HiggsCharacterisation: SM_HC3.fr

File SM_HC3.fr, 26.0 KB (added by mawatari, 13 years ago)

SM model file slightly modified to the Higgs Characterisation project. Please load it together with the main file v3.x.

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1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Standard model ******)
3(****** ******)
4(****** Authors: N. Christensen, C. Duhr, B. Fuks ******)
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(*- This model has been slightly modified by P. de Aquino to be adapted to the Higgs Characterisation project. *)
13(*- The Higgs has been named as X0. *)
14(*- The Lagrangian of the Fermions has been rewritten in the old format, avoiding the use of DC[field,index]. *)
15
16
17(* ************************** *)
18(* ***** Information ***** *)
19(* ************************** *)
20M$ModelName = "Standard Model";
21
22M$Information = {
23 Authors -> {"N. Christensen", "C. Duhr", "B. Fuks"},
24 Version -> "1.4.3",
25 Date -> "27. 18. 2012",
26 Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)", "IPHC Strasbourg / University of Strasbourg"},
27 Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "benjamin.fuks@cnrs.in2p3.fr"},
28 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"
29};
30
31FeynmanGauge = True;
32
33(* ************************** *)
34(* ***** Change log ***** *)
35(* ************************** *)
36
37(* v1.4.3: Updated conventions for the symmetric structure constants of SU3. *)
38(* v1.4.2: Set FeynmanGauge=True as default again. *)
39(* v1.4: Added SU(2) representation. *)
40(* -> Modification in the field declarations (doublets are added) *)
41(* -> Modification in the Lagrangian (much simpler). *)
42(* v1.3: Added yukawa couplings for all fermions for gauge invariance. *)
43(* Added yukawa couplings for 1st generation fermions to Massless.rst. *)
44(* Updated parameters to PDG 2010. *)
45(* v1.2: Set FeynmanGauge=True as default. *)
46(* Set Gluonic ghosts to be included in both gauges. *)
47(* v1.1: Fixed yukawa couplings in Feynman gauge. *)
48(* Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. *)
49(* Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. *)
50
51
52(* ************************** *)
53(* ***** Gauge groups ***** *)
54(* ************************** *)
55M$GaugeGroups = {
56 U1Y == {
57 Abelian -> True,
58 CouplingConstant -> g1,
59 GaugeBoson -> B,
60 Charge -> Y
61 },
62 SU2L == {
63 Abelian -> False,
64 CouplingConstant -> gw,
65 GaugeBoson -> Wi,
66 StructureConstant -> Eps,
67 Representations -> {Ta,SU2D},
68 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
69 },
70 SU3C == {
71 Abelian -> False,
72 CouplingConstant -> gs,
73 GaugeBoson -> G,
74 StructureConstant -> f,
75 Representations -> {T,Colour},
76 SymmetricTensor -> dSUN
77 }
78};
79
80
81(* ************************** *)
82(* ***** Indices ***** *)
83(* ************************** *)
84
85IndexRange[Index[SU2W ]] = Unfold[Range[3]];
86IndexRange[Index[SU2D ]] = Unfold[Range[2]];
87IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
88IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
89IndexRange[Index[Generation]] = Range[3];
90
91IndexStyle[SU2W, j];
92IndexStyle[SU2D, k];
93IndexStyle[Gluon, a];
94IndexStyle[Colour, m];
95IndexStyle[Generation, f];
96
97
98(* ************************** *)
99(* *** Interaction orders *** *)
100(* *** (as used by mg5) *** *)
101(* ************************** *)
102
103M$InteractionOrderHierarchy = {
104 {QCD, 1},
105 {QED, 2}
106};
107
108
109(* ************************** *)
110(* **** Particle classes **** *)
111(* ************************** *)
112M$ClassesDescription = {
113
114(* Gauge bosons: physical vector fields *)
115 V[1] == {
116 ClassName -> A,
117 SelfConjugate -> True,
