B-L-SM: minimal_Zp.fr

File minimal_Zp.fr, 38.2 KB (added by L.Basso, 6 years ago)

Minimal Zp models FR file

Line 
1(***************************************************************************************************************)
2(******                       This is the FeynRules mod-file for the minimal Zp models                    ******)
3(******                                                                                                   ******)
4(******     Author: L. Basso                                                                              ******)
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$ModelName = "minimal_Zp";
13
14
15M$Information = {Authors -> "L. Basso",
16             Version -> "2.0",
17             Date -> "09-06-2011",
18             Institutions -> {"University of Southampton", "RAL-PPD, Didcot, UK", "Albert-Ludwigs-UniversitÀt Freiburg"},
19             Emails -> {"lorenzo.basso@physik.uni-freiburg.de"},
20             References -> {"L.~Basso, G.M.~Pruna and S.~Moretti, \"A Renormalisation Group Equation Study of the Scalar Sector of the Minimal B-L Extension of the Standard Model,\",  Phys.,Rev. D 82, 055018 (2010) [arXiv:1004.3039 [hep-ph]]", "L.~Basso, G.M.~Pruna and S.~Moretti, \"A Theoretical constraints on the couplings of non-exotic minimal Z' bosons,\",  JHEP 1108 122 (2011) [arXiv:1106.4762 [hep-ph]]"},
21             URLs -> "http://feynrules.phys.ucl.ac.be/..."};
22
23FeynmanGauge = True;
24
25
26(******* Index definitions ********)
27
28IndexRange[ Index[Generation] ] = Range[3]
29
30IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
31
32IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
33
34IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
35
36
37IndexStyle[Colour, i]
38
39IndexStyle[Generation, f]
40
41IndexStyle[Gluon ,a]
42
43IndexStyle[SU2W ,k]
44
45
46
47(******* Gauge parameters (for FeynArts) ********)
48
49GaugeXi[ V[1] ] = GaugeXi[A];
50GaugeXi[ V[2] ] = GaugeXi[Z];
51GaugeXi[ V[3] ] = GaugeXi[W];
52GaugeXi[ V[4] ] = GaugeXi[G];
53GaugeXi[ V[7] ] = GaugeXi[Zp];
54GaugeXi[ S[1] ] = 1;
55GaugeXi[ S[2] ] = GaugeXi[Z];
56GaugeXi[ S[3] ] = GaugeXi[W];
57GaugeXi[ S[4] ] = 1;
58GaugeXi[ S[5] ] = GaugeXi[Zp];
59GaugeXi[ U[1] ] = GaugeXi[A];
60GaugeXi[ U[2] ] = GaugeXi[Z];
61GaugeXi[ U[31] ] = GaugeXi[W];
62GaugeXi[ U[32] ] = GaugeXi[W];
63GaugeXi[ U[4] ] = GaugeXi[G];
64GaugeXi[ U[7] ] = GaugeXi[Zp];
65
66
67(***** Setting for interaction order (as e.g. used by MadGraph 5)  ******)
68
69M$InteractionOrderHierarchy = {
70     {QCD, 1},
71     {QED, 2}
72    };
73
74
75(****************  Parameters *************)
76
77M$Parameters = {
78
79  (* External parameters *)
80
81
82  \[Alpha]EWM1== {
83        ParameterType -> External,
84        BlockName -> BLINPUTS,
85        ParameterName -> aEWM1,
86        InteractionOrder -> {QED, -2},
87        Value -> 127.9,
88        Description -> "Inverse of the electroweak coupling constant at Z-pole"},
89
90  Gf == {
91        ParameterType -> External,
92        BlockName -> BLINPUTS,
93        InteractionOrder -> {QED, 2},
94        Value -> 1.16637 * 10^(-5),
95        Description -> "Fermi constant"},
96
97  \[Alpha]S == {
98        ParameterType -> External,
99        BlockName -> BLINPUTS,
100        TeX -> Subscript[\[Alpha], s],
101        ParameterName -> aS,
102        InteractionOrder -> {QCD, 2},
103        Value -> 0.1184,
104        Description -> "Strong coupling constant at the Z pole."},
105
106  MW == {
107        ParameterType -> External,
108        BlockName -> BLINPUTS,
109        Value -> 80.292,
110        Description -> "W mass"},
111
112  MZp == {
113        ParameterType -> External,
114        BlockName -> BLINPUTS,
115        Value -> 1500.00,
116        Description -> "Zp mass"},
117         
118  g1p == {
119        ParameterType -> External,
120        BlockName -> BLINPUTS,
121        InteractionOrder -> {QED, 1},
122        Value -> 0.2,
123        Description -> "Zp coupling"},
124 
125  gt == {
126        ParameterType -> External,
127        BlockName -> BLINPUTS,
128        InteractionOrder -> {QED, 1},
129        Value -> -0.1,
130        Description -> "Z-Zp mixing coupling"},
131
132  ymdo == {
133        ParameterType -> External,
134        BlockName -> YUKAWA,
135        Value -> 5.04*10^(-3),
136        OrderBlock -> {1},
137        Description -> "Down Yukawa mass"},
138
139
140  ymup == {
141        ParameterType -> External,
142        BlockName -> YUKAWA,
143        Value -> 2.55*10^(-3),
144        OrderBlock -> {2},
145        Description -> "Up Yukawa mass"},
146
147  yms == {
148        ParameterType -> External,
149        BlockName -> YUKAWA,
150        Value -> 0.101,
151        OrderBlock -> {3},
152        Description -> "Strange Yukawa mass"},
153       
154  ymc == {
155        ParameterType -> External,
156        BlockName -> YUKAWA,
157        Value -> 1.27,
158        OrderBlock -> {4},
159        Description -> "Charm Yukawa mass"},
160
161  ymb == {
162        ParameterType -> External,
163        BlockName -> YUKAWA,
164        Value -> 4.7,
165        OrderBlock -> {5},
166        Description -> "Bottom Yukawa mass"},
167
168  ymt == {
169        ParameterType -> External,
170        BlockName -> YUKAWA,
171        Value -> 172.0,
172        OrderBlock -> {6},
173        Description -> "Top Yukawa mass"},
174
175  yme == {
176        ParameterType -> External,
177        BlockName -> YUKAWA,
178        Value -> 0.000511,
