Hillmodel: HillModel.fr

File HillModel.fr, 21.1 KB (added by Claude Duhr, 16 years ago)

The model file for the Hill model

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5(**************** This is the FeynRules model-file for the Hill model **************)
6
7M$ModelName = "HillModel";
8
9M$Information = {Authors -> {"P. Aquino", "C. Duhr"},
10 Institutions -> {"Universite catholique de Louvain (CP3)"},
11 Emails -> {priscila@fma.if.usp.br, claude.duhr@uclouvain.be},
12 Date -> "14. 06. 2009",
13 Version -> "1.0",
14 References -> "\"The minimal non-minimal Standard Model\", J.J. van der Bij, Phys.Lett.B636:56-59,2006, hep-ph/0603082",
15 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/Hillmodel"};
16
17
18FeynmanGauge=False;
19
20(******* Index definitions ********)
21
22IndexRange[ Index[Generation] ] = Range[3]
23
24IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
25
26IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
27
28IndexRange[ Index[SU2W] ] = Range[3]
29
30
31IndexStyle[Colour, i]
32
33IndexStyle[Generation, f]
34
35IndexStyle[Gluon ,a]
36
37
38(**************** Parameters *************)
39
40M$Parameters = {
41
42 (* External parameters *)
43
44 \[Alpha]EW == {
45 ParameterType -> External,
46 BlockName -> SMINPUTS,
47 ParameterName -> aEW,
48 InteractionOrder -> {QED, 2},
49 Value -> 1/132.50698,
50 Description -> "Electroweak coupling constant"},
51
52 Gf == {
53 ParameterType -> External,
54 BlockName -> SMINPUTS,
55 InteractionOrder -> {QED, 2},
56 Value -> 1.16639 * 10^(-5),
57 Description -> "Fermi constant"},
58
59 \[Alpha]S == {
60 ParameterType -> External,
61 BlockName -> SMINPUTS,
62 ParameterName -> aS,
63 InteractionOrder -> {QCD, 2},
64 Value -> 0.118,
65 Description -> "Strong coupling constant"},
66
67 ZM == {
68 ParameterType -> External,
69 BlockName -> SMINPUTS,
70 Value -> 91.188,
71 Description -> "Z mass"},
72
73 ymc == {
74 ParameterType -> External,
75 BlockName -> MGYUKAWA,
76 Value -> 1.42,
77 OrderBlock -> {4},
78 Description -> "Charm Yukawa mass"},
79
80 ymb == {
81 ParameterType -> External,
82 BlockName -> MGYUKAWA,
83 Value -> 4.7,
84 OrderBlock -> {5},
85 Description -> "Bottom Yukawa mass"},
86
87 ymt == {
88 ParameterType -> External,
89 BlockName -> MGYUKAWA,
90 Value -> 174.3,
91 OrderBlock -> {6},
92 Description -> "Top Yukawa mass"},
93
94 ymtau == {
95 ParameterType -> External,
96 BlockName -> MGYUKAWA,
97 Value -> 1.777,
98 OrderBlock -> {15},
99 Description -> "Tau Yukawa mass"},
100
101 ymm == {
102 Value -> 0.105},
103
104 (* Internal Parameters *)
105
106 WM == {
107 ParameterType -> Internal,
108 Value -> Sqrt[ZM^2/2+Sqrt[ZM^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*ZM^2]],
109 Description -> "W mass"},
110
111 sw2 == {
112 ParameterType -> Internal,
113 Value -> 1-(WM/ZM)^2,
114 Description -> "Squared Sin of the Weinberg angle"},
115
116 ee == {
117 TeX -> e,
118 ParameterType -> Internal,
119 Value -> Sqrt[4 Pi \[Alpha]EW],
120 InteractionOrder -> {QED, 1},
121 Description -> "Electric coupling constant"},
122
123 cw == {
124 TeX -> Subscript[c, w],
125 ParameterType -> Internal,
126 Value -> Sqrt[1 - sw2],
127 Description -> "Cos of the Weinberg angle"},
128
129 sw == {
130 TeX -> Subscript[s, w],
131 ParameterType -> Internal,
132 Value -> Sqrt[sw2],
133 Description -> "Sin of the Weinberg angle"},
134
135 gw == {
136 TeX -> Subscript[g, w],
137 ParameterType -> Internal,
138 Value -> ee / sw,
139 InteractionOrder -> {QED, 1},
140 Description -> "Weak coupling constant"},
141
142 g1 == {
143 TeX -> Subscript[g, 1],
144 ParameterType -> Internal,
145 Value -> ee / cw,
146 InteractionOrder -> {QED, 1},
147 Description -> "U(1)Y coupling constant"},
148
149 gs == {
150 TeX -> Subscript[g, s],
151 ParameterType -> Internal,
152 Value -> Sqrt[4 Pi \[Alpha]S],
153 InteractionOrder -> {QCD, 1},
154 ParameterName -> G,
155 Description -> "Strong coupling constant"},
156
157 v == {
