TFCNC: TFCNC.fr

File TFCNC.fr, 23.1 KB (added by Mathieu Buchkremer, 12 years ago)
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1(***************************************************************************************************************)
2(****** FeynRules model file for top-Higgs flavor changing couplings ******)
3(****** ******)
4(****** Authors: M. Buchkremer, G. Cacciapaglia, A. Deandrea,L. Panizzi ******)
5(****** ******)
6(***************************************************************************************************************)
7
8M$ModelName = "TFCNC";
9
10
11M$Information = {Authors -> {"M. Buchkremer","G. Cacciapaglia","A. Deandrea","L. Panizzi"},
12 Version -> "2.0",
13 Date -> "24. 12. 2013",
14 Institutions -> {"Universite catholique de Louvain (CP3)","Universite de Lyon (CNRS/IN2P3)","University of Southampton (School of Physics and Astronomy)"},
15 Emails -> {"mathieu.buchkremer@uclouvain.be", "g.cacciapaglia@ipnl.in2p3.fr","deandrea@ipnl.in2p3.fr", "l.panizzi@soton.ac.uk"}};
16
17(*
18 Top quark mass (172 GeV), and all parameters updated to 2010 PDG values
19 FeynmanGauge=True set as default.
20 Gluonic ghosts to be included in both gauges.
21 Fixed yukawa couplings in Feynman gauge.
22 Yukawa couplings are included for all fermions for gauge invariance.
23 Yukawa couplings for 1st generation fermions require Massless.rst.
24*)
25
26FeynmanGauge = True;
27
28
29(******* Index definitions ********)
30
31IndexRange[ Index[Generation] ] = Range[3]
32
33IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
34
35IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
36
37IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
38
39
40IndexStyle[Colour, i]
41
42IndexStyle[Generation, f]
43
44IndexStyle[Gluon ,a]
45
46IndexStyle[SU2W ,k]
47
48
49(******* Gauge parameters (for FeynArts) ********)
50
51GaugeXi[ V[1] ] = GaugeXi[A];
52GaugeXi[ V[2] ] = GaugeXi[Z];
53GaugeXi[ V[3] ] = GaugeXi[W];
54GaugeXi[ V[4] ] = GaugeXi[G];
55GaugeXi[ S[1] ] = 1;
56GaugeXi[ S[2] ] = GaugeXi[Z];
57GaugeXi[ S[3] ] = GaugeXi[W];
58GaugeXi[ U[1] ] = GaugeXi[A];
59GaugeXi[ U[2] ] = GaugeXi[Z];
60GaugeXi[ U[31] ] = GaugeXi[W];
61GaugeXi[ U[32] ] = GaugeXi[W];
62GaugeXi[ U[4] ] = GaugeXi[G];
63
64
65(**************** Parameters *************)
66
67M$Parameters = {
68
69 (* External parameters *)
70
71 \[Alpha]EWM1== {
72 ParameterType -> External,
73 BlockName -> SMINPUTS,
74 ParameterName -> aEWM1,
75 InteractionOrder -> {QED, -2},
76 Value -> 127.9,
77 Description -> "Inverse of the electroweak coupling constant"},
78
79 Gf == {
80 ParameterType -> External,
81 BlockName -> SMINPUTS,
82 TeX -> Subscript[G, f],
83 InteractionOrder -> {QED, 2},
84 Value -> 1.16637 * 10^(-5),
85 Description -> "Fermi constant"},
86
87 \[Alpha]S == {
88 ParameterType -> External,
89 BlockName -> SMINPUTS,
90 TeX -> Subscript[\[Alpha], s],
91 ParameterName -> aS,
92 InteractionOrder -> {QCD, 2},
93 Value -> 0.1184,
94 Description -> "Strong coupling constant at the Z pole."},
95
96 ymdo == {
97 ParameterType -> External,
98 BlockName -> YUKAWA,
99 Value -> 5.04*10^(-3),
100 OrderBlock -> {1},
101 Description -> "Down Yukawa mass"},
102
103
104 ymup == {
105 ParameterType -> External,
106 BlockName -> YUKAWA,
107 Value -> 2.55*10^(-3),
108 OrderBlock -> {2},
109 Description -> "Up Yukawa mass"},
110
111 yms == {
112 ParameterType -> External,
113 BlockName -> YUKAWA,
114 Value -> 0.101,
115 OrderBlock -> {3},
116 Description -> "Strange Yukawa mass"},
117
118
119 ymc == {
120 ParameterType -> External,
121 BlockName -> YUKAWA,
122 Value -> 1.27,
123 OrderBlock -> {4},
124 Description -> "Charm Yukawa mass"},
125
126 ymb == {
