SILH: SILH.fr

File SILH.fr, 24.3 KB (added by Claude Duhr, 17 years ago)

The model file

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the SILH model ******)
3(****** ******)
4(****** Authors: C. Degrande ******)
5(****** ******)
6(****** Only unitary gauge is implemented ******)
7(****** Only the first order in \[Xi](see parameters) is implemented ******)
8(***************************************************************************************************************)
9
10M$ModelName = "SILH";
11
12
13M$Information = {Authors -> {"C. Degrande"},
14 Date->"12/06/2009"
15 Institutions -> {"Universite catholique de Louvain (CP3)"},
16 Emails -> {"celine.degrande@uclouvain.be"},
17 Version -> 1,
18 URLs->"http://feynrules.phys.ucl.ac.be/view/Main/SILH"
19};
20
21
22(******* Index definitions ********)
23
24IndexRange[ Index[Generation] ] = Range[3]
25
26IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
27
28IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
29
30IndexRange[ Index[SU2W] ] = Range[3]
31
32
33IndexStyle[Colour, i]
34
35IndexStyle[Generation, f]
36
37IndexStyle[Gluon ,a]
38
39IndexStyle[SUW2 ,k]
40
41
42(******* Gauge parameters (for FeynArts) ********)
43
44GaugeXi[ V[1] ] = GaugeXi[A];
45GaugeXi[ V[2] ] = GaugeXi[Z];
46GaugeXi[ V[3] ] = GaugeXi[W];
47GaugeXi[ V[4] ] = GaugeXi[G];
48GaugeXi[ S[1] ] = 1;
49GaugeXi[ S[2] ] = GaugeXi[Z];
50GaugeXi[ S[3] ] = GaugeXi[W];
51GaugeXi[ U[1] ] = GaugeXi[A];
52GaugeXi[ U[2] ] = GaugeXi[Z];
53GaugeXi[ U[31] ] = GaugeXi[W];
54GaugeXi[ U[32] ] = GaugeXi[W];
55GaugeXi[ U[4] ] = GaugeXi[G];
56
57
58(**************** Parameters *************)
59
60M$Parameters = {
61
62 (* External SM parameters *)
63
64 \[Alpha]EWM1== {
65 ParameterType -> External,
66 BlockName -> SMINPUTS,
67 ParameterName -> aEWM1,
68 InteractionOrder -> {QED, -2},
69 Value -> 127.9,
70 Description -> "Inverse of the electroweak coupling constant"},
71
72 Gf == {
73 ParameterType -> External,
74 BlockName -> SMINPUTS,
75 InteractionOrder -> {QED, 2},
76 Value -> 1.16639 * 10^(-5),
77 Description -> "Fermi constant"},
78
79 \[Alpha]S == {
80 ParameterType -> External,
81 BlockName -> SMINPUTS,
82 ParameterName -> aS,
83 InteractionOrder -> {QCD, 2},
84 Value -> 0.118,
85 Description -> "Strong coupling constant at the Z pole."},
86
87
88 ZM == {
89 ParameterType -> External,
90 BlockName -> SMINPUTS,
91 Value -> 91.188,
92 Description -> "Z mass"},
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
124
125 (* External SILH Parameter *)
126
127 frho =={
128 TeX -> Subscript[f,\[Rho]],
129 ParameterType -> External,
130 Value -> 1 (*TeV*),
131 Description -> "sigma model scale"},
132
133 grho =={
134 TeX -> Subscript[g,\[Rho]],
135 ParameterType -> External,
136 Value -> 1,
137 Description -> "sigma model coupling"},
138
139 cH =={
140 TeX -> Subscript[c,H],
141 ParameterType -> External,
142 Value -> 1},
143
144 cT =={
145 TeX -> Subscript[c,T],
146 ParameterType -> External,
147 Value -> 1},
148
149 c6 =={
150 TeX -> Subscript[c,6],
151 ParameterType -> External,
152 Value -> 1},
153
154 cy =={
155 TeX -> Subscript[c,y],
156 ParameterType -> External,
157 Value -> 1},
158
159 cW =={
160 TeX -> Subscript[c,W],
161 ParameterType -> External,
162 Value -> 1},
163
164 cB =={
165 TeX -> Subscript[c,B],
166 ParameterType -> External,
167 Value -> 1},
168
169 cHW =={
