TypeIIISeeSaw: typeIIIseesaw1.0.fr

File typeIIIseesaw1.0.fr, 55.2 KB (added by Carla Biggio, 15 years ago)

TypeIIIseesaw1.0

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Standard model ******)
3(****** extended with a fermionic SU(2) triplet which give mass ******)
4(****** to one neutrino via a type III seesaw mechanism ******)
5(****** ******)
6(****** Authors: C. Biggio, F. Bonnet ******)
7(****** ******)
8(****** Choose whether Feynman gauge is desired. ******)
9(****** If set to False, unitary gauge is assumed. ****)
10(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
11(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
12(***************************************************************************************************************)
13
14M$ModelName = "typeIIIseesaw1";
15
16
17M$Information = {Authors -> {"C.Biggio", "F. Bonnet"},
18 Version -> "1.0",
19 Date -> "16. 03. 2011",
20 Institutions -> {"IFAE/UAB", "INFN Padova"},
21 Emails -> {"biggio@ifae.es", "bonnet@pd.infn.it"},
22 URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/TypeIIIseesaw"};
23
24FeynmanGauge = False;
25
26
27(******* Index definitions ********)
28
29IndexRange[ Index[Generation] ] = Range[3]
30
31IndexRange[ Index[LeptonGeneration] ] = Range[4]
32
33IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
34
35IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
36
37IndexRange[ Index[SU2W] ] = Range[3]
38
39
40IndexStyle[Colour, i]
41
42IndexStyle[Generation, f]
43
44IndexStyle[LeptonGeneration, fl]
45
46IndexStyle[Gluon ,a]
47
48IndexStyle[SU2W ,k]
49
50
51(******* Gauge parameters (for FeynArts) ********)
52
53GaugeXi[ V[1] ] = GaugeXi[A];
54GaugeXi[ V[2] ] = GaugeXi[Z];
55GaugeXi[ V[3] ] = GaugeXi[W];
56GaugeXi[ V[4] ] = GaugeXi[G];
57GaugeXi[ S[1] ] = 1;
58GaugeXi[ S[2] ] = GaugeXi[Z];
59GaugeXi[ S[3] ] = GaugeXi[W];
60GaugeXi[ U[1] ] = GaugeXi[A];
61GaugeXi[ U[2] ] = GaugeXi[Z];
62GaugeXi[ U[31] ] = GaugeXi[W];
63GaugeXi[ U[32] ] = GaugeXi[W];
64GaugeXi[ U[4] ] = GaugeXi[G];
65
66
67(**************** Parameters *************)
68
69M$Parameters = {
70
71 (* External parameters *)
72
73 \[Alpha]EWM1== {
74 ParameterType -> External,
75 BlockName -> SMINPUTS,
76 ParameterName -> aEWM1,
77 InteractionOrder -> {QED, -2},
78 Value -> 127.9,
79 Description -> "Inverse of the electroweak coupling constant"},
80
81 Gf == {
82 ParameterType -> External,
83 BlockName -> SMINPUTS,
84 TeX -> Subscript[G, f],
85 InteractionOrder -> {QED, 2},
86 Value -> 1.16639 * 10^(-5),
87 Description -> "Fermi constant"},
88
89 \[Alpha]S == {
90 ParameterType -> External,
91 BlockName -> SMINPUTS,
92 TeX -> Subscript[\[Alpha], s],
93 ParameterName -> aS,
94 InteractionOrder -> {QCD, 2},
95 Value -> 0.118,
96 Description -> "Strong coupling constant at the Z pole."},
97
98 ymc == {
99 ParameterType -> External,
100 BlockName -> YUKAWA,
101 Value -> 1.42,
102 OrderBlock -> {4},
103 Description -> "Charm Yukawa mass"},
104
105 ymb == {
106 ParameterType -> External,
107 BlockName -> YUKAWA,
108 Value -> 4.7,
109 OrderBlock -> {5},
110 Description -> "Bottom Yukawa mass"},
111
112 ymt == {
113 ParameterType -> External,
114 BlockName -> YUKAWA,
115 Value -> 174.3,
116 OrderBlock -> {6},
117 Description -> "Top Yukawa mass"},
118
119 mv1 == {
120 ParameterType -> External,
121 BlockName -> NEWMASSES,
122 Value -> 0,
123 OrderBlock -> {1},
124 Description -> "nu1 mass"},
125
126 mv2 == {
127 ParameterType -> External,
128 BlockName -> NEWMASSES,
129 Value -> 0,
130 OrderBlock -> {2},
131 Description -> "nu2 mass"},
132
133 mv3 == {
134 ParameterType -> External,
135 BlockName -> NEWMASSES,
136 Value -> 0,
137 OrderBlock -> {3},
138 Description -> "nu3 mass"},
