AnomalousGaugeCoupling: quartic.fr

File quartic.fr, 36.1 KB (added by Oscar Eboli, 12 years ago)

This is the main file. It contains the definitions for the SM and all quartic interactions.

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$ModelName = "Standard Model and anomalous quartic couplings";
13
14
15M$Information = {Authors -> {"N. Christensen", "C. Duhr", "modified by OJPE and MCGG"},
16 Version -> "1.4",
17 Date -> "02. 06. 2009, last change 13. 08. 2012",
18 Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)",
19 "USP", "Stony Brook"},
20 Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "eboli@fma.if.usp.br",
21 "concha@max2.physics.sunysb.edu"},
22 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"};
23
24(*
25 V1.3 - Updated Top quark mass to 2010 PDG value (172 GeV)
26 V1.2 - Set FeynmanGauge=True as default.
27 Set Gluonic ghosts to be included in both gauges.
28 V1.1 - Fixed yukawa couplings in Feynman gauge.
29 Changed yd[n] CKM[n,m] to yd[m] CKM[n,m].
30 Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]].
31 V1.3 - Added yukawa couplings for all fermions for gauge invariance.
32 Added yukawa couplings for 1st generation fermions to Massless.rst.
33 Updated parameters to PDG 2010.
34 V1.4 Anomalous quartic gauge-boson couplings added by OJPE and MCGG
35*)
36
37FeynmanGauge = True;
38
39(* FR$DSign=-1 *)
40
41(******* Index definitions ********)
42
43IndexRange[ Index[Generation] ] = Range[3]
44
45IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
46
47IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
48
49IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
50
51
52IndexStyle[Colour, i]
53
54IndexStyle[Generation, f]
55
56IndexStyle[Gluon ,a]
57
58IndexStyle[SU2W ,k]
59
60
61(******* Gauge parameters (for FeynArts) ********)
62
63GaugeXi[ V[1] ] = GaugeXi[A];
64GaugeXi[ V[2] ] = GaugeXi[Z];
65GaugeXi[ V[3] ] = GaugeXi[W];
66GaugeXi[ V[4] ] = GaugeXi[G];
67GaugeXi[ S[1] ] = 1;
68GaugeXi[ S[2] ] = GaugeXi[Z];
69GaugeXi[ S[3] ] = GaugeXi[W];
70GaugeXi[ U[1] ] = GaugeXi[A];
71GaugeXi[ U[2] ] = GaugeXi[Z];
72GaugeXi[ U[31] ] = GaugeXi[W];
73GaugeXi[ U[32] ] = GaugeXi[W];
74GaugeXi[ U[4] ] = GaugeXi[G];
75
76
77(**************** Parameters *************)
78
79M$Parameters = {
80
81 (* External parameters *)
82
83 \[Alpha]EWM1== {
84 ParameterType -> External,
85 BlockName -> SMINPUTS,
86 ParameterName -> aEWM1,
87 InteractionOrder -> {QED, -2},
88 Value -> 127.9,
89 Description -> "Inverse of the electroweak coupling constant"},
90
91
92 Gf == {
93 ParameterType -> External,
94 BlockName -> SMINPUTS,
95 TeX -> Subscript[G, f],
96 InteractionOrder -> {QED, 2},
97 Value -> 1.16637 * 10^(-5),
98 Description -> "Fermi constant"},
99
100 \[Alpha]S == {
101 ParameterType -> External,
102 BlockName -> SMINPUTS,
103 TeX -> Subscript[\[Alpha], s],
104 ParameterName -> aS,
105 InteractionOrder -> {QCD, 2},
106 Value -> 0.1184,
107 Description -> "Strong coupling constant at the Z pole."},
108
109 ymdo == {
110 ParameterType -> External,
111 BlockName -> YUKAWA,
112 Value -> 5.04*10^(-3),
113 OrderBlock -> {1},
114 Description -> "Down Yukawa mass"},
115
116
117 ymup == {
118 ParameterType -> External,
119 BlockName -> YUKAWA,
120 Value -> 2.55*10^(-3),
121 OrderBlock -> {2},
122 Description -> "Up Yukawa mass"},
123
124 yms == {
125 ParameterType -> External,
126 BlockName -> YUKAWA,
127 Value -> 0.101,
128 OrderBlock -> {3},
129 Description -> "Strange Yukawa mass"},
130
131
132 ymc == {
133 ParameterType -> External,
134 BlockName -> YUKAWA,
135 Value -> 1.27,
136 OrderBlock -> {4},
137 Description -> "Charm Yukawa mass"},
138
139 ymb == {
140 ParameterType -> External,
141 BlockName -> YUKAWA,
142 Value -> 4.7,
143 OrderBlock -> {5},
144 Description -> "Bottom Yukawa mass"},
145
146 ymt == {
147 ParameterType -> External,
148 BlockName -> YUKAWA,
149 Value -> 172.0,
150 OrderBlock -> {6},
151 Description -> "Top Yukawa mass"},
152
153 yme == {
154 ParameterType -> External,
155 BlockName -> YUKAWA,
156 Value -> 5.11*10^(-4),
157 OrderBlock -> {11},
158 Description -> "Electron Yukawa mass"},
159
160 ymm == {
