HiggsTopCurrents: HiggsTopCurrents.fr

File HiggsTopCurrents.fr, 25.0 KB (added by Jeff Dror, 9 years ago)
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1(***************************************************************************************************************)
2(****** FeynRules model-file for the Standard Model + some dim 6 operators for composite top quark ******)
3(****** ******)
4(****** Authors: J. Dror, E. Salvioni ******)
5(****** ******)
6(****** Model is based on Standard Model FeynRules model-file ******)
7(***************************************************************************************************************)
8
9(* ************************** *)
10(* ***** Information ***** *)
11(* ************************** *)
12M$ModelName = "HiggsTopCurrents";
13
14M$Information = {
15 Authors -> {"J. Dror", "E. Salvioni"},
16 Version -> "1.0.0",
17 Date -> "02.06.2016",
18 Institutions -> {"Cornell University", "University of California, Davis"},
19 Emails -> {"ajd268@cornell.edu", "esalvioni@ucdavid.edu"}
20};
21
22FeynmanGauge = True;
23
24(* ************************** *)
25(* ***** vevs ***** *)
26(* ************************** *)
27M$vevs = { {Phi[2],vev} };
28
29(* ************************** *)
30(* ***** Gauge groups ***** *)
31(* ************************** *)
32M$GaugeGroups = {
33 U1Y == {
34 Abelian -> True,
35 CouplingConstant -> g1,
36 GaugeBoson -> B,
37 Charge -> Y
38 },
39 SU2L == {
40 Abelian -> False,
41 CouplingConstant -> gw,
42 GaugeBoson -> Wi,
43 StructureConstant -> Eps,
44 Representations -> {Ta,SU2D},
45 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
46 },
47 SU3C == {
48 Abelian -> False,
49 CouplingConstant -> gs,
50 GaugeBoson -> G,
51 StructureConstant -> f,
52 Representations -> {T,Colour},
53 SymmetricTensor -> dSUN
54 }
55};
56
57
58(* ************************** *)
59(* ***** Indices ***** *)
60(* ************************** *)
61
62IndexRange[Index[SU2W ]] = Unfold[Range[3]];
63IndexRange[Index[SU2D ]] = Unfold[Range[2]];
64IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
65IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
66IndexRange[Index[Generation]] = Range[3];
67
68IndexStyle[SU2W, j];
69IndexStyle[SU2D, k];
70IndexStyle[Gluon, a];
71IndexStyle[Colour, m];
72IndexStyle[Generation, f];
73
74
75(* ************************** *)
76(* *** Interaction orders *** *)
77(* *** (as used by mg5) *** *)
78(* ************************** *)
79
80M$InteractionOrderHierarchy = {
81 {QCD, 1},
82 {QED, 2}
83};
84
85
86(* ************************** *)
87(* **** Particle classes **** *)
88(* ************************** *)
89M$ClassesDescription = {
90
91(* Gauge bosons: physical vector fields *)
92 V[1] == {
93 ClassName -> A,
94 SelfConjugate -> True,
95 Mass -> 0,
96 Width -> 0,
97 ParticleName -> "a",
98 PDG -> 22,
99 PropagatorLabel -> "a",
100 PropagatorType -> W,
101 PropagatorArrow -> None,
102 FullName -> "Photon"
103 },
104 V[2] == {
105 ClassName -> Z,
106 SelfConjugate -> True,
107 Mass -> {MZ, 91.1876},
108 Width -> {WZ, 2.4952},
109 ParticleName -> "Z",
110 PDG -> 23,
111 PropagatorLabel -> "Z",
112 PropagatorType -> Sine,
113 PropagatorArrow -> None,
114 FullName -> "Z"
115 },
116 V[3] == {
117 ClassName -> W,
118 SelfConjugate -> False,
119 Mass -> {MW, Internal},
120 Width -> {WW, 2.085},
121 ParticleName -> "W+",
122 AntiParticleName -> "W-",
123 QuantumNumbers -> {Q -> 1},
124 PDG -> 24,
125 PropagatorLabel -> "W",
126 PropagatorType -> Sine,
127 PropagatorArrow -> Forward,
128 FullName -> "W"
129 },
130 V[4] == {
131 ClassName -> G,
132 SelfConjugate -> True,
133 Indices -> {Index[Gluon]},
134 Mass -> 0,
135 Width -> 0,
136 ParticleName -> "g",
137 PDG -> 21,
138 PropagatorLabel -> "G",
139 PropagatorType -> C,
140 PropagatorArrow -> None,
141 FullName -> "G"
142 },
143
144(* Ghosts: related to physical gauge bosons *)
145 U[1] == {
146 ClassName -> ghA,
147 SelfConjugate -> False,
148 Ghost -> A,
