FourthGeneration: 4Gen.fr

File 4Gen.fr, 22.7 KB (added by Claude Duhr, 15 years ago)

4th generation model file

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the 4th generation model ******)
3(****** ******)
4(****** Authors: 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
12
13(*
14 This model is based on the SM implmentation of FeynRules,
15 and basically obtained by just increasing the range of the Index of type Generation from 3 to 4
16*)
17
18
19
20M$ModelName = "4th_Generation_Complex_CKM";
21
22
23
24M$Information = {Authors -> {"C. Duhr"},
25 Version -> "1.1",
26 Date -> "02. 11. 2010",
27 Institutions -> {"IPPP, Durham"},
28 Emails -> {"claude.duhr@durham.ac.uk"}};
29
30(*V1.1 - Fixed yukawa couplings in Feynman gauge.
31 Changed yd[n] CKM[n,m] to yd[m] CKM[n,m].
32 Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]].
33*)
34
35FeynmanGauge = False;
36
37
38(******* Index definitions ********)
39
40IndexRange[ Index[Generation] ] = Range[3]
41
42IndexRange[ Index[QuarkGeneration] ] = Range[4]
43
44IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
45
46IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
47
48IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
49
50
51IndexStyle[Colour, i]
52
53IndexStyle[Generation, f]
54
55IndexStyle[QuarkGeneration, q]
56
57IndexStyle[Gluon ,a]
58
59IndexStyle[SU2W ,k]
60
61
62(******* Gauge parameters (for FeynArts) ********)
63
64GaugeXi[ V[1] ] = GaugeXi[A];
65GaugeXi[ V[2] ] = GaugeXi[Z];
66GaugeXi[ V[3] ] = GaugeXi[W];
67GaugeXi[ V[4] ] = GaugeXi[G];
68GaugeXi[ S[1] ] = 1;
69GaugeXi[ S[2] ] = GaugeXi[Z];
70GaugeXi[ S[3] ] = GaugeXi[W];
71GaugeXi[ U[1] ] = GaugeXi[A];
72GaugeXi[ U[2] ] = GaugeXi[Z];
73GaugeXi[ U[31] ] = GaugeXi[W];
74GaugeXi[ U[32] ] = GaugeXi[W];
75GaugeXi[ U[4] ] = GaugeXi[G];
76
77
78(**************** Parameters *************)
79
80M$Parameters = {
81
82 (* External parameters *)
83
84 \[Alpha]EWM1== {
85 ParameterType -> External,
86 BlockName -> SMINPUTS,
87 ParameterName -> aEWM1,
88 InteractionOrder -> {QED, -2},
89 Value -> 127.9,
90 Description -> "Inverse of the electroweak coupling constant"},
91
92 Gf == {
93 ParameterType -> External,
94 BlockName -> SMINPUTS,
95 TeX -> Subscript[G, f],
96 InteractionOrder -> {QED, 2},
97 Value -> 1.16639 * 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 -> 0.1172,
107 Description -> "Strong coupling constant at the Z pole."},
108
109
110 ymc == {
111 ParameterType -> External,
112 BlockName -> YUKAWA,
113 Value -> 1.42,
114 OrderBlock -> {4},
115 Description -> "Charm Yukawa mass"},
116
117 ymb == {
118 ParameterType -> External,
119 BlockName -> YUKAWA,
120 Value -> 4.7,
121 OrderBlock -> {5},
122 Description -> "Bottom Yukawa mass"},
123
124 ymbp == {
125 ParameterType -> External,
126 BlockName -> YUKAWA,
127 Value -> 500,
128 OrderBlock -> {7},
129 Description -> "Bottom-prime Yukawa mass"},
130
131 ymt == {
132 ParameterType -> External,
133 BlockName -> YUKAWA,
134 Value -> 174.3,
135 OrderBlock -> {6},
136 Description -> "Top Yukawa mass"},
137
138 ymtp == {
139 ParameterType -> External,
140 BlockName -> YUKAWA,
141 Value -> 700,
142 OrderBlock -> {8},
143 Description -> "Top-prime Yukawa mass"},
144
145 ymtau == {
146 ParameterType -> External,
147 BlockName -> YUKAWA,
148 Value -> 1.777,
149 OrderBlock -> {15},
150 Description -> "Tau Yukawa mass"},
151
152
153 (* Internal Parameters *)
154
155 \[Alpha]EW == {
