HiddenAbelianHiggsModel: Hidden.fr

File Hidden.fr, 22.3 KB (added by BenjF, 8 years ago)

Model file

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1(***************************************************************************************************************)
2(******                       This is the FeynRules mod-file for the Abelian higgs model                  ******)
3(******                                                                                                   ******)
4(******     Authors: C. Duhr                                                                              ******)
5(******                                                                                                   ******)
6(***************************************************************************************************************)
7
8M$ModelName = "Abelian_Higgs_Model";
9
10
11M$Information = {Authors -> {"C. Duhr"},
12             Date -> "02. 06. 2009",
13             Institutions -> {"Universite catholique de Louvain (CP3)"},
14             Emails -> {"claude.duhr@uclouvain.be"},
15             Version -> "1.1",
16             References -> "  J. D. Wells, \"How to Find a Hidden World at the Large Hadron Collider,\", [arXiv:0803.1243 [hep-ph]]",
17             URLs   -> "http://feynrules.phys.ucl.ac.be/view/Main/HiddenAbelianHiggsModel"};
18
19(*
20   v1.1: changed name for full Lagrangian from LSM to LHAHM
21   v1.2: Benj: the lambda parameter had the same name as the leptons, which was making the code crashing.
22*)
23
24(* The U(1)X charge of the abelian Higgs is a free parameter *)
25
26qX = 1;
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[SUW2 ,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        InteractionOrder -> {QED, 2},
83        Value -> 1.16639 * 10^(-5),
84        Description -> "Fermi constant"},
85
86  \[Alpha]S == {
87        ParameterType -> External,
88        BlockName -> SMINPUTS,
89        ParameterName -> aS,
90        InteractionOrder -> {QCD, 2},
91        Value -> 0.118,
92        Description -> "Strong coupling constant at the Z pole."},
93
94
95  ymc == {
96        ParameterType -> External,
97        BlockName -> YUKAWA,
98        Value -> 1.42,
99        OrderBlock -> {4},
100        Description -> "Charm Yukawa mass"},
101
102 ymb == {
103        ParameterType -> External,
104        BlockName -> YUKAWA,
105        Value -> 4.7,
106        OrderBlock -> {5},
107        Description -> "Bottom Yukawa mass"},
108
109  ymt == {
110        ParameterType -> External,
111        BlockName -> YUKAWA,
112        Value -> 174.3,
113        OrderBlock -> {6},
114        Description -> "Top Yukawa mass"},
115
116  ymtau == {
117        ParameterType -> External,
118        BlockName -> YUKAWA,
119        Value -> 1.777,
120        OrderBlock -> {15},
121        Description -> "Tau Yukawa mass"},
122
123   \[Lambda] == {
124        ParameterType -> External,
125        BlockName -> HIGGS,
126        ParameterName -> lam,
127        Value -> 0.42568,
128        InteractionOrder -> {QED, 2},
129        Description -> "SM Higgs self-coupling"},
130
131   cabi == {
132        TeX -> Subscript[\[Theta], c],
133        ParameterType -> External,
134        BlockName -> CKMBLOCK,
135        OrderBlock -> {1},
136        Value -> 0.488,
137        Description -> "Cabibbo angle"},
138
139
140(* New hidden external parameters *)
141
142  \[Alpha]XM1 == {
143        ParameterType -> External,
144        BlockName -> HIDDEN,
145        ParameterName -> aXM1,
146        InteractionOrder -> {QED, -2},
147        Value -> 127.9,
148        Description -> "Inverse of the U(1)X coupling constant"},
149
150   \[Eta] == {
151        ParameterType -> External,
152        BlockName -> HIDDEN,
153        ParameterName -> eta,
154        Value -> 0.01,
155        Description -> "U(1)X - U(1)Y mixing parameter"},
156
157   \[Rho] == {
158        ParameterType -> External,
159        BlockName -> HIDDEN,
160        ParameterName -> rho,
161        Value -> 0.010142,
162        InteractionOrder -> {QED, 2},
