ASperGe: 2HDM_mix.fr

File 2HDM_mix.fr, 30.0 KB (added by Karen De Causmaecker, 13 years ago)

Two Higgs Doublet Model (2HDM) including the mixings

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1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Standard model ******)
3(****** ******)
4(****** Authors: N. Christensen, C. Duhr, B. Fuks ******)
5(****** Adapted by A. Alloul for mass diagonalization ******)
6(****** ******)
7(****** Choose whether Feynman gauge is desired. ******)
8(****** If set to False, unitary gauge is assumed. ****)
9(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
10(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
11(***************************************************************************************************************)
12
13(* ************************** *)
14(* ***** Information ***** *)
15(* ************************** *)
16M$ModelName = "2HDM_mix";
17
18M$Information = {
19 Authors -> "K. De Causmaecker",
20 Version -> "1.0.0",
21 Date -> "11. 01. 2013",
22 Institutions -> "IIHE - Vrije Universiteit Brussel",
23 Emails -> "Karen.De.Causmaecker@vub.ac.be"
24};
25
26FeynmanGauge = True;
27
28(* ************************** *)
29(* ***** Change log ***** *)
30(* ************************** *)
31
32(* v1.0.0: 2HDM adapted for the mass diagonalization routine*)
33
34(* ************************** *)
35(* ***** vevs & mixings ***** *)
36(* ************************** *)
37M$vevs = { {phi1[2],vev1} };
38
39M$MixingsDescription = {
40 Mix["1u"] == {
41 MassBasis -> {A, Z},
42 GaugeBasis -> {B, Wi[3]},
43 MixingMatrix -> UG,
44 BlockName -> WEAKMIX
45 },
46
47 Mix["2"] == {
48 MassBasis -> {W, Wbar},
49 GaugeBasis -> {Wi[1], Wi[2]},
50 Value -> {{1/Sqrt[2], -I/Sqrt[2]}, {1/Sqrt[2], I/Sqrt[2]}}
51 },
52
53 Mix["1p"] == {
54 MassBasis -> {{H0}, {G0}},
55 GaugeBasis -> {phi1[2]},
56 Value -> {{{1}}, {{1}}}
57 },
58
59 Mix["2p"] == {
60 MassBasis -> {{R0}, {I0}},
61 GaugeBasis -> {phi2[2]},
62 Value -> {{{1}}, {{1}}}
63 },
64
65 Mix["1s"] == {
66 MassBasis -> {h1, h2, h3},
67 GaugeBasis -> {H0, R0, I0},
68 MixingMatrix -> NH,
69 BlockName -> NHMIX
70 },
71
72 Mix["2s"] == {
73 MassBasis -> {HP1},
74 GaugeBasis -> {phi1[1]},
75 MixingMatrix -> CH1,
76 BlockName -> CH1MIX
77 },
78
79 Mix["3s"] == {
80 MassBasis -> {HP2},
81 GaugeBasis -> {phi2[1]},
82 MixingMatrix -> CH2,
83 BlockName -> CH2MIX
84 },
85
86 Mix["4a"] == {
87 MassBasis -> {dq[1, _], dq[2, _], dq[3, _]},
88 GaugeBasis -> {{QL[2, 1, _], QL[2, 2, _], QL[2, 3, _]}, {dR[1, _], dR[2, _], dR[3, _]}},
89 MixingMatrix -> {CKM, _},
90 Inverse -> {True, _},
91 Value -> {_, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}
92 },
93
94 Mix["4b"] == {
95 MassBasis -> {uq[1, _], uq[2, _], uq[3, _]},
96 GaugeBasis -> {{QL[1, 1, _], QL[1, 2, _], QL[1, 3, _]}, {uR[1, _], uR[2, _], uR[3, _]}}, Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}
97 },
98
99 Mix["5a"] == {
100 MassBasis -> {l[1], l[2], l[3]},
101 GaugeBasis -> {{LL[2, 1], LL[2, 2], LL[2, 3]}, {lR[1], lR[2], lR[3]}}, Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}
102 },
103
104 Mix["5b"] == {
105 MassBasis -> {vl[1], vl[2], vl[3]},