179        OrderBlock -> {11},
180        Description -> "Electron Yukawa mass"},
181
182  ymmu == {
183        ParameterType -> External,
184        BlockName -> YUKAWA,
185        Value -> 0.1057,
186        OrderBlock -> {13},
187        Description -> "Muon Yukawa mass"},
188
189  ymtau == {
190        ParameterType -> External,
191        BlockName -> YUKAWA,
192        Value -> 1.777,
193        OrderBlock -> {15},
194        Description -> "Tau Yukawa mass"},
195
196  MH1 == {
197        ParameterType -> External,
198        BlockName -> BLINPUTS,
199        Value -> 120.00,
200        Description -> "H1 mass"},
201
202  MH2 == {
203        ParameterType -> External,
204        BlockName -> BLINPUTS,
205        Value -> 450.00,
206        Description -> "H2 mass"},
207
208
209  Sa == {
210        ParameterType -> External,
211        BlockName -> BLINPUTS,
212        Value -> 0.1,
213        Description -> "Sine of Higgses mixing angle"},
214
215  sw2 == {
216        ParameterType -> External,
217        BlockName -> BLINPUTS,
218        Value -> 0.232,
219        Description -> "Squared Sin of the Weinberg angle"},
220
221
222
223   (* Internal Parameters *)
224                       
225  \[Alpha]EW == {
226        ParameterType -> Internal,
227        Value -> 1/\[Alpha]EWM1,
228        TeX -> Subscript[\[Alpha], EW],
229        ParameterName -> aEW,
230        InteractionOrder -> {QED, 2},
231        Description -> "Electroweak coupling contant"},
232
233
234   ee == {
235        TeX -> e,
236        ParameterType -> Internal,
237        Value -> Sqrt[4 Pi \[Alpha]EW],
238        InteractionOrder -> {QED, 1},
239        Description -> "Electric coupling constant"},
240
241   cw == {
242        TeX -> Subscript[c, w],
243        ParameterType -> Internal,
244        Value -> Sqrt[1 - sw2],
245        Description -> "Cos of the Weinberg angle"}, 
246
247   sw == {
248        TeX -> Subscript[s, w],
249        ParameterType -> Internal,
250        Value -> Sqrt[sw2],
251        Description -> "Sin of the Weinberg angle"}, 
252
253   gw == {
254        TeX -> Subscript[g, w],
255        ParameterType -> Internal,
256        Value -> ee / sw,
257        Definitions -> {gw -> ee / sw},
258        InteractionOrder -> {QED, 1},
259        Description -> "Weak coupling constant"},
260
261   g1 == {
262        TeX -> Subscript[g, 1],
263        ParameterType -> Internal,
264        Value -> ee / cw,
265        Definitions -> {g1 -> ee / cw},
266        InteractionOrder -> {QED, 1},
267        Description -> "U(1)Y coupling constant"},
268
269   gs == {
270        TeX -> Subscript[g, s],
271        ParameterType -> Internal,
272        Value -> Sqrt[4 Pi \[Alpha]S],
273        InteractionOrder -> {QCD, 1},
274        ParameterName -> G,
275        Description -> "Strong coupling constant"},
276
277   v == {
278        ParameterType -> Internal,
279        BlockName -> VEV,
280        Value -> 2*MW*sw/ee,
281        InteractionOrder -> {QED, -1},
282        Description -> "H1 VEV"},
283
284
285   x == {
286        ParameterType -> Internal,
287        BlockName -> VEV,
288        Value -> MZp/(2*g1p)*Sqrt[1-gt^2*v^2/(4*MZp^2-v^2*(gw^2+g1^2))],
289        InteractionOrder -> {QED, -1},
290        Description -> "H2 VEV"},
291
292
293  Ca == {
294        ParameterType -> Internal,
295        Value -> Sqrt[1-Sa^2],
296        ParameterName -> Ca,
297        Description -> "Cosine of Higgses mixing angle"},
298
299
300   yl == {
301        TeX -> Superscript[y, l],
302        Indices -> {Index[Generation]},
303        AllowSummation -> True,
304        ParameterType -> Internal,
305        Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymmu / v, yl[3] -> Sqrt[2] ymtau / v},
306        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
307        InteractionOrder -> {QED, 1},
308        ComplexParameter -> False,
309        Description -> "Lepton Yukawa coupling"},
310
311   yu == {
312        Indices -> {Index[Generation]},
313        AllowSummation -> True,
314        AllowSummation -> True,
315        ParameterType -> Internal,
316        Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
317        ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
318        InteractionOrder -> {QED, 1},
319        ComplexParameter -> False,
320        Description -> "U-quark Yukawa coupling"},
321
322   yd == {
323        TeX -> Superscript[y, d],
324        Indices -> {Index[Generation]},
325        AllowSummation -> True,
326        ParameterType -> Internal,
327        Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
328        ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
329        InteractionOrder -> {QED, 1},
330        ComplexParameter -> False,
331        Description -> "D-quark Yukawa coupling"},
332
333   ynd == {
334        Indices -> {Index[Generation]},
335        AllowSummation -> True,
336        ParameterType -> Internal,
337        Value -> {ynd[1] -> Sqrt[2*MnL1*MnH1]/v,
338                  ynd[2] -> Sqrt[2*MnL2*MnH2]/v,
339                  ynd[3] -> Sqrt[2*MnL3*MnH3]/v},
340        ParameterName -> {ynd[1] -> ynd1,
341                          ynd[2] -> ynd2,
342                          ynd[3] -> ynd3},
343        InteractionOrder -> {QED, 1},
344        ComplexParameter -> False,
345        Description -> "Dirac neutrino Yukawa coupling"},
346
347   ynm == {
348        Indices -> {Index[Generation]},
349        AllowSummation -> True,
350        ParameterType -> Internal,
