StandardModel: SM_old.fr

File SM_old.fr, 22.8 KB (added by BenjF, 5 years ago)

Older implementation of the SM

Line 
1(***************************************************************************************************************)
2(******                       This is the FeynRules mod-file for the Standard model                       ******)
3(******                                                                                                   ******)
4(******     Authors: N. Christensen, C. Duhr                                                              ******)
5(******                                                                                                   ******)
6(****** Choose whether Feynman gauge is desired.                                                          ******)
7(****** If set to False, unitary gauge is assumed.                                                          ****)
8(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
9(****** Feynman gauge is not supported in MadGraph and Sherpa.                                              ****)
10(***************************************************************************************************************)
11
12M$ModelName = "Standard Model";
13
14
15M$Information = {Authors -> {"N. Christensen", "C. Duhr"},
16             Version -> "1.3",
17             Date -> "02. 06. 2009",
18             Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)"},
19             Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be"},
20             URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"};
21
22(*
23  V1.3 - Updated Top quark mass to 2010 PDG value (172 GeV)
24  V1.2 - Set FeynmanGauge=True as default. 
25         Set Gluonic ghosts to be included in both gauges.
26  V1.1 - Fixed yukawa couplings in Feynman gauge.
27        Changed yd[n] CKM[n,m] to yd[m] CKM[n,m].
28        Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]].
29  V1.3 - Added yukawa couplings for all fermions for gauge invariance.
30         Added yukawa couplings for 1st generation fermions to Massless.rst.
31         Updated parameters to PDG 2010.
32*)
33
34FeynmanGauge = True;
35
36
37(******* Index definitions ********)
38
39IndexRange[ Index[Generation] ] = Range[3]
40
41IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
42
43IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
44
45IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
46
47
48IndexStyle[Colour, i]
49
50IndexStyle[Generation, f]
51
52IndexStyle[Gluon ,a]
53
54IndexStyle[SU2W ,k]
55
56
57(******* Gauge parameters (for FeynArts) ********)
58
59GaugeXi[ V[1] ] = GaugeXi[A];
60GaugeXi[ V[2] ] = GaugeXi[Z];
61GaugeXi[ V[3] ] = GaugeXi[W];
62GaugeXi[ V[4] ] = GaugeXi[G];
63GaugeXi[ S[1] ] = 1;
64GaugeXi[ S[2] ] = GaugeXi[Z];
65GaugeXi[ S[3] ] = GaugeXi[W];
66GaugeXi[ U[1] ] = GaugeXi[A];
67GaugeXi[ U[2] ] = GaugeXi[Z];
68GaugeXi[ U[31] ] = GaugeXi[W];
69GaugeXi[ U[32] ] = GaugeXi[W];
70GaugeXi[ U[4] ] = GaugeXi[G];
71
72(***** Setting for interaction order (as e.g. used by MadGraph 5)  ******)
73
74M$InteractionOrderHierarchy = {
75     {QCD, 1},
76     {QED, 2}
77    };
78
79
80(****************  Parameters *************)
81
82M$Parameters = {
83
84  (* External parameters *)
85
86  \[Alpha]EWM1== {
87        ParameterType -> External,
88        BlockName -> SMINPUTS,
89        ParameterName -> aEWM1,
90        InteractionOrder -> {QED, -2},
91        Value -> 127.9,
92        Description -> "Inverse of the electroweak coupling constant"},
93
94  Gf == {
95        ParameterType -> External,
96        BlockName -> SMINPUTS,
97        TeX -> Subscript[G, f],
98        InteractionOrder -> {QED, 2},
99        Value -> 1.16637 * 10^(-5),
100        Description -> "Fermi constant"},
101
102  \[Alpha]S == {
103        ParameterType -> External,
104        BlockName -> SMINPUTS,
105        TeX -> Subscript[\[Alpha], s],
106        ParameterName -> aS,
107        InteractionOrder -> {QCD, 2},
108        Value -> 0.1184,
109        Description -> "Strong coupling constant at the Z pole."},
110
111  ymdo == {
112        ParameterType -> External,
113        BlockName -> YUKAWA,
114        Value -> 5.04*10^(-3),
115        OrderBlock -> {1},
116        Description -> "Down Yukawa mass"},
117
118
119  ymup == {
120        ParameterType -> External,
121        BlockName -> YUKAWA,