158 ParameterType -> Internal,
159 Value -> 2*MW*sw/ee,
160 InteractionOrder -> {QED, -1}},
161
162 \[Lambda]0 == {
163 TeX -> Subscript[\[Lambda], 0],
164 Value -> 0.2,
165 InteractionOrder -> {QED, 2},
166 ParameterName -> l0},
167
168
169 yl == {
170 Indices -> {Index[Generation]},
171 AllowSummation -> True,
172 ParameterType -> Internal,
173 ComplexParameter -> False,
174 Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> -ymtau / v},
175 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
176 InteractionOrder -> {QED, 1},
177 Definitions -> {yl[1] -> 0, yl[2] ->0},
178 Description -> "Lepton Yukawa coupling"},
179
180 yu == {
181 Indices -> {Index[Generation]},
182 AllowSummation -> True,
183 ParameterType -> Internal,
184 ComplexParameter -> False,
185 Value -> {yu[1] -> 0, yu[2] -> - ymc / v, yu[3] -> -ymt / v},
186 ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
187 InteractionOrder -> {QED, 1},
188 ComplexParameter -> False,
189 Definitions -> {yu[1] -> 0},
190 Description -> "U-quark Yukawa coupling"},
191
192 yd == {
193 Indices -> {Index[Generation]},
194 AllowSummation -> True,
195 ParameterType -> Internal,
196 ComplexParameter -> False,
197 Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> -ymb / v},
198 ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
199 InteractionOrder -> {QED, 1},
200 Definitions -> {yd[1] -> 0, yd[2] -> 0},
201 Description -> "D-quark Yukawa coupling"},
202
203 cabi == {
204 TeX -> Subscript[\[Theta], c],
205 ParameterType -> External,
206 BlockName -> CKMBLOCK,
207 OrderBlock -> {1},
208 Value -> 0.488,
209 Description -> "Cabibbo angle"},
210
211 CKM == {
212 Indices -> {Index[Generation], Index[Generation]},
213 TensorClass -> CKM,
214 Unitary -> True,
215 Definitions -> {CKM[3, 3] -> 1,
216 CKM[i_, 3] :> 0 /; i != 3,
217 CKM[3, i_] :> 0 /; i != 3},
218 Value -> {CKM[1,2] -> Sin[cabi],
219 CKM[1,1] -> Cos[cabi],
220 CKM[2,1] -> -Sin[cabi],
221 CKM[2,2] -> Cos[cabi]},
222 Description -> "CKM-Matrix"},
223
224 f1 == {Value -> 500,
225 TeX -> Subscript[f, 1],
226 InteractionOrder -> {QED, -1}},
227
228 \[Lambda]1 == {Value -> 0.2,
229 TeX -> Subscript[\[Lambda], 1],
230 InteractionOrder -> {QED, 2},
231 ParameterName -> l1},
232
233 tha == {Value -> 2.88,
234 TeX -> Subscript[\[Theta], a],
235 Description -> "Scalar mixing angle"},
236
237 ca == {ParameterType -> Internal,
238 Value -> Cos[tha],
239 TeX -> Subscript[c,a],
240 Description -> "Cos of the scalar mixing angle"},
241
242 sa == {ParameterType -> Internal,
243 Value -> Sin[tha],
244 TeX -> Subscript[s,a],
245 Description -> "Sin of the scalar mixing angle"}
246}
247
248
249(************** Gauge Groups ******************)
250
251M$GaugeGroups = {
252
253 U1Y == {
254 Abelian -> True,
255 GaugeBoson -> B,
256 Charge -> Y,
257 CouplingConstant -> ee},
258
259 SU2L == {
260 Abelian -> False,
261 GaugeBoson -> Wi,
262 StructureConstant -> ep,
263 CouplingConstant -> gw,
264 Definitions -> {ep -> Eps}},
265
266 SU3C == {
267 Abelian -> False,
268 GaugeBoson -> G,
269 StructureConstant -> f,
270 DTerm -> dSUN,
271 Representations -> {T, Colour},
272 CouplingConstant -> gs}
273}
274
275(********* Particle Classes **********)
276
277M$ClassesDescription = {
278
279(*** Fermions ***)
280
281 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
282 F[1] == {
283 ClassName -> vl,
284 ClassMembers -> {ve,vm,vt},
285 FlavorIndex -> Generation,
286 SelfConjugate -> False,
287 Indices -> {Index[Generation]},
288 Mass -> 0,
289 Width -> 0,
290 QuantumNumbers -> {LeptonNumber -> 1},
291 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
292 PropagatorType -> S,
293 PropagatorArrow -> Forward,
294 PDG -> {12,14,16},
295 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
296
297 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
298 F[2] == {
299 ClassName -> l,
300 ClassMembers -> {e, m, tt},
301 FlavorIndex -> Generation,
302 SelfConjugate -> False,
303 Indices -> {Index[Generation]},