149 QuantumNumbers -> {GhostNumber -> 1},
150 Mass -> 0,
151 Width -> 0,
152 PropagatorLabel -> "uA",
153 PropagatorType -> GhostDash,
154 PropagatorArrow -> Forward
155 },
156 U[2] == {
157 ClassName -> ghZ,
158 SelfConjugate -> False,
159 Ghost -> Z,
160 QuantumNumbers -> {GhostNumber -> 1},
161 Mass -> {MZ,91.1876},
162 Width -> {WZ, 2.4952},
163 PropagatorLabel -> "uZ",
164 PropagatorType -> GhostDash,
165 PropagatorArrow -> Forward
166 },
167 U[31] == {
168 ClassName -> ghWp,
169 SelfConjugate -> False,
170 Ghost -> W,
171 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
172 Mass -> {MW,Internal},
173 Width -> {WW, 2.085},
174 PropagatorLabel -> "uWp",
175 PropagatorType -> GhostDash,
176 PropagatorArrow -> Forward
177 },
178 U[32] == {
179 ClassName -> ghWm,
180 SelfConjugate -> False,
181 Ghost -> Wbar,
182 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
183 Mass -> {MW,Internal},
184 Width -> {WW, 2.085},
185 PropagatorLabel -> "uWm",
186 PropagatorType -> GhostDash,
187 PropagatorArrow -> Forward
188 },
189 U[4] == {
190 ClassName -> ghG,
191 SelfConjugate -> False,
192 Indices -> {Index[Gluon]},
193 Ghost -> G,
194 QuantumNumbers ->{GhostNumber -> 1},
195 Mass -> 0,
196 Width -> 0,
197 PropagatorLabel -> "uG",
198 PropagatorType -> GhostDash,
199 PropagatorArrow -> Forward
200 },
201
202(* Gauge bosons: unphysical vector fields *)
203 V[11] == {
204 ClassName -> B,
205 Unphysical -> True,
206 SelfConjugate -> True,
207 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
208 },
209 V[12] == {
210 ClassName -> Wi,
211 Unphysical -> True,
212 SelfConjugate -> True,
213 Indices -> {Index[SU2W]},
214 FlavorIndex -> SU2W,
215 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]}
216 },
217
218(* Ghosts: related to unphysical gauge bosons *)
219 U[11] == {
220 ClassName -> ghB,
221 Unphysical -> True,
222 SelfConjugate -> False,
223 Ghost -> B,
224 Definitions -> { ghB -> -sw ghZ + cw ghA}
225 },
226 U[12] == {
227 ClassName -> ghWi,
228 Unphysical -> True,
229 SelfConjugate -> False,
230 Ghost -> Wi,
231 Indices -> {Index[SU2W]},
232 FlavorIndex -> SU2W,
233 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
234 } ,
235
236(* Fermions: physical fields *)
237 F[1] == {
238 ClassName -> vl,
239 ClassMembers -> {ve,vm,vt},
240 Indices -> {Index[Generation]},
241 FlavorIndex -> Generation,
242 SelfConjugate -> False,
243 Mass -> 0,
244 Width -> 0,
245 QuantumNumbers -> {LeptonNumber -> 1},
246 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
247 PropagatorType -> S,
248 PropagatorArrow -> Forward,
249 PDG -> {12,14,16},
250 ParticleName -> {"ve","vm","vt"},
251 AntiParticleName -> {"ve~","vm~","vt~"},
252 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
253 },
254 F[2] == {
255 ClassName -> l,
256 ClassMembers -> {e, mu, ta},
257 Indices -> {Index[Generation]},
258 FlavorIndex -> Generation,
259 SelfConjugate -> False,
260 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
261 Width -> 0,
262 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
263 PropagatorLabel -> {"l", "e", "mu", "ta"},
264 PropagatorType -> Straight,
265 PropagatorArrow -> Forward,
266 PDG -> {11, 13, 15},
267 ParticleName -> {"e-", "mu-", "ta-"},
268 AntiParticleName -> {"e+", "mu+", "ta+"},
269 FullName -> {"Electron", "Muon", "Tau"}
270 },
271 F[3] == {
272 ClassName -> uq,
273 ClassMembers -> {u, c, t},
274 Indices -> {Index[Generation], Index[Colour]},
275 FlavorIndex -> Generation,
276 SelfConjugate -> False,
277 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
278 Width -> {0, 0, {WT,1.50833649}},
279 QuantumNumbers -> {Q -> 2/3},
280 PropagatorLabel -> {"uq", "u", "c", "t"},
281 PropagatorType -> Straight,
282 PropagatorArrow -> Forward,
283 PDG -> {2, 4, 6},
284 ParticleName -> {"u", "c", "t" },
285 AntiParticleName -> {"u~", "c~", "t~"},
286 FullName -> {"u-quark", "c-quark", "t-quark"}
287 },
288 F[4] == {
289 ClassName -> dq,
290 ClassMembers -> {d, s, b},
