RSmodel: RS.fr

File RS.fr, 29.0 KB (added by PriscilaAquino, 8 years ago)

RS model file

Line 
1(***************************************************************************************************************)
2(******               This is the FeynRules mod-file for the Large Extra Dimensions                       ******)
3(******                                                                                                   ******)
4(******     Author: Priscila de Aquino                                                                ******)
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$ModelName = "RS";
13
14M$Information = {Authors -> {"Priscila de Aquino"},
15             Date -> "22.11.2011",
16             Institute -> {"Katholieke Universiteit Leuven & Universite Catholique Louvain - CP3"},
17             Emails -> {"priscila@itf.kuleuven.be"},
18             Version -> "2.1"};
19
20FeynmanGauge = False;
21
22
23(*****************************************************************************************)
24(****************************** Index definitions ****************************************)
25(*****************************************************************************************)
26
27IndexRange[ Index[Generation] ] = Range[3]
28
29IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
30
31IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
32
33IndexRange[Index[SU2W]] = Unfold[Range[3]]
34
35IndexStyle[Colour, i]
36
37IndexStyle[Generation, f]
38
39IndexStyle[Gluon ,a]
40
41IndexStyle[SU2W ,k]
42
43(*****************************************************************************************)
44(*************************************  Parameters ***************************************)
45(*****************************************************************************************)
46
47M$Parameters = {
48
49  (* External parameters *)
50
51  \[Alpha]EWM1== {
52        ParameterType -> External,
53        BlockName -> SMINPUTS,
54        ParameterName -> aEWM1,
55        InteractionOrder -> {QED, -2},
56        Value -> 127.9,
57        Description -> "Inverse of the electroweak coupling constant"},
58
59  Gf == {
60        ParameterType -> External,
61        BlockName -> SMINPUTS,
62        InteractionOrder -> {QED, 2},
63        Value -> 1.166 * 10^(-5),
64        Description -> "Fermi constant"},
65
66  \[Alpha]S == {
67        ParameterType -> External,
68        BlockName -> SMINPUTS,
69        ParameterName -> aS,
70        InteractionOrder -> {QCD, 2},
71        Value -> 0.118,
72        Description -> "Strong coupling constant at the Z pole."},
73
74  ymc == {
75        ParameterType -> External,
76        BlockName -> YUKAWA,
77        Value -> 1.42,
78        OrderBlock -> {4},
79        Description -> "Charm Yukawa mass"},
80
81 ymb == {
82        ParameterType -> External,
83        BlockName -> YUKAWA,
84        Value -> 4.2,
85        OrderBlock -> {5},
86        Description -> "Bottom Yukawa mass"},
87
88  ymt == {
89        ParameterType -> External,
90        BlockName -> YUKAWA,
91        Value -> 174.3,
92        OrderBlock -> {6},
93        Description -> "Top Yukawa mass"},
94
95  ymtau == {
96        ParameterType -> External,
97        BlockName -> YUKAWA,
98        Value -> 1.777,
99        OrderBlock -> {15},
100        Description -> "Tau Yukawa mass"},
101
102    LRS == {
103        ParameterType -> External,
104        Value -> 3000,
105        Description -> "Cutoff of the theory"},
106
107   (* Internal Parameters *)
108
109  \[Alpha]EW == {
110        ParameterType -> Internal,
111        Value -> 1/\[Alpha]EWM1,
112        ParameterName -> aEW,
113        InteractionOrder -> {QED, 2},
114        Description -> "Electroweak coupling contant"},
115
116  sw2 == {
117        ParameterType -> External,
118(*        Value -> 1-(MW/MZ)^2, *)
119        Value -> 0.2312,
120        Description -> "Squared Sin of the Weinberg angle"},
121
122   ee == {
123        TeX -> e,
124        ParameterType -> Internal,
125        Value -> Sqrt[4 Pi \[Alpha]EW],
126        InteractionOrder -> {QED, 1},
127        Description -> "Electric coupling constant"},
128
129   cw == {
130        TeX -> Subscript[c, w],
131        ParameterType -> Internal,
132        Value -> Sqrt[1 - sw2],
133        Description -> "Cos of the Weinberg angle"}, 
134
135   sw == {
136        TeX -> Subscript[s, w],
137        ParameterType -> Internal,
138        Value -> Sqrt[sw2],
139        Description -> "Sin of the Weinberg angle"}, 
