TechniColor: MWT_101030.fr

File MWT_101030.fr, 30.9 KB (added by CP3-Origins, 15 years ago)

MWT FeynRules file

Line 
1
2(* This is the model file for (N)MWT Unitary gauge *)
3
4M$ModelName = "MWT";
5
6M$Information = {Authors -> "M. Jarvinen",
7 Date -> "30. 10. 2010",
8 Version -> 1.0
9 };
10
11
12(* Index definition *)
13
14IndexRange[ Index[Generation] ] = Range[3]
15
16IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
17
18IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
19
20
21IndexRange[ Index[FixedChargedVector] ] = Range[3]
22IndexRange[ Index[ChargedVector] ] = Range[3]
23IndexRange[ Index[FixedNeutralVector] ] = Range[4]
24IndexRange[ Index[NeutralVector] ] = Range[4]
25IndexRange[ Index[SU2Index] ] = Range[2]
26IndexRange[ Index[SU2Adjoint] ] = Range[3]
27
28
29IndexFormat[ChargedVector, f]
30IndexFormat[NeutralVector, f]
31IndexFormat[SU2Index, i]
32IndexFormat[SU2Adjoint, k]
33IndexStyle[Colour, i]
34IndexStyle[Generation, f]
35IndexStyle[Gluon ,a]
36
37
38
39(* Parameter list *)
40
41M$Parameters = {
42
43 \[Alpha]S == {
44 ParameterType -> External,
45 BlockName -> SMInput,
46 TeX -> Subscript[\[Alpha], s],
47 ParameterName -> aS,
48 InteractionOrder -> {QCD, 2},
49 Value -> 0.118,
50 Description -> "Strong coupling constant at the Z pole"},
51
52
53 EE == {
54 InteractionOrder -> {QED, 1},
55 ParameterType -> External,
56 Value -> 0.313429,
57 TeX -> e,
58 BlockName -> SMInput,
59 Description -> "Electron charge"
60 },
61
62
63 GF == {
64 InteractionOrder -> {QED, 2},
65 ParameterType -> External,
66 Value -> 0.0000116637,
67 TeX -> Subscript[G, F],
68 BlockName -> SMInput,
69 Description -> "Fermi coupling constant"
70 },
71
72 MZ == {
73 ParameterType -> External,
74 Value -> 91.1876,
75 TeX -> Subscript[M, Z],
76 BlockName -> SMInput,
77 Description -> "Z Mass"
78 },
79
80
81 gt == {
82 InteractionOrder -> {QED, 1},
83 ParameterType -> External,
84 Value -> 2,
85 TeX -> Subscript[g, t],
86 BlockName -> TCInput,
87 Description -> "g^tilde"
88 },
89
90 MA == {
91 ParameterType -> External,
92 Value -> 750,
93 TeX -> Subscript[M, A],
94 BlockName -> TCInput,
95 Description -> "mass of the axial"
96 },
97
98 PS == {
99 ParameterType -> External,
100 Value -> 0.3,
101 BlockName -> TCInput,
102 Description -> "S parameter"
103 },
104
105 rs == {
106 ParameterType -> External,
107 Value -> 0.,
108 TeX -> Subscript[r, s],
109 BlockName -> TCInput,
110 Description -> "C-M parameter"
111 },
112
113 MH == {
114 ParameterType -> External,
115 Value -> 200,
116 TeX -> Subscript[M, H],
117 BlockName -> TCInput,
118 Description -> "Higgs Mass"
119 },
120
121 MC == {
122 ParameterType -> External,
123 BlockName -> YUKAWA,
124 Value -> 1.3,
125 OrderBlock -> {4},
126 Description -> "Charm quark mass"},
127
128 MB == {
129 ParameterType -> External,
130 BlockName -> YUKAWA,
131 Value -> 4.2,
132 OrderBlock -> {5},
133 Description -> "Bottom quark mass"},
134
135 MT == {
136 ParameterType -> External,
137 BlockName -> YUKAWA,
138 Value -> 172,
139 OrderBlock -> {6},
140 Description -> "Top quark mass"},
141
142 MTA == {
143 ParameterType -> External,
144 BlockName -> YUKAWA,
145 Value -> 1.777,
146 OrderBlock -> {15},
147 Description -> "Tau lepton mass"},
148
149
150 gs == {
151 InteractionOrder -> {QCD, 1},
152 ParameterType -> Internal,
153 Value -> Sqrt[4 Pi \[Alpha]S],
154 TeX -> Subscript[g, s],
155 ParameterName -> G,
156 BlockName -> Constr,
157 Description -> "Strong coupling constant (Z point)"
158 },
159
160 v == {
161 ParameterType -> Internal,
162 Value -> Sqrt[gt^2*(2*Sqrt[2]*Pi - GF*MA^2*PS) - 4*GF*MA^2*(-4*Pi + Sqrt[2*Pi]*Sqrt[8*Pi - gt^2*PS])]/(2*Sqrt[GF*gt^2]*Sqrt[Pi]),
163 BlockName -> Constr,
164 InteractionOrder -> {QED, -1},
165 Description -> "SM VEV"
166 },
167
168 r3 == {
169 ParameterType -> Internal,
170 Value -> (-4*GF*MA^2*(-4*Pi + Sqrt[2*Pi]*Sqrt[8*Pi - gt^2*PS]))/(gt^2*(2*Sqrt[2]*Pi - GF*MA^2*PS) - 4*GF*MA^2*(-4*Pi + Sqrt[2*Pi]*Sqrt[8*Pi - gt^2*PS])),
