SILH: SILH.2.fr

File SILH.2.fr, 25.5 KB (added by degrande, 5 years ago)
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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->"08/02/2012"
15   Institutions -> {"Universite catholique de Louvain (CP3)"},
16   Emails -> {"celine.degrande@uclouvain.be"},
17   Version -> "1.0",
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] ] = Unfold[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(****************   Orders ****************)
58
59M$InteractionOrderHierarchy = {
60{QCD, 1},
61{QED, 2},
62{NP,2}
63}
64
65M$InteractionOrderLimit = {
66{QCD, 99},
67{QED, 99},
68{NP,1}
69}
70
71
72(****************  Parameters *************)
73
74M$Parameters = {
75
76  (* External SM parameters *)
77
78  \[Alpha]EWM1== {
79        ParameterType -> External,
80        BlockName -> SMINPUTS,
81        ParameterName -> aEWM1,
82        InteractionOrder -> {QED, -2},
83        Value -> 127.9,
84        Description -> "Inverse of the electroweak coupling constant"},
85
86  Gf == {
87        ParameterType -> External,
88        BlockName -> SMINPUTS,
89        InteractionOrder -> {QED, 2},
90        Value -> 1.16639 * 10^(-5),
91        Description -> "Fermi constant"},
92
93  \[Alpha]S == {
94        ParameterType -> External,
95        BlockName -> SMINPUTS,
96        ParameterName -> aS,
97        InteractionOrder -> {QCD, 2},
98        Value -> 0.118,
99        Description -> "Strong coupling constant at the Z pole."},
100
101
102  ZM == {
103        ParameterType -> External,
104        BlockName -> SMINPUTS,
105        Value -> 91.188,
106        Description -> "Z mass"},
107
108
109  ymc == {
110        ParameterType -> External,
111        BlockName -> YUKAWA,
112        Value -> 1.42,
113        OrderBlock -> {4},
114        Description -> "Charm Yukawa mass"},
115
116  ymb == {
117        ParameterType -> External,
118        BlockName -> YUKAWA,
119        Value -> 4.7,
120        OrderBlock -> {5},
121        Description -> "Bottom Yukawa mass"},
122
123  ymt == {
124        ParameterType -> External,
125        BlockName -> YUKAWA,
126        Value -> 174.3,
127        OrderBlock -> {6},
128        Description -> "Top Yukawa mass"},
129
130  ymtau == {
131        ParameterType -> External,
132        BlockName -> YUKAWA,
133        Value -> 1.777,
134        OrderBlock -> {15},
135        Description -> "Tau Yukawa mass"},
136
137
138
139        (* External SILH Parameter *)
140
141  frho =={
142        TeX -> Subscript[f,\[Rho]],
143        ParameterType -> External,
144        Value -> 1 (*TeV*),
145        Description -> "sigma model scale"},
146
147  grho =={
148        TeX -> Subscript[g,\[Rho]],
149        ParameterType -> External,
150        Value -> 1,
151        Description -> "sigma model coupling"},
152
153  cH =={
154        TeX -> Subscript[c,H],
155        ParameterType -> External,
156        Value -> 1,
157        InteractionOrder ->{QED,-1}},
158
159  cT =={
160        TeX -> Subscript[c,T],
161        ParameterType -> External,
162        Value -> 1,
163        InteractionOrder ->{QED,-1}},
164
165  c6 =={
166        TeX -> Subscript[c,6],
167        ParameterType -> External,
168        Value -> 1,
169        InteractionOrder ->{QED,-1}},
170
171  cy =={
172        TeX -> Subscript[c,y],
173        ParameterType -> External,
174        Value -> 1,
175        InteractionOrder ->{QED,-1}},
176
177  c6W =={
178        TeX -> Subscript[c,W],
179        ParameterType -> External,
180        Value -> 1,
181        InteractionOrder ->{QED,-3}},
182
183  cB =={
184        TeX -> Subscript[c,B],
185        ParameterType -> External,
186        Value -> 1,
187        InteractionOrder ->{QED,-3}},
188
189  cHW =={
190        TeX -> Subscript[c,HW],
191        ParameterType -> External,
192        Value -> 1,
193        InteractionOrder ->{QED,-3}},
194
195  cHB =={
196        TeX -> Subscript[c,HB],
197        ParameterType -> External,
198        Value -> 1,
199        InteractionOrder ->{QED,-3}},
200
201  cga =={
202        TeX -> Subscript[c,\[Gamma]],
203        ParameterType -> External,
204        Value -> 1,
205        InteractionOrder ->{QED,-5}},
206
207  cg =={
208        TeX -> Subscript[c,g],
209        ParameterType -> External,
210        Value -> 1,
211        InteractionOrder ->{QED,-1}},
212