122        Value -> 2.55*10^(-3),
123        OrderBlock -> {2},
124        Description -> "Up Yukawa mass"},
125
126  yms == {
127        ParameterType -> External,
128        BlockName -> YUKAWA,
129        Value -> 0.101,
130        OrderBlock -> {3},
131        Description -> "Strange Yukawa mass"},
132
133
134  ymc == {
135        ParameterType -> External,
136        BlockName -> YUKAWA,
137        Value -> 1.27,
138        OrderBlock -> {4},
139        Description -> "Charm Yukawa mass"},
140
141 ymb == {
142        ParameterType -> External,
143        BlockName -> YUKAWA,
144        Value -> 4.7,
145        OrderBlock -> {5},
146        Description -> "Bottom Yukawa mass"},
147
148  ymt == {
149        ParameterType -> External,
150        BlockName -> YUKAWA,
151        Value -> 172.0,
152        OrderBlock -> {6},
153        Description -> "Top Yukawa mass"},
154
155  yme == {
156        ParameterType -> External,
157        BlockName -> YUKAWA,
158        Value ->  5.11*10^(-4),
159        OrderBlock -> {11},
160        Description -> "Electron Yukawa mass"},
161
162  ymm == {
163        ParameterType -> External,
164        BlockName -> YUKAWA,
165        Value -> 0.10566,
166        OrderBlock -> {13},
167        Description -> "Muon Yukawa mass"},
168
169  ymtau == {
170        ParameterType -> External,
171        BlockName -> YUKAWA,
172        Value -> 1.777,
173        OrderBlock -> {15},
174        Description -> "Tau Yukawa mass"},
175
176   cabi == {
177        TeX -> Subscript[\[Theta], c],
178        ParameterType -> External,
179        BlockName -> CKMBLOCK,
180        Value -> 0.227736,
181        Description -> "Cabibbo angle"},
182
183
184   (* Internal Parameters *)
185
186  \[Alpha]EW == {
187        ParameterType -> Internal,
188        Value -> 1/\[Alpha]EWM1,
189        TeX -> Subscript[\[Alpha], EW],
190        ParameterName -> aEW,
191        InteractionOrder -> {QED, 2},
192        Description -> "Electroweak coupling contant"},
193
194
195  MW == {
196        ParameterType -> Internal,
197        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
198        TeX  -> Subscript[M, W],
199        Description -> "W mass"},
200
201  sw2 == {
202        ParameterType -> Internal,
203        Value -> 1-(MW/MZ)^2,
204        Description -> "Squared Sin of the Weinberg angle"},
205
206   ee == {
207        TeX -> e,
208        ParameterType -> Internal,
209        Value -> Sqrt[4 Pi \[Alpha]EW],
210        InteractionOrder -> {QED, 1},
211        Description -> "Electric coupling constant"},
212
213   cw == {
214        TeX -> Subscript[c, w],
215        ParameterType -> Internal,
216        Value -> Sqrt[1 - sw2],
217        Description -> "Cos of the Weinberg angle"}, 
218
219   sw == {
220        TeX -> Subscript[s, w],
221        ParameterType -> Internal,
222        Value -> Sqrt[sw2],
223        Description -> "Sin of the Weinberg angle"}, 
224
225   gw == {
226        TeX -> Subscript[g, w],
227        ParameterType -> Internal,
228        Value -> ee / sw,
229        InteractionOrder -> {QED, 1},
230        Description -> "Weak coupling constant"},
231
232   g1 == {
233        TeX -> Subscript[g, 1],
234        ParameterType -> Internal,
235        Value -> ee / cw,
236        InteractionOrder -> {QED, 1},
237        Description -> "U(1)Y coupling constant"},
238
239   gs == {
240        TeX -> Subscript[g, s],
241        ParameterType -> Internal,
242        Value -> Sqrt[4 Pi \[Alpha]S],
243        InteractionOrder -> {QCD, 1},
244        ParameterName -> G,
245        Description -> "Strong coupling constant"},
246
247
248   v == {
249        ParameterType -> Internal,
250        Value -> 2*MW*sw/ee,
251        InteractionOrder -> {QED, -1},
252        Description -> "Higgs VEV"},
253
254   \[Lambda] == {
255        ParameterType -> Internal,
256        Value -> MH^2/(2*v^2),
257        InteractionOrder -> {QED, 2},
258        ParameterName -> lam,
259        Description -> "Higgs quartic coupling"},
260
261   muH == {
262        ParameterType -> Internal,
263        Value -> Sqrt[v^2 \[Lambda]],
264        TeX -> \[Mu],
265        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
266
267
268   yl == {
269        TeX -> Superscript[y, l],
270        Indices -> {Index[Generation]},
271        AllowSummation -> True,