171 TeX -> Subscript[r,3],
172 BlockName -> Constr,
173 Description -> "C-M parameter"
174 },
175
176 r2 == {
177 ParameterType -> Internal,
178 Value -> r3-1,
179 TeX -> Subscript[r,2],
180 BlockName -> Constr,
181 Description -> "C-M parameter"
182 },
183
184 f == {
185 ParameterType -> Internal,
186 Value -> Sqrt[(16*GF*MA^2*Pi + gt^2*(2*Sqrt[2]*Pi - GF*MA^2*PS))/(GF*gt^2)]/(2*Sqrt[Pi]),
187 BlockName -> Constr,
188 Description -> "Vector meson mass scale"
189 },
190
191 MV == {
192 ParameterType -> Internal,
193 Value -> Sqrt[gt^2/(2*Sqrt[2]*GF) + MA^2*(1 - (gt^2*PS)/(8*Pi))],
194 BlockName -> IntConstr,
195 Description -> "Strong vector meson mass"
196 },
197
198 FV == {
199 ParameterType -> Internal,
200 Value -> Sqrt[2]*MV/gt,
201 BlockName -> IntConstr,
202 Description -> "Strong vector decay constant"
203 },
204
205 FPi == {
206 ParameterType -> Internal,
207 Value -> 1/Sqrt[Sqrt[2]*GF],
208 BlockName -> IntConstr,
209 Description -> "Strong pion decay constant"
210 },
211
212 FA == {
213 ParameterType -> Internal,
214 Value -> Sqrt[FV^2-FPi^2],
215 BlockName -> IntConstr,
216 Description -> "Strong axial decay constant"
217 },
218
219
220 ZM == {
221 ParameterType -> Internal,
222 Value -> MZ,
223 BlockName -> InternalMasses,
224 Description -> "Z mass"
225 },
226
227 g2 == {
228 InteractionOrder -> {QED, 1},
229 ParameterType -> Internal,
230 Value-> Sqrt[2]/Sqrt[EE^(-2) - 2/gt^2 + Sqrt[MZ^2*(MA^2 - MZ^2)*(MV^2 - MZ^2)*(FV^2 + (EE^(-2) - 2/gt^2)*(MV^2 - MZ^2))*(FA^2*MA^2 + (MA^2 - MZ^2)*(-FV^2 + MZ^2/EE^2 - (2*MZ^2)/gt^2))]/(MZ^2*(MA^2 - MZ^2)*(-MV^2 + MZ^2))],
231 TeX -> Subscript[g,2],
232 BlockName -> Constr,
233 Description -> "Electroweak SU2L gauge coupling"
234 },
235
236 g1 == {
237 InteractionOrder -> {QED, 1},
238 ParameterType -> Internal,
239 Value-> 1/Sqrt[1/EE^2 - 1/g2^2 - 2/gt^2],
240 TeX -> Subscript[g,1],
241 BlockName -> Constr,
242 Description -> "Electroweak U1Y gauge coupling"
243 },
244
245
246 M1N == {
247 ParameterType -> Internal,
248 Value -> Sqrt[(FV^2*(g1^2 + g2^2) + 2*(MA^2 + MV^2))*MZ^2 - 2*MZ^4 - Sqrt[-16*FPi^2*MA^2*(FV^2*g1^2*g2^2 + (g1^2 + g2^2)*MV^2)*MZ^2 + 4*MZ^4*(FV^2*(g1^2 + g2^2) + 2*(MA^2 + MV^2 - MZ^2))^2]/2]/(2*MZ),
249 BlockName -> InternalMasses,
250 Description -> "Neutral heavy vector meson R1 mass"
251 },
252
253 M2N == {
254 ParameterType -> Internal,
255 Value -> Sqrt[(FV^2*(g1^2 + g2^2) + 2*(MA^2 + MV^2))*MZ^2 - 2*MZ^4 + Sqrt[-16*FPi^2*MA^2*(FV^2*g1^2*g2^2 + (g1^2 + g2^2)*MV^2)*MZ^2 + 4*MZ^4*(FV^2*(g1^2 + g2^2) + 2*(MA^2 + MV^2 - MZ^2))^2]/2]/(2*MZ),
256 BlockName -> InternalMasses,
257 Description -> "Neutral heavy vector meson R2 mass"
258 },
259
260 ThetaC == {
261 ParameterType -> Internal,
262 Value -> ArcCos[(2*FV^6*g2^6 + 3*FV^4*g2^4*(MA^2 + MV^2) + 2*(MA^2 - 2*MV^2)*(-9*FPi^2*g2^2*MA^2 + 8*MA^4 + 4*MA^2*MV^2 - 4*MV^4) + 3*FV^2*g2^2*(-3*FPi^2*g2^2*MA^2 + 2*(MA^4 - 4*MA^2*MV^2 + MV^4)))/ (2*(FV^4*g2^4 - 3*FPi^2*g2^2*MA^2 + FV^2*g2^2*(MA^2 + MV^2) + 4*(MA^4 - MA^2*MV^2 + MV^4))^(3/2))],
263 BlockName -> IntConstr,
264 Description -> "Charged vector meson mass angle"
265 },
266
267 MW == {
268 ParameterType -> Internal,
269 Value -> Sqrt[((FV^2*g2^2)/2 + MA^2 + MV^2)/3 - (Sqrt[FV^4*g2^4 + 3*FA^2*g2^2*MA^2 + FV^2*g2^2*(-2*MA^2 + MV^2) + 4*(MA^4 - MA^2*MV^2 + MV^4)]*Sin[Pi/6 + ThetaC/3])/3],
270 BlockName -> InternalMasses,
271 Description -> "W mass"
272 },
273
274
275 M1C == {
276 ParameterType -> Internal,
277 Value -> Sqrt[((FV^2*g2^2)/2 + MA^2 + MV^2)/3 - (Sqrt[FV^4*g2^4 + 3*FA^2*g2^2*MA^2 + FV^2*g2^2*(-2*MA^2 + MV^2) + 4*(MA^4 - MA^2*MV^2 + MV^4)]*Sin[Pi/6 - ThetaC/3])/3],
278 BlockName -> InternalMasses,
279 Description -> "Charged heavy vector meson R1 mass"
280 },
281
282 M2C == {
283 ParameterType -> Internal,
284 Value -> Sqrt[((FV^2*g2^2)/2 + MA^2 + MV^2)/3 + (Sqrt[FV^4*g2^4 + 3*FA^2*g2^2*MA^2 + FV^2*g2^2*(-2*MA^2 + MV^2) + 4*(MA^4 - MA^2*MV^2 + MV^4)]*Cos[ThetaC/3])/3],