304 Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
305 Width -> 0,
306 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
307 PropagatorLabel -> {"l", "e", "m", "tt"},
308 PropagatorType -> Straight,
309 ParticleName -> {"e-", "m-", "tt-"},
310 AntiParticleName -> {"e+", "m+", "tt+"},
311 PropagatorArrow -> Forward,
312 PDG -> {11, 13, 15},
313 FullName -> {"Electron", "Muon", "Tau"} },
314
315 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
316 F[3] == {
317 ClassMembers -> {u, c, t},
318 ClassName -> uq,
319 FlavorIndex -> Generation,
320 SelfConjugate -> False,
321 Indices -> {Index[Generation], Index[Colour]},
322 Mass -> {Mu, {MU, 0}, {MC, 0}, {MT, 174.3}},
323 Width -> {0, 0, {WT, 1.50833649}},
324 QuantumNumbers -> {Q -> 2/3},
325 PropagatorLabel -> {"uq", "u", "c", "t"},
326 PropagatorType -> Straight,
327 PropagatorArrow -> Forward,
328 PDG -> {2, 4, 6},
329 FullName -> {"u-quark", "c-quark", "t-quark"}},
330
331 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
332 F[4] == {
333 ClassMembers -> {d, s, b},
334 ClassName -> dq,
335 FlavorIndex -> Generation,
336 SelfConjugate -> False,
337 Indices -> {Index[Generation], Index[Colour]},
338 Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
339 Width -> 0,
340 QuantumNumbers -> {Q -> -1/3},
341 PropagatorLabel -> {"dq", "d", "s", "b"},
342 PropagatorType -> Straight,
343 PropagatorArrow -> Forward,
344 PDG -> {1,3,5},
345 FullName -> {"d-quark", "s-quark", "b-quark"} },
346
347(*** Gauge bosons ***)
348
349 (* Gauge bosons: Q = 0 *)
350 V[1] == {
351 ClassName -> A,
352 SelfConjugate -> True,
353 Indices -> {},
354 Mass -> 0,
355 PropagatorLabel -> "a",
356 PropagatorType -> W,
357 PropagatorArrow -> None,
358 PDG -> 22,
359 FullName -> "Photon" },
360
361 V[2] == {
362 ClassName -> Z,
363 SelfConjugate -> True,
364 Indices -> {},
365 Mass -> {MZ, 91.188},
366 Width -> {WZ, 2.44140351},
367 PropagatorLabel -> "Z",
368 PropagatorType -> Sine,
369 PropagatorArrow -> None,
370 PDG -> 23,
371 FullName -> "Z" },
372
373 (* Gauge bosons: Q = -1 *)
374 V[3] == {
375 ClassName -> W,
376 SelfConjugate -> False,
377 Indices -> {},
378 Mass -> {MW, 80.419},
379 Width -> {WW, 2.04759951},
380 QuantumNumbers -> {Q -> 1},
381 PropagatorLabel -> "W",
382 PropagatorType -> Sine,
383 PropagatorArrow -> Forward,
384 ParticleName ->"W+",
385 AntiParticleName ->"W-",
386 PDG -> 24,
387 FullName -> "W" },
388
389V[4] == {
390 ClassName -> G,
391 SelfConjugate -> True,
392 Indices -> {Index[Gluon]},
393 Mass -> 0,
394 PropagatorLabel -> {"G"},
395 PropagatorType -> C,
396 PropagatorArrow -> None,
397 PDG -> 21,
398 FullName -> "G" },
399
400V[5] == {
401 ClassName -> Wi,
402 Unphysical -> True,
403 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
404 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
405 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
406 SelfConjugate -> True,
407 Indices -> {Index[SU2W]},
408 FlavorIndex -> SU2W,
409 Mass -> 0,
410 PDG -> {1,2,3}},
411
412V[6] == {
413 ClassName -> B,
414 SelfConjugate -> True,
415 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
416 Indices -> {},
417 Mass -> 0,
418 Unphysical -> True},
419
420(*** Scalars ***)
421
422
423 (* physical Higgs: Q = 0 *)
424
425 S[1] == {
426 ClassName -> h1,
427 SelfConjugate -> True,
428 Mass -> {Mh1, 78.5},
429 Width -> {Wh1, 0.005}},
430
431S[2] == {
432 ClassName -> h2,
433 SelfConjugate -> True,
434 Mass -> {Mh2, 326},
435 Width -> {Wh2, 0.005}},
436
437S[3] == {
438 ClassName -> H,
439 SelfConjugate -> True,
440 Unphysical -> True,
441 Definitions -> {H -> ca h1- sa h2}},
442
443S[4] == {
444 ClassName -> h,
445 SelfConjugate -> True,
446 Unphysical -> True,
447 Definitions -> {h -> sa h1 +ca h2}};
448
449S[5] == {
450 ClassName -> phi,
451 SelfConjugate -> True,
452 Mass -> {Mphi, 120},
453 Width -> Wphi,
454 PropagatorLabel -> "Phi",
455 PropagatorType -> D,
456 PropagatorArrow -> None,
457 ParticleName ->"phi0",