106 GaugeBasis -> {LL[1, 1], LL[1, 2], LL[1, 3]},
107 Value -> {{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}}
108 }
109};
110
111
112(* ************************** *)
113(* ***** Gauge groups ***** *)
114(* ************************** *)
115M$GaugeGroups = {
116 U1Y == {
117 Abelian -> True,
118 CouplingConstant -> g1,
119 GaugeBoson -> B,
120 Charge -> Y
121 },
122
123 SU2L == {
124 Abelian -> False,
125 CouplingConstant -> gw,
126 GaugeBoson -> Wi,
127 StructureConstant -> Eps,
128 Representations -> {Ta,SU2D},
129 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
130 },
131
132 SU3C == {
133 Abelian -> False,
134 CouplingConstant -> gs,
135 GaugeBoson -> G,
136 StructureConstant -> f,
137 Representations -> {T,Colour},
138 DTerm -> dSUN
139 }
140};
141
142
143(* ************************** *)
144(* ***** Indices ***** *)
145(* ************************** *)
146
147IndexRange[Index[SU2W ]] = Unfold[Range[3]];
148IndexRange[Index[SU2D ]] = Unfold[Range[2]];
149IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
150IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
151IndexRange[Index[Generation]] = Range[3];
152IndexRange[Index[Higgs ]] = Unfold[Range[3]];
153
154IndexStyle[SU2W, j];
155IndexStyle[SU2D, k];
156IndexStyle[Gluon, a];
157IndexStyle[Colour, m];
158IndexStyle[Generation, f];
159IndexStyle[Higgs, h];
160
161
162(* ************************** *)
163(* *** Interaction orders *** *)
164(* *** (as used by mg5) *** *)
165(* ************************** *)
166
167M$InteractionOrderHierarchy = {
168 {QCD, 1},
169 {QED, 2}
170};
171
172
173(* ************************** *)
174(* **** Particle classes **** *)
175(* ************************** *)
176M$ClassesDescription = {
177
178(* Gauge bosons: physical vector fields *)
179
180 V[1] == {
181 ClassName -> A,
182 SelfConjugate -> True,
183 Mass -> 0,
184 Width -> 0,
185 ParticleName -> "a",
186 PDG -> 22,
187 PropagatorLabel -> "a",
188 PropagatorType -> W,
189 PropagatorArrow -> None,
190 FullName -> "Photon"
191 },
192
193 V[2] == {
194 ClassName -> Z,
195 SelfConjugate -> True,
196 Mass -> MZ,
197 Width -> {WZ, 2.4952},
198 ParticleName -> "Z",
199 PDG -> 23,
200 PropagatorLabel -> "Z",
201 PropagatorType -> Sine,
202 PropagatorArrow -> None,
203 FullName -> "Z"
204 },
205
206 V[3] == {
207 ClassName -> W,
208 SelfConjugate -> False,
209 Mass -> MW,
210 Width -> {WW, 2.085},
211 ParticleName -> "W+",
212 AntiParticleName -> "W-",
213 QuantumNumbers -> {Q -> 1},
214 PDG -> 24,
215 PropagatorLabel -> "W",
216 PropagatorType -> Sine,
217 PropagatorArrow -> Forward,
218 FullName -> "W"
219 },
220
221 V[4] == {
222 ClassName -> G,
223 SelfConjugate -> True,
224 Indices -> {Index[Gluon]},
225 Mass -> 0,
226 Width -> 0,
227 ParticleName -> "g",
228 PDG -> 21,
229 PropagatorLabel -> "G",
230 PropagatorType -> C,
231 PropagatorArrow -> None,
232 FullName -> "G"
233 },
234
235(* Ghosts: related to physical gauge bosons *)
236
237 U[1] == {
238 ClassName -> ghA,
239 SelfConjugate -> False,
240 Ghost -> A,
241 QuantumNumbers -> {GhostNumber -> 1},
242 Mass -> 0,
243 PropagatorLabel -> "uA",