285 BlockName -> InternalMasses,
286 Description -> "Charged heavy vector meson R2 mass"
287 },
288
289 HM == {
290 ParameterType -> Internal,
291 Value -> MH,
292 BlockName -> InternalMasses,
293 Description -> "Higgs Mass"
294 },
295
296 CM == {
297 ParameterType -> Internal,
298 BlockName -> InternalMasses,
299 Value -> MC,
300 Description -> "Charm mass"},
301
302 BM == {
303 ParameterType -> Internal,
304 BlockName -> InternalMasses,
305 Value -> MB,
306 Description -> "Bottom mass"},
307
308 TM == {
309 ParameterType -> Internal,
310 BlockName -> InternalMasses,
311 Value -> MT,
312 Description -> "Top mass"},
313
314 TAM == {
315 ParameterType -> Internal,
316 BlockName -> InternalMasses,
317 Value -> MTA,
318 Description -> "Tau mass"},
319
320 VC11 == {
321 ParameterType -> Internal,
322 Value -> g2^2*FV^2/2,
323 BlockName -> Mixing
324 },
325
326 VC12 == {
327 ParameterType -> Internal,
328 Value -> -g2*FA*MA/2,
329 BlockName -> Mixing
330 },
331
332 VC13 == {
333 ParameterType -> Internal,
334 Value -> -g2*FV*MV/2,
335 BlockName -> Mixing
336 },
337
338 VC21 == {
339 ParameterType -> Internal,
340 Value -> VC12,
341 BlockName -> Mixing
342 },
343
344 VC22 == {
345 ParameterType -> Internal,
346 Value -> MA^2,
347 BlockName -> Mixing
348 },
349
350 VC23 == {
351 ParameterType -> Internal,
352 Value -> 0,
353 BlockName -> Mixing
354 },
355
356 VC31 == {
357 ParameterType -> Internal,
358 Value -> VC13,
359 BlockName -> Mixing
360 },
361
362 VC32 == {
363 ParameterType -> Internal,
364 Value -> 0,
365 BlockName -> Mixing
366 },
367
368 VC33 == {
369 ParameterType -> Internal,
370 Value -> MV^2,
371 BlockName -> Mixing
372 },
373
374 VN11 == {
375 ParameterType -> Internal,
376 Value -> g1^2*FV^2/2 ,
377 BlockName -> Mixing
378 },
379
380 VN12 == {
381 ParameterType -> Internal,
382 Value -> 0 ,
383 BlockName -> Mixing
384 },
385
386 VN13 == {
387 ParameterType -> Internal,
388 Value -> g1*FA*MA/2,
389 BlockName -> Mixing
390 },
391
392 VN14 == {
393 ParameterType -> Internal,
394 Value -> -g1*FV*MV/2,
395 BlockName -> Mixing
396 },
397
398 VN21 == {
399 ParameterType -> Internal,
400 Value -> 0,
401 BlockName -> Mixing
402 },
403
404 VN22 == {
405 ParameterType -> Internal,
406 Value -> g2^2*FV^2/2,
407 BlockName -> Mixing
408 },
409
410 VN23 == {
411 ParameterType -> Internal,
412 Value -> -g2*FA*MA/2,
413 BlockName -> Mixing
414 },
415
416 VN24 == {
417 ParameterType -> Internal,
418 Value -> -g2*FV*MV/2,
419 BlockName -> Mixing
420 },
421
422 VN31 == {
423 ParameterType -> Internal,
424 Value -> VN13,
425 BlockName -> Mixing
426 },
427
428 VN32 == {
429 ParameterType -> Internal,
430 Value -> VN23,
431 BlockName -> Mixing
432 },
433
434 VN33 == {
435 ParameterType -> Internal,
436 Value -> MA^2,
437 BlockName -> Mixing
438 },
439
440 VN34 == {
441 ParameterType -> Internal,
442 Value -> 0,
443 BlockName -> Mixing
444 },
445
446 VN41 == {
447 ParameterType -> Internal,
448 Value -> VN14,
449 BlockName -> Mixing
450 },
451
452 VN42 == {
453 ParameterType -> Internal,
454 Value -> VN24,
455 BlockName -> Mixing
456 },
457
458 VN43 == {
459 ParameterType -> Internal,
460 Value -> 0,
461 BlockName -> Mixing
462 },
463
464 VN44 == {
465 ParameterType -> Internal,
466 Value -> MV^2,
467 BlockName -> Mixing
468 },
469
470
471 CN1 == {
472 ParameterType -> Internal,
473 Description -> "Charged vector meson normalization factor",
474 Value -> 1/Sqrt[(-MW^2 + VC22)^2*VC13^2 + VC12^2*(MW^2 - VC33)^2 + (-MW^2 + VC22)^2*(MW^2 - VC33)^2],
475 BlockName -> Mixing
476 },
477
478 CN2 == {
479 ParameterType -> Internal,
480 Description -> "Charged vector meson normalization factor",
481 Value -> 1/Sqrt[(-M1C^2 + VC22)^2*VC13^2 + VC12^2*(M1C^2 - VC33)^2 + (-M1C^2 + VC22)^2*(M1C^2 - VC33)^2],
482 BlockName -> Mixing
483 },
484
485 CN3 == {
486 ParameterType -> Internal,
