StandardModel: SM_old.fr

File SM_old.fr, 22.8 KB (added by Benjamin Fuks, 14 years ago)

Older implementation of the SM

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Standard model ******)
3(****** ******)
4(****** Authors: N. Christensen, C. Duhr ******)
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$ModelName = "Standard Model";
13
14
15M$Information = {Authors -> {"N. Christensen", "C. Duhr"},
16 Version -> "1.3",
17 Date -> "02. 06. 2009",
18 Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)"},
19 Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be"},
20 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"};
21
22(*
23 V1.3 - Updated Top quark mass to 2010 PDG value (172 GeV)
24 V1.2 - Set FeynmanGauge=True as default.
25 Set Gluonic ghosts to be included in both gauges.
26 V1.1 - Fixed yukawa couplings in Feynman gauge.
27 Changed yd[n] CKM[n,m] to yd[m] CKM[n,m].
28 Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]].
29 V1.3 - Added yukawa couplings for all fermions for gauge invariance.
30 Added yukawa couplings for 1st generation fermions to Massless.rst.
31 Updated parameters to PDG 2010.
32*)
33
34FeynmanGauge = True;
35
36
37(******* Index definitions ********)
38
39IndexRange[ Index[Generation] ] = Range[3]
40
41IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
42
43IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
44
45IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
46
47
48IndexStyle[Colour, i]
49
50IndexStyle[Generation, f]
51
52IndexStyle[Gluon ,a]
53
54IndexStyle[SU2W ,k]
55
56
57(******* Gauge parameters (for FeynArts) ********)
58
59GaugeXi[ V[1] ] = GaugeXi[A];
60GaugeXi[ V[2] ] = GaugeXi[Z];
61GaugeXi[ V[3] ] = GaugeXi[W];
62GaugeXi[ V[4] ] = GaugeXi[G];
63GaugeXi[ S[1] ] = 1;
64GaugeXi[ S[2] ] = GaugeXi[Z];
65GaugeXi[ S[3] ] = GaugeXi[W];
66GaugeXi[ U[1] ] = GaugeXi[A];
67GaugeXi[ U[2] ] = GaugeXi[Z];
68GaugeXi[ U[31] ] = GaugeXi[W];
69GaugeXi[ U[32] ] = GaugeXi[W];
70GaugeXi[ U[4] ] = GaugeXi[G];
71
72(***** Setting for interaction order (as e.g. used by MadGraph 5) ******)
73
74M$InteractionOrderHierarchy = {
75 {QCD, 1},
76 {QED, 2}
77 };
78
79
80(**************** Parameters *************)
81
82M$Parameters = {
83
84 (* External parameters *)
85
86 \[Alpha]EWM1== {
87 ParameterType -> External,
88 BlockName -> SMINPUTS,
89 ParameterName -> aEWM1,
90 InteractionOrder -> {QED, -2},
91 Value -> 127.9,
92 Description -> "Inverse of the electroweak coupling constant"},
93
94 Gf == {
95 ParameterType -> External,
96 BlockName -> SMINPUTS,
97 TeX -> Subscript[G, f],
98 InteractionOrder -> {QED, 2},
99 Value -> 1.16637 * 10^(-5),
100 Description -> "Fermi constant"},
101
102 \[Alpha]S == {
103 ParameterType -> External,
104 BlockName -> SMINPUTS,
105 TeX -> Subscript[\[Alpha], s],
106 ParameterName -> aS,
107 InteractionOrder -> {QCD, 2},
108 Value -> 0.1184,
109 Description -> "Strong coupling constant at the Z pole."},
110
111 ymdo == {
112 ParameterType -> External,
113 BlockName -> YUKAWA,
114 Value -> 5.04*10^(-3),
115 OrderBlock -> {1},
116 Description -> "Down Yukawa mass"},
117
118
119 ymup == {
120 ParameterType -> External,
121 BlockName -> YUKAWA,
122 Value -> 2.55*10^(-3),
123 OrderBlock -> {2},
124 Description -> "Up Yukawa mass"},
125
126 yms == {
127 ParameterType -> External,
128 BlockName -> YUKAWA,
129 Value -> 0.101,
130 OrderBlock -> {3},
131 Description -> "Strange Yukawa mass"},
132
133
134 ymc == {
135 ParameterType -> External,
136 BlockName -> YUKAWA,
137 Value -> 1.27,
138 OrderBlock -> {4},
139 Description -> "Charm Yukawa mass"},
140
141 ymb == {
142 ParameterType -> External,
143 BlockName -> YUKAWA,
144 Value -> 4.7,
145 OrderBlock -> {5},
146 Description -> "Bottom Yukawa mass"},
147
148 ymt == {
149 ParameterType -> External,
150 BlockName -> YUKAWA,
151 Value -> 172.0,
152 OrderBlock -> {6},
153 Description -> "Top Yukawa mass"},
154
155 yme == {
156 ParameterType -> External,
157 BlockName -> YUKAWA,
158 Value -> 5.11*10^(-4),
159 OrderBlock -> {11},
160 Description -> "Electron Yukawa mass"},
161
162 ymm == {
163 ParameterType -> External,
164 BlockName -> YUKAWA,
165 Value -> 0.10566,
166 OrderBlock -> {13},
