DMGISM0: SM_CKM.fr

File SM_CKM.fr, 26.6 KB (added by GiorgioBusoni, 7 years ago)

SM file with all non-zero CKM matrix elements

Line 
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(* ************************** *)
13(* ***** Information ***** *)
14(* ************************** *)
15M$ModelName = "Standard Model";
16
17M$Information = {
18 Authors -> {"N. Christensen", "C. Duhr", "B. Fuks"},
19 Version -> "1.4.7",
20 Date -> "28. 09. 2016",
21 Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)", "IPHC Strasbourg / University of Strasbourg"},
22 Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "benjamin.fuks@cnrs.in2p3.fr"},
23 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"
24};
25
26FeynmanGauge = True;
27
28(* ************************** *)
29(* ***** NLO Variables ****** *)
30(******************************)
31
32FR$LoopSwitches = {{Gf, MW}};
33FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
34 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
35
36(* ************************** *)
37(* ***** Change log ***** *)
38(* ************************** *)
39
40(* v1.4.7: Index issue with the ghost Lagrangian (special thanks to S. Iwamoto *)
41(* v1.4.6: NLO variable added. *)
42(* v1.4.5: Added widths for ghosts. *)
43(* v1.4.4: Changed widths of goldstone bosons to be the same as for the W and Z bosons *)
44(* v1.4.3: Updated conventions for the symmetric structure constants of SU3. *)
45(* v1.4.2: Set FeynmanGauge=True as default again. *)
46(* v1.4: Added SU(2) representation. *)
47(* -> Modification in the field declarations (doublets are added) *)
48(* -> Modification in the Lagrangian (much simpler). *)
49(* v1.3: Added yukawa couplings for all fermions for gauge invariance. *)
50(* Added yukawa couplings for 1st generation fermions to Massless.rst. *)
51(* Updated parameters to PDG 2010. *)
52(* v1.2: Set FeynmanGauge=True as default. *)
53(* Set Gluonic ghosts to be included in both gauges. *)
54(* v1.1: Fixed yukawa couplings in Feynman gauge. *)
55(* Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. *)
56(* Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. *)
57
58(* ************************** *)
59(* ***** vevs ***** *)
60(* ************************** *)
61M$vevs = { {Phi[2],vev} };
62
63(* ************************** *)
64(* ***** Gauge groups ***** *)
65(* ************************** *)
66M$GaugeGroups = {
67 U1Y == {
68 Abelian -> True,
69 CouplingConstant -> g1,
70 GaugeBoson -> B,
71 Charge -> Y
72 },
73 SU2L == {
74 Abelian -> False,
75 CouplingConstant -> gw,
76 GaugeBoson -> Wi,
77 StructureConstant -> Eps,
78 Representations -> {Ta,SU2D},
79 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
80 },
81 SU3C == {
82 Abelian -> False,
83 CouplingConstant -> gs,
84 GaugeBoson -> G,
85 StructureConstant -> f,
86 Representations -> {T,Colour},
87 SymmetricTensor -> dSUN
88 }
89};
90
91
92(* ************************** *)
93(* ***** Indices ***** *)
94(* ************************** *)
95
96IndexRange[Index[SU2W ]] = Unfold[Range[3]];
97IndexRange[Index[SU2D ]] = Unfold[Range[2]];
98IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
99IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
100IndexRange[Index[Generation]] = Range[3];
101
102IndexStyle[SU2W, j];
103IndexStyle[SU2D, k];
104IndexStyle[Gluon, a];
105IndexStyle[Colour, m];
106IndexStyle[Generation, f];
107
108
109(* ************************** *)
110(* *** Interaction orders *** *)
111(* *** (as used by mg5) *** *)
112(* ************************** *)
113
114M$InteractionOrderHierarchy = {
115 {QCD, 1},
116 {QED, 2}
117};
118
119
120(* ************************** *)
121(* **** Particle classes **** *)
122(* ************************** *)
123M$ClassesDescription = {
124