291 Indices -> {Index[Generation], Index[Colour]},
292 FlavorIndex -> Generation,
293 SelfConjugate -> False,
294 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
295 Width -> 0,
296 QuantumNumbers -> {Q -> -1/3},
297 PropagatorLabel -> {"dq", "d", "s", "b"},
298 PropagatorType -> Straight,
299 PropagatorArrow -> Forward,
300 PDG -> {1,3,5},
301 ParticleName -> {"d", "s", "b" },
302 AntiParticleName -> {"d~", "s~", "b~"},
303 FullName -> {"d-quark", "s-quark", "b-quark"}
304 },
305
306(* Fermions: unphysical fields *)
307 F[11] == {
308 ClassName -> LL,
309 Unphysical -> True,
310 Indices -> {Index[SU2D], Index[Generation]},
311 FlavorIndex -> SU2D,
312 SelfConjugate -> False,
313 QuantumNumbers -> {Y -> -1/2},
314 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]] }
315 },
316 F[12] == {
317 ClassName -> lR,
318 Unphysical -> True,
319 Indices -> {Index[Generation]},
320 FlavorIndex -> Generation,
321 SelfConjugate -> False,
322 QuantumNumbers -> {Y -> -1},
323 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
324 },
325 F[13] == {
326 ClassName -> QL,
327 Unphysical -> True,
328 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
329 FlavorIndex -> SU2D,
330 SelfConjugate -> False,
331 QuantumNumbers -> {Y -> 1/6},
332 Definitions -> {
333 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
334 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
335 },
336 F[14] == {
337 ClassName -> uR,
338 Unphysical -> True,
339 Indices -> {Index[Generation], Index[Colour]},
340 FlavorIndex -> Generation,
341 SelfConjugate -> False,
342 QuantumNumbers -> {Y -> 2/3},
343 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
344 },
345 F[15] == {
346 ClassName -> dR,
347 Unphysical -> True,
348 Indices -> {Index[Generation], Index[Colour]},
349 FlavorIndex -> Generation,
350 SelfConjugate -> False,
351 QuantumNumbers -> {Y -> -1/3},
352 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
353 },
354
355(* Higgs: physical scalars *)
356 S[1] == {
357 ClassName -> H,
358 SelfConjugate -> True,
359 Mass -> {MH,125},
360 Width -> {WH,0.00407},
361 PropagatorLabel -> "H",
362 PropagatorType -> D,
363 PropagatorArrow -> None,
364 PDG -> 25,
365 ParticleName -> "H",
366 FullName -> "H"
367 },
368
369(* Higgs: physical scalars *)
370 S[2] == {
371 ClassName -> G0,
372 SelfConjugate -> True,
373 Goldstone -> Z,
374 Mass -> {MZ, 91.1876},
375 Width -> {WZ, 2.4952},
376 PropagatorLabel -> "Go",
377 PropagatorType -> D,
378 PropagatorArrow -> None,
379 PDG -> 250,
380 ParticleName -> "G0",
381 FullName -> "G0"
382 },
383 S[3] == {
384 ClassName -> GP,
385 SelfConjugate -> False,
386 Goldstone -> W,
387 Mass -> {MW, Internal},
388 QuantumNumbers -> {Q -> 1},
389 Width -> {WW, 2.085},
390 PropagatorLabel -> "GP",
391 PropagatorType -> D,
392 PropagatorArrow -> None,
393 PDG -> 251,
394 ParticleName -> "G+",
395 AntiParticleName -> "G-",
396 FullName -> "GP"
397 },
398
399(* Higgs: unphysical scalars *)
400 S[11] == {
401 ClassName -> Phi,
402 Unphysical -> True,
403 Indices -> {Index[SU2D]},
404 FlavorIndex -> SU2D,
405 SelfConjugate -> False,
406 QuantumNumbers -> {Y -> 1/2},
407 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
408 }
409};
410
411
412(* ************************** *)
413(* ***** Gauge ***** *)
414(* ***** Parameters ***** *)
415(* ***** (FeynArts) ***** *)
416(* ************************** *)
417
418GaugeXi[ V[1] ] = GaugeXi[A];
419GaugeXi[ V[2] ] = GaugeXi[Z];
420GaugeXi[ V[3] ] = GaugeXi[W];
421GaugeXi[ V[4] ] = GaugeXi[G];
422GaugeXi[ S[1] ] = 1;
423GaugeXi[ S[2] ] = GaugeXi[Z];
424GaugeXi[ S[3] ] = GaugeXi[W];
425GaugeXi[ U[1] ] = GaugeXi[A];
426GaugeXi[ U[2] ] = GaugeXi[Z];
427GaugeXi[ U[31] ] = GaugeXi[W];
428GaugeXi[ U[32] ] = GaugeXi[W];
429GaugeXi[ U[4] ] = GaugeXi[G];
430
431
432(* ************************** *)
433(* ***** Parameters ***** *)
434(* ************************** *)
435M$Parameters = {
436
437 (* External parameters *)
