SILH: SILH.fr

File SILH.fr, 24.3 KB (added by claudeduhr, 8 years ago)

The model file

Line 
1(***************************************************************************************************************)
2(******                       This is the FeynRules mod-file for the SILH model                           ******)
3(******                                                                                                   ******)
4(******     Authors: C. Degrande                                                                          ******)
5(******                                                                                                   ******)
6(****** Only unitary gauge is implemented                                                                 ******)
7(****** Only the first order in \[Xi](see parameters) is implemented                                      ******)
8(***************************************************************************************************************)
9
10M$ModelName = "SILH";
11
12
13M$Information = {Authors -> {"C. Degrande"},
14   Date->"12/06/2009"
15   Institutions -> {"Universite catholique de Louvain (CP3)"},
16   Emails -> {"celine.degrande@uclouvain.be"},
17   Version -> 1,
18   URLs->"http://feynrules.phys.ucl.ac.be/view/Main/SILH"
19};
20
21
22(******* Index definitions ********)
23
24IndexRange[ Index[Generation] ] = Range[3]
25
26IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
27
28IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
29
30IndexRange[ Index[SU2W] ] = Range[3]
31
32
33IndexStyle[Colour, i]
34
35IndexStyle[Generation, f]
36
37IndexStyle[Gluon ,a]
38
39IndexStyle[SUW2 ,k]
40
41
42(******* Gauge parameters (for FeynArts) ********)
43
44GaugeXi[ V[1] ] = GaugeXi[A];
45GaugeXi[ V[2] ] = GaugeXi[Z];
46GaugeXi[ V[3] ] = GaugeXi[W];
47GaugeXi[ V[4] ] = GaugeXi[G];
48GaugeXi[ S[1] ] = 1;
49GaugeXi[ S[2] ] = GaugeXi[Z];
50GaugeXi[ S[3] ] = GaugeXi[W];
51GaugeXi[ U[1] ] = GaugeXi[A];
52GaugeXi[ U[2] ] = GaugeXi[Z];
53GaugeXi[ U[31] ] = GaugeXi[W];
54GaugeXi[ U[32] ] = GaugeXi[W];
55GaugeXi[ U[4] ] = GaugeXi[G];
56
57
58(****************  Parameters *************)
59
60M$Parameters = {
61
62  (* External SM parameters *)
63
64  \[Alpha]EWM1== {
65        ParameterType -> External,
66        BlockName -> SMINPUTS,
67        ParameterName -> aEWM1,
68        InteractionOrder -> {QED, -2},
69        Value -> 127.9,
70        Description -> "Inverse of the electroweak coupling constant"},
71
72  Gf == {
73        ParameterType -> External,
74        BlockName -> SMINPUTS,
75        InteractionOrder -> {QED, 2},
76        Value -> 1.16639 * 10^(-5),
77        Description -> "Fermi constant"},
78
79  \[Alpha]S == {
80        ParameterType -> External,
81        BlockName -> SMINPUTS,
82        ParameterName -> aS,
83        InteractionOrder -> {QCD, 2},
84        Value -> 0.118,
85        Description -> "Strong coupling constant at the Z pole."},
86
87
88  ZM == {
89        ParameterType -> External,
90        BlockName -> SMINPUTS,
91        Value -> 91.188,
92        Description -> "Z mass"},
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
124
125        (* External SILH Parameter *)
126
127  frho =={
128        TeX -> Subscript[f,\[Rho]],
129        ParameterType -> External,
130        Value -> 1 (*TeV*),
131        Description -> "sigma model scale"},
132
133  grho =={
134        TeX -> Subscript[g,\[Rho]],
135        ParameterType -> External,
136        Value -> 1,
137        Description -> "sigma model coupling"},
138
139  cH =={
140        TeX -> Subscript[c,H],
141        ParameterType -> External,
142        Value -> 1},
143
144  cT =={
145        TeX -> Subscript[c,T],
146        ParameterType -> External,
147        Value -> 1},
148
149  c6 =={
150        TeX -> Subscript[c,6],
151        ParameterType -> External,
152        Value -> 1},
153
154  cy =={
155        TeX -> Subscript[c,y],