244 PropagatorType -> GhostDash,
245 PropagatorArrow -> Forward
246 },
247
248 U[2] == {
249 ClassName -> ghZ,
250 SelfConjugate -> False,
251 Ghost -> Z,
252 QuantumNumbers -> {GhostNumber -> 1},
253 Mass -> MZ,
254 PropagatorLabel -> "uZ",
255 PropagatorType -> GhostDash,
256 PropagatorArrow -> Forward
257 },
258
259 U[31] == {
260 ClassName -> ghWp,
261 SelfConjugate -> False,
262 Ghost -> W,
263 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
264 Mass -> {MW,Internal},
265 PropagatorLabel -> "uWp",
266 PropagatorType -> GhostDash,
267 PropagatorArrow -> Forward
268 },
269
270 U[32] == {
271 ClassName -> ghWm,
272 SelfConjugate -> False,
273 Ghost -> Wbar,
274 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
275 Mass -> MW,
276 PropagatorLabel -> "uWm",
277 PropagatorType -> GhostDash,
278 PropagatorArrow -> Forward
279 },
280
281 U[4] == {
282 ClassName -> ghG,
283 SelfConjugate -> False,
284 Indices -> {Index[Gluon]},
285 Ghost -> G,
286 QuantumNumbers ->{GhostNumber -> 1},
287 Mass -> 0,
288 PropagatorLabel -> "uG",
289 PropagatorType -> GhostDash,
290 PropagatorArrow -> Forward
291 },
292
293(* Gauge bosons: unphysical vector fields *)
294
295 V[11] == {
296 ClassName -> B,
297 Unphysical -> True,
298 SelfConjugate -> True
299 },
300
301 V[12] == {
302 ClassName -> Wi,
303 Unphysical -> True,
304 SelfConjugate -> True,
305 Indices -> {Index[SU2W]},
306 FlavorIndex -> SU2W
307 },
308
309(* Ghosts: related to unphysical gauge bosons *)
310
311 U[11] == {
312 ClassName -> ghB,
313 Unphysical -> True,
314 SelfConjugate -> False,
315 Ghost -> B,
316 Definitions -> { ghB -> -(ee/gw) ghZ + (ee/g1) ghA}
317 },
318
319 U[12] == {
320 ClassName -> ghWi,
321 Unphysical -> True,
322 SelfConjugate -> False,
323 Ghost -> Wi,
324 Indices -> {Index[SU2W]},
325 FlavorIndex -> SU2W,
326 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> (ee/g1) ghZ+(ee/gw) ghA}
327 },
328
329(* Fermions: physical fields *)
330
331 F[1] == {
332 ClassName -> vl,
333 ClassMembers -> {ve,vm,vt},
334 Indices -> {Index[Generation]},
335 FlavorIndex -> Generation,
336 SelfConjugate -> False,
337 Mass -> 0,
338 Width -> 0,
339 QuantumNumbers -> {LeptonNumber -> 1},
340 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
341 PropagatorType -> S,
342 PropagatorArrow -> Forward,
343 PDG -> {12,14,16},
344 ParticleName -> {"ve","vm","vt"},
345 AntiParticleName -> {"ve~","vm~","vt~"},
346 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
347 },
348
349 F[2] == {
350 ClassName -> l,
351 ClassMembers -> {e, mu, ta},
352 Indices -> {Index[Generation]},
353 FlavorIndex -> Generation,
354 SelfConjugate -> False,
355 Mass -> {Ml, {Me,5.11*^-4}, {MM,0.10566}, {MTA,1.777}},
356 Width -> 0,
357 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
358 PropagatorLabel -> {"l", "e", "mu", "ta"},
359 PropagatorType -> Straight,
360 PropagatorArrow -> Forward,
361 PDG -> {11, 13, 15},
362 ParticleName -> {"e-", "mu-", "ta-"},
363 AntiParticleName -> {"e+", "mu+", "ta+"},
364 FullName -> {"Electron", "Muon", "Tau"}
365 },
366
367 F[3] == {
368 ClassName -> uq,
369 ClassMembers -> {u, c, t},