438 aEWM1 == {
439 ParameterType -> External,
440 BlockName -> SMINPUTS,
441 OrderBlock -> 1,
442 Value -> 127.9,
443 InteractionOrder -> {QED,-2},
444 Description -> "Inverse of the EW coupling constant at the Z pole"
445 },
446 Gf == {
447 ParameterType -> External,
448 BlockName -> SMINPUTS,
449 OrderBlock -> 2,
450 Value -> 1.16637*^-5,
451 InteractionOrder -> {QED,2},
452 TeX -> Subscript[G,f],
453 Description -> "Fermi constant"
454 },
455 aS == {
456 ParameterType -> External,
457 BlockName -> SMINPUTS,
458 OrderBlock -> 3,
459 Value -> 0.1184,
460 InteractionOrder -> {QCD,2},
461 TeX -> Subscript[\[Alpha],s],
462 Description -> "Strong coupling constant at the Z pole"
463 },
464 cutoff == {
465 ParameterType -> External,
466 BlockName -> HDO,
467 OrderBlock -> 1,
468 Value -> 246.221,
469 InteractionOrder -> {QED,0},
470 Description -> "scale of HDO. Default is equal to Higg's VEV ."
471 },
472 cR == {
473 ParameterType -> External,
474 BlockName -> HDO,
475 OrderBlock -> 2,
476 Value -> 1,
477 InteractionOrder -> {QED,2},
478 Description -> "coefficient of tRtR operator"
479 },
480 cL1 == {
481 ParameterType -> External,
482 BlockName -> HDO,
483 OrderBlock -> 3,
484 Value -> 1,
485 InteractionOrder -> {QED,2},
486 Description -> "coefficient of qLqL1 operator"
487 },
488 cL3 == {
489 ParameterType -> External,
490 BlockName -> HDO,
491 OrderBlock -> 4,
492 Value -> 1,
493 InteractionOrder -> {QED,2},
494 Description -> "coefficient of qLqL3 operator"
495 },
496 ymdo == {
497 ParameterType -> External,
498 BlockName -> YUKAWA,
499 OrderBlock -> 1,
500 Value -> 5.04*^-3,
501 Description -> "Down Yukawa mass"
502 },
503 ymup == {
504 ParameterType -> External,
505 BlockName -> YUKAWA,
506 OrderBlock -> 2,
507 Value -> 2.55*^-3,
508 Description -> "Up Yukawa mass"
509 },
510 yms == {
511 ParameterType -> External,
512 BlockName -> YUKAWA,
513 OrderBlock -> 3,
514 Value -> 0.101,
515 Description -> "Strange Yukawa mass"
516 },
517 ymc == {
518 ParameterType -> External,
519 BlockName -> YUKAWA,
520 OrderBlock -> 4,
521 Value -> 1.27,
522 Description -> "Charm Yukawa mass"
523 },
524 ymb == {
525 ParameterType -> External,
526 BlockName -> YUKAWA,
527 OrderBlock -> 5,
528 Value -> 4.7,
529 Description -> "Bottom Yukawa mass"
530 },
531 ymt == {
532 ParameterType -> External,
533 BlockName -> YUKAWA,
534 OrderBlock -> 6,
535 Value -> 172,
536 Description -> "Top Yukawa mass"
537 },
538 yme == {
539 ParameterType -> External,
540 BlockName -> YUKAWA,
541 OrderBlock -> 11,
542 Value -> 5.11*^-4,
543 Description -> "Electron Yukawa mass"
544 },
545 ymm == {
546 ParameterType -> External,
547 BlockName -> YUKAWA,
548 OrderBlock -> 13,
549 Value -> 0.10566,
550 Description -> "Muon Yukawa mass"
551 },
552 ymtau == {
553 ParameterType -> External,
554 BlockName -> YUKAWA,
555 OrderBlock -> 15,
556 Value -> 1.777,
557 Description -> "Tau Yukawa mass"
558 },
559 cabi == {
560 ParameterType -> External,
561 BlockName -> CKMBLOCK,
562 OrderBlock -> 1,
563 Value -> 0.227736,
564 TeX -> Subscript[\[Theta], c],
565 Description -> "Cabibbo angle"
566 },
567
568 (* Internal Parameters *)
569 aEW == {
570 ParameterType -> Internal,
571 Value -> 1/aEWM1,