213  c2W =={
214        TeX -> Subscript[c,2W],
215        ParameterType -> External,
216        Value -> 1},
217
218  c2B =={
219        TeX -> Subscript[c,2B],
220        ParameterType -> External,
221        Value -> 1},
222
223  c2g =={
224        TeX -> Subscript[c,2g],
225        ParameterType -> External,
226        Value -> 1},
227
228  c3W =={
229        TeX -> Subscript[c,3W],
230        ParameterType -> External,
231        Value -> 1},
232
233  c3B =={
234        TeX -> Subscript[c,3B],
235        ParameterType -> External,
236        Value -> 1},
237
238
239   (* Internal Parameters *)
240
241  \[Alpha]EW == {
242        ParameterType -> Internal,
243        Value -> 1/\[Alpha]EWM1,
244        ParameterName -> aEW,
245        InteractionOrder -> {QED, 2},
246        Description -> "Electroweak coupling contant"},
247
248
249  MW == {
250        ParameterType -> Internal,
251        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
252        Description -> "W mass"},
253
254  sw2 == {
255        ParameterType -> Internal,
256        Value -> 1-(MW/MZ)^2,
257        Description -> "Squared Sin of the Weinberg angle"},
258
259   ee == {
260        TeX -> e,
261        ParameterType -> Internal,
262        Value -> Sqrt[4 Pi \[Alpha]EW],
263        InteractionOrder -> {QED, 1},
264        Description -> "Electric coupling constant"},
265
266   cw == {
267        TeX -> Subscript[c, w],
268        ParameterType -> Internal,
269        Value -> Sqrt[1 - sw2],
270        Description -> "Cos of the Weinberg angle"}, 
271
272   sw == {
273        TeX -> Subscript[s, w],
274        ParameterType -> Internal,
275        Value -> Sqrt[sw2],
276        Description -> "Sin of the Weinberg angle"}, 
277
278   gw == {
279        TeX -> Subscript[g, w],
280        ParameterType -> Internal,
281        Value -> ee / sw,
282        InteractionOrder -> {QED, 1},
283        Description -> "Weak coupling constant"},
284
285   g1 == {
286        TeX -> Subscript[g, 1],
287        ParameterType -> Internal,
288        Value -> ee / cw,
289        InteractionOrder -> {QED, 1},
290        Description -> "U(1)Y coupling constant"},
291
292   gs == {
293        TeX -> Subscript[g, s],
294        ParameterType -> Internal,
295        Value -> Sqrt[4 Pi \[Alpha]S],
296        InteractionOrder -> {QCD, 1},
297        ParameterName -> G,
298        Description -> "Strong coupling constant"},
299
300   v == {
301        ParameterType -> Internal,
302        Value -> 2*MW*sw/ee,
303        InteractionOrder -> {QED, -1},
304        Description -> "Higgs VEV"},
305
306   Xi == {
307          TeX -> \[Xi],
308          InteractionOrder -> {NP,1},
309        ParameterType -> Internal,
310        Value -> v^2/frho^2,
311        Description -> "ratio of frho and the Higgs vev"},
312
313   \[Lambda] == {
314        ParameterType -> Internal,
315        Value -> MH^2/(2*v^2)(1+cH*Xi-3/2 c6*Xi),
316        InteractionOrder -> {QED, 2},
317        ParameterName -> lam,
318        Description -> "Higgs quartic coupling"},
319
320   muH == {
321        ParameterType -> Internal,
322        Value -> Sqrt[v^2 \[Lambda](1+3/4 c6 Xi)],
323        TeX -> \[Mu],
324        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
325
326
327   yl == {
328        Indices -> {Index[Generation]},
329        AllowSummation -> True,
330        ParameterType -> Internal,
331        Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v (1+cy/2Xi)},
332        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
333        InteractionOrder -> {QED, 1},
334        ComplexParameter -> False,
335        Definitions -> {yl[1] -> 0, yl[2] ->0},
336        Description -> "Lepton Yukawa coupling"},
337
338   yu == {
339        Indices -> {Index[Generation]},
340        AllowSummation -> True,
341        ParameterType -> Internal,
342        Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v (1+cy/2Xi), yu[3] -> Sqrt[2] ymt / v (1+cy/2Xi)},
343        ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
344        InteractionOrder -> {QED, 1},
345        ComplexParameter -> False,
346        Definitions -> {yu[1] -> 0},
347        Description -> "U-quark Yukawa coupling"},
348
349   yd == {
350        Indices -> {Index[Generation]},
351        AllowSummation -> True,
352        ParameterType -> Internal,