351        Value -> {ynm[1] -> (MnH1-MnL1)/Sqrt[2]/x,
352                  ynm[2] -> (MnH2-MnL2)/Sqrt[2]/x,
353                  ynm[3] -> (MnH3-MnL3)/Sqrt[2]/x},
354        ParameterName -> {ynm[1] -> ynm1, ynm[2] -> ynm2, ynm[3] -> ynm3},
355        InteractionOrder -> {QED, 1},
356        ComplexParameter -> False,
357        Description -> "Majorana neutrino Yukawa coupling"},
358
359   Mdd == {
360        Indices -> {Index[Generation]},
361        AllowSummation -> True,
362        ParameterType -> Internal,
363        Value -> {Mdd[1] -> ynd1*v/Sqrt[2],
364                  Mdd[2] -> ynd2*v/Sqrt[2],
365                  Mdd[3] -> ynd3*v/Sqrt[2]},
366        ParameterName -> {Mdd[1] -> Mdd1, Mdd[2] -> Mdd2, Mdd[3] -> Mdd3},
367        ComplexParameter -> False,
368        Description -> "Neutrino Dirac Mass"},
369
370   s12 == {
371        TeX -> Subscript[S\[Theta], 12],
372        ParameterType -> External,
373        BlockName -> CKMBLOCK,
374        Value -> 0.221,
375        Description -> "Sin(theta_12), PDG-94"},
376
377   s23 == {
378        TeX -> Subscript[S\[Theta], 23],
379        ParameterType -> External,
380        BlockName -> CKMBLOCK,
381        Value -> 0.040,
382        Description -> "Sin(theta_23), PDG-94"},
383
384   s13 == {
385        TeX -> Subscript[S\[Theta], 13],
386        ParameterType -> External,
387        BlockName -> CKMBLOCK,
388        Value -> 0.0035,
389        Description -> "Sin(theta_13), PDG-94"},
390
391   c12 == {
392        TeX -> Subscript[C\[Theta], 12],
393        ParameterType -> Internal,
394        BlockName -> CKMBLOCK,
395        Value -> Sqrt[1-s12^2],
396        Description -> "Cos(theta_12)"},
397
398   c23 == {
399        TeX -> Subscript[C\[Theta], 23],
400        ParameterType -> Internal,
401        BlockName -> CKMBLOCK,
402        Value -> Sqrt[1-s23^2],
403        Description -> "Cos(theta_23)"},
404
405   c13 == {
406        TeX -> Subscript[C\[Theta], 13],
407        ParameterType -> Internal,
408        BlockName -> CKMBLOCK,
409        Value -> Sqrt[1-s13^2],
410        Description -> "Cos(theta_13)"},
411
412  CKM == {
413       Indices -> {Index[Generation], Index[Generation]},
414       TensorClass -> CKM,
415       Unitary -> True,
416       Value -> {CKM[1,1] -> c12*c13,
417                   CKM[1,2] -> s12*c13,
418                   CKM[1,3] -> s13,
419                   CKM[2,1] -> -s12*c23-c12*s23*s13,
420                   CKM[2,2] -> c12*c23-s12*s23*s13,
421                   CKM[2,3] -> s23*c13,
422                   CKM[3,1] -> s12*s23-c12*c23*s13,
423                   CKM[3,2] -> -c12*s23-s12*c23*s13,
424                   CKM[3,3] -> c23*c13},                   
425       Description -> "CKM-Matrix"},
426
427   San == {
428        Indices -> {Index[Generation]},
429        AllowSummation -> True,
430        ParameterType -> Internal,
431        Value -> {San[1] -> Sin[ArcSin[-2*Mdd1/Sqrt[4*Mdd1^2+(MnH1-MnL1)^2]]/2],
432                  San[2] -> Sin[ArcSin[-2*Mdd2/Sqrt[4*Mdd2^2+(MnH2-MnL2)^2]]/2],
433                  San[3] -> Sin[ArcSin[-2*Mdd3/Sqrt[4*Mdd3^2+(MnH3-MnL3)^2]]/2]},
434        ParameterName -> {San[1] -> San1, San[2] -> San2, San[3] -> San3},
435        ComplexParameter -> False,
436        Description -> "Sin-array of neutrino mass-eigenstates"},
437
438   Can == {
439        Indices -> {Index[Generation]},
440        AllowSummation -> True,
441        ParameterType -> Internal,
442        Value -> {Can[1] -> Sqrt[1-San1^2],
443                  Can[2] -> Sqrt[1-San2^2],
444                  Can[3] -> Sqrt[1-San3^2]},
445        Definitions -> {Can[1]*San1-> Sa2n1/2,
446                  Can[2]*San2-> Sa2n2/2,
447                  Can[3]*San3-> Sa2n3/2,
448                  Can[1]^2 -San1^2-> Ca2n1,
449                  Can[2]^2 -San2^2-> Ca2n2,
450                  Can[3]^2 -San3^2-> Ca2n3},
451        ParameterName -> {Can[1] -> Can1, Can[2] -> Can2, Can[3] -> Can3},
452        ComplexParameter -> False,
453        Description -> "Cos-array of neutrino mass-eigenstates"},
454
455       
456
457   \[Lambda]1 == {
458        ParameterType -> Internal,
459        Value -> MH1^2 /(2*v^2)*Ca^2 + MH2^2 /(2*v^2)*Sa^2,
460        ParameterName -> lam1,
461        InteractionOrder -> {QED, 2},
462        Description -> "Lambda 1"},
463
464   \[Lambda]2 == {
465        ParameterType -> Internal,
466        Value -> MH1^2 /(2*x^2)*Sa^2 + MH2^2 /(2*x^2)*Ca^2,
467        ParameterName -> lam2,
468        InteractionOrder -> {QED, 2},
469        Description -> "Lambda 2"},
470
471   \[Lambda]3 == {
472        ParameterType -> Internal,
473        Value -> (MH2^2 - MH1^2)/(x*v)*Sa*Ca,
474        ParameterName -> lam3,
475        InteractionOrder -> {QED, 2},
476        Description -> "Lambda 3, mixing parameter"},
477
478   mu2H1 == {
479        ParameterType -> Internal,
480        Value -> - \[Lambda]1 * v^2 - \[Lambda]3 /2 * x^2,
481        TeX -> m^2,
482        Description -> "Coefficient of the quadratic piece of the H1 potential"},
483
484   mu2H2 == {
485        ParameterType -> Internal,
486        Value -> - \[Lambda]3 /2 * v^2 - \[Lambda]2 * x^2,
487        TeX -> \[Mu]^2,
488        Description -> "Coefficient of the quadratic piece of the H2 potential"},
489
490
491   Sp2num == {
492        ParameterType -> Internal,
493        Value -> 2*gt*Sqrt[(ee/sw)^2+(ee/cw)^2]},
494
495   Cp2num == {
496        ParameterType -> Internal,
497        Value -> gt^2+16*(x/v)^2*g1p^2-(ee/sw)^2-(ee/cw)^2},
498
499   Sp == {