163        Description -> "Abelian Higgs self-coupling"},
164 
165   \[Kappa] == {
166        ParameterType -> External,
167        BlockName -> HIDDEN,
168        ParameterName -> kap,
169        Value -> 0.0977392,
170        InteractionOrder -> {QED, 2},
171        Description -> "Coupling between the abelian and the SM Higgs"},   
172
173
174   (* Internal Parameters *)
175
176(* Weak Mixing *)
177
178   cw == {
179        TeX -> Subscript[c, w],
180        ParameterType -> Internal,
181        Value -> MW/MZ,
182        Description -> "Cos of the Weinberg angle"}, 
183
184   sw == {
185        TeX -> Subscript[s, w],
186        ParameterType -> Internal,
187        Value -> Sqrt[1-cw^2],
188        Description -> "Sin of the Weinberg angle"},
189
190(* Gauge couplings *)
191 
192  \[Alpha]EW == {
193        ParameterType -> Internal,
194        Value -> 1/\[Alpha]EWM1,
195        ParameterName -> aEW,
196        InteractionOrder -> {QED, 2},
197        Description -> "Electroweak coupling constant"},
198
199   ee == {
200        TeX -> e,
201        ParameterType -> Internal,
202        Value -> Sqrt[4 Pi \[Alpha]EW],
203        InteractionOrder -> {QED, 1},
204        Description -> "Electric coupling constant"},
205
206   gw == {
207        TeX -> Subscript[g, w],
208        ParameterType -> Internal,
209        Value -> ee / sw,
210        InteractionOrder -> {QED, 1},
211        Description -> "Weak coupling constant"},
212
213   g1 == {
214        TeX -> Subscript[g, 1],
215        ParameterType -> Internal,
216        Value -> ee / cw,
217        InteractionOrder -> {QED, 1},
218        Description -> "U(1)Y coupling constant"},
219
220   gs == {
221        TeX -> Subscript[g, s],
222        ParameterType -> Internal,
223        Value -> Sqrt[4 Pi \[Alpha]S],
224        InteractionOrder -> {QCD, 1},
225        ParameterName -> G,
226        Description -> "Strong coupling constant"},
227
228  \[Alpha]X == {
229        ParameterType -> Internal,
230        Value -> 1/\[Alpha]XM1,
231        ParameterName -> aX,
232        InteractionOrder -> {QED, 2},
233        Description -> "U(1)X coupling contant"},
234
235   gX == {
236        TeX -> Subscript[g, X],
237        ParameterType -> Internal,
238        Value -> Sqrt[4 Pi \[Alpha]X],
239        InteractionOrder -> {QED, 1},
240        Description -> "U(1)X coupling constant"},
241
242(* New scales *)
243
244  MZ0 == {
245       ParameterType -> Internal,
246       Value -> MZ,
247       Description -> "Z mass before mixing"},
248
249  MX =={
250       ParameterType -> Internal,
251       Value -> MZp,
252       Description -> "X mass before mixing"},
253
254  \[CapitalDelta]Z =={
255       ParameterType -> Internal,
256       Value -> MX^2/MZ0^2,
257       ParameterName -> DZ,
258       Description -> "Ratio of scales"},
259
260
261(* Higgs sector *)
262
263
264
265  v == {
266        ParameterType -> Internal,
267        Value -> 1/Sqrt[Gf* Sqrt[2]],
268        InteractionOrder -> {QED, -1},
269        Description -> "SM Higgs VEV"},
270
271  \[Xi] == {
272        ParameterType -> Internal,
273        Value -> MX/qX/gX,
274        InteractionOrder -> {QED, -1},
275        ParameterName -> xi,
276        Description -> "Abelian Higgs VEV"},
277
278  MH1 == {
279        ParameterType -> Internal,
280        Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 - Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]],
281        Description -> "Mass of H1"},
282
283  MH2 == {
284        ParameterType -> Internal,
285        Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 + Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]],
286        Description -> "Mass of H2"},
287
288  \[Mu]SM2 =={
289        TeX -> Subsuperscript[\[Mu], SM, 2],
290        ParameterType -> Internal,
291        Value ->  (\[Rho] v^2 + \[Kappa] \[Xi]^2)/2,
292        ParameterName -> muSM2,
293        Description -> "Quadratic SM potential term"},
294
295  \[Mu]H2 =={
296        TeX -> Subsuperscript[\[Mu], H, 2],
297        ParameterType -> Internal,
298        Value ->  (\[Kappa] v^2 + \[Lambda] \[Xi]^2)/2,
