VLC_LN: VLC.fr

File VLC.fr, 26.9 KB (added by DanieleBarducci, 6 years ago)

FeynRules file for the model

Line 
1
2
3(* ************************** *)
4(* ***** Information ***** *)
5(* ************************** *)
6M$ModelName = "VLC_LN";
7
8M$Information = {
9 Authors -> {"Daniele Barducci, Michele Redi, Andrea Tesi"},
10 Version -> "1.0",
11 Date -> "28. 05. 2018",
12 Institutions -> {"SISSA and INFN Section of Trieste", "INFN Section of Florence"},
13 Emails -> {"daniele.barducci@sissa.it"},
14 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"
15};
16
17FeynmanGauge = True;
18
19(* ************************** *)
20(* ***** NLO Variables ****** *)
21(******************************)
22
23FR$LoopSwitches = {{Gf, MW}};
24FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
25 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
26
27(* ************************** *)
28(* ***** Change log ***** *)
29(* ************************** *)
30
31(* v1.4.7: Index issue with the ghost Lagrangian (special thanks to S. Iwamoto *)
32(* v1.4.6: NLO variable added. *)
33(* v1.4.5: Added widths for ghosts. *)
34(* v1.4.4: Changed widths of goldstone bosons to be the same as for the W and Z bosons *)
35(* v1.4.3: Updated conventions for the symmetric structure constants of SU3. *)
36(* v1.4.2: Set FeynmanGauge=True as default again. *)
37(* v1.4: Added SU(2) representation. *)
38(* -> Modification in the field declarations (doublets are added) *)
39(* -> Modification in the Lagrangian (much simpler). *)
40(* v1.3: Added yukawa couplings for all fermions for gauge invariance. *)
41(* Added yukawa couplings for 1st generation fermions to Massless.rst. *)
42(* Updated parameters to PDG 2010. *)
43(* v1.2: Set FeynmanGauge=True as default. *)
44(* Set Gluonic ghosts to be included in both gauges. *)
45(* v1.1: Fixed yukawa couplings in Feynman gauge. *)
46(* Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. *)
47(* Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. *)
48
49(* ************************** *)
50(* ***** vevs ***** *)
51(* ************************** *)
52M$vevs = { {Phi[2],vev} };
53
54(* ************************** *)
55(* ***** Gauge groups ***** *)
56(* ************************** *)
57M$GaugeGroups = {
58 U1Y == {
59 Abelian -> True,
60 CouplingConstant -> g1,
61 GaugeBoson -> B,
62 Charge -> Y
63 },
64 SU2L == {
65 Abelian -> False,
66 CouplingConstant -> gw,
67 GaugeBoson -> Wi,
68 StructureConstant -> Eps,
69 Representations -> {Ta,SU2D},
70 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
71 },
72 SU3C == {
73 Abelian -> False,
74 CouplingConstant -> gs,
75 GaugeBoson -> G,
76 StructureConstant -> f,
77 Representations -> {T,Colour},
78 SymmetricTensor -> dSUN
79 }
80};
81
82
83(* ************************** *)
84(* ***** Indices ***** *)
85(* ************************** *)
86
87IndexRange[Index[SU2W ]] = Unfold[Range[3]];
88IndexRange[Index[SU2D ]] = Unfold[Range[2]];
89IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
90IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
91IndexRange[Index[Generation]] = Range[3];
92
93IndexStyle[SU2W, j];
94IndexStyle[SU2D, k];
95IndexStyle[Gluon, a];
96IndexStyle[Colour, m];
97IndexStyle[Generation, f];
98
99
100(* ************************** *)
101(* *** Interaction orders *** *)
102(* *** (as used by mg5) *** *)
103(* ************************** *)
104
105M$InteractionOrderHierarchy = {