353        Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v (1+cy/2Xi)},
354        ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
355        InteractionOrder -> {QED, 1},
356        ComplexParameter -> False,
357        Definitions -> {yd[1] -> 0, yd[2] -> 0},
358        Description -> "D-quark Yukawa coupling"},
359
360   cabi == {
361        TeX -> Subscript[\[Theta], c],
362        ParameterType -> External,
363        BlockName -> CKMBLOCK,
364        OrderBlock -> {1},
365        Value -> 0.488,
366        Description -> "Cabibbo angle"},
367
368  CKM == {
369       Indices -> {Index[Generation], Index[Generation]},
370       TensorClass -> CKM,
371       Unitary -> True,
372       Definitions -> {CKM[3, 3] -> 1,
373                       CKM[i_, 3] :> 0 /; i != 3,
374                       CKM[3, i_] :> 0 /; i != 3},
375       Value -> {CKM[1,2] -> Sin[cabi],
376                   CKM[1,1] -> Cos[cabi],
377                   CKM[2,1] -> -Sin[cabi],
378                   CKM[2,2] -> Cos[cabi]},
379       Description -> "CKM-Matrix"},
380
381  mrho =={
382        TeX -> Subscript[m,\[Rho]],
383        ParameterType -> Internal,
384        Value -> grho*frho,
385        Description -> "sigma model mass"}
386}
387
388
389(************** Gauge Groups ******************)
390
391M$GaugeGroups = {
392
393  U1Y == {
394        Abelian -> True,
395        GaugeBoson -> B,
396        Charge -> Y,
397        CouplingConstant -> g1},
398
399  SU2L == {
400        Abelian -> False,
401        GaugeBoson -> Wi,
402        StructureConstant -> Eps,
403        CouplingConstant -> gw},
404
405  SU3C == {
406        Abelian -> False,
407        GaugeBoson -> G,
408        StructureConstant -> f,
409        SymmetricTensor -> dSUN,
410        Representations -> {T, Colour},
411        CouplingConstant -> gs}
412}
413
414(********* Particle Classes **********)
415
416M$ClassesDescription = {
417
418(********** Fermions ************)
419        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
420  F[1] == {
421        ClassName -> vl,
422        ClassMembers -> {ve,vm,vt},
423        FlavorIndex -> Generation,
424        SelfConjugate -> False,
425        Indices -> {Index[Generation]},
426        Mass -> 0,
427        Width -> 0,
428        QuantumNumbers -> {LeptonNumber -> 1},
429        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
430        PropagatorType -> S,
431        PropagatorArrow -> Forward,
432        PDG -> {12,14,16},
433        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
434
435        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
436  F[2] == {
437        ClassName -> l,
438        ClassMembers -> {e, m, tt},
439        FlavorIndex -> Generation,
440        SelfConjugate -> False,
441        Indices -> {Index[Generation]},
442        Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
443        Width -> 0,
444        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
445        PropagatorLabel -> {"l", "e", "m", "tt"},
446        PropagatorType -> Straight,
447        ParticleName -> {"e-", "m-", "tt-"},
448        AntiParticleName -> {"e+", "m+", "tt+"},
449        PropagatorArrow -> Forward,
450        PDG -> {11, 13, 15},
451        FullName -> {"Electron", "Muon", "Tau"} },
452
453        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
454  F[3] == {
455        ClassMembers -> {u, c, t},
456        ClassName -> uq,
457        FlavorIndex -> Generation,
458        SelfConjugate -> False,
459        Indices -> {Index[Generation], Index[Colour]},
460        Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
461        Width -> {0, 0, {WT, 1.50833649}},
462        QuantumNumbers -> {Q -> 2/3},
463        PropagatorLabel -> {"uq", "u", "c", "t"},
464        PropagatorType -> Straight,
465        PropagatorArrow -> Forward,
466        PDG -> {2, 4, 6},
467        FullName -> {"u-quark", "c-quark", "t-quark"}},
468
469        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
470  F[4] == {
471        ClassMembers -> {d, s, b},
472        ClassName -> dq,
473        FlavorIndex -> Generation,
474        SelfConjugate -> False,
475        Indices -> {Index[Generation], Index[Colour]},
476        Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
477        Width -> 0,
478        QuantumNumbers -> {Q -> -1/3},
479        PropagatorLabel -> {"dq", "d", "s", "b"},
