NMSSM: nmssm.fr

File nmssm.fr, 49.3 KB (added by BenjF, 7 years ago)

NMSSM FR model file

Line 
1(* ********************************************************* *)
2(* *****                                               ***** *)
3(* *****  FeynRules model file: the NMSSM              ***** *)
4(* *****  Author: B. Fuks                              ***** *)
5(* *****                                               ***** *)
6(* ********************************************************* *)
7
8(* ************************** *)
9(* *****  Information   ***** *)
10(* ************************** *)
11M$ModelName = "NMSSM";
12M$Information = { Authors->{"Benjamin Fuks"}, Emails->{"fuks@cern.ch"}, Institutions->{"IPHC Strasbourg / University of Strasbourg"},
13                  Date->"31.07.12", Version->"1.0.9",
14                  References->{""},
15                  URLs->{"http://feynrules.phys.ucl.ac.be/view/Main/NMSSM"} };
16
17(* v1.0.1:  small bug in the ghost sector corrected                                          *)
18(* v1.0.2:  change of notation for the physical fields -> matching FeynArts standards        *)
19(* v1.0.3:  bilinear soft higgs mixing parameter not implemented                             *)
20(* v1.0.4:  renaming of SP to SPot (variable name clashing). Thanks to Kentarou Mawatari.    *)
21(* v1.0.5:  small bug in the definition of the CKM matrix. Thanks to Antonio Mariano.        *)
22(* v1.0.6:  Inversion of two SLHA counters for the Higgs soft masses. Thanks to Flip Tanedo. *)
23(* v1.0.7:  Symbols for the pseudoscalar Higgs masses in conflict with Feynarts conventions. *)
24(*           --> changed to MxA0. Rewriting of the treatment of the golstone entries of the  *)
25(*          pseudoscalar Higgs mixing matrix. Thanks to Markos Maniatis.                     *)
26(* v1.0.8:  Interaction orders.                                                              *)
27(* v1.0.9:  Adding the Feynman gauge flag.                                                   *)
28(* v1.0.10: The coupling order of the singlet vev was missing (thanks to Peter Richardson).  *)
29
30
31(* ************************** *)
32(* *****      Flags     ***** *)
33(* ************************** *)
34$CKMDiag = True;   (* CKM  = identity or not *)
35$MNSDiag = True;   (* PMNS = identity or not *)
36FeynmanGauge = True;
37
38
39(* ************************** *)
40(* *****  Gauge groups  ***** *)
41(* ************************** *)
42M$GaugeGroups = {
43  U1Y  == { Abelian->True,  CouplingConstant->gp, Superfield->BSF, Charge->Y, GUTNormalization->3/5},
44  SU2L == { Abelian->False, CouplingConstant->gw, Superfield->WSF,
45            StructureConstant->ep, Representations->{Ta,SU2D}, Definitions->{Ta[a__]->PauliSigma[a]/2, ep->Eps}},
46  SU3C == { Abelian->False, CouplingConstant->gs, Superfield->GSF,
47            StructureConstant->f,  Representations->{{T,Colour}, {Tb,Colourb}}, DTerm->dSUN}
48};
49
50
51(* ************************** *)
52(* *** Interaction orders *** *)
53(* ************************** *)
54M$InteractionOrderHierarchy = { {QCD, 1}, {QED, 2} };
55
56
57(* ************************** *)
58(* *****    Indices     ***** *)
59(* ************************** *)
60IndexRange[Index[SU2W]] =   Unfold[Range[3]]; IndexStyle[SU2W,j];  IndexRange[Index[SU2D]] =   Unfold[Range[2]]; IndexStyle[SU2D,k];
61IndexRange[Index[Gluon ]] = NoUnfold[Range[8]]; IndexStyle[Gluon, a];  IndexRange[Index[Colour ]] = NoUnfold[Range[3]]; IndexStyle[Colour, m];
62IndexRange[Index[Colourb]] = NoUnfold[Range[3]]; IndexStyle[Colourb,m];
63IndexRange[Index[NEU ]] = Range[5];           IndexStyle[NEU, i];
64IndexRange[Index[CHA ]] = Range[2];           IndexStyle[CHA, i];
65IndexRange[Index[GEN ]] = Range[3];           IndexStyle[GEN, f];
66IndexRange[Index[SCA ]] = Range[6];           IndexStyle[SCA, i];
67IndexRange[Index[SHig]] = Range[3];           IndexStyle[SHig,n];
68IndexRange[Index[PHig]] = Range[2];           IndexStyle[PHig,n];
69
70
71
72(* ************************** *)
73(* *****  Superfields   ***** *)
74(* ************************** *)
75M$Superfields = {
76  VSF[1] == { ClassName->BSF, GaugeBoson->B,  Gaugino->bow},
77  VSF[2] == { ClassName->WSF, GaugeBoson->Wi, Gaugino->wow, Indices->{Index[SU2W]}},
78  VSF[3] == { ClassName->GSF, GaugeBoson->G,  Gaugino->gow, Indices->{Index[Gluon] }},
79  CSF[1] == { ClassName->HU, Chirality->Left, Weyl->huw, Scalar->hus, QuantumNumbers->{Y-> 1/2}, Indices->{Index[SU2D]}},
80  CSF[2] == { ClassName->HD, Chirality->Left, Weyl->hdw, Scalar->hds, QuantumNumbers->{Y->-1/2}, Indices->{Index[SU2D]}},
81  CSF[3] == { ClassName->LL, Chirality->Left, Weyl->LLw, Scalar->LLs, QuantumNumbers->{Y->-1/2}, Indices->{Index[SU2D], Index[GEN]}},
82  CSF[4] == { ClassName->ER, Chirality->Left, Weyl->ERw, Scalar->ERs, QuantumNumbers->{Y-> 1},   Indices->{Index[GEN]}},
83  CSF[5] == { ClassName->VR, Chirality->Left, Weyl->VRw, Scalar->VRs, Indices->{Index[GEN]}},
84  CSF[6] == { ClassName->QL, Chirality->Left, Weyl->QLw, Scalar->QLs, QuantumNumbers->{Y-> 1/6}, Indices->{Index[SU2D], Index[GEN], Index[Colour]}},
85  CSF[7] == { ClassName->UR, Chirality->Left, Weyl->URw, Scalar->URs, QuantumNumbers->{Y->-2/3}, Indices->{Index[GEN], Index[Colourb]}           },
86  CSF[8] == { ClassName->DR, Chirality->Left, Weyl->DRw, Scalar->DRs, QuantumNumbers->{Y-> 1/3}, Indices->{Index[GEN], Index[Colourb]}           },
87  CSF[9] == { ClassName->SPF,Chirality->Left, Weyl->SPw, Scalar->SPs}
88};
89
90(* ************************** *)
91(* *****     Fields     ***** *)
92(* ************************** *)
93M$ClassesDescription = {
94(* Gauge bosons: unphysical vector fields *)
95  V[11] == { ClassName->B, Unphysical->True, SelfConjugate->True,
96            Definitions->{B[mu_]->-sw Z[mu]+cw A[mu]} },
97  V[12] == { ClassName->Wi, Unphysical->True, SelfConjugate->True, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