140
141   gw == {
142        TeX -> Subscript[g, w],
143        ParameterType -> Internal,
144        Value -> ee / sw,
145        InteractionOrder -> {QED, 1},
146        Description -> "Weak coupling constant"},
147
148   g1 == {
149        TeX -> Subscript[g, 1],
150        ParameterType -> Internal,
151        Value -> ee / cw,
152        InteractionOrder -> {QED, 1},
153        Description -> "U(1)Y coupling constant"},
154
155   gs == {
156        TeX -> Subscript[g, s],
157        ParameterType -> Internal,
158        Value -> Sqrt[4 Pi \[Alpha]S],
159        InteractionOrder -> {QCD, 1},
160        ParameterName -> G,
161        Description -> "Strong coupling constant"},
162
163   v == {
164        ParameterType -> Internal,
165        Value -> 2*MW*sw/ee,
166        InteractionOrder -> {QED, -1},
167        Description -> "Higgs VEV"},
168
169   \[Lambda] == {
170        ParameterType -> Internal,
171        Value -> MH^2/(2*v^2),
172        InteractionOrder -> {QED, 2},
173        ParameterName -> lam,
174        Description -> "Higgs quartic coupling"},
175
176   muH == {
177        ParameterType -> Internal,
178        Value -> Sqrt[v^2 \[Lambda]],
179        TeX -> \[Mu],
180        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
181
182
183   yl == {
184        Indices -> {Index[Generation]},
185        AllowSummation -> True,
186        ParameterType -> Internal,
187        Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v},
188        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
189        InteractionOrder -> {QED, 1},
190        ComplexParameter -> False,
191        Description -> "Lepton Yukawa coupling"},
192
193   yu == {
194        Indices -> {Index[Generation]},
195        AllowSummation -> True,
196        ParameterType -> Internal,
197        Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
198        ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
199        InteractionOrder -> {QED, 1},
200        ComplexParameter -> False,
201        Description -> "U-quark Yukawa coupling"},
202
203   yd == {
204        Indices -> {Index[Generation]},
205        AllowSummation -> True,
206        ParameterType -> Internal,
207        Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
208        ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
209        InteractionOrder -> {QED, 1},
210        ComplexParameter -> False,
211        Description -> "D-quark Yukawa coupling"},
212
213   cabi == {
214        TeX -> Subscript[\[Theta], c],
215        ParameterType -> External,
216        BlockName -> CKMBLOCK,
217        OrderBlock -> {1},
218        Value -> 0.488,
219        Description -> "Cabibbo angle"},
220
221  CKM == {
222       Indices -> {Index[Generation], Index[Generation]},
223       TensorClass -> CKM,
224       Unitary -> True,
225       Value -> {CKM[1,1] -> 1,
226                   CKM[1,2] -> 0,
227                   CKM[2,1] -> 0,
228                   CKM[2,2] -> 1,
229                   CKM[1,3] -> 0,
230                   CKM[3,1] -> 0,
231                   CKM[2,3] -> 0,
232                   CKM[3,2] -> 0,
233                   CKM[3,3] -> 1},
234       Description -> "CKM-Matrix"},
235
236   kappa == {
237        TeX -> \[Kappa]_F,
238        ParameterType -> Internal,
239(*        Value -> Sqrt[16 Pi GN] *)
240        InteractionOrder -> {QTD, 1},
241        Value -> 2/LRS}
242}
243
244TeXFormat[mphi, Subscript[m, phi]]
245TeXFormat[mpsi, Subscript[m, psi]]
246TeXFormat[mG, Subscript[m, G]]
247
248(*****************************************************************************************)
249(********************************* Gauge Groups ******************************************)
250(*****************************************************************************************)
251
252M$GaugeGroups = {
253
254  U1Y == {
255        Abelian -> True,
256        GaugeBoson -> B,
257        Charge -> Y,
258        CouplingConstant -> g1},
259
260  SU2L == {
261        Abelian -> False,
262        GaugeBoson -> Wi,
263        StructureConstant -> Eps,
264        CouplingConstant -> gw},
265
266  SU3C == {
267        Abelian -> False,
268        GaugeBoson -> G,
269        StructureConstant -> f,
270        SymmetricTensor -> dSUN,
271        Representations -> {T, Colour},
272        CouplingConstant -> gs}
273}
274(*****************************************************************************************)