127 ParameterType -> External,
128 BlockName -> YUKAWA,
129 Value -> 4.7,
130 OrderBlock -> {5},
131 Description -> "Bottom Yukawa mass"},
132
133 ymt == {
134 ParameterType -> External,
135 BlockName -> YUKAWA,
136 Value -> 172.0,
137 OrderBlock -> {6},
138 Description -> "Top Yukawa mass"},
139
140 yme == {
141 ParameterType -> External,
142 BlockName -> YUKAWA,
143 Value -> 5.11*10^(-4),
144 OrderBlock -> {11},
145 Description -> "Electron Yukawa mass"},
146
147 ymm == {
148 ParameterType -> External,
149 BlockName -> YUKAWA,
150 Value -> 0.10566,
151 OrderBlock -> {13},
152 Description -> "Muon Yukawa mass"},
153
154 ymtau == {
155 ParameterType -> External,
156 BlockName -> YUKAWA,
157 Value -> 1.777,
158 OrderBlock -> {15},
159 Description -> "Tau Yukawa mass"},
160
161 cabi == {
162 TeX -> Subscript[\[Theta], c],
163 ParameterType -> External,
164 BlockName -> CKMBLOCK,
165 Value -> 0.227736,
166 Description -> "Cabibbo angle"},
167
168 KuH == {
169 ParameterType -> External,
170 BlockName -> FCNC,
171 Value -> 0,
172 Description -> "TuH coupling"},
173
174 KcH == {
175 ParameterType -> External,
176 BlockName -> FCNC,
177 Value -> 1,
178 Description -> "TcH coupling"},
179
180 (* Internal Parameters *)
181
182 \[Alpha]EW == {
183 ParameterType -> Internal,
184 Value -> 1/\[Alpha]EWM1,
185 TeX -> Subscript[\[Alpha], EW],
186 ParameterName -> aEW,
187 InteractionOrder -> {QED, 2},
188 Description -> "Electroweak coupling contant"},
189
190
191 MW == {
192 ParameterType -> Internal,
193 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
194 TeX -> Subscript[M, W],
195 Description -> "W mass"},
196
197 sw2 == {
198 ParameterType -> Internal,
199 Value -> 1-(MW/MZ)^2,
200 Description -> "Squared Sin of the Weinberg angle"},
201
202 ee == {
203 TeX -> e,
204 ParameterType -> Internal,
205 Value -> Sqrt[4 Pi \[Alpha]EW],
206 InteractionOrder -> {QED, 1},
207 Description -> "Electric coupling constant"},
208
209 cw == {
210 TeX -> Subscript[c, w],
211 ParameterType -> Internal,
212 Value -> Sqrt[1 - sw2],
213 Description -> "Cos of the Weinberg angle"},
214
215 sw == {
216 TeX -> Subscript[s, w],
217 ParameterType -> Internal,
218 Value -> Sqrt[sw2],
219 Description -> "Sin of the Weinberg angle"},
220
221 gw == {
222 TeX -> Subscript[g, w],
223 ParameterType -> Internal,
224 Value -> ee / sw,
225 InteractionOrder -> {QED, 1},
226 Description -> "Weak coupling constant"},
227
228 g1 == {
229 TeX -> Subscript[g, 1],
230 ParameterType -> Internal,
231 Value -> ee / cw,
232 InteractionOrder -> {QED, 1},
233 Description -> "U(1)Y coupling constant"},
234
235 gs == {
236 TeX -> Subscript[g, s],
237 ParameterType -> Internal,
238 Value -> Sqrt[4 Pi \[Alpha]S],
239 InteractionOrder -> {QCD, 1},
240 ParameterName -> G,
241 Description -> "Strong coupling constant"},
242
243
244 v == {
245 ParameterType -> Internal,
246 Value -> 2*MW*sw/ee,
247 InteractionOrder -> {QED, -1},
248 Description -> "Higgs VEV"},
249
250 \[Lambda] == {
251 ParameterType -> Internal,
252 Value -> MH^2/(2*v^2),
253 InteractionOrder -> {QED, 2},
254 ParameterName -> lam,
255 Description -> "Higgs quartic coupling"},
256
257 muH == {
258 ParameterType -> Internal,
259 Value -> Sqrt[v^2 \[Lambda]],
260 TeX -> \[Mu],
261 Description -> "Coefficient of the quadratic piece of the Higgs potential"},
262
263
264 yl == {
265 TeX -> Superscript[y, l],
266 Indices -> {Index[Generation]},
267 AllowSummation -> True,
268 ParameterType -> Internal,
269 Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
270 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
271 InteractionOrder -> {QED, 1},
272 ComplexParameter -> False,