272        ParameterType -> Internal,
273        Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
274        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
275        InteractionOrder -> {QED, 1},
276        ComplexParameter -> False,
277        Description -> "Lepton Yukawa coupling"},
278
279   yu == {
280        TeX -> Superscript[y, u],
281        Indices -> {Index[Generation]},
282        AllowSummation -> True,
283        ParameterType -> Internal,
284        Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
285        ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
286        InteractionOrder -> {QED, 1},
287        ComplexParameter -> False,
288        Description -> "U-quark Yukawa coupling"},
289
290   yd == {
291        TeX -> Superscript[y, d],
292        Indices -> {Index[Generation]},
293        AllowSummation -> True,
294        ParameterType -> Internal,
295        Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
296        ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
297        InteractionOrder -> {QED, 1},
298        ComplexParameter -> False,
299        Description -> "D-quark Yukawa coupling"},
300
301(* N. B. : only Cabibbo mixing! *)
302  CKM == {
303       Indices -> {Index[Generation], Index[Generation]},
304       TensorClass -> CKM,
305       Unitary -> True,
306       Value -> {CKM[1,1] -> Cos[cabi],
307                 CKM[1,2] -> Sin[cabi],
308                 CKM[1,3] -> 0,
309                 CKM[2,1] -> -Sin[cabi],
310                 CKM[2,2] -> Cos[cabi],
311                 CKM[2,3] -> 0,
312                 CKM[3,1] -> 0,
313                 CKM[3,2] -> 0,
314                 CKM[3,3] -> 1},
315       Description -> "CKM-Matrix"}
316}
317
318
319(************** Gauge Groups ******************)
320
321M$GaugeGroups = {
322
323  U1Y == {
324        Abelian -> True,
325        GaugeBoson -> B,
326        Charge -> Y,
327        CouplingConstant -> g1},
328
329  SU2L == {
330        Abelian -> False,
331        GaugeBoson -> Wi,
332        StructureConstant -> Eps,
333        CouplingConstant -> gw},
334
335  SU3C == {
336        Abelian -> False,
337        GaugeBoson -> G,
338        StructureConstant -> f,
339        SymmetricTensor -> dSUN,
340        Representations -> {T, Colour},
341        CouplingConstant -> gs}
342}
343
344(********* Particle Classes **********)
345
346M$ClassesDescription = {
347
348(********** Fermions ************)
349        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
350  F[1] == {
351        ClassName -> vl,
352        ClassMembers -> {ve,vm,vt},
353        FlavorIndex -> Generation,
354        SelfConjugate -> False,
355        Indices -> {Index[Generation]},
356        Mass -> 0,
357        Width -> 0,
358        QuantumNumbers -> {LeptonNumber -> 1},
359        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
360        PropagatorType -> S,
361        PropagatorArrow -> Forward,
362        PDG -> {12,14,16},
363        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
364
365        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
366  F[2] == {
367        ClassName -> l,
368        ClassMembers -> {e, m, tt},
369        FlavorIndex -> Generation,
370        SelfConjugate -> False,
371        Indices -> {Index[Generation]},
372        Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
373        Width -> 0,
374        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
375        PropagatorLabel -> {"l", "e", "m", "tt"},
376        PropagatorType -> Straight,
377        ParticleName -> {"e-", "m-", "tt-"},
378        AntiParticleName -> {"e+", "m+", "tt+"},
379        PropagatorArrow -> Forward,
380        PDG -> {11, 13, 15},
381        FullName -> {"Electron", "Muon", "Tau"} },
382
383        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
384  F[3] == {
385        ClassMembers -> {u, c, t},
386        ClassName -> uq,
387        FlavorIndex -> Generation,
388        SelfConjugate -> False,
389        Indices -> {Index[Generation], Index[Colour]},
390        Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}},
391        Width -> {0, 0, {WT, 1.50833649}},
392        QuantumNumbers -> {Q -> 2/3},
393        PropagatorLabel -> {"uq", "u", "c", "t"},
394        PropagatorType -> Straight,
395        PropagatorArrow -> Forward,
396        PDG -> {2, 4, 6},
