TFCNC: TFCNC.fr

File TFCNC.fr, 23.1 KB (added by buchkremer, 7 years ago)
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1(***************************************************************************************************************)
2(******                       FeynRules model file for top-Higgs flavor changing couplings                ******)
3(******                                                                                                   ******)
4(******     Authors: M. Buchkremer, G. Cacciapaglia, A. Deandrea,L. Panizzi                               ******)
5(******                                                                                                   ******)
6(***************************************************************************************************************)
7
8M$ModelName = "TFCNC";
9
10
11M$Information = {Authors -> {"M. Buchkremer","G. Cacciapaglia","A. Deandrea","L. Panizzi"},
12             Version -> "2.0",
13             Date -> "24. 12. 2013",
14             Institutions -> {"Universite catholique de Louvain (CP3)","Universite de Lyon (CNRS/IN2P3)","University of Southampton (School of Physics and Astronomy)"},
15             Emails -> {"mathieu.buchkremer@uclouvain.be", "g.cacciapaglia@ipnl.in2p3.fr","deandrea@ipnl.in2p3.fr", "l.panizzi@soton.ac.uk"}};
16
17(*
18  Top quark mass  (172 GeV), and all parameters updated to 2010 PDG values
19  FeynmanGauge=True set as default. 
20  Gluonic ghosts to be included in both gauges.
21  Fixed yukawa couplings in Feynman gauge.
22  Yukawa couplings are included for all fermions for gauge invariance.
23  Yukawa couplings for 1st generation fermions require Massless.rst.
24*)
25
26FeynmanGauge = True;
27
28
29(******* Index definitions ********)
30
31IndexRange[ Index[Generation] ] = Range[3]
32
33IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
34
35IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
36
37IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
38
39
40IndexStyle[Colour, i]
41
42IndexStyle[Generation, f]
43
44IndexStyle[Gluon ,a]
45
46IndexStyle[SU2W ,k]
47
48
49(******* Gauge parameters (for FeynArts) ********)
50
51GaugeXi[ V[1] ] = GaugeXi[A];
52GaugeXi[ V[2] ] = GaugeXi[Z];
53GaugeXi[ V[3] ] = GaugeXi[W];
54GaugeXi[ V[4] ] = GaugeXi[G];
55GaugeXi[ S[1] ] = 1;
56GaugeXi[ S[2] ] = GaugeXi[Z];
57GaugeXi[ S[3] ] = GaugeXi[W];
58GaugeXi[ U[1] ] = GaugeXi[A];
59GaugeXi[ U[2] ] = GaugeXi[Z];
60GaugeXi[ U[31] ] = GaugeXi[W];
61GaugeXi[ U[32] ] = GaugeXi[W];
62GaugeXi[ U[4] ] = GaugeXi[G];
63
64
65(****************  Parameters *************)
66
67M$Parameters = {
68
69  (* External parameters *)
70
71  \[Alpha]EWM1== {
72        ParameterType -> External,
73        BlockName -> SMINPUTS,
74        ParameterName -> aEWM1,
75        InteractionOrder -> {QED, -2},
76        Value -> 127.9,
77        Description -> "Inverse of the electroweak coupling constant"},
78
79  Gf == {
80        ParameterType -> External,
81        BlockName -> SMINPUTS,
82        TeX -> Subscript[G, f],
83        InteractionOrder -> {QED, 2},
84        Value -> 1.16637 * 10^(-5),
85        Description -> "Fermi constant"},
86
87  \[Alpha]S == {
88        ParameterType -> External,
89        BlockName -> SMINPUTS,
90        TeX -> Subscript[\[Alpha], s],
91        ParameterName -> aS,
92        InteractionOrder -> {QCD, 2},
93        Value -> 0.1184,
94        Description -> "Strong coupling constant at the Z pole."},
95
96  ymdo == {
97        ParameterType -> External,
98        BlockName -> YUKAWA,
99        Value -> 5.04*10^(-3),
100        OrderBlock -> {1},
101        Description -> "Down Yukawa mass"},
102
103
104  ymup == {
105        ParameterType -> External,
106        BlockName -> YUKAWA,
107        Value -> 2.55*10^(-3),
108        OrderBlock -> {2},
109        Description -> "Up Yukawa mass"},
110
111  yms == {
112        ParameterType -> External,
113        BlockName -> YUKAWA,
114        Value -> 0.101,
115        OrderBlock -> {3},
116        Description -> "Strange Yukawa mass"},
117
118
119  ymc == {
120        ParameterType -> External,
121        BlockName -> YUKAWA,
122        Value -> 1.27,
123        OrderBlock -> {4},
124        Description -> "Charm Yukawa mass"},
125
126 ymb == {
127        ParameterType -> External,
128        BlockName -> YUKAWA,
129        Value -> 4.7,
130        OrderBlock -> {5},
131        Description -> "Bottom Yukawa mass"},
132
