RPVMSSM: rpvmssm.fr

File rpvmssm.fr, 49.7 KB (added by BenjF, 6 years ago)

RPVMSSM-SF model file

Line 
1(* ********************************************************* *)
2(* *****                                               ***** *)
3(* *****  FeynRules model file: MSSM with RPV          ***** *)
4(* *****  Author: B. Fuks                              ***** *)
5(* *****                                               ***** *)
6(* ********************************************************* *)
7
8(* ************************** *)
9(* *****  Information   ***** *)
10(* ************************** *)
11M$ModelName = "RPVMSSM";
12M$Information = { Authors->{"Benjamin Fuks"}, Emails->{"fuks@cern.ch"}, Institutions->{"IPHC Strasbourg / University of Strasbourg"},
13                  Date->"20.03.12", Version->"1.0.3",
14                  References->{"B. Fuks, arXiv:1202.4769 [hep-ph]"},
15                  URLs->{"http://feynrules.phys.ucl.ac.be/view/Main/RPVMSSM"} };
16
17
18(* v1.0.1: renaming of SP to SPot (variable name clashing). Thanks to Kentarou Mawatari. *)
19(* v1.0.2: small bug in the definition of the CKM matrix. Thanks Antonio Mariano.        *)
20(* v1.0.3: new references for the model files.                                           *)
21
22(* ************************** *)
23(* *****      Flags     ***** *)
24(* ************************** *)
25$CKMDiag = True;   (* CKM  = identity or not *)
26$MNSDiag = True;   (* PMNS = identity or not *)
27
28
29(* ************************** *)
30(* *****  Gauge groups  ***** *)
31(* ************************** *)
32M$GaugeGroups = {
33  U1Y  == { Abelian->True,  CouplingConstant->gp, Superfield->BSF, Charge->Y, GUTNormalization->3/5},
34  SU2L == { Abelian->False, CouplingConstant->gw, Superfield->WSF,
35            StructureConstant->ep, Representations->{Ta,SU2D}, Definitions->{Ta[a__]->PauliSigma[a]/2, ep->Eps}},
36  SU3C == { Abelian->False, CouplingConstant->gs, Superfield->GSF,
37            StructureConstant->f,  Representations->{{T,Colour}, {Tb,Colourb}}, DTerm->dSUN}
38};
39
40(* ************************** *)
41(* *****    Indices     ***** *)
42(* ************************** *)
43IndexRange[Index[SU2W]] =   Unfold[Range[3]]; IndexStyle[SU2W,j];  IndexRange[Index[SU2D]] =   Unfold[Range[2]]; IndexStyle[SU2D,k];
44IndexRange[Index[Gluon ]] = NoUnfold[Range[8]]; IndexStyle[Gluon, a];  IndexRange[Index[Colour ]] = NoUnfold[Range[3]]; IndexStyle[Colour, m];
45IndexRange[Index[Colourb]] = NoUnfold[Range[3]]; IndexStyle[Colourb,m];
46IndexRange[Index[NEU ]] = Range[4];           IndexStyle[NEU, i];
47IndexRange[Index[CHA ]] = Range[2];           IndexStyle[CHA, i];
48IndexRange[Index[GEN ]] = Range[3];           IndexStyle[GEN, f];
49IndexRange[Index[SCA ]] = Range[6];           IndexStyle[SCA, i];
50
51
52(* ************************** *)
53(* *****  Superfields   ***** *)
54(* ************************** *)
55M$Superfields = {
56  VSF[1] == { ClassName->BSF, GaugeBoson->B,  Gaugino->bow},
57  VSF[2] == { ClassName->WSF, GaugeBoson->Wi, Gaugino->wow, Indices->{Index[SU2W]}},
58  VSF[3] == { ClassName->GSF, GaugeBoson->G,  Gaugino->gow, Indices->{Index[Gluon] }},
59  CSF[1] == { ClassName->HU, Chirality->Left, Weyl->huw, Scalar->hus, QuantumNumbers->{Y-> 1/2}, Indices->{Index[SU2D]}},
60  CSF[2] == { ClassName->HD, Chirality->Left, Weyl->hdw, Scalar->hds, QuantumNumbers->{Y->-1/2}, Indices->{Index[SU2D]}},
61  CSF[3] == { ClassName->LL, Chirality->Left, Weyl->LLw, Scalar->LLs, QuantumNumbers->{Y->-1/2}, Indices->{Index[SU2D], Index[GEN]}},
62  CSF[4] == { ClassName->ER, Chirality->Left, Weyl->ERw, Scalar->ERs, QuantumNumbers->{Y-> 1},   Indices->{Index[GEN]}},
63  CSF[5] == { ClassName->VR, Chirality->Left, Weyl->VRw, Scalar->VRs, Indices->{Index[GEN]}},
64  CSF[6] == { ClassName->QL, Chirality->Left, Weyl->QLw, Scalar->QLs, QuantumNumbers->{Y-> 1/6}, Indices->{Index[SU2D], Index[GEN], Index[Colour]}},
65  CSF[7] == { ClassName->UR, Chirality->Left, Weyl->URw, Scalar->URs, QuantumNumbers->{Y->-2/3}, Indices->{Index[GEN], Index[Colourb]}           },
66  CSF[8] == { ClassName->DR, Chirality->Left, Weyl->DRw, Scalar->DRs, QuantumNumbers->{Y-> 1/3}, Indices->{Index[GEN], Index[Colourb]}           }
67};
68
69(* ************************** *)
70(* *****     Fields     ***** *)
71(* ************************** *)
72M$ClassesDescription = {
73(* Gauge bosons: unphysical vector fields *)
74  V[11] == { ClassName->B, Unphysical->True, SelfConjugate->True,
75            Definitions->{B[mu_]->-sw Z[mu]+cw A[mu]} },
76  V[12] == { ClassName->Wi, Unphysical->True, SelfConjugate->True, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
77             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]} },
78
79(* Gauge bosons: physical vector fields *)
80  V[1] == { ClassName->A, SelfConjugate->True,  Mass->0,  Width->0,  ParticleName->"a",
81            PDG->22, PropagatorLabel->"A", PropagatorType->Sine, PropagatorArrow->None},
82  V[2] == { ClassName->Z, SelfConjugate->True,  Mass->MZ, Width->WZ, ParticleName->"Z",
83            PDG->23, PropagatorLabel->"Z", PropagatorType->Sine, PropagatorArrow->None},
84  V[3] == { ClassName->W, SelfConjugate->False, Mass->MW, Width->WW, ParticleName->"W+", AntiParticleName->"W-", QuantumNumbers->{Q->1},
85            PDG->24, PropagatorLabel->"W", PropagatorType->Sine, PropagatorArrow->Forward},
86  V[4] == { ClassName->G, SelfConjugate->True, Indices->{Index[Gluon]}, Mass->0, Width->0, ParticleName->"g",
87            PDG->21, PropagatorLabel->"G", PropagatorType->C,    PropagatorArrow->None },
88
89(* Gauginos: unphysical Weyls *)
90  W[20] == { ClassName->bow, Unphysical->True, Chirality->Left, SelfConjugate->False,
91             Definitions->{bow[s_]:>Module[{i}, -I*Conjugate[NN[i,1]]*neuw[s,i]]}},
92  W[21] == { ClassName->wow, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