156 ParameterType -> Internal,
157 Value -> 1/\[Alpha]EWM1,
158 TeX -> Subscript[\[Alpha], EW],
159 ParameterName -> aEW,
160 InteractionOrder -> {QED, 2},
161 Description -> "Electroweak coupling contant"},
162
163
164 MW == {
165 ParameterType -> Internal,
166 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
167 TeX -> Subscript[M, W],
168 Description -> "W mass"},
169
170 sw2 == {
171 ParameterType -> Internal,
172 Value -> 1-(MW/MZ)^2,
173 Description -> "Squared Sin of the Weinberg angle"},
174
175 ee == {
176 TeX -> e,
177 ParameterType -> Internal,
178 Value -> Sqrt[4 Pi \[Alpha]EW],
179 InteractionOrder -> {QED, 1},
180 Description -> "Electric coupling constant"},
181
182 cw == {
183 TeX -> Subscript[c, w],
184 ParameterType -> Internal,
185 Value -> Sqrt[1 - sw2],
186 Description -> "Cos of the Weinberg angle"},
187
188 sw == {
189 TeX -> Subscript[s, w],
190 ParameterType -> Internal,
191 Value -> Sqrt[sw2],
192 Description -> "Sin of the Weinberg angle"},
193
194 gw == {
195 TeX -> Subscript[g, w],
196 ParameterType -> Internal,
197 Value -> ee / sw,
198 InteractionOrder -> {QED, 1},
199 Description -> "Weak coupling constant"},
200
201 g1 == {
202 TeX -> Subscript[g, 1],
203 ParameterType -> Internal,
204 Value -> ee / cw,
205 InteractionOrder -> {QED, 1},
206 Description -> "U(1)Y coupling constant"},
207
208 gs == {
209 TeX -> Subscript[g, s],
210 ParameterType -> Internal,
211 Value -> Sqrt[4 Pi \[Alpha]S],
212 InteractionOrder -> {QCD, 1},
213 ParameterName -> G,
214 Description -> "Strong coupling constant"},
215
216
217 v == {
218 ParameterType -> Internal,
219 Value -> 2*MW*sw/ee,
220 InteractionOrder -> {QED, -1},
221 Description -> "Higgs VEV"},
222
223 \[Lambda] == {
224 ParameterType -> Internal,
225 Value -> MH^2/(2*v^2),
226 InteractionOrder -> {QED, 2},
227 ParameterName -> lam,
228 Description -> "Higgs quartic coupling"},
229
230 muH == {
231 ParameterType -> Internal,
232 Value -> Sqrt[v^2 \[Lambda]],
233 TeX -> \[Mu],
234 Description -> "Coefficient of the quadratic piece of the Higgs potential"},
235
236
237 yl == {
238 TeX -> Superscript[y, l],
239 Indices -> {Index[Generation]},
240 AllowSummation -> True,
241 ParameterType -> Internal,
242 Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v},
243 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
244 InteractionOrder -> {QED, 1},
245 ComplexParameter -> False,
246 Description -> "Lepton Yukawa coupling"},
247
248 yu == {
249 TeX -> Superscript[y, u],
250 Indices -> {Index[QuarkGeneration]},
251 AllowSummation -> True,
252 ParameterType -> Internal,
253 Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v, yu[4] -> Sqrt[2] ymtp / v},
254 ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt, yu[4] -> ytp},
255 InteractionOrder -> {QED, 1},
256 ComplexParameter -> False,
257 Description -> "U-quark Yukawa coupling"},
258
259 yd == {
260 TeX -> Superscript[y, d],
261 Indices -> {Index[QuarkGeneration]},
262 AllowSummation -> True,
263 ParameterType -> Internal,
264 Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v, yd[4] -> Sqrt[2] ymbp / v},
265 ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb, yd[4] -> ybp},
266 InteractionOrder -> {QED, 1},
267 ComplexParameter -> False,
268 Description -> "D-quark Yukawa coupling"},
269
270(* N. B. : only Cabibbo mixing! *)
271
272
273
274 RCKM == {
275 ParameterType -> External,
276 Indices -> {Index[QuarkGeneration], Index[QuarkGeneration]},