133  ymt == {
134        ParameterType -> External,
135        BlockName -> YUKAWA,
136        Value -> 172.0,
137        OrderBlock -> {6},
138        Description -> "Top Yukawa mass"},
139
140  yme == {
141        ParameterType -> External,
142        BlockName -> YUKAWA,
143        Value ->  5.11*10^(-4),
144        OrderBlock -> {11},
145        Description -> "Electron Yukawa mass"},
146
147  ymm == {
148        ParameterType -> External,
149        BlockName -> YUKAWA,
150        Value -> 0.10566,
151        OrderBlock -> {13},
152        Description -> "Muon Yukawa mass"},
153
154  ymtau == {
155        ParameterType -> External,
156        BlockName -> YUKAWA,
157        Value -> 1.777,
158        OrderBlock -> {15},
159        Description -> "Tau Yukawa mass"},
160
161   cabi == {
162        TeX -> Subscript[\[Theta], c],
163        ParameterType -> External,
164        BlockName -> CKMBLOCK,
165        Value -> 0.227736,
166        Description -> "Cabibbo angle"},
167
168   KuH == {
169        ParameterType -> External,
170        BlockName -> FCNC,
171        Value -> 0,
172        Description -> "TuH coupling"},
173
174   KcH == {
175        ParameterType -> External,
176        BlockName -> FCNC,
177        Value -> 1,
178        Description -> "TcH coupling"},
179
180   (* Internal Parameters *)
181
182  \[Alpha]EW == {
183        ParameterType -> Internal,
184        Value -> 1/\[Alpha]EWM1,
185        TeX -> Subscript[\[Alpha], EW],
186        ParameterName -> aEW,
187        InteractionOrder -> {QED, 2},
188        Description -> "Electroweak coupling contant"},
189
190
191  MW == {
192        ParameterType -> Internal,
193        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
194        TeX  -> Subscript[M, W],
195        Description -> "W mass"},
196
197  sw2 == {
198        ParameterType -> Internal,
199        Value -> 1-(MW/MZ)^2,
200        Description -> "Squared Sin of the Weinberg angle"},
201
202   ee == {
203        TeX -> e,
204        ParameterType -> Internal,
205        Value -> Sqrt[4 Pi \[Alpha]EW],
206        InteractionOrder -> {QED, 1},
207        Description -> "Electric coupling constant"},
208
209   cw == {
210        TeX -> Subscript[c, w],
211        ParameterType -> Internal,
212        Value -> Sqrt[1 - sw2],
213        Description -> "Cos of the Weinberg angle"}, 
214
215   sw == {
216        TeX -> Subscript[s, w],
217        ParameterType -> Internal,
218        Value -> Sqrt[sw2],
219        Description -> "Sin of the Weinberg angle"}, 
220
221   gw == {
222        TeX -> Subscript[g, w],
223        ParameterType -> Internal,
224        Value -> ee / sw,
225        InteractionOrder -> {QED, 1},
226        Description -> "Weak coupling constant"},
227
228   g1 == {
229        TeX -> Subscript[g, 1],
230        ParameterType -> Internal,
231        Value -> ee / cw,
232        InteractionOrder -> {QED, 1},
233        Description -> "U(1)Y coupling constant"},
234
235   gs == {
236        TeX -> Subscript[g, s],
237        ParameterType -> Internal,
238        Value -> Sqrt[4 Pi \[Alpha]S],
239        InteractionOrder -> {QCD, 1},
240        ParameterName -> G,
241        Description -> "Strong coupling constant"},
242
243
244   v == {
245        ParameterType -> Internal,
246        Value -> 2*MW*sw/ee,
247        InteractionOrder -> {QED, -1},
248        Description -> "Higgs VEV"},
249
250   \[Lambda] == {
251        ParameterType -> Internal,
252        Value -> MH^2/(2*v^2),
253        InteractionOrder -> {QED, 2},
254        ParameterName -> lam,
255        Description -> "Higgs quartic coupling"},
256
257   muH == {
258        ParameterType -> Internal,
259        Value -> Sqrt[v^2 \[Lambda]],
260        TeX -> \[Mu],
261        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
262
263
264   yl == {
265        TeX -> Superscript[y, l],
266        Indices -> {Index[Generation]},
267        AllowSummation -> True,
268        ParameterType -> Internal,
269        Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
270        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
271        InteractionOrder -> {QED, 1},
272        ComplexParameter -> False,
273        Description -> "Lepton Yukawa coupling"},
274
275   yu == {
276        TeX -> Superscript[y, u],
277        Indices -> {Index[Generation]},
278        AllowSummation -> True,
279        ParameterType -> Internal,
280        Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
