HiggsCharacterisation: SM_HC.fr

File SM_HC.fr, 24.8 KB (added by mawatari, 9 years ago)

SM model file slightly modified to the Higgs Characterisation project. Please load it together with the main file v4.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 K. Mawatari to be adapted to the Higgs Characterisation model. *)
13(*- The Higgs has been named as X0. *)
14
15(* ************************** *)
16(* ***** Information ***** *)
17(* ************************** *)
18M$ModelName = "Standard Model";
19
20M$Information = {
21 Authors -> {"N. Christensen", "C. Duhr", "B. Fuks"},
22 Version -> "1.4.5",
23 Date -> "21. 11. 2012",
24 Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)", "IPHC Strasbourg / University of Strasbourg"},
25 Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "benjamin.fuks@cnrs.in2p3.fr"},
26 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"
27};
28
29FeynmanGauge = True;
30
31(* ************************** *)
32(* ***** Change log ***** *)
33(* ************************** *)
34
35(* v1.4.5: Added widths for ghosts. *)
36(* v1.4.4: Changed widths of goldstone bosons to be the same as for the W and Z bosons *)
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(* ***** vevs ***** *)
53(* ************************** *)
54M$vevs = { {Phi[2],vev} };
55
56(* ************************** *)
57(* ***** Gauge groups ***** *)
58(* ************************** *)
59M$GaugeGroups = {
60 U1Y == {
61 Abelian -> True,
62 CouplingConstant -> g1,
63 GaugeBoson -> B,
64 Charge -> Y
65 },
66 SU2L == {
67 Abelian -> False,
68 CouplingConstant -> gw,
69 GaugeBoson -> Wi,
70 StructureConstant -> Eps,
71 Representations -> {Ta,SU2D},
72 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
73 },
74 SU3C == {
75 Abelian -> False,
76 CouplingConstant -> gs,
77 GaugeBoson -> G,
78 StructureConstant -> f,
79 Representations -> {T,Colour},
80 SymmetricTensor -> dSUN
81 }
82};
83
84
85(* ************************** *)
86(* ***** Indices ***** *)
87(* ************************** *)
88
89IndexRange[Index[SU2W ]] = Unfold[Range[3]];
90IndexRange[Index[SU2D ]] = Unfold[Range[2]];
91IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
92IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
93IndexRange[Index[Generation]] = Range[3];
94
95IndexStyle[SU2W, j];
96IndexStyle[SU2D, k];
97IndexStyle[Gluon, a];
98IndexStyle[Colour, m];
99IndexStyle[Generation, f];
100
101
102(* ************************** *)
103(* *** Interaction orders *** *)
104(* *** (as used by mg5) *** *)
105(* ************************** *)
106
107M$InteractionOrderHierarchy = {
108 {QCD, 1},
109 {QED, 2}
110};
111
112
113(* ************************** *)
114(* **** Particle classes **** *)
115(* ************************** *)
116M$ClassesDescription = {
117
118(* Gauge bosons: physical vector fields *)
119 V[1] == {
120 ClassName -> A,
121 SelfConjugate -> True,
122 Mass -> 0,
123 Width -> 0,
124 ParticleName -> "a",
125 PDG -> 22,
126 PropagatorLabel -> "a",
127 PropagatorType -> W,
128 PropagatorArrow -> None,
129 FullName -> "Photon"
130 },
131 V[2] == {
132 ClassName -> Z,
133 SelfConjugate -> True,
134 Mass -> {MZ, 91.1876},
135 Width -> {WZ, 2.4952},
136 ParticleName -> "Z",
137 PDG -> 23,
138 PropagatorLabel -> "Z",
139 PropagatorType -> Sine,
140 PropagatorArrow -> None,
141 FullName -> "Z"
142 },
143 V[3] == {
144 ClassName -> W,