139
140 yme == {
141 ParameterType -> External,
142 BlockName -> YUKAWA,
143 Value -> 0,
144 OrderBlock -> {13},
145 Description -> "Electron Yukawa mass"},
146
147 ymm == {
148 ParameterType -> External,
149 BlockName -> YUKAWA,
150 Value -> 0,
151 OrderBlock -> {14},
152 Description -> "Muon Yukawa mass"},
153
154 ymtau == {
155 ParameterType -> External,
156 BlockName -> YUKAWA,
157 Value -> 1.777,
158 OrderBlock -> {15},
159 Description -> "Tau Yukawa mass"},
160
161 cabi == {
162 TeX -> Subscript[\[Theta], c],
163 ParameterType -> External,
164 BlockName -> CKMBLOCK,
165 Value -> 0.227736,
166 OrderBlock -> {1},
167 Description -> "Cabibbo angle"},
168
169 mtr == {
170 ParameterType -> External,
171 BlockName -> NEWMASSES,
172 Value -> 100.8,
173 OrderBlock -> {4},
174 Description -> "Neutral triplet Majorana mass"},
175
176 mtrm == {
177 ParameterType -> External,
178 BlockName -> NEWMASSES,
179 Value -> 101,
180 OrderBlock -> {5},
181 Description -> "Charged triplet Majorana mass"},
182
183 Ve == {
184 ParameterType -> External,
185 BlockName -> MIXING,
186 Value -> 0,
187 OrderBlock -> {1},
188 Description -> "Electron mixing"},
189
190 Vm == {
191 ParameterType -> External,
192 BlockName -> MIXING,
193 Value -> 0.063,
194 OrderBlock -> {2},
195 Description -> "Muon mixing"},
196
197 Vtt == {
198 ParameterType -> External,
199 BlockName -> MIXING,
200 Value -> 0,
201 OrderBlock -> {3},
202 Description -> "Tau mixing"},
203
204 theta13 == {
205 TeX -> Subscript[\[Theta], 13],
206 ParameterType -> External,
207 BlockName -> CKMBLOCK,
208 Value -> 0.1,
209 OrderBlock -> {2},
210 Description -> "PMNS theta13"},
211
212 theta12 == {
213 TeX -> Subscript[\[Theta], 12],
214 ParameterType -> External,
215 BlockName -> CKMBLOCK,
216 Value -> 0.60,
217 OrderBlock -> {3},
218 Description -> "PMNS solar angle"},
219
220 theta23 == {
221 TeX -> Subscript[\[Theta], 23],
222 ParameterType -> External,
223 BlockName -> CKMBLOCK,
224 Value -> 0.75,
225 OrderBlock -> {4},
226 Description -> "PMNS athmospheric angle"},
227
228
229
230 (* Internal Parameters *)
231
232 \[Alpha]EW == {
233 ParameterType -> Internal,
234 Value -> 1/\[Alpha]EWM1,
235 TeX -> Subscript[\[Alpha], EW],
236 ParameterName -> aEW,
237 InteractionOrder -> {QED, 2},
238 Description -> "Electroweak coupling contant"},
239
240
241 MW == {
242 ParameterType -> Internal,
243 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
244 TeX -> Subscript[M, W],
245 Description -> "W mass"},
246
247 sw2 == {
248 ParameterType -> Internal,
249 Value -> 1-(MW/MZ)^2,
250 Description -> "Squared Sin of the Weinberg angle"},
251
252 ee == {
253 TeX -> e,
254 ParameterType -> Internal,
255 Value -> Sqrt[4 Pi \[Alpha]EW],
256 InteractionOrder -> {QED, 1},
257 Description -> "Electric coupling constant"},
258
259 cw == {
260 TeX -> Subscript[c, w],
261 ParameterType -> Internal,
262 Value -> Sqrt[1 - sw2],
263 Description -> "Cos of the Weinberg angle"},
264
265 sw == {
266 TeX -> Subscript[s, w],
267 ParameterType -> Internal,
268 Value -> Sqrt[sw2],
269 Description -> "Sin of the Weinberg angle"},
270
271 gw == {
272 TeX -> Subscript[g, w],
273 ParameterType -> Internal,
274 Value -> ee / sw,
275 InteractionOrder -> {QED, 1},
276 Description -> "Weak coupling constant"},
277
278 g1 == {
279 TeX -> Subscript[g, 1],
280 ParameterType -> Internal,
281 Value -> ee / cw,
282 InteractionOrder -> {QED, 1},
283 Description -> "U(1)Y coupling constant"},
284
285 gs == {
286 TeX -> Subscript[g, s],
287 ParameterType -> Internal,
288 Value -> Sqrt[4 Pi \[Alpha]S],
289 InteractionOrder -> {QCD, 1},
290 ParameterName -> G,
291 Description -> "Strong coupling constant"},
292
293 v == {