106 {QCD, 1},
107 {QED, 2},
108 {NP, 2}
109};
110
111
112(* ************************** *)
113(* **** Particle classes **** *)
114(* ************************** *)
115M$ClassesDescription = {
116
117(* **** NEW Particle **** *)
118
119 S[101] == {
120 ClassName -> pi0,
121 SelfConjugate-> True,
122 Mass->{mpi0, 200.},
123 Width -> {wpi0, 1.0},
124 PDG->10001,
125 ParticleName -> "pi0"
126 },
127
128 S[102] == {
129 ClassName -> pip,
130 SelfConjugate-> False,
131 Mass->{mpip, 200.},
132 Width -> {wpip, 1.0},
133 PDG->10002,
134 QuantumNumbers -> {Q -> 1},
135 ParticleName -> "pi+",
136 AntiParticleName -> "pi-"
137 },
138
139 V[101] == {
140 ClassName -> rho0,
141 SelfConjugate-> True,
142 Mass->{mrho, Internal},
143 Width -> {wrho0, 1.0},
144 PDG->20001,
145 ParticleName -> "rho0"
146 },
147
148 V[102] == {
149 ClassName -> rhop,
150 SelfConjugate-> False,
151 Mass->{mrho, Internal},
152 Width -> {wrhop, 1.0},
153 PDG->20002,
154 QuantumNumbers -> {Q -> 1},
155 ParticleName -> "rho+",
156 AntiParticleName -> "rho-"
157 },
158
159(* **** END NEW Particle **** *)
160
161(* Gauge bosons: physical vector fields *)
162 V[1] == {
163 ClassName -> A,
164 SelfConjugate -> True,
165 Mass -> 0,
166 Width -> 0,
167 ParticleName -> "a",
168 PDG -> 22,
169 PropagatorLabel -> "a",
170 PropagatorType -> W,
171 PropagatorArrow -> None,
172 FullName -> "Photon"
173 },
174 V[2] == {
175 ClassName -> Z,
176 SelfConjugate -> True,
177 Mass -> {MZ, 91.1876},
178 Width -> {WZ, 2.4952},
179 ParticleName -> "Z",
180 PDG -> 23,
181 PropagatorLabel -> "Z",
182 PropagatorType -> Sine,
183 PropagatorArrow -> None,
184 FullName -> "Z"
185 },
186 V[3] == {
187 ClassName -> W,
188 SelfConjugate -> False,
189 Mass -> {MW, Internal},
190 Width -> {WW, 2.085},
191 ParticleName -> "W+",
192 AntiParticleName -> "W-",
193 QuantumNumbers -> {Q -> 1},
194 PDG -> 24,
195 PropagatorLabel -> "W",
196 PropagatorType -> Sine,
197 PropagatorArrow -> Forward,
198 FullName -> "W"
199 },
200 V[4] == {
201 ClassName -> G,
202 SelfConjugate -> True,
203 Indices -> {Index[Gluon]},
204 Mass -> 0,
205 Width -> 0,
206 ParticleName -> "g",
207 PDG -> 21,
208 PropagatorLabel -> "G",
209 PropagatorType -> C,
210 PropagatorArrow -> None,
211 FullName -> "G"
212 },
213
214(* Ghosts: related to physical gauge bosons *)
215 U[1] == {
216 ClassName -> ghA,
217 SelfConjugate -> False,
218 Ghost -> A,
219 QuantumNumbers -> {GhostNumber -> 1},
220 Mass -> 0,
221 Width -> 0,
222 PropagatorLabel -> "uA",
223 PropagatorType -> GhostDash,
224 PropagatorArrow -> Forward
225 },
226 U[2] == {
227 ClassName -> ghZ,
228 SelfConjugate -> False,
229 Ghost -> Z,
230 QuantumNumbers -> {GhostNumber -> 1},
231 Mass -> {MZ,91.1876},
232 Width -> {WZ, 2.4952},
233 PropagatorLabel -> "uZ",
234 PropagatorType -> GhostDash,
235 PropagatorArrow -> Forward
236 },
237 U[31] == {
238 ClassName -> ghWp,
239 SelfConjugate -> False,
240 Ghost -> W,
241 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
242 Mass -> {MW,Internal},
243 Width -> {WW, 2.085},
244 PropagatorLabel -> "uWp",
245 PropagatorType -> GhostDash,
246 PropagatorArrow -> Forward
247 },
248 U[32] == {
249 ClassName -> ghWm,
250 SelfConjugate -> False,
251 Ghost -> Wbar,
252 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
253 Mass -> {MW,Internal},
254 Width -> {WW, 2.085},
255 PropagatorLabel -> "uWm",
256 PropagatorType -> GhostDash,
257 PropagatorArrow -> Forward