170 TeX -> Subscript[c,HW],
171 ParameterType -> External,
172 Value -> 1},
173
174 cHB =={
175 TeX -> Subscript[c,HB],
176 ParameterType -> External,
177 Value -> 1},
178
179 cga =={
180 TeX -> Subscript[c,\[Gamma]],
181 ParameterType -> External,
182 Value -> 1},
183
184 cg =={
185 TeX -> Subscript[c,g],
186 ParameterType -> External,
187 Value -> 1},
188
189 c2W =={
190 TeX -> Subscript[c,2W],
191 ParameterType -> External,
192 Value -> 1},
193
194 c2B =={
195 TeX -> Subscript[c,2B],
196 ParameterType -> External,
197 Value -> 1},
198
199 c2g =={
200 TeX -> Subscript[c,2g],
201 ParameterType -> External,
202 Value -> 1},
203
204 c3W =={
205 TeX -> Subscript[c,3W],
206 ParameterType -> External,
207 Value -> 1},
208
209 c3B =={
210 TeX -> Subscript[c,3B],
211 ParameterType -> External,
212 Value -> 1},
213
214
215 (* Internal Parameters *)
216
217 \[Alpha]EW == {
218 ParameterType -> Internal,
219 Value -> 1/\[Alpha]EWM1,
220 ParameterName -> aEW,
221 InteractionOrder -> {QED, 2},
222 Description -> "Electroweak coupling contant"},
223
224
225 MW == {
226 ParameterType -> Internal,
227 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
228 Description -> "W mass"},
229
230 sw2 == {
231 ParameterType -> Internal,
232 Value -> 1-(MW/MZ)^2,
233 Description -> "Squared Sin of the Weinberg angle"},
234
235 ee == {
236 TeX -> e,
237 ParameterType -> Internal,
238 Value -> Sqrt[4 Pi \[Alpha]EW],
239 InteractionOrder -> {QED, 1},
240 Description -> "Electric coupling constant"},
241
242 cw == {
243 TeX -> Subscript[c, w],
244 ParameterType -> Internal,
245 Value -> Sqrt[1 - sw2],
246 Description -> "Cos of the Weinberg angle"},
247
248 sw == {
249 TeX -> Subscript[s, w],
250 ParameterType -> Internal,
251 Value -> Sqrt[sw2],
252 Description -> "Sin of the Weinberg angle"},
253
254 gw == {
255 TeX -> Subscript[g, w],
256 ParameterType -> Internal,
257 Value -> ee / sw,
258 InteractionOrder -> {QED, 1},
259 Description -> "Weak coupling constant"},
260
261 g1 == {
262 TeX -> Subscript[g, 1],
263 ParameterType -> Internal,
264 Value -> ee / cw,
265 InteractionOrder -> {QED, 1},
266 Description -> "U(1)Y coupling constant"},
267
268 gs == {
269 TeX -> Subscript[g, s],
270 ParameterType -> Internal,
271 Value -> Sqrt[4 Pi \[Alpha]S],
272 InteractionOrder -> {QCD, 1},
273 ParameterName -> G,
274 Description -> "Strong coupling constant"},
275
276 v == {
277 ParameterType -> Internal,
278 Value -> 2*MW*sw/ee,
279 InteractionOrder -> {QED, -1},
280 Description -> "Higgs VEV"},
281
282 \[Xi] == {
283 ParameterType -> Internal,
284 Value -> v^2/frho^2,
285 InteractionOrder -> {QED, -1},
286 Description -> "Higgs VEV"},
287
288 \[Lambda] == {
289 ParameterType -> Internal,
290 Value -> MH^2/(2*v^2)(1+cH*\[Xi]-3/2 c6*\[Xi]),
291 InteractionOrder -> {QED, 2},
292 ParameterName -> lam,
293 Description -> "Higgs quartic coupling"},
294
295 muH == {
296 ParameterType -> Internal,
297 Value -> Sqrt[v^2 \[Lambda](1+3/4 c6 \[Xi])],
298 TeX -> \[Mu],
299 Description -> "Coefficient of the quadratic piece of the Higgs potential"},
300
301
302 yl == {
303 Indices -> {Index[Generation]},
304 AllowSummation -> True,
305 ParameterType -> Internal,
306 Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v (1+cy/2\[Xi])},
307 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
308 InteractionOrder -> {QED, 1},