500        AllowSummation -> True,
501        ParameterType -> Internal,
502        Value -> Sin[ArcSin[Sp2num/Sqrt[Sp2num^2+Cp2num^2]]/2],
503        ComplexParameter -> False,
504        Description -> "Sin-array of neutrino mass-eigenstates"},
505
506   Cp == {
507        AllowSummation -> True,
508        ParameterType -> Internal,
509        Value -> Sqrt[1-Sp^2],
510        ComplexParameter -> False,
511        Description -> "Cos-array of neutrino mass-eigenstates"},
512
513
514   Cn == {
515        ParameterType -> Internal,
516        ComplexParameter -> False,
517        Value -> (ee/sw)^2+(ee/cw)^2+gt^2+16*(x/v)^2*g1p^2},
518
519   Dn == {
520        ParameterType -> Internal,
521        ComplexParameter -> False,
522        Value -> 64*((ee/sw)^2+(ee/cw)^2)*g1p^2*v^2*x^2},
523       
524
525   MZ == {
526        ParameterType -> Internal,
527        Value -> Sqrt[(Cn*v^2-Sqrt[-Dn+v^4*Cn^2])/8],
528        Description -> "Z mass"},
529
530   S2gNum == {
531        ParameterType -> Internal,
532        ComplexParameter -> False,
533        Value -> 8*x/v*gt*g1p},
534
535   C2gNum == {
536        ParameterType -> Internal,
537        ComplexParameter -> False,
538        Value -> (ee/sw)^2+(ee/cw)^2+gt^2-16*(x/v)^2*g1p^2},   
539
540   
541   sg == {
542        ParameterType -> Internal,
543        ComplexParameter -> False,
544        Value -> Sin[ArcSin[-S2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2],
545        Description -> "cosine of Z-Zp goldostone mixing angle"},
546       
547   cg == {
548        ParameterType -> Internal,
549        ComplexParameter -> False,
550        Value -> Sqrt[1-sg^2],
551        Description -> "sine of Z-Zp goldstone mixing angle"}
552(*        Value -> Cos[ArcCos[-C2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2], *)
553}
554
555(************** Gauge Groups ******************)
556
557M$GaugeGroups = {
558
559  U1BL == {
560        Abelian -> True,
561        GaugeBoson -> Bp,
562        Charge -> BL,
563        CouplingConstant -> g1p},
564 
565  U1Y == {
566        Abelian -> True,
567        GaugeBoson -> B,
568        Charge -> Y,
569        CouplingConstant -> g1},
570
571  SU2L == {
572        Abelian -> False,
573        GaugeBoson -> Wi,
574        StructureConstant -> Eps,
575        CouplingConstant -> gw},
576
577  SU3C == {
578        Abelian -> False,
579        GaugeBoson -> G,
580        StructureConstant -> f,
581        SymmetricTensor -> dSUN,
582        Representations -> {T, Colour},
583        CouplingConstant -> gs}
584}
585
586(********* Particle Classes **********)
587
588M$ClassesDescription = {
589
590(********** Fermions ************)
591
592        (* Mass-Eigenstate light neutrino: Q = 0, BL= -1 *)
593
594  F[11] == {
595        ClassName -> nL,
596        ClassMembers -> {nL1, nL2, nL3},
597        FlavorIndex -> Generation,
598        SelfConjugate -> True,
599        Indices -> {Index[Generation]},
600        Mass -> {MnL, {MnL1, 10^(-9)}, {MnL2, 10^(-9)}, {MnL3, 10^(-9)}},
601        Width -> 0,
602        PropagatorLabel -> {"nL", "nul1", "nul2", "nul3"},
603        PropagatorType -> Straight,
604        ParticleName -> {"n1", "n2", "n3"},
605        PropagatorArrow -> Forward,
606        PDG -> {12, 14, 16},
607        FullName -> {"Light neutrino 1", "Light neutrino 2", "Light neutrino 3"} },
608
609        (* Mass-Eigenstate heavy neutrino: Q = 0, BL= -1 *)
610
611  F[12] == {
612        ClassName -> nH,
613        ClassMembers -> {nH1, nH2, nH3},
614        FlavorIndex -> Generation,
615        SelfConjugate -> True,
616        Indices -> {Index[Generation]},
617        Mass -> {MnH, {MnH1, 200.00}, {MnH2, 200.00}, {MnH3, 200.00}},
618        Width -> 10^(-13),
619        PropagatorLabel -> {"nH", "nuh1", "nuh2", "nuh3"},
620        PropagatorType -> Straight,
621        ParticleName -> {"~n1", "~n2", "~n3"},
622        PropagatorArrow -> Forward,
623        PDG -> {9100012, 9100014, 9100016},
624        FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"} },
625
626        (* Left-handed neutrino: unphysical *)
627  F[13] == {
628        ClassName -> nF,
629        ClassMembers -> {nF1,nF2,nF3},
630        FlavorIndex -> Generation,
631        SelfConjugate -> True,
632        Indices -> {Index[Generation]},
633        Unphysical -> True,
634        Definitions -> {nF[s_,i_] -> Can[i] nL[s,i]-San[i] nH[s,i]},
635        FullName -> {"Majorana LH component of Dirac neutrino 1",
636                    "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} },
637
638        (* Right-handed neutrino: unphysical *)
639  F[14] == {
640        ClassName -> nR,
641        ClassMembers -> {nR1,nR2,nR3},
642        FlavorIndex -> Generation,
643        SelfConjugate -> True,
644        Indices -> {Index[Generation]},
645        Unphysical -> True,
646        Definitions -> {nR[s_,i_] -> San[i] nL[s,i]+Can[i] nH[s,i]},
647        FullName -> {"Majorana LH component of Dirac neutrino 1", "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} },
648
649
650        (* Flavour-eigenstate neutrino: unphysical *)
651  F[15] == {
652        ClassName -> vl,
653        ClassMembers -> {vle,vlm,vlt},
654        FlavorIndex -> Generation,
655        SelfConjugate -> False,
656        Indices -> {Index[Generation]},
657        QuantumNumbers -> {Q -> 0, LeptonNumber -> 1, BarionLepton -> -1},
658        Unphysical -> True,
659        Definitions -> {vl[s_,i_] -> left[nF[s,i]]+right[nR[s,i]]},
660        ParticleName -> {"nue", "num", "nut"},