125(* Gauge bosons: physical vector fields *)
126 V[1] == {
127 ClassName -> A,
128 SelfConjugate -> True,
129 Mass -> 0,
130 Width -> 0,
131 ParticleName -> "a",
132 PDG -> 22,
133 PropagatorLabel -> "a",
134 PropagatorType -> W,
135 PropagatorArrow -> None,
136 FullName -> "Photon"
137 },
138 V[2] == {
139 ClassName -> Z,
140 SelfConjugate -> True,
141 Mass -> {MZ, 91.1876},
142 Width -> {WZ, 2.4952},
143 ParticleName -> "Z",
144 PDG -> 23,
145 PropagatorLabel -> "Z",
146 PropagatorType -> Sine,
147 PropagatorArrow -> None,
148 FullName -> "Z"
149 },
150 V[3] == {
151 ClassName -> W,
152 SelfConjugate -> False,
153 Mass -> {MW, Internal},
154 Width -> {WW, 2.085},
155 ParticleName -> "W+",
156 AntiParticleName -> "W-",
157 QuantumNumbers -> {Q -> 1},
158 PDG -> 24,
159 PropagatorLabel -> "W",
160 PropagatorType -> Sine,
161 PropagatorArrow -> Forward,
162 FullName -> "W"
163 },
164 V[4] == {
165 ClassName -> G,
166 SelfConjugate -> True,
167 Indices -> {Index[Gluon]},
168 Mass -> 0,
169 Width -> 0,
170 ParticleName -> "g",
171 PDG -> 21,
172 PropagatorLabel -> "G",
173 PropagatorType -> C,
174 PropagatorArrow -> None,
175 FullName -> "G"
176 },
177
178(* Ghosts: related to physical gauge bosons *)
179 U[1] == {
180 ClassName -> ghA,
181 SelfConjugate -> False,
182 Ghost -> A,
183 QuantumNumbers -> {GhostNumber -> 1},
184 Mass -> 0,
185 Width -> 0,
186 PropagatorLabel -> "uA",
187 PropagatorType -> GhostDash,
188 PropagatorArrow -> Forward
189 },
190 U[2] == {
191 ClassName -> ghZ,
192 SelfConjugate -> False,
193 Ghost -> Z,
194 QuantumNumbers -> {GhostNumber -> 1},
195 Mass -> {MZ,91.1876},
196 Width -> {WZ, 2.4952},
197 PropagatorLabel -> "uZ",
198 PropagatorType -> GhostDash,
199 PropagatorArrow -> Forward
200 },
201 U[31] == {
202 ClassName -> ghWp,
203 SelfConjugate -> False,
204 Ghost -> W,
205 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
206 Mass -> {MW,Internal},
207 Width -> {WW, 2.085},
208 PropagatorLabel -> "uWp",
209 PropagatorType -> GhostDash,
210 PropagatorArrow -> Forward
211 },
212 U[32] == {
213 ClassName -> ghWm,
214 SelfConjugate -> False,
215 Ghost -> Wbar,
216 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
217 Mass -> {MW,Internal},
218 Width -> {WW, 2.085},
219 PropagatorLabel -> "uWm",
220 PropagatorType -> GhostDash,
221 PropagatorArrow -> Forward
222 },
223 U[4] == {
224 ClassName -> ghG,
225 SelfConjugate -> False,
226 Indices -> {Index[Gluon]},
227 Ghost -> G,
228 PDG -> 82,
229 QuantumNumbers ->{GhostNumber -> 1},
230 Mass -> 0,
231 Width -> 0,
232 PropagatorLabel -> "uG",
233 PropagatorType -> GhostDash,
234 PropagatorArrow -> Forward
235 },
236
237(* Gauge bosons: unphysical vector fields *)
238 V[11] == {
239 ClassName -> B,
240 Unphysical -> True,
241 SelfConjugate -> True,
242 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
243 },
244 V[12] == {
245 ClassName -> Wi,
246 Unphysical -> True,
247 SelfConjugate -> True,
248 Indices -> {Index[SU2W]},
249 FlavorIndex -> SU2W,
250 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]}
251 },
252
253(* Ghosts: related to unphysical gauge bosons *)
254 U[11] == {
255 ClassName -> ghB,
256 Unphysical -> True,
257 SelfConjugate -> False,
258 Ghost -> B,
259 Definitions -> { ghB -> -sw ghZ + cw ghA}
260 },
261 U[12] == {
262 ClassName -> ghWi,
263 Unphysical -> True,
264 SelfConjugate -> False,
265 Ghost -> Wi,
266 Indices -> {Index[SU2W]},
267 FlavorIndex -> SU2W,
268 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
269 } ,
270
271(* Fermions: physical fields *)
272 F[1] == {
273 ClassName -> vl,
274 ClassMembers -> {ve,vm,vt},
275 Indices -> {Index[Generation]},
276 FlavorIndex -> Generation,
277 SelfConjugate -> False,
278 Mass -> 0,
279 Width -> 0,