277 BlockName -> RCKM,
278 ComplexParameter -> False,
279 Value -> {RCKM[1,1] :> 1,
280 RCKM[1,2] :> 0,
281 RCKM[1,3] :> 0,
282 RCKM[1,4] :> 0,
283 RCKM[2,1] :> 0,
284 RCKM[2,2] :> 0.99995,
285 RCKM[2,3] :> 0,
286 RCKM[2,4] :> 0.01,
287 RCKM[3,1] :> 0,
288 RCKM[3,2] :> -0.001,
289 RCKM[3,3] :> 0.995,
290 RCKM[3,4] :> 0.1,
291 RCKM[4,1] :> 0,
292 RCKM[4,2] :> -0.01,
293 RCKM[4,3] :> -0.1,
294 RCKM[4,4] :> 0.99495},
295 Description -> "Real Part of the CKM matrix"},
296
297 ICKM == {
298 ParameterType -> External,
299 Indices -> {Index[QuarkGeneration], Index[QuarkGeneration]},
300 BlockName -> ICKM,
301 ComplexParameter -> False,
302 Value -> {ICKM[1,1] :> 0,
303 ICKM[1,2] :> 0,
304 ICKM[1,3] :> 0,
305 ICKM[1,4] :> 0,
306 ICKM[2,1] :> 0,
307 ICKM[2,2] :> 0,
308 ICKM[2,3] :> 0,
309 ICKM[2,4] :> 0,
310 ICKM[3,1] :> 0,
311 ICKM[3,2] :> 0,
312 ICKM[3,3] :> 0,
313 ICKM[3,4] :> 0,
314 ICKM[4,1] :> 0,
315 ICKM[4,2] :> 0,
316 ICKM[4,3] :> 0,
317 ICKM[4,4] :> 0},
318 Description -> "Imaginary Part of the CKM matrix"},
319
320
321
322 CKM == {
323 Indices -> {Index[QuarkGeneration], Index[QuarkGeneration]},
324 Unitary -> True,
325 Value -> {CKM[i_,j_] :> RCKM[i,j] + I ICKM[i,j]},
326 Description -> "CKM-Matrix"}
327}
328
329
330(************** Gauge Groups ******************)
331
332M$GaugeGroups = {
333
334 U1Y == {
335 Abelian -> True,
336 GaugeBoson -> B,
337 Charge -> Y,
338 CouplingConstant -> g1},
339
340 SU2L == {
341 Abelian -> False,
342 GaugeBoson -> Wi,
343 StructureConstant -> Eps,
344 CouplingConstant -> gw},
345
346 SU3C == {
347 Abelian -> False,
348 GaugeBoson -> G,
349 StructureConstant -> f,
350 SymmetricTensor -> dSUN,
351 Representations -> {T, Colour},
352 CouplingConstant -> gs}
353}
354
355(********* Particle Classes **********)
356
357M$ClassesDescription = {
358
359(********** Fermions ************)
360 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
361 F[1] == {
362 ClassName -> vl,
363 ClassMembers -> {ve,vm,vt},
364 FlavorIndex -> Generation,
365 SelfConjugate -> False,
366 Indices -> {Index[Generation]},
367 Mass -> 0,
368 Width -> 0,
369 QuantumNumbers -> {LeptonNumber -> 1},
370 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
371 PropagatorType -> S,
372 PropagatorArrow -> Forward,
373 PDG -> {12,14,16},
374 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
375
376 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
377 F[2] == {
378 ClassName -> l,
379 ClassMembers -> {e, m, tt},
380 FlavorIndex -> Generation,
381 SelfConjugate -> False,
382 Indices -> {Index[Generation]},
383 Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
384 Width -> 0,
385 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
386 PropagatorLabel -> {"l", "e", "m", "tt"},
387 PropagatorType -> Straight,
388 ParticleName -> {"e-", "m-", "tt-"},
389 AntiParticleName -> {"e+", "m+", "tt+"},
390 PropagatorArrow -> Forward,
391 PDG -> {11, 13, 15},
392 FullName -> {"Electron", "Muon", "Tau"} },
393
394 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
395 F[3] == {
396 ClassMembers -> {u, c, t, tp},
397 ClassName -> uq,
398 FlavorIndex -> QuarkGeneration,
399 SelfConjugate -> False,
400 Indices -> {Index[QuarkGeneration], Index[Colour]},
401 Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}, {MTp, 700}},
402 Width -> {0, 0, {WT, 1.4516}, {WTp, 14.109}},
403 QuantumNumbers -> {Q -> 2/3},
404 PropagatorLabel -> {"uq", "u", "c", "t", "tp"},