145 SelfConjugate -> False,
146 Mass -> {MW, Internal},
147 Width -> {WW, 2.085},
148 ParticleName -> "W+",
149 AntiParticleName -> "W-",
150 QuantumNumbers -> {Q -> 1},
151 PDG -> 24,
152 PropagatorLabel -> "W",
153 PropagatorType -> Sine,
154 PropagatorArrow -> Forward,
155 FullName -> "W"
156 },
157 V[4] == {
158 ClassName -> G,
159 SelfConjugate -> True,
160 Indices -> {Index[Gluon]},
161 Mass -> 0,
162 Width -> 0,
163 ParticleName -> "g",
164 PDG -> 21,
165 PropagatorLabel -> "G",
166 PropagatorType -> C,
167 PropagatorArrow -> None,
168 FullName -> "G"
169 },
170
171(* Ghosts: related to physical gauge bosons *)
172 U[1] == {
173 ClassName -> ghA,
174 SelfConjugate -> False,
175 Ghost -> A,
176 QuantumNumbers -> {GhostNumber -> 1},
177 Mass -> 0,
178 Width -> 0,
179 PropagatorLabel -> "uA",
180 PropagatorType -> GhostDash,
181 PropagatorArrow -> Forward
182 },
183 U[2] == {
184 ClassName -> ghZ,
185 SelfConjugate -> False,
186 Ghost -> Z,
187 QuantumNumbers -> {GhostNumber -> 1},
188 Mass -> {MZ,91.1876},
189 Width -> {WZ, 2.4952},
190 PropagatorLabel -> "uZ",
191 PropagatorType -> GhostDash,
192 PropagatorArrow -> Forward
193 },
194 U[31] == {
195 ClassName -> ghWp,
196 SelfConjugate -> False,
197 Ghost -> W,
198 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
199 Mass -> {MW,Internal},
200 Width -> {WW, 2.085},
201 PropagatorLabel -> "uWp",
202 PropagatorType -> GhostDash,
203 PropagatorArrow -> Forward
204 },
205 U[32] == {
206 ClassName -> ghWm,
207 SelfConjugate -> False,
208 Ghost -> Wbar,
209 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
210 Mass -> {MW,Internal},
211 Width -> {WW, 2.085},
212 PropagatorLabel -> "uWm",
213 PropagatorType -> GhostDash,
214 PropagatorArrow -> Forward
215 },
216 U[4] == {
217 ClassName -> ghG,
218 SelfConjugate -> False,
219 Indices -> {Index[Gluon]},
220 Ghost -> G,
221 QuantumNumbers ->{GhostNumber -> 1},
222 Mass -> 0,
223 Width -> 0,
224 PropagatorLabel -> "uG",
225 PropagatorType -> GhostDash,
226 PropagatorArrow -> Forward
227 },
228
229(* Gauge bosons: unphysical vector fields *)
230 V[11] == {
231 ClassName -> B,
232 Unphysical -> True,
233 SelfConjugate -> True,
234 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
235 },
236 V[12] == {
237 ClassName -> Wi,
238 Unphysical -> True,
239 SelfConjugate -> True,
240 Indices -> {Index[SU2W]},
241 FlavorIndex -> SU2W,
242 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]}
243 },
244
245(* Ghosts: related to unphysical gauge bosons *)
246 U[11] == {
247 ClassName -> ghB,
248 Unphysical -> True,
249 SelfConjugate -> False,
250 Ghost -> B,
251 Definitions -> { ghB -> -sw ghZ + cw ghA}
252 },
253 U[12] == {
254 ClassName -> ghWi,
255 Unphysical -> True,
256 SelfConjugate -> False,
257 Ghost -> Wi,
258 Indices -> {Index[SU2W]},
259 FlavorIndex -> SU2W,
260 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
261 } ,
262
263(* Fermions: physical fields *)
264 F[1] == {
265 ClassName -> vl,
266 ClassMembers -> {ve,vm,vt},
267 Indices -> {Index[Generation]},
268 FlavorIndex -> Generation,
269 SelfConjugate -> False,
270 Mass -> 0,
271 Width -> 0,
272 QuantumNumbers -> {LeptonNumber -> 1},
273 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
274 PropagatorType -> S,
275 PropagatorArrow -> Forward,
276 PDG -> {12,14,16},
277 ParticleName -> {"ve","vm","vt"},
278 AntiParticleName -> {"ve~","vm~","vt~"},