258 },
259 U[4] == {
260 ClassName -> ghG,
261 SelfConjugate -> False,
262 Indices -> {Index[Gluon]},
263 Ghost -> G,
264 PDG -> 82,
265 QuantumNumbers ->{GhostNumber -> 1},
266 Mass -> 0,
267 Width -> 0,
268 PropagatorLabel -> "uG",
269 PropagatorType -> GhostDash,
270 PropagatorArrow -> Forward
271 },
272
273(* Gauge bosons: unphysical vector fields *)
274 V[11] == {
275 ClassName -> B,
276 Unphysical -> True,
277 SelfConjugate -> True,
278 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
279 },
280 V[12] == {
281 ClassName -> Wi,
282 Unphysical -> True,
283 SelfConjugate -> True,
284 Indices -> {Index[SU2W]},
285 FlavorIndex -> SU2W,
286 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]}
287 },
288
289(* Ghosts: related to unphysical gauge bosons *)
290 U[11] == {
291 ClassName -> ghB,
292 Unphysical -> True,
293 SelfConjugate -> False,
294 Ghost -> B,
295 Definitions -> { ghB -> -sw ghZ + cw ghA}
296 },
297 U[12] == {
298 ClassName -> ghWi,
299 Unphysical -> True,
300 SelfConjugate -> False,
301 Ghost -> Wi,
302 Indices -> {Index[SU2W]},
303 FlavorIndex -> SU2W,
304 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
305 } ,
306
307(* Fermions: physical fields *)
308 F[1] == {
309 ClassName -> vl,
310 ClassMembers -> {ve,vm,vt},
311 Indices -> {Index[Generation]},
312 FlavorIndex -> Generation,
313 SelfConjugate -> False,
314 Mass -> 0,
315 Width -> 0,
316 QuantumNumbers -> {LeptonNumber -> 1},
317 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
318 PropagatorType -> S,
319 PropagatorArrow -> Forward,
320 PDG -> {12,14,16},
321 ParticleName -> {"ve","vm","vt"},
322 AntiParticleName -> {"ve~","vm~","vt~"},
323 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
324 },
325 F[2] == {
326 ClassName -> l,
327 ClassMembers -> {e, mu, ta},
328 Indices -> {Index[Generation]},
329 FlavorIndex -> Generation,
330 SelfConjugate -> False,
331 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
332 Width -> 0,
333 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
334 PropagatorLabel -> {"l", "e", "mu", "ta"},
335 PropagatorType -> Straight,
336 PropagatorArrow -> Forward,
337 PDG -> {11, 13, 15},
338 ParticleName -> {"e-", "mu-", "ta-"},
339 AntiParticleName -> {"e+", "mu+", "ta+"},
340 FullName -> {"Electron", "Muon", "Tau"}
341 },
342 F[3] == {
343 ClassName -> uq,
344 ClassMembers -> {u, c, t},
345 Indices -> {Index[Generation], Index[Colour]},
346 FlavorIndex -> Generation,
347 SelfConjugate -> False,
348 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
349 Width -> {0, 0, {WT,1.50833649}},
350 QuantumNumbers -> {Q -> 2/3},
351 PropagatorLabel -> {"uq", "u", "c", "t"},
352 PropagatorType -> Straight,
353 PropagatorArrow -> Forward,
354 PDG -> {2, 4, 6},
355 ParticleName -> {"u", "c", "t" },
356 AntiParticleName -> {"u~", "c~", "t~"},
357 FullName -> {"u-quark", "c-quark", "t-quark"}
358 },
359 F[4] == {
360 ClassName -> dq,
361 ClassMembers -> {d, s, b},
362 Indices -> {Index[Generation], Index[Colour]},
363 FlavorIndex -> Generation,
364 SelfConjugate -> False,
365 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
366 Width -> 0,
367 QuantumNumbers -> {Q -> -1/3},
368 PropagatorLabel -> {"dq", "d", "s", "b"},
369 PropagatorType -> Straight,
370 PropagatorArrow -> Forward,
371 PDG -> {1,3,5},
372 ParticleName -> {"d", "s", "b" },
373 AntiParticleName -> {"d~", "s~", "b~"},
374 FullName -> {"d-quark", "s-quark", "b-quark"}