161 ParameterType -> External,
162 BlockName -> YUKAWA,
163 Value -> 0.10566,
164 OrderBlock -> {13},
165 Description -> "Muon Yukawa mass"},
166
167 ymtau == {
168 ParameterType -> External,
169 BlockName -> YUKAWA,
170 Value -> 1.777,
171 OrderBlock -> {15},
172 Description -> "Tau Yukawa mass"},
173
174 cabi == {
175 TeX -> Subscript[\[Theta], c],
176 ParameterType -> External,
177 BlockName -> CKMBLOCK,
178 Value -> 0.227736,
179 Description -> "Cabibbo angle"},
180
181(* OjpE *)
182
183 FS0 == {
184 ParameterType -> External,
185 BlockName -> ANOINPUTS,
186 TeX -> Subscript[f, S0],
187 InteractionOrder -> {NP, 1},
188 Value -> 1.,
189 Description -> "L_S,0 coefficient"},
190
191
192 FS1 == {
193 ParameterType -> External,
194 BlockName -> ANOINPUTS,
195 TeX -> Subscript[f, S1],
196 InteractionOrder -> {NP, 1},
197 Value -> 1.,
198 Description -> "L_S,1 coefficient"},
199
200 FM0 == {
201 ParameterType -> External,
202 BlockName -> ANOINPUTS,
203 TeX -> Subscript[f, M0],
204 InteractionOrder -> {NP, 1},
205 Value -> 1.,
206 Description -> "L_M,0 coefficient"},
207
208 FM1 == {
209 ParameterType -> External,
210 BlockName -> ANOINPUTS,
211 TeX -> Subscript[f, M1],
212 InteractionOrder -> {NP, 1},
213 Value -> 1.,
214 Description -> "L_M,1 coefficient"},
215
216 FM2 == {
217 ParameterType -> External,
218 BlockName -> ANOINPUTS,
219 TeX -> Subscript[f, M2],
220 InteractionOrder -> {NP, 1},
221 Value -> 1.,
222 Description -> "L_M,2 coefficient"},
223
224 FM3 == {
225 ParameterType -> External,
226 BlockName -> ANOINPUTS,
227 TeX -> Subscript[f, M3],
228 InteractionOrder -> {NP, 1},
229 Value -> 1.,
230 Description -> "L_M,3 coefficient"},
231
232 FM4 == {
233 ParameterType -> External,
234 BlockName -> ANOINPUTS,
235 TeX -> Subscript[f, M4],
236 InteractionOrder -> {NP, 1},
237 Value -> 1.,
238 Description -> "L_M,4 coefficient"},
239
240 FM5 == {
241 ParameterType -> External,
242 BlockName -> ANOINPUTS,
243 TeX -> Subscript[f, M5],
244 InteractionOrder -> {NP, 1},
245 Value -> 1.,
246 Description -> "L_M,5 coefficient"},
247
248 FM6 == {
249 ParameterType -> External,
250 BlockName -> ANOINPUTS,
251 TeX -> Subscript[f, M6],
252 InteractionOrder -> {NP, 1},
253 Value -> 1.,
254 Description -> "L_M,6 coefficient"},
255
256 FM7 == {
257 ParameterType -> External,
258 BlockName -> ANOINPUTS,
259 TeX -> Subscript[f, M7],
260 InteractionOrder -> {NP, 1},
261 Value -> 1.,
262 Description -> "L_M,7 coefficient"},
263
264 FT0 == {
265 ParameterType -> External,
266 BlockName -> ANOINPUTS,
267 TeX -> Subscript[f, T0],
268 InteractionOrder -> {NP, 1},
269 Value -> 1.,
270 Description -> "L_T,0 coefficient"},
271
272 FT1 == {
273 ParameterType -> External,
274 BlockName -> ANOINPUTS,
275 TeX -> Subscript[f, T1],
276 InteractionOrder -> {NP, 1},
277 Value -> 1.,
278 Description -> "L_T,1 coefficient"},
279
280 FT2 == {
281 ParameterType -> External,
282 BlockName -> ANOINPUTS,
283 TeX -> Subscript[f, T2],
284 InteractionOrder -> {NP, 1},
285 Value -> 1.,
286 Description -> "L_T,2 coefficient"},
287
288 FT3 == {
289 ParameterType -> External,
290 BlockName -> ANOINPUTS,
291 TeX -> Subscript[f, T3],
292 InteractionOrder -> {NP, 1},
293 Value -> 1.,
294 Description -> "L_T,3 coefficient"},
295
296 FT4 == {
297 ParameterType -> External,
298 BlockName -> ANOINPUTS,
299 TeX -> Subscript[f, T4],
300 InteractionOrder -> {NP, 1},
301 Value -> 1.,
302 Description -> "L_T,4 coefficient"},
303
304 FT5 == {
305 ParameterType -> External,
306 BlockName -> ANOINPUTS,
307 TeX -> Subscript[f, T5],
308 InteractionOrder -> {NP, 1},
309 Value -> 1.,
310 Description -> "L_T,5 coefficient"},
311
312 FT6 == {
313 ParameterType -> External,
314 BlockName -> ANOINPUTS,
315 TeX -> Subscript[f, T6],
316 InteractionOrder -> {NP, 1},
317 Value -> 1.,
318 Description -> "L_T,6 coefficient"},
319
320 FT7 == {
321 ParameterType -> External,
322 BlockName -> ANOINPUTS,
323 TeX -> Subscript[f, T7],
324 InteractionOrder -> {NP, 1},
325 Value -> 1.,
326 Description -> "L_T,7 coefficient"},
327
328 FT8 == {
329 ParameterType -> External,
330 BlockName -> ANOINPUTS,
331 TeX -> Subscript[f, T8],
