AnomalousGaugeCoupling: quartic.fr

File quartic.fr, 36.1 KB (added by eboli, 5 years ago)

This is the main file. It contains the definitions for the SM and all quartic interactions.

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$ModelName = "Standard Model and anomalous quartic couplings";
13
14
15M$Information = {Authors -> {"N. Christensen", "C. Duhr", "modified by OJPE and MCGG"},
16             Version -> "1.4",
17             Date -> "02. 06. 2009, last change 13. 08. 2012",
18             Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)",
19                              "USP", "Stony Brook"},
20             Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "eboli@fma.if.usp.br",
21                        "concha@max2.physics.sunysb.edu"},
22             URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"};
23
24(*
25  V1.3 - Updated Top quark mass to 2010 PDG value (172 GeV)
26  V1.2 - Set FeynmanGauge=True as default. 
27         Set Gluonic ghosts to be included in both gauges.
28  V1.1 - Fixed yukawa couplings in Feynman gauge.
29        Changed yd[n] CKM[n,m] to yd[m] CKM[n,m].
30        Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]].
31  V1.3 - Added yukawa couplings for all fermions for gauge invariance.
32         Added yukawa couplings for 1st generation fermions to Massless.rst.
33         Updated parameters to PDG 2010.
34  V1.4 Anomalous quartic gauge-boson couplings added by OJPE and MCGG
35*)
36
37FeynmanGauge = True;
38
39(* FR$DSign=-1 *)
40
41(******* Index definitions ********)
42
43IndexRange[ Index[Generation] ] = Range[3]
44
45IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
46
47IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
48
49IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
50
51
52IndexStyle[Colour, i]
53
54IndexStyle[Generation, f]
55
56IndexStyle[Gluon ,a]
57
58IndexStyle[SU2W ,k]
59
60
61(******* Gauge parameters (for FeynArts) ********)
62
63GaugeXi[ V[1] ] = GaugeXi[A];
64GaugeXi[ V[2] ] = GaugeXi[Z];
65GaugeXi[ V[3] ] = GaugeXi[W];
66GaugeXi[ V[4] ] = GaugeXi[G];
67GaugeXi[ S[1] ] = 1;
68GaugeXi[ S[2] ] = GaugeXi[Z];
69GaugeXi[ S[3] ] = GaugeXi[W];
70GaugeXi[ U[1] ] = GaugeXi[A];
71GaugeXi[ U[2] ] = GaugeXi[Z];
72GaugeXi[ U[31] ] = GaugeXi[W];
73GaugeXi[ U[32] ] = GaugeXi[W];
74GaugeXi[ U[4] ] = GaugeXi[G];
75
76
77(****************  Parameters *************)
78
79M$Parameters = {
80
81  (* External parameters *)
82
83  \[Alpha]EWM1== {
84        ParameterType -> External,
85        BlockName -> SMINPUTS,
86        ParameterName -> aEWM1,
87        InteractionOrder -> {QED, -2},
88        Value -> 127.9,
89        Description -> "Inverse of the electroweak coupling constant"},
90
91
92  Gf == {
93        ParameterType -> External,
94        BlockName -> SMINPUTS,
95        TeX -> Subscript[G, f],
96        InteractionOrder -> {QED, 2},
97        Value -> 1.16637 * 10^(-5),
98        Description -> "Fermi constant"},
99
100  \[Alpha]S == {
101        ParameterType -> External,
102        BlockName -> SMINPUTS,
103        TeX -> Subscript[\[Alpha], s],
104        ParameterName -> aS,
105        InteractionOrder -> {QCD, 2},
106        Value -> 0.1184,
107        Description -> "Strong coupling constant at the Z pole."},
108
109  ymdo == {
110        ParameterType -> External,
111        BlockName -> YUKAWA,
112        Value -> 5.04*10^(-3),
113        OrderBlock -> {1},
114        Description -> "Down Yukawa mass"},
115
116
117  ymup == {
118        ParameterType -> External,
119        BlockName -> YUKAWA,
120        Value -> 2.55*10^(-3),
121        OrderBlock -> {2},
122        Description -> "Up Yukawa mass"},
123
124  yms == {
125        ParameterType -> External,
126        BlockName -> YUKAWA,
127        Value -> 0.101,
128        OrderBlock -> {3},
129        Description -> "Strange Yukawa mass"},
130
131
132  ymc == {
133        ParameterType -> External,
134        BlockName -> YUKAWA,
135        Value -> 1.27,
136        OrderBlock -> {4},
137        Description -> "Charm Yukawa mass"},
138
139 ymb == {
140        ParameterType -> External,
141        BlockName -> YUKAWA,
142        Value -> 4.7,
143        OrderBlock -> {5},
144        Description -> "Bottom Yukawa mass"},
145
146  ymt == {
147        ParameterType -> External,
148        BlockName -> YUKAWA,
149        Value -> 172.0,
150        OrderBlock -> {6},
151        Description -> "Top Yukawa mass"},
152
153  yme == {
154        ParameterType -> External,
155        BlockName -> YUKAWA,
156        Value ->  5.11*10^(-4),
157        OrderBlock -> {11},
158        Description -> "Electron Yukawa mass"},
159
160  ymm == {
161        ParameterType -> External,
162        BlockName -> YUKAWA,
163        Value -> 0.10566,
164        OrderBlock -> {13},
165        Description -> "Muon Yukawa mass"},