280 QuantumNumbers -> {LeptonNumber -> 1},
281 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
282 PropagatorType -> S,
283 PropagatorArrow -> Forward,
284 PDG -> {12,14,16},
285 ParticleName -> {"ve","vm","vt"},
286 AntiParticleName -> {"ve~","vm~","vt~"},
287 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
288 },
289 F[2] == {
290 ClassName -> l,
291 ClassMembers -> {e, mu, ta},
292 Indices -> {Index[Generation]},
293 FlavorIndex -> Generation,
294 SelfConjugate -> False,
295 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
296 Width -> 0,
297 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
298 PropagatorLabel -> {"l", "e", "mu", "ta"},
299 PropagatorType -> Straight,
300 PropagatorArrow -> Forward,
301 PDG -> {11, 13, 15},
302 ParticleName -> {"e-", "mu-", "ta-"},
303 AntiParticleName -> {"e+", "mu+", "ta+"},
304 FullName -> {"Electron", "Muon", "Tau"}
305 },
306 F[3] == {
307 ClassName -> uq,
308 ClassMembers -> {u, c, t},
309 Indices -> {Index[Generation], Index[Colour]},
310 FlavorIndex -> Generation,
311 SelfConjugate -> False,
312 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
313 Width -> {0, 0, {WT,1.50833649}},
314 QuantumNumbers -> {Q -> 2/3},
315 PropagatorLabel -> {"uq", "u", "c", "t"},
316 PropagatorType -> Straight,
317 PropagatorArrow -> Forward,
318 PDG -> {2, 4, 6},
319 ParticleName -> {"u", "c", "t" },
320 AntiParticleName -> {"u~", "c~", "t~"},
321 FullName -> {"u-quark", "c-quark", "t-quark"}
322 },
323 F[4] == {
324 ClassName -> dq,
325 ClassMembers -> {d, s, b},
326 Indices -> {Index[Generation], Index[Colour]},
327 FlavorIndex -> Generation,
328 SelfConjugate -> False,
329 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
330 Width -> 0,
331 QuantumNumbers -> {Q -> -1/3},
332 PropagatorLabel -> {"dq", "d", "s", "b"},
333 PropagatorType -> Straight,
334 PropagatorArrow -> Forward,
335 PDG -> {1,3,5},
336 ParticleName -> {"d", "s", "b" },
337 AntiParticleName -> {"d~", "s~", "b~"},
338 FullName -> {"d-quark", "s-quark", "b-quark"}
339 },
340
341(* Fermions: unphysical fields *)
342 F[11] == {
343 ClassName -> LL,
344 Unphysical -> True,
345 Indices -> {Index[SU2D], Index[Generation]},
346 FlavorIndex -> SU2D,
347 SelfConjugate -> False,
348 QuantumNumbers -> {Y -> -1/2},
349 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]] }
350 },
351 F[12] == {
352 ClassName -> lR,
353 Unphysical -> True,
354 Indices -> {Index[Generation]},
355 FlavorIndex -> Generation,
356 SelfConjugate -> False,
357 QuantumNumbers -> {Y -> -1},
358 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
359 },
360 F[13] == {
361 ClassName -> QL,
362 Unphysical -> True,
363 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
364 FlavorIndex -> SU2D,
365 SelfConjugate -> False,
366 QuantumNumbers -> {Y -> 1/6},
367 Definitions -> {
368 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
369 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
370 },
371 F[14] == {
372 ClassName -> uR,
373 Unphysical -> True,
374 Indices -> {Index[Generation], Index[Colour]},
375 FlavorIndex -> Generation,
376 SelfConjugate -> False,
377 QuantumNumbers -> {Y -> 2/3},
378 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
379 },
380 F[15] == {
381 ClassName -> dR,
382 Unphysical -> True,
383 Indices -> {Index[Generation], Index[Colour]},
384 FlavorIndex -> Generation,
385 SelfConjugate -> False,
386 QuantumNumbers -> {Y -> -1/3},
387 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
388 },
389
390(* Higgs: physical scalars *)
391 S[1] == {
392 ClassName -> H,
393 SelfConjugate -> True,
394 Mass -> {MH,125},
395 Width -> {WH,0.00407},
396 PropagatorLabel -> "H",
397 PropagatorType -> D,
398 PropagatorArrow -> None,
399 PDG -> 25,
400 ParticleName -> "H",
401 FullName -> "H"