93             Definitions->{
94               wow[s_,1]:>Module[{i},(Conjugate[UU[i,1]]*chmw[s,i]+Conjugate[VV[i,1]]*chpw[s,i])/(I*Sqrt[2])],
95               wow[s_,2]:>Module[{i},(Conjugate[UU[i,1]]*chmw[s,i]-Conjugate[VV[i,1]]*chpw[s,i])/(-Sqrt[2])],
96               wow[s_,3]:>Module[{i},-I*Conjugate[NN[i,2]]*neuw[s,i]]} },
97  W[22] == { ClassName->gow,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[Gluon]},  Definitions->{gow[inds__]->-I*goww[inds]} },
98
99(* Higgsinos: unphysical Weyls *)
100  W[23] == { ClassName->huw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
101             Definitions->{
102               huw[s_,1]:> Module[{i}, Conjugate[VV[i,2]]*chpw[s,i]],
103               huw[s_,2]:> Module[{i}, Conjugate[NN[i,4]]*neuw[s,i]] } },
104  W[24] == { ClassName->hdw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
105             Definitions->{
106               hdw[s_,1]:> Module[{i}, Conjugate[NN[i,3]]*neuw[s,i]],
107               hdw[s_,2]:> Module[{i}, Conjugate[UU[i,2]]*chmw[s,i]]} },
108
109(* Gauginos/Higgsinos: physical Weyls *)
110  W[1] == { ClassName->neuw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[NEU]}, FlavorIndex->NEU },
111  W[2] == { ClassName->chpw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[CHA]}, FlavorIndex->CHA, QuantumNumbers->{Q-> 1} } ,
112  W[3] == { ClassName->chmw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[CHA]}, FlavorIndex->CHA, QuantumNumbers->{Q->-1} } ,
113  W[4] == { ClassName->goww, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[Gluon]} },
114
115(* Gauginos/Higgsinos: physical Diracs *)
116  F[1] == { ClassName->neu, SelfConjugate->True,  Indices->{Index[NEU]}, FlavorIndex->NEU, WeylComponents->neuw,
117            ParticleName->{"n1","n2","n3","n4"},
118            ClassMembers->{neu1,neu2,neu3,neu4}, Mass->{Mneu,Mneu1,Mneu2,Mneu3,Mneu4}, Width->{Wneu,Wneu1,Wneu2,Wneu3,Wneu4},
119            PDG->{1000022,1000023,1000025,1000035}, PropagatorLabel->{"neu","neu1","neu2","neu3","neu4"}, PropagatorType->Straight, PropagatorArrow->None },
120  F[2] == { ClassName->ch,  SelfConjugate->False, Indices->{Index[CHA]}, FlavorIndex->CHA, WeylComponents->{chpw,chmwbar},
121            ParticleName->{"x1+","x2+"}, AntiParticleName->{"x1-","x2-"}, QuantumNumbers->{Q ->1},
122            ClassMembers->{ch1,ch2}, Mass->{Mch,Mch1,Mch2}, Width->{Wch,Wch1,Wch2},
123            PDG->{1000024,1000037}, PropagatorLabel->{"ch","ch1","ch2"}, PropagatorType->Straight, PropagatorArrow->Forward },
124  F[3] == { ClassName->go,  SelfConjugate->True, Indices->{Index[Gluon]}, WeylComponents->goww, Mass->Mgo, Width->Wgo, ParticleName->"go",
125            PDG->1000021, PropagatorLabel->"go", PropagatorType->Straight, PropagatorArrow->None },
126
127(* Higgs: unphysical scalars  *)
128 S[21] == { ClassName->hus,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
129            Definitions->{ hus[1]->Cos[beta]*H + Sin[beta]*GP, hus[2]-> (vu + Cos[alp]*h0 + Sin[alp]*H0 + I*Cos[beta]*A0 + I*Sin[beta]*G0)/Sqrt[2] } },
130 S[22] == { ClassName->hds,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
131            Definitions->{ hds[1]->(vd - Sin[alp]*h0 + Cos[alp]*H0 + I*Sin[beta]*A0 - I*Cos[beta]*G0)/Sqrt[2],hds[2]->Sin[beta]*Hbar - Cos[beta]*GPbar} },
132
133(* Higgs: physical fields and Goldstones *)
134  S[1] == { ClassName->h0, SelfConjugate->True, Mass->MH01, Width->WH01, ParticleName->"h01",
135            PDG->25, PropagatorLabel->"h0", PropagatorType->ScalarDash,  PropagatorArrow->None},
136  S[2] == { ClassName->H0, SelfConjugate->True, Mass->MH02, Width->WH02, ParticleName->"h02",
137            PDG->35, PropagatorLabel->"H0", PropagatorType->ScalarDash,  PropagatorArrow->None},
138  S[3] == { ClassName->A0, SelfConjugate->True, Mass->MA0 , Width->WA0,  ParticleName->"A0" ,
139            PDG->36, PropagatorLabel->"A0", PropagatorType->ScalarDash,  PropagatorArrow->None},
140  S[4] == { ClassName->H,  SelfConjugate->False, QuantumNumbers->{Q-> 1}, Mass->MH, Width->WH,
141            ParticleName->"H+", AntiParticleName->"H-",
142            PDG->37,  PropagatorLabel->"H", PropagatorType->ScalarDash,  PropagatorArrow->Forward},
143  S[5] == { ClassName->G0, SelfConjugate->True, Mass->MZ, Width->WG0, Goldstone->Z,
144            ParticleName->"G0",
145            PDG->250, PropagatorLabel->"G0", PropagatorType->D, PropagatorArrow->None},
146  S[6] == { ClassName->GP, SelfConjugate->False, QuantumNumbers->{Q-> 1}, Mass->MW, Width->WGP, Goldstone->W,
147            ParticleName->"G+", AntiParticleName->"G-",
148            PDG->251, PropagatorLabel->"GP", PropagatorType->D, PropagatorArrow->None },
149
150(* Fermions: unphysical Weyls *)
151 W[25] == { ClassName->LLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D],Index[GEN]},              FlavorIndex->SU2D,
152            QuantumNumbers->{Y->-1/2},
153            Definitions->{LLw[s_,1,ff_]:>Module[{ff2}, PMNS[ff,ff2]*vLw[s,ff2]], LLw[s_,2,ff_]->eLw[s,ff]}},
154 W[26] == { ClassName->QLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D],Index[GEN],Index[Colour]},FlavorIndex->SU2D,
155            QuantumNumbers->{Y->1/6},
156            Definitions->{QLw[s_,1,ff_,cc_]->uLw[s,ff,cc], QLw[s_,2,ff_,cc_]:>Module[{ff2}, CKM[ff,ff2] dLw[s,ff2,cc]]}},
157
158(* Fermions: physical Weyls *)
159  W[5] == { ClassName->vLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
160  W[6] == { ClassName->eLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
161  W[7] == { ClassName->VRw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
162  W[8] == { ClassName->ERw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1} },
163  W[9] == { ClassName->uLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]},  FlavorIndex->GEN },
164  W[10]== { ClassName->dLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]},  FlavorIndex->GEN },