480        PropagatorType -> Straight,
481        PropagatorArrow -> Forward,
482        PDG -> {1,3,5},
483        FullName -> {"d-quark", "s-quark", "b-quark"} },
484
485(********** Ghosts **********)
486        U[1] == {
487       ClassName -> ghA,
488       SelfConjugate -> False,
489       Indices -> {},
490       Ghost -> A,
491       Mass -> 0,
492       QuantumNumbers -> {GhostNumber -> 1},
493       PropagatorLabel -> uA,
494       PropagatorType -> GhostDash,
495       PropagatorArrow -> Forward},
496
497        U[2] == {
498       ClassName -> ghZ,
499       SelfConjugate -> False,
500       Indices -> {},
501       Mass -> {MZ, 91.188},
502       Ghost -> Z,
503       QuantumNumbers -> {GhostNumber -> 1},
504       PropagatorLabel -> uZ,
505       PropagatorType -> GhostDash,
506       PropagatorArrow -> Forward},
507
508        U[31] == {
509       ClassName -> ghWp,
510       SelfConjugate -> False,
511       Indices -> {},
512       Mass -> {MW, Internal},
513       Ghost -> W,
514       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
515       PropagatorLabel -> uWp,
516       PropagatorType -> GhostDash,
517       PropagatorArrow -> Forward},
518
519   U[32] == {
520       ClassName -> ghWm,
521       SelfConjugate -> False,
522       Indices -> {},
523       Mass -> {MW, Internal},
524       Ghost -> Wbar,
525       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
526       PropagatorLabel -> uWm,
527       PropagatorType -> GhostDash,
528       PropagatorArrow -> Forward},
529
530        U[4] == {
531       ClassName -> ghG,
532       SelfConjugate -> False,
533       Indices -> {Index[Gluon]},
534       Ghost -> G,
535       Mass -> 0,
536       QuantumNumbers -> {GhostNumber -> 1},
537       PropagatorLabel -> uG,
538       PropagatorType -> GhostDash,
539       PropagatorArrow -> Forward},
540
541        U[5] == {
542        ClassName -> ghWi,
543        Unphysical -> True,
544        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
545                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
546                        ghWi[3] -> cw ghZ + sw ghA},
547        SelfConjugate -> False,
548        Ghost -> Wi,
549        Indices -> {Index[SU2W]},
550        FlavorIndex -> SU2W},
551
552        U[6] == {
553        ClassName -> ghB,
554        SelfConjugate -> False,
555        Definitions -> {ghB -> -sw ghZ + cw ghA},
556        Indices -> {},
557        Ghost -> B,
558        Unphysical -> True},
559
560(************ Gauge Bosons ***************)
561        (* Gauge bosons: Q = 0 *)
562  V[1] == {
563        ClassName -> A,
564        SelfConjugate -> True,
565        Indices -> {},
566        Mass -> 0,
567        Width -> 0,
568        PropagatorLabel -> "a",
569        PropagatorType -> W,
570        PropagatorArrow -> None,
571        PDG -> 22,
572        FullName -> "Photon" },
573
574  V[2] == {
575        ClassName -> Z,
576        SelfConjugate -> True,
577        Indices -> {},
578        Mass -> {MZ, 91.188},
579        Width -> {WZ, 2.44140351},
580        PropagatorLabel -> "Z",
581        PropagatorType -> Sine,
582        PropagatorArrow -> None,
583        PDG -> 23,
584        FullName -> "Z" },
585
586        (* Gauge bosons: Q = -1 *)
587  V[3] == {
588        ClassName -> W,
589        SelfConjugate -> False,
590        Indices -> {},
591        Mass -> {MW, Internal},
592        Width -> {WW, 2.04759951},
593        QuantumNumbers -> {Q -> 1},
594        PropagatorLabel -> "W",
595        PropagatorType -> Sine,
596        PropagatorArrow -> Forward,
597        ParticleName ->"W+",
598        AntiParticleName ->"W-",
599        PDG -> 24,
600        FullName -> "W" },
601
602V[4] == {
603        ClassName -> G,
604        SelfConjugate -> True,
605        Indices -> {Index[Gluon]},
606        Mass -> 0,
607        Width -> 0,
608        PropagatorLabel -> G,
609        PropagatorType -> C,
610        PropagatorArrow -> None,
611        PDG -> 21,
612        FullName -> "G" },
613
614V[5] == {
615        ClassName -> Wi,
616        Unphysical -> True,
617        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
618                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
619                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
620        SelfConjugate -> True,