279 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
280 },
281 F[2] == {
282 ClassName -> l,
283 ClassMembers -> {e, mu, ta},
284 Indices -> {Index[Generation]},
285 FlavorIndex -> Generation,
286 SelfConjugate -> False,
287 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
288 Width -> 0,
289 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
290 PropagatorLabel -> {"l", "e", "mu", "ta"},
291 PropagatorType -> Straight,
292 PropagatorArrow -> Forward,
293 PDG -> {11, 13, 15},
294 ParticleName -> {"e-", "mu-", "ta-"},
295 AntiParticleName -> {"e+", "mu+", "ta+"},
296 FullName -> {"Electron", "Muon", "Tau"}
297 },
298 F[3] == {
299 ClassName -> uq,
300 ClassMembers -> {u, c, t},
301 Indices -> {Index[Generation], Index[Colour]},
302 FlavorIndex -> Generation,
303 SelfConjugate -> False,
304 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
305 Width -> {0, 0, {WT,1.50833649}},
306 QuantumNumbers -> {Q -> 2/3},
307 PropagatorLabel -> {"uq", "u", "c", "t"},
308 PropagatorType -> Straight,
309 PropagatorArrow -> Forward,
310 PDG -> {2, 4, 6},
311 ParticleName -> {"u", "c", "t" },
312 AntiParticleName -> {"u~", "c~", "t~"},
313 FullName -> {"u-quark", "c-quark", "t-quark"}
314 },
315 F[4] == {
316 ClassName -> dq,
317 ClassMembers -> {d, s, b},
318 Indices -> {Index[Generation], Index[Colour]},
319 FlavorIndex -> Generation,
320 SelfConjugate -> False,
321 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
322 Width -> 0,
323 QuantumNumbers -> {Q -> -1/3},
324 PropagatorLabel -> {"dq", "d", "s", "b"},
325 PropagatorType -> Straight,
326 PropagatorArrow -> Forward,
327 PDG -> {1,3,5},
328 ParticleName -> {"d", "s", "b" },
329 AntiParticleName -> {"d~", "s~", "b~"},
330 FullName -> {"d-quark", "s-quark", "b-quark"}
331 },
332
333(* Fermions: unphysical fields *)
334 F[11] == {
335 ClassName -> LL,
336 Unphysical -> True,
337 Indices -> {Index[SU2D], Index[Generation]},
338 FlavorIndex -> SU2D,
339 SelfConjugate -> False,
340 QuantumNumbers -> {Y -> -1/2},
341 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]] }
342 },
343 F[12] == {
344 ClassName -> lR,
345 Unphysical -> True,
346 Indices -> {Index[Generation]},
347 FlavorIndex -> Generation,
348 SelfConjugate -> False,
349 QuantumNumbers -> {Y -> -1},
350 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
351 },
352 F[13] == {
353 ClassName -> QL,
354 Unphysical -> True,
355 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
356 FlavorIndex -> SU2D,
357 SelfConjugate -> False,
358 QuantumNumbers -> {Y -> 1/6},
359 Definitions -> {
360 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
361 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
362 },
363 F[14] == {
364 ClassName -> uR,
365 Unphysical -> True,
366 Indices -> {Index[Generation], Index[Colour]},
367 FlavorIndex -> Generation,
368 SelfConjugate -> False,
369 QuantumNumbers -> {Y -> 2/3},
370 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
371 },
372 F[15] == {
373 ClassName -> dR,
374 Unphysical -> True,
375 Indices -> {Index[Generation], Index[Colour]},
376 FlavorIndex -> Generation,
377 SelfConjugate -> False,
378 QuantumNumbers -> {Y -> -1/3},
379 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
380 },
381
382(* Higgs: physical scalars *)
383(* S[1] == {
384 ClassName -> H,
385 SelfConjugate -> True,
386 Mass -> {MH,125},
387 Width -> {WH,0.00407},