294 ParameterType -> Internal,
295 Value -> 2*MW*sw/ee,
296 InteractionOrder -> {QED, -1},
297 Description -> "Higgs VEV"},
298
299 \[Lambda] == {
300 ParameterType -> Internal,
301 Value -> MH^2/(2*v^2),
302 InteractionOrder -> {QED, 2},
303 ParameterName -> lam,
304 Description -> "Higgs quartic coupling"},
305
306 muH == {
307 ParameterType -> Internal,
308 Value -> Sqrt[v^2 \[Lambda]],
309 TeX -> \[Mu],
310 Description -> "Coefficient of the quadratic piece of the Higgs potential"},
311
312 yl == {
313 TeX -> Superscript[y, l],
314 Indices -> {Index[LeptonGeneration]},
315 AllowSummation -> True,
316 ParameterType -> Internal,
317 Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v, yl[4] -> 0},
318 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau, yl[4] -> useless},
319 InteractionOrder -> {QED, 1},
320 ComplexParameter -> False,
321 Description -> "Standard Model lepton Yukawa coupling"},
322
323 yu == {
324 TeX -> Superscript[y, u],
325 Indices -> {Index[Generation]},
326 AllowSummation -> True,
327 ParameterType -> Internal,
328 Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
329 ParameterName -> {yu[1] -> yu, yu[2] -> yc, yu[3] -> yt},
330 InteractionOrder -> {QED, 1},
331 ComplexParameter -> False,
332 Description -> "U-quark Yukawa coupling"},
333
334 yd == {
335 TeX -> Superscript[y, d],
336 Indices -> {Index[Generation]},
337 AllowSummation -> True,
338 ParameterType -> Internal,
339 Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v},
340 ParameterName -> {yd[1] -> yd, yd[2] -> ys, yd[3] -> yb},
341 InteractionOrder -> {QED, 1},
342 ComplexParameter -> False,
343 Description -> "D-quark Yukawa coupling"},
344
345(* N. B. : only Cabibbo mixing! *)
346 CKM == {
347 Indices -> {Index[Generation], Index[Generation]},
348 TensorClass -> CKM,
349 Unitary -> True,
350 Value -> {CKM[1,1] -> Cos[cabi],
351 CKM[1,2] -> Sin[cabi],
352 CKM[1,3] -> 0,
353 CKM[2,1] -> -Sin[cabi],
354 CKM[2,2] -> Cos[cabi],
355 CKM[2,3] -> 0,
356 CKM[3,1] -> 0,
357 CKM[3,2] -> 0,
358 CKM[3,3] -> 1},
359 Description -> "CKM-Matrix"},
360
361(* N. B. : no phases! *)
362 PMNS == {
363 Indices -> {Index[Generation], Index[Generation]},
364 TensorClass -> CKM,
365 Unitary -> True,
366 Value -> {PMNS[1,1] -> Cos[theta13] Cos[theta12],
367 PMNS[1,2] -> Cos[theta13] Sin[theta12],
368 PMNS[1,3] -> Sin[theta13],
369 PMNS[2,1] -> -Cos[theta23]*Sin[theta12] - Sin[theta23]*Sin[theta13]*Cos[theta12],
370 PMNS[2,2] -> Cos[theta23]*Cos[theta12] - Sin[theta23]*Sin[theta13]*Sin[theta12],
371 PMNS[2,3] -> Sin[theta23]*Cos[theta13],
372 PMNS[3,1] -> Sin[theta23]*Sin[theta12] - Cos[theta23]*Sin[theta13]*Cos[theta12],
373 PMNS[3,2] -> -Sin[theta23]*Cos[theta12] - Cos[theta23]*Sin[theta13]*Sin[theta12],
374 PMNS[3,3] -> Cos[theta23]*Cos[theta13]},
375 Description -> "PMNS-Matrix"},
376
377
378(***********************************************)
379(********** COUPLINGS **********)
380(***********************************************)
381
382 gCCL == {
383 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
384 TensorClass -> CKM,
385 ComplexParameter -> False,
386 Value -> {gCCL[1,1] -> Cos[theta12] Cos[theta13] + 1/2 (Ve^2 Cos[theta12] Cos[theta13] +
387 Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
388 Ve Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
389 gCCL[1,2] -> Cos[theta13] Sin[theta12] + 1/2 (Ve^2 Cos[theta13] Sin[theta12] +
390 Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
391 Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
392 gCCL[1,3] -> Sin[theta13] + 1/2 (Ve Vtt Cos[theta13] Cos[theta23] + Ve^2 Sin[theta13] + Ve Vm Cos[theta13] Sin[theta23]),
393 gCCL[1,4] -> - Ve,
394 gCCL[2,1] -> -Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23] +