332 InteractionOrder -> {NP, 1},
333 Value -> 1.,
334 Description -> "L_T,8 coefficient"},
335
336 FT9 == {
337 ParameterType -> External,
338 BlockName -> ANOINPUTS,
339 TeX -> Subscript[f, T9],
340 InteractionOrder -> {NP, 1},
341 Value -> 1.,
342 Description -> "L_T,9 coefficient"},
343
344(* ------------------------------------------------------- *)
345
346 (* Internal Parameters *)
347
348 \[Alpha]EW == {
349 ParameterType -> Internal,
350 Value -> 1/\[Alpha]EWM1,
351 TeX -> Subscript[\[Alpha], EW],
352 ParameterName -> aEW,
353 InteractionOrder -> {QED, 2},
354 Description -> "Electroweak coupling contant"},
355
356
357 MW == {
358 ParameterType -> Internal,
359 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
360 TeX -> Subscript[M, W],
361 Description -> "W mass"},
362
363 sw2 == {
364 ParameterType -> Internal,
365 Value -> 1-(MW/MZ)^2,
366 Description -> "Squared Sin of the Weinberg angle"},
367
368 ee == {
369 TeX -> e,
370 ParameterType -> Internal,
371 Value -> Sqrt[4 Pi \[Alpha]EW],
372 InteractionOrder -> {QED, 1},
373 Description -> "Electric coupling constant"},
374
375 cw == {
376 TeX -> Subscript[c, w],
377 ParameterType -> Internal,
378 Value -> Sqrt[1 - sw2],
379 Description -> "Cos of the Weinberg angle"},
380
381 sw == {
382 TeX -> Subscript[s, w],
383 ParameterType -> Internal,
384 Value -> Sqrt[sw2],
385 Description -> "Sin of the Weinberg angle"},
386
387 gw == {
388 TeX -> Subscript[g, w],
389 ParameterType -> Internal,
390 Value -> ee / sw,
391 InteractionOrder -> {QED, 1},
392 Description -> "Weak coupling constant"},
393
394 g1 == {
395 TeX -> Subscript[g, 1],
396 ParameterType -> Internal,
397 Value -> ee / cw,
398 InteractionOrder -> {QED, 1},
399 Description -> "U(1)Y coupling constant"},
400
401 gs == {
402 TeX -> Subscript[g, s],
403 ParameterType -> Internal,
404 Value -> Sqrt[4 Pi \[Alpha]S],
405 InteractionOrder -> {QCD, 1},
406 ParameterName -> G,
407 Description -> "Strong coupling constant"},
408
409
410 v == {
411 ParameterType -> Internal,
412 Value -> 2*MW*sw/ee,
413 InteractionOrder -> {QED, -1},
414 Description -> "Higgs VEV"},
415
416 \[Lambda] == {
417 ParameterType -> Internal,
418 Value -> MH^2/(2*v^2),
419 InteractionOrder -> {QED, 2},
420 ParameterName -> lam,
421 Description -> "Higgs quartic coupling"},
422
423 muH == {
424 ParameterType -> Internal,
425 Value -> Sqrt[v^2 \[Lambda]],
426 TeX -> \[Mu],
427 Description -> "Coefficient of the quadratic piece of the Higgs potential"},
428
429
430 yl == {
431 TeX -> Superscript[y, l],
432 Indices -> {Index[Generation]},
433 AllowSummation -> True,
434 ParameterType -> Internal,
435 Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
436 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
437 InteractionOrder -> {QED, 1},
438 ComplexParameter -> False,
439 Description -> "Lepton Yukawa coupling"},
440
441 yu == {
442 TeX -> Superscript[y, u],
443 Indices -> {Index[Generation]},
444 AllowSummation -> True,
445 ParameterType -> Internal,
446 Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
447 ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
448 InteractionOrder -> {QED, 1},
449 ComplexParameter -> False,
450 Description -> "U-quark Yukawa coupling"},
451
452 yd == {
453 TeX -> Superscript[y, d],
454 Indices -> {Index[Generation]},
455 AllowSummation -> True,
456 ParameterType -> Internal,
457 Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
458 ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
459 InteractionOrder -> {QED, 1},
460 ComplexParameter -> False,
461 Description -> "D-quark Yukawa coupling"},
462
463(* N. B. : only Cabibbo mixing! *)
464 CKM == {
465 Indices -> {Index[Generation], Index[Generation]},
466 TensorClass -> CKM,
467 Unitary -> True,
468 Value -> {CKM[1,1] -> Cos[cabi],
469 CKM[1,2] -> Sin[cabi],
470 CKM[1,3] -> 0,
471 CKM[2,1] -> -Sin[cabi],
472 CKM[2,2] -> Cos[cabi],
473 CKM[2,3] -> 0,
474 CKM[3,1] -> 0,
475 CKM[3,2] -> 0,
476 CKM[3,3] -> 1},
477 Description -> "CKM-Matrix"}
478}
479
480
481(************** Gauge Groups ******************)
482
483M$GaugeGroups = {
484
485 U1Y == {
486 Abelian -> True,