165  W[11]== { ClassName->URw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y->-2/3} },
166  W[12]== { ClassName->DRw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1/3} },
167
168(* Fermions: physical Dirac *)
169  F[4] == { ClassName->vl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, WeylComponents->{vLw,VRwbar},
170            ParticleName->{"ve","vm","vt"}, AntiParticleName->{"ve~","vm~","vt~"},
171            ClassMembers->{ve,vm,vt}, Mass->{Mvl,Mve,Mvm,Mvt}, Width->0,
172            PDG->{12,14,16}, PropagatorLabel->{"v","ve","vm","vt"}, PropagatorType->Straight, PropagatorArrow->Forward},
173  F[5] == { ClassName->l, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, WeylComponents->{eLw,ERwbar}, QuantumNumbers->{Q->-1},
174            ParticleName->{"e-","mu-","tau-"}, AntiParticleName->{"e+","mu+","tau+"},
175            ClassMembers->{e,m,ta}, Mass->{Ml,Me,Mm,Mta}, Width->0,
176            PDG->{11,13,15}, PropagatorLabel->{"l","e","mu","tau"}, PropagatorType->Straight, PropagatorArrow->Forward},
177  F[6] == { ClassName->uq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, WeylComponents->{uLw,URwbar}, QuantumNumbers->{Q-> 2/3},
178            ParticleName->{"u","c","t"}, AntiParticleName->{"u~","c~","t~"},
179            ClassMembers->{u,c,t}, Mass->{Muq,MU,MC,MT}, Width->{Wuq,0,0,WT},
180            PDG->{2,4,6}, PropagatorLabel->{"uq","u","c","t"}, PropagatorType->Straight, PropagatorArrow->Forward},
181  F[7] == { ClassName->dq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, WeylComponents->{dLw,DRwbar}, QuantumNumbers->{Q->-1/3},
182            ParticleName->{"d","s","b"}, AntiParticleName->{"d~","s~","b~"},
183            ClassMembers->{d,s,b}, Mass->{Mdq,MD,MS,MB}, Width->0,
184            PDG->{1,3,5}, PropagatorLabel->{"dq","d","s","b"}, PropagatorType->Straight, PropagatorArrow->Forward},
185
186(* Sfermion: unphysical scalars *)
187 S[23] == { ClassName->LLs,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D], Index[GEN]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
188            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]] } },
189 S[24] == { ClassName->ERs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1},
190            Definitions->{ ERs[ff_] :> Module[{ff2}, slbar[ff2]*RlR[ff2,ff]]} },
191 S[25] == { ClassName->VRs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
192            Definitions->{ VRs[_] -> 0 } },
193 S[26] == { ClassName->QLs,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D], Index[GEN],Index[Colour]}, FlavorIndex->SU2D, QuantumNumbers->{Y->1/6},
194            Definitions->{
195              QLs[1,ff_,cc_]:>Module[{ff2},Conjugate[RuL[ff2,ff]]*su[ff2,cc]],
196              QLs[2,ff_,cc_]:>Module[{ff2,ff3},Conjugate[RdL[ff2,ff3]]*CKM[ff,ff3]*sd[ff2,cc]]}},
197 S[27] == { ClassName->URs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y->-2/3},
198            Definitions->{ URs[ff_,cc_]:>Module[{ff2}, subar[ff2,cc]*RuR[ff2,ff]]} },
199 S[28] == { ClassName->DRs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1/3},
200            Definitions->{ DRs[ff_,cc_]:>Module[{ff2}, sdbar[ff2,cc]*RdR[ff2,ff]]} },
201
202(* Sfermion: physical scalars *)
203 S[7] == {  ClassName->sn, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
204            ParticleName->{"sv1","sv2","sv3"}, AntiParticleName->{"sv1~","sv2~","sv3~"},
205            ClassMembers-> {sn1, sn2, sn3}, Mass->{Msn,Msn1,Msn2,Msn3}, Width->{Wsn,Wsn1,Wsn2,Wsn3},
206            PDG->{1000012,1000014,1000016}, PropagatorLabel->{"sn","sn1","sn2","sn3"}, PropagatorType->ScalarDash, PropagatorArrow->Forward },
207 S[8] == {  ClassName->sl, SelfConjugate->False, Indices->{Index[SCA]}, FlavorIndex->SCA, QuantumNumbers->{Q->-1},
208            ParticleName->{"sl1-","sl2-","sl3-","sl4-","sl5-","sl6-"}, AntiParticleName->{"sl1+","sl2+","sl3+","sl4+","sl5+","sl6+"},
209            ClassMembers->{sl1,sl2,sl3,sl4,sl5,sl6}, Mass->{Msl,Msl1,Msl2,Msl3,Msl4,Msl5,Msl6}, Width->{Wsl,Wsl1,Wsl2,Wsl3,Wsl4,Wsl5,Wsl6},
210            PDG->{1000011,1000013,1000015,2000011,2000013,2000015}, PropagatorLabel->{"sl","sl1","sl2","sl3","sl4","sl5","sl6"},
211            PropagatorType->ScalarDash, PropagatorArrow->Forward},
212 S[9] == {  ClassName->su, SelfConjugate->False, Indices->{Index[SCA],Index[Colour]}, FlavorIndex->SCA, QuantumNumbers->{Q-> 2/3},
213            ParticleName->{"su1","su2","su3","su4","su5","su6"}, AntiParticleName->{"su1~","su2~","su3~","su4~","su5~","su6~"},
214            ClassMembers->{su1,su2,su3,su4,su5,su6}, Mass->{Msu,Msu1,Msu2,Msu3,Msu4,Msu5,Msu6}, Width->{Wsu,Wsu1,Wsu2,Wsu3,Wsu4,Wsu5,Wsu6},
215            PDG->{1000002,1000004,1000006,2000002,2000004,2000006}, PropagatorLabel->{"su","su1","su2","su3","su4","su5","su6"},
216            PropagatorType->ScalarDash, PropagatorArrow->Forward},
217 S[10]== {  ClassName->sd, SelfConjugate->False, Indices->{Index[SCA],Index[Colour]}, FlavorIndex->SCA, QuantumNumbers->{Q->-1/3},
218            ParticleName->{"sd1","sd2","sd3","sd4","sd5","sd6"}, AntiParticleName->{"sd1~","sd2~","sd3~","sd4~","sd5~","sd6~"},
219            ClassMembers->{sd1,sd2,sd3,sd4,sd5,sd6}, Mass->{Msd,Msd1,Msd2,Msd3,Msd4,Msd5,Msd6}, Width->{Wsd,Wsd1,Wsd2,Wsd3,Wsd4,Wsd5,Wsd6},
220            PDG->{1000001,1000003,1000005,2000001,2000003,2000005}, PropagatorLabel->{"sd","sd1","sd2","sd3","sd4","sd5","sd6"},
221            PropagatorType->ScalarDash, PropagatorArrow->Forward},
222
223(* Ghost: related to unphysical gauge bosons *)
224  U[11] == { ClassName->ghWi, Unphysical->True, SelfConjugate->False, Ghost->Wi, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
225             Definitions->{ghWi[1]->(ghWp+ghWm)/Sqrt[2], ghWi[2]->(ghWm-ghWp)/(I*Sqrt[2]), ghWi[3]->cw ghZ+sw ghA} } ,
226  U[12] == { ClassName->ghB, Unphysical->True, SelfConjugate->False, Ghost->B,