402 },
403
404(* Higgs: physical scalars *)
405 S[2] == {
406 ClassName -> G0,
407 SelfConjugate -> True,
408 Goldstone -> Z,
409 Mass -> {MZ, 91.1876},
410 Width -> {WZ, 2.4952},
411 PropagatorLabel -> "Go",
412 PropagatorType -> D,
413 PropagatorArrow -> None,
414 PDG -> 250,
415 ParticleName -> "G0",
416 FullName -> "G0"
417 },
418 S[3] == {
419 ClassName -> GP,
420 SelfConjugate -> False,
421 Goldstone -> W,
422 Mass -> {MW, Internal},
423 QuantumNumbers -> {Q -> 1},
424 Width -> {WW, 2.085},
425 PropagatorLabel -> "GP",
426 PropagatorType -> D,
427 PropagatorArrow -> None,
428 PDG -> 251,
429 ParticleName -> "G+",
430 AntiParticleName -> "G-",
431 FullName -> "GP"
432 },
433
434(* Higgs: unphysical scalars *)
435 S[11] == {
436 ClassName -> Phi,
437 Unphysical -> True,
438 Indices -> {Index[SU2D]},
439 FlavorIndex -> SU2D,
440 SelfConjugate -> False,
441 QuantumNumbers -> {Y -> 1/2},
442 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
443 }
444};
445
446
447(* ************************** *)
448(* ***** Gauge ***** *)
449(* ***** Parameters ***** *)
450(* ***** (FeynArts) ***** *)
451(* ************************** *)
452
453GaugeXi[ V[1] ] = GaugeXi[A];
454GaugeXi[ V[2] ] = GaugeXi[Z];
455GaugeXi[ V[3] ] = GaugeXi[W];
456GaugeXi[ V[4] ] = GaugeXi[G];
457GaugeXi[ S[1] ] = 1;
458GaugeXi[ S[2] ] = GaugeXi[Z];
459GaugeXi[ S[3] ] = GaugeXi[W];
460GaugeXi[ U[1] ] = GaugeXi[A];
461GaugeXi[ U[2] ] = GaugeXi[Z];
462GaugeXi[ U[31] ] = GaugeXi[W];
463GaugeXi[ U[32] ] = GaugeXi[W];
464GaugeXi[ U[4] ] = GaugeXi[G];
465
466
467(* ************************** *)
468(* ***** Parameters ***** *)
469(* ************************** *)
470M$Parameters = {
471
472 (* External parameters *)
473 aEWM1 == {
474 ParameterType -> External,
475 BlockName -> SMINPUTS,
476 OrderBlock -> 1,
477 Value -> 127.9,
478 InteractionOrder -> {QED,-2},
479 Description -> "Inverse of the EW coupling constant at the Z pole"
480 },
481 Gf == {
482 ParameterType -> External,
483 BlockName -> SMINPUTS,
484 OrderBlock -> 2,
485 Value -> 1.16637*^-5,
486 InteractionOrder -> {QED,2},
487 TeX -> Subscript[G,f],
488 Description -> "Fermi constant"
489 },
490 aS == {
491 ParameterType -> External,
492 BlockName -> SMINPUTS,
493 OrderBlock -> 3,
494 Value -> 0.1184,
495 InteractionOrder -> {QCD,2},
496 TeX -> Subscript[\[Alpha],s],
497 Description -> "Strong coupling constant at the Z pole"
498 },
499 ymdo == {
500 ParameterType -> External,
501 BlockName -> YUKAWA,
502 OrderBlock -> 1,
503 Value -> 5.04*^-3,
504 Description -> "Down Yukawa mass"
505 },
506 ymup == {
507 ParameterType -> External,
508 BlockName -> YUKAWA,
509 OrderBlock -> 2,
510 Value -> 2.55*^-3,
511 Description -> "Up Yukawa mass"
512 },
513 yms == {
514 ParameterType -> External,
515 BlockName -> YUKAWA,
516 OrderBlock -> 3,
517 Value -> 0.101,
518 Description -> "Strange Yukawa mass"
519 },
520 ymc == {
521 ParameterType -> External,
522 BlockName -> YUKAWA,
523 OrderBlock -> 4,
524 Value -> 1.27,
525 Description -> "Charm Yukawa mass"
526 },
527 ymb == {
528 ParameterType -> External,
529 BlockName -> YUKAWA,
530 OrderBlock -> 5,
531 Value -> 4.7,
532 Description -> "Bottom Yukawa mass"
533 },
534 ymt == {
535 ParameterType -> External,
536 BlockName -> YUKAWA,
537 OrderBlock -> 6,
538 Value -> 172,
539 Description -> "Top Yukawa mass"
540 },
541 yme == {
542 ParameterType -> External,
543 BlockName -> YUKAWA,
544 OrderBlock -> 11,
545 Value -> 5.11*^-4,
546 Description -> "Electron Yukawa mass"
547 },
548 ymm == {
549 ParameterType -> External,
550 BlockName -> YUKAWA,
551 OrderBlock -> 13,
552 Value -> 0.10566,
553 Description -> "Muon Yukawa mass"
554 },
555 ymtau == {
556 ParameterType -> External,
557 BlockName -> YUKAWA,
558 OrderBlock -> 15,