370 Indices -> {Index[Generation], Index[Colour]},
371 FlavorIndex -> Generation,
372 SelfConjugate -> False,
373 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
374 Width -> {0, 0, {WT,1.50833649}},
375 QuantumNumbers -> {Q -> 2/3},
376 PropagatorLabel -> {"uq", "u", "c", "t"},
377 PropagatorType -> Straight,
378 PropagatorArrow -> Forward,
379 PDG -> {2, 4, 6},
380 ParticleName -> {"u", "c", "t" },
381 AntiParticleName -> {"u~", "c~", "t~"},
382 FullName -> {"u-quark", "c-quark", "t-quark"}
383 },
384
385 F[4] == {
386 ClassName -> dq,
387 ClassMembers -> {d, s, b},
388 Indices -> {Index[Generation], Index[Colour]},
389 FlavorIndex -> Generation,
390 SelfConjugate -> False,
391 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
392 Width -> 0,
393 QuantumNumbers -> {Q -> -1/3},
394 PropagatorLabel -> {"dq", "d", "s", "b"},
395 PropagatorType -> Straight,
396 PropagatorArrow -> Forward,
397 PDG -> {1,3,5},
398 ParticleName -> {"d", "s", "b" },
399 AntiParticleName -> {"d~", "s~", "b~"},
400 FullName -> {"d-quark", "s-quark", "b-quark"}
401 },
402
403(* Fermions: unphysical fields *)
404
405 F[11] == {
406 ClassName -> LL,
407 Unphysical -> True,
408 Indices -> {Index[SU2D], Index[Generation]},
409 FlavorIndex -> SU2D,
410 SelfConjugate -> False,
411 QuantumNumbers -> {Y -> -1/2}
412 },
413
414 F[12] == {
415 ClassName -> lR,
416 Unphysical -> True,
417 Indices -> {Index[Generation]},
418 FlavorIndex -> Generation,
419 SelfConjugate -> False,
420 QuantumNumbers -> {Y -> -1}
421 },
422
423 F[13] == {
424 ClassName -> QL,
425 Unphysical -> True,
426 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
427 FlavorIndex -> SU2D,
428 SelfConjugate -> False,
429 QuantumNumbers -> {Y -> 1/6}
430 },
431
432 F[14] == {
433 ClassName -> uR,
434 Unphysical -> True,
435 Indices -> {Index[Generation], Index[Colour]},
436 FlavorIndex -> Generation,
437 SelfConjugate -> False,
438 QuantumNumbers -> {Y -> 2/3}
439 },
440
441 F[15] == {
442 ClassName -> dR,
443 Unphysical -> True,
444 Indices -> {Index[Generation], Index[Colour]},
445 FlavorIndex -> Generation,
446 SelfConjugate -> False,
447 QuantumNumbers -> {Y -> -1/3}
448 },
449
450(* Higgs unphysical scalars *)
451(* Unphysical scalar fields *)
452
453 S[100] == {
454 ClassName -> phi1,
455 Unphysical -> True,
456 SelfConjugate -> False,
457 Indices -> {Index[SU2D]},
458 FlavorIndex -> SU2D,
459 QuantumNumbers-> {Y -> 1/2}
460 },
461
462 S[101] == {
463 ClassName -> phi2,
464 Unphysical -> True,
465 SelfConjugate -> False,
466 Indices -> {Index[SU2D]},
467 FlavorIndex -> SU2D,
468 QuantumNumbers-> {Y -> 1/2}
469 },
470
471 S[110] == {
472 ClassName -> H0,
473 Unphysical -> True,
474 SelfConjugate -> True
475 },
476
477 S[111] == {
478 ClassName -> R0,
479 Unphysical -> True,
480 SelfConjugate -> True
481 },
482
483 S[112] == {
484 ClassName -> I0,
485 Unphysical -> True,
486 SelfConjugate -> True
487 },
488
489
490(* Higgs physical scalars *)
491
492 S[103] == {
493 ClassName -> G0,
494 SelfConjugate -> True,
495 ParticleName -> "G0"
496 },
497
498 S[104] == {
499 ClassName -> H,
500 SelfConjugate -> True,
501 Indices -> {Index[Higgs]},