395 1/2 (Ve Vm Cos[theta12] Cos[theta13] + Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
396 Sin[theta12] Sin[theta23]) + Vm^2 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
397 gCCL[2,2] -> Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23] +
398 1/2 (Ve Vm Cos[theta13] Sin[theta12] + Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
399 Vm^2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
400 gCCL[2,3] -> Cos[theta13] Sin[theta23] + 1/2 (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] + Vm^2 Cos[theta13] Sin[theta23]),
401 gCCL[2,4] -> - Vm,
402 gCCL[3,1] -> -Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23] + 1/2 (Ve Vtt Cos[theta12] Cos[theta13] +
403 Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
404 Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
405 gCCL[3,2] -> -Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23] + 1/2 (Ve Vtt Cos[theta13] Sin[theta12] +
406 Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
407 Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
408 gCCL[3,3] -> Cos[theta13] Cos[theta23] + 1/2 (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] + Vm Vtt Cos[theta13] Sin[theta23]),
409 gCCL[3,4] -> - Vtt,
410 gCCL[4,1] -> 0,
411 gCCL[4,2] -> 0,
412 gCCL[4,3] -> 0,
413 gCCL[4,4] -> Sqrt[2] (1 + 1/2 (-Ve^2 - Vm^2 - Vtt^2))},
414 Description -> "gCCL-Matrix"},
415
416
417
418
419 gCCR == {
420 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
421 TensorClass -> CKM,
422 ComplexParameter -> False,
423 Value -> {gCCR[1,1] -> 0,
424 gCCR[1,2] -> 0,
425 gCCR[1,3] -> 0,
426 gCCR[1,4] -> -Sqrt[2]*yme/mtr*Ve,
427 gCCR[2,1] -> 0,
428 gCCR[2,2] -> 0,
429 gCCR[2,3] -> 0,
430 gCCR[2,4] -> -Sqrt[2]*ymm/mtr*Vm,
431 gCCR[3,1] -> 0,
432 gCCR[3,2] -> 0,
433 gCCR[3,3] -> 0,
434 gCCR[3,4] -> -Sqrt[2]*ymtau/mtr*Vtt,
435 gCCR[4,1] -> -( Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
436 Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
437 gCCR[4,2] -> - (Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
438 Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
439 gCCR[4,3] -> - (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]),
440 gCCR[4,4] -> 1 + 1/2 (-Ve^2 - Vm^2 - Vtt^2)},
441 Description -> "gCCR-Matrix"},
442
443
444
445
446
447 gNCL == {
448 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
449 TensorClass -> CKM,
450 Hermitian -> True,
451 Value -> {gNCL[1,1] -> 1/2-cw^2-Ve^2,
452 gNCL[1,2] -> Ve*Vm,
453 gNCL[1,3] -> Ve*Vtt,
454 gNCL[1,4] -> Ve/Sqrt[2],
455 gNCL[2,1] -> Ve*Vm,
456 gNCL[2,2] -> 1/2-cw^2-Vm^2,
457 gNCL[2,3] -> Vm*Vtt,
458 gNCL[2,4] -> Vm/Sqrt[2],
459 gNCL[3,1] -> Ve*Vtt,
460 gNCL[3,2] -> Vm*Vtt,
461 gNCL[3,3] -> 1/2-cw^2-Vtt^2,
462 gNCL[3,4] -> Vtt/Sqrt[2],
463 gNCL[4,1] -> Ve/Sqrt[2],
464 gNCL[4,2] -> Vm/Sqrt[2],
465 gNCL[4,3] -> Vtt/Sqrt[2],
466 gNCL[4,4] -> Ve^2+Vm^2+Vtt^2-cw^2},
467 Description -> "gNCL-Matrix"},
468
469
470
471 gNCR == {
472 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
473 TensorClass -> CKM,
474 Hermitian -> True,
475 Value -> {gNCR[1,1] -> 1-cw^2,
476 gNCR[1,2] -> 0,
477 gNCR[1,3] -> 0,
478 gNCR[1,4] -> Sqrt[2]*yme/mtr*Ve,
479 gNCR[2,1] -> 0,
480 gNCR[2,2] -> 1-cw^2,
481 gNCR[2,3] -> 0,
482 gNCR[2,4] -> Sqrt[2]*ymm/mtr*Vm,
483 gNCR[3,1] -> 0,
484 gNCR[3,2] -> 0,
485 gNCR[3,3] -> 1-cw^2,
486 gNCR[3,4] -> Sqrt[2]*ymtau/mtr*Vtt,
487 gNCR[4,1] -> Sqrt[2]*yme/mtr*Ve,
488 gNCR[4,2] -> Sqrt[2]*ymm/mtr*Vm,
489 gNCR[4,3] -> Sqrt[2]*ymtau/mtr*Vtt,
490 gNCR[4,4] -> -cw^2},
491 Description -> "gNCR-Matrix"},
492
493
494
495
496
497
498 gNCnu == {
499 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
500 TensorClass -> CKM,
501 Hermitian -> True,