275(******************************* Particle Classes ****************************************)
276(*****************************************************************************************)
277
278M$ClassesDescription = {
279
280(************************************ Fermions *******************************************)
281
282        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
283  F[1] == {
284        ClassName -> vl,
285        ClassMembers -> {ve,vm,vt},
286        FlavorIndex -> Generation,
287        SelfConjugate -> False,
288        Indices -> {Index[Generation]},
289        Mass -> 0,
290        Width -> 0,
291        QuantumNumbers -> {LeptonNumber -> 1},
292        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
293        PropagatorType -> S,
294        PropagatorArrow -> Forward,
295        PDG -> {12,14,16},
296        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
297
298        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
299  F[2] == {
300        ClassName -> l,
301        ClassMembers -> {e, m, tt},
302        FlavorIndex -> Generation,
303        SelfConjugate -> False,
304        Indices -> {Index[Generation]},
305        Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
306        Width -> 0,
307        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
308        PropagatorLabel -> {"l", "e", "m", "tt"},
309        PropagatorType -> Straight,
310        ParticleName -> {"e-", "m-", "tt-"},
311        AntiParticleName -> {"e+", "m+", "tt+"},
312        PropagatorArrow -> Forward,
313        PDG -> {11, 13, 15},
314        FullName -> {"Electron", "Muon", "Tau"} },
315
316        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
317  F[3] == {
318        ClassMembers -> {u, c, t},
319        ClassName -> uq,
320        FlavorIndex -> Generation,
321        SelfConjugate -> False,
322        Indices -> {Index[Generation], Index[Colour]},
323        Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
324        Width -> {0, 0, {WT, 1.51013490}},
325        QuantumNumbers -> {Q -> 2/3},
326        PropagatorLabel -> {"uq", "u", "c", "t"},
327        PropagatorType -> Straight,
328        PropagatorArrow -> Forward,
329        PDG -> {2, 4, 6},
330        FullName -> {"u-quark", "c-quark", "t-quark"}},
331
332        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
333  F[4] == {
334        ClassMembers -> {d, s, b},
335        ClassName -> dq,
336        FlavorIndex -> Generation,
337        SelfConjugate -> False,
338        Indices -> {Index[Generation], Index[Colour]},
339        Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.2}},
340        Width -> 0,
341        QuantumNumbers -> {Q -> -1/3},
342        PropagatorLabel -> {"dq", "d", "s", "b"},
343        PropagatorType -> Straight,
344        PropagatorArrow -> Forward,
345        PDG -> {1,3,5},
346        FullName -> {"d-quark", "s-quark", "b-quark"} },
347
348(************************************ Gauge Bosons ***************************************)
349
350        (* Gauge bosons: Q = 0 *)
351  V[1] == {
352        ClassName -> A,
353        SelfConjugate -> True,
354        Indices -> {},
355        Mass -> 0,
356        Width -> 0,
357        PropagatorLabel -> "a",
358        PropagatorType -> W,
359        PropagatorArrow -> None,
360        PDG -> 22,
361        FullName -> "Photon" },
362
363  V[2] == {
364        ClassName -> Z,
365        SelfConjugate -> True,
366        Indices -> {},
367        Mass -> {MZ, 91.5445000},
368        Width -> {WZ, 2.44639985},
369        PropagatorLabel -> "Z",
370        PropagatorType -> Sine,
371        PropagatorArrow -> None,
372        PDG -> 23,
373        FullName -> "Z" },
374
375        (* Gauge bosons: Q = -1 *)
376  V[3] == {
377        ClassName -> W,
378        SelfConjugate -> False,
379        Indices -> {},
380        Mass -> {MW, 80.2673592},
381        Width -> {WW, 2.03535570},
382        QuantumNumbers -> {Q -> 1},
383        PropagatorLabel -> "W",
384        PropagatorType -> Sine,
385        PropagatorArrow -> Forward,
386        ParticleName ->"W+",
387        AntiParticleName ->"W-",
388        PDG -> 24,
389        FullName -> "W" },
390
391V[4] == {
392        ClassName -> G,
393        SelfConjugate -> True,
394        Indices -> {Index[Gluon]},
395        Mass -> {mG,0},
396        Width -> 0,
397        PropagatorLabel -> G,
398        PropagatorType -> C,
399        PropagatorArrow -> None,
400        PDG -> 21,
401        FullName -> "G" },
402
