HiddenAbelianHiggsModel: Hidden.fr

File Hidden.fr, 22.3 KB (added by Benjamin Fuks, 13 years ago)

Model file

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1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Abelian higgs model ******)
3(****** ******)
4(****** Authors: C. Duhr ******)
5(****** ******)
6(***************************************************************************************************************)
7
8M$ModelName = "Abelian_Higgs_Model";
9
10
11M$Information = {Authors -> {"C. Duhr"},
12 Date -> "02. 06. 2009",
13 Institutions -> {"Universite catholique de Louvain (CP3)"},
14 Emails -> {"claude.duhr@uclouvain.be"},
15 Version -> "1.1",
16 References -> " J. D. Wells, \"How to Find a Hidden World at the Large Hadron Collider,\", [arXiv:0803.1243 [hep-ph]]",
17 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/HiddenAbelianHiggsModel"};
18
19(*
20 v1.1: changed name for full Lagrangian from LSM to LHAHM
21 v1.2: Benj: the lambda parameter had the same name as the leptons, which was making the code crashing.
22*)
23
24(* The U(1)X charge of the abelian Higgs is a free parameter *)
25
26qX = 1;
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[SUW2 ,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 InteractionOrder -> {QED, 2},
83 Value -> 1.16639 * 10^(-5),
84 Description -> "Fermi constant"},
85
86 \[Alpha]S == {
87 ParameterType -> External,
88 BlockName -> SMINPUTS,
89 ParameterName -> aS,
90 InteractionOrder -> {QCD, 2},
91 Value -> 0.118,
92 Description -> "Strong coupling constant at the Z pole."},
93
94
95 ymc == {
96 ParameterType -> External,
97 BlockName -> YUKAWA,
98 Value -> 1.42,
99 OrderBlock -> {4},
100 Description -> "Charm Yukawa mass"},
101
102 ymb == {
103 ParameterType -> External,
104 BlockName -> YUKAWA,
105 Value -> 4.7,
106 OrderBlock -> {5},
107 Description -> "Bottom Yukawa mass"},
108
109 ymt == {
110 ParameterType -> External,
111 BlockName -> YUKAWA,
112 Value -> 174.3,
113 OrderBlock -> {6},
114 Description -> "Top Yukawa mass"},
115
116 ymtau == {
117 ParameterType -> External,
118 BlockName -> YUKAWA,
119 Value -> 1.777,
120 OrderBlock -> {15},
121 Description -> "Tau Yukawa mass"},
122
123 \[Lambda] == {
124 ParameterType -> External,
125 BlockName -> HIGGS,
126 ParameterName -> lam,
127 Value -> 0.42568,
128 InteractionOrder -> {QED, 2},
129 Description -> "SM Higgs self-coupling"},
130
131 cabi == {
132 TeX -> Subscript[\[Theta], c],
133 ParameterType -> External,
134 BlockName -> CKMBLOCK,
135 OrderBlock -> {1},
136 Value -> 0.488,
137 Description -> "Cabibbo angle"},
138
139
140(* New hidden external parameters *)
141
142 \[Alpha]XM1 == {
143 ParameterType -> External,
144 BlockName -> HIDDEN,
145 ParameterName -> aXM1,
146 InteractionOrder -> {QED, -2},
147 Value -> 127.9,
148 Description -> "Inverse of the U(1)X coupling constant"},
149
150 \[Eta] == {
151 ParameterType -> External,
152 BlockName -> HIDDEN,
153 ParameterName -> eta,
154 Value -> 0.01,
155 Description -> "U(1)X - U(1)Y mixing parameter"},
156
157 \[Rho] == {
158 ParameterType -> External,
159 BlockName -> HIDDEN,
160 ParameterName -> rho,
161 Value -> 0.010142,
162 InteractionOrder -> {QED, 2},
163 Description -> "Abelian Higgs self-coupling"},
164
165 \[Kappa] == {
166 ParameterType -> External,
167 BlockName -> HIDDEN,
168 ParameterName -> kap,
169 Value -> 0.0977392,
170 InteractionOrder -> {QED, 2},