98             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]} },
99
100(* Gauge bosons: physical vector fields *)
101  V[1] == { ClassName->A, SelfConjugate->True,  Mass->0,  Width->0,  ParticleName->"a",
102            PDG->22, PropagatorLabel->"A", PropagatorType->Sine, PropagatorArrow->None},
103  V[2] == { ClassName->Z, SelfConjugate->True,  Mass->MZ, Width->WZ, ParticleName->"Z",
104            PDG->23, PropagatorLabel->"Z", PropagatorType->Sine, PropagatorArrow->None},
105  V[3] == { ClassName->W, SelfConjugate->False, Mass->MW, Width->WW, ParticleName->"W+", AntiParticleName->"W-", QuantumNumbers->{Q->1},
106            PDG->24, PropagatorLabel->"W", PropagatorType->Sine, PropagatorArrow->Forward},
107  V[5] == { ClassName->G, SelfConjugate->True, Indices->{Index[Gluon]}, Mass->0, Width->0, ParticleName->"g",
108            PDG->21, PropagatorLabel->"G", PropagatorType->C,    PropagatorArrow->None },
109
110(* Gauginos: unphysical Weyls *)
111  W[20] == { ClassName->bow, Unphysical->True, Chirality->Left, SelfConjugate->False,
112             Definitions->{bow[s_]:>Module[{i}, -I*Conjugate[NN[i,1]]*neuw[s,i]]}},
113  W[21] == { ClassName->wow, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
114             Definitions->{
115               wow[s_,1]:>Module[{i},(Conjugate[UU[i,1]]*chmw[s,i]+Conjugate[VV[i,1]]*chpw[s,i])/(I*Sqrt[2])],
116               wow[s_,2]:>Module[{i},(Conjugate[UU[i,1]]*chmw[s,i]-Conjugate[VV[i,1]]*chpw[s,i])/(-Sqrt[2])],
117               wow[s_,3]:>Module[{i},-I*Conjugate[NN[i,2]]*neuw[s,i]]} },
118  W[22] == { ClassName->gow,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[Gluon]},  Definitions->{gow[inds__]->-I*goww[inds]} },
119
120(* Higgsinos: unphysical Weyls *)
121  W[23] == { ClassName->huw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
122             Definitions->{
123               huw[s_,1]:> Module[{i}, Conjugate[VV[i,2]]*chpw[s,i]],
124               huw[s_,2]:> Module[{i}, Conjugate[NN[i,4]]*neuw[s,i]] } },
125  W[24] == { ClassName->hdw,  Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
126             Definitions->{
127               hdw[s_,1]:> Module[{i}, Conjugate[NN[i,3]]*neuw[s,i]],
128               hdw[s_,2]:> Module[{i}, Conjugate[UU[i,2]]*chmw[s,i]]} },
129(* Singlino field *)
130  W[25] == { ClassName->SPw, Unphysical->True, Chirality->Left, SelfConjugate->False, Definitions->{SPw[s_]:>Module[{i},Conjugate[NN[i,5]]*neuw[s,i]]}},
131
132(* Gauginos/Higgsinos/singlino: physical Weyls *)
133  W[1] == { ClassName->neuw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[NEU]}, FlavorIndex->NEU },
134  W[2] == { ClassName->chpw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[CHA]}, FlavorIndex->CHA, QuantumNumbers->{Q-> 1} } ,
135  W[3] == { ClassName->chmw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[CHA]}, FlavorIndex->CHA, QuantumNumbers->{Q->-1} } ,
136  W[4] == { ClassName->goww, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[Gluon]} },
137
138(* Gauginos/Higgsinos/singlino: physical Diracs *)
139  F[11] == { ClassName->neu, SelfConjugate->True,  Indices->{Index[NEU]}, FlavorIndex->NEU, WeylComponents->neuw,
140            ParticleName->{"n1","n2","n3","n4","n5"}, PDG->{1000022,1000023,1000025,1000035,1000045},
141            ClassMembers->{neu1,neu2,neu3,neu4,neu5}, Mass->{Mneu,Mneu1,Mneu2,Mneu3,Mneu4,Mneu5}, Width->{Wneu,Wneu1,Wneu2,Wneu3,Wneu4,Wneu5},
142            PropagatorLabel->{"neu","neu1","neu2","neu3","neu4","neu5"}, PropagatorType->Straight, PropagatorArrow->None},
143  F[12] == { ClassName->ch,  SelfConjugate->False, Indices->{Index[CHA]}, FlavorIndex->CHA, WeylComponents->{chpw,chmwbar},
144            ParticleName->{"x1+","x2+"}, AntiParticleName->{"x1-","x2-"}, QuantumNumbers->{Q ->1},
145            ClassMembers->{ch1,ch2}, Mass->{Mch,Mch1,Mch2}, Width->{Wch,Wch1,Wch2},
146            PDG->{1000024,1000037}, PropagatorLabel->{"ch","ch1","ch2"}, PropagatorType->Straight, PropagatorArrow->Forward },
147  F[15] == { ClassName->go,  SelfConjugate->True, Indices->{Index[Gluon]}, WeylComponents->goww, Mass->Mgo, Width->Wgo, ParticleName->"go",
148            PDG->1000021, PropagatorLabel->"go", PropagatorType->Straight, PropagatorArrow->None },
149
150(* Higgs: unphysical scalars  *)
151 S[21] == { ClassName->hus,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y-> 1/2},
152            Definitions->{
153              hus[1]->Cos[beta]*H + Sin[beta]*GP,
154              hus[2] :> Module[{mm},(vu + Conjugate[US[mm,2]]*h0[mm] + I*Conjugate[UP[mm,2]]*A0[mm] + I*Conjugate[UP32]*G0)/Sqrt[2]]}},
155 S[22] == { ClassName->hds,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
156            Definitions->{
157              hds[1] :> Module[{mm},(vd + Conjugate[US[mm,1]]*h0[mm] + I*Conjugate[UP[mm,1]]*A0[mm] + I*Conjugate[UP31]*G0)/Sqrt[2]],
158              hds[2]->Sin[beta]*Hbar - Cos[beta]*GPbar} },
159
160(* Singlet field *)
161 S[23] == { ClassName->SPs, Unphysical->True, SelfConjugate->False,
162            Definitions->{SPs :> Module[{mm}, (vs + Conjugate[US[mm,3]]*h0[mm] + I*Conjugate[UP[mm,3]]*A0[mm] + I*Conjugate[UP33]*G0)/Sqrt[2]]} },
163
164(* Higgs: physical fields and Goldstones *)
165  S[1] == { ClassName->h0, SelfConjugate->True, Indices->{Index[SHig]}, FlavorIndex->SHig,
166            ParticleName->{"h01","h02","h03"}, ClassMembers->{h01,h02,h03}, Mass->{MH0,MH01,MH02,MH03}, Width->{WH0,WH01,WH02,WH03},
167            PDG->{25,35,45}, PropagatorLabel->{"h0","h01","h02","h03"}, PropagatorType->ScalarDash, PropagatorArrow->None},
168  S[2] == { ClassName->A0, SelfConjugate->True, Indices->{Index[PHig]}, FlavorIndex->PHig,
169            ParticleName->{"a01","a02"}, ClassMembers->{a01,a02}, Mass->{MxA0,MxA01,MxA02}, Width->{WA0,WA01,WA02},
170            PDG->{36,46}, PropagatorLabel->{"a0","a01","a02"}, PropagatorType->ScalarDash, PropagatorArrow->None},