167 Description -> "Muon Yukawa mass"},
168
169 ymtau == {
170 ParameterType -> External,
171 BlockName -> YUKAWA,
172 Value -> 1.777,
173 OrderBlock -> {15},
174 Description -> "Tau Yukawa mass"},
175
176 cabi == {
177 TeX -> Subscript[\[Theta], c],
178 ParameterType -> External,
179 BlockName -> CKMBLOCK,
180 Value -> 0.227736,
181 Description -> "Cabibbo angle"},
182
183
184 (* Internal Parameters *)
185
186 \[Alpha]EW == {
187 ParameterType -> Internal,
188 Value -> 1/\[Alpha]EWM1,
189 TeX -> Subscript[\[Alpha], EW],
190 ParameterName -> aEW,
191 InteractionOrder -> {QED, 2},
192 Description -> "Electroweak coupling contant"},
193
194
195 MW == {
196 ParameterType -> Internal,
197 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
198 TeX -> Subscript[M, W],
199 Description -> "W mass"},
200
201 sw2 == {
202 ParameterType -> Internal,
203 Value -> 1-(MW/MZ)^2,
204 Description -> "Squared Sin of the Weinberg angle"},
205
206 ee == {
207 TeX -> e,
208 ParameterType -> Internal,
209 Value -> Sqrt[4 Pi \[Alpha]EW],
210 InteractionOrder -> {QED, 1},
211 Description -> "Electric coupling constant"},
212
213 cw == {
214 TeX -> Subscript[c, w],
215 ParameterType -> Internal,
216 Value -> Sqrt[1 - sw2],
217 Description -> "Cos of the Weinberg angle"},
218
219 sw == {
220 TeX -> Subscript[s, w],
221 ParameterType -> Internal,
222 Value -> Sqrt[sw2],
223 Description -> "Sin of the Weinberg angle"},
224
225 gw == {
226 TeX -> Subscript[g, w],
227 ParameterType -> Internal,
228 Value -> ee / sw,
229 InteractionOrder -> {QED, 1},
230 Description -> "Weak coupling constant"},
231
232 g1 == {
233 TeX -> Subscript[g, 1],
234 ParameterType -> Internal,
235 Value -> ee / cw,
236 InteractionOrder -> {QED, 1},
237 Description -> "U(1)Y coupling constant"},
238
239 gs == {
240 TeX -> Subscript[g, s],
241 ParameterType -> Internal,
242 Value -> Sqrt[4 Pi \[Alpha]S],
243 InteractionOrder -> {QCD, 1},
244 ParameterName -> G,
245 Description -> "Strong coupling constant"},
246
247
248 v == {
249 ParameterType -> Internal,
250 Value -> 2*MW*sw/ee,
251 InteractionOrder -> {QED, -1},
252 Description -> "Higgs VEV"},
253
254 \[Lambda] == {
255 ParameterType -> Internal,
256 Value -> MH^2/(2*v^2),
257 InteractionOrder -> {QED, 2},
258 ParameterName -> lam,
259 Description -> "Higgs quartic coupling"},
260
261 muH == {
262 ParameterType -> Internal,
263 Value -> Sqrt[v^2 \[Lambda]],
264 TeX -> \[Mu],
265 Description -> "Coefficient of the quadratic piece of the Higgs potential"},
266
267
268 yl == {
269 TeX -> Superscript[y, l],
270 Indices -> {Index[Generation]},
271 AllowSummation -> True,
272 ParameterType -> Internal,
273 Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
274 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
275 InteractionOrder -> {QED, 1},
276 ComplexParameter -> False,
277 Description -> "Lepton Yukawa coupling"},
278
279 yu == {
280 TeX -> Superscript[y, u],
281 Indices -> {Index[Generation]},
282 AllowSummation -> True,
283 ParameterType -> Internal,
284 Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
285 ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
286 InteractionOrder -> {QED, 1},
287 ComplexParameter -> False,
288 Description -> "U-quark Yukawa coupling"},
289
290 yd == {
291 TeX -> Superscript[y, d],
292 Indices -> {Index[Generation]},
293 AllowSummation -> True,
294 ParameterType -> Internal,
295 Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
296 ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
297 InteractionOrder -> {QED, 1},
298 ComplexParameter -> False,
299 Description -> "D-quark Yukawa coupling"},
300
301(* N. B. : only Cabibbo mixing! *)
302 CKM == {
303 Indices -> {Index[Generation], Index[Generation]},
304 TensorClass -> CKM,
305 Unitary -> True,
306 Value -> {CKM[1,1] -> Cos[cabi],
307 CKM[1,2] -> Sin[cabi],
308 CKM[1,3] -> 0,
309 CKM[2,1] -> -Sin[cabi],
310 CKM[2,2] -> Cos[cabi],
311 CKM[2,3] -> 0,
312 CKM[3,1] -> 0,
313 CKM[3,2] -> 0,
314 CKM[3,3] -> 1},
315 Description -> "CKM-Matrix"}
316}
317
318
319(************** Gauge Groups ******************)
320
321M$GaugeGroups = {
322
323 U1Y == {
324 Abelian -> True,
325 GaugeBoson -> B,
326 Charge -> Y,
327 CouplingConstant -> g1},