171 Description -> "Coupling between the abelian and the SM Higgs"},
172
173
174 (* Internal Parameters *)
175
176(* Weak Mixing *)
177
178 cw == {
179 TeX -> Subscript[c, w],
180 ParameterType -> Internal,
181 Value -> MW/MZ,
182 Description -> "Cos of the Weinberg angle"},
183
184 sw == {
185 TeX -> Subscript[s, w],
186 ParameterType -> Internal,
187 Value -> Sqrt[1-cw^2],
188 Description -> "Sin of the Weinberg angle"},
189
190(* Gauge couplings *)
191
192 \[Alpha]EW == {
193 ParameterType -> Internal,
194 Value -> 1/\[Alpha]EWM1,
195 ParameterName -> aEW,
196 InteractionOrder -> {QED, 2},
197 Description -> "Electroweak coupling constant"},
198
199 ee == {
200 TeX -> e,
201 ParameterType -> Internal,
202 Value -> Sqrt[4 Pi \[Alpha]EW],
203 InteractionOrder -> {QED, 1},
204 Description -> "Electric coupling constant"},
205
206 gw == {
207 TeX -> Subscript[g, w],
208 ParameterType -> Internal,
209 Value -> ee / sw,
210 InteractionOrder -> {QED, 1},
211 Description -> "Weak coupling constant"},
212
213 g1 == {
214 TeX -> Subscript[g, 1],
215 ParameterType -> Internal,
216 Value -> ee / cw,
217 InteractionOrder -> {QED, 1},
218 Description -> "U(1)Y coupling constant"},
219
220 gs == {
221 TeX -> Subscript[g, s],
222 ParameterType -> Internal,
223 Value -> Sqrt[4 Pi \[Alpha]S],
224 InteractionOrder -> {QCD, 1},
225 ParameterName -> G,
226 Description -> "Strong coupling constant"},
227
228 \[Alpha]X == {
229 ParameterType -> Internal,
230 Value -> 1/\[Alpha]XM1,
231 ParameterName -> aX,
232 InteractionOrder -> {QED, 2},
233 Description -> "U(1)X coupling contant"},
234
235 gX == {
236 TeX -> Subscript[g, X],
237 ParameterType -> Internal,
238 Value -> Sqrt[4 Pi \[Alpha]X],
239 InteractionOrder -> {QED, 1},
240 Description -> "U(1)X coupling constant"},
241
242(* New scales *)
243
244 MZ0 == {
245 ParameterType -> Internal,
246 Value -> MZ,
247 Description -> "Z mass before mixing"},
248
249 MX =={
250 ParameterType -> Internal,
251 Value -> MZp,
252 Description -> "X mass before mixing"},
253
254 \[CapitalDelta]Z =={
255 ParameterType -> Internal,
256 Value -> MX^2/MZ0^2,
257 ParameterName -> DZ,
258 Description -> "Ratio of scales"},
259
260
261(* Higgs sector *)
262
263
264
265 v == {
266 ParameterType -> Internal,
267 Value -> 1/Sqrt[Gf* Sqrt[2]],
268 InteractionOrder -> {QED, -1},
269 Description -> "SM Higgs VEV"},
270
271 \[Xi] == {
272 ParameterType -> Internal,
273 Value -> MX/qX/gX,
274 InteractionOrder -> {QED, -1},
275 ParameterName -> xi,
276 Description -> "Abelian Higgs VEV"},
277
278 MH1 == {
279 ParameterType -> Internal,
280 Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 - Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]],
281 Description -> "Mass of H1"},
282
283 MH2 == {
284 ParameterType -> Internal,
285 Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 + Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]],
286 Description -> "Mass of H2"},
287
288 \[Mu]SM2 =={
289 TeX -> Subsuperscript[\[Mu], SM, 2],
290 ParameterType -> Internal,
291 Value -> (\[Rho] v^2 + \[Kappa] \[Xi]^2)/2,
292 ParameterName -> muSM2,
293 Description -> "Quadratic SM potential term"},
294
295 \[Mu]H2 =={
296 TeX -> Subsuperscript[\[Mu], H, 2],
297 ParameterType -> Internal,
298 Value -> (\[Kappa] v^2 + \[Lambda] \[Xi]^2)/2,
299 ParameterName -> muH2,
300 Description -> "Quadratic abelian potential term"},
301