405 PropagatorType -> Straight,
406 PropagatorArrow -> Forward,
407 PDG -> {2, 4, 6, 8},
408 FullName -> {"u-quark", "c-quark", "t-quark", "t-prime-quark"}},
409
410 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
411 F[4] == {
412 ClassMembers -> {d, s, b, bp},
413 ClassName -> dq,
414 FlavorIndex -> QuarkGeneration,
415 SelfConjugate -> False,
416 Indices -> {Index[QuarkGeneration], Index[Colour]},
417 Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.104}, {MB, 4.7}, {MBp, 500}},
418 Width -> {0,0,0,{WBp,0.28454}},
419 QuantumNumbers -> {Q -> -1/3},
420 PropagatorLabel -> {"dq", "d", "s", "b", "bp"},
421 PropagatorType -> Straight,
422 PropagatorArrow -> Forward,
423 PDG -> {1,3,5,7},
424 FullName -> {"d-quark", "s-quark", "b-quark", "b-prime-quark"} },
425
426(********** Ghosts **********)
427 U[1] == {
428 ClassName -> ghA,
429 SelfConjugate -> False,
430 Indices -> {},
431 Ghost -> A,
432 Mass -> 0,
433 QuantumNumbers -> {GhostNumber -> 1},
434 PropagatorLabel -> uA,
435 PropagatorType -> GhostDash,
436 PropagatorArrow -> Forward},
437
438 U[2] == {
439 ClassName -> ghZ,
440 SelfConjugate -> False,
441 Indices -> {},
442 Mass -> {MZ, 91.188},
443 Ghost -> Z,
444 QuantumNumbers -> {GhostNumber -> 1},
445 PropagatorLabel -> uZ,
446 PropagatorType -> GhostDash,
447 PropagatorArrow -> Forward},
448
449 U[31] == {
450 ClassName -> ghWp,
451 SelfConjugate -> False,
452 Indices -> {},
453 Mass -> {MW, Internal},
454 Ghost -> W,
455 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
456 PropagatorLabel -> uWp,
457 PropagatorType -> GhostDash,
458 PropagatorArrow -> Forward},
459
460 U[32] == {
461 ClassName -> ghWm,
462 SelfConjugate -> False,
463 Indices -> {},
464 Mass -> {MW, Internal},
465 Ghost -> Wbar,
466 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
467 PropagatorLabel -> uWm,
468 PropagatorType -> GhostDash,
469 PropagatorArrow -> Forward},
470
471 U[4] == {
472 ClassName -> ghG,
473 SelfConjugate -> False,
474 Indices -> {Index[Gluon]},
475 Ghost -> G,
476 Mass -> 0,
477 QuantumNumbers -> {GhostNumber -> 1},
478 PropagatorLabel -> uG,
479 PropagatorType -> GhostDash,
480 PropagatorArrow -> Forward},
481
482 U[5] == {
483 ClassName -> ghWi,
484 Unphysical -> True,
485 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
486 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
487 ghWi[3] -> cw ghZ + sw ghA},
488 SelfConjugate -> False,
489 Ghost -> Wi,
490 Indices -> {Index[SU2W]},
491 FlavorIndex -> SU2W},
492
493 U[6] == {
494 ClassName -> ghB,
495 SelfConjugate -> False,
496 Definitions -> {ghB -> -sw ghZ + cw ghA},
497 Indices -> {},
498 Ghost -> B,
499 Unphysical -> True},
500
501(************ Gauge Bosons ***************)
502 (* Gauge bosons: Q = 0 *)
503 V[1] == {
504 ClassName -> A,
505 SelfConjugate -> True,
506 Indices -> {},
507 Mass -> 0,
508 Width -> 0,
509 PropagatorLabel -> "a",
510 PropagatorType -> W,
511 PropagatorArrow -> None,
512 PDG -> 22,
513 FullName -> "Photon" },
514
515 V[2] == {
516 ClassName -> Z,
517 SelfConjugate -> True,
518 Indices -> {},
519 Mass -> {MZ, 91.188},
520 Width -> {WZ, 2.44140351},
521 PropagatorLabel -> "Z",
522 PropagatorType -> Sine,
523 PropagatorArrow -> None,
524 PDG -> 23,
525 FullName -> "Z" },
526
527 (* Gauge bosons: Q = -1 *)
528 V[3] == {
529 ClassName -> W,
530 SelfConjugate -> False,
531 Indices -> {},
532 Mass -> {MW, Internal},
533 Width -> {WW, 2.04759951},
