SILH: SILH.2.fr

File SILH.2.fr, 25.5 KB (added by Céline Degrande, 12 years ago)
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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->"08/02/2012"
15 Institutions -> {"Universite catholique de Louvain (CP3)"},
16 Emails -> {"celine.degrande@uclouvain.be"},
17 Version -> "1.0",
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] ] = Unfold[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(**************** Orders ****************)
58
59M$InteractionOrderHierarchy = {
60{QCD, 1},
61{QED, 2},
62{NP,2}
63}
64
65M$InteractionOrderLimit = {
66{QCD, 99},
67{QED, 99},
68{NP,1}
69}
70
71
72(**************** Parameters *************)
73
74M$Parameters = {
75
76 (* External SM parameters *)
77
78 \[Alpha]EWM1== {
79 ParameterType -> External,
80 BlockName -> SMINPUTS,
81 ParameterName -> aEWM1,
82 InteractionOrder -> {QED, -2},
83 Value -> 127.9,
84 Description -> "Inverse of the electroweak coupling constant"},
85
86 Gf == {
87 ParameterType -> External,
88 BlockName -> SMINPUTS,
89 InteractionOrder -> {QED, 2},
90 Value -> 1.16639 * 10^(-5),
91 Description -> "Fermi constant"},
92
93 \[Alpha]S == {
94 ParameterType -> External,
95 BlockName -> SMINPUTS,
96 ParameterName -> aS,
97 InteractionOrder -> {QCD, 2},
98 Value -> 0.118,
99 Description -> "Strong coupling constant at the Z pole."},
100
101
102 ZM == {
103 ParameterType -> External,
104 BlockName -> SMINPUTS,
105 Value -> 91.188,
106 Description -> "Z mass"},
107
108
109 ymc == {
110 ParameterType -> External,
111 BlockName -> YUKAWA,
112 Value -> 1.42,
113 OrderBlock -> {4},
114 Description -> "Charm Yukawa mass"},
115
116 ymb == {
117 ParameterType -> External,
118 BlockName -> YUKAWA,
119 Value -> 4.7,
120 OrderBlock -> {5},
121 Description -> "Bottom Yukawa mass"},
122
123 ymt == {
124 ParameterType -> External,
125 BlockName -> YUKAWA,
126 Value -> 174.3,
127 OrderBlock -> {6},
128 Description -> "Top Yukawa mass"},
129
130 ymtau == {
131 ParameterType -> External,
132 BlockName -> YUKAWA,
133 Value -> 1.777,
134 OrderBlock -> {15},
135 Description -> "Tau Yukawa mass"},
136
137
138
139 (* External SILH Parameter *)
140
141 frho =={
142 TeX -> Subscript[f,\[Rho]],
143 ParameterType -> External,
144 Value -> 1 (*TeV*),
145 Description -> "sigma model scale"},
146
147 grho =={
148 TeX -> Subscript[g,\[Rho]],
149 ParameterType -> External,
150 Value -> 1,
151 Description -> "sigma model coupling"},
152
153 cH =={
154 TeX -> Subscript[c,H],
155 ParameterType -> External,
156 Value -> 1,
157 InteractionOrder ->{QED,-1}},
158
159 cT =={
160 TeX -> Subscript[c,T],
161 ParameterType -> External,
162 Value -> 1,
163 InteractionOrder ->{QED,-1}},
164
165 c6 =={
166 TeX -> Subscript[c,6],
167 ParameterType -> External,
168 Value -> 1,
169 InteractionOrder ->{QED,-1}},
170
171 cy =={
172 TeX -> Subscript[c,y],
173 ParameterType -> External,
174 Value -> 1,
175 InteractionOrder ->{QED,-1}},
176
177 c6W =={
178 TeX -> Subscript[c,W],
179 ParameterType -> External,
180 Value -> 1,
181 InteractionOrder ->{QED,-3}},
182
183 cB =={
184 TeX -> Subscript[c,B],
185 ParameterType -> External,
186 Value -> 1,
187 InteractionOrder ->{QED,-3}},
188
189 cHW =={
190 TeX -> Subscript[c,HW],
191 ParameterType -> External,
192 Value -> 1,
193 InteractionOrder ->{QED,-3}},
194
195 cHB =={
196 TeX -> Subscript[c,HB],
197 ParameterType -> External,
198 Value -> 1,
199 InteractionOrder ->{QED,-3}},
200
201 cga =={
202 TeX -> Subscript[c,\[Gamma]],
203 ParameterType -> External,
204 Value -> 1,
205 InteractionOrder ->{QED,-5}},
206
207 cg =={
208 TeX -> Subscript[c,g],
209 ParameterType -> External,
210 Value -> 1,
211 InteractionOrder ->{QED,-1}},
212
213 c2W =={