118 Mass -> 0,
119 Width -> 0,
120 ParticleName -> "a",
121 PDG -> 22,
122 PropagatorLabel -> "a",
123 PropagatorType -> W,
124 PropagatorArrow -> None,
125 FullName -> "Photon"
126 },
127 V[2] == {
128 ClassName -> Z,
129 SelfConjugate -> True,
130 Mass -> {MZ, 91.1876},
131 Width -> {WZ, 2.4952},
132 ParticleName -> "Z",
133 PDG -> 23,
134 PropagatorLabel -> "Z",
135 PropagatorType -> Sine,
136 PropagatorArrow -> None,
137 FullName -> "Z"
138 },
139 V[3] == {
140 ClassName -> W,
141 SelfConjugate -> False,
142 Mass -> {MW, Internal},
143 Width -> {WW, 2.085},
144 ParticleName -> "W+",
145 AntiParticleName -> "W-",
146 QuantumNumbers -> {Q -> 1},
147 PDG -> 24,
148 PropagatorLabel -> "W",
149 PropagatorType -> Sine,
150 PropagatorArrow -> Forward,
151 FullName -> "W"
152 },
153 V[4] == {
154 ClassName -> G,
155 SelfConjugate -> True,
156 Indices -> {Index[Gluon]},
157 Mass -> 0,
158 Width -> 0,
159 ParticleName -> "g",
160 PDG -> 21,
161 PropagatorLabel -> "G",
162 PropagatorType -> C,
163 PropagatorArrow -> None,
164 FullName -> "G"
165 },
166
167(* Ghosts: related to physical gauge bosons *)
168 U[1] == {
169 ClassName -> ghA,
170 SelfConjugate -> False,
171 Ghost -> A,
172 QuantumNumbers -> {GhostNumber -> 1},
173 Mass -> 0,
174 PropagatorLabel -> "uA",
175 PropagatorType -> GhostDash,
176 PropagatorArrow -> Forward
177 },
178 U[2] == {
179 ClassName -> ghZ,
180 SelfConjugate -> False,
181 Ghost -> Z,
182 QuantumNumbers -> {GhostNumber -> 1},
183 Mass -> {MZ,91.1876},
184 PropagatorLabel -> "uZ",
185 PropagatorType -> GhostDash,
186 PropagatorArrow -> Forward
187 },
188 U[31] == {
189 ClassName -> ghWp,
190 SelfConjugate -> False,
191 Ghost -> W,
192 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
193 Mass -> {MW,Internal},
194 PropagatorLabel -> "uWp",
195 PropagatorType -> GhostDash,
196 PropagatorArrow -> Forward
197 },
198 U[32] == {
199 ClassName -> ghWm,
200 SelfConjugate -> False,
201 Ghost -> Wbar,
202 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
203 Mass -> {MW,Internal},
204 PropagatorLabel -> "uWm",
205 PropagatorType -> GhostDash,
206 PropagatorArrow -> Forward
207 },
208 U[4] == {
209 ClassName -> ghG,
210 SelfConjugate -> False,
211 Indices -> {Index[Gluon]},
212 Ghost -> G,
213 QuantumNumbers ->{GhostNumber -> 1},
214 Mass -> 0,
215 PropagatorLabel -> "uG",
216 PropagatorType -> GhostDash,
217 PropagatorArrow -> Forward
218 },
219
220(* Gauge bosons: unphysical vector fields *)
221 V[11] == {
222 ClassName -> B,
223 Unphysical -> True,
224 SelfConjugate -> True,
225 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
226 },
227 V[12] == {
228 ClassName -> Wi,
229 Unphysical -> True,
230 SelfConjugate -> True,
231 Indices -> {Index[SU2W]},
232 FlavorIndex -> SU2W,
233 Definitions -> { Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3] -> cw Z[mu] + sw A[mu]}
234 },
235
236(* Ghosts: related to unphysical gauge bosons *)
237 U[11] == {
238 ClassName -> ghB,
239 Unphysical -> True,
240 SelfConjugate -> False,
241 Ghost -> B,
242 Definitions -> { ghB -> -sw ghZ + cw ghA}
243 },
244 U[12] == {
245 ClassName -> ghWi,
246 Unphysical -> True,
247 SelfConjugate -> False,
248 Ghost -> Wi,
249 Indices -> {Index[SU2W]},
250 FlavorIndex -> SU2W,
251 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
252 } ,
253
254(* Fermions: physical fields *)
255 F[1] == {
256 ClassName -> vl,
257 ClassMembers -> {ve,vm,vt},
258 Indices -> {Index[Generation]},
259 FlavorIndex -> Generation,
260 SelfConjugate -> False,
261 Mass -> 0,
262 Width -> 0,
263 QuantumNumbers -> {LeptonNumber -> 1},
264 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
265 PropagatorType -> S,
266 PropagatorArrow -> Forward,
267 PDG -> {12,14,16},
268 ParticleName -> {"ve","vm","vt"},