302(* Mixing parameters *)
303
304
305 \[Theta]a == {
306 TeX -> Subscript[\[Theta], \[Alpha]],
307 ParameterType -> Internal,
308 Value -> ArcTan[-2 sw \[Eta]/(1-sw^2 \[Eta]^2 -\[CapitalDelta]Z)]/2,
309 ParameterName -> alp,
310 Description -> "Mixing in the weak sector"},
311
312 ca == {
313 TeX -> Subscript[c, \[Alpha]],
314 ParameterType -> Internal,
315 Value -> Cos[\[Theta]a],
316 Description -> "Cosine of alp"},
317
318 sa == {
319 TeX -> Subscript[s, \[Alpha]],
320 ParameterType -> Internal,
321 Value -> Sin[\[Theta]a],
322 Description -> "Sine of alp"},
323
324 \[Chi] == {
325 ParameterType -> Internal,
326 Value -> (Sqrt[1+4\[Eta]^2] - 1)/2/\[Eta],
327 ParameterName -> chi,
328 Description -> "kinetic mixing parameter"},
329
330(* Higgs *)
331
332 \[Theta]h == {
333 TeX -> Subscript[\[Theta], h],
334 ParameterType -> Internal,
335 Value -> ArcTan[\[Kappa] v \[Xi]/(\[Rho] \[Xi]^2 - \[Lambda] v^2)]/2,
336 ParameterName -> th,
337 Description -> "Mixing in the Higgs sector"},
338
339 ch == {
340 TeX -> Subscript[c, h],
341 ParameterType -> Internal,
342 Value -> Cos[\[Theta]h],
343 Description -> "Cosine of th"},
344
345 sh == {
346 TeX -> Subscript[s, h],
347 ParameterType -> Internal,
348 Value -> Sin[\[Theta]h],
349 Description -> "Sine of th"},
350
351(* Yukawa sector *)
352
353 yl == {
354 Indices -> {Index[Generation]},
355 AllowSummation -> True,
356 ParameterType -> Internal,
357 Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v},
358 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
359 InteractionOrder -> {QED, 1},
360 ComplexParameter -> False,
361 Definitions -> {yl[1] -> 0, yl[2] ->0},
362 Description -> "Lepton Yukawa coupling"},
363
364 yu == {
365 Indices -> {Index[Generation]},
366 AllowSummation -> True,
367 ParameterType -> Internal,
368 Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
369 ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
370 InteractionOrder -> {QED, 1},
371 ComplexParameter -> False,
372 Definitions -> {yu[1] -> 0},
373 Description -> "U-quark Yukawa coupling"},
374
375 yd == {
376 Indices -> {Index[Generation]},
377 AllowSummation -> True,
378 ParameterType -> Internal,
379 Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
380 ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
381 InteractionOrder -> {QED, 1},
382 ComplexParameter -> False,
383 Definitions -> {yd[1] -> 0, yd[2] -> 0},
384 Description -> "D-quark Yukawa coupling"},
385
386
387 CKM == {
388 Indices -> {Index[Generation], Index[Generation]},
389 TensorClass -> CKM,
390 Unitary -> True,
391 Definitions -> {CKM[3, 3] -> 1,
392 CKM[i_, 3] :> 0 /; i != 3,
393 CKM[3, i_] :> 0 /; i != 3},
394 Value -> {CKM[1,2] -> Sin[cabi],
395 CKM[1,1] -> Cos[cabi],
396 CKM[2,1] -> -Sin[cabi],
397 CKM[2,2] -> Cos[cabi]},
398 Description -> "CKM-Matrix"}
399
400
401
402}
403
404
405(************** Gauge Groups ******************)
406
407M$GaugeGroups = {
408
409 U1Y == {
410 Abelian -> True,
411 GaugeBoson -> B,
412 Charge -> Y,
413 CouplingConstant -> g1},
414
415 U1X == {
416 Abelian -> True,
417 GaugeBoson -> X,
418 Charge -> QX,
419 CouplingConstant -> ee},
420
421 SU2L == {
422 Abelian -> False,
423 GaugeBoson -> Wi,
424 StructureConstant -> Eps,
425 CouplingConstant -> gw},
426
427 SU3C == {
428 Abelian -> False,
429 GaugeBoson -> G,
430 StructureConstant -> f,
431 SymmetricTensor -> dSUN,
432 Representations -> {T, Colour},