166
167  ymtau == {
168        ParameterType -> External,
169        BlockName -> YUKAWA,
170        Value -> 1.777,
171        OrderBlock -> {15},
172        Description -> "Tau Yukawa mass"},
173
174   cabi == {
175        TeX -> Subscript[\[Theta], c],
176        ParameterType -> External,
177        BlockName -> CKMBLOCK,
178        Value -> 0.227736,
179        Description -> "Cabibbo angle"},
180
181(* OjpE *)
182
183  FS0 == {
184        ParameterType -> External,
185        BlockName -> ANOINPUTS,
186        TeX -> Subscript[f, S0],
187        InteractionOrder -> {NP, 1},
188        Value -> 1.,
189        Description -> "L_S,0 coefficient"},
190
191
192  FS1 == {
193        ParameterType -> External,
194        BlockName -> ANOINPUTS,
195        TeX -> Subscript[f, S1],
196        InteractionOrder -> {NP, 1},
197        Value -> 1.,
198        Description -> "L_S,1 coefficient"},
199
200  FM0 == {
201        ParameterType -> External,
202        BlockName -> ANOINPUTS,
203        TeX -> Subscript[f, M0],
204        InteractionOrder -> {NP, 1},
205        Value -> 1.,
206        Description -> "L_M,0 coefficient"},
207
208  FM1 == {
209        ParameterType -> External,
210        BlockName -> ANOINPUTS,
211        TeX -> Subscript[f, M1],
212        InteractionOrder -> {NP, 1},
213        Value -> 1.,
214        Description -> "L_M,1 coefficient"},
215
216  FM2 == {
217        ParameterType -> External,
218        BlockName -> ANOINPUTS,
219        TeX -> Subscript[f, M2],
220        InteractionOrder -> {NP, 1},
221        Value -> 1.,
222        Description -> "L_M,2 coefficient"},
223
224  FM3 == {
225        ParameterType -> External,
226        BlockName -> ANOINPUTS,
227        TeX -> Subscript[f, M3],
228        InteractionOrder -> {NP, 1},
229        Value -> 1.,
230        Description -> "L_M,3 coefficient"},
231
232  FM4 == {
233        ParameterType -> External,
234        BlockName -> ANOINPUTS,
235        TeX -> Subscript[f, M4],
236        InteractionOrder -> {NP, 1},
237        Value -> 1.,
238        Description -> "L_M,4 coefficient"},
239
240  FM5 == {
241        ParameterType -> External,
242        BlockName -> ANOINPUTS,
243        TeX -> Subscript[f, M5],
244        InteractionOrder -> {NP, 1},
245        Value -> 1.,
246        Description -> "L_M,5 coefficient"},
247
248  FM6 == {
249        ParameterType -> External,
250        BlockName -> ANOINPUTS,
251        TeX -> Subscript[f, M6],
252        InteractionOrder -> {NP, 1},
253        Value -> 1.,
254        Description -> "L_M,6 coefficient"},
255
256  FM7 == {
257        ParameterType -> External,
258        BlockName -> ANOINPUTS,
259        TeX -> Subscript[f, M7],
260        InteractionOrder -> {NP, 1},
261        Value -> 1.,
262        Description -> "L_M,7 coefficient"},
263
264  FT0 == {
265        ParameterType -> External,
266        BlockName -> ANOINPUTS,
267        TeX -> Subscript[f, T0],
268        InteractionOrder -> {NP, 1},
269        Value -> 1.,
270        Description -> "L_T,0 coefficient"},
271
272  FT1 == {
273        ParameterType -> External,
274        BlockName -> ANOINPUTS,
275        TeX -> Subscript[f, T1],
276        InteractionOrder -> {NP, 1},
277        Value -> 1.,
278        Description -> "L_T,1 coefficient"},
279
280  FT2 == {
281        ParameterType -> External,
282        BlockName -> ANOINPUTS,
283        TeX -> Subscript[f, T2],
284        InteractionOrder -> {NP, 1},
285        Value -> 1.,
286        Description -> "L_T,2 coefficient"},
287
288  FT3 == {
289        ParameterType -> External,
290        BlockName -> ANOINPUTS,
291        TeX -> Subscript[f, T3],
292        InteractionOrder -> {NP, 1},
293        Value -> 1.,
294        Description -> "L_T,3 coefficient"},
295
296  FT4 == {
297        ParameterType -> External,
298        BlockName -> ANOINPUTS,
299        TeX -> Subscript[f, T4],
300        InteractionOrder -> {NP, 1},
301        Value -> 1.,
302        Description -> "L_T,4 coefficient"},
303
304  FT5 == {
305        ParameterType -> External,
306        BlockName -> ANOINPUTS,
307        TeX -> Subscript[f, T5],
308        InteractionOrder -> {NP, 1},
309        Value -> 1.,
310        Description -> "L_T,5 coefficient"},
311
312  FT6 == {
313        ParameterType -> External,
314        BlockName -> ANOINPUTS,
315        TeX -> Subscript[f, T6],
316        InteractionOrder -> {NP, 1},
317        Value -> 1.,
318        Description -> "L_T,6 coefficient"},
319
320  FT7 == {
321        ParameterType -> External,
322        BlockName -> ANOINPUTS,
323        TeX -> Subscript[f, T7],
324        InteractionOrder -> {NP, 1},
325        Value -> 1.,
326        Description -> "L_T,7 coefficient"},
327
328  FT8 == {
329        ParameterType -> External,
330        BlockName -> ANOINPUTS,