572 InteractionOrder -> {QED,2},
573 TeX -> Subscript[\[Alpha], EW],
574 Description -> "Electroweak coupling contant"
575 },
576 MW == {
577 ParameterType -> Internal,
578 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
579 TeX -> Subscript[M,W],
580 Description -> "W mass"
581 },
582 sw2 == {
583 ParameterType -> Internal,
584 Value -> 1-(MW/MZ)^2,
585 Description -> "Squared Sin of the Weinberg angle"
586 },
587 ee == {
588 ParameterType -> Internal,
589 Value -> Sqrt[4 Pi aEW],
590 InteractionOrder -> {QED,1},
591 TeX -> e,
592 Description -> "Electric coupling constant"
593 },
594 cw == {
595 ParameterType -> Internal,
596 Value -> Sqrt[1-sw2],
597 TeX -> Subscript[c,w],
598 Description -> "Cosine of the Weinberg angle"
599 },
600 sw == {
601 ParameterType -> Internal,
602 Value -> Sqrt[sw2],
603 TeX -> Subscript[s,w],
604 Description -> "Sine of the Weinberg angle"
605 },
606 gw == {
607 ParameterType -> Internal,
608 Definitions -> {gw->ee/sw},
609 InteractionOrder -> {QED,1},
610 TeX -> Subscript[g,w],
611 Description -> "Weak coupling constant at the Z pole"
612 },
613 g1 == {
614 ParameterType -> Internal,
615 Definitions -> {g1->ee/cw},
616 InteractionOrder -> {QED,1},
617 TeX -> Subscript[g,1],
618 Description -> "U(1)Y coupling constant at the Z pole"
619 },
620 gs == {
621 ParameterType -> Internal,
622 Value -> Sqrt[4 Pi aS],
623 InteractionOrder -> {QCD,1},
624 TeX -> Subscript[g,s],
625 ParameterName -> G,
626 Description -> "Strong coupling constant at the Z pole"
627 },
628 vev == {
629 ParameterType -> Internal,
630 Value -> 2*MW*sw/ee,
631 InteractionOrder -> {QED,-1},
632 Description -> "Higgs vacuum expectation value"
633 },
634 lam == {
635 ParameterType -> Internal,
636 Value -> MH^2/(2*vev^2),
637 InteractionOrder -> {QED, 2},
638 Description -> "Higgs quartic coupling"
639 },
640 muH == {
641 ParameterType -> Internal,
642 Value -> Sqrt[vev^2 lam],
643 TeX -> \[Mu],
644 Description -> "Coefficient of the quadratic piece of the Higgs potential"
645 },
646 yl == {
647 ParameterType -> Internal,
648 Indices -> {Index[Generation], Index[Generation]},
649 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
650 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
651 InteractionOrder -> {QED, 1},
652 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
653 TeX -> Superscript[y, l],
654 Description -> "Lepton Yukawa couplings"
655 },
656 yu == {
657 ParameterType -> Internal,
658 Indices -> {Index[Generation], Index[Generation]},
659 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
660 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
661 InteractionOrder -> {QED, 1},
662 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
663 TeX -> Superscript[y, u],
664 Description -> "Up-type Yukawa couplings"
665 },
666 yd == {
667 ParameterType -> Internal,
668 Indices -> {Index[Generation], Index[Generation]},
669 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
670 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
671 InteractionOrder -> {QED, 1},
672 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
673 TeX -> Superscript[y, d],
674 Description -> "Down-type Yukawa couplings"
675 },