299        ParameterName -> muH2,
300        Description -> "Quadratic abelian potential term"},
301
302(* Mixing parameters *)
303 
304
305   \[Theta]a == {
306        TeX -> Subscript[\[Theta], \[Alpha]],
307        ParameterType -> Internal,
308        Value -> ArcTan[-2 sw \[Eta]/(1-sw^2 \[Eta]^2 -\[CapitalDelta]Z)]/2,
309        ParameterName  -> alp,
310        Description -> "Mixing in the weak sector"},
311
312   ca == {
313        TeX -> Subscript[c, \[Alpha]],
314        ParameterType -> Internal,
315        Value -> Cos[\[Theta]a],
316        Description -> "Cosine of alp"},
317
318   sa == {
319        TeX -> Subscript[s, \[Alpha]],
320        ParameterType -> Internal,
321        Value -> Sin[\[Theta]a],
322        Description -> "Sine of alp"},
323
324   \[Chi] == {
325        ParameterType -> Internal,
326        Value -> (Sqrt[1+4\[Eta]^2] - 1)/2/\[Eta],
327        ParameterName -> chi,
328        Description -> "kinetic mixing parameter"},
329
330(* Higgs *)
331
332    \[Theta]h == {
333        TeX -> Subscript[\[Theta], h],
334        ParameterType -> Internal,
335        Value -> ArcTan[\[Kappa] v \[Xi]/(\[Rho] \[Xi]^2 - \[Lambda] v^2)]/2,
336        ParameterName  -> th,
337        Description -> "Mixing in the Higgs sector"},
338
339   ch == {
340        TeX -> Subscript[c, h],
341        ParameterType -> Internal,
342        Value -> Cos[\[Theta]h],
343        Description -> "Cosine of th"},
344
345   sh == {
346        TeX -> Subscript[s, h],
347        ParameterType -> Internal,
348        Value -> Sin[\[Theta]h],
349        Description -> "Sine of th"},
350       
351(* Yukawa sector *)
352
353   yl == {
354        Indices -> {Index[Generation]},
355        AllowSummation -> True,
356        ParameterType -> Internal,
357        Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v},
358        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
359        InteractionOrder -> {QED, 1},
360        ComplexParameter -> False,
361        Definitions -> {yl[1] -> 0, yl[2] ->0},
362        Description -> "Lepton Yukawa coupling"},
363
364   yu == {
365        Indices -> {Index[Generation]},
366        AllowSummation -> True,
367        ParameterType -> Internal,
368        Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
369        ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
370        InteractionOrder -> {QED, 1},
371        ComplexParameter -> False,
372        Definitions -> {yu[1] -> 0},
373        Description -> "U-quark Yukawa coupling"},
374
375   yd == {
376        Indices -> {Index[Generation]},
377        AllowSummation -> True,
378        ParameterType -> Internal,
379        Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
380        ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
381        InteractionOrder -> {QED, 1},
382        ComplexParameter -> False,
383        Definitions -> {yd[1] -> 0, yd[2] -> 0},
384        Description -> "D-quark Yukawa coupling"},
385
386
387  CKM == {
388       Indices -> {Index[Generation], Index[Generation]},
389       TensorClass -> CKM,
390       Unitary -> True,
391       Definitions -> {CKM[3, 3] -> 1,
392                       CKM[i_, 3] :> 0 /; i != 3,
393                       CKM[3, i_] :> 0 /; i != 3},
394       Value -> {CKM[1,2] -> Sin[cabi],
395                   CKM[1,1] -> Cos[cabi],
396                   CKM[2,1] -> -Sin[cabi],
397                   CKM[2,2] -> Cos[cabi]},
398       Description -> "CKM-Matrix"}
399
400
401
402}
403
404
405(************** Gauge Groups ******************)
406
407M$GaugeGroups = {
408
409  U1Y == {
410        Abelian -> True,
411        GaugeBoson -> B,
412        Charge -> Y,
413        CouplingConstant -> g1},
414
415  U1X == {
416        Abelian -> True,
417        GaugeBoson -> X,
418        Charge -> QX,
419        CouplingConstant -> ee},
420
421  SU2L == {
422        Abelian -> False,
423        GaugeBoson -> Wi,
424        StructureConstant -> Eps,
425        CouplingConstant -> gw},
426
427  SU3C == {
428        Abelian -> False,
429        GaugeBoson -> G,