433 CouplingConstant -> gs}
434}
435
436(********* Particle Classes **********)
437
438M$ClassesDescription = {
439
440(********** Fermions ************)
441 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
442 F[1] == {
443 ClassName -> vl,
444 ClassMembers -> {ve,vm,vt},
445 FlavorIndex -> Generation,
446 SelfConjugate -> False,
447 Indices -> {Index[Generation]},
448 Mass -> 0,
449 Width -> 0,
450 QuantumNumbers -> {LeptonNumber -> 1},
451 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
452 PropagatorType -> S,
453 PropagatorArrow -> Forward,
454 PDG -> {12,14,16},
455 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
456
457 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
458 F[2] == {
459 ClassName -> l,
460 ClassMembers -> {e, m, tt},
461 FlavorIndex -> Generation,
462 SelfConjugate -> False,
463 Indices -> {Index[Generation]},
464 Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
465 Width -> 0,
466 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
467 PropagatorLabel -> {"l", "e", "m", "tt"},
468 PropagatorType -> Straight,
469 ParticleName -> {"e-", "m-", "tt-"},
470 AntiParticleName -> {"e+", "m+", "tt+"},
471 PropagatorArrow -> Forward,
472 PDG -> {11, 13, 15},
473 FullName -> {"Electron", "Muon", "Tau"} },
474
475 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
476 F[3] == {
477 ClassMembers -> {u, c, t},
478 ClassName -> uq,
479 FlavorIndex -> Generation,
480 SelfConjugate -> False,
481 Indices -> {Index[Generation], Index[Colour]},
482 Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
483 Width -> {0, 0, {WT, 1.50833649}},
484 QuantumNumbers -> {Q -> 2/3},
485 PropagatorLabel -> {"uq", "u", "c", "t"},
486 PropagatorType -> Straight,
487 PropagatorArrow -> Forward,
488 PDG -> {2, 4, 6},
489 FullName -> {"u-quark", "c-quark", "t-quark"}},
490
491 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
492 F[4] == {
493 ClassMembers -> {d, s, b},
494 ClassName -> dq,
495 FlavorIndex -> Generation,
496 SelfConjugate -> False,
497 Indices -> {Index[Generation], Index[Colour]},
498 Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
499 Width -> 0,
500 QuantumNumbers -> {Q -> -1/3},
501 PropagatorLabel -> {"dq", "d", "s", "b"},
502 PropagatorType -> Straight,
503 PropagatorArrow -> Forward,
504 PDG -> {1,3,5},
505 FullName -> {"d-quark", "s-quark", "b-quark"} },
506
507(********** Ghosts **********)
508
509 U[1] == {
510 ClassName -> ghG,
511 SelfConjugate -> False,
512 Indices -> {Index[Gluon]},
513 Ghost -> G,
514 Mass -> 0,
515 Width -> 0,
516 QuantumNumbers -> {GhostNumber -> 1},
517 PropagatorLabel -> uG,
518 PropagatorType -> GhostDash,
519 PropagatorArrow -> Forward},
520
521
522(************ Gauge Bosons ***************)
523 (* Gauge bosons: Q = 0 *)
524 V[1] == {
525 ClassName -> A,
526 SelfConjugate -> True,
527 Indices -> {},
528 Mass -> 0,
529 Width -> 0,
530 PropagatorLabel -> "a",
531 PropagatorType -> W,
532 PropagatorArrow -> None,
533 PDG -> 22,
534 FullName -> "Photon" },
535
536 V[21] == {
537 ClassName -> Z,
538 SelfConjugate -> True,
539 Indices -> {},
540 Mass -> {MZ, 91.188},
541 Width -> {WZ, 2.44140351},
542 PropagatorLabel -> "Z",
543 PropagatorType -> Sine,
544 PropagatorArrow -> None,
545 PDG -> 23,
546 FullName -> "Z" },
547
548 V[22] == {
549 ClassName -> Zp,
550 SelfConjugate -> True,
551 Indices -> {},
552 Mass -> {MZp, 500},
553 Width -> {WZp, 0.0008252},