331        TeX -> Subscript[f, T8],
332        InteractionOrder -> {NP, 1},
333        Value -> 1.,
334        Description -> "L_T,8 coefficient"},
335
336  FT9 == {
337        ParameterType -> External,
338        BlockName -> ANOINPUTS,
339        TeX -> Subscript[f, T9],
340        InteractionOrder -> {NP, 1},
341        Value -> 1.,
342        Description -> "L_T,9 coefficient"},
343
344(* ------------------------------------------------------- *)
345
346   (* Internal Parameters *)
347
348  \[Alpha]EW == {
349        ParameterType -> Internal,
350        Value -> 1/\[Alpha]EWM1,
351        TeX -> Subscript[\[Alpha], EW],
352        ParameterName -> aEW,
353        InteractionOrder -> {QED, 2},
354        Description -> "Electroweak coupling contant"},
355
356
357  MW == {
358        ParameterType -> Internal,
359        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
360        TeX  -> Subscript[M, W],
361        Description -> "W mass"},
362
363  sw2 == {
364        ParameterType -> Internal,
365        Value -> 1-(MW/MZ)^2,
366        Description -> "Squared Sin of the Weinberg angle"},
367
368   ee == {
369        TeX -> e,
370        ParameterType -> Internal,
371        Value -> Sqrt[4 Pi \[Alpha]EW],
372        InteractionOrder -> {QED, 1},
373        Description -> "Electric coupling constant"},
374
375   cw == {
376        TeX -> Subscript[c, w],
377        ParameterType -> Internal,
378        Value -> Sqrt[1 - sw2],
379        Description -> "Cos of the Weinberg angle"}, 
380
381   sw == {
382        TeX -> Subscript[s, w],
383        ParameterType -> Internal,
384        Value -> Sqrt[sw2],
385        Description -> "Sin of the Weinberg angle"}, 
386
387   gw == {
388        TeX -> Subscript[g, w],
389        ParameterType -> Internal,
390        Value -> ee / sw,
391        InteractionOrder -> {QED, 1},
392        Description -> "Weak coupling constant"},
393
394   g1 == {
395        TeX -> Subscript[g, 1],
396        ParameterType -> Internal,
397        Value -> ee / cw,
398        InteractionOrder -> {QED, 1},
399        Description -> "U(1)Y coupling constant"},
400
401   gs == {
402        TeX -> Subscript[g, s],
403        ParameterType -> Internal,
404        Value -> Sqrt[4 Pi \[Alpha]S],
405        InteractionOrder -> {QCD, 1},
406        ParameterName -> G,
407        Description -> "Strong coupling constant"},
408
409
410   v == {
411        ParameterType -> Internal,
412        Value -> 2*MW*sw/ee,
413        InteractionOrder -> {QED, -1},
414        Description -> "Higgs VEV"},
415
416   \[Lambda] == {
417        ParameterType -> Internal,
418        Value -> MH^2/(2*v^2),
419        InteractionOrder -> {QED, 2},
420        ParameterName -> lam,
421        Description -> "Higgs quartic coupling"},
422
423   muH == {
424        ParameterType -> Internal,
425        Value -> Sqrt[v^2 \[Lambda]],
426        TeX -> \[Mu],
427        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
428
429
430   yl == {
431        TeX -> Superscript[y, l],
432        Indices -> {Index[Generation]},
433        AllowSummation -> True,
434        ParameterType -> Internal,
435        Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
436        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
437        InteractionOrder -> {QED, 1},
438        ComplexParameter -> False,
439        Description -> "Lepton Yukawa coupling"},
440
441   yu == {
442        TeX -> Superscript[y, u],
443        Indices -> {Index[Generation]},
444        AllowSummation -> True,
445        ParameterType -> Internal,
446        Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
447        ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
448        InteractionOrder -> {QED, 1},
449        ComplexParameter -> False,
450        Description -> "U-quark Yukawa coupling"},
451
452   yd == {
453        TeX -> Superscript[y, d],
454        Indices -> {Index[Generation]},
455        AllowSummation -> True,
456        ParameterType -> Internal,
457        Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
458        ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
459        InteractionOrder -> {QED, 1},
460        ComplexParameter -> False,
461        Description -> "D-quark Yukawa coupling"},
462
463(* N. B. : only Cabibbo mixing! *)
464  CKM == {
465       Indices -> {Index[Generation], Index[Generation]},
466       TensorClass -> CKM,
467       Unitary -> True,
468       Value -> {CKM[1,1] -> Cos[cabi],
469                 CKM[1,2] -> Sin[cabi],
470                 CKM[1,3] -> 0,
471                 CKM[2,1] -> -Sin[cabi],
472                 CKM[2,2] -> Cos[cabi],
473                 CKM[2,3] -> 0,
474                 CKM[3,1] -> 0,
475                 CKM[3,2] -> 0,
476                 CKM[3,3] -> 1},
477       Description -> "CKM-Matrix"}
478}