309 ComplexParameter -> False,
310 Definitions -> {yl[1] -> 0, yl[2] ->0},
311 Description -> "Lepton Yukawa coupling"},
312
313 yu == {
314 Indices -> {Index[Generation]},
315 AllowSummation -> True,
316 ParameterType -> Internal,
317 Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v (1+cy/2\[Xi]), yu[3] -> Sqrt[2] ymt / v (1+cy/2\[Xi])},
318 ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
319 InteractionOrder -> {QED, 1},
320 ComplexParameter -> False,
321 Definitions -> {yu[1] -> 0},
322 Description -> "U-quark Yukawa coupling"},
323
324 yd == {
325 Indices -> {Index[Generation]},
326 AllowSummation -> True,
327 ParameterType -> Internal,
328 Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v (1+cy/2\[Xi])},
329 ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
330 InteractionOrder -> {QED, 1},
331 ComplexParameter -> False,
332 Definitions -> {yd[1] -> 0, yd[2] -> 0},
333 Description -> "D-quark Yukawa coupling"},
334
335 cabi == {
336 TeX -> Subscript[\[Theta], c],
337 ParameterType -> External,
338 BlockName -> CKMBLOCK,
339 OrderBlock -> {1},
340 Value -> 0.488,
341 Description -> "Cabibbo angle"},
342
343 CKM == {
344 Indices -> {Index[Generation], Index[Generation]},
345 TensorClass -> CKM,
346 Unitary -> True,
347 Definitions -> {CKM[3, 3] -> 1,
348 CKM[i_, 3] :> 0 /; i != 3,
349 CKM[3, i_] :> 0 /; i != 3},
350 Value -> {CKM[1,2] -> Sin[cabi],
351 CKM[1,1] -> Cos[cabi],
352 CKM[2,1] -> -Sin[cabi],
353 CKM[2,2] -> Cos[cabi]},
354 Description -> "CKM-Matrix"},
355
356 mrho =={
357 TeX -> Subscript[m,\[Rho]],
358 ParameterType -> Internal,
359 Value -> grho*frho,
360 Description -> "sigma model mass"}
361}
362
363
364(************** Gauge Groups ******************)
365
366M$GaugeGroups = {
367
368 U1Y == {
369 Abelian -> True,
370 GaugeBoson -> B,
371 Charge -> Y,
372 CouplingConstant -> g1},
373
374 SU2L == {
375 Abelian -> False,
376 GaugeBoson -> Wi,
377 StructureConstant -> Eps,
378 CouplingConstant -> gw},
379
380 SU3C == {
381 Abelian -> False,
382 GaugeBoson -> G,
383 StructureConstant -> f,
384 SymmetricTensor -> dSUN,
385 Representations -> {T, Colour},
386 CouplingConstant -> gs}
387}
388
389(********* Particle Classes **********)
390
391M$ClassesDescription = {
392
393(********** Fermions ************)
394 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
395 F[1] == {
396 ClassName -> vl,
397 ClassMembers -> {ve,vm,vt},
398 FlavorIndex -> Generation,
399 SelfConjugate -> False,
400 Indices -> {Index[Generation]},
401 Mass -> 0,
402 Width -> 0,
403 QuantumNumbers -> {LeptonNumber -> 1},
404 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
405 PropagatorType -> S,
406 PropagatorArrow -> Forward,
407 PDG -> {12,14,16},
408 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
409
410 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
411 F[2] == {
412 ClassName -> l,
413 ClassMembers -> {e, m, tt},
414 FlavorIndex -> Generation,
415 SelfConjugate -> False,
416 Indices -> {Index[Generation]},
417 Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
418 Width -> 0,
419 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
420 PropagatorLabel -> {"l", "e", "m", "tt"},
421 PropagatorType -> Straight,
422 ParticleName -> {"e-", "m-", "tt-"},
423 AntiParticleName -> {"e+", "m+", "tt+"},
424 PropagatorArrow -> Forward,
425 PDG -> {11, 13, 15},
426 FullName -> {"Electron", "Muon", "Tau"} },