397        FullName -> {"u-quark", "c-quark", "t-quark"}},
398
399        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
400  F[4] == {
401        ClassMembers -> {d, s, b},
402        ClassName -> dq,
403        FlavorIndex -> Generation,
404        SelfConjugate -> False,
405        Indices -> {Index[Generation], Index[Colour]},
406        Mass -> {Md, {MD,  5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
407        Width -> 0,
408        QuantumNumbers -> {Q -> -1/3},
409        PropagatorLabel -> {"dq", "d", "s", "b"},
410        PropagatorType -> Straight,
411        PropagatorArrow -> Forward,
412        PDG -> {1,3,5},
413        FullName -> {"d-quark", "s-quark", "b-quark"} },
414
415(********** Ghosts **********)
416        U[1] == {
417       ClassName -> ghA,
418       SelfConjugate -> False,
419       Indices -> {},
420       Ghost -> A,
421       Mass -> 0,
422       Width -> 0,
423       QuantumNumbers -> {GhostNumber -> 1},
424       PropagatorLabel -> uA,
425       PropagatorType -> GhostDash,
426       PropagatorArrow -> Forward},
427
428        U[2] == {
429       ClassName -> ghZ,
430       SelfConjugate -> False,
431       Indices -> {},
432       Mass -> {MZ, 91.1876},
433       Width -> {WZ, Internal},
434       Ghost -> Z,
435       QuantumNumbers -> {GhostNumber -> 1},
436       PropagatorLabel -> uZ,
437       PropagatorType -> GhostDash,
438       PropagatorArrow -> Forward},
439
440        U[31] == {
441       ClassName -> ghWp,
442       SelfConjugate -> False,
443       Indices -> {},
444       Mass -> {MW, Internal},
445       Width -> {WW, Internal},
446       Ghost -> W,
447       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
448       PropagatorLabel -> uWp,
449       PropagatorType -> GhostDash,
450       PropagatorArrow -> Forward},
451
452   U[32] == {
453       ClassName -> ghWm,
454       SelfConjugate -> False,
455       Indices -> {},
456       Mass -> {MW, Internal},
457       Width -> {WW, Internal},
458       Ghost -> Wbar,
459       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
460       PropagatorLabel -> uWm,
461       PropagatorType -> GhostDash,
462       PropagatorArrow -> Forward},
463
464        U[4] == {
465       ClassName -> ghG,
466       SelfConjugate -> False,
467       Indices -> {Index[Gluon]},
468       Ghost -> G,
469       Mass -> 0,
470       QuantumNumbers -> {GhostNumber -> 1},
471       PropagatorLabel -> uG,
472       PropagatorType -> GhostDash,
473       PropagatorArrow -> Forward},
474
475        U[5] == {
476        ClassName -> ghWi,
477        Unphysical -> True,
478        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
479                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
480                        ghWi[3] -> cw ghZ + sw ghA},
481        SelfConjugate -> False,
482        Ghost -> Wi,
483        Indices -> {Index[SU2W]},
484        FlavorIndex -> SU2W},
485
486        U[6] == {
487        ClassName -> ghB,
488        SelfConjugate -> False,
489        Definitions -> {ghB -> -sw ghZ + cw ghA},
490        Indices -> {},
491        Ghost -> B,
492        Unphysical -> True},
493
494(************ Gauge Bosons ***************)
495        (* Gauge bosons: Q = 0 *)
496  V[1] == {
497        ClassName -> A,
498        SelfConjugate -> True,
499        Indices -> {},
500        Mass -> 0,
501        Width -> 0,
502        PropagatorLabel -> "a",
503        PropagatorType -> W,
504        PropagatorArrow -> None,
505        PDG -> 22,
506        FullName -> "Photon" },
507
508  V[2] == {
509        ClassName -> Z,
510        SelfConjugate -> True,
511        Indices -> {},
512        Mass -> {MZ, 91.1876},
513        Width -> {WZ, 2.4952},
514        PropagatorLabel -> "Z",
515        PropagatorType -> Sine,
516        PropagatorArrow -> None,
517        PDG -> 23,
518        FullName -> "Z" },
519
520        (* Gauge bosons: Q = -1 *)
521  V[3] == {
522        ClassName -> W,
523        SelfConjugate -> False,
524        Indices -> {},
525        Mass -> {MW, Internal},
526        Width -> {WW, 2.085},
527        QuantumNumbers -> {Q -> 1},
528        PropagatorLabel -> "W",
529        PropagatorType -> Sine,
530        PropagatorArrow -> Forward,
531        ParticleName ->"W+",
532        AntiParticleName ->"W-",
533        PDG -> 24,
534        FullName -> "W" },
535
536V[4] == {