458 PDG -> 250,
459 FullName -> "Phi",
460 Goldstone -> Z },
461
462S[6] == {
463 ClassName -> phi2,
464 SelfConjugate -> False,
465 Mass -> {Mphi2, 120},
466 Width -> Wphi2,
467 PropagatorLabel -> "Phi2",
468 PropagatorType -> D,
469 PropagatorArrow -> None,
470 ParticleName ->"phi+",
471 AntiParticleName ->"phi-",
472 PDG -> 251,
473 FullName -> "Phi2",
474 Goldstone -> W,
475 QuantumNumbers -> {Q -> 1}},
476
477
478(********* Ghost Fields ****************)(********** Ghosts **********)
479 U[1] == {
480 ClassName -> ghA,
481 SelfConjugate -> False,
482 Indices -> {},
483 Ghost -> A},
484
485 U[2] == {
486 ClassName -> ghZ,
487 SelfConjugate -> False,
488 Indices -> {},
489 Ghost -> Z},
490
491 U[31] == {
492 ClassName -> ghWp,
493 SelfConjugate -> False,
494 Indices -> {},
495 Ghost -> W,
496 QuantumNumbers -> {Q-> 1}},
497
498 U[32] == {
499 ClassName -> ghWm,
500 SelfConjugate -> False,
501 Indices -> {},
502 Ghost -> Wbar,
503 QuantumNumbers -> {Q-> -1}},
504
505 U[4] == {
506 ClassName -> ghG,
507 SelfConjugate -> False,
508 Indices -> {Index[Gluon]},
509 Ghost -> G},
510
511 U[5] == {
512 ClassName -> ghWi,
513 Unphysical -> True,
514 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
515 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
516 ghWi[3] -> cw ghZ + sw ghA},
517 SelfConjugate -> False,
518 Indices -> {Index[SU2W]},
519 FlavorIndex -> SU2W},
520
521 U[6] == {
522 ClassName -> ghB,
523 SelfConjugate -> False,
524 Definitions -> {ghB -> -sw ghZ + cw ghA},
525 Indices -> {},
526 Unphysical -> True}
527
528
529}
530
531(*****************************************************************************************)
532
533(* SM Lagrangian *)
534
535(******************** Gauge F^2 Lagrangian terms*************************)
536(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
537 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw ep[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
538 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw ep[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
539
540 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
541
542 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
543 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
544
545
546(********************* Fermion Lagrangian terms*************************)
547(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
548 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
549
550 Lkin = I uqbar.Ga[mu].del[uq, mu] +
551 I dqbar.Ga[mu].del[dq, mu] +
552 I lbar.Ga[mu].del[l, mu] +
553 I vlbar.Ga[mu].del[vl, mu];
554
555 LQCD = gs (uqbar.Ga[mu].T[a].uq +
556 dqbar.Ga[mu].T[a].dq)G[mu, a];
557
558 LBright =
559 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
560 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
561 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
562
563 LBleft =
564 -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
565 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
566 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
567 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
568
569 LWleft = ee/sw/2(
570 vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
571 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
572
573 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
574 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
575
576 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
577 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
578
579 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
580 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
581 );
582
583 Lkin + LQCD + LBright + LBleft + LWleft];
584
585(******************** Higgs Lagrangian terms****************************)
586 Phi := If[FeynmanGauge, {I phi2, (v + H - I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
587 Phibar := If[FeynmanGauge, {-I phi2bar, (v + H + I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