214 TeX -> Subscript[c,2W],
215 ParameterType -> External,
216 Value -> 1},
217
218 c2B =={
219 TeX -> Subscript[c,2B],
220 ParameterType -> External,
221 Value -> 1},
222
223 c2g =={
224 TeX -> Subscript[c,2g],
225 ParameterType -> External,
226 Value -> 1},
227
228 c3W =={
229 TeX -> Subscript[c,3W],
230 ParameterType -> External,
231 Value -> 1},
232
233 c3B =={
234 TeX -> Subscript[c,3B],
235 ParameterType -> External,
236 Value -> 1},
237
238
239 (* Internal Parameters *)
240
241 \[Alpha]EW == {
242 ParameterType -> Internal,
243 Value -> 1/\[Alpha]EWM1,
244 ParameterName -> aEW,
245 InteractionOrder -> {QED, 2},
246 Description -> "Electroweak coupling contant"},
247
248
249 MW == {
250 ParameterType -> Internal,
251 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
252 Description -> "W mass"},
253
254 sw2 == {
255 ParameterType -> Internal,
256 Value -> 1-(MW/MZ)^2,
257 Description -> "Squared Sin of the Weinberg angle"},
258
259 ee == {
260 TeX -> e,
261 ParameterType -> Internal,
262 Value -> Sqrt[4 Pi \[Alpha]EW],
263 InteractionOrder -> {QED, 1},
264 Description -> "Electric coupling constant"},
265
266 cw == {
267 TeX -> Subscript[c, w],
268 ParameterType -> Internal,
269 Value -> Sqrt[1 - sw2],
270 Description -> "Cos of the Weinberg angle"},
271
272 sw == {
273 TeX -> Subscript[s, w],
274 ParameterType -> Internal,
275 Value -> Sqrt[sw2],
276 Description -> "Sin of the Weinberg angle"},
277
278 gw == {
279 TeX -> Subscript[g, w],
280 ParameterType -> Internal,
281 Value -> ee / sw,
282 InteractionOrder -> {QED, 1},
283 Description -> "Weak coupling constant"},
284
285 g1 == {
286 TeX -> Subscript[g, 1],
287 ParameterType -> Internal,
288 Value -> ee / cw,
289 InteractionOrder -> {QED, 1},
290 Description -> "U(1)Y coupling constant"},
291
292 gs == {
293 TeX -> Subscript[g, s],
294 ParameterType -> Internal,
295 Value -> Sqrt[4 Pi \[Alpha]S],
296 InteractionOrder -> {QCD, 1},
297 ParameterName -> G,
298 Description -> "Strong coupling constant"},
299
300 v == {
301 ParameterType -> Internal,
302 Value -> 2*MW*sw/ee,
303 InteractionOrder -> {QED, -1},
304 Description -> "Higgs VEV"},
305
306 Xi == {
307 TeX -> \[Xi],
308 InteractionOrder -> {NP,1},
309 ParameterType -> Internal,
310 Value -> v^2/frho^2,
311 Description -> "ratio of frho and the Higgs vev"},
312
313 \[Lambda] == {
314 ParameterType -> Internal,
315 Value -> MH^2/(2*v^2)(1+cH*Xi-3/2 c6*Xi),
316 InteractionOrder -> {QED, 2},
317 ParameterName -> lam,
318 Description -> "Higgs quartic coupling"},
319
320 muH == {
321 ParameterType -> Internal,
322 Value -> Sqrt[v^2 \[Lambda](1+3/4 c6 Xi)],
323 TeX -> \[Mu],
324 Description -> "Coefficient of the quadratic piece of the Higgs potential"},
325
326
327 yl == {
328 Indices -> {Index[Generation]},
329 AllowSummation -> True,
330 ParameterType -> Internal,
331 Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v (1+cy/2Xi)},
332 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
333 InteractionOrder -> {QED, 1},
334 ComplexParameter -> False,
335 Definitions -> {yl[1] -> 0, yl[2] ->0},
336 Description -> "Lepton Yukawa coupling"},
337
338 yu == {
339 Indices -> {Index[Generation]},
340 AllowSummation -> True,
341 ParameterType -> Internal,
342 Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v (1+cy/2Xi), yu[3] -> Sqrt[2] ymt / v (1+cy/2Xi)},
343 ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
344 InteractionOrder -> {QED, 1},
345 ComplexParameter -> False,
346 Definitions -> {yu[1] -> 0},
347 Description -> "U-quark Yukawa coupling"},
348
349 yd == {
350 Indices -> {Index[Generation]},
351 AllowSummation -> True,
352 ParameterType -> Internal,
353 Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v (1+cy/2Xi)},