554 PropagatorLabel -> "Zp",
555 PropagatorType -> Sine,
556 PropagatorArrow -> None,
557 PDG -> 1023,
558 FullName -> "Zp" },
559
560 V[210] == {
561 ClassName -> Bp,
562 SelfConjugate -> True,
563 Unphysical -> True,
564 Indices -> {},
565 Mass -> 0,
566 Width -> 0,
567 Definitions -> {Bp[mu_] :> cw A[mu] -sw ca Z[mu] + sw sa Zp[mu]}},
568
569 V[220] == {
570 ClassName -> Xp,
571 SelfConjugate -> True,
572 Unphysical -> True,
573 Indices -> {},
574 Mass -> 0,
575 Width -> 0,
576 Definitions -> {Xp[mu_] :> sa Z[mu] + ca Zp[mu]}},
577
578
579 (* Gauge bosons: Q = -1 *)
580 V[3] == {
581 ClassName -> W,
582 SelfConjugate -> False,
583 Indices -> {},
584 Mass -> {MW, 80.419},
585 Width -> {WW, 2.04759951},
586 QuantumNumbers -> {Q -> 1},
587 PropagatorLabel -> "W",
588 PropagatorType -> Sine,
589 PropagatorArrow -> Forward,
590 ParticleName ->"W+",
591 AntiParticleName ->"W-",
592 PDG -> 24,
593 FullName -> "W" },
594
595V[4] == {
596 ClassName -> G,
597 SelfConjugate -> True,
598 Indices -> {Index[Gluon]},
599 Mass -> 0,
600 Width -> 0,
601 PropagatorLabel -> G,
602 PropagatorType -> C,
603 PropagatorArrow -> None,
604 PDG -> 21,
605 FullName -> "G" },
606
607V[5] == {
608 ClassName -> Wi,
609 Unphysical -> True,
610 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
611 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
612 Wi[mu_, 3] -> -cw sa Zp[mu] + cw ca Z[mu] + sw A[mu]},
613 SelfConjugate -> True,
614 Indices -> {Index[SU2W]},
615 FlavorIndex -> SU2W,
616 Mass -> 0,
617 PDG -> {1,2,3}},
618
619V[6] == {
620 ClassName -> B,
621 SelfConjugate -> True,
622 Definitions -> {B[mu_] -> Bp[mu] + \[Eta] Xp[mu]},
623 Indices -> {},
624 Mass -> 0,
625 Unphysical -> True},
626
627V[61] == {
628 ClassName -> X,
629 SelfConjugate -> True,
630 Definitions -> {X[mu_] -> \[Chi] \[Eta] Xp[mu]},
631 Indices -> {},
632 Mass -> 0,
633 Unphysical -> True},
634
635
636
637(************ Scalar Fields **********)
638 (* physical Higgs: Q = 0 *)
639 S[11] == {
640 ClassName -> h1,
641 SelfConjugate -> True,
642 Mass -> {MH1, Internal},
643 Width -> {WH1, 0.00282299},
644 PropagatorLabel -> "h1",
645 PropagatorType -> D,
646 PropagatorArrow -> None,
647 PDG -> 25,
648 FullName -> "h1" },
649
650 S[12] == {
651 ClassName -> h2,
652 SelfConjugate -> True,
653 Mass -> {MH2, Internal},
654 Width -> {WH2, 5.23795},
655 PropagatorLabel -> "h2",
656 PropagatorType -> D,
657 PropagatorArrow -> None,
658 PDG -> 35,
659 FullName -> "h2" },
660
661 S[110] == {
662 ClassName -> H,
663 SelfConjugate -> True,
664 Unphysical -> True,
665 Definitions -> {H -> ch h1 + sh h2}},
666
667 S[120] == {
668 ClassName -> phih,
669 SelfConjugate -> False,
670 Unphysical -> True,
671 Definitions -> {phih -> \[Xi]/Sqrt[2]-sh h1 + ch h2}}
672}
673
674
675
676(*****************************************************************************************)
677
678(* SM Lagrangian *)
679
680(******************** Gauge F^2 Lagrangian terms*************************)
681(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
682 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
683 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
684
685 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[X[nu], mu] - del[X[mu], nu])^2 +
686 \[Chi]/2 (del[X[nu], mu] - del[X[mu], nu]) (del[B[nu], mu] - del[B[mu], nu]) -
687
688 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