156        ParameterType -> External,
157        Value -> 1},
158
159  cW =={
160        TeX -> Subscript[c,W],
161        ParameterType -> External,
162        Value -> 1},
163
164  cB =={
165        TeX -> Subscript[c,B],
166        ParameterType -> External,
167        Value -> 1},
168
169  cHW =={
170        TeX -> Subscript[c,HW],
171        ParameterType -> External,
172        Value -> 1},
173
174  cHB =={
175        TeX -> Subscript[c,HB],
176        ParameterType -> External,
177        Value -> 1},
178
179  cga =={
180        TeX -> Subscript[c,\[Gamma]],
181        ParameterType -> External,
182        Value -> 1},
183
184  cg =={
185        TeX -> Subscript[c,g],
186        ParameterType -> External,
187        Value -> 1},
188
189  c2W =={
190        TeX -> Subscript[c,2W],
191        ParameterType -> External,
192        Value -> 1},
193
194  c2B =={
195        TeX -> Subscript[c,2B],
196        ParameterType -> External,
197        Value -> 1},
198
199  c2g =={
200        TeX -> Subscript[c,2g],
201        ParameterType -> External,
202        Value -> 1},
203
204  c3W =={
205        TeX -> Subscript[c,3W],
206        ParameterType -> External,
207        Value -> 1},
208
209  c3B =={
210        TeX -> Subscript[c,3B],
211        ParameterType -> External,
212        Value -> 1},
213
214
215   (* Internal Parameters *)
216
217  \[Alpha]EW == {
218        ParameterType -> Internal,
219        Value -> 1/\[Alpha]EWM1,
220        ParameterName -> aEW,
221        InteractionOrder -> {QED, 2},
222        Description -> "Electroweak coupling contant"},
223
224
225  MW == {
226        ParameterType -> Internal,
227        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
228        Description -> "W mass"},
229
230  sw2 == {
231        ParameterType -> Internal,
232        Value -> 1-(MW/MZ)^2,
233        Description -> "Squared Sin of the Weinberg angle"},
234
235   ee == {
236        TeX -> e,
237        ParameterType -> Internal,
238        Value -> Sqrt[4 Pi \[Alpha]EW],
239        InteractionOrder -> {QED, 1},
240        Description -> "Electric coupling constant"},
241
242   cw == {
243        TeX -> Subscript[c, w],
244        ParameterType -> Internal,
245        Value -> Sqrt[1 - sw2],
246        Description -> "Cos of the Weinberg angle"}, 
247
248   sw == {
249        TeX -> Subscript[s, w],
250        ParameterType -> Internal,
251        Value -> Sqrt[sw2],
252        Description -> "Sin of the Weinberg angle"}, 
253
254   gw == {
255        TeX -> Subscript[g, w],
256        ParameterType -> Internal,
257        Value -> 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        InteractionOrder -> {QED, 1},
266        Description -> "U(1)Y coupling constant"},
267
268   gs == {
269        TeX -> Subscript[g, s],
270        ParameterType -> Internal,
271        Value -> Sqrt[4 Pi \[Alpha]S],
272        InteractionOrder -> {QCD, 1},
273        ParameterName -> G,
274        Description -> "Strong coupling constant"},
275
276   v == {
277        ParameterType -> Internal,
278        Value -> 2*MW*sw/ee,
279        InteractionOrder -> {QED, -1},
280        Description -> "Higgs VEV"},
281
282   \[Xi] == {
283        ParameterType -> Internal,
284        Value -> v^2/frho^2,
285        InteractionOrder -> {QED, -1},
286        Description -> "Higgs VEV"},
287
288   \[Lambda] == {
289        ParameterType -> Internal,
290        Value -> MH^2/(2*v^2)(1+cH*\[Xi]-3/2 c6*\[Xi]),
291        InteractionOrder -> {QED, 2},
292        ParameterName -> lam,
293        Description -> "Higgs quartic coupling"},
294
295   muH == {
296        ParameterType -> Internal,
297        Value -> Sqrt[v^2 \[Lambda](1+3/4 c6 \[Xi])],
298        TeX -> \[Mu],
299        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
300
301
302   yl == {
303        Indices -> {Index[Generation]},
304        AllowSummation -> True,
305        ParameterType -> Internal,