487 Description -> "Charged vector meson normalization factor",
488 Value -> 1/Sqrt[(-M2C^2 + VC22)^2*VC13^2 + VC12^2*(M2C^2 - VC33)^2 + (-M2C^2 + VC22)^2*(M2C^2 - VC33)^2],
489 BlockName -> Mixing
490 },
491
492
493 C11 == {
494 ParameterType -> Internal,
495 Description -> "Charged vector meson mixing matrix element in VA base",
496 Value -> (-MW^2 + VC22)*(-MW^2 + VC33)*CN1,
497 BlockName -> Mixing
498 },
499
500 C12 == {
501 ParameterType -> Internal,
502 Description -> "Charged vector meson mixing matrix element in VA base",
503 Value -> (-M1C^2 + VC22)*(-M1C^2 + VC33)*CN2,
504 BlockName -> Mixing
505 },
506
507 C13 == {
508 ParameterType -> Internal,
509 Description -> "Charged vector meson mixing matrix element in VA base",
510 Value -> (-M2C^2 + VC22)*(-M2C^2 + VC33)*CN3,
511 BlockName -> Mixing
512 },
513
514 C21 == {
515 ParameterType -> Internal,
516 Description -> "Charged vector meson mixing matrix element in VA base",
517 Value -> VC12*(MW^2 - VC33)*CN1,
518 BlockName -> Mixing
519 },
520
521 C22 == {
522 ParameterType -> Internal,
523 Description -> "Charged vector meson mixing matrix element in VA base",
524 Value -> VC12*(M1C^2 - VC33)*CN2,
525 BlockName -> Mixing
526 },
527
528 C23 == {
529 ParameterType -> Internal,
530 Description -> "Charged vector meson mixing matrix element in VA base",
531 Value -> VC12*(M2C^2 - VC33)*CN3,
532 BlockName -> Mixing
533 },
534
535 C31 == {
536 ParameterType -> Internal,
537 Description -> "Charged vector meson mixing matrix element in VA base",
538 Value -> (MW^2 - VC22)*VC13*CN1,
539 BlockName -> Mixing
540 },
541
542 C32 == {
543 ParameterType -> Internal,
544 Description -> "Charged vector meson mixing matrix element in VA base",
545 Value -> (M1C^2 - VC22)*VC13*CN2,
546 BlockName -> Mixing
547 },
548
549 C33 == {
550 ParameterType -> Internal,
551 Description -> "Charged vector meson mixing matrix element in VA base",
552 Value -> (M2C^2 - VC22)*VC13*CN3,
553 BlockName -> Mixing
554 },
555
556 NN2 == {
557 ParameterType -> Internal,
558 Description -> "Neutral vector meson normalization factor",
559 Value -> 1/Sqrt[(g1 - g2)^2*(g1 + g2)^2*gt^2*(MZ^2 - VN33)^2*VN24^2 + g1^2*g2^2*(MZ^2 - VN33)^2*(Sqrt[2]*g2*VN24 + gt*(MZ^2 - VN44))^2 + g2^2*(MZ^2 - VN33)^2*(Sqrt[2]*g1^2*VN24 + g2*gt*(MZ^2 - VN44))^2 + VN23^2*(2*Sqrt[2]*g1^2*g2*VN24 + (g1^2 + g2^2)*gt*(MZ^2 - VN44))^2],
560 BlockName -> Mixing
561 },
562
563 NN3 == {
564 ParameterType -> Internal,
565 Description -> "Neutral vector meson normalization factor",
566 Value -> 1/Sqrt[(g1 - g2)^2*(g1 + g2)^2*gt^2*(M1N^2 - VN33)^2*VN24^2 + g1^2*g2^2*(M1N^2 - VN33)^2*(Sqrt[2]*g2*VN24 + gt*(M1N^2 - VN44))^2 + g2^2*(M1N^2 - VN33)^2*(Sqrt[2]*g1^2*VN24 + g2*gt*(M1N^2 - VN44))^2 + VN23^2*(2*Sqrt[2]*g1^2*g2*VN24 + (g1^2 + g2^2)*gt*(M1N^2 - VN44))^2],
567 BlockName -> Mixing
568 },
569
570 NN4 == {
571 ParameterType -> Internal,
572 Description -> "Neutral vector meson normalization factor",
573 Value -> 1/Sqrt[(g1 - g2)^2*(g1 + g2)^2*gt^2*(M2N^2 - VN33)^2*VN24^2 + g1^2*g2^2*(M2N^2 - VN33)^2*(Sqrt[2]*g2*VN24 + gt*(M2N^2 - VN44))^2 + g2^2*(M2N^2 - VN33)^2*(Sqrt[2]*g1^2*VN24 + g2*gt*(M2N^2 - VN44))^2 + VN23^2*(2*Sqrt[2]*g1^2*g2*VN24 + (g1^2 + g2^2)*gt*(M2N^2 - VN44))^2],
574 BlockName -> Mixing
575 },
576
577
578 N11 == {
579 ParameterType -> Internal,
580 Description -> "Neutral vector meson mixing matrix element in VA base",
581 Value -> EE/g1,
582 BlockName -> Mixing
583 },
584
585 N12 == {
586 ParameterType -> Internal,
587 Description -> "Neutral vector meson mixing matrix element in VA base",
588 Value -> g1*g2*(-MZ^2 + VN33)*(Sqrt[2]*g2*VN24 + gt*(MZ^2 - VN44))*NN2,
589 BlockName -> Mixing
590 },
591
592 N13 == {
593 ParameterType -> Internal,
594 Description -> "Neutral vector meson mixing matrix element in VA base",
595 Value -> g1*g2*(-M1N^2 + VN33)*(Sqrt[2]*g2*VN24 + gt*(M1N^2 - VN44))*NN3,
596 BlockName -> Mixing
597 },
598
599 N14 == {