328
329 SU2L == {
330 Abelian -> False,
331 GaugeBoson -> Wi,
332 StructureConstant -> Eps,
333 CouplingConstant -> gw},
334
335 SU3C == {
336 Abelian -> False,
337 GaugeBoson -> G,
338 StructureConstant -> f,
339 SymmetricTensor -> dSUN,
340 Representations -> {T, Colour},
341 CouplingConstant -> gs}
342}
343
344(********* Particle Classes **********)
345
346M$ClassesDescription = {
347
348(********** Fermions ************)
349 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
350 F[1] == {
351 ClassName -> vl,
352 ClassMembers -> {ve,vm,vt},
353 FlavorIndex -> Generation,
354 SelfConjugate -> False,
355 Indices -> {Index[Generation]},
356 Mass -> 0,
357 Width -> 0,
358 QuantumNumbers -> {LeptonNumber -> 1},
359 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
360 PropagatorType -> S,
361 PropagatorArrow -> Forward,
362 PDG -> {12,14,16},
363 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
364
365 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
366 F[2] == {
367 ClassName -> l,
368 ClassMembers -> {e, m, tt},
369 FlavorIndex -> Generation,
370 SelfConjugate -> False,
371 Indices -> {Index[Generation]},
372 Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
373 Width -> 0,
374 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
375 PropagatorLabel -> {"l", "e", "m", "tt"},
376 PropagatorType -> Straight,
377 ParticleName -> {"e-", "m-", "tt-"},
378 AntiParticleName -> {"e+", "m+", "tt+"},
379 PropagatorArrow -> Forward,
380 PDG -> {11, 13, 15},
381 FullName -> {"Electron", "Muon", "Tau"} },
382
383 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
384 F[3] == {
385 ClassMembers -> {u, c, t},
386 ClassName -> uq,
387 FlavorIndex -> Generation,
388 SelfConjugate -> False,
389 Indices -> {Index[Generation], Index[Colour]},
390 Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}},
391 Width -> {0, 0, {WT, 1.50833649}},
392 QuantumNumbers -> {Q -> 2/3},
393 PropagatorLabel -> {"uq", "u", "c", "t"},
394 PropagatorType -> Straight,
395 PropagatorArrow -> Forward,
396 PDG -> {2, 4, 6},
397 FullName -> {"u-quark", "c-quark", "t-quark"}},
398
399 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
400 F[4] == {
401 ClassMembers -> {d, s, b},
402 ClassName -> dq,
403 FlavorIndex -> Generation,
404 SelfConjugate -> False,
405 Indices -> {Index[Generation], Index[Colour]},
406 Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
407 Width -> 0,
408 QuantumNumbers -> {Q -> -1/3},
409 PropagatorLabel -> {"dq", "d", "s", "b"},
410 PropagatorType -> Straight,
411 PropagatorArrow -> Forward,
412 PDG -> {1,3,5},
413 FullName -> {"d-quark", "s-quark", "b-quark"} },
414
415(********** Ghosts **********)
416 U[1] == {
417 ClassName -> ghA,
418 SelfConjugate -> False,
419 Indices -> {},
420 Ghost -> A,
421 Mass -> 0,
422 Width -> 0,
423 QuantumNumbers -> {GhostNumber -> 1},
424 PropagatorLabel -> uA,
425 PropagatorType -> GhostDash,
426 PropagatorArrow -> Forward},
427
428 U[2] == {
429 ClassName -> ghZ,
430 SelfConjugate -> False,
431 Indices -> {},
432 Mass -> {MZ, 91.1876},
433 Width -> {WZ, Internal},
434 Ghost -> Z,
435 QuantumNumbers -> {GhostNumber -> 1},
436 PropagatorLabel -> uZ,
437 PropagatorType -> GhostDash,
438 PropagatorArrow -> Forward},
439
440 U[31] == {
441 ClassName -> ghWp,
442 SelfConjugate -> False,
443 Indices -> {},
444 Mass -> {MW, Internal},
445 Width -> {WW, Internal},
446 Ghost -> W,
447 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
448 PropagatorLabel -> uWp,
449 PropagatorType -> GhostDash,
450 PropagatorArrow -> Forward},
451
452 U[32] == {
453 ClassName -> ghWm,
454 SelfConjugate -> False,
455 Indices -> {},
456 Mass -> {MW, Internal},
457 Width -> {WW, Internal},
458 Ghost -> Wbar,
459 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
460 PropagatorLabel -> uWm,
461 PropagatorType -> GhostDash,
462 PropagatorArrow -> Forward},
463
464 U[4] == {
465 ClassName -> ghG,
466 SelfConjugate -> False,
467 Indices -> {Index[Gluon]},
468 Ghost -> G,
469 Mass -> 0,
470 QuantumNumbers -> {GhostNumber -> 1},
471 PropagatorLabel -> uG,
472 PropagatorType -> GhostDash,
473 PropagatorArrow -> Forward},
474
475 U[5] == {
476 ClassName -> ghWi,
477 Unphysical -> True,