171  S[5] == { ClassName->H,  SelfConjugate->False, QuantumNumbers->{Q-> 1}, Mass->MH, Width->WH,
172            ParticleName->"H+", AntiParticleName->"H-",
173            PDG->37,  PropagatorLabel->"H", PropagatorType->ScalarDash,  PropagatorArrow->Forward},
174  S[4] == { ClassName->G0, SelfConjugate->True, Mass->MZ, Width->WG0, Goldstone->Z,
175            ParticleName->"G0",
176            PDG->250, PropagatorLabel->"G0", PropagatorType->D, PropagatorArrow->None},
177  S[6] == { ClassName->GP, SelfConjugate->False, QuantumNumbers->{Q-> 1}, Mass->MW, Width->WGP, Goldstone->W,
178            ParticleName->"G+", AntiParticleName->"G-",
179            PDG->251, PropagatorLabel->"GP", PropagatorType->D, PropagatorArrow->None },
180
181(* Fermions: unphysical Weyls *)
182 W[26] == { ClassName->LLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D],Index[GEN]},              FlavorIndex->SU2D,
183            QuantumNumbers->{Y->-1/2},
184            Definitions->{LLw[s_,1,ff_]:>Module[{ff2}, PMNS[ff,ff2]*vLw[s,ff2]], LLw[s_,2,ff_]->eLw[s,ff]}},
185 W[27] == { ClassName->QLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[SU2D],Index[GEN],Index[Colour]},FlavorIndex->SU2D,
186            QuantumNumbers->{Y->1/6},
187            Definitions->{QLw[s_,1,ff_,cc_]->uLw[s,ff,cc], QLw[s_,2,ff_,cc_]:>Module[{ff2}, CKM[ff,ff2] dLw[s,ff2,cc]]}},
188
189(* Fermions: physical Weyls *)
190  W[5] == { ClassName->vLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
191  W[6] == { ClassName->eLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
192  W[7] == { ClassName->VRw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN },
193  W[8] == { ClassName->ERw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1} },
194  W[9] == { ClassName->uLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]},  FlavorIndex->GEN },
195  W[10]== { ClassName->dLw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]},  FlavorIndex->GEN },
196  W[11]== { ClassName->URw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y->-2/3} },
197  W[12]== { ClassName->DRw, Unphysical->True, Chirality->Left, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1/3} },
198
199(* Fermions: physical Dirac *)
200  F[1] == { ClassName->vl, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, WeylComponents->{vLw,VRwbar},
201            ParticleName->{"ve","vm","vt"}, AntiParticleName->{"ve~","vm~","vt~"},
202            ClassMembers->{ve,vm,vt}, Mass->{Mvl,Mve,Mvm,Mvt}, Width->0,
203            PDG->{12,14,16}, PropagatorLabel->{"v","ve","vm","vt"}, PropagatorType->Straight, PropagatorArrow->Forward},
204  F[2] == { ClassName->l, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, WeylComponents->{eLw,ERwbar}, QuantumNumbers->{Q->-1},
205            ParticleName->{"e-","mu-","tau-"}, AntiParticleName->{"e+","mu+","tau+"},
206            ClassMembers->{e,m,ta}, Mass->{Ml,Me,Mm,Mta}, Width->0,
207            PDG->{11,13,15}, PropagatorLabel->{"l","e","mu","tau"}, PropagatorType->Straight, PropagatorArrow->Forward},
208  F[3] == { ClassName->uq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, WeylComponents->{uLw,URwbar}, QuantumNumbers->{Q-> 2/3},
209            ParticleName->{"u","c","t"}, AntiParticleName->{"u~","c~","t~"},
210            ClassMembers->{u,c,t}, Mass->{Muq,MU,MC,MT}, Width->{Wuq,0,0,WT},
211            PDG->{2,4,6}, PropagatorLabel->{"uq","u","c","t"}, PropagatorType->Straight, PropagatorArrow->Forward},
212  F[4] == { ClassName->dq, SelfConjugate->False, Indices->{Index[GEN],Index[Colour]}, FlavorIndex->GEN, WeylComponents->{dLw,DRwbar}, QuantumNumbers->{Q->-1/3},
213            ParticleName->{"d","s","b"}, AntiParticleName->{"d~","s~","b~"},
214            ClassMembers->{d,s,b}, Mass->{Mdq,MD,MS,MB}, Width->0,
215            PDG->{1,3,5}, PropagatorLabel->{"dq","d","s","b"}, PropagatorType->Straight, PropagatorArrow->Forward},
216
217(* Sfermion: unphysical scalars *)
218 S[24] == { ClassName->LLs,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D], Index[GEN]}, FlavorIndex->SU2D, QuantumNumbers->{Y->-1/2},
219            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]] } },
220 S[25] == { ClassName->ERs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1},
221            Definitions->{ ERs[ff_] :> Module[{ff2}, slbar[ff2]*RlR[ff2,ff]]} },
222 S[26] == { ClassName->VRs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
223            Definitions->{ VRs[_] -> 0 } },
224 S[27] == { ClassName->QLs,  Unphysical->True, SelfConjugate->False, Indices->{Index[SU2D], Index[GEN],Index[Colour]}, FlavorIndex->SU2D, QuantumNumbers->{Y->1/6},
225            Definitions->{
226              QLs[1,ff_,cc_]:>Module[{ff2},Conjugate[RuL[ff2,ff]]*su[ff2,cc]],
227              QLs[2,ff_,cc_]:>Module[{ff2,ff3},Conjugate[RdL[ff2,ff3]]*CKM[ff,ff3]*sd[ff2,cc]]}},
228 S[28] == { ClassName->URs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y->-2/3},
229            Definitions->{ URs[ff_,cc_]:>Module[{ff2}, subar[ff2,cc]*RuR[ff2,ff]]} },
230 S[29] == { ClassName->DRs, Unphysical->True, SelfConjugate->False, Indices->{Index[GEN],Index[Colourb]}, FlavorIndex->GEN, QuantumNumbers->{Y-> 1/3},
231            Definitions->{ DRs[ff_,cc_]:>Module[{ff2}, sdbar[ff2,cc]*RdR[ff2,ff]]} },
232
233(* Sfermion: physical scalars *)
234 S[11] == {  ClassName->sn, SelfConjugate->False, Indices->{Index[GEN]}, FlavorIndex->GEN,
235            ParticleName->{"sv1","sv2","sv3"}, AntiParticleName->{"sv1~","sv2~","sv3~"},
236            ClassMembers-> {sn1, sn2, sn3}, Mass->{Msn,Msn1,Msn2,Msn3}, Width->{Wsn,Wsn1,Wsn2,Wsn3},
237            PDG->{1000012,1000014,1000016}, PropagatorLabel->{"sn","sn1","sn2","sn3"}, PropagatorType->ScalarDash, PropagatorArrow->Forward },
238 S[12] == {  ClassName->sl, SelfConjugate->False, Indices->{Index[SCA]}, FlavorIndex->SCA, QuantumNumbers->{Q->-1},
239            ParticleName->{"sl1-","sl2-","sl3-","sl4-","sl5-","sl6-"}, AntiParticleName->{"sl1+","sl2+","sl3+","sl4+","sl5+","sl6+"},