600 ParameterType -> Internal,
601 Description -> "Neutral vector meson mixing matrix element in VA base",
602 Value -> g1*g2*(-M2N^2 + VN33)*(Sqrt[2]*g2*VN24 + gt*(M2N^2 - VN44))*NN4,
603 BlockName -> Mixing
604 },
605
606 N21 == {
607 ParameterType -> Internal,
608 Description -> "Neutral vector meson mixing matrix element in VA base",
609 Value -> EE/g2,
610 BlockName -> Mixing
611 },
612
613 N22 == {
614 ParameterType -> Internal,
615 Description -> "Neutral vector meson mixing matrix element in VA base",
616 Value -> -(g2*(-MZ^2 + VN33)*(Sqrt[2]*g1^2*VN24 + g2*gt*(MZ^2 - VN44)))*NN2,
617 BlockName -> Mixing
618 },
619
620 N23 == {
621 ParameterType -> Internal,
622 Description -> "Neutral vector meson mixing matrix element in VA base",
623 Value -> -(g2*(-M1N^2 + VN33)*(Sqrt[2]*g1^2*VN24 + g2*gt*(M1N^2 - VN44)))*NN3,
624 BlockName -> Mixing
625 },
626
627 N24 == {
628 ParameterType -> Internal,
629 Description -> "Neutral vector meson mixing matrix element in VA base",
630 Value -> -(g2*(-M2N^2 + VN33)*(Sqrt[2]*g1^2*VN24 + g2*gt*(M2N^2 - VN44)))*NN4,
631 BlockName -> Mixing
632 },
633
634 N31 == {
635 ParameterType -> Internal,
636 Description -> "Neutral vector meson mixing matrix element in VA base",
637 Value -> 0,
638 BlockName -> Mixing
639 },
640
641 N32 == {
642 ParameterType -> Internal,
643 Description -> "Neutral vector meson mixing matrix element in VA base",
644 Value -> VN23*(2*Sqrt[2]*g1^2*g2*VN24 + (g1^2 + g2^2)*gt*(MZ^2 - VN44))*NN2,
645 BlockName -> Mixing
646 },
647
648 N33 == {
649 ParameterType -> Internal,
650 Description -> "Neutral vector meson mixing matrix element in VA base",
651 Value -> VN23*(2*Sqrt[2]*g1^2*g2*VN24 + (g1^2 + g2^2)*gt*(M1N^2 - VN44))*NN3,
652 BlockName -> Mixing
653 },
654
655 N34 == {
656 ParameterType -> Internal,
657 Description -> "Neutral vector meson mixing matrix element in VA base",
658 Value -> VN23*(2*Sqrt[2]*g1^2*g2*VN24 + (g1^2 + g2^2)*gt*(M2N^2 - VN44))*NN4,
659 BlockName -> Mixing
660 },
661
662 N41 == {
663 ParameterType -> Internal,
664 Description -> "Neutral vector meson mixing matrix element in VA base",
665 Value -> Sqrt[2]*EE/gt,
666 BlockName -> Mixing
667 },
668
669 N42 == {
670 ParameterType -> Internal,
671 Description -> "Neutral vector meson mixing matrix element in VA base",
672 Value -> (g1^2 - g2^2)*gt*(-MZ^2 + VN33)*VN24*NN2,
673 BlockName -> Mixing
674 },
675
676 N43 == {
677 ParameterType -> Internal,
678 Description -> "Neutral vector meson mixing matrix element in VA base",
679 Value -> (g1^2 - g2^2)*gt*(-M1N^2 + VN33)*VN24*NN3,
680 BlockName -> Mixing
681 },
682
683 N44 == {
684 ParameterType -> Internal,
685 Description -> "Neutral vector meson mixing matrix element in VA base",
686 Value -> (g1^2 - g2^2)*gt*(-M2N^2 + VN33)*VN24*NN4,
687 BlockName -> Mixing
688 },
689
690
691
692
693 yl == {
694 Indices -> {Index[Generation]},
695 AllowSummation -> True,
696 ParameterType -> Internal,
697 Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] MTA / v},
698 ParameterName -> {yl[1] -> ye, yl[2] -> ymu, yl[3] -> yta},
699 InteractionOrder -> {QED, 1},
700 ComplexParameter -> False,
701 Definitions -> {yl[1] -> 0, yl[2] ->0},
702 Description -> "Lepton Yukawa coupling"},
703
704 yu == {
705 Indices -> {Index[Generation]},
706 AllowSummation -> True,
707 ParameterType -> Internal,
708 Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] MC / v, yu[3] -> Sqrt[2] MT / v},
709 ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
710 InteractionOrder -> {QED, 1},
711 ComplexParameter -> False,
712 Definitions -> {yu[1] -> 0},
713 Description -> "U-quark Yukawa coupling"},
714
715 yd == {
716 Indices -> {Index[Generation]},
717 AllowSummation -> True,
718 ParameterType -> Internal,
719 Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] MB / v},
720 ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
721 InteractionOrder -> {QED, 1},
722 ComplexParameter -> False,