306        Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v (1+cy/2\[Xi])},
307        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
308        InteractionOrder -> {QED, 1},
309        ComplexParameter -> False,
310        Definitions -> {yl[1] -> 0, yl[2] ->0},
311        Description -> "Lepton Yukawa coupling"},
312
313   yu == {
314        Indices -> {Index[Generation]},
315        AllowSummation -> True,
316        ParameterType -> Internal,
317        Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v (1+cy/2\[Xi]), yu[3] -> Sqrt[2] ymt / v (1+cy/2\[Xi])},
318        ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
319        InteractionOrder -> {QED, 1},
320        ComplexParameter -> False,
321        Definitions -> {yu[1] -> 0},
322        Description -> "U-quark Yukawa coupling"},
323
324   yd == {
325        Indices -> {Index[Generation]},
326        AllowSummation -> True,
327        ParameterType -> Internal,
328        Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v (1+cy/2\[Xi])},
329        ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
330        InteractionOrder -> {QED, 1},
331        ComplexParameter -> False,
332        Definitions -> {yd[1] -> 0, yd[2] -> 0},
333        Description -> "D-quark Yukawa coupling"},
334
335   cabi == {
336        TeX -> Subscript[\[Theta], c],
337        ParameterType -> External,
338        BlockName -> CKMBLOCK,
339        OrderBlock -> {1},
340        Value -> 0.488,
341        Description -> "Cabibbo angle"},
342
343  CKM == {
344       Indices -> {Index[Generation], Index[Generation]},
345       TensorClass -> CKM,
346       Unitary -> True,
347       Definitions -> {CKM[3, 3] -> 1,
348                       CKM[i_, 3] :> 0 /; i != 3,
349                       CKM[3, i_] :> 0 /; i != 3},
350       Value -> {CKM[1,2] -> Sin[cabi],
351                   CKM[1,1] -> Cos[cabi],
352                   CKM[2,1] -> -Sin[cabi],
353                   CKM[2,2] -> Cos[cabi]},
354       Description -> "CKM-Matrix"},
355
356  mrho =={
357        TeX -> Subscript[m,\[Rho]],
358        ParameterType -> Internal,
359        Value -> grho*frho,
360        Description -> "sigma model mass"}
361}
362
363
364(************** Gauge Groups ******************)
365
366M$GaugeGroups = {
367
368  U1Y == {
369        Abelian -> True,
370        GaugeBoson -> B,
371        Charge -> Y,
372        CouplingConstant -> g1},
373
374  SU2L == {
375        Abelian -> False,
376        GaugeBoson -> Wi,
377        StructureConstant -> Eps,
378        CouplingConstant -> gw},
379
380  SU3C == {
381        Abelian -> False,
382        GaugeBoson -> G,
383        StructureConstant -> f,
384        SymmetricTensor -> dSUN,
385        Representations -> {T, Colour},
386        CouplingConstant -> gs}
387}
388
389(********* Particle Classes **********)
390
391M$ClassesDescription = {
392
393(********** Fermions ************)
394        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
395  F[1] == {
396        ClassName -> vl,
397        ClassMembers -> {ve,vm,vt},
398        FlavorIndex -> Generation,
399        SelfConjugate -> False,
400        Indices -> {Index[Generation]},
401        Mass -> 0,
402        Width -> 0,
403        QuantumNumbers -> {LeptonNumber -> 1},
404        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
405        PropagatorType -> S,
406        PropagatorArrow -> Forward,
407        PDG -> {12,14,16},
408        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
409
410        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
411  F[2] == {
412        ClassName -> l,
413        ClassMembers -> {e, m, tt},
414        FlavorIndex -> Generation,
415        SelfConjugate -> False,
416        Indices -> {Index[Generation]},
417        Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
418        Width -> 0,
419        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