676(* N. B. : only Cabibbo mixing! *)
677 CKM == {
678 ParameterType -> Internal,
679 Indices -> {Index[Generation], Index[Generation]},
680 Unitary -> True,
681 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
682 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
683 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
684 TeX -> Superscript[V,CKM],
685 Description -> "CKM-Matrix"
686}
687};
688
689(* ************************** *)
690(* ***** Lagrangian ***** *)
691(* ************************** *)
692
693LGauge := Block[{mu,nu,ii,aa},
694 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]];
695
696LFermions := Block[{mu},
697 ExpandIndices[I*(
698 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]),
699 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
700
701LHiggs := Block[{ii,mu, feynmangaugerules},
702 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
703
704 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
705 ];
706
707LHDO := Block[{ii,jj,kk,tt,iso,mu,sp1,sp2,cc,feynmangaugerules,operators},
708 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
709
710 operators = ExpandIndices[cR*I/(cutoff^2) Phibar[ii] DC[Phi[ii],mu] uRbar[sp1,3,cc].Ga[mu,sp1,sp2].uR[sp2,3,cc] + cL1*I/(cutoff^2) Phibar[ii] DC[Phi[ii],mu] QLbar[sp1,jj,3,cc].Ga[mu,sp1,sp2].QL[sp2,jj,3,cc] + 4*cL3*I/(cutoff^2) Phibar[ii] Ta[iso,ii,kk] DC[Phi[kk],mu] Ta[iso,jj,tt] QLbar[sp1,jj,3,cc].Ga[mu,sp1,sp2].QL[sp2,tt,3,cc], FlavorExpand-> {SU2W,SU2D}];
711
712(* neglect (1,3) and (2,3) terms in the CKM matrix: *)
713 operators = operators /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[3, b] IndexDelta[3, c], CKM[a_, b_] -> IndexDelta[3, b], Conjugate[CKM[a_, c_]] -> IndexDelta[3, c]};
714operators+HC[operators]/.feynmangaugerules
715 ];
716
717LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
718 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
719
720 yuk = ExpandIndices[
721 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
722 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
723 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
724 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
725 yuk+HC[yuk]/.feynmangaugerules
726 ];
727
728LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
729 (* Pure gauge piece *)
730 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
731 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
732 LGhs = -ghGbar.del[DC[ghG,mu],mu];
733
734 (* Scalar pieces: see Peskin pages 739-742 *)
735 (* phi1 and phi2 are the real degrees of freedom of GP *)
736 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
737 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
738 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
739 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
740 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
741 doublet0 = {0, vev/Sqrt[2]};
742 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}];
743 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
744 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
745
746ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
747
748Ltot:= LGauge + LFermions + LHiggs + LYukawa + LGhost + LHDO;
749