723 Definitions -> {yd[1] -> 0, yd[2] -> 0},
724 Description -> "D-quark Yukawa coupling"},
725
726 cabi == {
727 TeX -> Subscript[\[Theta], c],
728 ParameterType -> External,
729 BlockName -> CKMBLOCK,
730 OrderBlock -> {1},
731 Value -> 0.227736,
732 Description -> "Cabibbo angle"},
733
734 CKM == {
735 Indices -> {Index[Generation], Index[Generation]},
736 TensorClass -> CKM,
737 Unitary -> True,
738 Definitions -> {CKM[3, 3] -> 1,
739 CKM[i_, 3] :> 0 /; i != 3,
740 CKM[3, i_] :> 0 /; i != 3},
741 Value -> {CKM[1,2] -> Sin[cabi],
742 CKM[1,1] -> Cos[cabi],
743 CKM[2,1] -> -Sin[cabi],
744 CKM[2,2] -> Cos[cabi]},
745 Description -> "CKM-Matrix"},
746
747 CKMT == {
748 Indices -> {Index[Generation], Index[Generation]},
749 TensorClass -> CKM,
750 Unitary -> True,
751 Definitions -> {CKMT[3, 3] -> 1,
752 CKMT[i_, 3] :> 0 /; i != 3,
753 CKMT[3, i_] :> 0 /; i != 3},
754 Value -> {CKMT[1,2] -> -Sin[cabi],
755 CKMT[1,1] -> Cos[cabi],
756 CKMT[2,1] -> Sin[cabi],
757 CKMT[2,2] -> Cos[cabi]},
758 Description -> "Hermitean conjugate of CKM-Matrix"}
759
760}
761
762
763(* Gauge group list *)
764
765M$GaugeGroups = {
766
767 U1Y == {
768 Abelian -> True,
769 GaugeBoson -> B,
770 Charge -> Y,
771 CouplingConstant -> g1},
772
773 SU2L == {
774 Abelian -> False,
775 GaugeBoson -> Wi,
776 StructureConstant -> Eps,
777 CouplingConstant -> g2
778 },
779
780 SU3C == {
781 Abelian -> False,
782 GaugeBoson -> G,
783 StructureConstant -> f,
784 SymmetricTensor -> dSUN,
785 Representations -> {T, Colour},
786 CouplingConstant -> gs}
787
788}
789
790
791Wind=1;ACind=2;VCind=3;
792Aind=1;Zind=2;ANind=3;VNind=4;
793
794CM[1,1] = C11; CM[1,2] = C12;CM[1,3] = C13; CM[2,1] = C21;CM[2,2] = C22;CM[2,3] = C23;CM[3,1] = C31;CM[3,2] = C32;CM[3,3] = C33;
795NM[1,1] = N11; NM[1,2] = N12; NM[1,3] = N13; NM[1,4] = N14; NM[2,1] = N21; NM[2,2] = N22; NM[2,3] = N23; NM[2,4] = N24; NM[3,1] = N31; NM[3,2] = N32; NM[3,3] = N33; NM[3,4] = N34; NM[4,1] = N41; NM[4,2] = N42; NM[4,3] = N43; NM[4,4] = N44;
796
797(* Particle classes list *)
798
799M$ClassesDescription = {
800
801 S[1] == {
802 ClassName -> H,
803 SelfConjugate -> True,
804 Mass -> {HM,Internal},
805 PDG -> 25,
806 Width -> {wH,1.},
807 FullName -> "Composite Higgs boson"
808 },
809
810 V[1] == {
811 ClassName -> VN,
812 ClassMembers -> {A,Z,R1N,R2N},
813 SelfConjugate -> True,
814 Indices -> {Index[NeutralVector]},
815 FlavorIndex -> NeutralVector,
816 ParticleName -> {"A","Z","R1","R2"},
817 PropagatorType -> C,
818 PropagatorArrow -> None,
819 PDG -> {22,23,50,51},
820 Mass -> {0,{ZM,Internal},{M1N,Internal},{M2N,Internal}},
821 Width -> {0,{wZ,2.4952},{w1N,1.},{w2N,1.}},
822 FullName -> {"Photon", "Z boson", "Neutral R1", "Neutral R2" }
823 },
824
825
826 V[2] == {
827 ClassName -> VC,
828 ClassMembers -> {W,R1C,R2C},
829 SelfConjugate -> False,
830 Indices -> {Index[ChargedVector]},
831 FlavorIndex -> ChargedVector,
832 ParticleName -> {"W+","R1+","R2+"},
833 AntiParticleName -> {"W-","R1-","R2-"},
834 QuantumNumbers -> {Q -> 1},
835 PropagatorType -> C,
836 PropagatorArrow -> None,
837 PDG -> {24,52,53},
838 Mass -> {{MW,Internal},{M1C,Internal},{M2C,Internal}},
839 Width -> {{wW,2.141},{w1C,1.},{w2C,1.}},
840 FullName -> {"W boson", "Charged R1", "Charged R2" }
841 },
842
843
844 V[3] == {
845 ClassName -> B,
846 Unphysical -> True,
847 SelfConjugate -> True,
848 Definitions -> {B[mu_] -> Sum[NM[Aind,f] VN[mu,f],{f,4}]},
849 Indices -> {},
850 Mass -> 0,
851 FullName -> "U1Y B gauge field"
852 },
853
854 V[4] == {
855 ClassName -> VCt,
856 Unphysical -> True,
857 SelfConjugate -> False,
858 Definitions -> Table[VCt[mu_,k] -> Sum[CM[k,f] VC[mu,f],{f,3}],{k,3}],
859 Indices -> {Index[ChargedVector]},
860 Mass -> 0 ,
861 FullName -> "Charged vector strong and weak eigenstates"
862 },
863
864 V[5] == {
865 ClassName -> Wi,
866 Unphysical -> True,
867 Definitions -> {Wi[mu_, 1] -> (VCt[mu,Wind] + VCtbar[mu,Wind])/Sqrt[2],