388 PropagatorLabel -> "H",
389 PropagatorType -> D,
390 PropagatorArrow -> None,
391 PDG -> 25,
392 ParticleName -> "H",
393 FullName -> "H"
394 }, *)
395
396(* Higgs: physical scalars *)
397 S[2] == {
398 ClassName -> G0,
399 SelfConjugate -> True,
400 Goldstone -> Z,
401 Mass -> {MZ, 91.1876},
402 Width -> {WZ, 2.4952},
403 PropagatorLabel -> "Go",
404 PropagatorType -> D,
405 PropagatorArrow -> None,
406 PDG -> 250,
407 ParticleName -> "G0",
408 FullName -> "G0"
409 },
410 S[3] == {
411 ClassName -> GP,
412 SelfConjugate -> False,
413 Goldstone -> W,
414 Mass -> {MW, Internal},
415 QuantumNumbers -> {Q -> 1},
416 Width -> {WW, 2.085},
417 PropagatorLabel -> "GP",
418 PropagatorType -> D,
419 PropagatorArrow -> None,
420 PDG -> 251,
421 ParticleName -> "G+",
422 AntiParticleName -> "G-",
423 FullName -> "GP"
424 },
425
426(* Higgs: unphysical scalars *)
427 S[11] == {
428 ClassName -> Phi,
429 Unphysical -> True,
430 Indices -> {Index[SU2D]},
431 FlavorIndex -> SU2D,
432 SelfConjugate -> False,
433 QuantumNumbers -> {Y -> 1/2},
434 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + ca X0 + I G0)/Sqrt[2] }
435 }
436};
437
438
439(* ************************** *)
440(* ***** Gauge ***** *)
441(* ***** Parameters ***** *)
442(* ***** (FeynArts) ***** *)
443(* ************************** *)
444
445GaugeXi[ V[1] ] = GaugeXi[A];
446GaugeXi[ V[2] ] = GaugeXi[Z];
447GaugeXi[ V[3] ] = GaugeXi[W];
448GaugeXi[ V[4] ] = GaugeXi[G];
449GaugeXi[ S[1] ] = 1;
450GaugeXi[ S[2] ] = GaugeXi[Z];
451GaugeXi[ S[3] ] = GaugeXi[W];
452GaugeXi[ U[1] ] = GaugeXi[A];
453GaugeXi[ U[2] ] = GaugeXi[Z];
454GaugeXi[ U[31] ] = GaugeXi[W];
455GaugeXi[ U[32] ] = GaugeXi[W];
456GaugeXi[ U[4] ] = GaugeXi[G];
457
458
459(* ************************** *)
460(* ***** Parameters ***** *)
461(* ************************** *)
462M$Parameters = {
463
464 (* External parameters *)
465 aEWM1 == {
466 ParameterType -> External,
467 BlockName -> SMINPUTS,
468 OrderBlock -> 1,
469 Value -> 127.9,
470 InteractionOrder -> {QED,-2},
471 Description -> "Inverse of the EW coupling constant at the Z pole"
472 },
473 Gf == {
474 ParameterType -> External,
475 BlockName -> SMINPUTS,
476 OrderBlock -> 2,
477 Value -> 1.16637*^-5,
478 InteractionOrder -> {QED,2},
479 TeX -> Subscript[G,f],
480 Description -> "Fermi constant"
481 },
482 aS == {
483 ParameterType -> External,
484 BlockName -> SMINPUTS,
485 OrderBlock -> 3,
486 Value -> 0.1184,
487 InteractionOrder -> {QCD,2},
488 TeX -> Subscript[\[Alpha],s],
489 Description -> "Strong coupling constant at the Z pole"
490 },
491 ymdo == {
492 ParameterType -> External,
493 BlockName -> YUKAWA,
494 OrderBlock -> 1,
495 Value -> 5.04*^-3,
496 Description -> "Down Yukawa mass"
497 },
498 ymup == {
499 ParameterType -> External,
500 BlockName -> YUKAWA,
501 OrderBlock -> 2,
502 Value -> 2.55*^-3,
503 Description -> "Up Yukawa mass"
504 },
505 yms == {
506 ParameterType -> External,
507 BlockName -> YUKAWA,
508 OrderBlock -> 3,
509 Value -> 0.101,
510 Description -> "Strange Yukawa mass"
511 },
512 ymc == {
513 ParameterType -> External,
514 BlockName -> YUKAWA,
515 OrderBlock -> 4,
516 Value -> 1.27,
517 Description -> "Charm Yukawa mass"
518 },
519 ymb == {
520 ParameterType -> External,
521 BlockName -> YUKAWA,
522 OrderBlock -> 5,
523 Value -> 4.7,
524 Description -> "Bottom Yukawa mass"
525 },
526 ymt == {