354 ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
355 InteractionOrder -> {QED, 1},
356 ComplexParameter -> False,
357 Definitions -> {yd[1] -> 0, yd[2] -> 0},
358 Description -> "D-quark Yukawa coupling"},
359
360 cabi == {
361 TeX -> Subscript[\[Theta], c],
362 ParameterType -> External,
363 BlockName -> CKMBLOCK,
364 OrderBlock -> {1},
365 Value -> 0.488,
366 Description -> "Cabibbo angle"},
367
368 CKM == {
369 Indices -> {Index[Generation], Index[Generation]},
370 TensorClass -> CKM,
371 Unitary -> True,
372 Definitions -> {CKM[3, 3] -> 1,
373 CKM[i_, 3] :> 0 /; i != 3,
374 CKM[3, i_] :> 0 /; i != 3},
375 Value -> {CKM[1,2] -> Sin[cabi],
376 CKM[1,1] -> Cos[cabi],
377 CKM[2,1] -> -Sin[cabi],
378 CKM[2,2] -> Cos[cabi]},
379 Description -> "CKM-Matrix"},
380
381 mrho =={
382 TeX -> Subscript[m,\[Rho]],
383 ParameterType -> Internal,
384 Value -> grho*frho,
385 Description -> "sigma model mass"}
386}
387
388
389(************** Gauge Groups ******************)
390
391M$GaugeGroups = {
392
393 U1Y == {
394 Abelian -> True,
395 GaugeBoson -> B,
396 Charge -> Y,
397 CouplingConstant -> g1},
398
399 SU2L == {
400 Abelian -> False,
401 GaugeBoson -> Wi,
402 StructureConstant -> Eps,
403 CouplingConstant -> gw},
404
405 SU3C == {
406 Abelian -> False,
407 GaugeBoson -> G,
408 StructureConstant -> f,
409 SymmetricTensor -> dSUN,
410 Representations -> {T, Colour},
411 CouplingConstant -> gs}
412}
413
414(********* Particle Classes **********)
415
416M$ClassesDescription = {
417
418(********** Fermions ************)
419 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
420 F[1] == {
421 ClassName -> vl,
422 ClassMembers -> {ve,vm,vt},
423 FlavorIndex -> Generation,
424 SelfConjugate -> False,
425 Indices -> {Index[Generation]},
426 Mass -> 0,
427 Width -> 0,
428 QuantumNumbers -> {LeptonNumber -> 1},
429 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
430 PropagatorType -> S,
431 PropagatorArrow -> Forward,
432 PDG -> {12,14,16},
433 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
434
435 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
436 F[2] == {
437 ClassName -> l,
438 ClassMembers -> {e, m, tt},
439 FlavorIndex -> Generation,
440 SelfConjugate -> False,
441 Indices -> {Index[Generation]},
442 Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}},
443 Width -> 0,
444 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
445 PropagatorLabel -> {"l", "e", "m", "tt"},
446 PropagatorType -> Straight,
447 ParticleName -> {"e-", "m-", "tt-"},
448 AntiParticleName -> {"e+", "m+", "tt+"},
449 PropagatorArrow -> Forward,
450 PDG -> {11, 13, 15},
451 FullName -> {"Electron", "Muon", "Tau"} },
452
453 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
454 F[3] == {
455 ClassMembers -> {u, c, t},
456 ClassName -> uq,
457 FlavorIndex -> Generation,
458 SelfConjugate -> False,
459 Indices -> {Index[Generation], Index[Colour]},
460 Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}},
461 Width -> {0, 0, {WT, 1.50833649}},
462 QuantumNumbers -> {Q -> 2/3},
463 PropagatorLabel -> {"uq", "u", "c", "t"},
464 PropagatorType -> Straight,
465 PropagatorArrow -> Forward,
466 PDG -> {2, 4, 6},
467 FullName -> {"u-quark", "c-quark", "t-quark"}},
468
469 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
470 F[4] == {
471 ClassMembers -> {d, s, b},
472 ClassName -> dq,
473 FlavorIndex -> Generation,
474 SelfConjugate -> False,
475 Indices -> {Index[Generation], Index[Colour]},
476 Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}},
477 Width -> 0,
478 QuantumNumbers -> {Q -> -1/3},
479 PropagatorLabel -> {"dq", "d", "s", "b"},
480 PropagatorType -> Straight,
481 PropagatorArrow -> Forward,
482 PDG -> {1,3,5},