430        StructureConstant -> f,
431        SymmetricTensor -> dSUN,
432        Representations -> {T, Colour},
433        CouplingConstant -> gs}
434}
435
436(********* Particle Classes **********)
437
438M$ClassesDescription = {
439
440(********** Fermions ************)
441        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
442  F[1] == {
443        ClassName -> vl,
444        ClassMembers -> {ve,vm,vt},
445        FlavorIndex -> Generation,
446        SelfConjugate -> False,
447        Indices -> {Index[Generation]},
448        Mass -> 0,
449        Width -> 0,
450        QuantumNumbers -> {LeptonNumber -> 1},
451        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
452        PropagatorType -> S,
453        PropagatorArrow -> Forward,
454        PDG -> {12,14,16},
455        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
456
457        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
458  F[2] == {
459        ClassName -> l,
460        ClassMembers -> {e, m, tt},
461        FlavorIndex -> Generation,
462        SelfConjugate -> False,
463        Indices -> {Index[Generation]},
464        Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
465        Width -> 0,
466        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
467        PropagatorLabel -> {"l", "e", "m", "tt"},
468        PropagatorType -> Straight,
469        ParticleName -> {"e-", "m-", "tt-"},
470        AntiParticleName -> {"e+", "m+", "tt+"},
471        PropagatorArrow -> Forward,
472        PDG -> {11, 13, 15},
473        FullName -> {"Electron", "Muon", "Tau"} },
474
475        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
476  F[3] == {
477        ClassMembers -> {u, c, t},
478        ClassName -> uq,
479        FlavorIndex -> Generation,
480        SelfConjugate -> False,
481        Indices -> {Index[Generation], Index[Colour]},
482        Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
483        Width -> {0, 0, {WT, 1.50833649}},
484        QuantumNumbers -> {Q -> 2/3},
485        PropagatorLabel -> {"uq", "u", "c", "t"},
486        PropagatorType -> Straight,
487        PropagatorArrow -> Forward,
488        PDG -> {2, 4, 6},
489        FullName -> {"u-quark", "c-quark", "t-quark"}},
490
491        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
492  F[4] == {
493        ClassMembers -> {d, s, b},
494        ClassName -> dq,
495        FlavorIndex -> Generation,
496        SelfConjugate -> False,
497        Indices -> {Index[Generation], Index[Colour]},
498        Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
499        Width -> 0,
500        QuantumNumbers -> {Q -> -1/3},
501        PropagatorLabel -> {"dq", "d", "s", "b"},
502        PropagatorType -> Straight,
503        PropagatorArrow -> Forward,
504        PDG -> {1,3,5},
505        FullName -> {"d-quark", "s-quark", "b-quark"} },
506
507(********** Ghosts **********)
508
509        U[1] == {
510       ClassName -> ghG,
511       SelfConjugate -> False,
512       Indices -> {Index[Gluon]},
513       Ghost -> G,
514       Mass -> 0,
515       Width -> 0,
516       QuantumNumbers -> {GhostNumber -> 1},
517       PropagatorLabel -> uG,
518       PropagatorType -> GhostDash,
519       PropagatorArrow -> Forward},
520
521
522(************ Gauge Bosons ***************)
523        (* Gauge bosons: Q = 0 *)
524  V[1] == {
525        ClassName -> A,
526        SelfConjugate -> True,
527        Indices -> {},
528        Mass -> 0,
529        Width -> 0,
530        PropagatorLabel -> "a",
531        PropagatorType -> W,
532        PropagatorArrow -> None,
533        PDG -> 22,
534        FullName -> "Photon" },
535
536  V[21] == {
537        ClassName -> Z,
538        SelfConjugate -> True,
539        Indices -> {},
540        Mass -> {MZ, 91.188},
541        Width -> {WZ, 2.44140351},
542        PropagatorLabel -> "Z",
543        PropagatorType -> Sine,
544        PropagatorArrow -> None,
545        PDG -> 23,
546        FullName -> "Z" },
547
548  V[22] == {
549        ClassName -> Zp,
550        SelfConjugate -> True,
551        Indices -> {},