375 },
376
377(* Fermions: unphysical fields *)
378 F[11] == {
379 ClassName -> LL,
380 Unphysical -> True,
381 Indices -> {Index[SU2D], Index[Generation]},
382 FlavorIndex -> SU2D,
383 SelfConjugate -> False,
384 QuantumNumbers -> {Y -> -1/2},
385 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]] }
386 },
387 F[12] == {
388 ClassName -> lR,
389 Unphysical -> True,
390 Indices -> {Index[Generation]},
391 FlavorIndex -> Generation,
392 SelfConjugate -> False,
393 QuantumNumbers -> {Y -> -1},
394 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
395 },
396 F[13] == {
397 ClassName -> QL,
398 Unphysical -> True,
399 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
400 FlavorIndex -> SU2D,
401 SelfConjugate -> False,
402 QuantumNumbers -> {Y -> 1/6},
403 Definitions -> {
404 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
405 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
406 },
407 F[14] == {
408 ClassName -> uR,
409 Unphysical -> True,
410 Indices -> {Index[Generation], Index[Colour]},
411 FlavorIndex -> Generation,
412 SelfConjugate -> False,
413 QuantumNumbers -> {Y -> 2/3},
414 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
415 },
416 F[15] == {
417 ClassName -> dR,
418 Unphysical -> True,
419 Indices -> {Index[Generation], Index[Colour]},
420 FlavorIndex -> Generation,
421 SelfConjugate -> False,
422 QuantumNumbers -> {Y -> -1/3},
423 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
424 },
425
426(* Higgs: physical scalars *)
427 S[1] == {
428 ClassName -> H,
429 SelfConjugate -> True,
430 Mass -> {MH,125},
431 Width -> {WH,0.00407},
432 PropagatorLabel -> "H",
433 PropagatorType -> D,
434 PropagatorArrow -> None,
435 PDG -> 25,
436 ParticleName -> "H",
437 FullName -> "H"
438 },
439
440(* Higgs: physical scalars *)
441 S[2] == {
442 ClassName -> G0,
443 SelfConjugate -> True,
444 Goldstone -> Z,
445 Mass -> {MZ, 91.1876},
446 Width -> {WZ, 2.4952},
447 PropagatorLabel -> "Go",
448 PropagatorType -> D,
449 PropagatorArrow -> None,
450 PDG -> 250,
451 ParticleName -> "G0",
452 FullName -> "G0"
453 },
454 S[3] == {
455 ClassName -> GP,
456 SelfConjugate -> False,
457 Goldstone -> W,
458 Mass -> {MW, Internal},
459 QuantumNumbers -> {Q -> 1},
460 Width -> {WW, 2.085},
461 PropagatorLabel -> "GP",
462 PropagatorType -> D,
463 PropagatorArrow -> None,
464 PDG -> 251,
465 ParticleName -> "G+",
466 AntiParticleName -> "G-",
467 FullName -> "GP"
468 },
469
470(* Higgs: unphysical scalars *)
471 S[11] == {
472 ClassName -> Phi,
473 Unphysical -> True,
474 Indices -> {Index[SU2D]},
475 FlavorIndex -> SU2D,
476 SelfConjugate -> False,
477 QuantumNumbers -> {Y -> 1/2},
478 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
479 }
480};
481
482
483(* ************************** *)
484(* ***** Gauge ***** *)
485(* ***** Parameters ***** *)
486(* ***** (FeynArts) ***** *)
487(* ************************** *)
488
489GaugeXi[ V[1] ] = GaugeXi[A];
490GaugeXi[ V[2] ] = GaugeXi[Z];
491GaugeXi[ V[3] ] = GaugeXi[W];
492GaugeXi[ V[4] ] = GaugeXi[G];
493GaugeXi[ S[1] ] = 1;
494GaugeXi[ S[2] ] = GaugeXi[Z];
495GaugeXi[ S[3] ] = GaugeXi[W];
496GaugeXi[ U[1] ] = GaugeXi[A];
497GaugeXi[ U[2] ] = GaugeXi[Z];
498GaugeXi[ U[31] ] = GaugeXi[W];
499GaugeXi[ U[32] ] = GaugeXi[W];
500GaugeXi[ U[4] ] = GaugeXi[G];
501
502
503(* ************************** *)
504(* ***** Parameters ***** *)
505(* ************************** *)