537        ClassName -> G,
538        SelfConjugate -> True,
539        Indices -> {Index[Gluon]},
540        Mass -> 0,
541        Width -> 0,
542        PropagatorLabel -> G,
543        PropagatorType -> C,
544        PropagatorArrow -> None,
545        PDG -> 21,
546        FullName -> "G" },
547
548V[5] == {
549        ClassName -> Wi,
550        Unphysical -> True,
551        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
552                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
553                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
554        SelfConjugate -> True,
555        Indices -> {Index[SU2W]},
556        FlavorIndex -> SU2W,
557        Mass -> 0,
558        PDG -> {1,2,3}},
559
560V[6] == {
561        ClassName -> B,
562        SelfConjugate -> True,
563        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
564        Indices -> {},
565        Mass -> 0,
566        Unphysical -> True},
567
568
569(************ Scalar Fields **********)
570        (* physical Higgs: Q = 0 *)
571  S[1] == {
572        ClassName -> H,
573        SelfConjugate -> True,
574        Mass -> {MH, 120},
575        Width -> {WH, 0.00575308848},
576        PropagatorLabel -> "H",
577        PropagatorType -> D,
578        PropagatorArrow -> None,
579        PDG -> 25,
580        TeXParticleName -> "\\phi",
581        TeXClassName -> "\\phi",
582        FullName -> "H" },
583
584S[2] == {
585        ClassName -> phi,
586        SelfConjugate -> True,
587        Mass -> {MZ, 91.1876},
588        Width -> Wphi,
589        PropagatorLabel -> "Phi",
590        PropagatorType -> D,
591        PropagatorArrow -> None,
592        ParticleName ->"phi0",
593        PDG -> 250,
594        FullName -> "Phi",
595        Goldstone -> Z },
596
597S[3] == {
598        ClassName -> phi2,
599        SelfConjugate -> False,
600        Mass -> {MW, Internal},
601        Width -> Wphi2,
602        PropagatorLabel -> "Phi2",
603        PropagatorType -> D,
604        PropagatorArrow -> None,
605        ParticleName ->"phi+",
606        AntiParticleName ->"phi-",
607        PDG -> 251,
608        FullName -> "Phi2",
609        TeXClassName -> "\\phi^+",
610        TeXParticleName -> "\\phi^+",
611        TeXAntiParticleName -> "\\phi^-",
612        Goldstone -> W,
613        QuantumNumbers -> {Q -> 1}}
614}
615
616
617
618
619(*****************************************************************************************)
620
621(* SM Lagrangian *)
622
623(******************** Gauge F^2 Lagrangian terms*************************)
624(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
625 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
626                                        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
627       
628        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
629       
630        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
631                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
632
633
634(********************* Fermion Lagrangian terms*************************)
635(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
636 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
637
638    Lkin = I uqbar.Ga[mu].del[uq, mu] +
639        I dqbar.Ga[mu].del[dq, mu] +
640        I lbar.Ga[mu].del[l, mu] +
641        I vlbar.Ga[mu].del[vl, mu];
642
643    LQCD = gs (uqbar.Ga[mu].T[a].uq +
644        dqbar.Ga[mu].T[a].dq)G[mu, a];
645
646    LBright =
647       -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
648        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
649        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
650
651    LBleft =
652       -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
653        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
654        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
655        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
656       
657    LWleft = ee/sw/2(
658        vlbar.Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
659        lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
660       
661        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
662        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
663       
664        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