661        AntiParticleName -> {"nue-bar", "num-bar", "nut-bar"},
662        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
663       
664
665        (* Leptons (electron): I_3 = -1/2, Q = -1, BL= -1 *)
666  F[2] == {
667        ClassName -> l,
668        ClassMembers -> {e, m, tt},
669        FlavorIndex -> Generation,
670        SelfConjugate -> False,
671        Indices -> {Index[Generation]},
672        Mass -> {Ml, {ME, 0.000511}, {MM, 0.1057}, {MTA, 1.777}},
673        Width -> 0,
674        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1, BarionLepton -> -1},
675        PropagatorLabel -> {"l", "e", "m", "tt"},
676        PropagatorType -> Straight,
677        ParticleName -> {"e", "m", "l"},
678        AntiParticleName -> {"E", "M", "L"},
679        PropagatorArrow -> Forward,
680        PDG -> {11, 13, 15},
681        FullName -> {"Electron", "Muon", "Tau"} },
682
683        (* Quarks (u): I_3 = +1/2, Q = +2/3, BL=1/3 *)
684  F[3] == {
685        ClassMembers -> {u, c, t},
686        ClassName -> uq,
687        FlavorIndex -> Generation,
688        SelfConjugate -> False,
689        Indices -> {Index[Generation], Index[Colour]},
690        Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.27}, {MT, 172.0}},
691        Width -> {0, 0, {WT, 1.50833649}},
692        QuantumNumbers -> {Q -> 2/3, BarionLepton -> 1/3},
693        PropagatorLabel -> {"uq", "u", "c", "t"},
694        ParticleName -> {"u", "c", "t"},
695        AntiParticleName -> {"U", "C", "T"},   
696        PropagatorType -> Straight,
697        PropagatorArrow -> Forward,
698        PDG -> {2, 4, 6},
699        FullName -> {"u-quark", "c-quark", "t-quark"}},
700
701        (* Quarks (d): I_3 = -1/2, Q = -1/3, BL=1/3 *)
702  F[4] == {
703        ClassMembers -> {d, s, b},
704        ClassName -> dq,
705        FlavorIndex -> Generation,
706        SelfConjugate -> False,
707        Indices -> {Index[Generation], Index[Colour]},
708        Mass -> {Md, {MD,  5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
709        Width -> 0,
710        QuantumNumbers -> {Q -> -1/3, BarionLepton -> 1/3},
711        ParticleName -> {"d", "s", "b"},
712        AntiParticleName -> {"D", "S", "B"},
713        PropagatorLabel -> {"dq", "d", "s", "b"},
714        PropagatorType -> Straight,
715        PropagatorArrow -> Forward,
716        PDG -> {1,3,5},
717        FullName -> {"d-quark", "s-quark", "b-quark"} },
718
719       
720(********** Ghosts **********)
721        U[1] == {
722       ClassName -> ghA,
723       SelfConjugate -> False,
724       Indices -> {},
725       Ghost -> A,
726       Mass -> 0,
727       QuantumNumbers -> {GhostNumber -> 1},
728       PropagatorLabel -> uA,
729       PropagatorType -> GhostDash,
730       PropagatorArrow -> Forward},
731
732        U[2] == {
733       ClassName -> ghZ,
734       SelfConjugate -> False,
735       Indices -> {},
736       Mass -> {MZ, Internal},
737       Ghost -> Z,
738       QuantumNumbers -> {GhostNumber -> 1},
739       PropagatorLabel -> uZ,
740       PropagatorType -> GhostDash,
741       PropagatorArrow -> Forward},
742
743        U[31] == {
744       ClassName -> ghWp,
745       SelfConjugate -> False,
746       Indices -> {},
747       Mass -> {MW, Internal},
748       Ghost -> W,
749       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
750       PropagatorLabel -> uWp,
751       PropagatorType -> GhostDash,
752       PropagatorArrow -> Forward},
753
754   U[32] == {
755       ClassName -> ghWm,
756       SelfConjugate -> False,
757       Indices -> {},
758       Mass -> {MW, Internal},
759       Ghost -> Wbar,
760       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
761       PropagatorLabel -> uWm,
762       PropagatorType -> GhostDash,
763       PropagatorArrow -> Forward},
764
765        U[4] == {
766       ClassName -> ghG,
767       SelfConjugate -> False,
768       Indices -> {Index[Gluon]},
769       Ghost -> G,
770       Mass -> 0,
771       QuantumNumbers -> {GhostNumber -> 1},
772       PropagatorLabel -> uG,
773       PropagatorType -> GhostDash,
774       PropagatorArrow -> Forward},
775
776        U[5] == {
777        ClassName -> ghWi,
778        Unphysical -> True,
779        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
780                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
781                        ghWi[3] -> cw*Cp ghZ + sw ghA - cw*Sp ghZp},
782        SelfConjugate -> False,
783        Indices -> {Index[SU2W]},
784        FlavorIndex -> SU2W,
785        Ghost -> Wi},
786
787        U[6] == {
788        ClassName -> ghB,
789        SelfConjugate -> False,
790        Definitions -> {ghB -> -sw*Cp ghZ + cw ghA + sw*Sp ghZp},
791        Indices -> {},
792        Unphysical -> True,
793        Ghost -> B},
794
795        U[7] == {
796       ClassName -> ghZp,
797       SelfConjugate -> False,
798       Indices -> {},
799       Mass -> {MZp, Internal},
800       Ghost -> Zp,
801       QuantumNumbers -> {GhostNumber -> 1},
802       PropagatorLabel -> uZp,
803       PropagatorType -> GhostDash,
804       PropagatorArrow -> Forward},
805
806        U[8] == {
807        ClassName -> ghBp,
808        SelfConjugate -> False,
809        Definitions -> {ghBp -> Sp ghZ + Cp ghZp},
810        Indices -> {},
811        Unphysical -> True,
812        Ghost -> Bp},
813
814(************ Gauge Bosons ***************)
815        (* Gauge bosons: Q = 0 *)
816  V[1] == {
817        ClassName -> A,
818        SelfConjugate -> True,