559 Value -> 1.777,
560 Description -> "Tau Yukawa mass"
561 },
562 Vus == {
563 ParameterType -> External,
564 BlockName -> CKMBLOCK,
565 OrderBlock -> 1,
566 Value -> 0.2248,
567 TeX -> Subscript[V, us],
568 Description -> "CKM matrix entry Vus"
569 },
570 Vud == {
571 ParameterType -> External,
572 BlockName -> CKMBLOCK,
573 OrderBlock -> 2,
574 Value -> 0.97417,
575 TeX -> Subscript[V, ud],
576 Description -> "CKM matrix entry Vud"
577 },
578 Vcb == {
579 ParameterType -> External,
580 BlockName -> CKMBLOCK,
581 OrderBlock -> 3,
582 Value -> 0.0405,
583 TeX -> Subscript[V, cb],
584 Description -> "CKM matrix entry Vcb"
585 },
586 Vub == {
587 ParameterType -> External,
588 BlockName -> CKMBLOCK,
589 OrderBlock -> 4,
590 Value -> 0.00409,
591 TeX -> Subscript[V, ub],
592 Description -> "CKM matrix entry Vub"
593 },
594
595 (* Internal Parameters *)
596 aEW == {
597 ParameterType -> Internal,
598 Value -> 1/aEWM1,
599 InteractionOrder -> {QED,2},
600 TeX -> Subscript[\[Alpha], EW],
601 Description -> "Electroweak coupling contant"
602 },
603 MW == {
604 ParameterType -> Internal,
605 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
606 TeX -> Subscript[M,W],
607 Description -> "W mass"
608 },
609 sw2 == {
610 ParameterType -> Internal,
611 Value -> 1-(MW/MZ)^2,
612 Description -> "Squared Sin of the Weinberg angle"
613 },
614 ee == {
615 ParameterType -> Internal,
616 Value -> Sqrt[4 Pi aEW],
617 InteractionOrder -> {QED,1},
618 TeX -> e,
619 Description -> "Electric coupling constant"
620 },
621 cw == {
622 ParameterType -> Internal,
623 Value -> Sqrt[1-sw2],
624 TeX -> Subscript[c,w],
625 Description -> "Cosine of the Weinberg angle"
626 },
627 sw == {
628 ParameterType -> Internal,
629 Value -> Sqrt[sw2],
630 TeX -> Subscript[s,w],
631 Description -> "Sine of the Weinberg angle"
632 },
633 gw == {
634 ParameterType -> Internal,
635 Definitions -> {gw->ee/sw},
636 InteractionOrder -> {QED,1},
637 TeX -> Subscript[g,w],
638 Description -> "Weak coupling constant at the Z pole"
639 },
640 g1 == {
641 ParameterType -> Internal,
642 Definitions -> {g1->ee/cw},
643 InteractionOrder -> {QED,1},
644 TeX -> Subscript[g,1],
645 Description -> "U(1)Y coupling constant at the Z pole"
646 },
647 gs == {
648 ParameterType -> Internal,
649 Value -> Sqrt[4 Pi aS],
650 InteractionOrder -> {QCD,1},
651 TeX -> Subscript[g,s],
652 ParameterName -> G,
653 Description -> "Strong coupling constant at the Z pole"
654 },
655 vev == {
656 ParameterType -> Internal,
657 Value -> 2*MW*sw/ee,
658 InteractionOrder -> {QED,-1},
659 Description -> "Higgs vacuum expectation value"
660 },
661 lam == {
662 ParameterType -> Internal,
663 Value -> MH^2/(2*vev^2),
664 InteractionOrder -> {QED, 2},
665 Description -> "Higgs quartic coupling"
666 },
667 muH == {
668 ParameterType -> Internal,
669 Value -> Sqrt[vev^2 lam],
670 TeX -> \[Mu],
671 Description -> "Coefficient of the quadratic piece of the Higgs potential"
672 },
673 yl == {
674 ParameterType -> Internal,
675 Indices -> {Index[Generation], Index[Generation]},
676 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
677 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
678 InteractionOrder -> {QED, 1},
679 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
680 TeX -> Superscript[y, l],
681 Description -> "Lepton Yukawa couplings"
682 },
683 yu == {
684 ParameterType -> Internal,
685 Indices -> {Index[Generation], Index[Generation]},
686 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
687 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
688 InteractionOrder -> {QED, 1},
689 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
690 TeX -> Superscript[y, u],
691 Description -> "Up-type Yukawa couplings"
692 },
693 yd == {