420        PropagatorLabel -> {"l", "e", "m", "tt"},
421        PropagatorType -> Straight,
422        ParticleName -> {"e-", "m-", "tt-"},
423        AntiParticleName -> {"e+", "m+", "tt+"},
424        PropagatorArrow -> Forward,
425        PDG -> {11, 13, 15},
426        FullName -> {"Electron", "Muon", "Tau"} },
427
428        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
429  F[3] == {
430        ClassMembers -> {u, c, t},
431        ClassName -> uq,
432        FlavorIndex -> Generation,
433        SelfConjugate -> False,
434        Indices -> {Index[Generation], Index[Colour]},
435        Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
436        Width -> {0, 0, {WT, 1.50833649}},
437        QuantumNumbers -> {Q -> 2/3},
438        PropagatorLabel -> {"uq", "u", "c", "t"},
439        PropagatorType -> Straight,
440        PropagatorArrow -> Forward,
441        PDG -> {2, 4, 6},
442        FullName -> {"u-quark", "c-quark", "t-quark"}},
443
444        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
445  F[4] == {
446        ClassMembers -> {d, s, b},
447        ClassName -> dq,
448        FlavorIndex -> Generation,
449        SelfConjugate -> False,
450        Indices -> {Index[Generation], Index[Colour]},
451        Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
452        Width -> 0,
453        QuantumNumbers -> {Q -> -1/3},
454        PropagatorLabel -> {"dq", "d", "s", "b"},
455        PropagatorType -> Straight,
456        PropagatorArrow -> Forward,
457        PDG -> {1,3,5},
458        FullName -> {"d-quark", "s-quark", "b-quark"} },
459
460(********** Ghosts **********)
461        U[1] == {
462       ClassName -> ghA,
463       SelfConjugate -> False,
464       Indices -> {},
465       Ghost -> A,
466       Mass -> 0,
467       QuantumNumbers -> {GhostNumber -> 1},
468       PropagatorLabel -> uA,
469       PropagatorType -> GhostDash,
470       PropagatorArrow -> Forward},
471
472        U[2] == {
473       ClassName -> ghZ,
474       SelfConjugate -> False,
475       Indices -> {},
476       Mass -> {MZ, 91.188},
477       Ghost -> Z,
478       QuantumNumbers -> {GhostNumber -> 1},
479       PropagatorLabel -> uZ,
480       PropagatorType -> GhostDash,
481       PropagatorArrow -> Forward},
482
483        U[31] == {
484       ClassName -> ghWp,
485       SelfConjugate -> False,
486       Indices -> {},
487       Mass -> {MW, Internal},
488       Ghost -> W,
489       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
490       PropagatorLabel -> uWp,
491       PropagatorType -> GhostDash,
492       PropagatorArrow -> Forward},
493
494   U[32] == {
495       ClassName -> ghWm,
496       SelfConjugate -> False,
497       Indices -> {},
498       Mass -> {MW, Internal},
499       Ghost -> Wbar,
500       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
501       PropagatorLabel -> uWm,
502       PropagatorType -> GhostDash,
503       PropagatorArrow -> Forward},
504
505        U[4] == {
506       ClassName -> ghG,
507       SelfConjugate -> False,
508       Indices -> {Index[Gluon]},
509       Ghost -> G,
510       Mass -> 0,
511       QuantumNumbers -> {GhostNumber -> 1},
512       PropagatorLabel -> uG,
513       PropagatorType -> GhostDash,
514       PropagatorArrow -> Forward},
515
516        U[5] == {
517        ClassName -> ghWi,
518        Unphysical -> True,
519        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
520                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
521                        ghWi[3] -> cw ghZ + sw ghA},
522        SelfConjugate -> False,
523        Ghost -> Wi,
524        Indices -> {Index[SU2W]},
525        FlavorIndex -> SU2W},
526
527        U[6] == {
528        ClassName -> ghB,
529        SelfConjugate -> False,
530        Definitions -> {ghB -> -sw ghZ + cw ghA},
531        Indices -> {},
532        Ghost -> B,
533        Unphysical -> True},