240            ClassMembers->{sl1,sl2,sl3,sl4,sl5,sl6}, Mass->{Msl,Msl1,Msl2,Msl3,Msl4,Msl5,Msl6}, Width->{Wsl,Wsl1,Wsl2,Wsl3,Wsl4,Wsl5,Wsl6},
241            PDG->{1000011,1000013,1000015,2000011,2000013,2000015}, PropagatorLabel->{"sl","sl1","sl2","sl3","sl4","sl5","sl6"},
242            PropagatorType->ScalarDash, PropagatorArrow->Forward},
243 S[13] == {  ClassName->su, SelfConjugate->False, Indices->{Index[SCA],Index[Colour]}, FlavorIndex->SCA, QuantumNumbers->{Q-> 2/3},
244            ParticleName->{"su1","su2","su3","su4","su5","su6"}, AntiParticleName->{"su1~","su2~","su3~","su4~","su5~","su6~"},
245            ClassMembers->{su1,su2,su3,su4,su5,su6}, Mass->{Msu,Msu1,Msu2,Msu3,Msu4,Msu5,Msu6}, Width->{Wsu,Wsu1,Wsu2,Wsu3,Wsu4,Wsu5,Wsu6},
246            PDG->{1000002,1000004,1000006,2000002,2000004,2000006}, PropagatorLabel->{"su","su1","su2","su3","su4","su5","su6"},
247            PropagatorType->ScalarDash, PropagatorArrow->Forward},
248 S[14]== {  ClassName->sd, SelfConjugate->False, Indices->{Index[SCA],Index[Colour]}, FlavorIndex->SCA, QuantumNumbers->{Q->-1/3},
249            ParticleName->{"sd1","sd2","sd3","sd4","sd5","sd6"}, AntiParticleName->{"sd1~","sd2~","sd3~","sd4~","sd5~","sd6~"},
250            ClassMembers->{sd1,sd2,sd3,sd4,sd5,sd6}, Mass->{Msd,Msd1,Msd2,Msd3,Msd4,Msd5,Msd6}, Width->{Wsd,Wsd1,Wsd2,Wsd3,Wsd4,Wsd5,Wsd6},
251            PDG->{1000001,1000003,1000005,2000001,2000003,2000005}, PropagatorLabel->{"sd","sd1","sd2","sd3","sd4","sd5","sd6"},
252            PropagatorType->ScalarDash, PropagatorArrow->Forward},
253
254(* Ghost: related to unphysical gauge bosons *)
255  U[11] == { ClassName->ghWi, Unphysical->True, SelfConjugate->False, Ghost->Wi, Indices->{Index[SU2W]}, FlavorIndex->SU2W,
256             Definitions->{ghWi[1]->(ghWp+ghWm)/Sqrt[2], ghWi[2]->(ghWm-ghWp)/(I*Sqrt[2]), ghWi[3]->cw ghZ+sw ghA} } ,
257  U[12] == { ClassName->ghB, Unphysical->True, SelfConjugate->False, Ghost->B,
258             Definitions->{ghB->-sw ghZ+cw ghA} },
259
260(* Ghost: related to physical gauge bosons *)
261  U[5] == { ClassName->ghG, SelfConjugate->False, Indices->{Index[Gluon]}, Ghost->G, QuantumNumbers->{GhostNumber->1},
262            Mass->0, Width->0, ParticleName->"ghG", PropagatorLabel->"uG", PropagatorType->GhostDash, PropagatorArrow->Forward},
263  U[1] == { ClassName->ghA, SelfConjugate->False, Ghost->A, QuantumNumbers->{GhostNumber->1},
264            Mass->0, Width->0, ParticleName->"ghA", PropagatorLabel->"uA", PropagatorType->GhostDash, PropagatorArrow->Forward},
265  U[2] == { ClassName->ghZ, SelfConjugate->False, Ghost->Z, QuantumNumbers->{GhostNumber->1},
266            Mass->{MZ,Internal}, Width->WZ, ParticleName->"ghZ", PropagatorLabel->"uZ", PropagatorType->GhostDash, PropagatorArrow->Forward},
267  U[4] == { ClassName->ghWp, SelfConjugate->False, Ghost->W, QuantumNumbers->{GhostNumber->1, Q->1},
268            Mass->{MW,Internal}, Width->WW, ParticleName->"ghWp", PropagatorLabel->"uWp", PropagatorType->GhostDash, PropagatorArrow->Forward},
269  U[3] == { ClassName->ghWm, SelfConjugate->False, Ghost->Wbar, QuantumNumbers->{GhostNumber->1, Q->-1},
270            Mass->{MW,Internal}, Width->WW, ParticleName->"ghWm", PropagatorLabel->"uWm", PropagatorType->GhostDash, PropagatorArrow->Forward}
271};
272
273
274(* ************************** *)
275(* *****   Parameters   ***** *)
276(* ************************** *)
277M$Parameters = {
278(* Mixing: external parameters *)
279  RMNS== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->UPMNS,
280           Description->"Neutrino PMNS mixing matrix (real part)"},
281  IMNS== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMUPMNS,
282           Description->"Neutrino PMNS mixing matrix (imaginary part)"},
283  RCKM== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->VCKM,
284           Description->"CKM mixing matrix (real part)"},
285  ICKM== { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMVCKM,
286           Description->"CKM mixing matrix (imaginary part)"},
287  RNN == { ParameterType->External, ComplexParameter->False, Indices->{Index[NEU],Index[NEU]}, BlockName->NMNMIX,
288           Description->"Neutralino mixing matrix (real part)"},
289  INN == { ParameterType->External, ComplexParameter->False, Indices->{Index[NEU],Index[NEU]}, BlockName->IMNMNMIX,
290           Description->"Neutralino mixing matrix (imaginary part)"},
291  RUU == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->UMIX,
292           Description->"Chargino mixing matrix U (real part)"},
293  IUU == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->IMUMIX,
294           Description->"Chargino mixing matrix U (imaginary part)"},
295  RVV == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->VMIX,
296           Description->"Chargino mixing matrix V (real part)"},
297  IVV == { ParameterType->External, ComplexParameter->False, Indices->{Index[CHA],Index[CHA]}, BlockName->IMVMIX,
298           Description->"Chargino mixing matrix V (imaginary part)"},
299  RRn == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->SNUMIX,
300           Description->"Sneutrino mixing matrix (real part)"},
301  IRn == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMSNUMIX,
302           Description->"Sneutrino mixing matrix (imaginary part)"},
303  RRl == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->SELMIX,
304           Description->"Slepton mixing matrix (real part)"},
305  IRl == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMSELMIX,
306           Description->"Slepton mixing matrix (imaginary part)"},
307  RRu == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->USQMIX,
308           Description->"Up squark mixing matrix (real part)"},
309  IRu == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMUSQMIX,
310           Description->"Up squark mixing matrix (imaginary part)"},