621        Indices -> {Index[SU2W]},
622        FlavorIndex -> SU2W,
623        Mass -> 0,
624        PDG -> {1,2,3}},
625
626V[6] == {
627        ClassName -> B,
628        SelfConjugate -> True,
629        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
630        Indices -> {},
631        Mass -> 0,
632        Unphysical -> True},
633
634
635(************ Scalar Fields **********)
636        (* physical Higgs: Q = 0 *)
637  S[1] == {
638        ClassName -> H,
639        SelfConjugate -> True,
640        Mass -> {MH, 120},
641        Width -> {WH, 0.00575308848},
642        PropagatorLabel -> "H",
643        PropagatorType -> D,
644        PropagatorArrow -> None,
645        PDG -> 25,
646        FullName -> "H" },
647
648S[2] == {
649        ClassName -> phi,
650        SelfConjugate -> True,
651        Mass -> {MZ, 91.188},
652        Width -> Wphi,
653        PropagatorLabel -> "Phi",
654        PropagatorType -> D,
655        PropagatorArrow -> None,
656        ParticleName ->"phi0",
657        PDG -> 250,
658        FullName -> "Phi",
659        Goldstone -> Z },
660
661S[3] == {
662        ClassName -> phi2,
663        SelfConjugate -> False,
664        Mass -> {MW, Internal},
665        Width -> Wphi2,
666        PropagatorLabel -> "Phi2",
667        PropagatorType -> D,
668        PropagatorArrow -> None,
669        ParticleName ->"phi+",
670        AntiParticleName ->"phi-",
671        PDG -> 251,
672        FullName -> "Phi2",
673        Goldstone -> W,
674        QuantumNumbers -> {Q -> 1}}
675   
676}
677
678(*Renomalisation*)
679
680Hbare = H(1-cH Xi/2);
681Bbare[mu_] := B[mu](1+cB sw^2/cw^2*MW^2/mrho^2+cga g1^2*gw^2/grho^2*Xi/16/\[Pi]^2);
682Wibare[mu_,i_] := Wi[mu,i](1+c6W*MW^2/mrho^2);
683g1bare = g1(1-cB sw^2/cw^2*MW^2/mrho^2-cga g1^2*gw^2/grho^2*Xi/16/\[Pi]^2);
684gwbare = gw(1-c6W*MW^2/mrho^2);
685Gbare[mu_,a_] := G[mu,a](1+cg gs^2*yu[Index[Generation,3]]^2/grho^2*Xi/16/\[Pi]^2);
686gsbare = gs(1-cg gs^2*yu[Index[Generation,3]]^2/grho^2*Xi/16/\[Pi]^2);
687
688
689(*****************************************************************************************)
690
691(* SM Lagrangian *)
692
693(******************** Gauge F^2 Lagrangian terms*************************)
694(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
695 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])*
696        (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i4, i5] Wibare[mu, i4] Wibare[nu, i5]) -
697       
698        1/4 (del[Bbare[nu], mu] - del[Bbare[mu], nu])^2 -
699       
700        1/4 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a2, a3] Gbare[mu, a2] Gbare[nu, a3])*
701                 (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}]];
702
703
704(********************* Fermion Lagrangian terms*************************)
705(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
706 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
707
708    Lkin = I uqbar.Ga[mu].del[uq, mu] +
709        I dqbar.Ga[mu].del[dq, mu] +
710        I lbar.Ga[mu].del[l, mu] +
711        I vlbar.Ga[mu].del[vl, mu];
712
713    LQCD = gs (uqbar.Ga[mu].T[a].uq +
714        dqbar.Ga[mu].T[a].dq)G[mu, a];
715
716    LBright =
717     -2g1bare Bbare[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
718        4/3*g1bare Bbare[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
719        2g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
720
721    LBleft =
722     -g1bare Bbare[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
723        g1bare Bbare[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
724        g1bare/3 Bbare[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
725        g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
726       
727        LWleft = gwbare/2(
728           vlbar.Ga[mu].ProjM.vl Wibare[mu, 3] -              (*sigma3 = ( 1   0 )*)
729        lbar.Ga[mu].ProjM.l Wibare[mu, 3] +                (*         ( 0  -1 )*)
730       
731        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu](1+c6W*MW^2/mrho^2) +
732        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu](1+c6W*MW^2/mrho^2) +
733       
734        uqbar.Ga[mu].ProjM.uq Wibare[mu, 3] -              (*sigma3 = ( 1   0 )*)
735        dqbar.Ga[mu].ProjM.dq Wibare[mu, 3] +              (*         ( 0  -1 )*)
736       