479
480
481(************** Gauge Groups ******************)
482
483M$GaugeGroups = {
484
485  U1Y == {
486        Abelian -> True,
487        GaugeBoson -> B,
488        Charge -> Y,
489        CouplingConstant -> g1},
490
491  SU2L == {
492        Abelian -> False,
493        GaugeBoson -> Wi,
494        StructureConstant -> Eps,
495        CouplingConstant -> gw},
496
497  SU3C == {
498        Abelian -> False,
499        GaugeBoson -> G,
500        StructureConstant -> f,
501        SymmetricTensor -> dSUN,
502        Representations -> {T, Colour},
503        CouplingConstant -> gs}
504}
505
506(********* Particle Classes **********)
507
508M$ClassesDescription = {
509
510(********** Fermions ************)
511        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
512  F[1] == {
513        ClassName -> vl,
514        ClassMembers -> {ve,vm,vt},
515        FlavorIndex -> Generation,
516        SelfConjugate -> False,
517        Indices -> {Index[Generation]},
518        Mass -> 0,
519        Width -> 0,
520        QuantumNumbers -> {LeptonNumber -> 1},
521        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
522        PropagatorType -> S,
523        PropagatorArrow -> Forward,
524        PDG -> {12,14,16},
525        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
526
527        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
528  F[2] == {
529        ClassName -> l,
530        ClassMembers -> {e, m, tt},
531        FlavorIndex -> Generation,
532        SelfConjugate -> False,
533        Indices -> {Index[Generation]},
534        Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
535        Width -> 0,
536        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
537        PropagatorLabel -> {"l", "e", "m", "tt"},
538        PropagatorType -> Straight,
539        ParticleName -> {"e-", "m-", "tt-"},
540        AntiParticleName -> {"e+", "m+", "tt+"},
541        PropagatorArrow -> Forward,
542        PDG -> {11, 13, 15},
543        FullName -> {"Electron", "Muon", "Tau"} },
544
545        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
546  F[3] == {
547        ClassMembers -> {u, c, t},
548        ClassName -> uq,
549        FlavorIndex -> Generation,
550        SelfConjugate -> False,
551        Indices -> {Index[Generation], Index[Colour]},
552        Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}},
553        Width -> {0, 0, {WT, 1.50833649}},
554        QuantumNumbers -> {Q -> 2/3},
555        PropagatorLabel -> {"uq", "u", "c", "t"},
556        PropagatorType -> Straight,
557        PropagatorArrow -> Forward,
558        PDG -> {2, 4, 6},
559        FullName -> {"u-quark", "c-quark", "t-quark"}},
560
561        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
562  F[4] == {
563        ClassMembers -> {d, s, b},
564        ClassName -> dq,
565        FlavorIndex -> Generation,
566        SelfConjugate -> False,
567        Indices -> {Index[Generation], Index[Colour]},
568        Mass -> {Md, {MD,  5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
569        Width -> 0,
570        QuantumNumbers -> {Q -> -1/3},
571        PropagatorLabel -> {"dq", "d", "s", "b"},
572        PropagatorType -> Straight,
573        PropagatorArrow -> Forward,
574        PDG -> {1,3,5},
575        FullName -> {"d-quark", "s-quark", "b-quark"} },
576
577(********** Ghosts **********)
578        U[1] == {
579       ClassName -> ghA,
580       SelfConjugate -> False,
581       Indices -> {},
582       Ghost -> A,
583       Mass -> 0,
584       QuantumNumbers -> {GhostNumber -> 1},
585       PropagatorLabel -> uA,
586       PropagatorType -> GhostDash,
587       PropagatorArrow -> Forward},
588
589        U[2] == {
590       ClassName -> ghZ,
591       SelfConjugate -> False,
592       Indices -> {},
593       Mass -> {MZ, 91.1876},
594       Ghost -> Z,
595       QuantumNumbers -> {GhostNumber -> 1},
596       PropagatorLabel -> uZ,
597       PropagatorType -> GhostDash,
598       PropagatorArrow -> Forward},
599
600        U[31] == {
601       ClassName -> ghWp,
602       SelfConjugate -> False,
603       Indices -> {},
604       Mass -> {MW, Internal},
605       Ghost -> W,
606       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
607       PropagatorLabel -> uWp,
608       PropagatorType -> GhostDash,
609       PropagatorArrow -> Forward},
610
611   U[32] == {
612       ClassName -> ghWm,
613       SelfConjugate -> False,
614       Indices -> {},
615       Mass -> {MW, Internal},
616       Ghost -> Wbar,
617       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
618       PropagatorLabel -> uWm,
619       PropagatorType -> GhostDash,
620       PropagatorArrow -> Forward},
621
622        U[4] == {
623       ClassName -> ghG,
624       SelfConjugate -> False,
625       Indices -> {Index[Gluon]},