694 ParameterType -> Internal,
695 Indices -> {Index[Generation], Index[Generation]},
696 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
697 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
698 InteractionOrder -> {QED, 1},
699 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
700 TeX -> Superscript[y, d],
701 Description -> "Down-type Yukawa couplings"
702 },
703(* Full CKM, without delta CP *)
704
705 s12 == {
706 ParameterType -> Internal,
707 Value -> Vus/Sqrt[Vud^2+Vus^2],
708 TeX -> Sin\[Theta]_{12},
709 Description -> "sin of theta_12"
710 },
711
712 s23 == {
713 ParameterType -> Internal,
714 Value -> s12*Vcb/Vus,
715 TeX -> Sin\[Theta]_{23},
716 Description -> "sin of theta_23"
717 },
718
719 s13 == {
720 ParameterType -> Internal,
721 Value -> Vub,
722 TeX -> Sin\[Theta]_{13},
723 Description -> "sin of theta_13"
724 },
725
726 c12 == {
727 ParameterType -> Internal,
728 Value -> Sqrt[1-s12^2],
729 TeX -> Cos\[Theta]_{12},
730 Description -> "cos of theta_12"
731 },
732
733 c23 == {
734 ParameterType -> Internal,
735 Value -> Sqrt[1-s23^2],
736 TeX -> Cos\[Theta]_{23},
737 Description -> "cos of theta_23"
738 },
739
740 c13 == {
741 ParameterType -> Internal,
742 Value -> Sqrt[1-s13^2],
743 TeX -> Cos\[Theta]_{13},
744 Description -> "cos of theta_13"
745 },
746
747 CKM == {
748 ParameterType -> Internal,
749 Indices -> {Index[Generation], Index[Generation]},
750 Unitary -> True,
751 Value -> {CKM[1,1] -> c12*c13, CKM[1,2] -> s12*c13, CKM[1,3] -> s13,
752 CKM[2,1] -> -s12*c23-c12*s23*s13, CKM[2,2] -> c12*c23-s12*s23*s13, CKM[2,3] -> s23*c13,
753 CKM[3,1] -> s12*s23-c12*c23*s13, CKM[3,2] -> -c12*s23-s12*c23*s13, CKM[3,3] -> c23*c13},
754 TeX -> Superscript[V,CKM],
755 Description -> "CKM-Matrix"}
756};
757
758(* ************************** *)
759(* ***** Lagrangian ***** *)
760(* ************************** *)
761
762LGauge := Block[{mu,nu,ii,aa},
763 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]];
764
765LFermions := Block[{mu},
766 ExpandIndices[I*(
767 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]),
768 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
769
770LHiggs := Block[{ii,mu, feynmangaugerules},
771 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
772
773 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
774 ];
775
776LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
777 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
778
779 yuk = ExpandIndices[
780 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
781 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
782 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
783 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
784 yuk+HC[yuk]/.feynmangaugerules
785 ];
786
787LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
788 (* Pure gauge piece *)
789 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
790 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
791 LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
792
793 (* Scalar pieces: see Peskin pages 739-742 *)
794 (* phi1 and phi2 are the real degrees of freedom of GP *)
795 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
796 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
797 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
798 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
799 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
800 doublet0 = {0, vev/Sqrt[2]};
801 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}];
802 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
803 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
804
805ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
806
807LSM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;