502 FlavorIndex -> Higgs,
503 ClassMembers -> {h1, h2, h3},
504 PDG -> {25, 35, 36}
505
506 },
507
508 S[105] == {
509 ClassName -> HP1,
510 SelfConjugate -> False,
511 QuantumNumbers -> {Q -> 1},
512 ParticleName -> "h1+",
513 AntiParticleName -> "h1-",
514 PDG -> 100004
515
516 },
517
518 S[106] == {
519 ClassName -> HP2,
520 SelfConjugate -> False,
521 QuantumNumbers -> {Q -> 1},
522 ParticleName -> "h2+",
523 AntiParticleName -> "h2-",
524 PDG -> 100005
525 }
526};
527
528
529(* ************************** *)
530(* ***** Parameters ***** *)
531(* ************************** *)
532M$Parameters = {
533
534(* External parameters *)
535 aEWM1 == {
536 ParameterType -> External,
537 BlockName -> SMINPUTS,
538 OrderBlock -> 1,
539 Value -> 127.9,
540 InteractionOrder -> {QED,-2},
541 Description -> "Inverse of the EW coupling constant at the Z pole"
542 },
543
544 Gf == {
545 ParameterType -> External,
546 BlockName -> SMINPUTS,
547 OrderBlock -> 2,
548 Value -> 1.16637*^-5,
549 InteractionOrder -> {QED,2},
550 TeX -> Subscript[G,f],
551 Description -> "Fermi constant"
552 },
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
564 ymdo == {
565 ParameterType -> External,
566 BlockName -> YUKAWA,
567 OrderBlock -> 1,
568 Value -> 5.04*^-3,
569 Description -> "Down Yukawa mass"
570 },
571
572 ymup == {
573 ParameterType -> External,
574 BlockName -> YUKAWA,
575 OrderBlock -> 2,
576 Value -> 2.55*^-3,
577 Description -> "Up Yukawa mass"
578 },
579
580 yms == {
581 ParameterType -> External,
582 BlockName -> YUKAWA,
583 OrderBlock -> 3,
584 Value -> 0.101,
585 Description -> "Strange Yukawa mass"
586 },
587
588 ymc == {
589 ParameterType -> External,
590 BlockName -> YUKAWA,
591 OrderBlock -> 4,
592 Value -> 1.27,
593 Description -> "Charm Yukawa mass"
594 },
595
596 ymb == {
597 ParameterType -> External,
598 BlockName -> YUKAWA,
599 OrderBlock -> 5,
600 Value -> 4.7,
601 Description -> "Bottom Yukawa mass"
602 },
603
604 ymt == {
605 ParameterType -> External,
606 BlockName -> YUKAWA,
607 OrderBlock -> 6,
608 Value -> 172,
609 Description -> "Top Yukawa mass"
610 },
611
612 yme == {
613 ParameterType -> External,
614 BlockName -> YUKAWA,
615 OrderBlock -> 11,
616 Value -> 5.11*^-4,
617 Description -> "Electron Yukawa mass"
618 },
619
620 ymm == {
621 ParameterType -> External,
622 BlockName -> YUKAWA,
623 OrderBlock -> 13,
624 Value -> 0.10566,
625 Description -> "Muon Yukawa mass"
626 },
627
628 ymtau == {
629 ParameterType -> External,
630 BlockName -> YUKAWA,
631 OrderBlock -> 15,
632 Value -> 1.777,
633 Description -> "Tau Yukawa mass"
634 },
635
636 cabi == {
637 ParameterType -> External,
638 BlockName -> CKMBLOCK,
639 OrderBlock -> 1,
640 Value -> 0.227736,
641 TeX -> Subscript[\[Theta], c],
642 Description -> "Cabibbo angle"
643 },
644
645 (*Adam Modifs: 09/17/12*)
646
647 gw == {
648 ParameterType -> External,
649 BlockName -> Gauge,
650 OrderBlock -> 2,
651 Value -> 0.663922,
652 InteractionOrder -> {QED,1},
653 TeX -> Subscript[g,w],
654 Description -> "Weak coupling constant at the Z pole"
655 },
656
657 g1 == {
658 ParameterType -> External,