227             Definitions->{ghB->-sw ghZ+cw ghA} },
228
229(* Ghost: related to physical gauge bosons *)
230  U[1] == { ClassName->ghG, SelfConjugate->False, Indices->{Index[Gluon]}, Ghost->G, QuantumNumbers->{GhostNumber->1},
231            Mass->0, Width->0, ParticleName->"ghG", PropagatorLabel->"uG", PropagatorType->GhostDash, PropagatorArrow->Forward},
232  U[2] == { ClassName->ghA, SelfConjugate->False, Ghost->A, QuantumNumbers->{GhostNumber->1},
233            Mass->0, Width->0, ParticleName->"ghA", PropagatorLabel->"uA", PropagatorType->GhostDash, PropagatorArrow->Forward},
234  U[3] == { ClassName->ghZ, SelfConjugate->False, Ghost->Z, QuantumNumbers->{GhostNumber->1},
235            Mass->{MZ,Internal}, Width->WZ, ParticleName->"ghZ", PropagatorLabel->"uZ", PropagatorType->GhostDash, PropagatorArrow->Forward},
236  U[4] == { ClassName->ghWp, SelfConjugate->False, Ghost->W, QuantumNumbers->{GhostNumber->1, Q->1},
237            Mass->{MW,Internal}, Width->WW, ParticleName->"ghWp", PropagatorLabel->"uWp", PropagatorType->GhostDash, PropagatorArrow->Forward},
238  U[5] == { ClassName->ghWm, SelfConjugate->False, Ghost->Wbar, QuantumNumbers->{GhostNumber->1, Q->-1},
239            Mass->{MW,Internal}, Width->WW, ParticleName->"ghWm", PropagatorLabel->"uWm", PropagatorType->GhostDash, PropagatorArrow->Forward}
240};
241
242
243(* ************************** *)
244(* *****   Parameters   ***** *)
245(* ************************** *)
246M$Parameters = {
247(* Mixing: external parameters *)
248  RMNS== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->UPMNS,
249           Description->"Neutrino PMNS mixing matrix (real part)"},
250  IMNS== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMUPMNS,
251           Description->"Neutrino PMNS mixing matrix (imaginary part)"},
252  RCKM== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->VCKM,
253           Description->"CKM mixing matrix (real part)"},
254  ICKM== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMVCKM,
255           Description->"CKM mixing matrix (imaginary part)"},
256  RNN == { ParameterType->External, ComplexParameter->False, Indices->{Index[NEU],Index[NEU]}, BlockName->NMIX,
257           Description->"Neutralino mixing matrix (real part)"},
258  INN == { ParameterType->External, ComplexParameter->False, Indices->{Index[NEU],Index[NEU]}, BlockName->IMNMIX,
259           Description->"Neutralino mixing matrix (imaginary part)"},
260  RUU == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->UMIX,
261           Description->"Chargino mixing matrix U (real part)"},
262  IUU == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->IMUMIX,
263           Description->"Chargino mixing matrix U (imaginary part)"},
264  RVV == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->VMIX,
265           Description->"Chargino mixing matrix V (real part)"},
266  IVV == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->IMVMIX,
267           Description->"Chargino mixing matrix V (imaginary part)"},
268  RRn == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->SNUMIX,
269           Description->"Sneutrino mixing matrix (real part)"},
270  IRn == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMSNUMIX,
271           Description->"Sneutrino mixing matrix (imaginary part)"},
272  RRl == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->SELMIX,
273           Description->"Slepton mixing matrix (real part)"},
274  IRl == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMSELMIX,
275           Description->"Slepton mixing matrix (imaginary part)"},
276  RRu == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->USQMIX,
277           Description->"Up squark mixing matrix (real part)"},
278  IRu == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMUSQMIX,
279           Description->"Up squark mixing matrix (imaginary part)"},
280  RRd == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->DSQMIX,
281           Description->"Down squark mixing matrix (real part)"},
282  IRd == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMDSQMIX,
283           Description->"Down squark mixing matrix (imaginary part)"},
284  alp == { TeX->\[Alpha], ParameterType->External, ComplexParameter->False, BlockName->FRALPHA, Description-> "Neutral Higgses mixing angle"},
285
286(* Mixing: internal parameters *)
287  cw  == { TeX->Subscript[c,w],        ParameterType->Internal, ComplexParameter->False, Value->MW/MZ,        Description->"Cosine of the weak angle"}, 
288  sw  == { TeX->Subscript[s,w],        ParameterType->Internal, ComplexParameter->False, Value->Sqrt[1-cw^2], Description->"Sine of the weak angle"},
289  PMNS== { TeX->Superscript[U,pmns], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
290           If[$MNSDiag, Definitions:>{PMNS[i_,j_]:>0 /;(i!=j), PMNS[i_,j_]:>1/;(i==j)}, Value->{PMNS[i_,j_]:>RMNS[i,j]+I*IMNS[i,j]}],
291           Description-> "Neutrino PMNS mixing matrix"},
292  CKM == { TeX->Superscript[V,ckm], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
293           If[$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]}],
294           Description-> "CKM mixing matrix"},
295  NN  == { TeX->N, ParameterType-> Internal, ComplexParameter->True, Indices->{Index[NEU],Index[NEU]}, Unitary->True,
296           Value->{NN[i_,j_]:>RNN[i,j]+I*INN[i,j]}, Description-> "Neutralino mixing matrix"},
297  UU  == { TeX->U, ParameterType-> Internal, ComplexParameter->True, Indices->{Index[CHA],Index[CHA]}, Unitary->True,
298           Value->{UU[i_,j_]:>RUU[i,j]+I*IUU[i,j]}, Description-> "Chargino mixing matrix U"},
299  VV  == { TeX->V, ParameterType-> Internal, ComplexParameter->True, Indices->{Index[CHA],Index[CHA]}, Unitary->True,
300           Value->{VV[i_,j_]:>RVV[i,j]+I*IVV[i,j]}, Description-> "Chargino mixing matrix V"},