737        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu](1+c6W*MW^2/mrho^2) +
738        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu](1+c6W*MW^2/mrho^2)
739        );
740
741    Normal[Series[((Lkin + LQCD + LBright + LBleft + LWleft)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]]];
742
743(******************** Higgs Lagrangian terms****************************)
744 Phi :=  {0, (v + Hbare)/Sqrt[2]};
745 Phibar := {0, (v + Hbare)/Sqrt[2]};
746
747Dc[f_, mu_] := del[f, mu] - I g1bare Bbare[mu]/2 f -I gwbare/2 (Wvec[mu].PMVec).f;
748    Dcbar[f_, mu_] :=  del[f, mu] + I g1bare Bbare[mu]/2 f + I gwbare/2 f.(Wvec[mu].PMVec);
749 
750
751
752    PMVec = Table[PauliSigma[i], {i, 3}];   
753    Wvec[mu_] := {Wibare[mu, 1], Wibare[mu, 2], Wibare[mu, 3]};
754   
755
756    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
757
758    LHiggs := Normal[Series[(((Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
759   
760
761(*************** Yukawa Lagrangian***********************)
762LYuk := Module[{s,r,n,m,i},                                                    -
763              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Hbare)/Sqrt[2]  -
764              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Hbare)/Sqrt[2]  -
765              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+Hbare)/Sqrt[2]
766           ];
767
768LYukawa := Normal[Series[((LYuk + HC[LYuk])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
769
770
771
772(**************Ghost terms**************************)
773(* Now we need the ghost terms which are of the form:             *)
774(* - g * antighost * d_BRST G                                     *)
775(* where d_BRST G is BRST transform of the gauge fixing function. *)(*Not renormalized, only if FeynmanGauge*)
776
777LGhost := 0;
778               
779(*********Total SM Lagrangian*******)           
780LSM := Normal[Series[((LGauge + LHiggs + LFermions + LYukawa  + LGhost)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
781               
782
783
784                (**************    SILH LAGRANGIAN STARTING POINT     ********************)
785(** Better to introduce some useful short-hand notation here **)
786
787
788HH = Phibar.Phi;
789HDH[mu_] := (Phibar.Dc[Phi,mu] - Dcbar[Phibar,mu].Phi);
790
791FSWVec[mu_,nu_] := {FS[Wi,mu,nu,1],FS[Wi,mu,nu,2],FS[Wi,mu,nu,3]}
792
793DB[mu_] := del[FS[B,mu,nu],nu];
794
795DG[mu_, a1_] := I del[del[G[nu, a1], mu],mu] - I del[del[G[mu, a1], nu],mu] +
796               I gs f[a1, a2, a3] (del[G[mu, a2],mu] G[nu, a3] + G[mu,a2] del[G[nu,a3],mu] +
797                ( g1 B[mu]/2 + gw/2 (Wvec[mu].PMatVec) + gs Ga[mu].T[a]))
798               (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3]);
799 
800
801(***************** SILH Lagrangian**************************)
802               
803L6HT := Normal[Series[((cH/2/frho^2         del[HH,mu] del[HH,mu] +
804        cT/2/frho^2         HDH[mu] HDH[mu])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
805
806L6 := Normal[Series[((-c6 \[Lambda]/frho^2 HH^3)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
807
808L6Y :=  Normal[Series[((-cy / frho^2 * HH * LYukawa)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
809
810       
811L6W := Normal[Series[((I c6W 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}]];
812
813
814L6B := Normal[Series[((I cB g1/2/mrho^2 HDH[mu] DB[mu])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
815
816L6HW := 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}]];
817
818L6HB := 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}]];
819
820L6Ga := 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}]];
821
822L6G :=  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}]];
823
824L62W := Normal[Series[((c2W gw^2/2/grho^2/mrho^2    (del[(1+c6W*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}]];
825
826L62B := 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}]];
827
828L62g := 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}]];
829
830L63W := 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}]];
831
832L63g := 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}]];
833
834Lvec := L62W + L62B + L62g + L63W + L63g;
835
836LSILH = Normal[Series[((L6HT + L6W + L6B + L6HW + L6HB + L6Ga + L6G + L6Y + L6)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
837