552        Mass -> {MZp, 500},
553        Width -> {WZp, 0.0008252},
554        PropagatorLabel -> "Zp",
555        PropagatorType -> Sine,
556        PropagatorArrow -> None,
557        PDG -> 1023,
558        FullName -> "Zp" },
559
560  V[210] == {
561        ClassName -> Bp,
562        SelfConjugate -> True,
563        Unphysical -> True,
564        Indices -> {},
565        Mass -> 0,
566        Width -> 0,
567        Definitions -> {Bp[mu_] :> cw A[mu] -sw ca Z[mu] + sw sa Zp[mu]}},
568
569  V[220] == {
570        ClassName -> Xp,
571        SelfConjugate -> True,
572        Unphysical -> True,
573        Indices -> {},
574        Mass -> 0,
575        Width -> 0,
576        Definitions -> {Xp[mu_] :> sa Z[mu] + ca Zp[mu]}},
577
578
579        (* Gauge bosons: Q = -1 *)
580  V[3] == {
581        ClassName -> W,
582        SelfConjugate -> False,
583        Indices -> {},
584        Mass -> {MW, 80.419},
585        Width -> {WW, 2.04759951},
586        QuantumNumbers -> {Q -> 1},
587        PropagatorLabel -> "W",
588        PropagatorType -> Sine,
589        PropagatorArrow -> Forward,
590        ParticleName ->"W+",
591        AntiParticleName ->"W-",
592        PDG -> 24,
593        FullName -> "W" },
594
595V[4] == {
596        ClassName -> G,
597        SelfConjugate -> True,
598        Indices -> {Index[Gluon]},
599        Mass -> 0,
600        Width -> 0,
601        PropagatorLabel -> G,
602        PropagatorType -> C,
603        PropagatorArrow -> None,
604        PDG -> 21,
605        FullName -> "G" },
606
607V[5] == {
608        ClassName -> Wi,
609        Unphysical -> True,
610        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
611                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
612                        Wi[mu_, 3] -> -cw sa Zp[mu] + cw ca  Z[mu] + sw A[mu]},
613        SelfConjugate -> True,
614        Indices -> {Index[SU2W]},
615        FlavorIndex -> SU2W,
616        Mass -> 0,
617        PDG -> {1,2,3}},
618
619V[6] == {
620        ClassName -> B,
621        SelfConjugate -> True,
622        Definitions -> {B[mu_] -> Bp[mu] + \[Eta] Xp[mu]},
623        Indices -> {},
624        Mass -> 0,
625        Unphysical -> True},
626
627V[61] == {
628        ClassName -> X,
629        SelfConjugate -> True,
630        Definitions -> {X[mu_] -> \[Chi] \[Eta] Xp[mu]},
631        Indices -> {},
632        Mass -> 0,
633        Unphysical -> True},
634
635
636
637(************ Scalar Fields **********)
638        (* physical Higgs: Q = 0 *)
639  S[11] == {
640        ClassName -> h1,
641        SelfConjugate -> True,
642        Mass -> {MH1, Internal},
643        Width -> {WH1, 0.00282299},
644        PropagatorLabel -> "h1",
645        PropagatorType -> D,
646        PropagatorArrow -> None,
647        PDG -> 25,
648        FullName -> "h1" },
649
650  S[12] == {
651        ClassName -> h2,
652        SelfConjugate -> True,
653        Mass -> {MH2, Internal},
654        Width -> {WH2, 5.23795},
655        PropagatorLabel -> "h2",
656        PropagatorType -> D,
657        PropagatorArrow -> None,
658        PDG -> 35,
659        FullName -> "h2" },
660
661  S[110] == {
662        ClassName -> H,
663        SelfConjugate -> True,
664        Unphysical -> True,
665        Definitions -> {H -> ch h1 + sh h2}},
666
667  S[120] == {
668        ClassName -> phih,
669        SelfConjugate -> False,
670        Unphysical -> True,
671        Definitions -> {phih -> \[Xi]/Sqrt[2]-sh h1 + ch h2}}
672}
673
674
675
676(*****************************************************************************************)
677
678(* SM Lagrangian *)
679
680(******************** Gauge F^2 Lagrangian terms*************************)
681(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
682 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
683                                        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
684       
685        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[X[nu], mu] - del[X[mu], nu])^2 +
686        \[Chi]/2 (del[X[nu], mu] - del[X[mu], nu]) (del[B[nu], mu] - del[B[mu], nu]) -