301  Rl  == { TeX->Superscript[R,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
302           Value->{Rl[i_,j_]:>RRl[i,j]+I*IRl[i,j]}, Description-> "Slepton mixing matrix"},
303  Rn  == { TeX->Superscript[R,n], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
304           Value->{Rn[i_,j_]:>RRn[i,j]+I*IRn[i,j]}, Description-> "Sneutrino mixing matrix"},
305  Ru  == { TeX->Superscript[R,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
306           Value->{Ru[i_,j_]:>RRu[i,j]+I*IRu[i,j]}, Description-> "Up squark mixing matrix"},
307  Rd  == { TeX->Superscript[R,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
308           Value->{Rd[i_,j_]:>RRd[i,j]+I*IRd[i,j]}, Description-> "Down squark mixing matrix"},
309
310(* Left and right parts of the sfermion mixing matrices *)
311  RlL == { TeX->Superscript[RL,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
312            Definitions->{RlL[i_,j_]:>Rl[i,j]/;NumericQ[j]},  Description-> "Slepton mixing matrix - first three columns"},
313  RlR == { TeX->Superscript[RR,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
314            Definitions->{RlR[i_,j_]:>Rl[i,j+3]/;NumericQ[j]},Description-> "Slepton mixing matrix - last three columns"},
315  RuL == { TeX->Superscript[RL,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
316            Definitions->{RuL[i_,j_]:>Ru[i,j]/;NumericQ[j]},  Description-> "Up squark mixing matrix - first three columns"},
317  RuR == { TeX->Superscript[RR,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
318            Definitions->{RuR[i_,j_]:>Ru[i,j+3]/;NumericQ[j]},Description-> "Up squark mixing matrix - last three columns"},
319  RdL == { TeX->Superscript[RL,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
320            Definitions->{RdL[i_,j_]:>Rd[i,j]/;NumericQ[j]},  Description-> "Down squark mixing matrix - first three columns"},
321  RdR == { TeX->Superscript[RR,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
322            Definitions->{RdR[i_,j_]:>Rd[i,j+3]/;NumericQ[j]},Description-> "Down squark mixing matrix - last three columns"},
323
324(* Couplings constants: external parameters *)
325  aEWM1 == { TeX->Subsuperscript[\[Alpha],w,-1], ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->1, InteractionOrder->{QED,-2},
326             Description->"Inverse of the EW coupling constant at the Z pole"},
327  aS    == { TeX->Subscript[\[Alpha],s],         ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->3, InteractionOrder->{QCD, 2},
328             Description->"Strong coupling constant at the Z pole."},
329
330(* Couplings constants: internal parameters *)
331  ee == { TeX->e,              ParameterType->Internal, ComplexParameter->False, Value->Sqrt[4 Pi / aEWM1], InteractionOrder->{QED,1},
332          Description->"Electric coupling constant"},
333  gs == { TeX->Subscript[g,s], ParameterType->Internal, ComplexParameter->False, Value->Sqrt[4 Pi aS],      InteractionOrder->{QCD,1}, ParameterName->G,
334          Description->"Strong coupling constant"},
335  gp == { TeX->g',             ParameterType->Internal, ComplexParameter->False, Definitions-> {gp->ee/cw}, InteractionOrder->{QED,1},
336          Description->"Hypercharge coupling constant at the Z pole"},
337  gw == { TeX->Subscript[g,w], ParameterType->Internal, ComplexParameter->False, Definitions-> {gw->ee/sw}, InteractionOrder->{QED,1},
338          Description->"Weak coupling constant at the Z pole"},
339
340(* Higgs sector: external parameters *)
341  tb == { TeX->Subscript[t,b], ParameterType->External, ComplexParameter->False, BlockName->HMIX, OrderBlock->2, Description->"Ratio of the two Higgs vevs"},
342
343(* Higgs sector: internal parameters *)
344  beta == { TeX->\[Beta], ParameterType->Internal, ComplexParameter->False, Value->ArcTan[tb], Description->"Arctan of the ratio of the two Higgs vevs"},
345  vev  == { TeX->v,              ParameterType->Internal, ComplexParameter->False, Value->2*MZ*sw*cw/ee, InteractionOrder->{QED,-1},
346            Description->"Higgs vacuum expectation value"},
347  vd   == { TeX->Subscript[v,d], ParameterType->Internal, ComplexParameter->False, Value->vev*Cos[beta],    InteractionOrder->{QED,-1},
348            Description->"Down-type Higgs vacuum expectation value"},
349  vu   == { TeX->Subscript[v,u], ParameterType->Internal, ComplexParameter->False, Value->vev*Sin[beta],    InteractionOrder->{QED,-1},
350            Description->"Up-type Higgs vacuum expectation value"},
351
352(* Superpotential: external parameters *)
353  Ryu  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YU,
354            Description->"Up-type quark Yukawa matrix (real part)"},
355  Iyu  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYU,
356            Description->"Up-type quark Yukawa matrix (imaginary part)"},
357  Ryd  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YD,
358            Description->"Down-type quark Yukawa matrix (real part)"},
359  Iyd  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYD,
360            Description->"Down-type quark Yukawa matrix (imaginary part)"},
361  Rye  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YE,
362            Description->"Charged lepton Yukawa matrix (real part)"},
363  Iye  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYE,
364            Description->"Charged lepton Yukawa matrix (imaginary part)"},
365  RLLE == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->RVLAMLLE,
366            Description->"RPV superpotential LLE coupling (real part)"},
367  ILLE == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->IMRVLAMLLE,
368            Description->"RPV superpotential LLE coupling (imaginary parts)"},
369  RLQD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->RVLAMLQD,
370            Description->"RPV superpotential LQD coupling (real part)"},