273 Description -> "Lepton Yukawa coupling"},
274
275 yu == {
276 TeX -> Superscript[y, u],
277 Indices -> {Index[Generation]},
278 AllowSummation -> True,
279 ParameterType -> Internal,
280 Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
281 ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
282 InteractionOrder -> {QED, 1},
283 ComplexParameter -> False,
284 Description -> "U-quark Yukawa coupling"},
285
286 yd == {
287 TeX -> Superscript[y, d],
288 Indices -> {Index[Generation]},
289 AllowSummation -> True,
290 ParameterType -> Internal,
291 Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
292 ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
293 InteractionOrder -> {QED, 1},
294 ComplexParameter -> False,
295 Description -> "D-quark Yukawa coupling"},
296
297
298 (************** Internal Parameters, Top-Higgs FCNC couplings **************)
299
300 KtuH == {
301 ParameterType -> Internal,
302 BlockName -> FCNC,
303 ComplexParameter -> False,
304 Value -> KuH,
305 InteractionOrder -> {QED, 1},
306 Description -> "TuH coupling"},
307
308 KtcH == {
309 ParameterType -> Internal,
310 BlockName -> FCNC,
311 ComplexParameter -> False,
312 Value -> KcH,
313 InteractionOrder -> {QED, 1},
314 Description -> "TcH coupling"},
315
316(* N. B. : only Cabibbo mixing! *)
317 CKM == {
318 Indices -> {Index[Generation], Index[Generation]},
319 TensorClass -> CKM,
320 Unitary -> True,
321 Value -> {CKM[1,1] -> Cos[cabi],
322 CKM[1,2] -> Sin[cabi],
323 CKM[1,3] -> 0,
324 CKM[2,1] -> -Sin[cabi],
325 CKM[2,2] -> Cos[cabi],
326 CKM[2,3] -> 0,
327 CKM[3,1] -> 0,
328 CKM[3,2] -> 0,
329 CKM[3,3] -> 1},
330 Description -> "CKM-Matrix"}
331}
332
333
334(************** Gauge Groups ******************)
335
336M$GaugeGroups = {
337
338 U1Y == {
339 Abelian -> True,
340 GaugeBoson -> B,
341 Charge -> Y,
342 CouplingConstant -> g1},
343
344 SU2L == {
345 Abelian -> False,
346 GaugeBoson -> Wi,
347 StructureConstant -> Eps,
348 CouplingConstant -> gw},
349
350 SU3C == {
351 Abelian -> False,
352 GaugeBoson -> G,
353 StructureConstant -> f,
354 SymmetricTensor -> dSUN,
355 Representations -> {T, Colour},
356 CouplingConstant -> gs}
357}
358
359(********* Particle Classes **********)
360
361M$ClassesDescription = {
362
363(********** Fermions ************)
364 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
365 F[1] == {
366 ClassName -> vl,
367 ClassMembers -> {ve,vm,vt},
368 FlavorIndex -> Generation,
369 SelfConjugate -> False,
370 Indices -> {Index[Generation]},
371 Mass -> 0,
372 Width -> 0,
373 QuantumNumbers -> {LeptonNumber -> 1},
374 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
375 PropagatorType -> S,
376 PropagatorArrow -> Forward,
377 PDG -> {12,14,16},
378 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
379
380 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
381 F[2] == {
382 ClassName -> l,
383 ClassMembers -> {e, m, tt},
384 FlavorIndex -> Generation,
385 SelfConjugate -> False,
386 Indices -> {Index[Generation]},
387 Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
388 Width -> 0,
389 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
390 PropagatorLabel -> {"l", "e", "m", "tt"},
391 PropagatorType -> Straight,
392 ParticleName -> {"e-", "m-", "tt-"},
393 AntiParticleName -> {"e+", "m+", "tt+"},
394 PropagatorArrow -> Forward,
395 PDG -> {11, 13, 15},
396 FullName -> {"Electron", "Muon", "Tau"} },
397
398 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
399 F[3] == {
400 ClassMembers -> {u, c, t},
401 ClassName -> uq,
402 FlavorIndex -> Generation,
403 SelfConjugate -> False,
404 Indices -> {Index[Generation], Index[Colour]},
405 Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}},