269 AntiParticleName -> {"ve~","vm~","vt~"},
270 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
271 },
272 F[2] == {
273 ClassName -> l,
274 ClassMembers -> {e, mu, ta},
275 Indices -> {Index[Generation]},
276 FlavorIndex -> Generation,
277 SelfConjugate -> False,
278 Mass -> {Ml, {Me,5.11*^-4}, {MM,0.10566}, {MTA,1.777}},
279 Width -> 0,
280 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
281 PropagatorLabel -> {"l", "e", "mu", "ta"},
282 PropagatorType -> Straight,
283 PropagatorArrow -> Forward,
284 PDG -> {11, 13, 15},
285 ParticleName -> {"e-", "mu-", "ta-"},
286 AntiParticleName -> {"e+", "mu+", "ta+"},
287 FullName -> {"Electron", "Muon", "Tau"}
288 },
289 F[3] == {
290 ClassName -> uq,
291 ClassMembers -> {u, c, t},
292 Indices -> {Index[Generation], Index[Colour]},
293 FlavorIndex -> Generation,
294 SelfConjugate -> False,
295 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
296 Width -> {0, 0, {WT,1.50833649}},
297 QuantumNumbers -> {Q -> 2/3},
298 PropagatorLabel -> {"uq", "u", "c", "t"},
299 PropagatorType -> Straight,
300 PropagatorArrow -> Forward,
301 PDG -> {2, 4, 6},
302 ParticleName -> {"u", "c", "t" },
303 AntiParticleName -> {"u~", "c~", "t~"},
304 FullName -> {"u-quark", "c-quark", "t-quark"}
305 },
306 F[4] == {
307 ClassName -> dq,
308 ClassMembers -> {d, s, b},
309 Indices -> {Index[Generation], Index[Colour]},
310 FlavorIndex -> Generation,
311 SelfConjugate -> False,
312 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
313 Width -> 0,
314 QuantumNumbers -> {Q -> -1/3},
315 PropagatorLabel -> {"dq", "d", "s", "b"},
316 PropagatorType -> Straight,
317 PropagatorArrow -> Forward,
318 PDG -> {1,3,5},
319 ParticleName -> {"d", "s", "b" },
320 AntiParticleName -> {"d~", "s~", "b~"},
321 FullName -> {"d-quark", "s-quark", "b-quark"}
322 },
323
324(* Fermions: unphysical fields *)
325 F[11] == {
326 ClassName -> LL,
327 Unphysical -> True,
328 Indices -> {Index[SU2D], Index[Generation]},
329 FlavorIndex -> SU2D,
330 SelfConjugate -> False,
331 QuantumNumbers -> {Y -> -1/2},
332 Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] vl[sp2,ff]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
333 },
334 F[12] == {
335 ClassName -> lR,
336 Unphysical -> True,
337 Indices -> {Index[Generation]},
338 FlavorIndex -> Generation,
339 SelfConjugate -> False,
340 QuantumNumbers -> {Y -> -1},
341 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
342 },
343 F[13] == {
344 ClassName -> QL,
345 Unphysical -> True,
346 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
347 FlavorIndex -> SU2D,
348 SelfConjugate -> False,
349 QuantumNumbers -> {Y -> 1/6},
350 Definitions -> {
351 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
352 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
353 },
354 F[14] == {
355 ClassName -> uR,
356 Unphysical -> True,
357 Indices -> {Index[Generation], Index[Colour]},
358 FlavorIndex -> Generation,
359 SelfConjugate -> False,
360 QuantumNumbers -> {Y -> 2/3},
361 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
362 },
363 F[15] == {
364 ClassName -> dR,
365 Unphysical -> True,
366 Indices -> {Index[Generation], Index[Colour]},
367 FlavorIndex -> Generation,
368 SelfConjugate -> False,
369 QuantumNumbers -> {Y -> -1/3},
370 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
371 },
372
373(* Higgs: physical scalars *)
374 (* S[1] == {
375 ClassName -> H,
376 SelfConjugate -> True,
377 Mass -> {MH,120},
378 Width -> {WH,0.00575308848},
379 PropagatorLabel -> "H",
380 PropagatorType -> D,
381 PropagatorArrow -> None,
382 PDG -> 25,
383 ParticleName -> "H",
384 FullName -> "H"
385 }, *)
386
387(* Higgs: physical scalars *)
388 S[2] == {
389 ClassName -> G0,
390 SelfConjugate -> True,
391 Goldstone -> Z,