478 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
479 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
480 ghWi[3] -> cw ghZ + sw ghA},
481 SelfConjugate -> False,
482 Ghost -> Wi,
483 Indices -> {Index[SU2W]},
484 FlavorIndex -> SU2W},
485
486 U[6] == {
487 ClassName -> ghB,
488 SelfConjugate -> False,
489 Definitions -> {ghB -> -sw ghZ + cw ghA},
490 Indices -> {},
491 Ghost -> B,
492 Unphysical -> True},
493
494(************ Gauge Bosons ***************)
495 (* Gauge bosons: Q = 0 *)
496 V[1] == {
497 ClassName -> A,
498 SelfConjugate -> True,
499 Indices -> {},
500 Mass -> 0,
501 Width -> 0,
502 PropagatorLabel -> "a",
503 PropagatorType -> W,
504 PropagatorArrow -> None,
505 PDG -> 22,
506 FullName -> "Photon" },
507
508 V[2] == {
509 ClassName -> Z,
510 SelfConjugate -> True,
511 Indices -> {},
512 Mass -> {MZ, 91.1876},
513 Width -> {WZ, 2.4952},
514 PropagatorLabel -> "Z",
515 PropagatorType -> Sine,
516 PropagatorArrow -> None,
517 PDG -> 23,
518 FullName -> "Z" },
519
520 (* Gauge bosons: Q = -1 *)
521 V[3] == {
522 ClassName -> W,
523 SelfConjugate -> False,
524 Indices -> {},
525 Mass -> {MW, Internal},
526 Width -> {WW, 2.085},
527 QuantumNumbers -> {Q -> 1},
528 PropagatorLabel -> "W",
529 PropagatorType -> Sine,
530 PropagatorArrow -> Forward,
531 ParticleName ->"W+",
532 AntiParticleName ->"W-",
533 PDG -> 24,
534 FullName -> "W" },
535
536V[4] == {
537 ClassName -> G,
538 SelfConjugate -> True,
539 Indices -> {Index[Gluon]},
540 Mass -> 0,
541 Width -> 0,
542 PropagatorLabel -> G,
543 PropagatorType -> C,
544 PropagatorArrow -> None,
545 PDG -> 21,
546 FullName -> "G" },
547
548V[5] == {
549 ClassName -> Wi,
550 Unphysical -> True,
551 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
552 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
553 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
554 SelfConjugate -> True,
555 Indices -> {Index[SU2W]},
556 FlavorIndex -> SU2W,
557 Mass -> 0,
558 PDG -> {1,2,3}},
559
560V[6] == {
561 ClassName -> B,
562 SelfConjugate -> True,
563 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
564 Indices -> {},
565 Mass -> 0,
566 Unphysical -> True},
567
568
569(************ Scalar Fields **********)
570 (* physical Higgs: Q = 0 *)
571 S[1] == {
572 ClassName -> H,
573 SelfConjugate -> True,
574 Mass -> {MH, 120},
575 Width -> {WH, 0.00575308848},
576 PropagatorLabel -> "H",
577 PropagatorType -> D,
578 PropagatorArrow -> None,
579 PDG -> 25,
580 TeXParticleName -> "\\phi",
581 TeXClassName -> "\\phi",
582 FullName -> "H" },
583
584S[2] == {
585 ClassName -> phi,
586 SelfConjugate -> True,
587 Mass -> {MZ, 91.1876},
588 Width -> Wphi,
589 PropagatorLabel -> "Phi",
590 PropagatorType -> D,
591 PropagatorArrow -> None,
592 ParticleName ->"phi0",
593 PDG -> 250,
594 FullName -> "Phi",
595 Goldstone -> Z },
596
597S[3] == {
598 ClassName -> phi2,
599 SelfConjugate -> False,
600 Mass -> {MW, Internal},
601 Width -> Wphi2,
602 PropagatorLabel -> "Phi2",
603 PropagatorType -> D,
604 PropagatorArrow -> None,
605 ParticleName ->"phi+",
606 AntiParticleName ->"phi-",
607 PDG -> 251,
608 FullName -> "Phi2",
609 TeXClassName -> "\\phi^+",
610 TeXParticleName -> "\\phi^+",
611 TeXAntiParticleName -> "\\phi^-",
612 Goldstone -> W,
613 QuantumNumbers -> {Q -> 1}}
614}
615
616
617
618
619(*****************************************************************************************)
620
621(* SM Lagrangian *)
622
623(******************** Gauge F^2 Lagrangian terms*************************)
624(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
625 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
626 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
627
628 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
629
630 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
631 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
632
633
634(********************* Fermion Lagrangian terms*************************)
635(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
636 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
637
638 Lkin = I uqbar.Ga[mu].del[uq, mu] +
639 I dqbar.Ga[mu].del[dq, mu] +
640 I lbar.Ga[mu].del[l, mu] +
641 I vlbar.Ga[mu].del[vl, mu];