281        ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
282        InteractionOrder -> {QED, 1},
283        ComplexParameter -> False,
284        Description -> "U-quark Yukawa coupling"},
285
286   yd == {
287        TeX -> Superscript[y, d],
288        Indices -> {Index[Generation]},
289        AllowSummation -> True,
290        ParameterType -> Internal,
291        Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
292        ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
293        InteractionOrder -> {QED, 1},
294        ComplexParameter -> False,
295        Description -> "D-quark Yukawa coupling"},
296
297
298   (************** Internal Parameters, Top-Higgs FCNC couplings **************)
299
300  KtuH == {
301        ParameterType -> Internal,
302        BlockName -> FCNC,
303        ComplexParameter -> False,
304        Value -> KuH,
305        InteractionOrder -> {QED, 1},
306        Description -> "TuH coupling"},
307
308  KtcH == {
309        ParameterType -> Internal,
310        BlockName -> FCNC,
311        ComplexParameter -> False,
312        Value -> KcH,
313        InteractionOrder -> {QED, 1},
314        Description -> "TcH coupling"},
315
316(* N. B. : only Cabibbo mixing! *)
317  CKM == {
318       Indices -> {Index[Generation], Index[Generation]},
319       TensorClass -> CKM,
320       Unitary -> True,
321       Value -> {CKM[1,1] -> Cos[cabi],
322                 CKM[1,2] -> Sin[cabi],
323                 CKM[1,3] -> 0,
324                 CKM[2,1] -> -Sin[cabi],
325                 CKM[2,2] -> Cos[cabi],
326                 CKM[2,3] -> 0,
327                 CKM[3,1] -> 0,
328                 CKM[3,2] -> 0,
329                 CKM[3,3] -> 1},
330       Description -> "CKM-Matrix"}
331}
332
333
334(************** Gauge Groups ******************)
335
336M$GaugeGroups = {
337
338  U1Y == {
339        Abelian -> True,
340        GaugeBoson -> B,
341        Charge -> Y,
342        CouplingConstant -> g1},
343
344  SU2L == {
345        Abelian -> False,
346        GaugeBoson -> Wi,
347        StructureConstant -> Eps,
348        CouplingConstant -> gw},
349
350  SU3C == {
351        Abelian -> False,
352        GaugeBoson -> G,
353        StructureConstant -> f,
354        SymmetricTensor -> dSUN,
355        Representations -> {T, Colour},
356        CouplingConstant -> gs}
357}
358
359(********* Particle Classes **********)
360
361M$ClassesDescription = {
362
363(********** Fermions ************)
364        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
365  F[1] == {
366        ClassName -> vl,
367        ClassMembers -> {ve,vm,vt},
368        FlavorIndex -> Generation,
369        SelfConjugate -> False,
370        Indices -> {Index[Generation]},
371        Mass -> 0,
372        Width -> 0,
373        QuantumNumbers -> {LeptonNumber -> 1},
374        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
375        PropagatorType -> S,
376        PropagatorArrow -> Forward,
377        PDG -> {12,14,16},
378        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
379
380        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
381  F[2] == {
382        ClassName -> l,
383        ClassMembers -> {e, m, tt},
384        FlavorIndex -> Generation,
385        SelfConjugate -> False,
386        Indices -> {Index[Generation]},
387        Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
388        Width -> 0,
389        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
390        PropagatorLabel -> {"l", "e", "m", "tt"},
391        PropagatorType -> Straight,
392        ParticleName -> {"e-", "m-", "tt-"},
393        AntiParticleName -> {"e+", "m+", "tt+"},
394        PropagatorArrow -> Forward,
395        PDG -> {11, 13, 15},
396        FullName -> {"Electron", "Muon", "Tau"} },
397
398        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
399  F[3] == {
400        ClassMembers -> {u, c, t},
401        ClassName -> uq,
402        FlavorIndex -> Generation,
403        SelfConjugate -> False,
404        Indices -> {Index[Generation], Index[Colour]},
405        Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}},
406        Width -> {0, 0, {WT, 1.50833649}},
407        QuantumNumbers -> {Q -> 2/3},
408        PropagatorLabel -> {"uq", "u", "c", "t"},
409        PropagatorType -> Straight,
410        PropagatorArrow -> Forward,
411        PDG -> {2, 4, 6},
412        FullName -> {"u-quark", "c-quark", "t-quark"}},