403V[5] == {
404        ClassName -> Wi,
405        Unphysical -> True,
406        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
407                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
408                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
409        SelfConjugate -> True,
410        Indices -> {Index[SU2W]},
411        FlavorIndex -> SU2W,
412        Mass -> 0,
413        PDG -> {1,2,3}},
414
415V[6] == {
416        ClassName -> B,
417        SelfConjugate -> True,
418        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
419        Indices -> {},
420        Mass -> 0,
421        Unphysical -> True},
422
423(********** Ghosts **********)
424        U[1] == {
425       ClassName -> ghA,
426       SelfConjugate -> False,
427       Indices -> {},
428       Ghost -> A,
429       Mass -> 0,
430       QuantumNumbers -> {GhostNumber -> 1},
431       PropagatorLabel -> uA,
432       PropagatorType -> GhostDash,
433       PropagatorArrow -> Forward},
434
435        U[2] == {
436       ClassName -> ghZ,
437       SelfConjugate -> False,
438       Indices -> {},
439       Mass -> {MZ, 91.188},
440       Ghost -> Z,
441       QuantumNumbers -> {GhostNumber -> 1},
442       PropagatorLabel -> uZ,
443       PropagatorType -> GhostDash,
444       PropagatorArrow -> Forward},
445
446        U[31] == {
447       ClassName -> ghWp,
448       SelfConjugate -> False,
449       Indices -> {},
450       Mass -> {MW, 80.2673592},
451       Ghost -> W,
452       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
453       PropagatorLabel -> uWp,
454       PropagatorType -> GhostDash,
455       PropagatorArrow -> Forward},
456
457   U[32] == {
458       ClassName -> ghWm,
459       SelfConjugate -> False,
460       Indices -> {},
461       Mass -> {MW, 80.2673592},
462       Ghost -> Wbar,
463       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
464       PropagatorLabel -> uWm,
465       PropagatorType -> GhostDash,
466       PropagatorArrow -> Forward},
467
468        U[4] == {
469       ClassName -> ghG,
470       SelfConjugate -> False,
471       Indices -> {Index[Gluon]},
472       Ghost -> G,
473       Mass -> 0,
474       QuantumNumbers -> {GhostNumber -> 1},
475       PropagatorLabel -> uG,
476       PropagatorType -> GhostDash,
477       PropagatorArrow -> Forward},
478
479        U[5] == {
480        ClassName -> ghWi,
481        Unphysical -> True,
482        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
483                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
484                        ghWi[3] -> cw ghZ + sw ghA},
485        SelfConjugate -> False,
486        Ghost -> Wi,
487        Indices -> {Index[SU2W]},
488        FlavorIndex -> SU2W},
489
490        U[6] == {
491        ClassName -> ghB,
492        SelfConjugate -> False,
493        Definitions -> {ghB -> -sw ghZ + cw ghA},
494        Indices -> {},
495        Ghost -> B,
496        Unphysical -> True},
497
498(****************************** Scalar Fields *********************************************)
499       
500(* physical Higgs: Q = 0 *)
501  S[1] == {
502        ClassName -> H,
503        SelfConjugate -> True,
504        Mass -> {MH, 100},
505        Width -> {WH, 0.004276087},
506        PropagatorLabel -> "H",
507        PropagatorType -> D,
508        PropagatorArrow -> None,
509        PDG -> 25,
510        TeXParticleName -> "\\phi",
511        TeXClassName -> "\\phi",
512        FullName -> "H" },
513
514S[2] == {
515        ClassName -> phi,
516        SelfConjugate -> True,
517        Mass -> {MZ, 91.188},
518        Width -> Wphi,
519        PropagatorLabel -> "Phi",
520        PropagatorType -> D,
521        PropagatorArrow -> None,
522        ParticleName ->"phi0",
523        PDG -> 250,
524        FullName -> "Phi",
525        Goldstone -> Z },
526
527S[3] == {
528        ClassName -> phi2,
529        SelfConjugate -> False,
530        Mass -> {MW, 80.2673592},
531        Width -> Wphi2,
532        PropagatorLabel -> "Phi2",
533        PropagatorType -> D,
534        PropagatorArrow -> None,
535        ParticleName ->"phi+",
536        AntiParticleName ->"phi-",
537        PDG -> 251,
538        FullName -> "Phi2",
539        TeXClassName -> "\\phi^+",
540        TeXParticleName -> "\\phi^+",
541        TeXAntiParticleName -> "\\phi^-",
542        Goldstone -> W,
543        QuantumNumbers -> {Q -> 1}},
544
545(******************************* Spin 2 particles: graviton *****************************)