371  ILQD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->IMRVLAMLQD,
372            Description->"RPV superpotential LQD coupling (imaginary parts)"},
373  RLDD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->RVLAMUDD,
374            Description->"RPV superpotential UDD coupling (real part)"},
375  ILDD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->IMRVLAMUDD,
376            Description->"RPV superpotential UDD coupling (imaginary parts)"},
377  RMUH == { ParameterType->External, ComplexParameter->False, BlockName->HMIX,   OrderBlock->1, Description->"Off-diagonal Higgs mixing parameter (real part)"},
378  IMUH == { ParameterType->External, ComplexParameter->False, BlockName->IMHMIX, OrderBlock->1, Description->"Off-diagonal Higgs mixing parameter (imaginary part)"},
379
380
381
382(* Superpotential: internal parameters *)
383  yu  == { TeX->Superscript[y,u], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
384           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"},
385  yd  == { TeX->Superscript[y,d], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
386           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"},
387  ye  == { TeX->Superscript[y,e], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
388           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"},
389  LLLE== { TeX->Superscript[\[Lambda],LLE], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN],Index[GEN]},
390           Value->{LLLE[i_,j_,k_]:>RLLE[i,j,k]+I*ILLE[i,j,k]}, InteractionOrder->{QED,1}, Description->"Superpotential RPV LLE couplings"},
391  LLQD== { TeX->Superscript[\[Lambda],LQD], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN],Index[GEN]},
392           Value->{LLQD[i_,j_,k_]:>RLQD[i,j,k]+I*ILQD[i,j,k]}, InteractionOrder->{QED,1}, Description->"Superpotential RPV LQD couplings"},
393  LUDD== { TeX->Superscript[\[Lambda],UDD], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN],Index[GEN]},
394           Value->{LUDD[i_,j_,k_]:>RLDD[i,j,k]+I*ILDD[i,j,k]}, InteractionOrder->{QED,1}, Description->"Superpotential RPV UDD couplings"},
395  MUH == { TeX->\[Mu], ParameterType->Internal, ComplexParameter->True, Value->RMUH+I*IMUH, Description->"Off diagonal Higgs mixing parameter"},
396
397(* Soft terms: external parameters *)
398  RMx1 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT,   OrderBlock->1, Description->"Bino mass (real part)"},
399  IMx1 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->1, Description->"Bino mass (imaginary part)"},
400  RMx2 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT,   OrderBlock->2, Description->"Wino mass (real part)"},
401  IMx2 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->2, Description->"Wino mass (imaginary part)"},
402  RMx3 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT,   OrderBlock->3, Description->"Gluino mass (real part)"},
403  IMx3 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->3, Description->"Gluino mass (imaginary part)"},
404  mHu2 == { TeX->Subsuperscript[m,Subscript[H,u],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->21,
405            Description->"Up-type Higgs squared mass"},
406  mHd2 == { TeX->Subsuperscript[m,Subscript[H,d],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->22,
407            Description->"Down-type Higgs squared mass"},
408  MA2  == { TeX->Subsuperscript[m,A,2], ParameterType->External, ComplexParameter->False, BlockName->HMIX, OrderBlock->4,
409            Description->"Pseudoscalar Higgs squared mass"},
410  RmL2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSL2,
411            Description->"Left-handed slepton squared mass matrix (real part)"},
412  ImL2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSL2,
413            Description->"Left-handed slepton squared mass matrix (imaginary part)"},
414  RmE2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSE2,
415            Description->"Right-handed slepton squared mass matrix (real part)"},
416  ImE2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSE2,
417            Description->"Right-handed slepton squared mass matrix (imaginary part)"},
418  RmQ2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSQ2,
419            Description->"Left-handed squark squared mass matrix (real part)"},
420  ImQ2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSQ2,
421            Description->"Left-handed squark squared mass matrix (imaginary part)"},
422  RmU2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSU2,
423            Description->"Right-handed up-type squark squared mass matrix (real part)"},
424  ImU2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSU2,
425            Description->"Right-handed up-type squark squared mass matrix (imaginary part)"},
426  RmD2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSD2,
427            Description->"Right-handed down-type squark squared mass matrix (real part)"},
428  ImD2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSD2,
429            Description->"Right-handed down-type squark squared mass matrix (imaginary part)"},
430  Rte == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->TE,
431            Description->"Charged slepton trilinear coupling (real part)"},
432  Ite == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMTE,
433            Description->"Charged slepton trilinear coupling (imaginary part)"},
434  Rtu == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->TU,
435            Description->"Up-type squark trilinear coupling (real part)"},
436  Itu == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMTU,
437            Description->"Up-type squark trilinear coupling (imaginary part)"},
438  Rtd == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->TD,
439            Description->"Down-type squark trilinear coupling (real part)"},