588
589
590
591 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
592
593 PMVec = Table[PauliSigma[i], {i, 3}];
594 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
595
596 (*Y_phi=1*)
597 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
598 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
599
600 Vphi[Phi_, Phibar_] := muH^2 Phibar.Phi + \[Lambda]0 (Phibar.Phi)^2;
601
602 (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
603
604 (*The covariant derivative in terms of physical states is: *)
605 (* ( A + (cw^2-sw^2)/2cwsw Z 1/Sqrt[2]sw W+ ) *)
606 (* D phi = id phi + e ( ) phi *)
607 (* ( 1/Sqrt[2]sw W- -1/2cwsw Z ) *)
608
609 (*From this we can determine the mixing term. *)
610 (* *)
611 (* L_mix = - MW ( W- dphi+ + W+ dphi- ) - MZ Z dphi0 *)
612 (* This term must be cancelled in the gauge fixing Lagrangian.*)
613
614
615
616(*************** Yukawa Lagrangian***********************)
617LYuk := If[FeynmanGauge,
618 Module[{s,r,n,m,i}, -
619 yd[n] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
620 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] -
621
622 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*)
623 yu[n] HC[CKM[n,m]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) -
624
625 yl[n] vlbar[s,n].ProjP[s,r].l[r,n] (-I phi2) -
626 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H +I phi)/Sqrt[2]
627 ],
628 Module[{s,r,n,m,i}, -
629 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
630
631 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]
632 -
633 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]
634 ]
635 ];
636
637LYukawa := LYuk + HC[LYuk]/.HC[v]->v;
638
639
640(************Gauge Fix terms*************************)
641LGaugeFix := If[FeynmanGauge,
642 Block[{GFG,GFW,GFWbar,GFZ,GFA},
643
644 GFG[a_] := Module[{mu}, del[G[mu,a],mu] ];
645
646 GFW := Module[{mu}, del[W[mu],mu] + MW phi2 ];
647 GFWbar := Module[{mu}, del[Wbar[mu],mu] + MW phi2bar ];
648
649 GFZ := Module[{mu}, del[Z[mu],mu] + MZ phi ];
650
651 GFA := Module[{mu}, del[A[mu],mu] ];
652
653
654 - 1/2*GFG[a]GFG[a] - GFWbar*GFW - 1/2*GFZ^2 - 1/2*GFA^2 ]
655
656, 0];
657
658 (* We can determine the mixing term from this. *)
659 (* *)
660 (* L_mix = MW ( phi+ dW- + phi- dW+ ) + MZ phi0 dZ *)
661 (* This exactly cancels the mixing term from LHiggs. *)
662
663
664
665(**************Ghost terms**************************)
666(* Now we need the ghost terms which are of the form: *)
667(* - g * antighost * d_BRST G *)
668(* where d_BRST G is BRST transform of the gauge fixing function. *)
669
670LGhost := If[FeynmanGauge,
671 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
672
673 (***********First the pure gauge piece.**********************)
674 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
675 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
676
677 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw ep[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
678 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
679
680 dBRSTB[mu_] := cw/ee del[ghB, mu];
681 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
682
683 (***********Next the piece from the scalar field.************)
684 LGhostphi := - ee/(2*sw*cw) MW ( I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) -
685 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
686 ee/(2*sw) MW ( ( (v+H) - I phi) ghWpbar.ghWp +
687 ( (v+H) + I phi) ghWmbar.ghWm ) -
688 I ee/(2*sw) MZ ( phi2bar ghZbar.ghWp - phi2 ghZbar.ghWm ) -
689 ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
690
691
692 (***********Now add the pieces together.********************)
693 LGhostG + LGhostWi + LGhostB + LGhostphi]
694
695, 0];
696
697
698(*************** Hill Lagrangian***********************)
699
700LHill := 1/2 del[h, mu]^2 - l1 (f1 (h + v^2/2/f1) - HC[Phi].Phi)^2;
701
702(*********Total SM Lagrangian*******)
703Lag := LGauge + LHiggs + LFermions + LYukawa +LGhost + LGaugeFix+ LHill;
704