546
547T[1] == {
548     ClassName -> Gr,
549     SelfConjugate -> True,
550     ParticleName ->"y",
551     PDG -> 39,
552     Symmetric -> True,
553     Mass -> {MGr, 1000},
554     Width -> {WGr,10.6689}}
555
556}
557
558(*****************************************************************************************)
559(*                                                                                       *)
560(*                                   The Lagrangian                                      *)
561(*                                                                                       *)
562(*****************************************************************************************)
563
564(* Some shorthands (for nicer printing) *)
565
566Format[mu, TraditionalForm] = \[Mu];
567Format[nu, TraditionalForm] = \[Nu];
568Format[lam, TraditionalForm] = \[Lambda];
569Format[rho, TraditionalForm] = \[Rho];
570
571psi = \[Psi];
572psibar = \[Psi]bar;
573phi = \[Phi];
574phibar = \[Phi]bar;
575phiK = \[Sigma];
576
577(******************** SM Lagrangian *************************************)
578
579(******************** Gauge F^2 Lagrangian terms*************************)
580(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
581 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
582                                        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
583       
584        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
585       
586        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
587                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
588
589
590(********************* Fermion Lagrangian terms*************************)
591(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
592 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
593
594    Lkin = I uqbar.Ga[mu].del[uq, mu] +
595        I dqbar.Ga[mu].del[dq, mu] +
596        I lbar.Ga[mu].del[l, mu] +
597        I vlbar.Ga[mu].del[vl, mu];
598
599    LQCD = gs (uqbar.Ga[mu].T[a].uq +
600        dqbar.Ga[mu].T[a].dq)G[mu, a];
601
602    LBright =
603    -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +          (*Y_lR=-2*)
604        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
605        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
606
607    LBleft =
608    -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl -         (*Y_LL=-1*)
609        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
610        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
611        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
612       
613        LWleft = ee/sw/2(
614        vlbar.Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
615        lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
616       
617        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
618        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
619       
620        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
621        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
622       
623        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
624        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
625        );
626
627    Lkin + LQCD + LBright + LBleft + LWleft];
628
629(******************** Higgs Lagrangian terms****************************)
630 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
631 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
632 
633
634   
635 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
636   
637    PMVec = Table[PauliSigma[i], {i, 3}];   
638    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
639
640        (*Y_phi=1*)
641    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
642    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
643
644    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
645
646    (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
647   
648
649(*************** Yukawa Lagrangian***********************)
650LYuk := If[FeynmanGauge,
651
652      Module[{s,r,n,m,i},                                                                        -
653              yd[m] CKM[n,m]     uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2)              -
654              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2]   -
655         
656              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2]   + (*This sign from eps matrix*)       