689 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
690
691
692(********************* Fermion Lagrangian terms*************************)
693(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
694 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
695
696 Lkin = I uqbar.Ga[mu].del[uq, mu] +
697 I dqbar.Ga[mu].del[dq, mu] +
698 I lbar.Ga[mu].del[l, mu] +
699 I vlbar.Ga[mu].del[vl, mu];
700
701 LQCD = gs (uqbar.Ga[mu].T[a].uq +
702 dqbar.Ga[mu].T[a].dq)G[mu, a];
703
704 LBright =
705 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
706 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
707 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
708
709 LBleft =
710 -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
711 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
712 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
713 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
714
715 LWleft = ee/sw/2(
716 vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
717 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
718
719 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
720 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
721
722 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
723 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
724
725 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
726 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
727 );
728
729 Lkin + LQCD + LBright + LBleft + LWleft];
730
731(******************** Higgs Lagrangian terms****************************)
732 Phi := {0, (v + H)/Sqrt[2]};
733 Phibar := {0, (v + H)/Sqrt[2]};
734
735
736
737 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
738
739 PMVec = Table[PauliSigma[i], {i, 3}];
740 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
741
742 (*Y_phi=1*)
743 Dc[f_List, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
744 Dcbar[f_List, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
745
746 Dc[phih, mu_] := del[phih, mu] -I gX qX X[mu] phih;
747 Dc[phihbar, mu_] := del[phihbar, mu] +I gX qX X[mu] phihbar;
748
749 Vphi[Phi2SM_, Phi2H_] := -\[Mu]SM2 Phi2SM + \[Lambda] (Phi2SM)^2 -
750 \[Mu]H2 Phi2H + \[Rho] (Phi2H)^2 +
751 \[Kappa] (Phi2H) (Phi2SM) ;
752
753 (* The value of qX is set at the beginning of the notebook *)
754
755 (Dcbar[Phibar, mu]).Dc[Phi, mu] + Dc[phihbar,mu] Dc[phih, mu] - Vphi[Phibar.Phi, phihbar phih]];
756
757
758(*************** Yukawa Lagrangian***********************)
759LYuk := Module[{s,r,n,m,i}, -
760 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
761 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
762 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2]
763 ]
764
765LYukawa := LYuk + HC[LYuk];
766
767
768
769(**************Ghost terms**************************)
770(* Now we need the ghost terms which are of the form: *)
771(* - g * antighost * d_BRST G *)
772(* where d_BRST G is BRST transform of the gauge fixing function. *)
773
774LGhost :=
775 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
776
777 (***********First the pure gauge piece.**********************)
778 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
779 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
780
781 (***********Now add the pieces together.********************)
782 LGhostG]
783
784
785(*********Total SM Lagrangian*******)
786LHAHM := LGauge + LHiggs + LFermions + LYukawa + LGhost;
787
788