NLOModels: GGG.fr

File GGG.fr, 24.1 KB (added by bald, 6 years ago)

Feynrules model for the triple gluon field strength operator

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Gluon self-interaction effective operator ******)
3(****** ******)
4(****** Authors: V. Hirschi ******)
5(****** ******)
6(***************************************************************************************************************)
7
8(* ************************** *)
9(* ***** Information ***** *)
10(* ************************** *)
11M$ModelName = "Gluons effective operator";
12
13M$Information = {
14 Authors -> {"V.Hirschi"},
15 Institutions -> {"SLAC"},
16 Emails -> {"valentin.hirschi@gmai.com"}
17};
18
19FeynmanGauge = True;
20
21(* ************************** *)
22(* ***** NLO Variables ****** *)
23(******************************)
24
25FR$LoopSwitches = {{Gf, MW}};
26FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
27 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
28
29(* ************************** *)
30(* ***** vevs ***** *)
31(* ************************** *)
32M$vevs = { {Phi[2],vev} };
33
34(* ************************** *)
35(* ***** Gauge groups ***** *)
36(* ************************** *)
37M$GaugeGroups = {
38 U1Y == {
39 Abelian -> True,
40 CouplingConstant -> g1,
41 GaugeBoson -> B,
42 Charge -> Y
43 },
44 SU2L == {
45 Abelian -> False,
46 CouplingConstant -> gw,
47 GaugeBoson -> Wi,
48 StructureConstant -> Eps,
49 Representations -> {Ta,SU2D},
50 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
51 },
52 SU3C == {
53 Abelian -> False,
54 CouplingConstant -> gs,
55 GaugeBoson -> G,
56 StructureConstant -> f,
57 Representations -> {T,Colour},
58 SymmetricTensor -> dSUN
59 }
60};
61
62
63(* ************************** *)
64(* ***** Indices ***** *)
65(* ************************** *)
66
67IndexRange[Index[SU2W ]] = Unfold[Range[3]];
68IndexRange[Index[SU2D ]] = Unfold[Range[2]];
69IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
70IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
71IndexRange[Index[Generation]] = Range[3];
72
73IndexStyle[SU2W, j];
74IndexStyle[SU2D, k];
75IndexStyle[Gluon, a];
76IndexStyle[Colour, m];
77IndexStyle[Generation, f];
78
79
80(* ************************** *)
81(* *** Interaction orders *** *)
82(* *** (as used by mg5) *** *)
83(* ************************** *)
84
85M$InteractionOrderHierarchy = {
86 {QCD, 1},
87 {QED, 2},
88 {GGG, 1},
89 {DGDG, 1}
90};
91
92
93(* ************************** *)
94(* **** Particle classes **** *)
95(* ************************** *)
96M$ClassesDescription = {
97
98(* Gauge bosons: physical vector fields *)
99 V[1] == {
100 ClassName -> A,
101 SelfConjugate -> True,
102 Mass -> 0,
103 Width -> 0,
104 ParticleName -> "a",
105 PDG -> 22,
106 PropagatorLabel -> "a",
107 PropagatorType -> W,
108 PropagatorArrow -> None,
109 FullName -> "Photon"
110 },
111 V[2] == {
112 ClassName -> Z,
113 SelfConjugate -> True,
114 Mass -> {MZ, 91.1876},
115 Width -> {WZ, 2.4952},
116 ParticleName -> "Z",
117 PDG -> 23,
118 PropagatorLabel -> "Z",
119 PropagatorType -> Sine,
120 PropagatorArrow -> None,
121 FullName -> "Z"
122 },
123 V[3] == {
124 ClassName -> W,
125 SelfConjugate -> False,
126 Mass -> {MW, Internal},
127 Width -> {WW, 2.085},
128 ParticleName -> "W+",
129 AntiParticleName -> "W-",
130 QuantumNumbers -> {Q -> 1},
131 PDG -> 24,
132 PropagatorLabel -> "W",
133 PropagatorType -> Sine,
134 PropagatorArrow -> Forward,
135 FullName -> "W"
136 },
137 V[4] == {
138 ClassName -> G,
