TechniColor: MWT_101030.fr

File MWT_101030.fr, 30.9 KB (added by CP3-Origins, 10 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;