413
414        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
415  F[4] == {
416        ClassMembers -> {d, s, b},
417        ClassName -> dq,
418        FlavorIndex -> Generation,
419        SelfConjugate -> False,
420        Indices -> {Index[Generation], Index[Colour]},
421        Mass -> {Md, {MD,  5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
422        Width -> 0,
423        QuantumNumbers -> {Q -> -1/3},
424        PropagatorLabel -> {"dq", "d", "s", "b"},
425        PropagatorType -> Straight,
426        PropagatorArrow -> Forward,
427        PDG -> {1,3,5},
428        FullName -> {"d-quark", "s-quark", "b-quark"} },
429
430(********** Ghosts **********)
431        U[1] == {
432       ClassName -> ghA,
433       SelfConjugate -> False,
434       Indices -> {},
435       Ghost -> A,
436       Mass -> 0,
437       QuantumNumbers -> {GhostNumber -> 1},
438       PropagatorLabel -> uA,
439       PropagatorType -> GhostDash,
440       PropagatorArrow -> Forward},
441
442        U[2] == {
443       ClassName -> ghZ,
444       SelfConjugate -> False,
445       Indices -> {},
446       Mass -> {MZ, 91.1876},
447       Ghost -> Z,
448       QuantumNumbers -> {GhostNumber -> 1},
449       PropagatorLabel -> uZ,
450       PropagatorType -> GhostDash,
451       PropagatorArrow -> Forward},
452
453        U[31] == {
454       ClassName -> ghWp,
455       SelfConjugate -> False,
456       Indices -> {},
457       Mass -> {MW, Internal},
458       Ghost -> W,
459       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
460       PropagatorLabel -> uWp,
461       PropagatorType -> GhostDash,
462       PropagatorArrow -> Forward},
463
464   U[32] == {
465       ClassName -> ghWm,
466       SelfConjugate -> False,
467       Indices -> {},
468       Mass -> {MW, Internal},
469       Ghost -> Wbar,
470       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
471       PropagatorLabel -> uWm,
472       PropagatorType -> GhostDash,
473       PropagatorArrow -> Forward},
474
475        U[4] == {
476       ClassName -> ghG,
477       SelfConjugate -> False,
478       Indices -> {Index[Gluon]},
479       Ghost -> G,
480       Mass -> 0,
481       QuantumNumbers -> {GhostNumber -> 1},
482       PropagatorLabel -> uG,
483       PropagatorType -> GhostDash,
484       PropagatorArrow -> Forward},
485
486        U[5] == {
487        ClassName -> ghWi,
488        Unphysical -> True,
489        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
490                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
491                        ghWi[3] -> cw ghZ + sw ghA},
492        SelfConjugate -> False,
493        Ghost -> Wi,
494        Indices -> {Index[SU2W]},
495        FlavorIndex -> SU2W},
496
497        U[6] == {
498        ClassName -> ghB,
499        SelfConjugate -> False,
500        Definitions -> {ghB -> -sw ghZ + cw ghA},
501        Indices -> {},
502        Ghost -> B,
503        Unphysical -> True},
504
505(************ Gauge Bosons ***************)
506        (* Gauge bosons: Q = 0 *)
507  V[1] == {
508        ClassName -> A,
509        SelfConjugate -> True,
510        Indices -> {},
511        Mass -> 0,
512        Width -> 0,
513        PropagatorLabel -> "a",
514        PropagatorType -> W,
515        PropagatorArrow -> None,
516        PDG -> 22,
517        FullName -> "Photon" },
518
519  V[2] == {
520        ClassName -> Z,
521        SelfConjugate -> True,
522        Indices -> {},
523        Mass -> {MZ, 91.1876},
524        Width -> {WZ, 2.4952},
525        PropagatorLabel -> "Z",
526        PropagatorType -> Sine,
527        PropagatorArrow -> None,
528        PDG -> 23,
529        FullName -> "Z" },
530
531        (* Gauge bosons: Q = -1 *)
532  V[3] == {
533        ClassName -> W,
534        SelfConjugate -> False,
535        Indices -> {},
536        Mass -> {MW, Internal},
537        Width -> {WW, 2.085},
538        QuantumNumbers -> {Q -> 1},
539        PropagatorLabel -> "W",
540        PropagatorType -> Sine,
541        PropagatorArrow -> Forward,
542        ParticleName ->"W+",
543        AntiParticleName ->"W-",
544        PDG -> 24,
545        FullName -> "W" },
546
547V[4] == {
548        ClassName -> G,
549        SelfConjugate -> True,
550        Indices -> {Index[Gluon]},
551        Mass -> 0,
552        Width -> 0,
553        PropagatorLabel -> G,
554        PropagatorType -> C,
555        PropagatorArrow -> None,