506M$Parameters = {
507
508(* ***** NEW Parameters ***** *)
509
510 grho == {
511 ParameterType -> External,
512 BlockName -> VLCPARAM,
513 OrderBlock -> 1,
514 Value -> 7.0,
515 Description -> "Coupling of the strong sector",
516 InteractionOrder -> {NP,1}
517 },
518
519 mrho == {
520 ParameterType -> External,
521 BlockName -> VLCPARAM,
522 OrderBlock -> 2,
523 Value -> 2000.0,
524 TeX -> Subscript[m,rho],
525 Description -> "Mass of the spin-1 triplet"
526 },
527
528 gV == {
529 ParameterType -> Internal,
530 Value -> gw^2/grho,
531 Description -> "Couplings of heavy vector to SM " ,
532 InteractionOrder -> {NP,1}
533 },
534(* ***** END NEW Parameters ***** *)
535
536 (* External parameters *)
537 aEWM1 == {
538 ParameterType -> External,
539 BlockName -> SMINPUTS,
540 OrderBlock -> 1,
541 Value -> 127.9,
542 InteractionOrder -> {QED,-2},
543 Description -> "Inverse of the EW coupling constant at the Z pole"
544 },
545 Gf == {
546 ParameterType -> External,
547 BlockName -> SMINPUTS,
548 OrderBlock -> 2,
549 Value -> 1.16637*^-5,
550 InteractionOrder -> {QED,2},
551 TeX -> Subscript[G,f],
552 Description -> "Fermi constant"
553 },
554 aS == {
555 ParameterType -> External,
556 BlockName -> SMINPUTS,
557 OrderBlock -> 3,
558 Value -> 0.1184,
559 InteractionOrder -> {QCD,2},
560 TeX -> Subscript[\[Alpha],s],
561 Description -> "Strong coupling constant at the Z pole"
562 },
563 ymdo == {
564 ParameterType -> External,
565 BlockName -> YUKAWA,
566 OrderBlock -> 1,
567 Value -> 5.04*^-3,
568 Description -> "Down Yukawa mass"
569 },
570 ymup == {
571 ParameterType -> External,
572 BlockName -> YUKAWA,
573 OrderBlock -> 2,
574 Value -> 2.55*^-3,
575 Description -> "Up Yukawa mass"
576 },
577 yms == {
578 ParameterType -> External,
579 BlockName -> YUKAWA,
580 OrderBlock -> 3,
581 Value -> 0.101,
582 Description -> "Strange Yukawa mass"
583 },
584 ymc == {
585 ParameterType -> External,
586 BlockName -> YUKAWA,
587 OrderBlock -> 4,
588 Value -> 1.27,
589 Description -> "Charm Yukawa mass"
590 },
591 ymb == {
592 ParameterType -> External,
593 BlockName -> YUKAWA,
594 OrderBlock -> 5,
595 Value -> 4.7,
596 Description -> "Bottom Yukawa mass"
597 },
598 ymt == {
599 ParameterType -> External,
600 BlockName -> YUKAWA,
601 OrderBlock -> 6,
602 Value -> 172,
603 Description -> "Top Yukawa mass"
604 },
605 yme == {
606 ParameterType -> External,
607 BlockName -> YUKAWA,
608 OrderBlock -> 11,
609 Value -> 5.11*^-4,
610 Description -> "Electron Yukawa mass"
611 },
612 ymm == {
613 ParameterType -> External,
614 BlockName -> YUKAWA,
615 OrderBlock -> 13,
616 Value -> 0.10566,
617 Description -> "Muon Yukawa mass"
618 },
619 ymtau == {
620 ParameterType -> External,
621 BlockName -> YUKAWA,
622 OrderBlock -> 15,
623 Value -> 1.777,
624 Description -> "Tau Yukawa mass"
625 },
626 cabi == {
627 ParameterType -> External,
628 BlockName -> CKMBLOCK,
629 OrderBlock -> 1,
630 Value -> 0.227736,
631 TeX -> Subscript[\[Theta], c],
632 Description -> "Cabibbo angle"
633 },
634
635 (* Internal Parameters *)
636 aEW == {
637 ParameterType -> Internal,
638 Value -> 1/aEWM1,
639 InteractionOrder -> {QED,2},
640 TeX -> Subscript[\[Alpha], EW],
641 Description -> "Electroweak coupling contant"
642 },
643 MW == {
644 ParameterType -> Internal,
645 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
646 TeX -> Subscript[M,W],
647 Description -> "W mass"
648 },
649 sw2 == {