311  RRd == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->DSQMIX,
312           Description->"Down squark mixing matrix (real part)"},
313  IRd == { ParameterType->External, ComplexParameter->False, Indices->{Index[SCA],Index[SCA]}, BlockName->IMDSQMIX,
314           Description->"Down squark mixing matrix (imaginary part)"},
315
316(* Mixing: internal parameters *)
317  cw  == { TeX->Subscript[c,w],        ParameterType->Internal, ComplexParameter->False, Value->MW/MZ,        Description->"Cosine of the weak angle"}, 
318  sw  == { TeX->Subscript[s,w],        ParameterType->Internal, ComplexParameter->False, Value->Sqrt[1-cw^2], Description->"Sine of the weak angle"},
319  PMNS== { TeX->Superscript[U,pmns], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
320           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]}],
321           Description-> "Neutrino PMNS mixing matrix"},
322  CKM == { TeX->Superscript[V,ckm], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
323           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]}],
324           Description-> "CKM mixing matrix"},
325  NN  == { TeX->N, ParameterType-> Internal, ComplexParameter->True, Indices->{Index[NEU],Index[NEU]}, Unitary->True,
326           Value->{NN[i_,j_]:>RNN[i,j]+I*INN[i,j]}, Description-> "Neutralino mixing matrix"},
327  UU  == { TeX->U, ParameterType-> Internal, ComplexParameter->True, Indices->{Index[CHA],Index[CHA]}, Unitary->True,
328           Value->{UU[i_,j_]:>RUU[i,j]+I*IUU[i,j]}, Description-> "Chargino mixing matrix U"},
329  VV  == { TeX->V, ParameterType-> Internal, ComplexParameter->True, Indices->{Index[CHA],Index[CHA]}, Unitary->True,
330           Value->{VV[i_,j_]:>RVV[i,j]+I*IVV[i,j]}, Description-> "Chargino mixing matrix V"},
331  Rl  == { TeX->Superscript[R,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
332           Value->{Rl[i_,j_]:>RRl[i,j]+I*IRl[i,j]}, Description-> "Slepton mixing matrix"},
333  Rn  == { TeX->Superscript[R,n], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, Unitary->True,
334           Value->{Rn[i_,j_]:>RRn[i,j]+I*IRn[i,j]}, Description-> "Sneutrino mixing matrix"},
335  Ru  == { TeX->Superscript[R,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
336           Value->{Ru[i_,j_]:>RRu[i,j]+I*IRu[i,j]}, Description-> "Up squark mixing matrix"},
337  Rd  == { TeX->Superscript[R,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[SCA]}, Unitary->True,
338           Value->{Rd[i_,j_]:>RRd[i,j]+I*IRd[i,j]}, Description-> "Down squark mixing matrix"},
339
340(* Left and right parts of the sfermion mixing matrices *)
341  RlL == { TeX->Superscript[RL,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
342            Definitions->{RlL[i_,j_]:>Rl[i,j]/;NumericQ[j]},  Description-> "Slepton mixing matrix - first three columns"},
343  RlR == { TeX->Superscript[RR,l], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
344            Definitions->{RlR[i_,j_]:>Rl[i,j+3]/;NumericQ[j]},Description-> "Slepton mixing matrix - last three columns"},
345  RuL == { TeX->Superscript[RL,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
346            Definitions->{RuL[i_,j_]:>Ru[i,j]/;NumericQ[j]},  Description-> "Up squark mixing matrix - first three columns"},
347  RuR == { TeX->Superscript[RR,u], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
348            Definitions->{RuR[i_,j_]:>Ru[i,j+3]/;NumericQ[j]},Description-> "Up squark mixing matrix - last three columns"},
349  RdL == { TeX->Superscript[RL,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
350            Definitions->{RdL[i_,j_]:>Rd[i,j]/;NumericQ[j]},  Description-> "Down squark mixing matrix - first three columns"},
351  RdR == { TeX->Superscript[RR,d], ParameterType-> Internal, ComplexParameter->True, Indices->{Index[SCA],Index[GEN]}, Unitary->False,
352            Definitions->{RdR[i_,j_]:>Rd[i,j+3]/;NumericQ[j]},Description-> "Down squark mixing matrix - last three columns"},
353
354(* Couplings constants: external parameters *)
355  aEWM1 == { TeX->Subsuperscript[\[Alpha],w,-1], ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->1, InteractionOrder->{QED,-2},
356             Description->"Inverse of the EW coupling constant at the Z pole"},
357  aS    == { TeX->Subscript[\[Alpha],s],         ParameterType->External, ComplexParameter->False, BlockName->SMINPUTS, OrderBlock->3, InteractionOrder->{QCD, 2},
358             Description->"Strong coupling constant at the Z pole."},
359
360(* Couplings constants: internal parameters *)
361  ee == { TeX->e,              ParameterType->Internal, ComplexParameter->False, Value->Sqrt[4 Pi / aEWM1], InteractionOrder->{QED,1},
362          Description->"Electric coupling constant"},
363  gs == { TeX->Subscript[g,s], ParameterType->Internal, ComplexParameter->False, Value->Sqrt[4 Pi aS],      InteractionOrder->{QCD,1}, ParameterName->G,
364          Description->"Strong coupling constant"},
365  gp == { TeX->g',             ParameterType->Internal, ComplexParameter->False, Definitions-> {gp->ee/cw}, InteractionOrder->{QED,1},
366          Description->"Hypercharge coupling constant at the Z pole"},
367  gw == { TeX->Subscript[g,w], ParameterType->Internal, ComplexParameter->False, Definitions-> {gw->ee/sw}, InteractionOrder->{QED,1},
368          Description->"Weak coupling constant at the Z pole"},
369
370(* Higgs sector: external parameters *)
371  tb == { TeX->Subscript[t,b], ParameterType->External, ComplexParameter->False, BlockName->HMIX, OrderBlock->2, Description->"Ratio of the two Higgs vevs"},
372
373(* Higgs sector: internal parameters *)
374  beta == { TeX->\[Beta], ParameterType->Internal, ComplexParameter->False, Value->ArcTan[tb], Description->"Arctan of the ratio of the two Higgs vevs"},
375  vev  == { TeX->v,              ParameterType->Internal, ComplexParameter->False, Value->2*MZ*sw*cw/ee, InteractionOrder->{QED,-1},