819        Indices -> {},
820        Mass -> 0,
821        Width -> 0,
822        PropagatorLabel -> "a",
823        PropagatorType -> W,
824        PropagatorArrow -> None,
825        PDG -> 22,
826        FullName -> "Photon" },
827
828  V[2] == {
829        ClassName -> Z,
830        SelfConjugate -> True,
831        Indices -> {},
832        Mass -> {MZ, Internal},
833        Width -> {WZ, 2.4952},
834        PropagatorLabel -> "Z",
835        PropagatorType -> Sine,
836        PropagatorArrow -> None,
837        PDG -> 23,
838        FullName -> "Z" },
839
840        (* Gauge bosons: Q = -1 *)
841  V[3] == {
842        ClassName -> W,
843        SelfConjugate -> False,
844        Indices -> {},
845        Mass -> {MW, Internal},
846        Width -> {WW, 2.085},
847        QuantumNumbers -> {Q -> 1},
848        PropagatorLabel -> "W",
849        PropagatorType -> Sine,
850        PropagatorArrow -> Forward,
851        ParticleName ->"W+",
852        AntiParticleName ->"W-",
853        PDG -> 24,
854        FullName -> "W" },
855
856V[4] == {
857        ClassName -> G,
858        SelfConjugate -> True,
859        Indices -> {Index[Gluon]},
860        Mass -> 0,
861        Width -> 0,
862        PropagatorLabel -> G,
863        PropagatorType -> C,
864        PropagatorArrow -> None,
865        PDG -> 21,
866        FullName -> "G" },
867
868V[5] == {
869        ClassName -> Wi,
870        Unphysical -> True,
871        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
872                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
873                        Wi[mu_, 3] -> sw A[mu] + cw*Cp Z[mu] - cw*Sp Zp[mu]},
874        SelfConjugate -> True,
875        Indices -> {Index[SU2W]},
876        FlavorIndex -> SU2W,
877        Mass -> 0,
878        PDG -> {1,2,3}},
879
880V[6] == {
881        ClassName -> B,
882        SelfConjugate -> True,
883        Definitions -> {B[mu_] -> cw A[mu] - sw*Cp Z[mu] + sw*Sp Zp[mu]},
884        Indices -> {},
885        Mass -> 0,
886        Unphysical -> True},
887
888V[7] == {
889        ClassName -> Zp,
890        SelfConjugate -> True,
891        Indices -> {},
892        Mass -> {MZp, Internal},
893        Width -> {WZp, 80.00},
894        PropagatorLabel -> "Zp",
895        PropagatorType -> Sine,
896        PropagatorArrow -> None,
897        PDG -> 9900032,
898        FullName -> "Zp" },
899
900V[8] == {
901        ClassName -> Bp,
902        SelfConjugate -> True,
903        Definitions -> {Bp[mu_] ->  Sp Z[mu] + Cp Zp[mu]},
904        Indices -> {},
905        Unphysical -> True},
906
907
908(************ Scalar Fields **********)
909        (* physical Higgs: Q = 0 *)
910  S[1] == {
911        ClassName -> H1,
912        SelfConjugate -> True,
913        Mass -> {MH1, Internal},
914        Width -> {WH1, 1.5},
915        PropagatorLabel -> "H1",
916        PropagatorType -> D,
917        PropagatorArrow -> None,
918        PDG -> 9900025,
919        FullName -> "H1" },
920
921  S[2] == {
922        ClassName -> phiZ,
923        SelfConjugate -> True,
924        Mass -> {MZ, Internal},
925        Width -> Wphi,
926        PropagatorLabel -> "PhiZ",
927        PropagatorType -> D,
928        PropagatorArrow -> None,
929        ParticleName ->"phiZ",
930        PDG -> 9900250,
931        FullName -> "PhiZ",
932        Goldstone -> Z },
933
934  S[3] == {
935        ClassName -> phi2,
936        SelfConjugate -> False,
937        Mass -> {MW, Internal},
938        Width -> Wphi2,
939        PropagatorLabel -> "Phi2",
940        PropagatorType -> D,
941        PropagatorArrow -> None,
942        ParticleName ->"phi+",
943        AntiParticleName ->"phi-",
944        PDG -> 9900251,
945        FullName -> "Phi2",
946        Goldstone -> W,
947        QuantumNumbers -> {Q -> 1}},
948
949  S[4] == {
950        ClassName -> H2,
951        SelfConjugate -> True,
952        Mass -> {MH2, Internal},
953        Width -> {WH2, 10},
954        PropagatorLabel -> "H2",
955        PropagatorType -> D,
956        PropagatorArrow -> None,
957        PDG -> 9900026,
958        FullName -> "H2" },
959   
960  S[5] == {
961        ClassName -> phiZp,
962        SelfConjugate -> True,
963        Mass -> {MZp, Internal},
964        Width -> WphiZp,
965        PropagatorLabel -> "PhiZp",
966        PropagatorType -> D,
967        PropagatorArrow -> None,
968        ParticleName ->"phiZp",
969        PDG -> 9900252,
970        FullName -> "PhiZp",
971        Goldstone -> Zp },
972       
973  S[6] == {
974        ClassName -> phi,
975        Unphysical -> True,
976        Definitions -> {phi -> cg phiZ - sg phiZp},
977        SelfConjugate -> True},
978
979  S[7] == {
980        ClassName -> phip,
981        Unphysical -> True,
982        Definitions -> {phip -> sg phiZ + cg phiZp},
983        SelfConjugate -> True},
984
985  S[8] == {
986        ClassName -> phic,
987        Unphysical -> True,
988        Definitions -> {phic[1] -> (phi2 + phi2bar)/Sqrt[2],
989                        phic[2] -> (phi2bar - phi2)/Sqrt[2]/I},
990        SelfConjugate -> False}
991       
992}
993
994
995(*****************************************************************************************)
996
997(* mZp Lagrangian *)
998
999(******************** Gauge F^2 Lagrangian terms*************************)
1000(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1001 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
1002        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
1003       