556        PDG -> 21,
557        FullName -> "G" },
558
559V[5] == {
560        ClassName -> Wi,
561        Unphysical -> True,
562        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
563                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
564                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
565        SelfConjugate -> True,
566        Indices -> {Index[SU2W]},
567        FlavorIndex -> SU2W,
568        Mass -> 0,
569        PDG -> {1,2,3}},
570
571V[6] == {
572        ClassName -> B,
573        SelfConjugate -> True,
574        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
575        Indices -> {},
576        Mass -> 0,
577        Unphysical -> True},
578
579
580(************ Scalar Fields **********)
581        (* physical Higgs: Q = 0 *)
582  S[1] == {
583        ClassName -> H,
584        SelfConjugate -> True,
585        Mass -> {MH, 120},
586        Width -> {WH, 0.00575308848},
587        PropagatorLabel -> "H",
588        PropagatorType -> D,
589        PropagatorArrow -> None,
590        PDG -> 25,
591        TeXParticleName -> "\\phi",
592        TeXClassName -> "\\phi",
593        FullName -> "H" },
594
595S[2] == {
596        ClassName -> phi,
597        SelfConjugate -> True,
598        Mass -> {MZ, 91.1876},
599        Width -> Wphi,
600        PropagatorLabel -> "Phi",
601        PropagatorType -> D,
602        PropagatorArrow -> None,
603        ParticleName ->"phi0",
604        PDG -> 250,
605        FullName -> "Phi",
606        Goldstone -> Z },
607
608S[3] == {
609        ClassName -> phi2,
610        SelfConjugate -> False,
611        Mass -> {MW, Internal},
612        Width -> Wphi2,
613        PropagatorLabel -> "Phi2",
614        PropagatorType -> D,
615        PropagatorArrow -> None,
616        ParticleName ->"phi+",
617        AntiParticleName ->"phi-",
618        PDG -> 251,
619        FullName -> "Phi2",
620        TeXClassName -> "\\phi^+",
621        TeXParticleName -> "\\phi^+",
622        TeXAntiParticleName -> "\\phi^-",
623        Goldstone -> W,
624        QuantumNumbers -> {Q -> 1}}
625}
626
627
628
629
630(*****************************************************************************************)
631
632(* SM Lagrangian *)
633
634(******************** Gauge F^2 Lagrangian terms*************************)
635(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
636 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
637                                        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
638       
639        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
640       
641        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
642                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
643
644
645(********************* Fermion Lagrangian terms*************************)
646(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
647 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
648
649    Lkin = I uqbar.Ga[mu].del[uq, mu] +
650        I dqbar.Ga[mu].del[dq, mu] +
651        I lbar.Ga[mu].del[l, mu] +
652        I vlbar.Ga[mu].del[vl, mu];
653
654    LQCD = gs (uqbar.Ga[mu].T[a].uq +
655        dqbar.Ga[mu].T[a].dq)G[mu, a];
656
657    LBright =
658       -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
659        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
660        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
661
662    LBleft =
663       -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
664        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
665        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
666        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
667       
668    LWleft = ee/sw/2(
669        vlbar.Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
670        lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
671       
672        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
673        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
674       
675        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
676        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
677       
678        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
679        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
680        );
681
682    Lkin + LQCD + LBright + LBleft + LWleft];
683
684(******************** Higgs Lagrangian terms****************************)