376            Description->"Higgs vacuum expectation value"},
377  vd   == { TeX->Subscript[v,d], ParameterType->Internal, ComplexParameter->False, Value->vev*Cos[beta],    InteractionOrder->{QED,-1},
378            Description->"Down-type Higgs vacuum expectation value"},
379  vu   == { TeX->Subscript[v,u], ParameterType->Internal, ComplexParameter->False, Value->vev*Sin[beta],    InteractionOrder->{QED,-1},
380            Description->"Up-type Higgs vacuum expectation value"},
381
382(* Superpotential: external parameters *)
383  Ryu  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YU,
384            Description->"Up-type quark Yukawa matrix (real part)"},
385  Iyu  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYU,
386            Description->"Up-type quark Yukawa matrix (imaginary part)"},
387  Ryd  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YD,
388            Description->"Down-type quark Yukawa matrix (real part)"},
389  Iyd  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYD,
390            Description->"Down-type quark Yukawa matrix (imaginary part)"},
391  Rye  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->YE,
392            Description->"Charged lepton Yukawa matrix (real part)"},
393  Iye  == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMYE,
394            Description->"Charged lepton Yukawa matrix (imaginary part)"},
395
396(* Superpotential: internal parameters *)
397  yu  == { TeX->Superscript[y,u], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
398           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"},
399  yd  == { TeX->Superscript[y,d], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
400           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"},
401  ye  == { TeX->Superscript[y,e], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
402           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"},
403
404(* Soft terms: external parameters *)
405  RMx1 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT,   OrderBlock->1, Description->"Bino mass (real part)"},
406  IMx1 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->1, Description->"Bino mass (imaginary part)"},
407  RMx2 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT,   OrderBlock->2, Description->"Wino mass (real part)"},
408  IMx2 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->2, Description->"Wino mass (imaginary part)"},
409  RMx3 == { ParameterType->External, ComplexParameter->False, BlockName->MSOFT,   OrderBlock->3, Description->"Gluino mass (real part)"},
410  IMx3 == { ParameterType->External, ComplexParameter->False, BlockName->IMMSOFT, OrderBlock->3, Description->"Gluino mass (imaginary part)"},
411  mHu2 == { TeX->Subsuperscript[m,Subscript[H,u],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->22,
412            Description->"Up-type Higgs squared mass"},
413  mHd2 == { TeX->Subsuperscript[m,Subscript[H,d],2], ParameterType->External, ComplexParameter->False, BlockName->MSOFT, OrderBlock->21,
414            Description->"Down-type Higgs squared mass"},
415  MA2  == { TeX->Subsuperscript[m,A,2], ParameterType->External, ComplexParameter->False, BlockName->HMIX, OrderBlock->4,
416            Description->"Pseudoscalar Higgs squared mass"},
417  RmL2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSL2,
418            Description->"Left-handed slepton squared mass matrix (real part)"},
419  ImL2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSL2,
420            Description->"Left-handed slepton squared mass matrix (imaginary part)"},
421  RmE2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSE2,
422            Description->"Right-handed slepton squared mass matrix (real part)"},
423  ImE2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSE2,
424            Description->"Right-handed slepton squared mass matrix (imaginary part)"},
425  RmQ2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSQ2,
426            Description->"Left-handed squark squared mass matrix (real part)"},
427  ImQ2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSQ2,
428            Description->"Left-handed squark squared mass matrix (imaginary part)"},
429  RmU2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSU2,
430            Description->"Right-handed up-type squark squared mass matrix (real part)"},
431  ImU2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSU2,
432            Description->"Right-handed up-type squark squared mass matrix (imaginary part)"},
433  RmD2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->MSD2,
434            Description->"Right-handed down-type squark squared mass matrix (real part)"},
435  ImD2 == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMMSD2,
436            Description->"Right-handed down-type squark squared mass matrix (imaginary part)"},
437  Rte == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->TE,
438            Description->"Charged slepton trilinear coupling (real part)"},
439  Ite == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMTE,
440            Description->"Charged slepton trilinear coupling (imaginary part)"},
441  Rtu == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->TU,
442            Description->"Up-type squark trilinear coupling (real part)"},
443  Itu == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMTU,
444            Description->"Up-type squark trilinear coupling (imaginary part)"},
445  Rtd == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->TD,
446            Description->"Down-type squark trilinear coupling (real part)"},
447  Itd == { ParameterType->External, ComplexParameter->False, Indices->{Index[GEN],Index[GEN]}, BlockName->IMTD,
448            Description->"Down-type squark trilinear coupling (imaginary part)"},
449
450(* Soft terms: internal parameters *)