406 Width -> {0, 0, {WT, 1.50833649}},
407 QuantumNumbers -> {Q -> 2/3},
408 PropagatorLabel -> {"uq", "u", "c", "t"},
409 PropagatorType -> Straight,
410 PropagatorArrow -> Forward,
411 PDG -> {2, 4, 6},
412 FullName -> {"u-quark", "c-quark", "t-quark"}},
413
414 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
415 F[4] == {
416 ClassMembers -> {d, s, b},
417 ClassName -> dq,
418 FlavorIndex -> Generation,
419 SelfConjugate -> False,
420 Indices -> {Index[Generation], Index[Colour]},
421 Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
422 Width -> 0,
423 QuantumNumbers -> {Q -> -1/3},
424 PropagatorLabel -> {"dq", "d", "s", "b"},
425 PropagatorType -> Straight,
426 PropagatorArrow -> Forward,
427 PDG -> {1,3,5},
428 FullName -> {"d-quark", "s-quark", "b-quark"} },
429
430(********** Ghosts **********)
431 U[1] == {
432 ClassName -> ghA,
433 SelfConjugate -> False,
434 Indices -> {},
435 Ghost -> A,
436 Mass -> 0,
437 QuantumNumbers -> {GhostNumber -> 1},
438 PropagatorLabel -> uA,
439 PropagatorType -> GhostDash,
440 PropagatorArrow -> Forward},
441
442 U[2] == {
443 ClassName -> ghZ,
444 SelfConjugate -> False,
445 Indices -> {},
446 Mass -> {MZ, 91.1876},
447 Ghost -> Z,
448 QuantumNumbers -> {GhostNumber -> 1},
449 PropagatorLabel -> uZ,
450 PropagatorType -> GhostDash,
451 PropagatorArrow -> Forward},
452
453 U[31] == {
454 ClassName -> ghWp,
455 SelfConjugate -> False,
456 Indices -> {},
457 Mass -> {MW, Internal},
458 Ghost -> W,
459 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
460 PropagatorLabel -> uWp,
461 PropagatorType -> GhostDash,
462 PropagatorArrow -> Forward},
463
464 U[32] == {
465 ClassName -> ghWm,
466 SelfConjugate -> False,
467 Indices -> {},
468 Mass -> {MW, Internal},
469 Ghost -> Wbar,
470 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
471 PropagatorLabel -> uWm,
472 PropagatorType -> GhostDash,
473 PropagatorArrow -> Forward},
474
475 U[4] == {
476 ClassName -> ghG,
477 SelfConjugate -> False,
478 Indices -> {Index[Gluon]},
479 Ghost -> G,
480 Mass -> 0,
481 QuantumNumbers -> {GhostNumber -> 1},
482 PropagatorLabel -> uG,
483 PropagatorType -> GhostDash,
484 PropagatorArrow -> Forward},
485
486 U[5] == {
487 ClassName -> ghWi,
488 Unphysical -> True,
489 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
490 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
491 ghWi[3] -> cw ghZ + sw ghA},
492 SelfConjugate -> False,
493 Ghost -> Wi,
494 Indices -> {Index[SU2W]},
495 FlavorIndex -> SU2W},
496
497 U[6] == {
498 ClassName -> ghB,
499 SelfConjugate -> False,
500 Definitions -> {ghB -> -sw ghZ + cw ghA},
501 Indices -> {},
502 Ghost -> B,
503 Unphysical -> True},
504
505(************ Gauge Bosons ***************)
506 (* Gauge bosons: Q = 0 *)
507 V[1] == {
508 ClassName -> A,
509 SelfConjugate -> True,
510 Indices -> {},
511 Mass -> 0,
512 Width -> 0,
513 PropagatorLabel -> "a",
514 PropagatorType -> W,
515 PropagatorArrow -> None,
516 PDG -> 22,
517 FullName -> "Photon" },
518
519 V[2] == {
520 ClassName -> Z,
521 SelfConjugate -> True,
522 Indices -> {},
523 Mass -> {MZ, 91.1876},
524 Width -> {WZ, 2.4952},
525 PropagatorLabel -> "Z",
526 PropagatorType -> Sine,
527 PropagatorArrow -> None,
528 PDG -> 23,
529 FullName -> "Z" },
530
531 (* Gauge bosons: Q = -1 *)
532 V[3] == {
533 ClassName -> W,
534 SelfConjugate -> False,
535 Indices -> {},
536 Mass -> {MW, Internal},
537 Width -> {WW, 2.085},
538 QuantumNumbers -> {Q -> 1},
539 PropagatorLabel -> "W",
540 PropagatorType -> Sine,
541 PropagatorArrow -> Forward,
542 ParticleName ->"W+",
543 AntiParticleName ->"W-",
544 PDG -> 24,
545 FullName -> "W" },
546
547V[4] == {
548 ClassName -> G,