868 Wi[mu_, 2] -> (VCtbar[mu,Wind] - VCt[mu,Wind])/Sqrt[2]/I,
869 Wi[mu_, 3] -> Sum[NM[Zind,f] VN[mu,f],{f,4}]},
870 SelfConjugate -> True,
871 Indices -> {Index[SU2Adjoint]},
872 FlavorIndex -> SU2Adjoint,
873 Mass -> 0,
874 PDG -> {1,2,3},
875 FullName -> "SU2L W gauge field"
876 },
877
878 V[6] == {
879 ClassName -> VV,
880 Unphysical -> True,
881 SelfConjugate -> True,
882 Indices -> {Index[SU2Adjoint]},
883 FlavorIndex -> SU2Adjoint,
884 Definitions->{VV[mu_,1]->(VCt[mu,VCind]+VCtbar[mu,VCind])/Sqrt[2],VV[mu_,2]->(VCtbar[mu,VCind]-VCt[mu,VCind])/Sqrt[2]/I,VV[mu_,3]-> Sum[(NM[VNind,f]) VN[mu,f],{f,4}]},
885 Mass -> 0,
886 FullName -> "Strong vector state"
887 },
888
889 V[7] == {
890 ClassName -> AV,
891 Unphysical -> True,
892 SelfConjugate -> True,
893 Indices -> {Index[SU2Adjoint]},
894 FlavorIndex -> SU2Adjoint,
895 Definitions->{AV[mu_,1]->(VCt[mu,ACind]+VCtbar[mu,ACind])/Sqrt[2],AV[mu_,2]->(VCtbar[mu,ACind]-VCt[mu,ACind])/Sqrt[2]/I,AV[mu_,3] ->Sum[(NM[ANind,f]) VN[mu,f],{f,4}]},
896 Mass -> 0,
897 FullName -> "Strong axial state"
898 },
899
900 V[8] == {
901 ClassName -> AL,
902 Unphysical -> True,
903 SelfConjugate -> True,
904 Indices -> {Index[SU2Adjoint]},
905 FlavorIndex -> SU2Adjoint,
906 Definitions->{AL[mu_,k_]->(VV[mu,k]+AV[mu,k])/Sqrt[2]},
907 Mass -> 0,
908 FullName -> "Left handed strong vector"
909 },
910
911 V[9] == {
912 ClassName -> AR,
913 Unphysical -> True,
914 SelfConjugate -> True,
915 Indices -> {Index[SU2Adjoint]},
916 FlavorIndex -> SU2Adjoint,
917 Definitions->{AR[mu_,k_]->(VV[mu,k]-AV[mu,k])/Sqrt[2]},
918 Mass -> 0,
919 FullName -> "Right handed strong vector"
920 },
921
922 V[10] == {
923 ClassName -> G,
924 SelfConjugate -> True,
925 Indices -> {Index[Gluon]},
926 Mass -> 0,
927 Width -> 0,
928 PropagatorLabel -> G,
929 PropagatorType -> C,
930 PropagatorArrow -> None,
931 PDG -> 21,
932 FullName -> "Gluon" },
933
934 F[1] == {
935 ClassName -> vl,
936 ClassMembers -> {ve,vm,vt},
937 FlavorIndex -> Generation,
938 SelfConjugate -> False,
939 Indices -> {Index[Generation]},
940 Mass -> 0,
941 Width -> 0,
942 QuantumNumbers -> {LeptonNumber -> 1},
943 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
944 PropagatorType -> S,
945 PropagatorArrow -> Forward,
946 PDG -> {12,14,16},
947 FullName -> {"Neutrino", "Mu-neutrino", "Tau-neutrino"} },
948
949 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
950 F[2] == {
951 ClassName -> l,
952 ClassMembers -> {e, mu, ta},
953 FlavorIndex -> Generation,
954 SelfConjugate -> False,
955 Indices -> {Index[Generation]},
956 Mass -> {Ml, {ME, 0}, {MMU, 0}, {TAM, Internal}},
957 Width -> 0,
958 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
959 PropagatorLabel -> {"l", "e", "mu", "ta"},
960 PropagatorType -> Straight,
961 ParticleName -> {"e-", "mu-", "ta-"},
962 AntiParticleName -> {"e+", "mu+", "ta+"},
963 PropagatorArrow -> Forward,
964 PDG -> {11, 13, 15},
965 FullName -> {"Electron", "Muon", "Tau"} },
966
967 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
968 F[3] == {
969 ClassMembers -> {u, c, t},
970 ClassName -> uq,
971 FlavorIndex -> Generation,
972 SelfConjugate -> False,
973 Indices -> {Index[Generation], Index[Colour]},
974 Mass -> {Mu, {MU, 0}, {CM, Internal}, {TM, Internal}},
975 Width -> {0, 0, {wT, 1.50833649}},
976 QuantumNumbers -> {Q -> 2/3},
977 PropagatorLabel -> {"uq", "u", "c", "t"},
978 PropagatorType -> Straight,
979 PropagatorArrow -> Forward,
980 PDG -> {2, 4, 6},
981 FullName -> {"u-quark", "c-quark", "t-quark"}},
982
983 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
984 F[4] == {
985 ClassMembers -> {d, s, b},
986 ClassName -> dq,
987 FlavorIndex -> Generation,
988 SelfConjugate -> False,
989 Indices -> {Index[Generation], Index[Colour]},
990 Mass -> {Md, {MD, 0}, {MS, 0}, {BM, Internal}},
991 Width -> 0,
992 QuantumNumbers -> {Q -> -1/3},
993 PropagatorLabel -> {"dq", "d", "s", "b"},
994 PropagatorType -> Straight,