502 Value -> {gNCnu[1,1] -> 1 - Cos[theta12] Cos[theta13] (Ve^2 Cos[theta12] Cos[theta13] +
503 Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
504 Ve Vm (-Cos[theta23] Sin[theta12] -
505 Cos[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] -
506 Cos[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta12] Cos[theta13] +
507 Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
508 Sin[theta12] Sin[theta23]) + Vm^2 (-Cos[theta23] Sin[theta12] -
509 Cos[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta12] Cos[theta23] Sin[theta13] +
510 Sin[theta12] Sin[theta23]) (Ve Vtt Cos[theta12] Cos[theta13] +
511 Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
512 Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
513 gNCnu[1,2] -> -Cos[theta13] Sin[theta12] (Ve^2 Cos[theta12] Cos[theta13] +
514 Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
515 Ve Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) - (Cos[theta12] Cos[theta23] -
516 Sin[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta12] Cos[theta13] +
517 Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
518 Vm^2 (-Cos[theta23] Sin[theta12] -
519 Cos[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] Sin[theta13] -
520 Cos[theta12] Sin[theta23]) (Ve Vtt Cos[theta12] Cos[theta13] +
521 Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
522 Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
523 gNCnu[1,3] -> -Sin[theta13] (Ve^2 Cos[theta12] Cos[theta13] + Ve Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
524 Sin[theta12] Sin[theta23]) + Ve Vm (-Cos[theta23] Sin[theta12] -
525 Cos[theta12] Sin[theta13] Sin[theta23])) - Cos[theta13] Sin[theta23] (Ve Vm Cos[theta12] Cos[theta13] +
526 Vm Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
527 Vm^2 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) -
528 Cos[theta13] Cos[theta23] (Ve Vtt Cos[theta12] Cos[theta13] +
529 Vtt^2 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
530 Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
531 gNCnu[1,4] -> Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
532 Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]),
533 gNCnu[2,1] -> -Cos[theta12] Cos[theta13] (Ve^2 Cos[theta13] Sin[theta12] +
534 Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
535 Ve Vm (Cos[theta12] Cos[theta23] -
536 Sin[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] -
537 Cos[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta13] Sin[theta12] +
538 Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
539 Vm^2 (Cos[theta12] Cos[theta23] -
540 Sin[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta12] Cos[theta23] Sin[theta13] +
541 Sin[theta12] Sin[theta23]) (Ve Vtt Cos[theta13] Sin[theta12] +
542 Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
543 Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
544 gNCnu[2,2] -> 1 - Cos[theta13] Sin[theta12] (Ve^2 Cos[theta13] Sin[theta12] +
545 Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
546 Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])) - (Cos[theta12] Cos[theta23] -
547 Sin[theta12] Sin[theta13] Sin[theta23]) (Ve Vm Cos[theta13] Sin[theta12] +
548 Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
549 Vm^2 (Cos[theta12] Cos[theta23] -
550 Sin[theta12] Sin[theta13] Sin[theta23])) - (-Cos[theta23] Sin[theta12] Sin[theta13] -
551 Cos[theta12] Sin[theta23]) (Ve Vtt Cos[theta13] Sin[theta12] +
552 Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
553 Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
554 gNCnu[2,3] -> -Sin[theta13] (Ve^2 Cos[theta13] Sin[theta12] +
555 Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
556 Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])) -