1004        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[Bp[nu], mu] - del[Bp[mu], nu])^2 -
1005       
1006        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
1007                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
1008
1009
1010(********************* Fermion Lagrangian terms*************************)
1011(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1012 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
1013
1014    Lkin = I uqbar.Ga[mu].del[uq, mu] +
1015        I dqbar.Ga[mu].del[dq, mu] +
1016        I lbar.Ga[mu].del[l, mu] +
1017        I left[anti[vl]].Ga[mu].del[left[vl],mu] +
1018        I right[anti[vl]].Ga[mu].del[right[vl],mu];
1019
1020    LQCD = gs (uqbar.Ga[mu].T[a].uq +
1021        dqbar.Ga[mu].T[a].dq)G[mu, a];
1022
1023    LBright =
1024       -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
1025        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
1026        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
1027
1028    LBleft =
1029       -ee/cw B[mu]/2 left[anti[vl]].Ga[mu].ProjM.vl -          (*Y_LL=-1*)
1030        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
1031        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
1032        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
1033       
1034    LWleft = ee/sw/2(
1035           left[anti[vl]].Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
1036           lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
1037       
1038        Sqrt[2] left[anti[vl]].Ga[mu].ProjM.l W[mu] +
1039        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
1040       
1041        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
1042        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
1043       
1044        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
1045        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
1046        );
1047
1048    LBpright =       
1049             - g1p Bp[mu] right[anti[vl]].Ga[mu].ProjP.vl +          (*Y_vlR=0, BL_vlR=-1*)
1050             (-1*gt -g1p) Bp[mu] lbar.Ga[mu].ProjP.l +           (*Y_lR=-1, BL_lR=-1*)
1051             (2/3*gt + g1p/3) Bp[mu] uqbar.Ga[mu].ProjP.uq +       (*Y_uR=2/3, BL_uR=1/3*)
1052             (-1/3*gt + g1p/3) Bp[mu] dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-1/3, BL_dR=1/3*)
1053
1054    LBpleft =
1055           - (gt/2 + g1p) Bp[mu] left[anti[vl]].Ga[mu].ProjM.vl -          (*Y_lL=-1/2, BL_vlL=-1*)
1056             (gt/2 + g1p) Bp[mu] lbar.Ga[mu].ProjM.l +           (*Y_lL=-1/2, BL_lL=-1*)
1057             (gt/3/2 + g1p/3) Bp[mu] uqbar.Ga[mu].ProjM.uq +       (*Y_qL=1/6, BL_uL=1/3*)
1058             (gt/3/2 + g1p/3) Bp[mu] dqbar.Ga[mu].ProjM.dq         (*Y_qL=1/6, BL_dL=1/3*)
1059             ;
1060
1061    Lkin + LQCD + LBright + LBleft + LWleft + LBpright + LBpleft ];
1062
1063(******************** Higgs Lagrangian terms****************************)
1064 Phi := If[FeynmanGauge, {-I phi2, (v + Ca*H1+Sa*H2 + I phi)/Sqrt[2]}, {0, (v + Ca*H1+Sa*H2)/Sqrt[2]}];
1065 Phibar := If[FeynmanGauge, {I phi2bar, (v + Ca*H1+Sa*H2 - I phi)/Sqrt[2]} ,{0, (v + Ca*H1+Sa*H2)/Sqrt[2]}];
1066 
1067 Chi := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 + I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}];
1068 Chibar := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 - I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}];
1069   
1070 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphichi, Dcp, Dcpbar},
1071   
1072    PMVec = Table[PauliSigma[i], {i, 3}];   
1073    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1074
1075        (*Y_phi=1/2*)
1076    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + gt/2 Bp[mu] f + ee/sw/2 (Wvec[mu].PMVec).f;
1077    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + gt/2 Bp[mu] f + ee/sw/2 f.(Wvec[mu].PMVec);
1078
1079        (*BL_phi=2*)
1080    Dcp[f_, mu_] := I del[f, mu] + 2*g1p Bp[mu] f ;
1081    Dcpbar[f_, mu_] := -I del[f, mu] + 2*g1p Bp[mu] f ;
1082
1083    Vphichi[Phi_, Phibar_, Chi_, Chibar_] := mu2H1 Phibar.Phi + mu2H2 Chibar.Chi +
1084        \[Lambda]1 (Phibar.Phi)^2 + \[Lambda]2 (Chibar.Chi)^2 + \[Lambda]3 (Phibar.Phi)*(Chibar.Chi);
1085
1086    (Dcbar[Phibar, mu]).Dc[Phi, mu] + (Dcpbar[Chibar, mu]).Dcp[Chi, mu] - Vphichi[Phi, Phibar, Chi, Chibar] 
1087
1088   ];
1089   
1090
1091
1092(*************** Yukawa Lagrangian***********************)
1093(*NOTE: Neutrino states have been expanded on the LH/RH components and the LH mass terms have been changed signs*)
1094
1095LYuk := If[FeynmanGauge,
1096
1097      Module[{s,r,n,m,i},                                                                -
1098              yd[m] CKM[n,m]     uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2)              -
1099              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2]   -
1100         
1101              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2 -I phi)/Sqrt[2]   + (*This sign from eps matrix*)
1102              yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)   
1103       
1104             - yl[n]    Can[n]    anti[nL][s,n].ProjP[s,r].l[r,n]      (-I phi2)
1105             + yl[n]    San[n]    anti[nH][s,n].ProjP[s,r].l[r,n]      (-I phi2)
1106
1107             - yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] +
1108              ynd[n]  San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n]         (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]+