139 SelfConjugate -> True,
140 Indices -> {Index[Gluon]},
141 Mass -> 0,
142 Width -> 0,
143 ParticleName -> "g",
144 PDG -> 21,
145 PropagatorLabel -> "G",
146 PropagatorType -> C,
147 PropagatorArrow -> None,
148 FullName -> "G"
149 },
150
151(* Ghosts: related to physical gauge bosons *)
152 U[1] == {
153 ClassName -> ghA,
154 SelfConjugate -> False,
155 Ghost -> A,
156 QuantumNumbers -> {GhostNumber -> 1},
157 Mass -> 0,
158 Width -> 0,
159 PropagatorLabel -> "uA",
160 PropagatorType -> GhostDash,
161 PropagatorArrow -> Forward
162 },
163 U[2] == {
164 ClassName -> ghZ,
165 SelfConjugate -> False,
166 Ghost -> Z,
167 QuantumNumbers -> {GhostNumber -> 1},
168 Mass -> {MZ,91.1876},
169 Width -> {WZ, 2.4952},
170 PropagatorLabel -> "uZ",
171 PropagatorType -> GhostDash,
172 PropagatorArrow -> Forward
173 },
174 U[31] == {
175 ClassName -> ghWp,
176 SelfConjugate -> False,
177 Ghost -> W,
178 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
179 Mass -> {MW,Internal},
180 Width -> {WW, 2.085},
181 PropagatorLabel -> "uWp",
182 PropagatorType -> GhostDash,
183 PropagatorArrow -> Forward
184 },
185 U[32] == {
186 ClassName -> ghWm,
187 SelfConjugate -> False,
188 Ghost -> Wbar,
189 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
190 Mass -> {MW,Internal},
191 Width -> {WW, 2.085},
192 PropagatorLabel -> "uWm",
193 PropagatorType -> GhostDash,
194 PropagatorArrow -> Forward
195 },
196 U[4] == {
197 ClassName -> ghG,
198 SelfConjugate -> False,
199 Indices -> {Index[Gluon]},
200 Ghost -> G,
201 PDG -> 82,
202 QuantumNumbers ->{GhostNumber -> 1},
203 Mass -> 0,
204 Width -> 0,
205 PropagatorLabel -> "uG",
206 PropagatorType -> GhostDash,
207 PropagatorArrow -> Forward
208 },
209
210(* Gauge bosons: unphysical vector fields *)
211 V[11] == {
212 ClassName -> B,
213 Unphysical -> True,
214 SelfConjugate -> True,
215 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
216 },
217 V[12] == {
218 ClassName -> Wi,
219 Unphysical -> True,
220 SelfConjugate -> True,
221 Indices -> {Index[SU2W]},
222 FlavorIndex -> SU2W,
223 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]}
224 },
225
226(* Ghosts: related to unphysical gauge bosons *)
227 U[11] == {
228 ClassName -> ghB,
229 Unphysical -> True,
230 SelfConjugate -> False,
231 Ghost -> B,
232 Definitions -> { ghB -> -sw ghZ + cw ghA}
233 },
234 U[12] == {
235 ClassName -> ghWi,
236 Unphysical -> True,
237 SelfConjugate -> False,
238 Ghost -> Wi,
239 Indices -> {Index[SU2W]},
240 FlavorIndex -> SU2W,
241 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
242 } ,
243
244(* Fermions: physical fields *)
245 F[1] == {
246 ClassName -> vl,
247 ClassMembers -> {ve,vm,vt},
248 Indices -> {Index[Generation]},
249 FlavorIndex -> Generation,
250 SelfConjugate -> False,
251 Mass -> 0,
252 Width -> 0,
253 QuantumNumbers -> {LeptonNumber -> 1},
254 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
255 PropagatorType -> S,
256 PropagatorArrow -> Forward,
257 PDG -> {12,14,16},
258 ParticleName -> {"ve","vm","vt"},
259 AntiParticleName -> {"ve~","vm~","vt~"},
260 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
261 },
262 F[2] == {
263 ClassName -> l,
264 ClassMembers -> {e, mu, ta},
265 Indices -> {Index[Generation]},
266 FlavorIndex -> Generation,
267 SelfConjugate -> False,
268 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
269 Width -> 0,
270 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
271 PropagatorLabel -> {"l", "e", "mu", "ta"},
272 PropagatorType -> Straight,
273 PropagatorArrow -> Forward,