557 Cos[theta13] Sin[theta23] (Ve Vm Cos[theta13] Sin[theta12] +
558 Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
559 Vm^2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])) -
560 Cos[theta13] Cos[theta23] (Ve Vtt Cos[theta13] Sin[theta12] +
561 Vtt^2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
562 Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
563 gNCnu[2,4] -> Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
564 Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]),
565 gNCnu[3,1] -> -Cos[theta12] Cos[theta13] (Ve Vtt Cos[theta13] Cos[theta23] + Ve^2 Sin[theta13] +
566 Ve Vm Cos[theta13] Sin[theta23]) - (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] +
567 Vm Vtt Cos[theta13] Sin[theta23]) (-Cos[theta12] Cos[theta23] Sin[theta13] +
568 Sin[theta12] Sin[theta23]) - (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] +
569 Vm^2 Cos[theta13] Sin[theta23]) (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]),
570 gNCnu[3,2] -> -Cos[theta13] Sin[theta12] (Ve Vtt Cos[theta13] Cos[theta23] + Ve^2 Sin[theta13] +
571 Ve Vm Cos[theta13] Sin[theta23]) - (-Cos[theta23] Sin[theta12] Sin[theta13] -
572 Cos[theta12] Sin[theta23]) (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] +
573 Vm Vtt Cos[theta13] Sin[theta23]) - (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] +
574 Vm^2 Cos[theta13] Sin[theta23]) (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]),
575 gNCnu[3,3] -> 1 - Sin[theta13] (Ve Vtt Cos[theta13] Cos[theta23] +
576 Ve^2 Sin[theta13] + Ve Vm Cos[theta13] Sin[theta23]) -
577 Cos[theta13] Sin[theta23] (Vm Vtt Cos[theta13] Cos[theta23] + Ve Vm Sin[theta13] +
578 Vm^2 Cos[theta13] Sin[theta23]) -
579 Cos[theta13] Cos[theta23] (Vtt^2 Cos[theta13] Cos[theta23] + Ve Vtt Sin[theta13] +
580 Vm Vtt Cos[theta13] Sin[theta23]),
581 gNCnu[3,4] -> Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23],
582 gNCnu[4,1] -> Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
583 Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]),
584 gNCnu[4,2] -> Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
585 Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]),
586 gNCnu[4,3] -> Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23],
587 gNCnu[4,4] -> Ve^2 + Vm^2 + Vtt^2},
588 Description -> "gNCnu-Matrix"},
589
590
591
592
593 gHlR == {
594 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
595 TensorClass -> CKM,
596 ComplexParameter -> False,
597 Value -> {gHlR[1,1] -> yme/v*(1-3*Ve^2),
598 gHlR[2,1] -> -3*yme/v*Ve*Vm,
599 gHlR[3,1] -> -3*yme/v*Ve*Vtt,
600 gHlR[4,1] -> Sqrt[2]*yme/v*Ve,
601 gHlR[1,2] -> -3*ymm/v*Ve*Vm,
602 gHlR[2,2] -> ymm/v*(1-3*Vm^2),
603 gHlR[3,2] -> -3*ymm/v*Vm*Vtt,
604 gHlR[4,2] -> Sqrt[2]*ymm/v*Vm,
605 gHlR[1,3] -> -3*ymtau/v*Ve*Vtt,
606 gHlR[2,3] -> -3*ymtau/v*Vm*Vtt,
607 gHlR[3,3] -> ymtau/v*(1-3*Vtt^2),
608 gHlR[4,3] -> Sqrt[2]*ymtau/v*Vtt,
609 gHlR[1,4] -> Sqrt[2]*mtr/v*Ve*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*yme^2/v/mtr*Ve,
610 gHlR[2,4] -> Sqrt[2]*mtr/v*Vm*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymm^2/v/mtr*Vm,
611 gHlR[3,4] -> Sqrt[2]*mtr/v*Vtt*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymtau^2/v/mtr*Vtt,
612 gHlR[4,4] -> 2*mtr/v*(Ve^2+Vm^2+Vtt^2)},
613 InteractionOrder -> {QED, 1},
614 Description -> "gHlR-Matrix"},
615
616
617
618
619 getalR == {
620 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
621 TensorClass -> CKM,
622 ComplexParameter -> False,
623 Value -> {getalR[1,1] -> yme/v*(1+Ve^2),
624 getalR[2,1] -> yme/v*Ve*Vm,
625 getalR[3,1] -> yme/v*Ve*Vtt,
626 getalR[4,1] -> Sqrt[2]*yme/v*Ve,
627 getalR[1,2] -> ymm/v*Ve*Vm,
628 getalR[2,2] -> ymm/v*(1+Vm^2),
629 getalR[3,2] -> ymm/v*Vm*Vtt,