650 ParameterType -> Internal,
651 Value -> 1-(MW/MZ)^2,
652 Description -> "Squared Sin of the Weinberg angle"
653 },
654 ee == {
655 ParameterType -> Internal,
656 Value -> Sqrt[4 Pi aEW],
657 InteractionOrder -> {QED,1},
658 TeX -> e,
659 Description -> "Electric coupling constant"
660 },
661 cw == {
662 ParameterType -> Internal,
663 Value -> Sqrt[1-sw2],
664 TeX -> Subscript[c,w],
665 Description -> "Cosine of the Weinberg angle"
666 },
667 sw == {
668 ParameterType -> Internal,
669 Value -> Sqrt[sw2],
670 TeX -> Subscript[s,w],
671 Description -> "Sine of the Weinberg angle"
672 },
673 gw == {
674 ParameterType -> Internal,
675 Definitions -> {gw->ee/sw},
676 InteractionOrder -> {QED,1},
677 TeX -> Subscript[g,w],
678 Description -> "Weak coupling constant at the Z pole"
679 },
680 g1 == {
681 ParameterType -> Internal,
682 Definitions -> {g1->ee/cw},
683 InteractionOrder -> {QED,1},
684 TeX -> Subscript[g,1],
685 Description -> "U(1)Y coupling constant at the Z pole"
686 },
687 gs == {
688 ParameterType -> Internal,
689 Value -> Sqrt[4 Pi aS],
690 InteractionOrder -> {QCD,1},
691 TeX -> Subscript[g,s],
692 ParameterName -> G,
693 Description -> "Strong coupling constant at the Z pole"
694 },
695 vev == {
696 ParameterType -> Internal,
697 Value -> 2*MW*sw/ee,
698 InteractionOrder -> {QED,-1},
699 Description -> "Higgs vacuum expectation value"
700 },
701 lam == {
702 ParameterType -> Internal,
703 Value -> MH^2/(2*vev^2),
704 InteractionOrder -> {QED, 2},
705 Description -> "Higgs quartic coupling"
706 },
707 muH == {
708 ParameterType -> Internal,
709 Value -> Sqrt[vev^2 lam],
710 TeX -> \[Mu],
711 Description -> "Coefficient of the quadratic piece of the Higgs potential"
712 },
713 yl == {
714 ParameterType -> Internal,
715 Indices -> {Index[Generation], Index[Generation]},
716 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
717 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
718 InteractionOrder -> {QED, 1},
719 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
720 TeX -> Superscript[y, l],
721 Description -> "Lepton Yukawa couplings"
722 },
723 yu == {
724 ParameterType -> Internal,
725 Indices -> {Index[Generation], Index[Generation]},
726 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
727 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
728 InteractionOrder -> {QED, 1},
729 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
730 TeX -> Superscript[y, u],
731 Description -> "Up-type Yukawa couplings"
732 },
733 yd == {
734 ParameterType -> Internal,
735 Indices -> {Index[Generation], Index[Generation]},
736 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
737 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
738 InteractionOrder -> {QED, 1},
739 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
740 TeX -> Superscript[y, d],
741 Description -> "Down-type Yukawa couplings"
742 },
743(* N. B. : only Cabibbo mixing! *)
744 CKM == {
745 ParameterType -> Internal,
746 Indices -> {Index[Generation], Index[Generation]},
747 Unitary -> True,
748 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
749 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
750 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
751 TeX -> Superscript[V,CKM],
752 Description -> "CKM-Matrix"}
753};
754
755(* ************************** *)
756(* ***** Lagrangian ***** *)
757(* ************************** *)
758