427
428 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
429 F[3] == {
430 ClassMembers -> {u, c, t},
431 ClassName -> uq,
432 FlavorIndex -> Generation,
433 SelfConjugate -> False,
434 Indices -> {Index[Generation], Index[Colour]},
435 Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
436 Width -> {0, 0, {WT, 1.50833649}},
437 QuantumNumbers -> {Q -> 2/3},
438 PropagatorLabel -> {"uq", "u", "c", "t"},
439 PropagatorType -> Straight,
440 PropagatorArrow -> Forward,
441 PDG -> {2, 4, 6},
442 FullName -> {"u-quark", "c-quark", "t-quark"}},
443
444 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
445 F[4] == {
446 ClassMembers -> {d, s, b},
447 ClassName -> dq,
448 FlavorIndex -> Generation,
449 SelfConjugate -> False,
450 Indices -> {Index[Generation], Index[Colour]},
451 Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
452 Width -> 0,
453 QuantumNumbers -> {Q -> -1/3},
454 PropagatorLabel -> {"dq", "d", "s", "b"},
455 PropagatorType -> Straight,
456 PropagatorArrow -> Forward,
457 PDG -> {1,3,5},
458 FullName -> {"d-quark", "s-quark", "b-quark"} },
459
460(********** Ghosts **********)
461 U[1] == {
462 ClassName -> ghA,
463 SelfConjugate -> False,
464 Indices -> {},
465 Ghost -> A,
466 Mass -> 0,
467 QuantumNumbers -> {GhostNumber -> 1},
468 PropagatorLabel -> uA,
469 PropagatorType -> GhostDash,
470 PropagatorArrow -> Forward},
471
472 U[2] == {
473 ClassName -> ghZ,
474 SelfConjugate -> False,
475 Indices -> {},
476 Mass -> {MZ, 91.188},
477 Ghost -> Z,
478 QuantumNumbers -> {GhostNumber -> 1},
479 PropagatorLabel -> uZ,
480 PropagatorType -> GhostDash,
481 PropagatorArrow -> Forward},
482
483 U[31] == {
484 ClassName -> ghWp,
485 SelfConjugate -> False,
486 Indices -> {},
487 Mass -> {MW, Internal},
488 Ghost -> W,
489 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
490 PropagatorLabel -> uWp,
491 PropagatorType -> GhostDash,
492 PropagatorArrow -> Forward},
493
494 U[32] == {
495 ClassName -> ghWm,
496 SelfConjugate -> False,
497 Indices -> {},
498 Mass -> {MW, Internal},
499 Ghost -> Wbar,
500 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
501 PropagatorLabel -> uWm,
502 PropagatorType -> GhostDash,
503 PropagatorArrow -> Forward},
504
505 U[4] == {
506 ClassName -> ghG,
507 SelfConjugate -> False,
508 Indices -> {Index[Gluon]},
509 Ghost -> G,
510 Mass -> 0,
511 QuantumNumbers -> {GhostNumber -> 1},
512 PropagatorLabel -> uG,
513 PropagatorType -> GhostDash,
514 PropagatorArrow -> Forward},
515
516 U[5] == {
517 ClassName -> ghWi,
518 Unphysical -> True,
519 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
520 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
521 ghWi[3] -> cw ghZ + sw ghA},
522 SelfConjugate -> False,
523 Ghost -> Wi,
524 Indices -> {Index[SU2W]},
525 FlavorIndex -> SU2W},
526
527 U[6] == {
528 ClassName -> ghB,
529 SelfConjugate -> False,
530 Definitions -> {ghB -> -sw ghZ + cw ghA},
531 Indices -> {},
532 Ghost -> B,
533 Unphysical -> True},
534
535(************ Gauge Bosons ***************)
536 (* Gauge bosons: Q = 0 *)
537 V[1] == {
538 ClassName -> A,
539 SelfConjugate -> True,
540 Indices -> {},
541 Mass -> 0,
542 Width -> 0,
543 PropagatorLabel -> "a",
544 PropagatorType -> W,
545 PropagatorArrow -> None,
546 PDG -> 22,
547 FullName -> "Photon" },
548
549 V[2] == {
550 ClassName -> Z,
551 SelfConjugate -> True,