440  Itd == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMTD,
441            Description->"Down-type squark trilinear coupling (imaginary part)"},
442  RTLE == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->RVTLLE,
443            Description->"Soft SUSY-breaking RPV LLE coupling (real part)"},
444  ITLE == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->IMRVTLLE,
445            Description->"Soft SUSY-breaking RPV LLE coupling (imaginary parts)"},
446  RTQD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->RVTLQD,
447            Description->"Soft SUSY-breaking RPV LQD coupling (real part)"},
448  ITQD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->IMRVTLQD,
449            Description->"Soft SUSY-breaking RPV LQD coupling (imaginary parts)"},
450  RTDD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->RVTUDD,
451            Description->"Soft SUSY-breaking RPV UDD coupling (real part)"},
452  ITDD == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN],Index[GEN]}, BlockName->IMRVTUDD,
453            Description->"Soft SUSY-breaking RPV UDD coupling (imaginary parts)"},
454
455(* Soft terms: internal parameters *)
456  Mx1 == { TeX->Subscript[M,1], ParameterType->Internal, ComplexParameter->True, Value->RMx1+I*IMx1, Description->"Bino mass"},
457  Mx2 == { TeX->Subscript[M,2], ParameterType->Internal, ComplexParameter->True, Value->RMx2+I*IMx2, Description->"Wino mass"},
458  Mx3 == { TeX->Subscript[M,3], ParameterType->Internal, ComplexParameter->True, Value->RMx3+I*IMx3, Description->"Gluino mass"},
459  bb  == { TeX->b, ParameterType->Internal, ComplexParameter->True, Value->(mHu2-mHd2-MZ^2*Cos[2*beta])*Tan[2*beta]/2, Description->"Higgs bilinear soft term"},
460  mL2 == { TeX->Subsuperscript[m,OverTilde[L],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
461           Value->{mL2[i_,j_]:>RmL2[i,j]+I*ImL2[i,j]}, Description-> "Left-handed slepton squared mass matrix"},
462  mE2 == { TeX->Subsuperscript[m,OverTilde[E],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
463           Value->{mE2[i_,j_]:>RmE2[i,j]+I*ImE2[i,j]}, Description-> "Right-handed slepton squared mass matrix"},
464  mQ2 == { TeX->Subsuperscript[m,OverTilde[Q],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
465           Value->{mQ2[i_,j_]:>RmQ2[i,j]+I*ImQ2[i,j]}, Description-> "Left-handed squark squared mass matrix"},
466  mU2 == { TeX->Subsuperscript[m,OverTilde[U],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
467           Value->{mU2[i_,j_]:>RmU2[i,j]+I*ImU2[i,j]}, Description-> "Right-handed up-type squark squared mass matrix"},
468  mD2 == { TeX->Subsuperscript[m,OverTilde[D],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
469           Value->{mD2[i_,j_]:>RmD2[i,j]+I*ImD2[i,j]}, Description-> "Right-handed down-type squark squared mass matrix"},
470  te  == { TeX->Subscript[T,e], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, InteractionOrder->{QED,1},
471           Value->{te[i_,j_]:>Rte[i,j]+I*Ite[i,j]}, Description-> "Charged slepton trilinear coupling"},
472  tu  == { TeX->Subscript[T,u], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, InteractionOrder->{QED,1},
473           Value->{tu[i_,j_]:>Rtu[i,j]+I*Itu[i,j]}, Description-> "Up-type squark trilinear coupling"},
474  td  == { TeX->Subscript[T,d], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, InteractionOrder->{QED,1},
475           Value->{td[i_,j_]:>Rtd[i,j]+I*Itd[i,j]}, Description-> "Down-type squark trilinear coupling"},
476  TLLE== { TeX->Superscript[T,LLE], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN],Index[GEN]},
477           Value->{TLLE[i_,j_,k_]:>RTLE[i,j,k]+I*ITLE[i,j,k]}, InteractionOrder->{QED,1}, Description->"RPV-LLE soft SUSY breaking trilinear couplings"},
478  TLQD== { TeX->Superscript[T,LQD], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN],Index[GEN]},
479           Value->{TLQD[i_,j_,k_]:>RTQD[i,j,k]+I*ITQD[i,j,k]}, InteractionOrder->{QED,1}, Description->"RPV-LQD soft SUSY breaking trilinear couplings"},
480  TUDD== { TeX->Superscript[T,UDD], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN],Index[GEN]},
481           Value->{TUDD[i_,j_,k_]:>RTDD[i,j,k]+I*ITDD[i,j,k]}, InteractionOrder->{QED,1}, Description->"RPV-UDD soft SUSY breaking trilinear couplings"}
482};
483
484(* ************************** *)
485(* ****  Diracification  **** *)
486(* ************************** *)
487ToDirac[exp_]:= Module[{tmp=Expand[exp],cnt=0,prg1=0,prg2=0,prgo1=0,prgo2=0,tot},
488  Colourb=Colour;
489
490  tmp = If[Head[tmp]===Plus,List@@tmp,List[tmp]]/.Tb[a_,i_,j_]->-T[a,j,i];
491
492  tmp = OptimizeIndex[#] &/@ tmp;
493  tot=Length[tmp];
494  Print["Flavor expansion: ", ProgressIndicator[Dynamic[prg1]]];
495  tmp = Module[{}, cnt++; prg1=cnt/tot;
496     Expand[(ExpandIndices[#, FlavorExpand->{SU2W, SU2D}] /. {
497         gp->ee/cw,
498         gw->ee/sw,
499         cw^n_?(Mod[#,2]===0&)->(1 - sw^2)^(n/2),
500         cw^n_?(Mod[#, 2]===1 &)->(1 - sw^2)^((n - 1)/2) cw,
501         Power[PauliSigma[a_,i_?(NumericQ[#] &),j_?(NumericQ[#] &)],2]->PauliSigma[1,i,j]^2 + PauliSigma[3,i,j]^2 + PauliSigma[2,i,j]^2,
502         PauliSigma[a_,i_?(NumericQ[#] &),j_?(NumericQ[#] &)] PauliSigma[a_,k_?(NumericQ[#] &),l_?(NumericQ[#] &)]->
503           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;
504   tmp = Plus@@tmp//.{
505           cw^n_?(Mod[#,2]===0&)->(1 - sw^2)^(n/2),
506           cw^n_?(Mod[#, 2]===1 &)->(1 - sw^2)^((n - 1)/2) cw,
507           Conjugate[CKM[a_, b_]]*CKM[a_, c_]->IndexDelta[b, c],
508           Conjugate[PMNS[a_, b_]]*PMNS[a_, c_]->IndexDelta[b, c]};
509   cnt=0; tot=Length[tmp];
510   Print["Opt 1: ",ProgressIndicator[Dynamic[prgo1]]];
511   tmp = Module[{}, cnt++; prgo1=cnt/tot;OptimizeIndex[#]] &/@ (List@@tmp);
512   Print["Weyl2Dirac: ",ProgressIndicator[Dynamic[prg2]]];cnt=0;