642
643 LQCD = gs (uqbar.Ga[mu].T[a].uq +
644 dqbar.Ga[mu].T[a].dq)G[mu, a];
645
646 LBright =
647 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
648 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
649 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
650
651 LBleft =
652 -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
653 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
654 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
655 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
656
657 LWleft = ee/sw/2(
658 vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
659 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
660
661 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
662 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
663
664 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
665 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
666
667 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
668 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
669 );
670
671 Lkin + LQCD + LBright + LBleft + LWleft];
672
673(******************** Higgs Lagrangian terms****************************)
674 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
675 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
676
677
678
679 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
680
681 PMVec = Table[PauliSigma[i], {i, 3}];
682 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
683
684 (*Y_phi=1*)
685 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
686 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
687
688 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
689
690 (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
691
692
693(*************** Yukawa Lagrangian***********************)
694LYuk := If[FeynmanGauge,
695
696 Module[{s,r,n,m,i}, -
697 yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
698 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] -
699
700 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*)
701 yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) -
702
703 yl[n] vlbar[s,n].ProjP[s,r].l[r,n] (-I phi2) -
704 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H +I phi)/Sqrt[2]
705 ],
706
707 Module[{s,r,n,m,i}, -
708 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
709 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
710 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]
711 ]
712 ];
713
714LYukawa := LYuk + HC[LYuk];
715
716
717
718(**************Ghost terms**************************)
719(* Now we need the ghost terms which are of the form: *)
720(* - g * antighost * d_BRST G *)
721(* where d_BRST G is BRST transform of the gauge fixing function. *)
722
723LGhost := If[FeynmanGauge,
724 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
725
726 (***********First the pure gauge piece.**********************)
727 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
728 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
729
730 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
731 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
732
733 dBRSTB[mu_] := cw/ee del[ghB, mu];
734 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
735
736 (***********Next the piece from the scalar field.************)
737 LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
738 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
739 ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) -
740 I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
741 ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
742
743
744 (***********Now add the pieces together.********************)
745 LGhostG + LGhostWi + LGhostB + LGhostphi]
746
747,
748
749 (*If unitary gauge, only include the gluonic ghost.*)
750 Block[{dBRSTG,LGhostG},
751
752 (***********First the pure gauge piece.**********************)
753 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
754 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
755
756 (***********Now add the pieces together.********************)
757 LGhostG]
758
759];
760
761(*********Total SM Lagrangian*******)
762LSM := LGauge + LHiggs + LFermions + LYukawa + LGhost;