995 PropagatorArrow -> Forward,
996 PDG -> {1,3,5},
997 FullName -> {"d-quark", "s-quark", "b-quark"} },
998
999 U[1] == {
1000 ClassName -> ghG,
1001 SelfConjugate -> False,
1002 Indices -> {Index[Gluon]},
1003 Ghost -> G,
1004 Mass -> 0,
1005 QuantumNumbers -> {GhostNumber -> 1},
1006 PropagatorLabel -> uG,
1007 PropagatorType -> GhostDash,
1008 PropagatorArrow -> Forward}
1009
1010}
1011
1012
1013
1014(************* Lagrangian *************)
1015
1016SM = {{(v+H)/Sqrt[2],0},{0,(v+H)/Sqrt[2]}};
1017SMbar = {{(v+H)/Sqrt[2],0},{0,(v+H)/Sqrt[2]}};
1018
1019WMX[mu_]={{Wi[mu,3]/2,(Wi[mu,1]-I Wi[mu,2])/2},{(Wi[mu,1]+I Wi[mu,2])/2,-Wi[mu,3]/2}};
1020BMX[mu_]={{B[mu]/2,0}, {0,-B[mu]/2}};
1021
1022DSM[mu_] = del[SM, mu] - I g2 WMX[mu].SM + I g1 SM.BMX[mu]
1023
1024DSMbar[mu_] = del[SMbar, mu] + I g2 SMbar.WMX[mu] - I g1 BMX[mu].SMbar
1025
1026AMXL[mu_] = {{AL[mu,3]/2,(AL[mu,1]-I AL[mu,2])/2}, {(AL[mu,1]+I AL[mu,2])/2,-AL[mu,3]/2}};
1027
1028AMXR[mu_] = {{AR[mu,3]/2,(AR[mu,1]-I AR[mu,2])/2}, {(AR[mu,1]+I AR[mu,2])/2,-AR[mu,3]/2}};
1029
1030CL[mu_] = AMXL[mu]-g2/gt WMX[mu];
1031CR[mu_] = AMXR[mu]-g1/gt BMX[mu];
1032
1033FTB[mu_,nu_] = del[ BMX[nu],mu] -del[BMX[mu],nu]
1034FTW[mu_,nu_] = del[ WMX[nu],mu] -del[WMX[mu],nu] - I g2 WMX[mu].WMX[nu] + I g2 WMX[nu].WMX[mu];
1035FTL[mu_,nu_] = del[ AMXL[nu],mu] -del[AMXL[mu],nu] -I gt AMXL[mu].AMXL[nu] + I gt AMXL[nu].AMXL[mu];
1036FTR[mu_,nu_] = del[ AMXR[nu],mu] -del[AMXR[mu],nu] -I gt AMXR[mu].AMXR[nu] + I gt AMXR[nu].AMXR[mu];
1037
1038
1039Lkin = -1/2 Tr[FTB[mu,nu].FTB[mu,nu]+FTW[mu,nu].FTW[mu,nu]+FTL[mu,nu].FTL[mu,nu]+FTR[mu,nu].FTR[mu,nu]]+ 1/2 Tr[DSM[mu].DSMbar[mu]]
1040
1041LHiggs = MH^2/4*Tr[SM.SM] -MH^2/v^2/8*Tr[SM.SM]^2;
1042
1043LMV = gt^2*f^2/4*Tr[CL[mu].CL[mu]+CR[mu].CR[mu]];
1044
1045LRT = 1/4 gt^2 rs Tr[CL[mu].CL[mu] + CR[mu].CR[mu]]*(Tr[SM.SMbar]-v*v) - gt^2 r2 Tr[CL[mu].SM.CR[mu].SMbar] - I/4 gt r3 Tr[CL[mu].(SM.DSMbar[mu] - DSM[mu].SMbar) + CR[mu].(SMbar.DSM[mu] - DSMbar[mu].SM)];
1046
1047(* LGA = -2 rg/v^2 Tr[FTL[mu,nu].SM.FTR[mu,nu].SMbar]; *)
1048
1049(* SM coupling: Copied from sm.fr *)
1050
1051LQCD = - 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*(del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5])+gs (uqbar.Ga[mu].T[a].uq + dqbar.Ga[mu].T[a].dq)G[mu, a];
1052
1053Lkinferm = I uqbar.Ga[mu].del[uq, mu] +
1054 I dqbar.Ga[mu].del[dq, mu] +
1055 I lbar.Ga[mu].del[l, mu] +
1056 I vlbar.Ga[mu].del[vl, mu];
1057
1058
1059 LBright =
1060 -2 g1 B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
1061 4 g1/3 B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
1062 2 g1/3 B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
1063
1064 LBleft =
1065 - g1 B[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*)
1066 g1 B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
1067 g1/3 B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
1068 g1/3 B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
1069
1070 LWleft = g2/2(
1071 vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
1072 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
1073
1074 Sqrt[2] vlbar.Ga[mu].ProjM.l VCt[mu,Wind] +
1075 Sqrt[2] lbar.Ga[mu].ProjM.vl VCtbar[mu,Wind]+
1076
1077 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
1078 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
1079
1080 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq VCt[mu,Wind] +
1081 Sqrt[2] dqbar.Ga[mu].ProjM.CKMT.uq VCtbar[mu,Wind]
1082 );
1083
1084LYuk = Module[{s,n,m,i}, -
1085 yd[n] dqbar[s,n,i].dq[s,n,i] (v+H)/Sqrt[2] -
1086 yu[n] uqbar[s,n,i].uq[s,n,i] (v+H)/Sqrt[2] -
1087 yl[n] lbar[s,n].l[s,n] (v+H)/Sqrt[2]
1088 ];
1089
1090LGhost := Block[{dBRSTG},
1091 dBRSTG[mu_,a_] := Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1092 - ghGbar[a].del[dBRSTG[mu,a],mu]
1093 ];
1094
1095
1096
1097LMWT = Lkin + LHiggs + LMV + LRT (*+ LGA*) + LQCD + Lkinferm + LBright + LBleft + LWleft + LYuk + LGhost;