549 SelfConjugate -> True,
550 Indices -> {Index[Gluon]},
551 Mass -> 0,
552 Width -> 0,
553 PropagatorLabel -> G,
554 PropagatorType -> C,
555 PropagatorArrow -> None,
556 PDG -> 21,
557 FullName -> "G" },
558
559V[5] == {
560 ClassName -> Wi,
561 Unphysical -> True,
562 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
563 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
564 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
565 SelfConjugate -> True,
566 Indices -> {Index[SU2W]},
567 FlavorIndex -> SU2W,
568 Mass -> 0,
569 PDG -> {1,2,3}},
570
571V[6] == {
572 ClassName -> B,
573 SelfConjugate -> True,
574 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
575 Indices -> {},
576 Mass -> 0,
577 Unphysical -> True},
578
579
580(************ Scalar Fields **********)
581 (* physical Higgs: Q = 0 *)
582 S[1] == {
583 ClassName -> H,
584 SelfConjugate -> True,
585 Mass -> {MH, 120},
586 Width -> {WH, 0.00575308848},
587 PropagatorLabel -> "H",
588 PropagatorType -> D,
589 PropagatorArrow -> None,
590 PDG -> 25,
591 TeXParticleName -> "\\phi",
592 TeXClassName -> "\\phi",
593 FullName -> "H" },
594
595S[2] == {
596 ClassName -> phi,
597 SelfConjugate -> True,
598 Mass -> {MZ, 91.1876},
599 Width -> Wphi,
600 PropagatorLabel -> "Phi",
601 PropagatorType -> D,
602 PropagatorArrow -> None,
603 ParticleName ->"phi0",
604 PDG -> 250,
605 FullName -> "Phi",
606 Goldstone -> Z },
607
608S[3] == {
609 ClassName -> phi2,
610 SelfConjugate -> False,
611 Mass -> {MW, Internal},
612 Width -> Wphi2,
613 PropagatorLabel -> "Phi2",
614 PropagatorType -> D,
615 PropagatorArrow -> None,
616 ParticleName ->"phi+",
617 AntiParticleName ->"phi-",
618 PDG -> 251,
619 FullName -> "Phi2",
620 TeXClassName -> "\\phi^+",
621 TeXParticleName -> "\\phi^+",
622 TeXAntiParticleName -> "\\phi^-",
623 Goldstone -> W,
624 QuantumNumbers -> {Q -> 1}}
625}
626
627
628
629
630(*****************************************************************************************)
631
632(* SM Lagrangian *)
633
634(******************** Gauge F^2 Lagrangian terms*************************)
635(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
636 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
637 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
638
639 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
640
641 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
642 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
643
644
645(********************* Fermion Lagrangian terms*************************)
646(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
647 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
648
649 Lkin = I uqbar.Ga[mu].del[uq, mu] +
650 I dqbar.Ga[mu].del[dq, mu] +
651 I lbar.Ga[mu].del[l, mu] +
652 I vlbar.Ga[mu].del[vl, mu];
653
654 LQCD = gs (uqbar.Ga[mu].T[a].uq +
655 dqbar.Ga[mu].T[a].dq)G[mu, a];
656
657 LBright =
658 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
659 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
660 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
661
662 LBleft =
663 -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
664 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
665 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
666 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
667
668 LWleft = ee/sw/2(
669 vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
670 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
671
672 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
673 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
674
675 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
676 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