483 FullName -> {"d-quark", "s-quark", "b-quark"} },
484
485(********** Ghosts **********)
486 U[1] == {
487 ClassName -> ghA,
488 SelfConjugate -> False,
489 Indices -> {},
490 Ghost -> A,
491 Mass -> 0,
492 QuantumNumbers -> {GhostNumber -> 1},
493 PropagatorLabel -> uA,
494 PropagatorType -> GhostDash,
495 PropagatorArrow -> Forward},
496
497 U[2] == {
498 ClassName -> ghZ,
499 SelfConjugate -> False,
500 Indices -> {},
501 Mass -> {MZ, 91.188},
502 Ghost -> Z,
503 QuantumNumbers -> {GhostNumber -> 1},
504 PropagatorLabel -> uZ,
505 PropagatorType -> GhostDash,
506 PropagatorArrow -> Forward},
507
508 U[31] == {
509 ClassName -> ghWp,
510 SelfConjugate -> False,
511 Indices -> {},
512 Mass -> {MW, Internal},
513 Ghost -> W,
514 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
515 PropagatorLabel -> uWp,
516 PropagatorType -> GhostDash,
517 PropagatorArrow -> Forward},
518
519 U[32] == {
520 ClassName -> ghWm,
521 SelfConjugate -> False,
522 Indices -> {},
523 Mass -> {MW, Internal},
524 Ghost -> Wbar,
525 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
526 PropagatorLabel -> uWm,
527 PropagatorType -> GhostDash,
528 PropagatorArrow -> Forward},
529
530 U[4] == {
531 ClassName -> ghG,
532 SelfConjugate -> False,
533 Indices -> {Index[Gluon]},
534 Ghost -> G,
535 Mass -> 0,
536 QuantumNumbers -> {GhostNumber -> 1},
537 PropagatorLabel -> uG,
538 PropagatorType -> GhostDash,
539 PropagatorArrow -> Forward},
540
541 U[5] == {
542 ClassName -> ghWi,
543 Unphysical -> True,
544 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
545 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
546 ghWi[3] -> cw ghZ + sw ghA},
547 SelfConjugate -> False,
548 Ghost -> Wi,
549 Indices -> {Index[SU2W]},
550 FlavorIndex -> SU2W},
551
552 U[6] == {
553 ClassName -> ghB,
554 SelfConjugate -> False,
555 Definitions -> {ghB -> -sw ghZ + cw ghA},
556 Indices -> {},
557 Ghost -> B,
558 Unphysical -> True},
559
560(************ Gauge Bosons ***************)
561 (* Gauge bosons: Q = 0 *)
562 V[1] == {
563 ClassName -> A,
564 SelfConjugate -> True,
565 Indices -> {},
566 Mass -> 0,
567 Width -> 0,
568 PropagatorLabel -> "a",
569 PropagatorType -> W,
570 PropagatorArrow -> None,
571 PDG -> 22,
572 FullName -> "Photon" },
573
574 V[2] == {
575 ClassName -> Z,
576 SelfConjugate -> True,
577 Indices -> {},
578 Mass -> {MZ, 91.188},
579 Width -> {WZ, 2.44140351},
580 PropagatorLabel -> "Z",
581 PropagatorType -> Sine,
582 PropagatorArrow -> None,
583 PDG -> 23,
584 FullName -> "Z" },
585
586 (* Gauge bosons: Q = -1 *)
587 V[3] == {
588 ClassName -> W,
589 SelfConjugate -> False,
590 Indices -> {},
591 Mass -> {MW, Internal},
592 Width -> {WW, 2.04759951},
593 QuantumNumbers -> {Q -> 1},
594 PropagatorLabel -> "W",
595 PropagatorType -> Sine,
596 PropagatorArrow -> Forward,
597 ParticleName ->"W+",
598 AntiParticleName ->"W-",
599 PDG -> 24,
600 FullName -> "W" },
601
602V[4] == {
603 ClassName -> G,
604 SelfConjugate -> True,
605 Indices -> {Index[Gluon]},
606 Mass -> 0,
607 Width -> 0,
608 PropagatorLabel -> G,
609 PropagatorType -> C,
610 PropagatorArrow -> None,
611 PDG -> 21,
612 FullName -> "G" },
613
614V[5] == {
615 ClassName -> Wi,
616 Unphysical -> True,
617 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
618 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
619 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
620 SelfConjugate -> True,
621 Indices -> {Index[SU2W]},
622 FlavorIndex -> SU2W,
623 Mass -> 0,
624 PDG -> {1,2,3}},
625
626V[6] == {
627 ClassName -> B,
628 SelfConjugate -> True,
629 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
630 Indices -> {},
631 Mass -> 0,
632 Unphysical -> True},
633
634
635(************ Scalar Fields **********)