1109              ynd[n]  San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n]         (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]-
1110
1111              ynd[n]  (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n]         (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]
1112
1113            - ynd[n]    San[n]    lbar[s,n].ProjP[s,r].nL[r,n]                       (I phi2bar)  +
1114              ynd[n]    Can[n]    lbar[s,n].ProjP[s,r].nH[r,n]                       (I phi2bar)  +
1115
1116              ynm[n] San[n] San[n]  anti[nL][s,n].ProjP[s,r].nL[r,n]          (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]-
1117              ynm[n] Can[n] Can[n]   anti[nH][s,n].ProjP[s,r].nH[r,n]          (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]-
1118
1119              ynm[n] 2 San[n] Can[n]  anti[nL][s,n].ProjP[s,r].nH[r,n]         (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]
1120
1121
1122           ],
1123           
1124           Module[{s,r,n,m,i},                                                              -
1125              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2]  -
1126              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2] 
1127
1128             - yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+Ca*H1+Sa*H2)/Sqrt[2] +
1129              ynd[n]  San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n]         (v+Ca*H1+Sa*H2)/Sqrt[2]+
1130              ynd[n]  San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n]         (v+Ca*H1+Sa*H2)/Sqrt[2]-
1131
1132              ynd[n]  (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n]         (v+Ca*H1+Sa*H2)/Sqrt[2]+
1133
1134
1135
1136              ynm[n] San[n] San[n]  anti[nL][s,n].ProjP[s,r].nL[r,n]          (x-Sa*H1+Ca*H2)/Sqrt[2]-
1137              ynm[n] Can[n] Can[n]   anti[nH][s,n].ProjP[s,r].nH[r,n]          (x-Sa*H1+Ca*H2)/Sqrt[2]-
1138
1139              ynm[n] 2 San[n] Can[n]  anti[nL][s,n].ProjP[s,r].nH[r,n]         (x-Sa*H1+Ca*H2)/Sqrt[2]
1140
1141           ]
1142         ];
1143
1144LYukawa := LYuk + HC[LYuk];
1145
1146
1147
1148(**************Ghost terms**************************)
1149(* Now we need the ghost terms which are of the form:             *)
1150(* - g * antighost * d_BRST G                                     *)
1151(* where d_BRST G is BRST transform of the gauge fixing function. *)
1152
1153LGhost := If[FeynmanGauge,
1154                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB, dBRSTBp, LGhostBp},
1155               
1156        (***********First the pure gauge piece.**********************) 
1157        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1158                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1159       
1160        dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
1161                LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];   
1162       
1163        dBRSTB[mu_] := cw/ee del[ghB, mu];
1164                LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
1165
1166        dBRSTBp[mu_] := 1/g1p del[ghBp, mu];
1167                LGhostBp := - g1p ghBpbar.del[dBRSTBp[mu],mu];
1168       
1169        (***********Next the piece from the scalar field.************)
1170        LGhostphi :=
1171        (*-   ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA )  +
1172                    I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
1173                     ee/(2*sw) MW ( ( (v+Ca*H1+Sa*H2) + I phi) ghWpbar.ghWp +
1174                  ( (v+Ca*H1+Sa*H2) - I phi) ghWmbar.ghWm   ) -
1175                I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
1176                                  ee/(2*sw*cw) MZ (v+Ca*H1+Sa*H2) ghZbar.ghZ *)
1177
11781/4*gw*v (-gw*(v+Ca*H1+Sa*H2) ghWibar[1].ghWi[1] +g1 phic[2] ghWibar[1].ghB +gw phic[2] ghWibar[1].ghWi[3] -gw phi ghWibar[1].ghWi[2] + gt phic[2] ghWibar[1].ghBp) +
11791/4*gw*v (-gw*(v+Ca*H1+Sa*H2) ghWibar[2].ghWi[2] -g1 phic[1] ghWibar[2].ghB -gw phic[1] ghWibar[2].ghWi[3] +gw phi ghWibar[2].ghWi[1] -gt phic[1] ghWibar[2].ghBp) +
11801/4*gw*v (g1*(v+Ca*H1+Sa*H2) ghWibar[3].ghB -gw*(v+Ca*H1+Sa*H2) ghWibar[3].ghWi[3] +gw phic[1] ghWibar[3].ghWi[2]
1181-gw phic[2] ghWibar[3].ghWi[1]   +gt (v+Ca*H1+Sa*H2) ghWibar[3].ghBp ) +
11821/4*g1*v (-g1*(v+Ca*H1+Sa*H2) ghBbar.ghB +gw*(v+Ca*H1+Sa*H2) ghBbar.ghWi[3] -gw phic[1] ghBbar.ghWi[2] +gw phic[2] ghBbar.ghWi[1] -gt*(v+Ca*H1+Sa*H2) ghBbar.ghBp) +
11831/4*gt*v (-g1*(v+Ca*H1+Sa*H2) ghBpbar.ghB +gw*(v+Ca*H1+Sa*H2) ghBpbar.ghWi[3] -gw phic[1] ghBpbar.ghWi[2] +gw phic[2] ghBpbar.ghWi[1] -gt (v+Ca*H1+Sa*H2) ghBpbar.ghBp) -
11844*g1p^2*x*(x-Sa*H1+Ca*H2) ghBpbar.ghBp
1185;
1186                       
1187        (***********Now add the pieces together.********************)
1188        LGhostG + LGhostWi + LGhostB + LGhostphi + LGhostBp ]
1189
1190,
1191
1192        (*If unitary gauge, only include the gluonic ghost.*)
1193                Block[{dBRSTG,LGhostG},
1194               
1195        (***********First the pure gauge piece.**********************) 
1196        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1197                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];                 
1198                       
1199        (***********Now add the pieces together.********************)
1200        LGhostG]
1201
1202];
1203               
1204(*********Total SM Lagrangian*******)           
1205LmZp := LGauge + LHiggs + LFermions + LYukawa  + LGhost;