274 PDG -> {11, 13, 15},
275 ParticleName -> {"e-", "mu-", "ta-"},
276 AntiParticleName -> {"e+", "mu+", "ta+"},
277 FullName -> {"Electron", "Muon", "Tau"}
278 },
279 F[3] == {
280 ClassName -> uq,
281 ClassMembers -> {u, c, t},
282 Indices -> {Index[Generation], Index[Colour]},
283 FlavorIndex -> Generation,
284 SelfConjugate -> False,
285 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
286 Width -> {0, 0, {WT,1.50833649}},
287 QuantumNumbers -> {Q -> 2/3},
288 PropagatorLabel -> {"uq", "u", "c", "t"},
289 PropagatorType -> Straight,
290 PropagatorArrow -> Forward,
291 PDG -> {2, 4, 6},
292 ParticleName -> {"u", "c", "t" },
293 AntiParticleName -> {"u~", "c~", "t~"},
294 FullName -> {"u-quark", "c-quark", "t-quark"}
295 },
296 F[4] == {
297 ClassName -> dq,
298 ClassMembers -> {d, s, b},
299 Indices -> {Index[Generation], Index[Colour]},
300 FlavorIndex -> Generation,
301 SelfConjugate -> False,
302 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
303 Width -> 0,
304 QuantumNumbers -> {Q -> -1/3},
305 PropagatorLabel -> {"dq", "d", "s", "b"},
306 PropagatorType -> Straight,
307 PropagatorArrow -> Forward,
308 PDG -> {1,3,5},
309 ParticleName -> {"d", "s", "b" },
310 AntiParticleName -> {"d~", "s~", "b~"},
311 FullName -> {"d-quark", "s-quark", "b-quark"}
312 },
313
314(* Fermions: unphysical fields *)
315 F[11] == {
316 ClassName -> LL,
317 Unphysical -> True,
318 Indices -> {Index[SU2D], Index[Generation]},
319 FlavorIndex -> SU2D,
320 SelfConjugate -> False,
321 QuantumNumbers -> {Y -> -1/2},
322 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]] }
323 },
324 F[12] == {
325 ClassName -> lR,
326 Unphysical -> True,
327 Indices -> {Index[Generation]},
328 FlavorIndex -> Generation,
329 SelfConjugate -> False,
330 QuantumNumbers -> {Y -> -1},
331 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
332 },
333 F[13] == {
334 ClassName -> QL,
335 Unphysical -> True,
336 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
337 FlavorIndex -> SU2D,
338 SelfConjugate -> False,
339 QuantumNumbers -> {Y -> 1/6},
340 Definitions -> {
341 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
342 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
343 },
344 F[14] == {
345 ClassName -> uR,
346 Unphysical -> True,
347 Indices -> {Index[Generation], Index[Colour]},
348 FlavorIndex -> Generation,
349 SelfConjugate -> False,
350 QuantumNumbers -> {Y -> 2/3},
351 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
352 },
353 F[15] == {
354 ClassName -> dR,
355 Unphysical -> True,
356 Indices -> {Index[Generation], Index[Colour]},
357 FlavorIndex -> Generation,
358 SelfConjugate -> False,
359 QuantumNumbers -> {Y -> -1/3},
360 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
361 },
362
363(* Higgs: physical scalars *)
364 S[1] == {
365 ClassName -> H,
366 SelfConjugate -> True,
367 Mass -> {MH,125},
368 Width -> {WH,0.00407},
369 PropagatorLabel -> "H",
370 PropagatorType -> D,
371 PropagatorArrow -> None,
372 PDG -> 25,
373 ParticleName -> "H",
374 FullName -> "H"
375 },
376
377(* Higgs: physical scalars *)
378 S[2] == {
379 ClassName -> G0,
380 SelfConjugate -> True,
381 Goldstone -> Z,
382 Mass -> {MZ, 91.1876},
383 Width -> {WZ, 2.4952},
384 PropagatorLabel -> "Go",
385 PropagatorType -> D,
386 PropagatorArrow -> None,
387 PDG -> 250,
388 ParticleName -> "G0",
389 FullName -> "G0"
390 },
391 S[3] == {
392 ClassName -> GP,
393 SelfConjugate -> False,
394 Goldstone -> W,
395 Mass -> {MW, Internal},
396 QuantumNumbers -> {Q -> 1},