636 (* physical Higgs: Q = 0 *)
637 S[1] == {
638 ClassName -> H,
639 SelfConjugate -> True,
640 Mass -> {MH, 120},
641 Width -> {WH, 0.00575308848},
642 PropagatorLabel -> "H",
643 PropagatorType -> D,
644 PropagatorArrow -> None,
645 PDG -> 25,
646 FullName -> "H" },
647
648S[2] == {
649 ClassName -> phi,
650 SelfConjugate -> True,
651 Mass -> {MZ, 91.188},
652 Width -> Wphi,
653 PropagatorLabel -> "Phi",
654 PropagatorType -> D,
655 PropagatorArrow -> None,
656 ParticleName ->"phi0",
657 PDG -> 250,
658 FullName -> "Phi",
659 Goldstone -> Z },
660
661S[3] == {
662 ClassName -> phi2,
663 SelfConjugate -> False,
664 Mass -> {MW, Internal},
665 Width -> Wphi2,
666 PropagatorLabel -> "Phi2",
667 PropagatorType -> D,
668 PropagatorArrow -> None,
669 ParticleName ->"phi+",
670 AntiParticleName ->"phi-",
671 PDG -> 251,
672 FullName -> "Phi2",
673 Goldstone -> W,
674 QuantumNumbers -> {Q -> 1}}
675
676}
677
678(*Renomalisation*)
679
680Hbare = H(1-cH Xi/2);
681Bbare[mu_] := B[mu](1+cB sw^2/cw^2*MW^2/mrho^2+cga g1^2*gw^2/grho^2*Xi/16/\[Pi]^2);
682Wibare[mu_,i_] := Wi[mu,i](1+c6W*MW^2/mrho^2);
683g1bare = g1(1-cB sw^2/cw^2*MW^2/mrho^2-cga g1^2*gw^2/grho^2*Xi/16/\[Pi]^2);
684gwbare = gw(1-c6W*MW^2/mrho^2);
685Gbare[mu_,a_] := G[mu,a](1+cg gs^2*yu[Index[Generation,3]]^2/grho^2*Xi/16/\[Pi]^2);
686gsbare = gs(1-cg gs^2*yu[Index[Generation,3]]^2/grho^2*Xi/16/\[Pi]^2);
687
688
689(*****************************************************************************************)
690
691(* SM Lagrangian *)
692
693(******************** Gauge F^2 Lagrangian terms*************************)
694(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
695 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])*
696 (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i4, i5] Wibare[mu, i4] Wibare[nu, i5]) -
697
698 1/4 (del[Bbare[nu], mu] - del[Bbare[mu], nu])^2 -
699
700 1/4 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a2, a3] Gbare[mu, a2] Gbare[nu, a3])*
701 (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}]];
702
703
704(********************* Fermion Lagrangian terms*************************)
705(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
706 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
707
708 Lkin = I uqbar.Ga[mu].del[uq, mu] +
709 I dqbar.Ga[mu].del[dq, mu] +
710 I lbar.Ga[mu].del[l, mu] +
711 I vlbar.Ga[mu].del[vl, mu];
712
713 LQCD = gs (uqbar.Ga[mu].T[a].uq +
714 dqbar.Ga[mu].T[a].dq)G[mu, a];
715
716 LBright =
717 -2g1bare Bbare[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
718 4/3*g1bare Bbare[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
719 2g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
720
721 LBleft =
722 -g1bare Bbare[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
723 g1bare Bbare[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
724 g1bare/3 Bbare[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
725 g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
726
727 LWleft = gwbare/2(
728 vlbar.Ga[mu].ProjM.vl Wibare[mu, 3] - (*sigma3 = ( 1 0 )*)
729 lbar.Ga[mu].ProjM.l Wibare[mu, 3] + (* ( 0 -1 )*)
730
731 Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu](1+c6W*MW^2/mrho^2) +
732 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu](1+c6W*MW^2/mrho^2) +
733
734 uqbar.Ga[mu].ProjM.uq Wibare[mu, 3] - (*sigma3 = ( 1 0 )*)
735 dqbar.Ga[mu].ProjM.dq Wibare[mu, 3] + (* ( 0 -1 )*)
736
737 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu](1+c6W*MW^2/mrho^2) +
738 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu](1+c6W*MW^2/mrho^2)
739 );
740
741 Normal[Series[((Lkin + LQCD + LBright + LBleft + LWleft)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]]];
742