392 Mass -> {MZ, 91.1876},
393 Width -> WGo,
394 PropagatorLabel -> "Go",
395 PropagatorType -> D,
396 PropagatorArrow -> None,
397 PDG -> 250,
398 ParticleName -> "G0",
399 FullName -> "G0"
400 },
401 S[3] == {
402 ClassName -> GP,
403 SelfConjugate -> False,
404 Goldstone -> W,
405 Mass -> {MW, Internal},
406 QuantumNumbers -> {Q -> 1},
407 Width -> WGP,
408 PropagatorLabel -> "GP",
409 PropagatorType -> D,
410 PropagatorArrow -> None,
411 PDG -> 251,
412 ParticleName -> "G+",
413 AntiParticleName -> "G-",
414 FullName -> "GP"
415 },
416
417(* Higgs: unphysical scalars *)
418 S[11] == {
419 ClassName -> Phi,
420 Unphysical -> True,
421 Indices -> {Index[SU2D]},
422 FlavorIndex -> SU2D,
423 SelfConjugate -> False,
424 QuantumNumbers -> {Y -> 1/2},
425 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + ca X0 + I G0)/Sqrt[2] }
426 }
427};
428
429
430(* ************************** *)
431(* ***** Gauge ***** *)
432(* ***** Parameters ***** *)
433(* ***** (FeynArts) ***** *)
434(* ************************** *)
435
436GaugeXi[ V[1] ] = GaugeXi[A];
437GaugeXi[ V[2] ] = GaugeXi[Z];
438GaugeXi[ V[3] ] = GaugeXi[W];
439GaugeXi[ V[4] ] = GaugeXi[G];
440GaugeXi[ S[1] ] = 1;
441GaugeXi[ S[2] ] = GaugeXi[Z];
442GaugeXi[ S[3] ] = GaugeXi[W];
443GaugeXi[ U[1] ] = GaugeXi[A];
444GaugeXi[ U[2] ] = GaugeXi[Z];
445GaugeXi[ U[31] ] = GaugeXi[W];
446GaugeXi[ U[32] ] = GaugeXi[W];
447GaugeXi[ U[4] ] = GaugeXi[G];
448
449
450(* ************************** *)
451(* ***** Parameters ***** *)
452(* ************************** *)
453M$Parameters = {
454
455 (* External parameters *)
456 aEWM1 == {
457 ParameterType -> External,
458 BlockName -> SMINPUTS,
459 OrderBlock -> 1,
460 Value -> 127.9,
461 InteractionOrder -> {QED,-2},
462 Description -> "Inverse of the EW coupling constant at the Z pole"
463 },
464 Gf == {
465 ParameterType -> External,
466 BlockName -> SMINPUTS,
467 OrderBlock -> 2,
468 Value -> 1.16637*^-5,
469 InteractionOrder -> {QED,2},
470 TeX -> Subscript[G,f],
471 Description -> "Fermi constant"
472 },
473 aS == {
474 ParameterType -> External,
475 BlockName -> SMINPUTS,
476 OrderBlock -> 3,
477 Value -> 0.1184,
478 InteractionOrder -> {QCD,2},
479 TeX -> Subscript[\[Alpha],s],
480 Description -> "Strong coupling constant at the Z pole"
481 },
482 ymdo == {
483 ParameterType -> External,
484 BlockName -> YUKAWA,
485 OrderBlock -> 1,
486 Value -> 5.04*^-3,
487 Description -> "Down Yukawa mass"
488 },
489 ymup == {
490 ParameterType -> External,
491 BlockName -> YUKAWA,
492 OrderBlock -> 2,
493 Value -> 2.55*^-3,
494 Description -> "Up Yukawa mass"
495 },
496 yms == {
497 ParameterType -> External,
498 BlockName -> YUKAWA,
499 OrderBlock -> 3,
500 Value -> 0.101,
501 Description -> "Strange Yukawa mass"
502 },
503 ymc == {
504 ParameterType -> External,
505 BlockName -> YUKAWA,
506 OrderBlock -> 4,
507 Value -> 1.27,
508 Description -> "Charm Yukawa mass"
509 },
510 ymb == {
511 ParameterType -> External,
512 BlockName -> YUKAWA,
513 OrderBlock -> 5,
514 Value -> 4.7,
515 Description -> "Bottom Yukawa mass"
516 },
517 ymt == {
518 ParameterType -> External,
519 BlockName -> YUKAWA,
520 OrderBlock -> 6,
521 Value -> 172,
522 Description -> "Top Yukawa mass"
523 },
524 yme == {
525 ParameterType -> External,
526 BlockName -> YUKAWA,
527 OrderBlock -> 11,
528 Value -> 5.11*^-4,
529 Description -> "Electron Yukawa mass"
530 },
531 ymm == {
532 ParameterType -> External,
533 BlockName -> YUKAWA,
534 OrderBlock -> 13,
535 Value -> 0.10566,
536 Description -> "Muon Yukawa mass"
537 },
538 ymtau == {
539 ParameterType -> External,
540 BlockName -> YUKAWA,
541 OrderBlock -> 15,
542 Value -> 1.777,
543 Description -> "Tau Yukawa mass"
544 },
545 cabi == {
546 ParameterType -> External,
547 BlockName -> CKMBLOCK,