657              yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)    -
658       
659              yl[n]              vlbar[s,n].ProjP[s,r].l[r,n]      (-I phi2)              -
660              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H +I phi)/Sqrt[2]
661           ],
662           
663           Module[{s,r,n,m,i},                                                    -
664              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
665              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
666              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]
667           ]
668         ];
669
670LYukawa := LYuk + HC[LYuk];
671
672
673
674(**************Ghost terms**************************)
675(* Now we need the ghost terms which are of the form:             *)
676(* - g * antighost * d_BRST G                                     *)
677(* where d_BRST G is BRST transform of the gauge fixing function. *)
678
679LGhost := If[FeynmanGauge,
680                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
681               
682        (***********First the pure gauge piece.**********************) 
683        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
684                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
685       
686        dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
687                LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];   
688       
689        dBRSTB[mu_] := cw/ee del[ghB, mu];
690                LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
691       
692        (***********Next the piece from the scalar field.************)
693        LGhostphi := -   ee/(2*sw*cw) MW ( - I phi2    ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA )  +
694                        I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA )    ) -
695                        ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm   ) -
696                        I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
697                        ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
698                       
699                       
700        (***********Now add the pieces together.********************)
701        LGhostG + LGhostWi + LGhostB + LGhostphi]
702
703, 0];
704               
705(*********Total SM Lagrangian*******)           
706LSM := LGauge + LHiggs + LFermions + LYukawa  + LGhost;
707
708
709(********************** Gravitational Coupling ******************************************)
710
711(*****************************************************************************************)
712(********************** Defining the cov derivatives *************************************)
713(*****************************************************************************************)
714
715covdelU[field_, mu_] :=
716  Module[{j, a},   del[field, mu] - I gs G[mu, a] T[a].field
717                 - I ee/cw 4/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
718
719covdelD[field_, mu_] :=
720  Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
721                 + I ee/cw 2/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
722
723covdelE[field_, mu_] :=
724  Module[{j, a},  del[field, mu]
725                 + I ee/cw 2 B[mu]/2 ProjP.field + I ee/cw B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
726
727(* Version 2.0 => fixed a sign problem and a factor 2 missing in the above derivative *)
728
729covdelN[field_, mu_] :=
730  Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
731
732(*****************************************************************************************)
733(******************** Defining the field strenght tensors:********************************)
734(*****************************************************************************************)
735
736FG[mu_,nu_,a1_,a2_,a3_] := del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3];
737
738FA[mu_,nu_] := del[B[nu], mu] - del[B[mu], nu];
739
740FW[mu_,nu_,i1_,i2_,i3_] := del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + ee/sw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3];
741
742
743
744(*****************************************************************************************)
745(******************* Defining the energy-momentum tensor T[mu,nu] ************************)
746(*****************************************************************************************)
747
748(* Gauge bosons *)
749