534
535(************ Gauge Bosons ***************)
536        (* Gauge bosons: Q = 0 *)
537  V[1] == {
538        ClassName -> A,
539        SelfConjugate -> True,
540        Indices -> {},
541        Mass -> 0,
542        Width -> 0,
543        PropagatorLabel -> "a",
544        PropagatorType -> W,
545        PropagatorArrow -> None,
546        PDG -> 22,
547        FullName -> "Photon" },
548
549  V[2] == {
550        ClassName -> Z,
551        SelfConjugate -> True,
552        Indices -> {},
553        Mass -> {MZ, 91.188},
554        Width -> {WZ, 2.44140351},
555        PropagatorLabel -> "Z",
556        PropagatorType -> Sine,
557        PropagatorArrow -> None,
558        PDG -> 23,
559        FullName -> "Z" },
560
561        (* Gauge bosons: Q = -1 *)
562  V[3] == {
563        ClassName -> W,
564        SelfConjugate -> False,
565        Indices -> {},
566        Mass -> {MW, Internal},
567        Width -> {WW, 2.04759951},
568        QuantumNumbers -> {Q -> 1},
569        PropagatorLabel -> "W",
570        PropagatorType -> Sine,
571        PropagatorArrow -> Forward,
572        ParticleName ->"W+",
573        AntiParticleName ->"W-",
574        PDG -> 24,
575        FullName -> "W" },
576
577V[4] == {
578        ClassName -> G,
579        SelfConjugate -> True,
580        Indices -> {Index[Gluon]},
581        Mass -> 0,
582        Width -> 0,
583        PropagatorLabel -> G,
584        PropagatorType -> C,
585        PropagatorArrow -> None,
586        PDG -> 21,
587        FullName -> "G" },
588
589V[5] == {
590        ClassName -> Wi,
591        Unphysical -> True,
592        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
593                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
594                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
595        SelfConjugate -> True,
596        Indices -> {Index[SU2W]},
597        FlavorIndex -> SU2W,
598        Mass -> 0,
599        PDG -> {1,2,3}},
600
601V[6] == {
602        ClassName -> B,
603        SelfConjugate -> True,
604        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
605        Indices -> {},
606        Mass -> 0,
607        Unphysical -> True},
608
609
610(************ Scalar Fields **********)
611        (* physical Higgs: Q = 0 *)
612  S[1] == {
613        ClassName -> H,
614        SelfConjugate -> True,
615        Mass -> {MH, 120},
616        Width -> {WH, 0.00575308848},
617        PropagatorLabel -> "H",
618        PropagatorType -> D,
619        PropagatorArrow -> None,
620        PDG -> 25,
621        FullName -> "H" },
622
623S[2] == {
624        ClassName -> phi,
625        SelfConjugate -> True,
626        Mass -> {MZ, 91.188},
627        Width -> Wphi,
628        PropagatorLabel -> "Phi",
629        PropagatorType -> D,
630        PropagatorArrow -> None,
631        ParticleName ->"phi0",
632        PDG -> 250,
633        FullName -> "Phi",
634        Goldstone -> Z },
635
636S[3] == {
637        ClassName -> phi2,
638        SelfConjugate -> False,
639        Mass -> {MW, Internal},
640        Width -> Wphi2,
641        PropagatorLabel -> "Phi2",
642        PropagatorType -> D,
643        PropagatorArrow -> None,
644        ParticleName ->"phi+",
645        AntiParticleName ->"phi-",
646        PDG -> 251,
647        FullName -> "Phi2",
648        Goldstone -> W,
649        QuantumNumbers -> {Q -> 1}}
650   
651}
652
653(*Renomalisation*)
654
655Hbare = H(1-cH \[Xi]/2);
656Bbare[mu_] := B[mu](1+cB sw^2/cw^2*MW^2/mrho^2+cga g1^2*gw^2/grho^2*\[Xi]/16/\[Pi]^2);
657Wibare[mu_,i_] := Wi[mu,i](1+cW*MW^2/mrho^2);
658g1bare = g1(1-cB sw^2/cw^2*MW^2/mrho^2-cga g1^2*gw^2/grho^2*\[Xi]/16/\[Pi]^2);
659gwbare = gw(1-cW*MW^2/mrho^2);
660Gbare[mu_,a_] := G[mu,a](1+cg gs^2*yu[Index[Generation,3]]^2/grho^2*\[Xi]/16/\[Pi]^2);
661gsbare = gs(1-cg gs^2*yu[Index[Generation,3]]^2/grho^2*\[Xi]/16/\[Pi]^2);
662
663