397 Width -> {WW, 2.085},
398 PropagatorLabel -> "GP",
399 PropagatorType -> D,
400 PropagatorArrow -> None,
401 PDG -> 251,
402 ParticleName -> "G+",
403 AntiParticleName -> "G-",
404 FullName -> "GP"
405 },
406
407(* Higgs: unphysical scalars *)
408 S[11] == {
409 ClassName -> Phi,
410 Unphysical -> True,
411 Indices -> {Index[SU2D]},
412 FlavorIndex -> SU2D,
413 SelfConjugate -> False,
414 QuantumNumbers -> {Y -> 1/2},
415 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
416 }
417};
418
419
420(* ************************** *)
421(* ***** Gauge ***** *)
422(* ***** Parameters ***** *)
423(* ***** (FeynArts) ***** *)
424(* ************************** *)
425
426GaugeXi[ V[1] ] = GaugeXi[A];
427GaugeXi[ V[2] ] = GaugeXi[Z];
428GaugeXi[ V[3] ] = GaugeXi[W];
429GaugeXi[ V[4] ] = GaugeXi[G];
430GaugeXi[ S[1] ] = 1;
431GaugeXi[ S[2] ] = GaugeXi[Z];
432GaugeXi[ S[3] ] = GaugeXi[W];
433GaugeXi[ U[1] ] = GaugeXi[A];
434GaugeXi[ U[2] ] = GaugeXi[Z];
435GaugeXi[ U[31] ] = GaugeXi[W];
436GaugeXi[ U[32] ] = GaugeXi[W];
437GaugeXi[ U[4] ] = GaugeXi[G];
438
439
440(* ************************** *)
441(* ***** Parameters ***** *)
442(* ************************** *)
443M$Parameters = {
444
445 (* External parameters *)
446 Kggg == {
447 ParameterType -> External,
448 BlockName -> BSMINPUTS,
449 OrderBlock -> 2,
450 Value -> 0.6,
451 InteractionOrder -> {GGG,1},
452 TeX -> Subscript[K,ggg],
453 Description -> "Coefficient of the GGG dim6 effective vertex"
454 },
455 Kdgdg == {
456 ParameterType -> External,
457 BlockName -> BSMINPUTS,
458 OrderBlock -> 3,
459 Value -> 0.6,
460 InteractionOrder -> {DGDG,1},
461 TeX -> Subscript[K,dgdg],
462 Description -> "Coefficient of the DGDG dim6 effective vertex"
463 },
464 Lambda == {
465 ParameterType -> External,
466 BlockName -> BSMINPUTS,
467 OrderBlock -> 1,
468 Value -> 1000.0,
469 Description -> "Defining scale of the effective theory"
470 },
471 aEWM1 == {
472 ParameterType -> External,
473 BlockName -> SMINPUTS,
474 OrderBlock -> 1,
475 Value -> 127.9,
476 InteractionOrder -> {QED,-2},
477 Description -> "Inverse of the EW coupling constant at the Z pole"
478 },
479 Gf == {
480 ParameterType -> External,
481 BlockName -> SMINPUTS,
482 OrderBlock -> 2,
483 Value -> 1.16637*^-5,
484 InteractionOrder -> {QED,2},
485 TeX -> Subscript[G,f],
486 Description -> "Fermi constant"
487 },
488 aS == {
489 ParameterType -> External,
490 BlockName -> SMINPUTS,
491 OrderBlock -> 3,
492 Value -> 0.1184,
493 InteractionOrder -> {QCD,2},
494 TeX -> Subscript[\[Alpha],s],
495 Description -> "Strong coupling constant at the Z pole"
496 },
497 ymdo == {
498 ParameterType -> External,
499 BlockName -> YUKAWA,
500 OrderBlock -> 1,
501 Value -> 5.04*^-3,
502 Description -> "Down Yukawa mass"
503 },
504 ymup == {
505 ParameterType -> External,
506 BlockName -> YUKAWA,
507 OrderBlock -> 2,
508 Value -> 2.55*^-3,
509 Description -> "Up Yukawa mass"
510 },
511 yms == {
512 ParameterType -> External,
513 BlockName -> YUKAWA,
514 OrderBlock -> 3,
515 Value -> 0.101,
516 Description -> "Strange Yukawa mass"
517 },
518 ymc == {
519 ParameterType -> External,
520 BlockName -> YUKAWA,
521 OrderBlock -> 4,
522 Value -> 1.27,
523 Description -> "Charm Yukawa mass"
524 },
525 ymb == {
526 ParameterType -> External,
527 BlockName -> YUKAWA,
528 OrderBlock -> 5,
529 Value -> 4.7,
530 Description -> "Bottom Yukawa mass"
531 },
532 ymt == {
533 ParameterType -> External,
534 BlockName -> YUKAWA,
535 OrderBlock -> 6,
536 Value -> 172,