685 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
686 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
687 
688
689   
690 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
691   
692    PMVec = Table[PauliSigma[i], {i, 3}];   
693    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
694
695        (*Y_phi=1*)
696    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
697    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
698
699    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
700
701    (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
702   
703
704(*************** Yukawa Lagrangian***********************)
705LYuk := If[FeynmanGauge,
706
707      Module[{s,r,n,m,i},                                                                 -
708              yd[m] CKM[n,m]     uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2)              -
709              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2]   -
710         
711              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2]   + (*This sign from eps matrix*)       
712              yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)    -
713       
714              yl[n]              vlbar[s,n].ProjP[s,r].l[r,n]      (-I phi2)              -
715              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H +I phi)/Sqrt[2]
716           ],
717           
718           Module[{s,r,n,m,i},                                                    -
719              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
720              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
721              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]
722           ]
723         ];
724
725LYukawa := LYuk + HC[LYuk];
726
727
728
729(**************Ghost terms**************************)
730(* Now we need the ghost terms which are of the form:             *)
731(* - g * antighost * d_BRST G                                     *)
732(* where d_BRST G is BRST transform of the gauge fixing function. *)
733
734LGhost := If[FeynmanGauge,
735                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
736               
737        (***********First the pure gauge piece.**********************) 
738        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
739                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
740       
741        dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
742                LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];   
743       
744        dBRSTB[mu_] := cw/ee del[ghB, mu];
745                LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
746       
747        (***********Next the piece from the scalar field.************)
748        LGhostphi := -   ee/(2*sw*cw) MW ( - I phi2    ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA )  +
749                        I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA )    ) -
750                        ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm   ) -
751                        I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
752                        ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
753                       
754                       
755        (***********Now add the pieces together.********************)
756        LGhostG + LGhostWi + LGhostB + LGhostphi]
757
758,
759
760        (*If unitary gauge, only include the gluonic ghost.*)
761                Block[{dBRSTG,LGhostG},
762               
763        (***********First the pure gauge piece.**********************) 
764        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
765                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];                 
766                       
767        (***********Now add the pieces together.********************)
768        LGhostG]
769
770];
771
772
773        (*************** Top-Higgs NC couplings *****************)
774
775LTFCNC :=+KtuH*(tbar.H.ProjP.u)+KtuH*(ubar.H.ProjM.t)+KtuH*(tbar.H.ProjM.u)+KtuH*(ubar.H.ProjP.t)+KtcH*(tbar.H.ProjP.c)+KtcH*(cbar.H.ProjM.t)+KtcH*(tbar.H.ProjM.c)+KtcH*(cbar.H.ProjP.t);
776               
777(*********Total SM Lagrangian*******)           
778LSM := LGauge + LHiggs + LFermions + LYukawa  + LGhost;
779
780(*********Total Lagrangian*******)             
781L := LGauge + LHiggs + LFermions + LYukawa  + LGhost + LTFCNC ;