664(*****************************************************************************************)
665
666(* SM Lagrangian *)
667
668(******************** Gauge F^2 Lagrangian terms*************************)
669(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
670 LGauge := Normal[Series[((-1/4 (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i2, i3] Wibare[mu, i2] Wibare[nu, i3])*
671        (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i4, i5] Wibare[mu, i4] Wibare[nu, i5]) -
672       
673        1/4 (del[Bbare[nu], mu] - del[Bbare[mu], nu])^2 -
674       
675        1/4 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a2, a3] Gbare[mu, a2] Gbare[nu, a3])*
676                 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a4, a5] Gbare[mu, a4] Gbare[nu, a5]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
677
678
679(********************* Fermion Lagrangian terms*************************)
680(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
681 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
682
683    Lkin = I uqbar.Ga[mu].del[uq, mu] +
684        I dqbar.Ga[mu].del[dq, mu] +
685        I lbar.Ga[mu].del[l, mu] +
686        I vlbar.Ga[mu].del[vl, mu];
687
688    LQCD = gs (uqbar.Ga[mu].T[a].uq +
689        dqbar.Ga[mu].T[a].dq)G[mu, a];
690
691    LBright =
692     -2g1bare Bbare[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
693        4/3*g1bare Bbare[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
694        2g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
695
696    LBleft =
697     -g1bare Bbare[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
698        g1bare Bbare[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
699        g1bare/3 Bbare[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
700        g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
701       
702        LWleft = gwbare/2(
703           vlbar.Ga[mu].ProjM.vl Wibare[mu, 3] -              (*sigma3 = ( 1   0 )*)
704        lbar.Ga[mu].ProjM.l Wibare[mu, 3] +                (*         ( 0  -1 )*)
705       
706        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu](1+cW*MW^2/mrho^2) +
707        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu](1+cW*MW^2/mrho^2) +
708       
709        uqbar.Ga[mu].ProjM.uq Wibare[mu, 3] -              (*sigma3 = ( 1   0 )*)
710        dqbar.Ga[mu].ProjM.dq Wibare[mu, 3] +              (*         ( 0  -1 )*)
711       
712        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu](1+cW*MW^2/mrho^2) +
713        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu](1+cW*MW^2/mrho^2)
714        );
715
716    Normal[Series[((Lkin + LQCD + LBright + LBleft + LWleft)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]];
717
718(******************** Higgs Lagrangian terms****************************)
719 Phi :=  {0, (v + Hbare)/Sqrt[2]};
720 Phibar := {0, (v + Hbare)/Sqrt[2]};
721
722Dc[f_, mu_] := del[f, mu] - I g1bare Bbare[mu]/2 f -I gwbare/2 (Wvec[mu].PMVec).f;
723    Dcbar[f_, mu_] :=  del[f, mu] + I g1bare Bbare[mu]/2 f + I gwbare/2 f.(Wvec[mu].PMVec);
724 
725
726
727    PMVec = Table[PauliSigma[i], {i, 3}];   
728    Wvec[mu_] := {Wibare[mu, 1], Wibare[mu, 2], Wibare[mu, 3]};
729   
730
731    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
732
733    LHiggs := Normal[Series[(((Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
734   
735
736(*************** Yukawa Lagrangian***********************)
737LYuk := Module[{s,r,n,m,i},                                                    -
738              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Hbare)/Sqrt[2]  -
739              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Hbare)/Sqrt[2]  -
740              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+Hbare)/Sqrt[2]
741           ];
742
743LYukawa := Normal[Series[((LYuk + HC[LYuk])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
744
745
746