527 ParameterType -> External,
528 BlockName -> YUKAWA,
529 OrderBlock -> 6,
530 Value -> 172,
531 Description -> "Top Yukawa mass"
532 },
533 yme == {
534 ParameterType -> External,
535 BlockName -> YUKAWA,
536 OrderBlock -> 11,
537 Value -> 5.11*^-4,
538 Description -> "Electron Yukawa mass"
539 },
540 ymm == {
541 ParameterType -> External,
542 BlockName -> YUKAWA,
543 OrderBlock -> 13,
544 Value -> 0.10566,
545 Description -> "Muon Yukawa mass"
546 },
547 ymtau == {
548 ParameterType -> External,
549 BlockName -> YUKAWA,
550 OrderBlock -> 15,
551 Value -> 1.777,
552 Description -> "Tau Yukawa mass"
553 },
554 cabi == {
555 ParameterType -> External,
556 BlockName -> CKMBLOCK,
557 OrderBlock -> 1,
558 Value -> 0.227736,
559 TeX -> Subscript[\[Theta], c],
560 Description -> "Cabibbo angle"
561 },
562
563 (* Internal Parameters *)
564 aEW == {
565 ParameterType -> Internal,
566 Value -> 1/aEWM1,
567 InteractionOrder -> {QED,2},
568 TeX -> Subscript[\[Alpha], EW],
569 Description -> "Electroweak coupling contant"
570 },
571 MW == {
572 ParameterType -> Internal,
573 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
574 TeX -> Subscript[M,W],
575 Description -> "W mass"
576 },
577 sw2 == {
578 ParameterType -> Internal,
579 Value -> 1-(MW/MZ)^2,
580 Description -> "Squared Sin of the Weinberg angle"
581 },
582 ee == {
583 ParameterType -> Internal,
584 Value -> Sqrt[4 Pi aEW],
585 InteractionOrder -> {QED,1},
586 TeX -> e,
587 Description -> "Electric coupling constant"
588 },
589 cw == {
590 ParameterType -> Internal,
591 Value -> Sqrt[1-sw2],
592 TeX -> Subscript[c,w],
593 Description -> "Cosine of the Weinberg angle"
594 },
595 sw == {
596 ParameterType -> Internal,
597 Value -> Sqrt[sw2],
598 TeX -> Subscript[s,w],
599 Description -> "Sine of the Weinberg angle"
600 },
601 gw == {
602 ParameterType -> Internal,
603 Definitions -> {gw->ee/sw},
604 InteractionOrder -> {QED,1},
605 TeX -> Subscript[g,w],
606 Description -> "Weak coupling constant at the Z pole"
607 },
608 g1 == {
609 ParameterType -> Internal,
610 Definitions -> {g1->ee/cw},
611 InteractionOrder -> {QED,1},
612 TeX -> Subscript[g,1],
613 Description -> "U(1)Y coupling constant at the Z pole"
614 },
615 gs == {
616 ParameterType -> Internal,
617 Value -> Sqrt[4 Pi aS],
618 InteractionOrder -> {QCD,1},
619 TeX -> Subscript[g,s],
620 ParameterName -> G,
621 Description -> "Strong coupling constant at the Z pole"
622 },
623 vev == {
624 ParameterType -> Internal,
625 Value -> 2*MW*sw/ee,
626 InteractionOrder -> {QED,-1},
627 Description -> "Higgs vacuum expectation value"
628 },
629 lam == {
630 ParameterType -> Internal,
631 Value -> MX0^2/(2*vev^2),
632 InteractionOrder -> {QED, 2},
633 Description -> "Higgs quartic coupling"
634 },
635 muH == {
636 ParameterType -> Internal,
637 Value -> Sqrt[vev^2 lam],
638 TeX -> \[Mu],
639 Description -> "Coefficient of the quadratic piece of the Higgs potential"
640 },
641 yl == {
642 ParameterType -> Internal,
643 Indices -> {Index[Generation], Index[Generation]},
644 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
645 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
646 InteractionOrder -> {QED, 1},
647 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
648 TeX -> Superscript[y, l],
649 Description -> "Lepton Yukawa couplings"
650 },
651 yu == {
652 ParameterType -> Internal,