759LGauge := Block[{mu,nu,ii,aa},
760 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]];
761
762LFermions := Block[{mu},
763 ExpandIndices[I*(
764 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]),
765 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
766
767LHiggs := Block[{ii,mu, feynmangaugerules},
768 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
769
770 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
771 ];
772
773LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
774 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
775
776 yuk = ExpandIndices[
777 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
778 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
779 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
780 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
781 yuk+HC[yuk]/.feynmangaugerules
782 ];
783
784LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
785 (* Pure gauge piece *)
786 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
787 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
788 LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
789
790 (* Scalar pieces: see Peskin pages 739-742 *)
791 (* phi1 and phi2 are the real degrees of freedom of GP *)
792 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
793 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
794 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
795 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
796 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
797 doublet0 = {0, vev/Sqrt[2]};
798 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}];
799 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
800 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
801
802ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
803
804
805(* **** NEW LAG **** *)
806
807LKinTriplet := (I del[pipbar, mu] gw pi0 Wi[mu, 1])/(2 Sqrt[2]) - (I del[pip, mu] gw pi0 Wi[mu, 1])/(2 Sqrt[2]) - (I del[pi0, mu] gw pipbar Wi[mu, 1])/(2 Sqrt[2]) + (I del[pi0, mu] gw pip Wi[mu, 1])/(2 Sqrt[2]) + (del[pipbar, mu] gw pi0 Wi[mu, 2])/(2 Sqrt[2]) + (del[pip, mu] gw pi0 Wi[mu, 2])/(2 Sqrt[2]) - (del[pi0, mu] gw pipbar Wi[mu, 2])/(2 Sqrt[2]) - (del[pi0,mu] gw pip Wi[mu, 2])/(2 Sqrt[2]) + 1/2 I del[pip, mu] gw pipbar Wi[mu, 3] - 1/2 I del[pipbar, mu] gw pip Wi[mu, 3];
808
809LAnomalyTriplet := ExpandIndices[grho/(32 mrho \[Pi]^2) 3 g1 gw Eps[mu, nu, rho, sig] FS[B, rho, sig] (((pip + pipbar) FS[Wi, mu, nu, 1])/Sqrt[2] + (I (pip - pipbar) FS[Wi, mu, nu, 2])/Sqrt[2] + pi0 FS[Wi, mu, nu, 3])];
810
811LRhoff := 1/Sqrt[2] gV (rhop[mu] (vlbar.Ga[mu].ProjM.l + ubar.Ga[mu].ProjM.d + cbar.Ga[mu].ProjM.s + tbar.Ga[mu].ProjM.b) + rhopbar[mu] (lbar.Ga[mu].ProjM.vl + dbar.Ga[mu].ProjM.u + sbar.Ga[mu].ProjM.c + bbar.Ga[mu].ProjM.t )) + 1/2 gV rho0[mu] (vlbar.Ga[mu].ProjM.vl + ubar.Ga[mu].ProjM.u + cbar.Ga[mu].ProjM.c + tbar.Ga[mu].ProjM.t - lbar.Ga[mu].ProjM.l -dbar.Ga[mu].ProjM.d - sbar.Ga[mu].ProjM.s - bbar.Ga[mu].ProjM.b);
812
813LRhoTriplet := grho 1/2 I del[pip, mu] pipbar rho0[mu] - grho 1/2 I del[pipbar, mu] pip rho0[mu] - grho 1/2 I del[pip, mu] pi0 rhopbar[mu] + grho 1/2 I del[pi0, mu] pip rhopbar[mu] + grho 1/2 I del[pipbar, mu] pi0 rhop[mu] - grho 1/2 I del[pi0, mu] pipbar rhop[mu];
814
815(* **** END NEW LAG **** *)
816
817LVLC:= LGauge + LFermions + LHiggs + LYukawa + LGhost + LKinTriplet + LAnomalyTriplet +LRhoff + LRhoTriplet;