451  Mx1 == { TeX->Subscript[M,1], ParameterType->Internal, ComplexParameter->True, Value->RMx1+I*IMx1, Description->"Bino mass"},
452  Mx2 == { TeX->Subscript[M,2], ParameterType->Internal, ComplexParameter->True, Value->RMx2+I*IMx2, Description->"Wino mass"},
453  Mx3 == { TeX->Subscript[M,3], ParameterType->Internal, ComplexParameter->True, Value->RMx3+I*IMx3, Description->"Gluino mass"},
454  mL2 == { TeX->Subsuperscript[m,OverTilde[L],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
455           Value->{mL2[i_,j_]:>RmL2[i,j]+I*ImL2[i,j]}, Description-> "Left-handed slepton squared mass matrix"},
456  mE2 == { TeX->Subsuperscript[m,OverTilde[E],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
457           Value->{mE2[i_,j_]:>RmE2[i,j]+I*ImE2[i,j]}, Description-> "Right-handed slepton squared mass matrix"},
458  mQ2 == { TeX->Subsuperscript[m,OverTilde[Q],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
459           Value->{mQ2[i_,j_]:>RmQ2[i,j]+I*ImQ2[i,j]}, Description-> "Left-handed squark squared mass matrix"},
460  mU2 == { TeX->Subsuperscript[m,OverTilde[U],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
461           Value->{mU2[i_,j_]:>RmU2[i,j]+I*ImU2[i,j]}, Description-> "Right-handed up-type squark squared mass matrix"},
462  mD2 == { TeX->Subsuperscript[m,OverTilde[D],2], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]},
463           Value->{mD2[i_,j_]:>RmD2[i,j]+I*ImD2[i,j]}, Description-> "Right-handed down-type squark squared mass matrix"},
464  te  == { TeX->Subscript[T,e], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, InteractionOrder->{QED,1},
465           Value->{te[i_,j_]:>Rte[i,j]+I*Ite[i,j]}, Description-> "Charged slepton trilinear coupling"},
466  tu  == { TeX->Subscript[T,u], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, InteractionOrder->{QED,1},
467           Value->{tu[i_,j_]:>Rtu[i,j]+I*Itu[i,j]}, Description-> "Up-type squark trilinear coupling"},
468  td  == { TeX->Subscript[T,d], ParameterType->Internal, ComplexParameter->True, Indices->{Index[GEN],Index[GEN]}, InteractionOrder->{QED,1},
469           Value->{td[i_,j_]:>Rtd[i,j]+I*Itd[i,j]}, Description-> "Down-type squark trilinear coupling"},
470
471(* NMSSM external parameters *)
472  NMl == { TeX->\[Lambda], ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->1, InteractionOrder->{QED,1},
473           Description->"Superpotential trilinear Higgs-singlet coupling"},
474  NMk == { TeX->\[Kappa],  ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->2, InteractionOrder->{QED,1},
475           Description->"Superpotential cubic singlet self-interaction"},
476  NMAl== { TeX->Subscript[A,\[Lambda]], ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->3,
477           Description->"Soft trilinear Higgs-singlet coupling"},
478  NMAk== { TeX->Subscript[A,\[Kappa]],  ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->4,
479           Description->"Soft cubic singlet self-interaction"},
480  mueff=={ TeX->Subscript[\[Mu],eff], ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->5,
481           Description->"Effective mu-parameter (vev of the singlet times NMl)"},
482  NMxF== { TeX->Subscript[\[Xi],F],  ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->6,
483           Description->"Superpotential linear singlet term"},
484  NMxS== { TeX->Subscript[\[Xi],S],  ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->7,
485           Description->"Soft linear singlet term"},
486  NMmu== { TeX->\[Mu]', ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->8,
487           Description->"Superpotential quadratic singlet term"},
488  MSP2== { TeX->Subsuperscript[M',S,2], ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->9,
489           Description->"Soft quadratic singlet term"},
490  MS2 == { TeX->Subsuperscript[M,S,2], ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->10,
491           Description->"Soft singlet mass term"},
492  bb  == { TeX->b, ParameterType->External, ComplexParameter->False, BlockName->NMSSMRUN, OrderBlock->12, Description->"Higgs bilinear soft term"},
493  US == { TeX->Superscript[U,S], ParameterType->External, ComplexParameter->False, Indices->{Index[SHig],Index[SHig]}, BlockName->NMHMIX,
494            Description->"Scalar Higgses mixing matrix"},
495  UP == { TeX->Superscript[U,P], ParameterType->External, ComplexParameter->False, Indices->{Index[PHig],Index[SHig]}, BlockName->NMAMIX,
496            Description->"Pseudoscalar Higgses mixing matrix"},
497
498(* NMSSM internal parameters *)
499  vs == { TeX->Subscript[v,s], ParameterType->Internal, ComplexParameter->False, Value->Sqrt[2] mueff/NMl, InteractionOrder ->{QED,-1}, Description->"Vev of the scalar singlet"},
500
501(* NMSSM Golstone mixing parameters *)
502  UP31=={ TeX->Subsuperscript[U,P,31], ParameterType->External, ComplexParameter->False, BlockName->FRUP, OrderBlock->1, Value->0,
503          Description->"Goldstone element of the Higgs mixing matrix"},
504  UP32=={ TeX->Subsuperscript[U,P,32], ParameterType->External, ComplexParameter->False, BlockName->FRUP, OrderBlock->2, Value->0,
505          Description->"Goldstone element of the Higgs mixing matrix"},
506  UP33=={ TeX->Subsuperscript[U,P,33], ParameterType->External, ComplexParameter->False, BlockName->FRUP, OrderBlock->3, Value->0,
507          Description->"Goldstone element of the Higgs mixing matrix"}
508};
509
510(* ************************** *)
511(* ****  Diracification  **** *)
512(* ************************** *)
513ToDirac[exp_]:= Module[{tmp=Expand[exp],cnt=0,prg1=0,prg2=0,prgo1=0,prgo2=0,tot},
514  Colourb=Colour;
515
516  tmp = If[Head[tmp]===Plus,List@@tmp,List[tmp]]/.Tb[a_,i_,j_]->-T[a,j,i];
517
518  tmp = OptimizeIndex[#] &/@ tmp;
519  tot=Length[tmp];
520  Print["Flavor expansion: ", ProgressIndicator[Dynamic[prg1]]];
521  tmp = Module[{}, cnt++; prg1=cnt/tot;
522     Expand[(ExpandIndices[#, FlavorExpand->{SU2W, SU2D}] /. {