487 GaugeBoson -> B,
488 Charge -> Y,
489 CouplingConstant -> g1},
490
491 SU2L == {
492 Abelian -> False,
493 GaugeBoson -> Wi,
494 StructureConstant -> Eps,
495 CouplingConstant -> gw},
496
497 SU3C == {
498 Abelian -> False,
499 GaugeBoson -> G,
500 StructureConstant -> f,
501 SymmetricTensor -> dSUN,
502 Representations -> {T, Colour},
503 CouplingConstant -> gs}
504}
505
506(********* Particle Classes **********)
507
508M$ClassesDescription = {
509
510(********** Fermions ************)
511 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
512 F[1] == {
513 ClassName -> vl,
514 ClassMembers -> {ve,vm,vt},
515 FlavorIndex -> Generation,
516 SelfConjugate -> False,
517 Indices -> {Index[Generation]},
518 Mass -> 0,
519 Width -> 0,
520 QuantumNumbers -> {LeptonNumber -> 1},
521 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
522 PropagatorType -> S,
523 PropagatorArrow -> Forward,
524 PDG -> {12,14,16},
525 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
526
527 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
528 F[2] == {
529 ClassName -> l,
530 ClassMembers -> {e, m, tt},
531 FlavorIndex -> Generation,
532 SelfConjugate -> False,
533 Indices -> {Index[Generation]},
534 Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
535 Width -> 0,
536 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
537 PropagatorLabel -> {"l", "e", "m", "tt"},
538 PropagatorType -> Straight,
539 ParticleName -> {"e-", "m-", "tt-"},
540 AntiParticleName -> {"e+", "m+", "tt+"},
541 PropagatorArrow -> Forward,
542 PDG -> {11, 13, 15},
543 FullName -> {"Electron", "Muon", "Tau"} },
544
545 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
546 F[3] == {
547 ClassMembers -> {u, c, t},
548 ClassName -> uq,
549 FlavorIndex -> Generation,
550 SelfConjugate -> False,
551 Indices -> {Index[Generation], Index[Colour]},
552 Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}},
553 Width -> {0, 0, {WT, 1.50833649}},
554 QuantumNumbers -> {Q -> 2/3},
555 PropagatorLabel -> {"uq", "u", "c", "t"},
556 PropagatorType -> Straight,
557 PropagatorArrow -> Forward,
558 PDG -> {2, 4, 6},
559 FullName -> {"u-quark", "c-quark", "t-quark"}},
560
561 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
562 F[4] == {
563 ClassMembers -> {d, s, b},
564 ClassName -> dq,
565 FlavorIndex -> Generation,
566 SelfConjugate -> False,
567 Indices -> {Index[Generation], Index[Colour]},
568 Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
569 Width -> 0,
570 QuantumNumbers -> {Q -> -1/3},
571 PropagatorLabel -> {"dq", "d", "s", "b"},
572 PropagatorType -> Straight,
573 PropagatorArrow -> Forward,
574 PDG -> {1,3,5},
575 FullName -> {"d-quark", "s-quark", "b-quark"} },
576
577(********** Ghosts **********)
578 U[1] == {
579 ClassName -> ghA,
580 SelfConjugate -> False,
581 Indices -> {},
582 Ghost -> A,
583 Mass -> 0,
584 QuantumNumbers -> {GhostNumber -> 1},
585 PropagatorLabel -> uA,
586 PropagatorType -> GhostDash,
587 PropagatorArrow -> Forward},
588
589 U[2] == {
590 ClassName -> ghZ,
591 SelfConjugate -> False,
592 Indices -> {},
593 Mass -> {MZ, 91.1876},
594 Ghost -> Z,
595 QuantumNumbers -> {GhostNumber -> 1},
596 PropagatorLabel -> uZ,
597 PropagatorType -> GhostDash,
598 PropagatorArrow -> Forward},
599
600 U[31] == {
601 ClassName -> ghWp,
602 SelfConjugate -> False,
603 Indices -> {},
604 Mass -> {MW, Internal},
605 Ghost -> W,
606 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
607 PropagatorLabel -> uWp,
608 PropagatorType -> GhostDash,
609 PropagatorArrow -> Forward},
610
611 U[32] == {
612 ClassName -> ghWm,
613 SelfConjugate -> False,
614 Indices -> {},
615 Mass -> {MW, Internal},
616 Ghost -> Wbar,
617 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
618 PropagatorLabel -> uWm,
619 PropagatorType -> GhostDash,
620 PropagatorArrow -> Forward},
621
622 U[4] == {
623 ClassName -> ghG,
624 SelfConjugate -> False,
625 Indices -> {Index[Gluon]},
626 Ghost -> G,
627 Mass -> 0,
628 QuantumNumbers -> {GhostNumber -> 1},
629 PropagatorLabel -> uG,
630 PropagatorType -> GhostDash,
631 PropagatorArrow -> Forward},
632
633 U[5] == {
634 ClassName -> ghWi,