750TG[mu_,nu_]:= ( -ME[mu,nu]. (-1/4 FA[rho, sig] FA[rho,sig] - 1/4 FW[rho,sig,i1,i2,i3] FW[rho,sig, i1,i4,i5] - 1/4 FG[rho,sig,a1,a2,a3] FG[rho,sig, a1,a4,a5])
751                -FA[mu,rho] FA[nu,rho] - FW[mu,rho,i1,i2,i3] FW[nu,rho, i1,i4,i5] - FG[mu,rho,a1,a2,a3] FG[nu,rho, a1,a2,a3]);
752
753(* Fermions *)
754
755TF[mu_,nu_] := (-ME[mu,nu] (I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho]
756                          + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho]
757                          + I vlbar.(Ga[rho].covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].vl, rho]
758                          + I lbar.(Ga[rho].covdelE[l, rho]  ) -1/2 del[I lbar.Ga[rho].l, rho]
759                         
760                          + ee/sw/Sqrt[2] (uqbar.Ga[rho].ProjM.CKM.dq W[rho] + dqbar.Ga[rho].ProjM.HC[CKM].uq Wbar[rho]
761                                         + vlbar.Ga[rho].ProjM.l W[rho] + lbar.Ga[rho].ProjM.vl Wbar[rho]) )
762               + (    I/2  uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu]
763                    + I/2  uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu]                   
764                    + I/2  dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu]
765                    + I/2  dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu]
766                    + I/2  vlbar.Ga[mu].covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].vl, mu]
767                    + I/2  vlbar.Ga[nu].covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].vl, nu]                   
768                    + I/2  lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu]
769                    + I/2  lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu]  )
770
771                + ee/sw/2/Sqrt[2] (uqbar.Ga[mu].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[nu]
772                              + uqbar.Ga[nu].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].ProjM.HC[CKM].uq Wbar[mu] 
773                              + vlbar.Ga[mu].ProjM.l W[nu] + lbar.Ga[mu].ProjM.vl Wbar[nu]
774                              + vlbar.Ga[nu].ProjM.l W[mu] + lbar.Ga[nu].ProjM.vl Wbar[mu]));
775
776(* Definitions for Higgs and Yukawa *)
777
778 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
779 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
780 
781 PMVec = Table[PauliSigma[i], {i, 3}];   
782 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
783
784 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
785 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
786 
787 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
788
789
790(* Higgs *)
791
792TH[mu_, nu_] := (-ME[mu,nu].(Dcbar[Phibar, rho]).Dc[Phi, rho] + ME[mu,nu] Vphi[Phi, Phibar] +
793    (Dcbar[Phibar, mu]).Dc[Phi, nu] + (Dcbar[Phibar, nu]).Dc[Phi, mu] );
794
795(* Yukawa *)
796
797TYuk:= Module[{s,r,n,m,i},                                                    -
798              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
799              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
800              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]];
801
802TY[mu_,nu_] := -ME[mu,nu](TYuk + HC[TYuk]);
803
804
805(* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators and unitary gauge for massive gauge boson propagators. *)
806
807TGF[mu_, nu_]:= (-ME[mu,nu].(del[del[G[sig, a1], sig], rho].G[rho, a1] + del[del[A[sig], sig], rho].A[rho] +
808                                                                1/2 del[G[rho, a1], rho].del[G[rho, a1], rho] + 1/2 del[A[rho], rho].del[A[rho], rho])
809                                        + (del[del[G[rho, a1], rho], mu].G[nu, a1] + del[del[A[rho], rho], mu].A[nu] +
810                                                   del[del[G[rho, a1], rho], nu].G[mu, a1] + del[del[A[rho], rho], nu].A[mu] ));
811
812(*****************************************************************************************)
813(*******************************  Writing the lagrangian *********************************)
814(*****************************************************************************************)
815
816LagH := -kappa/2 (Gr[mu,nu] TH[mu,nu]);
817
818LagG := -kappa/2 (Gr[mu,nu] (TG[mu,nu] + TGF[mu,nu]));
819
820LagF := -kappa/2 (Gr[mu,nu] TF[mu,nu]);
821
822LagY := -kappa/2 (Gr[mu,nu] TY[mu,nu]);
823
824LagRS := LagH + LagG + LagF + LagY;
825
826LagTot := LagRS + LSM;
827
828(*****************************************************************************************)
829