659 BlockName -> Gauge,
660 OrderBlock -> 1,
661 Value -> 0.355574,
662 InteractionOrder -> {QED,1},
663 TeX -> Subscript[g,1],
664 Description -> "U(1)Y coupling constant at the Z pole"
665 },
666
667 vev1 == {
668 ParameterType -> External,
669 BlockName -> HMIX,
670 OrderBlock -> 1,
671 InteractionOrder -> {QED,-1},
672 Description -> "vacuum expectation value of the first doublet"
673 },
674
675
676
677 (* Internal Parameters *)
678
679 aEW == {
680 ParameterType -> Internal,
681 Value -> 1/aEWM1,
682 InteractionOrder -> {QED,2},
683 TeX -> Subscript[\[Alpha], EW],
684 Description -> "Electroweak coupling contant"
685 },
686
687 ee == {
688 ParameterType -> Internal,
689 Value -> Sqrt[4 Pi aEW],
690 InteractionOrder -> {QED,1},
691 TeX -> e,
692 Description -> "Electric coupling constant"
693 },
694
695 gs == {
696 ParameterType -> Internal,
697 Value -> Sqrt[4*Pi*aS],
698 InteractionOrder -> {QCD,1},
699 TeX -> Subscript[g,s],
700 ParameterName -> G,
701 Description -> "Strong coupling constant at the Z pole"
702 },
703
704(*Internal parameters: Yukawa's*)
705
706 yl1 == {
707 ParameterType -> Internal,
708 Indices -> {Index[Generation], Index[Generation]},
709 Definitions -> {yl1[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
710 Value -> {yl1[1,1] -> Sqrt[2] yme/vev1, yl1[2,2] -> Sqrt[2] ymm/vev1, yl1[3,3] -> Sqrt[2] ymtau/vev1},
711 InteractionOrder -> {QED, 1},
712 ParameterName -> {yl1[1,1] -> ye, yl1[2,2] -> ym, yl1[3,3] -> ytau},
713 TeX -> Superscript[y, l1],
714 Description -> "Lepton Yukawa couplings"
715 },
716
717 yu1 == {
718 ParameterType -> Internal,
719 Indices -> {Index[Generation], Index[Generation]},
720 Definitions -> {yu1[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
721 Value -> {yu1[1,1] -> Sqrt[2] ymup/vev1, yu1[2,2] -> Sqrt[2] ymc/vev1, yu1[3,3] -> Sqrt[2] ymt/vev1},
722 InteractionOrder -> {QED, 1},
723 ParameterName -> {yu1[1,1] -> yup, yu1[2,2] -> yc, yu1[3,3] -> yt},
724 TeX -> Superscript[y, u1],
725 Description -> "Up-type Yukawa couplings"
726 },
727
728 yd1 == {
729 ParameterType -> Internal,
730 Indices -> {Index[Generation], Index[Generation]},
731 Definitions -> {yd1[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
732 Value -> {yd1[1,1] -> Sqrt[2] ymdo/vev1, yd1[2,2] -> Sqrt[2] yms/vev1, yd1[3,3] -> Sqrt[2] ymb/vev1},
733 InteractionOrder -> {QED, 1},
734 ParameterName -> {yd1[1,1] -> ydo, yd1[2,2] -> ys, yd1[3,3] -> yb},
735 TeX -> Superscript[y, d1],
736 Description -> "Down-type Yukawa couplings"
737 },
738
739 yl2 == {
740 ParameterType -> Internal,
741 Indices -> {Index[Generation], Index[Generation]},
742 Definitions -> {yl2[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
743 Value -> {yl2[1,1] -> Sqrt[2] yme/vev1, yl2[2,2] -> Sqrt[2] ymm/vev1, yl2[3,3] -> Sqrt[2] ymtau/vev1},
744 InteractionOrder -> {QED, 1},
745 ParameterName -> {yl2[1,1] -> ye, yl2[2,2] -> ym, yl2[3,3] -> ytau},
746 TeX -> Superscript[y, l2],
747 Description -> "Lepton Yukawa couplings"
748 },
749
750 yu2 == {
751 ParameterType -> Internal,
752 Indices -> {Index[Generation], Index[Generation]},