626       Ghost -> G,
627       Mass -> 0,
628       QuantumNumbers -> {GhostNumber -> 1},
629       PropagatorLabel -> uG,
630       PropagatorType -> GhostDash,
631       PropagatorArrow -> Forward},
632
633        U[5] == {
634        ClassName -> ghWi,
635        Unphysical -> True,
636        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
637                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
638                        ghWi[3] -> cw ghZ + sw ghA},
639        SelfConjugate -> False,
640        Ghost -> Wi,
641        Indices -> {Index[SU2W]},
642        FlavorIndex -> SU2W},
643
644        U[6] == {
645        ClassName -> ghB,
646        SelfConjugate -> False,
647        Definitions -> {ghB -> -sw ghZ + cw ghA},
648        Indices -> {},
649        Ghost -> B,
650        Unphysical -> True},
651
652(************ Gauge Bosons ***************)
653        (* Gauge bosons: Q = 0 *)
654  V[1] == {
655        ClassName -> A,
656        SelfConjugate -> True,
657        Indices -> {},
658        Mass -> 0,
659        Width -> 0,
660        PropagatorLabel -> "a",
661        PropagatorType -> W,
662        PropagatorArrow -> None,
663        PDG -> 22,
664        FullName -> "Photon" },
665
666  V[2] == {
667        ClassName -> Z,
668        SelfConjugate -> True,
669        Indices -> {},
670        Mass -> {MZ, 91.1876},
671        Width -> {WZ, 2.4952},
672        PropagatorLabel -> "Z",
673        PropagatorType -> Sine,
674        PropagatorArrow -> None,
675        PDG -> 23,
676        FullName -> "Z" },
677
678        (* Gauge bosons: Q = -1 *)
679  V[3] == {
680        ClassName -> W,
681        SelfConjugate -> False,
682        Indices -> {},
683        Mass -> {MW, Internal},
684        Width -> {WW, 2.085},
685        QuantumNumbers -> {Q -> 1},
686        PropagatorLabel -> "W",
687        PropagatorType -> Sine,
688        PropagatorArrow -> Forward,
689        ParticleName ->"W+",
690        AntiParticleName ->"W-",
691        PDG -> 24,
692        FullName -> "W" },
693
694V[4] == {
695        ClassName -> G,
696        SelfConjugate -> True,
697        Indices -> {Index[Gluon]},
698        Mass -> 0,
699        Width -> 0,
700        PropagatorLabel -> G,
701        PropagatorType -> C,
702        PropagatorArrow -> None,
703        PDG -> 21,
704        FullName -> "G" },
705
706V[5] == {
707        ClassName -> Wi,
708        Unphysical -> True,
709        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
710                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
711                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
712        SelfConjugate -> True,
713        Indices -> {Index[SU2W]},
714        FlavorIndex -> SU2W,
715        Mass -> 0,
716        PDG -> {1,2,3}},
717
718V[6] == {
719        ClassName -> B,
720        SelfConjugate -> True,
721        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
722        Indices -> {},
723        Mass -> 0,
724        Unphysical -> True},
725
726
727(************ Scalar Fields **********)
728        (* physical Higgs: Q = 0 *)
729  S[1] == {
730        ClassName -> H,
731        SelfConjugate -> True,
732        Mass -> {MH, 125},
733        Width -> {WH, 0.00575308848},
734        PropagatorLabel -> "H",
735        PropagatorType -> D,
736        PropagatorArrow -> None,
737        PDG -> 25,
738        TeXParticleName -> "\\phi",
739        TeXClassName -> "\\phi",
740        FullName -> "H" },
741
742S[2] == {
743        ClassName -> phi,
744        SelfConjugate -> True,
745        Mass -> {MZ, 91.1876},
746        Width -> Wphi,
747        PropagatorLabel -> "Phi",
748        PropagatorType -> D,
749        PropagatorArrow -> None,
750        ParticleName ->"phi0",
751        PDG -> 250,
752        FullName -> "Phi",
753        Goldstone -> Z },
754
755S[3] == {
756        ClassName -> phi2,
757        SelfConjugate -> False,
758        Mass -> {MW, Internal},
759        Width -> Wphi2,
760        PropagatorLabel -> "Phi2",
761        PropagatorType -> D,
762        PropagatorArrow -> None,
763        ParticleName ->"phi+",
764        AntiParticleName ->"phi-",
765        PDG -> 251,
766        FullName -> "Phi2",
767        TeXClassName -> "\\phi^+",
768        TeXParticleName -> "\\phi^+",
769        TeXAntiParticleName -> "\\phi^-",
770        Goldstone -> W,
771        QuantumNumbers -> {Q -> 1}}
772}
773
774
775
776
777(*****************************************************************************************)
778
779(* SM Lagrangian *)
780
781(******************** Gauge F^2 Lagrangian terms*************************)
782(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
783 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
784                                        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