747(**************Ghost terms**************************)
748(* Now we need the ghost terms which are of the form:             *)
749(* - g * antighost * d_BRST G                                     *)
750(* where d_BRST G is BRST transform of the gauge fixing function. *)(*Not renormalized, only if FeynmanGauge*)
751
752LGhost := 0;
753               
754(*********Total SM Lagrangian*******)           
755LSM := Normal[Series[((LGauge + LHiggs + LFermions + LYukawa  + LGhost)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
756               
757
758
759                (**************    SILH LAGRANGIAN STARTING POINT     ********************)
760(** Better to introduce some useful short-hand notation here **)
761
762
763HH = Phibar.Phi;
764HDH[mu_] := (Phibar.Dc[Phi,mu] - Dcbar[Phibar,mu].Phi);
765
766FSWVec[mu_,nu_] := {FS[Wi,mu,nu,1],FS[Wi,mu,nu,2],FS[Wi,mu,nu,3]}
767
768DB[mu_] := del[FS[B,mu,nu],nu];
769
770DG[mu_, a1_] := I del[del[G[nu, a1], mu],mu] - I del[del[G[mu, a1], nu],mu] +
771               I gs f[a1, a2, a3] (del[G[mu, a2],mu] G[nu, a3] + G[mu,a2] del[G[nu,a3],mu] +
772                ( g1 B[mu]/2 + gw/2 (Wvec[mu].PMatVec) + gs Ga[mu].T[a]))
773               (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3]);
774 
775
776(***************** SILH Lagrangian**************************)
777               
778L6HT := Normal[Series[((cH/2/frho^2         del[HH,mu] del[HH,mu] +
779        cT/2/frho^2         HDH[mu] HDH[mu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
780
781L6 := Normal[Series[((-c6 \[Lambda]/frho^2 HH^3)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
782
783L6Y :=  Normal[Series[((-cy / frho^2 * HH * LYukawa)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
784
785       
786L6W := Normal[Series[((I cW gw/2/mrho^2 (Phibar.PauliSigma[k].Dc[Phi,mu]-Dcbar[Phibar,mu].PauliSigma[k].Phi)*(del[FS[Wi,mu,nu,k],nu] + gw Eps[k1,k2,k] Wi[nu,k1] FS[Wi,mu,nu,k2]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
787
788
789L6B := Normal[Series[((I cB g1/2/mrho^2 HDH[mu] DB[mu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
790
791L6HW := Normal[Series[((I cHW gw/16/Pi^2/frho^2  (HC[Dc[Phi,mu]].PauliSigma[i].Dc[Phi,nu]) FS[Wi,mu,nu,i])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
792
793L6HB := Normal[Series[((I cHB g1/16/Pi^2/frho^2  (HC[Dc[Phi,mu]].Dc[Phi,nu]) FS[B,mu,nu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
794
795L6Ga := Normal[Series[((cga g1^2/16/Pi^2/frho^2 gw^2/grho^2 HH FS[B,mu,nu] FS[B,mu,nu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
796
797L6G :=  Normal[Series[((cg gs^2/16/Pi^2/frho^2 yu[Index[Generation,3]]^2/grho^2 HH FS[G,mu,nu,a] FS[G,mu,nu,a])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
798
799L62W := Normal[Series[((c2W gw^2/2/grho^2/mrho^2    (del[(1+cW*MW^2/mrho^2)FS[Wi,mu,nu,k],mu] + gw/2 Eps[k1,k2,k] Wi[mu,k1] FS[Wi,mu,nu,k2])*(del[FS[Wi,rho,nu,k],rho] + gw/2 Eps[k3,k4,k] Wi[rho,k3] FS[Wi,rho,nu,k4]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
800
801L62B := Normal[Series[((c2B g1^2/2/grho^2/mrho^2 del[FS[B,nu, mu],mu] del[FS[B,nu, rho],rho])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
802
803L62g := Normal[Series[((c2g gs^2/2/grho^2/mrho^2 (del[FS[G,mu,nu,a],mu] + gs f[a1,a2,a] G[mu,a1] FS[G,mu,nu,a2])*(del[FS[G,rho,nu,a],rho] + gs f[a3,a4,a] G[rho,a3] FS[G,rho,nu,a4]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
804
805L63W := Normal[Series[((c3W gw^3/16/Pi^2/mrho^2 Eps[i,j,k] FS[Wi,mu,nu,i] FS[Wi,nu,rho,j] FS[Wi,rho,mu,k])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
806
807L63g := Normal[Series[((c3g gs^3/16/Pi^2/mrho^2 f[a1,a2,a3] FS[G,mu,nu,a1] FS[G,nu,rho,a2] FS[G,rho,mu,a3])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
808
809Lvec := L62W + L62B + L62g + L63W + L63g;
810
811LSILH = Normal[Series[((L6HT + L6W + L6B + L6HW + L6HB + L6Ga + L6G + L6Y + L6)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
812