j] PauliSigma[3,k,l]})]] &/@ tmp;
570   tmp = Plus@@tmp//.{cw^n_?(Mod[#,2]===0&)->(1 - sw^2)^(n/2), cw^n_?(Mod[#, 2]===1 &)->(1 - sw^2)^((n - 1)/2) cw};
571   cnt=0; tot=Length[tmp];
572
573   Print["Opt 1: ",ProgressIndicator[Dynamic[prgo1]]];
574   tmp = Module[{}, cnt++; prgo1=cnt/tot;OptimizeIndex[#]] &/@ (List@@tmp);
575
576   Print["Weyl2Dirac: ",ProgressIndicator[Dynamic[prg2]]];cnt=0;
577   tmp = Module[{}, cnt++; prg2=cnt/tot; WeylToDirac[#]] &/@ tmp;
578
579   Print["Opt2: ",ProgressIndicator[Dynamic[prgo2]]];cnt=0;
580   tmp = Module[{}, cnt++; prgo2=cnt/tot;OptimizeIndex[#]] &/@ tmp;
581
582   Clear[Colourb];
583Expand[Plus@@tmp]];
584
585(* ************************** *)
586(* *****   Lagrangian   ***** *)
587(* ************************** *)
588(* LVector *)
589LVector := Plus@@ (Module[{tmp}, tmp = SF2Components[#]; Expand[tmp[[2, 5]] + tmp[[2, 6]]]] &/@ (List @@ VSFKineticTerms[]));
590
591(* LChiral *)
592LChiral :=  Plus@@( Theta2Thetabar2Component[#] &/@ (List @@ CSFKineticTerms[]) );
593
594(* Superpotential *)
595SPot:= Module[{ff1,ff2,ff3,cc1,aa},
596     yu[ff1,ff2] UR[ff1,cc1] (QL[1,ff2,cc1] HU[2] - QL[2,ff2,cc1] HU[1]) -
597     yd[ff1,ff3] Conjugate[CKM[ff2,ff3]] DR[ff1,cc1] (QL[1,ff2,cc1] HD[2] - QL[2,ff2,cc1] HD[1]) -
598     ye[ff1,ff2] ER[ff1]     (LL[1,ff2]     HD[2] - LL[2,ff2]     HD[1]) -
599     luB/2 (HU[1] PhiB RU[2] - HU[2] PhiB RU[1]) +
600     ldB/2 (HD[1] PhiB RD[2] - HD[2] PhiB RD[1]) +
601     luW (HU[1] PhiW[aa] Ta[aa,2,ff1] RU[ff1] - HU[2] PhiW[aa] Ta[aa,1,ff1] RU[ff1]) +
602     ldW (HD[1] PhiW[aa] Ta[aa,2,ff1] RD[ff1] - HD[2] PhiW[aa] Ta[aa,1,ff1] RD[ff1]) +
603     MUu (HU[1] RU[2] - HU[2] RU[1]) +
604     MUd (HD[1] RD[2] - HD[2] RD[1]) ];
605LSuperW:= ( Plus@@ (Module[{tmp},tmp=SF2Components[#];tmp[[2,5]]+tmp[[2,6]]] &/@ (List @@ Expand[SPot+HC[SPot]])) )/.{
606   Conjugate[CKM[a_, b_]]*CKM[a_, c_]->IndexDelta[b, c],
607   Conjugate[PMNS[a_, b_]]*PMNS[a_, c_]->IndexDelta[b, c]};
608
609(* Soft SUSY-breaking Lagrangian *)
610LSoft := Module[{tmp, Mino, MSca, Tri, Bil},
611  (* Gaugino mass terms *)
612    tmp=Module[{al,be,gl},
613      Sqrt[2] Mx1 Ueps[be,al] NC[theta[al], SuperfieldStrengthL[BSF, be    ], PhiB    ] +
614      Mx2 Ueps[be,al] NC[theta[al], SuperfieldStrengthL[WSF, be, gl], PhiW[gl]]/(Sqrt[2] gw) +
615      Mx3 Ueps[be,al] NC[theta[al], SuperfieldStrengthL[GSF, be, gl], PhiG[gl]]/(Sqrt[2] gs)];
616    Mino = ( Plus@@ (Module[{tmp},tmp=SF2Components[#];tmp[[2,5]]+tmp[[2,6]]] &/@ (List @@ Expand[Mino+HC[Mino]])) );
617  (* Bilinear couplings *)
618    Bil:=bb*(hus[1] hds[2] - hus[2] hds[1]) - m2G2/2 sigG[ii] sigG[ii] - m2W2/2 sigW[ii] sigW[ii]- m2B2/2 sigB sigB ;
619  (* Scalar mass terms *)
620    MSca:=Module[{ii,ff1,ff2,ff3,ff4,cc1},
621      - mHu2*HC[hus[ii]]*hus[ii] - mHd2*HC[hds[ii]]*hds[ii] -
622        mRu2*HC[rus[ii]]*rus[ii] - mRd2*HC[rds[ii]]*rds[ii] -
623        mL2[ff1,ff2]*HC[LLs[ii,ff1]]*LLs[ii,ff2] - mE2[ff1,ff2]*HC[ERs[ff1]]*ERs[ff2] -
624        CKM[ff1,ff2]*mQ2[ff2,ff3]*Conjugate[CKM[ff4,ff3]]*HC[QLs[ii,ff1,cc1]]*QLs[ii,ff4,cc1] -
625        mU2[ff1,ff2]*HC[URs[ff1,cc1]]*URs[ff2,cc1] -  mD2[ff1,ff2]*HC[DRs[ff1,cc1]]*DRs[ff2,cc1] -
626        m1G2 sigGbar[ii] sigG[ii] - m1W2 sigWbar[ii] sigW[ii] - m1B2 sigBbar sigB];
627  (* Everything together *)
628  Mino + MSca + Bil + HC[Bil]];
629
630(* Effective Lagrangians *)
631Lsglu := Module[{Lgss, Lqqs, Lggs},
632    Lqqs:= sgl[1,a] T[a,m,n] dqbar[sp,ff,m].dq[sp2,ff,n] (lamL ProjM[sp,sp2] + lamR ProjP[sp,sp2])+
633           sgl[1,a] T[a,m,n] uqbar[sp,ff,m].uq[sp2,ff,n] (lamL ProjM[sp,sp2] + lamR ProjP[sp,sp2]);
634    Lggs:= lamG dSUN[a,b,c] sgl[1,a] FS[G,mu,nu,b] FS[G,mu,nu,c];
635  Lqqs + Lggs + HC[Lqqs + Lggs]];
636
637(* Collecting all the pieces together *)
638Lag := ToDirac[SolveEqMotionF[SolveEqMotionD[LVector+LChiral+LSuperW+LSoft]]] + Lsglu;
639
640
641