743(******************** Higgs Lagrangian terms****************************)
744 Phi := {0, (v + Hbare)/Sqrt[2]};
745 Phibar := {0, (v + Hbare)/Sqrt[2]};
746
747Dc[f_, mu_] := del[f, mu] - I g1bare Bbare[mu]/2 f -I gwbare/2 (Wvec[mu].PMVec).f;
748 Dcbar[f_, mu_] := del[f, mu] + I g1bare Bbare[mu]/2 f + I gwbare/2 f.(Wvec[mu].PMVec);
749
750
751
752 PMVec = Table[PauliSigma[i], {i, 3}];
753 Wvec[mu_] := {Wibare[mu, 1], Wibare[mu, 2], Wibare[mu, 3]};
754
755
756 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
757
758 LHiggs := Normal[Series[(((Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
759
760
761(*************** Yukawa Lagrangian***********************)
762LYuk := Module[{s,r,n,m,i}, -
763 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Hbare)/Sqrt[2] -
764 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Hbare)/Sqrt[2] -
765 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Hbare)/Sqrt[2]
766 ];
767
768LYukawa := Normal[Series[((LYuk + HC[LYuk])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
769
770
771
772(**************Ghost terms**************************)
773(* Now we need the ghost terms which are of the form: *)
774(* - g * antighost * d_BRST G *)
775(* where d_BRST G is BRST transform of the gauge fixing function. *)(*Not renormalized, only if FeynmanGauge*)
776
777LGhost := 0;
778
779(*********Total SM Lagrangian*******)
780LSM := Normal[Series[((LGauge + LHiggs + LFermions + LYukawa + LGhost)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
781
782
783
784 (************** SILH LAGRANGIAN STARTING POINT ********************)
785(** Better to introduce some useful short-hand notation here **)
786
787
788HH = Phibar.Phi;
789HDH[mu_] := (Phibar.Dc[Phi,mu] - Dcbar[Phibar,mu].Phi);
790
791FSWVec[mu_,nu_] := {FS[Wi,mu,nu,1],FS[Wi,mu,nu,2],FS[Wi,mu,nu,3]}
792
793DB[mu_] := del[FS[B,mu,nu],nu];
794
795DG[mu_, a1_] := I del[del[G[nu, a1], mu],mu] - I del[del[G[mu, a1], nu],mu] +
796 I gs f[a1, a2, a3] (del[G[mu, a2],mu] G[nu, a3] + G[mu,a2] del[G[nu,a3],mu] +
797 ( g1 B[mu]/2 + gw/2 (Wvec[mu].PMatVec) + gs Ga[mu].T[a]))
798 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3]);
799
800
801(***************** SILH Lagrangian**************************)
802
803L6HT := Normal[Series[((cH/2/frho^2 del[HH,mu] del[HH,mu] +
804 cT/2/frho^2 HDH[mu] HDH[mu])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
805
806L6 := Normal[Series[((-c6 \[Lambda]/frho^2 HH^3)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
807
808L6Y := Normal[Series[((-cy / frho^2 * HH * LYukawa)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
809
810
811L6W := Normal[Series[((I c6W 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}]];
812
813
814L6B := Normal[Series[((I cB g1/2/mrho^2 HDH[mu] DB[mu])//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
815
816L6HW := 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}]];
817
818L6HB := 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}]];
819
820L6Ga := 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}]];
821
822L6G := 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}]];
823
824L62W := Normal[Series[((c2W gw^2/2/grho^2/mrho^2 (del[(1+c6W*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}]];
825
826L62B := 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}]];
827
828L62g := 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}]];
829
830L63W := 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}]];
831
832L63g := 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}]];
833
834Lvec := L62W + L62B + L62g + L63W + L63g;
835
836LSILH = Normal[Series[((L6HT + L6W + L6B + L6HW + L6HB + L6Ga + L6G + L6Y + L6)//.{mrho->grho*frho,frho->v/Sqrt[Xi]}),{Xi,0,1}]];
837