552 Indices -> {},
553 Mass -> {MZ, 91.188},
554 Width -> {WZ, 2.44140351},
555 PropagatorLabel -> "Z",
556 PropagatorType -> Sine,
557 PropagatorArrow -> None,
558 PDG -> 23,
559 FullName -> "Z" },
560
561 (* Gauge bosons: Q = -1 *)
562 V[3] == {
563 ClassName -> W,
564 SelfConjugate -> False,
565 Indices -> {},
566 Mass -> {MW, Internal},
567 Width -> {WW, 2.04759951},
568 QuantumNumbers -> {Q -> 1},
569 PropagatorLabel -> "W",
570 PropagatorType -> Sine,
571 PropagatorArrow -> Forward,
572 ParticleName ->"W+",
573 AntiParticleName ->"W-",
574 PDG -> 24,
575 FullName -> "W" },
576
577V[4] == {
578 ClassName -> G,
579 SelfConjugate -> True,
580 Indices -> {Index[Gluon]},
581 Mass -> 0,
582 Width -> 0,
583 PropagatorLabel -> G,
584 PropagatorType -> C,
585 PropagatorArrow -> None,
586 PDG -> 21,
587 FullName -> "G" },
588
589V[5] == {
590 ClassName -> Wi,
591 Unphysical -> True,
592 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
593 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
594 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
595 SelfConjugate -> True,
596 Indices -> {Index[SU2W]},
597 FlavorIndex -> SU2W,
598 Mass -> 0,
599 PDG -> {1,2,3}},
600
601V[6] == {
602 ClassName -> B,
603 SelfConjugate -> True,
604 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
605 Indices -> {},
606 Mass -> 0,
607 Unphysical -> True},
608
609
610(************ Scalar Fields **********)
611 (* physical Higgs: Q = 0 *)
612 S[1] == {
613 ClassName -> H,
614 SelfConjugate -> True,
615 Mass -> {MH, 120},
616 Width -> {WH, 0.00575308848},
617 PropagatorLabel -> "H",
618 PropagatorType -> D,
619 PropagatorArrow -> None,
620 PDG -> 25,
621 FullName -> "H" },
622
623S[2] == {
624 ClassName -> phi,
625 SelfConjugate -> True,
626 Mass -> {MZ, 91.188},
627 Width -> Wphi,
628 PropagatorLabel -> "Phi",
629 PropagatorType -> D,
630 PropagatorArrow -> None,
631 ParticleName ->"phi0",
632 PDG -> 250,
633 FullName -> "Phi",
634 Goldstone -> Z },
635
636S[3] == {
637 ClassName -> phi2,
638 SelfConjugate -> False,
639 Mass -> {MW, Internal},
640 Width -> Wphi2,
641 PropagatorLabel -> "Phi2",
642 PropagatorType -> D,
643 PropagatorArrow -> None,
644 ParticleName ->"phi+",
645 AntiParticleName ->"phi-",
646 PDG -> 251,
647 FullName -> "Phi2",
648 Goldstone -> W,
649 QuantumNumbers -> {Q -> 1}}
650
651}
652
653(*Renomalisation*)
654
655Hbare = H(1-cH \[Xi]/2);
656Bbare[mu_] := B[mu](1+cB sw^2/cw^2*MW^2/mrho^2+cga g1^2*gw^2/grho^2*\[Xi]/16/\[Pi]^2);
657Wibare[mu_,i_] := Wi[mu,i](1+cW*MW^2/mrho^2);
658g1bare = g1(1-cB sw^2/cw^2*MW^2/mrho^2-cga g1^2*gw^2/grho^2*\[Xi]/16/\[Pi]^2);
659gwbare = gw(1-cW*MW^2/mrho^2);
660Gbare[mu_,a_] := G[mu,a](1+cg gs^2*yu[Index[Generation,3]]^2/grho^2*\[Xi]/16/\[Pi]^2);
661gsbare = gs(1-cg gs^2*yu[Index[Generation,3]]^2/grho^2*\[Xi]/16/\[Pi]^2);
662
663
664(*****************************************************************************************)
665
666(* SM Lagrangian *)
667
668(******************** Gauge F^2 Lagrangian terms*************************)
669(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
670 LGauge := Normal[Series[((-1/4 (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i2, i3] Wibare[mu, i2] Wibare[nu, i3])*
671 (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i4, i5] Wibare[mu, i4] Wibare[nu, i5]) -
672
673 1/4 (del[Bbare[nu], mu] - del[Bbare[mu], nu])^2 -