534 QuantumNumbers -> {Q -> 1},
535 PropagatorLabel -> "W",
536 PropagatorType -> Sine,
537 PropagatorArrow -> Forward,
538 ParticleName ->"W+",
539 AntiParticleName ->"W-",
540 PDG -> 24,
541 FullName -> "W" },
542
543V[4] == {
544 ClassName -> G,
545 SelfConjugate -> True,
546 Indices -> {Index[Gluon]},
547 Mass -> 0,
548 Width -> 0,
549 PropagatorLabel -> G,
550 PropagatorType -> C,
551 PropagatorArrow -> None,
552 PDG -> 21,
553 FullName -> "G" },
554
555V[5] == {
556 ClassName -> Wi,
557 Unphysical -> True,
558 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
559 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
560 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
561 SelfConjugate -> True,
562 Indices -> {Index[SU2W]},
563 FlavorIndex -> SU2W,
564 Mass -> 0,
565 PDG -> {1,2,3}},
566
567V[6] == {
568 ClassName -> B,
569 SelfConjugate -> True,
570 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
571 Indices -> {},
572 Mass -> 0,
573 Unphysical -> True},
574
575
576(************ Scalar Fields **********)
577 (* physical Higgs: Q = 0 *)
578 S[1] == {
579 ClassName -> H,
580 SelfConjugate -> True,
581 Mass -> {MH, 120},
582 Width -> {WH, 0.00575308848},
583 PropagatorLabel -> "H",
584 PropagatorType -> D,
585 PropagatorArrow -> None,
586 PDG -> 25,
587 TeXParticleName -> "\\phi",
588 TeXClassName -> "\\phi",
589 FullName -> "H" },
590
591S[2] == {
592 ClassName -> phi,
593 SelfConjugate -> True,
594 Mass -> {MZ, 91.188},
595 Width -> Wphi,
596 PropagatorLabel -> "Phi",
597 PropagatorType -> D,
598 PropagatorArrow -> None,
599 ParticleName ->"phi0",
600 PDG -> 250,
601 FullName -> "Phi",
602 Goldstone -> Z },
603
604S[3] == {
605 ClassName -> phi2,
606 SelfConjugate -> False,
607 Mass -> {MW, Internal},
608 Width -> Wphi2,
609 PropagatorLabel -> "Phi2",
610 PropagatorType -> D,
611 PropagatorArrow -> None,
612 ParticleName ->"phi+",
613 AntiParticleName ->"phi-",
614 PDG -> 251,
615 FullName -> "Phi2",
616 TeXClassName -> "\\phi^+",
617 TeXParticleName -> "\\phi^+",
618 TeXAntiParticleName -> "\\phi^-",
619 Goldstone -> W,
620 QuantumNumbers -> {Q -> 1}}
621}
622
623
624
625
626(*****************************************************************************************)
627
628(* SM Lagrangian *)
629
630(******************** Gauge F^2 Lagrangian terms*************************)
631(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
632 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
633 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
634
635 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
636
637 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
638 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
639
640
641(********************* Fermion Lagrangian terms*************************)
642(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
643 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
644
645 Lkin = I uqbar.Ga[mu].del[uq, mu] +
646 I dqbar.Ga[mu].del[dq, mu] +
647 I lbar.Ga[mu].del[l, mu] +
648 I vlbar.Ga[mu].del[vl, mu];
649
650 LQCD = gs (uqbar.Ga[mu].T[a].uq +
651 dqbar.Ga[mu].T[a].dq)G[mu, a];
652
653 LBright =
654 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
655 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
656 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
657
658 LBleft =
659 -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
660 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