677
678 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
679 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
680 );
681
682 Lkin + LQCD + LBright + LBleft + LWleft];
683
684(******************** Higgs Lagrangian terms****************************)
685 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
686 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
687
688
689
690 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
691
692 PMVec = Table[PauliSigma[i], {i, 3}];
693 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
694
695 (*Y_phi=1*)
696 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
697 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
698
699 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
700
701 (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
702
703
704(*************** Yukawa Lagrangian***********************)
705LYuk := If[FeynmanGauge,
706
707 Module[{s,r,n,m,i}, -
708 yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
709 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] -
710
711 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*)
712 yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) -
713
714 yl[n] vlbar[s,n].ProjP[s,r].l[r,n] (-I phi2) -
715 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H +I phi)/Sqrt[2]
716 ],
717
718 Module[{s,r,n,m,i}, -
719 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
720 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
721 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]
722 ]
723 ];
724
725LYukawa := LYuk + HC[LYuk];
726
727
728
729(**************Ghost terms**************************)
730(* Now we need the ghost terms which are of the form: *)
731(* - g * antighost * d_BRST G *)
732(* where d_BRST G is BRST transform of the gauge fixing function. *)
733
734LGhost := If[FeynmanGauge,
735 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
736
737 (***********First the pure gauge piece.**********************)
738 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
739 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
740
741 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
742 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
743
744 dBRSTB[mu_] := cw/ee del[ghB, mu];
745 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
746
747 (***********Next the piece from the scalar field.************)
748 LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
749 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
750 ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) -
751 I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
752 ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
753
754
755 (***********Now add the pieces together.********************)
756 LGhostG + LGhostWi + LGhostB + LGhostphi]
757
758,
759
760 (*If unitary gauge, only include the gluonic ghost.*)
761 Block[{dBRSTG,LGhostG},
762
763 (***********First the pure gauge piece.**********************)
764 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
765 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
766
767 (***********Now add the pieces together.********************)
768 LGhostG]
769
770];
771
772
773 (*************** Top-Higgs NC couplings *****************)
774
775LTFCNC :=+KtuH*(tbar.H.ProjP.u)+KtuH*(ubar.H.ProjM.t)+KtuH*(tbar.H.ProjM.u)+KtuH*(ubar.H.ProjP.t)+KtcH*(tbar.H.ProjP.c)+KtcH*(cbar.H.ProjM.t)+KtcH*(tbar.H.ProjM.c)+KtcH*(cbar.H.ProjP.t);
776
777(*********Total SM Lagrangian*******)
778LSM := LGauge + LHiggs + LFermions + LYukawa + LGhost;
779
780(*********Total Lagrangian*******)
781L := LGauge + LHiggs + LFermions + LYukawa + LGhost + LTFCNC ;