665        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
666       
667        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
668        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
669        );
670
671    Lkin + LQCD + LBright + LBleft + LWleft];
672
673(******************** Higgs Lagrangian terms****************************)
674 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
675 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
676 
677
678   
679 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
680   
681    PMVec = Table[PauliSigma[i], {i, 3}];   
682    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
683
684        (*Y_phi=1*)
685    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
686    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
687
688    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
689
690    (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
691   
692
693(*************** Yukawa Lagrangian***********************)
694LYuk := If[FeynmanGauge,
695
696      Module[{s,r,n,m,i},                                                                 -
697              yd[m] CKM[n,m]     uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2)              -
698              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2]   -
699         
700              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2]   + (*This sign from eps matrix*)       
701              yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)    -
702       
703              yl[n]              vlbar[s,n].ProjP[s,r].l[r,n]      (-I phi2)              -
704              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H +I phi)/Sqrt[2]
705           ],
706           
707           Module[{s,r,n,m,i},                                                    -
708              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
709              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
710              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]
711           ]
712         ];
713
714LYukawa := LYuk + HC[LYuk];
715
716
717
718(**************Ghost terms**************************)
719(* Now we need the ghost terms which are of the form:             *)
720(* - g * antighost * d_BRST G                                     *)
721(* where d_BRST G is BRST transform of the gauge fixing function. *)
722
723LGhost := If[FeynmanGauge,
724                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
725               
726        (***********First the pure gauge piece.**********************) 
727        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
728                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
729       
730        dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
731                LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];   
732       
733        dBRSTB[mu_] := cw/ee del[ghB, mu];
734                LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
735       
736        (***********Next the piece from the scalar field.************)
737        LGhostphi := -   ee/(2*sw*cw) MW ( - I phi2    ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA )  +
738                        I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA )    ) -
739                        ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm   ) -
740                        I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
741                        ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
742                       
743                       
744        (***********Now add the pieces together.********************)
745        LGhostG + LGhostWi + LGhostB + LGhostphi]
746
747,
748
749        (*If unitary gauge, only include the gluonic ghost.*)
750                Block[{dBRSTG,LGhostG},
751               
752        (***********First the pure gauge piece.**********************) 
753        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
754                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];                 
755                       
756        (***********Now add the pieces together.********************)
757        LGhostG]
758
759];
760               
761(*********Total SM Lagrangian*******)           
762LSM := LGauge + LHiggs + LFermions + LYukawa  + LGhost;