513   tmp = Module[{}, cnt++; prg2=cnt/tot; WeylToDirac[#]] &/@ tmp;
514   Print["Opt2: ",ProgressIndicator[Dynamic[prgo2]]];cnt=0;
515   tmp = Module[{}, cnt++; prgo2=cnt/tot;OptimizeIndex[#]] &/@ tmp;
516   Clear[Colourb];
517Expand[Plus@@tmp]];
518
519(* ************************** *)
520(* *****   Lagrangian   ***** *)
521(* ************************** *)
522(* LVector *)
523LVector := Module[{}, Plus@@(Module[{tmp}, tmp = SF2Components[#]; Expand[tmp[[2, 5]] + tmp[[2, 6]]]] &/@ (List @@ VSFKineticTerms[]))];
524
525(* LChiral *)
526LChiral :=  Plus@@( Theta2Thetabar2Component[#] &/@ (List @@ CSFKineticTerms[]) );
527
528(* Superpotential *)
529SPot:= Module[{ff1,ff2,ff3,ff4,ff5,cc1,cc2,cc3},
530     yu[ff1,ff2] UR[ff1,cc1] (QL[1,ff2,cc1] HU[2] - QL[2,ff2,cc1] HU[1]) -
531     yd[ff1,ff3] Conjugate[CKM[ff2,ff3]] DR[ff1,cc1] (QL[1,ff2,cc1] HD[2] - QL[2,ff2,cc1] HD[1]) -
532     ye[ff1,ff2] ER[ff1]     (LL[1,ff2]     HD[2] - LL[2,ff2]     HD[1]) +
533     1/2 LUDD[ff1,ff2,ff3] Eps[cc1,cc2,cc3] UR[ff1, cc1] DR[ff2,cc2] DR[ff3,cc3] +
534     LLLE[ff1,ff2,ff3] Conjugate[PMNS[ff4,ff1]] LL[1,ff4] LL[2,ff2] ER[ff3] +
535     LLQD[ff4,ff5,ff3] Conjugate[CKM[ff2,ff5]] Conjugate[PMNS[ff1,ff4]] DR[ff3,cc1] (LL[1,ff1] QL[2,ff2,cc1] - LL[2,ff1] QL[1,ff2,cc1]) +
536     MUH (HU[1] HD[2] - HU[2] HD[1])];
537LSuperW:= ( Plus@@ (Module[{tmp},tmp=SF2Components[#];tmp[[2,5]]+tmp[[2,6]]] &/@ (List @@ Expand[SPot+HC[SPot]])) )/.{Conjugate[CKM[a_, b_]]*CKM[a_, c_]->IndexDelta[b, c], Conjugate[PMNS[a_, b_]]*PMNS[a_, c_]->IndexDelta[b, c]};
538
539(* Soft SUSY-breaking Lagrangian *)
540LSoft := Module[{Mino, MSca, Tri, Bil},
541  (* Gaugino mass terms *)
542    Mino:=Module[{s,gl}, - Mx1*bow[s].bow[s] -  Mx2*wow[s,gl].wow[s,gl] - Mx3*gow[s,gl].gow[s,gl]];
543  (* Scalar mass terms *)
544    MSca:=Module[{ii,ff1,ff2,ff3,ff4,ff5,cc1,cc2,cc3},
545      - mHu2*HC[hus[ii]]*hus[ii] - mHd2*HC[hds[ii]]*hds[ii] -
546        mL2[ff1,ff2]*HC[LLs[ii,ff1]]*LLs[ii,ff2] - mE2[ff1,ff2]*HC[ERs[ff1]]*ERs[ff2] -
547        CKM[ff1,ff2]*mQ2[ff2,ff3]*Conjugate[CKM[ff4,ff3]]*HC[QLs[ii,ff1,cc1]]*QLs[ii,ff4,cc1] -
548        mU2[ff1,ff2]*HC[URs[ff1,cc1]]*URs[ff2,cc1] -  mD2[ff1,ff2]*HC[DRs[ff1,cc1]]*DRs[ff2,cc1] ];
549  (* Trilinear couplings *)
550    Tri:=-tu[ff1,ff2]*URs[ff1,cc1] (QLs[1,ff2,cc1] hus[2] - QLs[2,ff2,cc1] hus[1]) +
551          Conjugate[CKM[ff3,ff2]]*td[ff1,ff2]*DRs[ff1,cc1] (QLs[1,ff3,cc1] hds[2] - QLs[2,ff3,cc1] hds[1]) +
552          te[ff1,ff2]*ERs[ff1] (LLs[1,ff2] hds[2] - LLs[2,ff2] hds[1]) -
553          1/2 TUDD[ff1,ff2,ff3] Eps[cc1,cc2,cc3] URs[ff1, cc1] DRs[ff2,cc2] DRs[ff3,cc3] -
554          TLLE[ff1,ff2,ff3] Conjugate[PMNS[ff4,ff1]] LLs[1,ff4] LLs[2,ff2] ERs[ff3] -
555          TLQD[ff4,ff5,ff3] Conjugate[CKM[ff2,ff5]] Conjugate[PMNS[ff1,ff4]] DRs[ff3,cc1] (LLs[1,ff1] QLs[2,ff2,cc1] - LLs[2,ff1] QLs[1,ff2,cc1]);
556  (* Bilinear couplings *)
557    Bil:=-bb*(hus[1] hds[2] - hus[2] hds[1]);
558  (* Everything together *)
559  (Mino+HC[Mino])/2 + MSca + Tri + HC[Tri] + Bil + HC[Bil]];
560
561(* Ghost Lagrangian and gauge fixing terms *)
562LFeynmanGFix := Module[{VectorizeU,VectorizeD, Phiu,Phid,Phiu0,Phid0, phid1,phid2,phiu1,phiu2, GF1,GF2,GF3,LGF, nrules, kk,ll, LGh1,LGh2,LGh3,LGhS,LGh, genu,gend, gh,ghbar},
563  (* Expression the doublets in the nu/nd basis *)
564  VectorizeU[{a_, b_}] := Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]} /. {Im[_]->0, Re[num_]->num}];
565  VectorizeD[{a_, b_}] := Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]} /. {Im[_]->0, Re[num_]->num}];
566
567  (* Higgs doublets *)
568  Phiu = Expand[ {(phiu1 + I phiu2)/Sqrt[2], (Cos[alp]*h0+Sin[alp]*H0 + I*Cos[beta]*A0+I*Sin[beta]*G0)/Sqrt[2]} ];
569  Phid = Expand[ {(-Sin[alp]*h0+Cos[alp]*H0 + I*Sin[beta]*A0-I*Cos[beta]*G0)/Sqrt[2], (phid1 + I phid2)/Sqrt[2]} ];
570  (* vevs *)
571  Phiu0 = {0, vu/Sqrt[2]};
572  Phid0 = {vd/Sqrt[2], 0};
573  (* Back to the physical Higgses and Goldstones *)
574  nrules := {
575     phid1 -> (-Cos[beta]*GPbar - Cos[beta]*GP + Sin[beta]*Hbar + Sin[beta]*H)/Sqrt[2],
576     phid2 -> (-Cos[beta]*GPbar + Cos[beta]*GP + Sin[beta]*Hbar - Sin[beta]*H)/(I Sqrt[2]),
577     phiu1 -> ( Sin[beta]*GP + Sin[beta]*GPbar + Cos[beta]*H + Cos[beta]*Hbar)/Sqrt[2],
578     phiu2 -> (Sin[beta]*GP - Sin[beta]*GPbar + Cos[beta]*H - Cos[beta]*Hbar)/(I Sqrt[2])};
579
580  (* Gauge-fixing functions *)
581  GF1     := Module[{mu}, del[B[mu]   , mu] - gp VectorizeU[-I/2 Phiu0].VectorizeU[Phiu] - gp VectorizeD[I/2 Phid0].VectorizeD[Phid] ];
582  GF2[k_] := Module[{mu}, del[Wi[mu,k], mu] - gw VectorizeU[-I/2 PauliSigma[k].Phiu0].VectorizeU[Phiu] - gw VectorizeD[-I/2 PauliSigma[k].Phid0].VectorizeD[Phid] ];
583  GF3[a_] := Module[{mu}, del[G[mu,a] , mu] ];
584  (* Gauge-fixing Lagrangian *)
585  LGF = Expand[-1/2*(GF1 HC[GF1] + Sum[GF2[kk] HC[GF2[kk]], {kk, 1, 3}]) /.nrules /. {HC[a_]->a, h0->0, H0->0, A0->0, H->0, Hbar->0}];
586  LGF = OptimizeIndex[Expand[ExpandIndices[LGF, FlavorExpand->SU2W]]];
587
588  (* Ghost Lagrangians *)
589  LGh1 = -ghBbar.del[DC[ghB,mu],mu];
590  LGh2 = -ghWibar[kk].del[DC[ghWi[kk], mu], mu];
591  LGh3 = -ghGbar[kk].del[DC[ghG[kk],mu],mu];
592  genu := {-I/2 gp IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
593  gend := { I/2 gp IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
594  gh    = {ghB,    ghWi[1],    ghWi[2],    ghWi[3]};
595  ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
596  LGhS = Sum[
597    -ghbar[[kk]].gh[[ll]] (VectorizeU[genu[[kk]].Phiu0].VectorizeU[genu[[ll]].(Phiu+Phiu0)] + VectorizeD[gend[[kk]].Phid0].VectorizeD[gend[[ll]].(Phid+Phid0)]),
598    {kk,1,4},{ll,1,4}];
599  LGh = ExpandIndices[LGh1+LGh2+LGh3+LGhS, FlavorExpand->SU2W] /.nrules;
600LGF+LGh];
601
602(* Collecting all the pieces together *)
603Lag := ToDirac[SolveEqMotionF[SolveEqMotionD[LVector+LChiral+LSuperW+LSoft]]] + LFeynmanGFix ;