635 Unphysical -> True,
636 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
637 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
638 ghWi[3] -> cw ghZ + sw ghA},
639 SelfConjugate -> False,
640 Ghost -> Wi,
641 Indices -> {Index[SU2W]},
642 FlavorIndex -> SU2W},
643
644 U[6] == {
645 ClassName -> ghB,
646 SelfConjugate -> False,
647 Definitions -> {ghB -> -sw ghZ + cw ghA},
648 Indices -> {},
649 Ghost -> B,
650 Unphysical -> True},
651
652(************ Gauge Bosons ***************)
653 (* Gauge bosons: Q = 0 *)
654 V[1] == {
655 ClassName -> A,
656 SelfConjugate -> True,
657 Indices -> {},
658 Mass -> 0,
659 Width -> 0,
660 PropagatorLabel -> "a",
661 PropagatorType -> W,
662 PropagatorArrow -> None,
663 PDG -> 22,
664 FullName -> "Photon" },
665
666 V[2] == {
667 ClassName -> Z,
668 SelfConjugate -> True,
669 Indices -> {},
670 Mass -> {MZ, 91.1876},
671 Width -> {WZ, 2.4952},
672 PropagatorLabel -> "Z",
673 PropagatorType -> Sine,
674 PropagatorArrow -> None,
675 PDG -> 23,
676 FullName -> "Z" },
677
678 (* Gauge bosons: Q = -1 *)
679 V[3] == {
680 ClassName -> W,
681 SelfConjugate -> False,
682 Indices -> {},
683 Mass -> {MW, Internal},
684 Width -> {WW, 2.085},
685 QuantumNumbers -> {Q -> 1},
686 PropagatorLabel -> "W",
687 PropagatorType -> Sine,
688 PropagatorArrow -> Forward,
689 ParticleName ->"W+",
690 AntiParticleName ->"W-",
691 PDG -> 24,
692 FullName -> "W" },
693
694V[4] == {
695 ClassName -> G,
696 SelfConjugate -> True,
697 Indices -> {Index[Gluon]},
698 Mass -> 0,
699 Width -> 0,
700 PropagatorLabel -> G,
701 PropagatorType -> C,
702 PropagatorArrow -> None,
703 PDG -> 21,
704 FullName -> "G" },
705
706V[5] == {
707 ClassName -> Wi,
708 Unphysical -> True,
709 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
710 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
711 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
712 SelfConjugate -> True,
713 Indices -> {Index[SU2W]},
714 FlavorIndex -> SU2W,
715 Mass -> 0,
716 PDG -> {1,2,3}},
717
718V[6] == {
719 ClassName -> B,
720 SelfConjugate -> True,
721 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
722 Indices -> {},
723 Mass -> 0,
724 Unphysical -> True},
725
726
727(************ Scalar Fields **********)
728 (* physical Higgs: Q = 0 *)
729 S[1] == {
730 ClassName -> H,
731 SelfConjugate -> True,
732 Mass -> {MH, 125},
733 Width -> {WH, 0.00575308848},
734 PropagatorLabel -> "H",
735 PropagatorType -> D,
736 PropagatorArrow -> None,
737 PDG -> 25,
738 TeXParticleName -> "\\phi",
739 TeXClassName -> "\\phi",
740 FullName -> "H" },
741
742S[2] == {
743 ClassName -> phi,
744 SelfConjugate -> True,
745 Mass -> {MZ, 91.1876},
746 Width -> Wphi,
747 PropagatorLabel -> "Phi",
748 PropagatorType -> D,
749 PropagatorArrow -> None,
750 ParticleName ->"phi0",
751 PDG -> 250,
752 FullName -> "Phi",
753 Goldstone -> Z },
754
755S[3] == {
756 ClassName -> phi2,
757 SelfConjugate -> False,
758 Mass -> {MW, Internal},
759 Width -> Wphi2,
760 PropagatorLabel -> "Phi2",
761 PropagatorType -> D,
762 PropagatorArrow -> None,
763 ParticleName ->"phi+",
764 AntiParticleName ->"phi-",
765 PDG -> 251,
766 FullName -> "Phi2",
767 TeXClassName -> "\\phi^+",
768 TeXParticleName -> "\\phi^+",
769 TeXAntiParticleName -> "\\phi^-",
770 Goldstone -> W,
771 QuantumNumbers -> {Q -> 1}}
772}
773
774
775
776
777(*****************************************************************************************)
778
779(* SM Lagrangian *)
780
781(******************** Gauge F^2 Lagrangian terms*************************)
782(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
783 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
784 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
785
786 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
787
788 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
789 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
790
791
792(********************* Fermion Lagrangian terms*************************)
793(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
794 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
795
796 Lkin = I uqbar.Ga[mu].del[uq, mu] +