674
675 1/4 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a2, a3] Gbare[mu, a2] Gbare[nu, a3])*
676 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a4, a5] Gbare[mu, a4] Gbare[nu, a5]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
677
678
679(********************* Fermion Lagrangian terms*************************)
680(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
681 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
682
683 Lkin = I uqbar.Ga[mu].del[uq, mu] +
684 I dqbar.Ga[mu].del[dq, mu] +
685 I lbar.Ga[mu].del[l, mu] +
686 I vlbar.Ga[mu].del[vl, mu];
687
688 LQCD = gs (uqbar.Ga[mu].T[a].uq +
689 dqbar.Ga[mu].T[a].dq)G[mu, a];
690
691 LBright =
692 -2g1bare Bbare[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
693 4/3*g1bare Bbare[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
694 2g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
695
696 LBleft =
697 -g1bare Bbare[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
698 g1bare Bbare[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
699 g1bare/3 Bbare[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
700 g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
701
702 LWleft = gwbare/2(
703 vlbar.Ga[mu].ProjM.vl Wibare[mu, 3] - (*sigma3 = ( 1 0 )*)
704 lbar.Ga[mu].ProjM.l Wibare[mu, 3] + (* ( 0 -1 )*)
705
706 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu](1+cW*MW^2/mrho^2) +
707 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu](1+cW*MW^2/mrho^2) +
708
709 uqbar.Ga[mu].ProjM.uq Wibare[mu, 3] - (*sigma3 = ( 1 0 )*)
710 dqbar.Ga[mu].ProjM.dq Wibare[mu, 3] + (* ( 0 -1 )*)
711
712 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu](1+cW*MW^2/mrho^2) +
713 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu](1+cW*MW^2/mrho^2)
714 );
715
716 Normal[Series[((Lkin + LQCD + LBright + LBleft + LWleft)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]];
717
718(******************** Higgs Lagrangian terms****************************)
719 Phi := {0, (v + Hbare)/Sqrt[2]};
720 Phibar := {0, (v + Hbare)/Sqrt[2]};
721
722Dc[f_, mu_] := del[f, mu] - I g1bare Bbare[mu]/2 f -I gwbare/2 (Wvec[mu].PMVec).f;
723 Dcbar[f_, mu_] := del[f, mu] + I g1bare Bbare[mu]/2 f + I gwbare/2 f.(Wvec[mu].PMVec);
724
725
726
727 PMVec = Table[PauliSigma[i], {i, 3}];
728 Wvec[mu_] := {Wibare[mu, 1], Wibare[mu, 2], Wibare[mu, 3]};
729
730
731 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
732
733 LHiggs := Normal[Series[(((Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
734
735
736(*************** Yukawa Lagrangian***********************)
737LYuk := Module[{s,r,n,m,i}, -
738 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Hbare)/Sqrt[2] -
739 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Hbare)/Sqrt[2] -
740 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Hbare)/Sqrt[2]
741 ];
742
743LYukawa := Normal[Series[((LYuk + HC[LYuk])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
744
745
746
747(**************Ghost terms**************************)
748(* Now we need the ghost terms which are of the form: *)
749(* - g * antighost * d_BRST G *)
750(* where d_BRST G is BRST transform of the gauge fixing function. *)(*Not renormalized, only if FeynmanGauge*)
751
752LGhost := 0;
753
754(*********Total SM Lagrangian*******)