785       
786        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
787       
788        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
789                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
790
791
792(********************* Fermion Lagrangian terms*************************)
793(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
794 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
795
796    Lkin = I uqbar.Ga[mu].del[uq, mu] +
797        I dqbar.Ga[mu].del[dq, mu] +
798        I lbar.Ga[mu].del[l, mu] +
799        I vlbar.Ga[mu].del[vl, mu];
800
801    LQCD = gs (uqbar.Ga[mu].T[a].uq +
802        dqbar.Ga[mu].T[a].dq)G[mu, a];
803
804    LBright =
805       -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
806        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
807        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
808
809    LBleft =
810       -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
811        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
812        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
813        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
814       
815    LWleft = ee/sw/2(
816        vlbar.Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
817        lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
818       
819        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
820        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
821       
822        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
823        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
824       
825        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
826        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
827        );
828
829    Lkin + LQCD + LBright + LBleft + LWleft];
830
831(******************** Higgs Lagrangian terms****************************)
832 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
833 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
834 
835
836   
837 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
838   
839    PMVec = Table[PauliSigma[i], {i, 3}];   
840    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
841
842        (*Y_phi=1*)
843    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
844    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
845
846    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
847
848    (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
849
850
851
852
853
854(*************** Yukawa Lagrangian***********************)
855LYuk := If[FeynmanGauge,
856
857      Module[{s,r,n,m,i},                                                                 -
858              yd[m] CKM[n,m]     uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2)              -
859              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2]   -
860         
861              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2]   + (*This sign from eps matrix*)       
862              yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)    -
863       
864              yl[n]              vlbar[s,n].ProjP[s,r].l[r,n]      (-I phi2)              -
865              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H +I phi)/Sqrt[2]
866           ],
867           
868           Module[{s,r,n,m,i},                                                    -
869              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
870              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
871              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]
872           ]
873         ];
874
875LYukawa := LYuk + HC[LYuk];
876
877
878
879(**************Ghost terms**************************)
880(* Now we need the ghost terms which are of the form:             *)
881(* - g * antighost * d_BRST G                                     *)
882(* where d_BRST G is BRST transform of the gauge fixing function. *)
883
884LGhost := If[FeynmanGauge,
885                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
886               
887        (***********First the pure gauge piece.**********************) 
888        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
889                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
890       
891        dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
892
893                LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];   
894       
895        dBRSTB[mu_] := cw/ee del[ghB, mu];
896                LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
897       
898        (***********Next the piece from the scalar field.************)
899        LGhostphi := -   ee/(2*sw*cw) MW ( - I phi2    ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA )  +