753 Definitions -> {yu2[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
754 Value -> {yu2[1,1] -> Sqrt[2] ymup/vev1, yu2[2,2] -> Sqrt[2] ymc/vev1, yu2[3,3] -> Sqrt[2] ymt/vev1},
755 InteractionOrder -> {QED, 1},
756 ParameterName -> {yu2[1,1] -> yup, yu2[2,2] -> yc, yu2[3,3] -> yt},
757 TeX -> Superscript[y, u2],
758 Description -> "Up-type Yukawa couplings"
759 },
760
761 yd2 == {
762 ParameterType -> Internal,
763 Indices -> {Index[Generation], Index[Generation]},
764 Definitions -> {yd2[i_?NumericQ, j_?NumericQ] :> 0. /; (i =!= j)},
765 Value -> {yd2[1,1] -> Sqrt[2] ymdo/vev1, yd2[2,2] -> Sqrt[2] yms/vev1, yd2[3,3] -> Sqrt[2] ymb/vev1},
766 InteractionOrder -> {QED, 1},
767 ParameterName -> {yd2[1,1] -> ydo, yd2[2,2] -> ys, yd2[3,3] -> yb},
768 TeX -> Superscript[y, d2],
769 Description -> "Down-type Yukawa couplings"
770 },
771
772
773(* Higgs potential parameters *)
774
775 lambda1 == {
776 BlockName -> Higgs,
777 OrderBlock -> 1,
778 ComplexParameter -> False,
779 Value -> 1,
780 ParameterType -> External
781 },
782
783 lambda2 == {
784 BlockName -> Higgs,
785 OrderBlock -> 2,
786 ComplexParameter -> False,
787 Value -> 1,
788 ParameterType -> External
789 },
790
791 lambda3 == {
792 BlockName -> Higgs,
793 OrderBlock -> 3,
794 ComplexParameter -> False,
795 Value -> 1,
796 ParameterType -> External
797 },
798
799 lambda4 == {
800 BlockName -> Higgs,
801 OrderBlock -> 4,
802 ComplexParameter -> False,
803 Value -> 1,
804 ParameterType -> External
805 },
806
807 lambda5 == {
808 ComplexParameter -> False,
809 OrderBlock -> 5,
810 ParameterType -> External,
811 BlockName -> Higgs,
812 Value -> 1,
813 Description -> "lambda5"
814 },
815
816 lambda6R == {
817 BlockName -> Higgs,
818 OrderBlock -> 6,
819 ComplexParameter -> False,
820 ParameterType -> External,
821 Value -> 1,
822 Description -> "real part of lambda6"
823 },
824
825 lambda6I == {
826 BlockName -> Higgs,
827 OrderBlock -> 7,
828 ComplexParameter -> False,
829 ParameterType -> External,
830 Value -> 1,
831 Description -> "imaginary part of lambda6"
832 },
833
834 lambda6 == {
835 ComplexParameter -> True,
836 ParameterType -> Internal,
837 Value -> lambda6R + I*lambda6I,
838 Description -> "lambda6"
839 },
840
841 lambda7R == {
842 BlockName -> Higgs,
843 OrderBlock -> 8,
844 ComplexParameter -> False,
845 ParameterType -> External,
846 Value -> 1,
847 Description -> "real part of lambda6"
848 },
849
850 lambda7I == {
851 BlockName -> Higgs,
852 OrderBlock -> 9,
853 ComplexParameter -> False,
854 ParameterType -> External,
855 Value -> 1,
856 Description -> "imaginary part of lambda6"
857 },
858
859 lambda7 == {
860 ParameterType -> Internal,
861 ComplexParameter -> True,
862 Value -> lambda7R + I*lambda7I,
863 Description -> "lambda7"
864 },
865
866 mu1 == {
867 ComplexParameter -> False,
868 ParameterType -> Internal,
869 Value -> -lambda1*vev1^2,
870 Description -> "mu1"
871 },
872
873 mu2 == {
874 BlockName -> Higgs,
875 OrderBlock -> 10,
876 ComplexParameter -> False,
877 ParameterType -> External,
878 Value -> 1,
879 Description -> "mu2"
880 },
881
882 mu3 == {
883 ComplexParameter -> True,
884 ParameterType -> Internal,