755LSM := Normal[Series[((LGauge + LHiggs + LFermions + LYukawa + LGhost)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
756
757
758
759 (************** SILH LAGRANGIAN STARTING POINT ********************)
760(** Better to introduce some useful short-hand notation here **)
761
762
763HH = Phibar.Phi;
764HDH[mu_] := (Phibar.Dc[Phi,mu] - Dcbar[Phibar,mu].Phi);
765
766FSWVec[mu_,nu_] := {FS[Wi,mu,nu,1],FS[Wi,mu,nu,2],FS[Wi,mu,nu,3]}
767
768DB[mu_] := del[FS[B,mu,nu],nu];
769
770DG[mu_, a1_] := I del[del[G[nu, a1], mu],mu] - I del[del[G[mu, a1], nu],mu] +
771 I gs f[a1, a2, a3] (del[G[mu, a2],mu] G[nu, a3] + G[mu,a2] del[G[nu,a3],mu] +
772 ( g1 B[mu]/2 + gw/2 (Wvec[mu].PMatVec) + gs Ga[mu].T[a]))
773 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3]);
774
775
776(***************** SILH Lagrangian**************************)
777
778L6HT := Normal[Series[((cH/2/frho^2 del[HH,mu] del[HH,mu] +
779 cT/2/frho^2 HDH[mu] HDH[mu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
780
781L6 := Normal[Series[((-c6 \[Lambda]/frho^2 HH^3)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
782
783L6Y := Normal[Series[((-cy / frho^2 * HH * LYukawa)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
784
785
786L6W := Normal[Series[((I cW gw/2/mrho^2 (Phibar.PauliSigma[k].Dc[Phi,mu]-Dcbar[Phibar,mu].PauliSigma[k].Phi)*(del[FS[Wi,mu,nu,k],nu] + gw Eps[k1,k2,k] Wi[nu,k1] FS[Wi,mu,nu,k2]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
787
788
789L6B := Normal[Series[((I cB g1/2/mrho^2 HDH[mu] DB[mu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
790
791L6HW := Normal[Series[((I cHW gw/16/Pi^2/frho^2 (HC[Dc[Phi,mu]].PauliSigma[i].Dc[Phi,nu]) FS[Wi,mu,nu,i])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
792
793L6HB := Normal[Series[((I cHB g1/16/Pi^2/frho^2 (HC[Dc[Phi,mu]].Dc[Phi,nu]) FS[B,mu,nu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
794
795L6Ga := Normal[Series[((cga g1^2/16/Pi^2/frho^2 gw^2/grho^2 HH FS[B,mu,nu] FS[B,mu,nu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
796
797L6G := Normal[Series[((cg gs^2/16/Pi^2/frho^2 yu[Index[Generation,3]]^2/grho^2 HH FS[G,mu,nu,a] FS[G,mu,nu,a])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
798
799L62W := Normal[Series[((c2W gw^2/2/grho^2/mrho^2 (del[(1+cW*MW^2/mrho^2)FS[Wi,mu,nu,k],mu] + gw/2 Eps[k1,k2,k] Wi[mu,k1] FS[Wi,mu,nu,k2])*(del[FS[Wi,rho,nu,k],rho] + gw/2 Eps[k3,k4,k] Wi[rho,k3] FS[Wi,rho,nu,k4]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
800
801L62B := Normal[Series[((c2B g1^2/2/grho^2/mrho^2 del[FS[B,nu, mu],mu] del[FS[B,nu, rho],rho])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
802
803L62g := Normal[Series[((c2g gs^2/2/grho^2/mrho^2 (del[FS[G,mu,nu,a],mu] + gs f[a1,a2,a] G[mu,a1] FS[G,mu,nu,a2])*(del[FS[G,rho,nu,a],rho] + gs f[a3,a4,a] G[rho,a3] FS[G,rho,nu,a4]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
804
805L63W := Normal[Series[((c3W gw^3/16/Pi^2/mrho^2 Eps[i,j,k] FS[Wi,mu,nu,i] FS[Wi,nu,rho,j] FS[Wi,rho,mu,k])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
806
807L63g := Normal[Series[((c3g gs^3/16/Pi^2/mrho^2 f[a1,a2,a3] FS[G,mu,nu,a1] FS[G,nu,rho,a2] FS[G,rho,mu,a3])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
808
809Lvec := L62W + L62B + L62g + L63W + L63g;
810
811LSILH = Normal[Series[((L6HT + L6W + L6B + L6HW + L6HB + L6Ga + L6G + L6Y + L6)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]];
812