537 Description -> "Top Yukawa mass"
538 },
539 yme == {
540 ParameterType -> External,
541 BlockName -> YUKAWA,
542 OrderBlock -> 11,
543 Value -> 5.11*^-4,
544 Description -> "Electron Yukawa mass"
545 },
546 ymm == {
547 ParameterType -> External,
548 BlockName -> YUKAWA,
549 OrderBlock -> 13,
550 Value -> 0.10566,
551 Description -> "Muon Yukawa mass"
552 },
553 ymtau == {
554 ParameterType -> External,
555 BlockName -> YUKAWA,
556 OrderBlock -> 15,
557 Value -> 1.777,
558 Description -> "Tau Yukawa mass"
559 },
560 cabi == {
561 ParameterType -> External,
562 BlockName -> CKMBLOCK,
563 OrderBlock -> 1,
564 Value -> 0.227736,
565 TeX -> Subscript[\[Theta], c],
566 Description -> "Cabibbo angle"
567 },
568
569 (* Internal Parameters *)
570 aEW == {
571 ParameterType -> Internal,
572 Value -> 1/aEWM1,
573 InteractionOrder -> {QED,2},
574 TeX -> Subscript[\[Alpha], EW],
575 Description -> "Electroweak coupling contant"
576 },
577 MW == {
578 ParameterType -> Internal,
579 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
580 TeX -> Subscript[M,W],
581 Description -> "W mass"
582 },
583 sw2 == {
584 ParameterType -> Internal,
585 Value -> 1-(MW/MZ)^2,
586 Description -> "Squared Sin of the Weinberg angle"
587 },
588 ee == {
589 ParameterType -> Internal,
590 Value -> Sqrt[4 Pi aEW],
591 InteractionOrder -> {QED,1},
592 TeX -> e,
593 Description -> "Electric coupling constant"
594 },
595 cw == {
596 ParameterType -> Internal,
597 Value -> Sqrt[1-sw2],
598 TeX -> Subscript[c,w],
599 Description -> "Cosine of the Weinberg angle"
600 },
601 sw == {
602 ParameterType -> Internal,
603 Value -> Sqrt[sw2],
604 TeX -> Subscript[s,w],
605 Description -> "Sine of the Weinberg angle"
606 },
607 gw == {
608 ParameterType -> Internal,
609 Definitions -> {gw->ee/sw},
610 InteractionOrder -> {QED,1},
611 TeX -> Subscript[g,w],
612 Description -> "Weak coupling constant at the Z pole"
613 },
614 g1 == {
615 ParameterType -> Internal,
616 Definitions -> {g1->ee/cw},
617 InteractionOrder -> {QED,1},
618 TeX -> Subscript[g,1],
619 Description -> "U(1)Y coupling constant at the Z pole"
620 },
621 gs == {
622 ParameterType -> Internal,
623 Value -> Sqrt[4 Pi aS],
624 InteractionOrder -> {QCD,1},
625 TeX -> Subscript[g,s],
626 ParameterName -> G,
627 Description -> "Strong coupling constant at the Z pole"
628 },
629 vev == {
630 ParameterType -> Internal,
631 Value -> 2*MW*sw/ee,
632 InteractionOrder -> {QED,-1},
633 Description -> "Higgs vacuum expectation value"
634 },
635 lam == {
636 ParameterType -> Internal,
637 Value -> MH^2/(2*vev^2),
638 InteractionOrder -> {QED, 2},
639 Description -> "Higgs quartic coupling"
640 },
641 muH == {
642 ParameterType -> Internal,
643 Value -> Sqrt[vev^2 lam],
644 TeX -> \[Mu],
645 Description -> "Coefficient of the quadratic piece of the Higgs potential"
646 },
647 yl == {
648 ParameterType -> Internal,
649 Indices -> {Index[Generation], Index[Generation]},
650 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
651 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
652 InteractionOrder -> {QED, 1},
653 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
654 TeX -> Superscript[y, l],
655 Description -> "Lepton Yukawa couplings"
656 },
657 yu == {
658 ParameterType -> Internal,
659 Indices -> {Index[Generation], Index[Generation]},
660 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
661 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
662 InteractionOrder -> {QED, 1},
663 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