885 Value -> -lambda6*vev1^2/2,
886 Description -> "mu3"
887 },
888
889(* N. B. : only Cabibbo mixing! *)
890 CKM == {
891 ParameterType -> Internal,
892 Indices -> {Index[Generation], Index[Generation]},
893 Unitary -> True,
894 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
895 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
896 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
897 TeX -> Superscript[V,CKM],
898 Description -> "CKM-Matrix"}
899
900};
901
902(* ************************** *)
903(* ***** Lagrangian ***** *)
904(* ************************** *)
905
906
907LGauge := Block[{mu,nu,ii,aa},
908 -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] ];
909
910LFermions := Block[{mu},
911 I*(
912 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])];
913
914LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk},
915
916 yuk =
917 - yd1[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] phi1[ii]
918 - yl1[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] phi1[ii]
919 - yu1[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] phi1bar[jj] Eps[ii, jj];
920
921 yuk +=
922 - yd2[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] phi2[ii]
923 - yl2[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] phi2[ii]
924 - yu2[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] phi2bar[jj] Eps[ii, jj];
925
926 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
927
928 yuk += HC[yuk]
929];
930
931LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
932 (* Pure gauge piece *)
933 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
934 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
935 LGhs = -ghGbar.del[DC[ghG,mu],mu];
936
937 (* Scalar pieces: see Peskin pages 739-742 *)
938 (* phi1 and phi2 are the real degrees of freedom of GP *)
939 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
940
941 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
942 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
943 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
944 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], phi2} /. MR$Definitions /. vev -> 0];
945 doublet0 = {0, vev/Sqrt[2]};
946 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}];
947 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
948 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
949
950LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0]];
951
952(* 2HDM potential *)
953
954LHiggsKin := Block[{ii, mu},
955DC[phi1bar[ii], mu] DC[phi1[ii], mu] +
956DC[phi2bar[ii], mu] DC[phi2[ii], mu]
957];
958
959P1 = {phi1[1], phi1[2]};
960P2 = {phi2[1], phi2[2]};
961
962P1bar = HC[P1];
963P2bar = HC[P2];
964
965P11 = HC[P1].P1;
966P12 = HC[P1].P2;
967P21 = HC[P2].P1;
968P22 = HC[P2].P2;
969
970V2HDM := mu1 P11 +mu2 P22 +mu3 P12 +HC[mu3] P21 +
971 lambda1 P11^2 + lambda2 P22^2 + lambda3 P11 P22 +
972 lambda4 P12 P21 + lambda5 P12^2 + Conjugate[lambda5] P21^2 +
973 P11 (lambda6 P12+ Conjugate[lambda6] P21) + P22 (lambda7 P12+ Conjugate[lambda7]P21);
974
975LHiggs := LHiggsKin - V2HDM;
976
977L2HDM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;