548 OrderBlock -> 1,
549 Value -> 0.227736,
550 TeX -> Subscript[\[Theta], c],
551 Description -> "Cabibbo angle"
552 },
553
554 (* Internal Parameters *)
555 aEW == {
556 ParameterType -> Internal,
557 Value -> 1/aEWM1,
558 InteractionOrder -> {QED,2},
559 TeX -> Subscript[\[Alpha], EW],
560 Description -> "Electroweak coupling contant"
561 },
562 MW == {
563 ParameterType -> Internal,
564 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
565 TeX -> Subscript[M,W],
566 Description -> "W mass"
567 },
568 sw2 == {
569 ParameterType -> Internal,
570 Value -> 1-(MW/MZ)^2,
571 Description -> "Squared Sin of the Weinberg angle"
572 },
573 ee == {
574 ParameterType -> Internal,
575 Value -> Sqrt[4 Pi aEW],
576 InteractionOrder -> {QED,1},
577 TeX -> e,
578 Description -> "Electric coupling constant"
579 },
580 cw == {
581 ParameterType -> Internal,
582 Value -> Sqrt[1-sw2],
583 TeX -> Subscript[c,w],
584 Description -> "Cosine of the Weinberg angle"
585 },
586 sw == {
587 ParameterType -> Internal,
588 Value -> Sqrt[sw2],
589 TeX -> Subscript[s,w],
590 Description -> "Sine of the Weinberg angle"
591 },
592 gw == {
593 ParameterType -> Internal,
594 Definitions -> {gw->ee/sw},
595 InteractionOrder -> {QED,1},
596 TeX -> Subscript[g,w],
597 Description -> "Weak coupling constant at the Z pole"
598 },
599 g1 == {
600 ParameterType -> Internal,
601 Definitions -> {g1->ee/cw},
602 InteractionOrder -> {QED,1},
603 TeX -> Subscript[g,1],
604 Description -> "U(1)Y coupling constant at the Z pole"
605 },
606 gs == {
607 ParameterType -> Internal,
608 Value -> Sqrt[4 Pi aS],
609 InteractionOrder -> {QCD,1},
610 TeX -> Subscript[g,s],
611 ParameterName -> G,
612 Description -> "Strong coupling constant at the Z pole"
613 },
614 vev == {
615 ParameterType -> Internal,
616 Value -> 2*MW*sw/ee,
617 InteractionOrder -> {QED,-1},
618 Description -> "Higgs vacuum expectation value"
619 },
620 lam == {
621 ParameterType -> Internal,
622 Value -> MX0^2/(2*vev^2),
623 InteractionOrder -> {QED, 2},
624 Description -> "Higgs quartic coupling"
625 },
626 muH == {
627 ParameterType -> Internal,
628 Value -> Sqrt[vev^2 lam],
629 TeX -> \[Mu],
630 Description -> "Coefficient of the quadratic piece of the Higgs potential"
631 },
632 yl == {
633 ParameterType -> Internal,
634 Indices -> {Index[Generation], Index[Generation]},
635 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
636 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
637 InteractionOrder -> {QED, 1},
638 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
639 TeX -> Superscript[y, l],
640 Description -> "Lepton Yukawa couplings"
641 },
642 yu == {
643 ParameterType -> Internal,
644 Indices -> {Index[Generation], Index[Generation]},
645 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
646 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
647 InteractionOrder -> {QED, 1},
648 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
649 TeX -> Superscript[y, u],
650 Description -> "Up-type Yukawa couplings"
651 },
652 yd == {
653 ParameterType -> Internal,
654 Indices -> {Index[Generation], Index[Generation]},
655 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
656 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
657 InteractionOrder -> {QED, 1},
658 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
659 TeX -> Superscript[y, d],
660 Description -> "Down-type Yukawa couplings"
661 },
662(* N. B. : only Cabibbo mixing! *)
663 CKM == {
664 ParameterType -> Internal,
665 Indices -> {Index[Generation], Index[Generation]},
666 Unitary -> True,
667 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
668 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
669 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
670 TeX -> Superscript[V,CKM],