797 I dqbar.Ga[mu].del[dq, mu] +
798 I lbar.Ga[mu].del[l, mu] +
799 I vlbar.Ga[mu].del[vl, mu];
800
801 LQCD = gs (uqbar.Ga[mu].T[a].uq +
802 dqbar.Ga[mu].T[a].dq)G[mu, a];
803
804 LBright =
805 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
806 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
807 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
808
809 LBleft =
810 -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
811 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
812 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
813 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
814
815 LWleft = ee/sw/2(
816 vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
817 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
818
819 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
820 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
821
822 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
823 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
824
825 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
826 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
827 );
828
829 Lkin + LQCD + LBright + LBleft + LWleft];
830
831(******************** Higgs Lagrangian terms****************************)
832 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
833 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
834
835
836
837 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
838
839 PMVec = Table[PauliSigma[i], {i, 3}];
840 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
841
842 (*Y_phi=1*)
843 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
844 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
845
846 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
847
848 (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
849
850
851
852
853
854(*************** Yukawa Lagrangian***********************)
855LYuk := If[FeynmanGauge,
856
857 Module[{s,r,n,m,i}, -
858 yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
859 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] -
860
861 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*)
862 yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) -
863
864 yl[n] vlbar[s,n].ProjP[s,r].l[r,n] (-I phi2) -
865 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H +I phi)/Sqrt[2]
866 ],
867
868 Module[{s,r,n,m,i}, -
869 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
870 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
871 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]
872 ]
873 ];
874
875LYukawa := LYuk + HC[LYuk];
876
877
878
879(**************Ghost terms**************************)
880(* Now we need the ghost terms which are of the form: *)
881(* - g * antighost * d_BRST G *)
882(* where d_BRST G is BRST transform of the gauge fixing function. *)
883
884LGhost := If[FeynmanGauge,
885 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
886
887 (***********First the pure gauge piece.**********************)
888 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
889 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
890
891 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
892
893 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
894
895 dBRSTB[mu_] := cw/ee del[ghB, mu];
896 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
897
898 (***********Next the piece from the scalar field.************)
899 LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
900 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
901 ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) -
902 I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
903 ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
904
905
906 (***********Now add the pieces together.********************)
907 LGhostG + LGhostWi + LGhostB + LGhostphi]
908
909,
910
911 (*If unitary gauge, only include the gluonic ghost.*)
912 Block[{dBRSTG,LGhostG},
913
914 (***********First the pure gauge piece.**********************)
915 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
916 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
917