664 TeX -> Superscript[y, u],
665 Description -> "Up-type Yukawa couplings"
666 },
667 yd == {
668 ParameterType -> Internal,
669 Indices -> {Index[Generation], Index[Generation]},
670 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
671 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
672 InteractionOrder -> {QED, 1},
673 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
674 TeX -> Superscript[y, d],
675 Description -> "Down-type Yukawa couplings"
676 },
677(* N. B. : only Cabibbo mixing! *)
678 CKM == {
679 ParameterType -> Internal,
680 Indices -> {Index[Generation], Index[Generation]},
681 Unitary -> True,
682 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
683 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
684 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
685 TeX -> Superscript[V,CKM],
686 Description -> "CKM-Matrix"}
687};
688
689(* ************************** *)
690(* ***** Lagrangian ***** *)
691(* ************************** *)
692
693LGGG := Block[{mu,nu,rho, aa,bb,cc},
694 (Kggg/Lambda^2) gs f[aa,bb,cc] FS[G,mu,nu,aa] FS[G,nu,rho,bb] FS[G,rho,mu,cc]];
695
696GGGngluons := Module[{CoefList},
697 CoefList = CoefficientList[Normal[Series[ExpandIndices[LGGG],{gs,0,4}]],gs];
698 Prepend[Table[CoefList[[i]]*(gs^(i-1)),{i,1,Length[CoefList]}],0]
699 ];
700
701LDGDG := Block[{mu,nu,rho, aa},
702 (Kdgdg/Lambda^2) DC[FS[G,mu,nu,aa],mu] DC[FS[G,rho,nu,aa],rho] ];
703
704DGDGngluons := Module[{CoefList},
705 CoefList = CoefficientList[Normal[Series[ExpandIndices[LDGDG],{gs,0,4}]],gs];
706 Prepend[Table[CoefList[[i]]*(gs^(i-1)),{i,1,Length[CoefList]}],0]
707 ]
708
709LGauge := Block[{mu,nu,ii,aa},
710 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]];
711
712LFermions := Block[{mu},
713 ExpandIndices[I*(
714 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]),
715 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
716
717LHiggs := Block[{ii,mu, feynmangaugerules},
718 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
719
720 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
721 ];
722
723LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
724 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
725
726 yuk = ExpandIndices[
727 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
728 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
729 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
730 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
731 yuk+HC[yuk]/.feynmangaugerules
732 ];
733
734LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
735 (* Pure gauge piece *)
736 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
737 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
738 LGhs = -ghGbar.del[DC[ghG,mu],mu];
739
740 (* Scalar pieces: see Peskin pages 739-742 *)
741 (* phi1 and phi2 are the real degrees of freedom of GP *)
742 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
743 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
744 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
745 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
746 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
747 doublet0 = {0, vev/Sqrt[2]};
748 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}];
749 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
750 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
751
752ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
753
754LSM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;
755
756LTOT:= LSM + LGGG + LDGDG