653 Indices -> {Index[Generation], Index[Generation]},
654 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
655 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
656 InteractionOrder -> {QED, 1},
657 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
658 TeX -> Superscript[y, u],
659 Description -> "Up-type Yukawa couplings"
660 },
661 yd == {
662 ParameterType -> Internal,
663 Indices -> {Index[Generation], Index[Generation]},
664 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
665 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
666 InteractionOrder -> {QED, 1},
667 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
668 TeX -> Superscript[y, d],
669 Description -> "Down-type Yukawa couplings"
670 },
671(* N. B. : only Cabibbo mixing! *)
672 CKM == {
673 ParameterType -> Internal,
674 Indices -> {Index[Generation], Index[Generation]},
675 Unitary -> True,
676 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
677 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
678 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
679 TeX -> Superscript[V,CKM],
680 Description -> "CKM-Matrix"}
681};
682
683(* ************************** *)
684(* ***** Lagrangian ***** *)
685(* ************************** *)
686
687LGauge := Block[{mu,nu,ii,aa},
688 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]];
689
690LFermions := Block[{mu},
691 ExpandIndices[I*(
692 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]),
693 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
694
695LHiggs := Block[{ii,mu, feynmangaugerules},
696 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
697
698 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
699 ];
700
701LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
702 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
703
704 yuk = ExpandIndices[
705 -kHbb yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
706 kHll yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
707 kHtt yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
708 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
709 yuk+HC[yuk]/.feynmangaugerules
710 ];
711
712(* LYukawaOdd := -I sa/vev ( kAbb MB bbar.Ga[5].b + kAll MTA tabar.Ga[5].ta + kAtt MT tbar.Ga[5].t ) X0; *)
713LYukawaOdd := -I sa/Sqrt[2] ( kAbb yb bbar.Ga[5].b + kAll ytau tabar.Ga[5].ta + kAtt yt tbar.Ga[5].t ) X0;
714
715LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
716 (* Pure gauge piece *)
717 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
718 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
719 LGhs = -ghGbar.del[DC[ghG,mu],mu];
720
721 (* Scalar pieces: see Peskin pages 739-742 *)
722 (* phi1 and phi2 are the real degrees of freedom of GP *)
723 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
724 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
725 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
726 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
727 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
728 doublet0 = {0, vev/Sqrt[2]};
729 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}];
730 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
731 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
732
733ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
734
735LSM:= LGauge + LFermions + kSM*LHiggs + LYukawa + LYukawaOdd + LGhost;