661 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
662 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
663
664 LWleft = ee/sw/2(
665 vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
666 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
667
668 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
669 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
670
671 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
672 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
673
674 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
675 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
676 );
677
678 Lkin + LQCD + LBright + LBleft + LWleft];
679
680(******************** Higgs Lagrangian terms****************************)
681 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
682 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
683
684
685
686 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
687
688 PMVec = Table[PauliSigma[i], {i, 3}];
689 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
690
691 (*Y_phi=1*)
692 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
693 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
694
695 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
696
697 (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
698
699
700(*************** Yukawa Lagrangian***********************)
701LYuk := If[FeynmanGauge,
702
703 Module[{s,r,n,m,i}, -
704 yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
705 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] -
706
707 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*)
708 yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) -
709
710 yl[n] vlbar[s,n].ProjP[s,r].l[r,n] (-I phi2) -
711 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H +I phi)/Sqrt[2]
712 ],
713
714 Module[{s,r,n,m,i}, -
715 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
716 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
717 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]
718 ]
719 ];
720
721LYukawa := LYuk + HC[LYuk];
722
723
724
725(**************Ghost terms**************************)
726(* Now we need the ghost terms which are of the form: *)
727(* - g * antighost * d_BRST G *)
728(* where d_BRST G is BRST transform of the gauge fixing function. *)
729
730LGhost := If[FeynmanGauge,
731 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
732
733 (***********First the pure gauge piece.**********************)
734 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
735 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
736
737 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
738 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
739
740 dBRSTB[mu_] := cw/ee del[ghB, mu];
741 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
742
743 (***********Next the piece from the scalar field.************)
744 LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
745 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
746 ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) -
747 I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
748 ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
749
750
751 (***********Now add the pieces together.********************)
752 LGhostG + LGhostWi + LGhostB + LGhostphi]
753
754, 0];
755
756(*********Total SM Lagrangian*******)
757L4Gen := LGauge + LHiggs + LFermions + LYukawa + LGhost;