918 (***********Now add the pieces together.********************)
919 LGhostG]
920
921];
922
923
924(* anomalous quartic couplings as defined in PRD74, 073005 *)
925
926
927(* S,0 *)
928
929LS0 := Block[{PMVec, WVec, Dc, Dcbar},
930
931 PMVec = Table[PauliSigma[i], {i, 3}];
932 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
933
934 (*Y_phi=1*)
935 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
936 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
937
938 FS0 (Dcbar[Phibar, mu]). Dc[Phi, nu] (Dcbar[Phibar, mu]).Dc[Phi, nu]
939
940];
941
942(* S,1 *)
943
944LS1 := Block[{PMVec, WVec, Dc, Dcbar},
945
946 PMVec = Table[PauliSigma[i], {i, 3}];
947 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
948
949 (*Y_phi=1*)
950 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
951 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
952
953 FS1 (Dcbar[Phibar, mu]). Dc[Phi, mu] (Dcbar[Phibar, nu]).Dc[Phi, nu]
954
955];
956
957
958(* M,0 *)
959
960LM0 := Block[{PMVec, WVec, FSVec, Dc, Dcbar},
961
962 PMVec = Table[PauliSigma[i], {i, 3}];
963 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
964 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
965
966 (*Y_phi=1*)
967 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
968 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
969
970
971 FM0/4 (Dcbar[Phibar, alpha]).Dc[Phi, alpha] Tr[(FSvec[mu,nu].PMVec).(FSvec[mu,nu].PMVec)]
972
973];
974
975
976(* M,1 *)
977
978LM1 := Block[{PMVec, WVec, FSvec, Dc, Dcbar},
979
980 PMVec = Table[PauliSigma[i], {i, 3}];
981 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
982 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
983
984 (*Y_phi=1*)
985 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
986 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
987
988
989 FM1/4 (Dcbar[Phibar, beta]).Dc[Phi, mu] Tr[(FSvec[mu,nu].PMVec).(FSvec[nu,beta].PMVec)]
990
991];
992
993
994
995(* M,2 *)
996
997LM2 := Block[{PMVec, WVec, Dc, Dcbar},
998
999 PMVec = Table[PauliSigma[i], {i, 3}];
1000 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1001
1002 (*Y_phi=1*)
1003 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1004 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1005
1006
1007(* FM2 (Dcbar[Phibar, mu]).Dc[Phi, mu] FS[B,mu,nu] FS[B,mu,nu] *)
1008
1009 FM2 (Dcbar[Phibar, beta]).Dc[Phi, beta] FS[B,mu,nu] FS[B,mu,nu]
1010
1011];
1012
1013(* M,3 *)
1014
1015LM3 := Block[{PMVec, WVec, Dc, Dcbar},
1016
1017 PMVec = Table[PauliSigma[i], {i, 3}];
1018 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1019
1020 (*Y_phi=1*)
1021 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1022 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1023
1024
1025
1026 FM3 (Dcbar[Phibar, mu]).Dc[Phi, beta] FS[B,mu,nu] FS[B,nu,beta]
1027];
1028
1029
1030(* M,4 *)
1031
1032LM4 := Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1033
1034 PMVec = Table[PauliSigma[i], {i, 3}];
1035 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1036 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1037
1038 (*Y_phi=1*)
1039 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1040 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1041
1042
1043
1044FM4/2 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).Dc[Phi, mu] FS[B,beta,nu]
1045
1046
1047];
1048
1049(* M,5 *)
1050
1051LM5 := Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1052
1053 PMVec = Table[PauliSigma[i], {i, 3}];
1054 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1055 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1056
1057 (*Y_phi=1*)
1058 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1059 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1060
1061
1062FM5/2 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).Dc[Phi, nu] FS[B,beta,mu]
1063
1064];
1065
1066
1067(* M,6 *)
1068
1069LM6 :=Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1070
1071 PMVec = Table[PauliSigma[i], {i, 3}];
1072 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1073 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1074
1075 (*Y_phi=1*)