630 getalR[4,2] -> Sqrt[2]*ymm/v*Vm,
631 getalR[1,3] -> ymtau/v*Ve*Vtt,
632 getalR[2,3] -> ymtau/v*Vm*Vtt,
633 getalR[3,3] -> ymtau/v*(1+Vtt^2),
634 getalR[4,3] -> Sqrt[2]*ymtau/v*Vtt,
635 getalR[1,4] -> -Sqrt[2]*mtr/v*Ve*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*yme^2/v/mtr*Ve,
636 getalR[2,4] -> -Sqrt[2]*mtr/v*Vm*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymm^2/v/mtr*Vm,
637 getalR[3,4] -> -Sqrt[2]*mtr/v*Vtt*(1-Ve^2-Vm^2-Vtt^2)+Sqrt[2]*ymtau^2/v/mtr*Vtt,
638 getalR[4,4] -> -2*mtr/v*(Ve^2+Vm^2+Vtt^2)},
639 InteractionOrder -> {QED, 1},
640 Description -> "getalR-Matrix"},
641
642
643
644
645 gHnuR == {
646 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
647 TensorClass -> CKM,
648 ComplexParameter -> False,
649 Value -> {gHnuR[1,1] -> Sqrt[2]/v*mv1,
650 gHnuR[2,1] -> 0,
651 gHnuR[3,1] -> 0,
652 gHnuR[4,1] -> Sqrt[2]/v*mv1*(Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
653 Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
654 gHnuR[1,2] -> 0,
655 gHnuR[2,2] -> Sqrt[2]/v*mv2,
656 gHnuR[3,2] -> 0,
657 gHnuR[4,2] -> Sqrt[2]/v*mv2*(Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
658 Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
659 gHnuR[1,3] -> 0,
660 gHnuR[2,3] -> 0,
661 gHnuR[3,3] -> Sqrt[2]/v*mv3,
662 gHnuR[4,3] -> Sqrt[2]/v*mv3*(Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]),
663 gHnuR[1,4] -> Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Sin[theta12] (-Vm Cos[theta23] + Vtt Sin[theta23]) +
664 Cos[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
665 gHnuR[2,4] -> Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Cos[theta12] (Vm Cos[theta23] - Vtt Sin[theta23]) +
666 Sin[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
667 gHnuR[3,4] -> Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Ve Sin[theta13] + Cos[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))),
668 gHnuR[4,4] -> Sqrt[2]*mtr/v*(Ve^2+Vm^2+Vtt^2)},
669 InteractionOrder -> {QED, 1},
670 Description -> "gHnuR-Matrix"},
671
672
673
674
675
676 getanuR == {
677 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
678 TensorClass -> CKM,
679 ComplexParameter -> False,
680 Value -> {getanuR[1,1] -> -Sqrt[2]/v*mv1,
681 getanuR[2,1] -> 0,
682 getanuR[3,1] -> 0,
683 getanuR[4,1] -> -(Sqrt[2]/v*mv1*(Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
684 Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]))),
685 getanuR[1,2] -> 0,
686 getanuR[2,2] -> -Sqrt[2]/v*mv2,
687 getanuR[3,2] -> 0,
688 getanuR[4,2] -> -(Sqrt[2]/v*mv2*(Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
689 Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
690 getanuR[1,3] -> 0,
691 getanuR[2,3] -> 0,
692 getanuR[3,3] -> -Sqrt[2]/v*mv3,
693 getanuR[4,3] -> -(Sqrt[2]/v*mv3*(Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23])),
694 getanuR[1,4] -> -(Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Sin[theta12] (-Vm Cos[theta23] + Vtt Sin[theta23]) +
695 Cos[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))))),
696 getanuR[2,4] -> -(Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Cos[theta12] (Vm Cos[theta23] - Vtt Sin[theta23]) +
697 Sin[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))))),
698 getanuR[3,4] -> -(Sqrt[2]*mtr/v*(-(-1 + Ve^2 + Vm^2 + Vtt^2) (Ve Sin[theta13] + Cos[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
699 getanuR[4,4] -> -(Sqrt[2]*mtr/v*(Ve^2+Vm^2+Vtt^2))},
700 InteractionOrder -> {QED, 1},
701 Description -> "getanuR-Matrix"},
702
703
704
705 gPhiL == {
706 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
707 TensorClass -> CKM,
708 ComplexParameter -> False,
709 Value -> {gPhiL[1,1] -> Sqrt[2]/v*yme*((1 - Ve^2/2) Cos[theta12] Cos[theta13] -