687       
688        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
689                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
690
691
692(********************* Fermion Lagrangian terms*************************)
693(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
694 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
695
696    Lkin = I uqbar.Ga[mu].del[uq, mu] +
697        I dqbar.Ga[mu].del[dq, mu] +
698        I lbar.Ga[mu].del[l, mu] +
699        I vlbar.Ga[mu].del[vl, mu];
700
701    LQCD = gs (uqbar.Ga[mu].T[a].uq +
702        dqbar.Ga[mu].T[a].dq)G[mu, a];
703
704    LBright =
705       -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
706        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
707        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
708
709    LBleft =
710     -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
711        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
712        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
713        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
714       
715        LWleft = ee/sw/2(
716           vlbar.Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
717        lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
718       
719        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
720        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
721       
722        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
723        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
724       
725        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
726        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
727        );
728
729    Lkin + LQCD + LBright + LBleft + LWleft];
730
731(******************** Higgs Lagrangian terms****************************)
732 Phi :=  {0, (v + H)/Sqrt[2]};
733 Phibar := {0, (v + H)/Sqrt[2]};
734 
735
736   
737 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
738   
739    PMVec = Table[PauliSigma[i], {i, 3}];   
740    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
741
742        (*Y_phi=1*)
743    Dc[f_List, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
744    Dcbar[f_List, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
745
746    Dc[phih, mu_] := del[phih, mu] -I gX qX X[mu] phih;
747    Dc[phihbar, mu_] := del[phihbar, mu] +I gX qX X[mu] phihbar;
748
749    Vphi[Phi2SM_, Phi2H_] := -\[Mu]SM2 Phi2SM + \[Lambda] (Phi2SM)^2 -
750              \[Mu]H2 Phi2H + \[Rho] (Phi2H)^2 +
751              \[Kappa] (Phi2H) (Phi2SM) ;
752
753    (* The value of qX is set at the beginning of the notebook *)
754
755    (Dcbar[Phibar, mu]).Dc[Phi, mu] + Dc[phihbar,mu] Dc[phih, mu] - Vphi[Phibar.Phi, phihbar phih]];
756   
757
758(*************** Yukawa Lagrangian***********************)
759LYuk :=    Module[{s,r,n,m,i},                                                    -
760              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
761              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
762              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]
763           ]
764
765LYukawa := LYuk + HC[LYuk];
766
767
768
769(**************Ghost terms**************************)
770(* Now we need the ghost terms which are of the form:             *)
771(* - g * antighost * d_BRST G                                     *)
772(* where d_BRST G is BRST transform of the gauge fixing function. *)
773
774LGhost :=
775                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
776               
777        (***********First the pure gauge piece.**********************) 
778        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
779                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
780                               
781        (***********Now add the pieces together.********************)
782        LGhostG]
783
784               
785(*********Total SM Lagrangian*******)           
786LHAHM := LGauge + LHiggs + LFermions + LYukawa  + LGhost;
787               
788