1076 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1077 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1078
1079
1080FM6/4 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).(FSvec[beta,nu].PMVec).Dc[Phi, mu]
1081
1082];
1083
1084(* M,7 *)
1085
1086LM7 :=Block[{PMVec, WVec, FSVec, Dc, Dcbar},
1087
1088 PMVec = Table[PauliSigma[i], {i, 3}];
1089 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1090 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1091
1092 (*Y_phi=1*)
1093 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1094 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1095
1096
1097FM7/4 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).(FSvec[beta,mu].PMVec).Dc[Phi, nu]
1098
1099];
1100
1101
1102(* T,0 *)
1103
1104LT0 := Block[{PMVec, FSVec },
1105
1106 PMVec = Table[PauliSigma[i], {i, 3}];
1107 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1108
1109 FT0/16 Tr[(FSvec[alpha,beta].PMVec).(FSvec[alpha,beta].PMVec)] Tr[(FSvec[mu,nu].PMVec).(FSvec[mu,nu].PMVec)]
1110
1111];
1112
1113(* T,1 *)
1114
1115LT1 := Block[{PMVec, FSVec},
1116
1117 PMVec = Table[PauliSigma[i], {i, 3}];
1118 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1119
1120 FT1/16 Tr[(FSvec[alpha,nu].PMVec).(FSvec[mu,beta].PMVec)] Tr[(FSvec[mu,beta].PMVec).(FSvec[alpha,nu].PMVec)]
1121
1122];
1123
1124
1125(* T,2 *)
1126
1127LT2 := Block[{PMVec, FSVec},
1128
1129 PMVec = Table[PauliSigma[i], {i, 3}];
1130 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1131
1132 FT2/16 Tr[(FSvec[alpha,mu].PMVec).(FSvec[mu,beta].PMVec)] Tr[(FSvec[beta,nu].PMVec).(FSvec[nu,alpha].PMVec)]
1133
1134];
1135
1136(* T,3 identicaly zero!*)
1137
1138LT3 := Block[{PMVec, FSVec},
1139
1140 PMVec = Table[PauliSigma[i], {i, 3}];
1141 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1142
1143 FT3/8 Tr[(FSvec[alpha,mu].PMVec).(FSvec[mu,beta].PMVec).(FSvec[nu,alpha].PMVec)] FS[B, beta, nu]
1144
1145];
1146
1147
1148(* T,4: identicaly zero *)
1149
1150LT4 := Block[{PMVec, FSVec},
1151
1152 PMVec = Table[PauliSigma[i], {i, 3}];
1153 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1154
1155
1156 FT4/8 Tr[(FSvec[alpha,mu].PMVec).(FSvec[alpha, mu].PMVec).(FSvec[beta, nu].PMVec)] FS[B, beta, nu]
1157
1158];
1159
1160
1161(* T,5 *)
1162
1163LT5 := Block[{PMVec, FSVec},
1164
1165 PMVec = Table[PauliSigma[i], {i, 3}];
1166 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1167
1168
1169 FT5/4 Tr[(FSvec[mu,nu].PMVec).(FSvec[mu, nu].PMVec)] FS[B, beta, alpha] FS[B, beta, alpha]
1170
1171];
1172
1173
1174(* T,6 *)
1175
1176LT6 := Block[{PMVec, FSVec},
1177
1178 PMVec = Table[PauliSigma[i], {i, 3}];
1179 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1180
1181 FT6/4 Tr[(FSvec[alpha,nu].PMVec).(FSvec[mu, beta].PMVec)] FS[B, mu, beta] FS[B, alpha, nu]
1182
1183];
1184
1185
1186(* T,7 *)
1187
1188LT7 := Block[{PMVec, FSVec},
1189
1190 PMVec = Table[PauliSigma[i], {i, 3}];
1191 FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]};
1192
1193 FT7/4 Tr[(FSvec[alpha, mu].PMVec).(FSvec[mu, beta].PMVec)] FS[B, beta, nu] FS[B, nu, alpha]
1194
1195];
1196
1197
1198(* T,8: *)
1199
1200LT8 := Block[{PMVec, WVec},
1201
1202 PMVec = Table[PauliSigma[i], {i, 3}];
1203 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1204
1205
1206 FT8 (del[B[nu], mu] - del[B[mu], nu] )*
1207 (del[B[nu], mu] - del[B[mu], nu] )*
1208 (del[B[beta], alpha] - del[B[alpha], beta] )*
1209 (del[B[beta], alpha] - del[B[alpha], beta] )
1210
1211];
1212
1213(* T,9: *)
1214
1215LT9 := Block[{PMVec, WVec},
1216
1217 PMVec = Table[PauliSigma[i], {I, 3}];
1218 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1219
1220FT9 FS[B, mu, nu] FS[B, nu, alpha] FS[B, alpha, beta] FS[B, beta, mu]
1221
1222];
1223
1224
1225(* ------------------------------------------------------- *)
1226
1227
1228 (*********Total SM Lagrangian in the unitary gauge*******)
1229
1230LSM := LGauge + LHiggs + LFermions + LYukawa ;
1231
1232LQS = LS0 + LS1;
1233
1234LQM = LM0 + LM1 + LM2 + LM3 + LM4 + LM5 + LM6 + LM7;
1235
1236LQT = LT0 + LT1 + LT2 + LT3 + LT4 + LT5 + LT6 + LT7 + LT8 + LT9;
1237
1238LQuartic := LSM + LQS + LQM + LQT;
1239
1240
1241
1242
1243