671 Description -> "CKM-Matrix"}
672};
673
674(* ************************** *)
675(* ***** Lagrangian ***** *)
676(* ************************** *)
677
678LGauge := Block[{mu,nu,ii,aa},
679 ExpandIndices[-1/4 FS[B,mu,nu] FS[B,mu,nu] - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa], FlavorExpand->SU2W]];
680
681(* LFermions := Block[{mu},
682 ExpandIndices[I*(
683 QLbar.Ga[mu].DC[QL, mu] + LLbar.Ga[mu].DC[LL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu] + lRbar.Ga[mu].DC[lR, mu]),
684 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}]; *)
685
686(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
687LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
688
689 Lkin = I uqbar.Ga[mu].del[uq, mu] +
690 I dqbar.Ga[mu].del[dq, mu] +
691 I lbar.Ga[mu].del[l, mu] +
692 I left[anti[vl]].Ga[mu].del[left[vl],mu] +
693 I right[anti[vl]].Ga[mu].del[right[vl],mu];
694
695 LQCD = gs (uqbar.Ga[mu].T[a].uq +
696 dqbar.Ga[mu].T[a].dq)G[mu, a];
697
698 LBright =
699 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
700 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
701 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
702
703 LBleft =
704 -ee/cw B[mu]/2 left[anti[vl]].Ga[mu].ProjM.vl - (*Y_LL=-1*)
705 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
706 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
707 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
708
709 LWleft = ee/sw/2(
710 left[anti[vl]].Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
711 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
712
713 Sqrt[2] left[anti[vl]].Ga[mu].ProjM.l W[mu] +
714 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
715
716 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
717 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
718
719 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
720 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
721 );
722
723 Lkin + LQCD + LBright + LBleft + LWleft ];
724
725LHiggs := Block[{ii,mu, feynmangaugerules},
726 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
727
728 ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
729 ];
730
731LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
732 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
733
734 yuk = ExpandIndices[
735 -kHbb yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
736 kHll yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
737 kHtt yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
738 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
739 yuk+HC[yuk]/.feynmangaugerules
740 ];
741
742LYukawaOdd := -I sa/vev ( kAll MTA tabar.Ga[5].ta + kAtt MT tbar.Ga[5].t + kAbb MB bbar.Ga[5].b ) X0;
743
744LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
745 (* Pure gauge piece *)
746 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
747 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
748 LGhs = -ghGbar.del[DC[ghG,mu],mu];
749
750 (* Scalar pieces: see Peskin pages 739-742 *)
751 (* phi1 and phi2 are the real degrees of freedom of GP *)
752 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
753 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
754 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
755 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
756 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
757 doublet0 = {0, vev/Sqrt[2]};
758 Vectorize[{a_, b_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]}/.{Im[_]->0, Re[num_]->num}];
759 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
760 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
761
762ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
763
764LSM:= LGauge + LFermions + kSM*LHiggs + LYukawa + LYukawaOdd + LGhost;