900                        I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA )    ) -
901                        ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm   ) -
902                        I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
903                        ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
904                       
905                       
906        (***********Now add the pieces together.********************)
907        LGhostG + LGhostWi + LGhostB + LGhostphi]
908
909,
910
911        (*If unitary gauge, only include the gluonic ghost.*)
912                Block[{dBRSTG,LGhostG},
913               
914        (***********First the pure gauge piece.**********************) 
915        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
916                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];                 
917                       
918        (***********Now add the pieces together.********************)
919        LGhostG]
920
921];
922
923
924(* anomalous quartic couplings as defined in PRD74, 073005 *)
925
926
927(* S,0 *)
928
929LS0 := Block[{PMVec, WVec, Dc, Dcbar},
930   
931    PMVec = Table[PauliSigma[i], {i, 3}];   
932    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
933
934        (*Y_phi=1*)
935    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
936    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
937
938 FS0  (Dcbar[Phibar, mu]). Dc[Phi, nu]   (Dcbar[Phibar, mu]).Dc[Phi, nu]
939
940];
941
942(* S,1 *)
943
944LS1 := Block[{PMVec, WVec, Dc, Dcbar},
945   
946    PMVec = Table[PauliSigma[i], {i, 3}];   
947    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
948
949        (*Y_phi=1*)
950    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
951    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
952
953 FS1  (Dcbar[Phibar, mu]). Dc[Phi, mu] (Dcbar[Phibar, nu]).Dc[Phi, nu]
954
955];
956
957
958(* M,0 *)
959
960LM0 := Block[{PMVec, WVec, FSVec, Dc, Dcbar},
961   
962    PMVec = Table[PauliSigma[i], {i, 3}];   
963    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
964    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
965
966        (*Y_phi=1*)
967    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
968    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
969
970
971 FM0/4  (Dcbar[Phibar, alpha]).Dc[Phi, alpha]  Tr[(FSvec[mu,nu].PMVec).(FSvec[mu,nu].PMVec)]
972
973];
974
975
976(* M,1 *)
977
978LM1 := Block[{PMVec, WVec, FSvec, Dc, Dcbar},
979   
980    PMVec = Table[PauliSigma[i], {i, 3}];   
981    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
982    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
983
984        (*Y_phi=1*)
985    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
986    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
987
988
989 FM1/4  (Dcbar[Phibar, beta]).Dc[Phi, mu]  Tr[(FSvec[mu,nu].PMVec).(FSvec[nu,beta].PMVec)]
990
991];
992
993
994
995(* M,2 *)
996
997LM2 := Block[{PMVec, WVec, Dc, Dcbar},
998   
999    PMVec = Table[PauliSigma[i], {i, 3}];   
1000    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1001
1002        (*Y_phi=1*)
1003    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1004    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1005
1006
1007(* FM2  (Dcbar[Phibar, mu]).Dc[Phi, mu]  FS[B,mu,nu] FS[B,mu,nu] *)
1008
1009 FM2  (Dcbar[Phibar, beta]).Dc[Phi, beta]  FS[B,mu,nu] FS[B,mu,nu]
1010
1011];
1012
1013(* M,3 *)
1014
1015LM3 := Block[{PMVec, WVec, Dc, Dcbar},
1016   
1017    PMVec = Table[PauliSigma[i], {i, 3}];   
1018    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1019
1020        (*Y_phi=1*)
1021    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1022    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1023
1024
1025
1026 FM3  (Dcbar[Phibar, mu]).Dc[Phi, beta]  FS[B,mu,nu] FS[B,nu,beta]
1027];
1028
1029
1030(* M,4 *)
1031
1032LM4 := Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1033
1034    PMVec = Table[PauliSigma[i], {i, 3}];   
1035    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1036    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1037
1038        (*Y_phi=1*)
1039    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1040    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1041
1042
1043
1044FM4/2  (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).Dc[Phi, mu] FS[B,beta,nu]
1045
1046
1047];
1048
1049(* M,5 *)
1050
1051LM5 := Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1052
1053    PMVec = Table[PauliSigma[i], {i, 3}];   
1054    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1055    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1056
1057        (*Y_phi=1*)
1058    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1059    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1060