523         gp->ee/cw,
524         gw->ee/sw,
525         cw^n_?(Mod[#,2]===0&)->(1 - sw^2)^(n/2),
526         cw^n_?(Mod[#, 2]===1 &)->(1 - sw^2)^((n - 1)/2) cw,
527         Power[PauliSigma[a_,i_?(NumericQ[#] &),j_?(NumericQ[#] &)],2]->PauliSigma[1,i,j]^2 + PauliSigma[3,i,j]^2 + PauliSigma[2,i,j]^2,
528         PauliSigma[a_,i_?(NumericQ[#] &),j_?(NumericQ[#] &)] PauliSigma[a_,k_?(NumericQ[#] &),l_?(NumericQ[#] &)]->
529           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;
530   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};
531   cnt=0; tot=Length[tmp];
532   Print["Opt 1: ",ProgressIndicator[Dynamic[prgo1]]];
533   tmp = Module[{}, cnt++; prgo1=cnt/tot;OptimizeIndex[#]] &/@ (List@@tmp);
534   Print["Weyl2Dirac: ",ProgressIndicator[Dynamic[prg2]]];cnt=0;
535   tmp = Module[{}, cnt++; prg2=cnt/tot; WeylToDirac[#]] &/@ tmp;
536   Print["Opt2: ",ProgressIndicator[Dynamic[prgo2]]];cnt=0;
537   tmp = Module[{}, cnt++; prgo2=cnt/tot;OptimizeIndex[#]] &/@ tmp;
538   Clear[Colourb];
539Expand[Plus@@tmp]];
540
541(* ************************** *)
542(* *****   Lagrangian   ***** *)
543(* ************************** *)
544(* LVector *)
545LVector := Module[{}, Plus@@(Module[{tmp}, tmp = SF2Components[#]; Expand[tmp[[2, 5]] + tmp[[2, 6]]]] &/@ (List @@ VSFKineticTerms[]))];
546
547(* LChiral *)
548LChiral :=  Plus@@( Theta2Thetabar2Component[#] &/@ (List @@ CSFKineticTerms[]) );
549
550(* Superpotential *)
551SPot:= Module[{ff1,ff2,ff3,cc1},
552     yu[ff1,ff2] UR[ff1,cc1] (QL[1,ff2,cc1] HU[2] - QL[2,ff2,cc1] HU[1]) -
553     yd[ff1,ff3] Conjugate[CKM[ff2,ff3]] DR[ff1,cc1] (QL[1,ff2,cc1] HD[2] - QL[2,ff2,cc1] HD[1]) -
554     ye[ff1,ff2] ER[ff1]     (LL[1,ff2]     HD[2] - LL[2,ff2]     HD[1]) +
555     NMl SPF (HU[1] HD[2] - HU[2] HD[1]) + 1/3 NMk*SPF^3 + NMmu SPF^2 + NMxF SPF];
556LSuperW:= ( 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];
557
558(* Soft SUSY-breaking Lagrangian *)
559LSoft := Module[{Mino, MSca, Tri, Bil},
560  (* Gaugino mass terms *)
561    Mino:=Module[{s,gl}, - Mx1*bow[s].bow[s] -  Mx2*wow[s,gl].wow[s,gl] - Mx3*gow[s,gl].gow[s,gl]];
562  (* Scalar mass terms *)
563    MSca:=Module[{ii,ff1,ff2,ff3,ff4,cc1},
564      - mHu2*HC[hus[ii]]*hus[ii] - mHd2*HC[hds[ii]]*hds[ii] - MS2*SPsbar*SPs - 
565        mL2[ff1,ff2]*HC[LLs[ii,ff1]]*LLs[ii,ff2] - mE2[ff1,ff2]*HC[ERs[ff1]]*ERs[ff2] -
566        CKM[ff1,ff2]*mQ2[ff2,ff3]*Conjugate[CKM[ff4,ff3]]*HC[QLs[ii,ff1,cc1]]*QLs[ii,ff4,cc1] -
567        mU2[ff1,ff2]*HC[URs[ff1,cc1]]*URs[ff2,cc1] -  mD2[ff1,ff2]*HC[DRs[ff1,cc1]]*DRs[ff2,cc1] ];
568  (* Trilinear couplings *)
569    Tri:=-tu[ff1,ff2]*URs[ff1,cc1] (QLs[1,ff2,cc1] hus[2] - QLs[2,ff2,cc1] hus[1]) +
570          Conjugate[CKM[ff3,ff2]]*td[ff1,ff2]*DRs[ff1,cc1] (QLs[1,ff3,cc1] hds[2] - QLs[2,ff3,cc1] hds[1]) +
571          te[ff1,ff2]*ERs[ff1] (LLs[1,ff2] hds[2] - LLs[2,ff2] hds[1]) -
572          NMl*NMAl*SPs (hus[1] hds[2] - hus[2] hds[1]) -
573          1/3 NMk*NMAk*SPs^3;
574  (* Linear and bilinear couplings *)
575    Bil:=-bb*(hus[1] hds[2] - hus[2] hds[1]) - MSP2*SPs^2 - NMxS*SPs;
576  (* Everything together *)
577  (Mino+HC[Mino])/2 + MSca + Tri + HC[Tri] + Bil + HC[Bil]];
578
579(* Ghost Lagrangian and gauge fixing terms *)
580LFeynmanGFix := Module[{VectorU,VectorD, Phiu,Phid,Phiu0,Phid0, phid1,phid2,phiu1,phiu2, GF1,GF2,GF3,LGF, nrules, kk,ll,mm, LGh1,LGh2,LGh3,LGhS,LGh, genu,gend, gh,ghbar},
581  (* Expression the doublets in the nu/nd basis *)
582  VectorU[{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}];
583  VectorD[{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}];
584
585  (* Higgs doublets *)
586  Phiu = Expand[ {(phiu1 + I phiu2)/Sqrt[2], (Conjugate[US[mm,2]]*h0[mm] + I*Conjugate[UP[mm,2]]*A0[mm] + I*Conjugate[UP32]*G0)/Sqrt[2]} ];
587  Phid = Expand[ {(Conjugate[US[mm,1]]*h0[mm] + I*Conjugate[UP[mm,1]]*A0[mm] + I*Conjugate[UP31]*G0)/Sqrt[2], (phid1 + I phid2)/Sqrt[2]} ];
588  (* vevs *)
589  Phiu0 = {0, vu/Sqrt[2]};
590  Phid0 = {vd/Sqrt[2], 0};
591  (* Back to the physical Higgses and Goldstones *)
592  nrules := {
593     phid1 -> (-Cos[beta]*GPbar - Cos[beta]*GP + Sin[beta]*Hbar + Sin[beta]*H)/Sqrt[2],
594     phid2 -> (-Cos[beta]*GPbar + Cos[beta]*GP + Sin[beta]*Hbar - Sin[beta]*H)/(I Sqrt[2]),
595     phiu1 -> ( Sin[beta]*GP + Sin[beta]*GPbar + Cos[beta]*H + Cos[beta]*Hbar)/Sqrt[2],
596     phiu2 -> (Sin[beta]*GP - Sin[beta]*GPbar + Cos[beta]*H - Cos[beta]*Hbar)/(I Sqrt[2])};
597
598  (* Gauge-fixing functions *)
599  GF1     := Module[{mu}, del[B[mu]   , mu] - gp VectorU[-I/2 Phiu0].VectorU[Phiu] - gp VectorD[I/2 Phid0].VectorD[Phid] ];
600  GF2[k_] := Module[{mu}, del[Wi[mu,k], mu] - gw VectorU[-I/2 PauliSigma[k].Phiu0].VectorU[Phiu] - gw VectorD[-I/2 PauliSigma[k].Phid0].VectorD[Phid] ];
601  GF3[a_] := Module[{mu}, del[G[mu,a] , mu] ];
602  (* Gauge-fixing Lagrangian *)
603  LGF = Expand[-1/2*(GF1 HC[GF1] + Sum[GF2[kk] HC[GF2[kk]], {kk, 1, 3}])/.nrules /. {HC[a_]->a, h0[_]->0, A0[_]->0, H->0, Hbar->0}];
604  LGF = OptimizeIndex[Expand[ExpandIndices[LGF, FlavorExpand->SU2W]]];
605
606  (* Ghost Lagrangians *)
607  LGh1 = -ghBbar.del[DC[ghB,mu],mu];
608  LGh2 = -ghWibar[kk].del[DC[ghWi[kk], mu], mu];
609  LGh3 = -ghGbar[kk].del[DC[ghG[kk],mu],mu];
610  genu := {-I/2 gp IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
611  gend := { I/2 gp IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
612  gh    = {ghB,    ghWi[1],    ghWi[2],    ghWi[3]};
613  ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
614  LGhS = Sum[
615    -ghbar[[kk]].gh[[ll]] (VectorU[genu[[kk]].Phiu0].VectorU[genu[[ll]].(Phiu+Phiu0)] + VectorD[gend[[kk]].Phid0].VectorD[gend[[ll]].(Phid+Phid0)]),
616    {kk,1,4},{ll,1,4}];
617  LGh = ExpandIndices[LGh1+LGh2+LGh3+LGhS, FlavorExpand->SU2W] /.nrules;
618LGF+LGh];
619
620(* Collecting all the pieces together *)
621Lag := ToDirac[SolveEqMotionF[SolveEqMotionD[LVector+LChiral+LSuperW+LSoft]]] + LFeynmanGFix ;