1061
1062FM5/2 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).Dc[Phi, nu] FS[B,beta,mu]
1063
1064];
1065
1066
1067(* M,6 *)
1068
1069LM6 :=Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1070
1071    PMVec = Table[PauliSigma[i], {i, 3}];   
1072    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1073    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1074
1075        (*Y_phi=1*)
1076    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1077    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1078
1079
1080FM6/4   (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).(FSvec[beta,nu].PMVec).Dc[Phi, mu]
1081
1082];
1083
1084(* M,7 *)
1085
1086LM7 :=Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1087
1088    PMVec = Table[PauliSigma[i], {i, 3}];   
1089    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1090    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1091
1092        (*Y_phi=1*)
1093    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1094    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1095
1096
1097FM7/4   (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).(FSvec[beta,mu].PMVec).Dc[Phi, nu]
1098
1099];
1100
1101
1102(* T,0 *)
1103
1104LT0 := Block[{PMVec, FSVec },
1105   
1106    PMVec = Table[PauliSigma[i], {i, 3}];   
1107    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1108
1109 FT0/16  Tr[(FSvec[alpha,beta].PMVec).(FSvec[alpha,beta].PMVec)]   Tr[(FSvec[mu,nu].PMVec).(FSvec[mu,nu].PMVec)]
1110
1111];
1112
1113(* T,1 *)
1114
1115LT1 := Block[{PMVec, FSVec},
1116 
1117    PMVec = Table[PauliSigma[i], {i, 3}];   
1118    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1119
1120 FT1/16  Tr[(FSvec[alpha,nu].PMVec).(FSvec[mu,beta].PMVec)]   Tr[(FSvec[mu,beta].PMVec).(FSvec[alpha,nu].PMVec)]
1121
1122];
1123
1124
1125(* T,2 *)
1126
1127LT2 := Block[{PMVec, FSVec},
1128
1129    PMVec = Table[PauliSigma[i], {i, 3}];   
1130    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1131
1132 FT2/16  Tr[(FSvec[alpha,mu].PMVec).(FSvec[mu,beta].PMVec)]   Tr[(FSvec[beta,nu].PMVec).(FSvec[nu,alpha].PMVec)]
1133
1134];
1135
1136(* T,3 identicaly zero!*)
1137
1138LT3 := Block[{PMVec, FSVec},
1139
1140    PMVec = Table[PauliSigma[i], {i, 3}];   
1141    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1142
1143 FT3/8  Tr[(FSvec[alpha,mu].PMVec).(FSvec[mu,beta].PMVec).(FSvec[nu,alpha].PMVec)]  FS[B, beta, nu]
1144
1145];
1146
1147
1148(* T,4: identicaly zero *)
1149
1150LT4 := Block[{PMVec, FSVec},
1151
1152    PMVec = Table[PauliSigma[i], {i, 3}];   
1153    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1154
1155
1156 FT4/8  Tr[(FSvec[alpha,mu].PMVec).(FSvec[alpha, mu].PMVec).(FSvec[beta, nu].PMVec)]  FS[B, beta, nu]
1157
1158];
1159
1160
1161(* T,5 *)
1162
1163LT5 := Block[{PMVec, FSVec},
1164   
1165    PMVec = Table[PauliSigma[i], {i, 3}];   
1166    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1167
1168
1169 FT5/4  Tr[(FSvec[mu,nu].PMVec).(FSvec[mu, nu].PMVec)] FS[B, beta, alpha] FS[B, beta, alpha]
1170
1171];
1172
1173
1174(* T,6 *)
1175
1176LT6 := Block[{PMVec, FSVec},
1177
1178    PMVec = Table[PauliSigma[i], {i, 3}];   
1179    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1180
1181 FT6/4  Tr[(FSvec[alpha,nu].PMVec).(FSvec[mu, beta].PMVec)] FS[B, mu, beta] FS[B, alpha, nu]
1182
1183];
1184
1185
1186(* T,7 *)
1187
1188LT7 := Block[{PMVec, FSVec},
1189   
1190    PMVec = Table[PauliSigma[i], {i, 3}];   
1191    FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1192
1193 FT7/4  Tr[(FSvec[alpha, mu].PMVec).(FSvec[mu, beta].PMVec)] FS[B, beta, nu] FS[B, nu, alpha]
1194
1195];
1196
1197
1198(* T,8: *)
1199
1200LT8 := Block[{PMVec, WVec},
1201   
1202    PMVec = Table[PauliSigma[i], {i, 3}];   
1203    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1204
1205
1206 FT8      (del[B[nu], mu] - del[B[mu], nu] )*
1207          (del[B[nu], mu] - del[B[mu], nu] )*
1208          (del[B[beta], alpha] - del[B[alpha], beta] )*
1209          (del[B[beta], alpha] - del[B[alpha], beta] )
1210
1211];
1212
1213(* T,9: *)
1214
1215LT9 := Block[{PMVec, WVec},
1216   
1217    PMVec = Table[PauliSigma[i], {I, 3}];   
1218    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1219
1220FT9 FS[B, mu, nu] FS[B, nu, alpha] FS[B, alpha, beta] FS[B, beta, mu]
1221
1222];
1223
1224
1225(* ------------------------------------------------------- *)
1226
1227
1228                (*********Total SM Lagrangian in the unitary gauge*******)             
1229
1230LSM := LGauge + LHiggs + LFermions + LYukawa ;
1231
1232LQS = LS0 + LS1;
1233
1234LQM = LM0 + LM1 + LM2 + LM3 + LM4 + LM5 + LM6 + LM7;
1235
1236LQT = LT0 + LT1 + LT2 + LT3 + LT4 + LT5 + LT6 + LT7 + LT8 + LT9;
1237
1238LQuartic := LSM + LQS + LQM + LQT;
1239
1240
1241           
1242
1243