710 1/2 Ve Vtt (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13]) -
711 1/2 Ve Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
712 gPhiL[1,2] -> Sqrt[2]/v*yme*((1 - Ve^2/2) Cos[theta13] Sin[theta12] -
713 1/2 Ve Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) -
714 1/2 Ve Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
715 gPhiL[1,3] -> Sqrt[2]/v*yme*( (1 - Ve^2/2) Sin[theta13] -
716 1/2 Ve Vtt Cos[theta13] Cos[theta23] - 1/2 Ve Vm Cos[theta13] Sin[theta23] ),
717 gPhiL[1,4] -> Sqrt[2]/v*yme Ve,
718 gPhiL[2,1] -> Sqrt[2]/v*ymm*( (1 - Vm^2/2) (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]) -
719 1/2 Ve Vm Cos[theta12] Cos[theta13] -
720 1/2 Vm Vtt (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13])),
721 gPhiL[2,2] -> Sqrt[2]/v*ymm*( (1 - Vm^2/2) (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]) -
722 1/2 Ve Vm Cos[theta13] Sin[theta12] -
723 1/2 Vm Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23])),
724 gPhiL[2,3] -> Sqrt[2]/v*ymm*( (1 - Vm^2/2) Cos[theta13] Sin[theta23] -
725 1/2 Vm Vtt Cos[theta13] Cos[theta23] - 1/2 Ve Vm Sin[theta13]),
726 gPhiL[2,4] -> Sqrt[2]/v* ymm Vm,
727 gPhiL[3,1] -> Sqrt[2]/v*ymtau*( (1 - Vtt^2/2) (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13]) -
728 1/2 Ve Vtt Cos[theta12] Cos[theta13] -
729 1/2 Vm Vtt (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
730 gPhiL[3,2] -> Sqrt[2]/v*ymtau*( (1 - Vtt^2/2) (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) -
731 1/2 Ve Vtt Cos[theta13] Sin[theta12] -
732 1/2 Vm Vtt (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
733 gPhiL[3,3] -> Sqrt[2]/v*ymtau*( (1 - Vtt^2/2) Cos[theta13] Cos[theta23] -
734 1/2 Ve Vtt Sin[theta13] - 1/2 Vm Vtt Cos[theta13] Sin[theta23]),
735 gPhiL[3,4] -> Sqrt[2]/v* ymtau Vtt,
736 gPhiL[4,1] -> 2/(mtr*v)*(Ve Cos[theta12] Cos[theta13] yme^2 +
737 ymtau^2 Vtt (Sin[theta12] Sin[theta23]-Cos[theta12] Cos[theta23] Sin[theta13]) +
738 ymm^2 Vm (-Cos[theta23] Sin[theta12]-Cos[theta12] Sin[theta13] Sin[theta23])),
739 gPhiL[4,2] -> 2/(mtr*v)*(Ve Cos[theta13] Sin[theta12] yme^2 +
740 ymtau^2 Vtt (-Cos[theta23] Sin[theta12] Sin[theta13]-Cos[theta12] Sin[theta23]) +
741 ymm^2 Vm (Cos[theta12] Cos[theta23]-Sin[theta12] Sin[theta13] Sin[theta23])),
742 gPhiL[4,3] -> 2/(mtr*v)*(Ve Sin[theta13] yme^2 + ymtau^2 Vtt Cos[theta13] Cos[theta23] + ymm^2 Vm Cos[theta13] Sin[theta23]),
743 gPhiL[4,4] -> 0 },
744 Description -> "gPhiL-Matrix"},
745
746
747
748gPhiR == {
749 Indices -> {Index[LeptonGeneration], Index[LeptonGeneration]},
750 TensorClass -> CKM,
751 ComplexParameter -> False,
752 Value -> {gPhiR[1,1] -> -Sqrt[2]/v*(mv1 Cos[theta12] Cos[theta13]),
753 gPhiR[1,2] -> -Sqrt[2]/v*(mv2 Cos[theta13] Sin[theta12]),
754 gPhiR[1,3] -> -Sqrt[2]/v*(mv3 Sin[theta13]),
755 gPhiR[1,4] -> (mtr/v*Sqrt[2])*(-1/2 Ve (3 Ve^2 + 3 Vm^2 + 3 Vtt^2 - 2)) -
756 2/v*Sqrt[2]( mv3 Sin[theta13] (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]) +
757 mv1 Cos[theta12] Cos[theta13] (Ve Cos[theta12] Cos[theta13] + Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] +
758 Sin[theta12] Sin[theta23]) + Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) +
759 mv2 Cos[theta13] Sin[theta12] (Ve Cos[theta13] Sin[theta12] + Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] -
760 Cos[theta12] Sin[theta23]) + Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
761 gPhiR[2,1] -> -Sqrt[2]/v*(mv1 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])),
762 gPhiR[2,2] -> -Sqrt[2]/v*(mv2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23])),
763 gPhiR[2,3] -> -Sqrt[2]/v*(mv3 Cos[theta13] Sin[theta23]),
764 gPhiR[2,4] -> (mtr/v*Sqrt[2])*(-1/2 Vm (3 Ve^2 + 3 Vm^2 + 3 Vtt^2 - 2)) -
765 2/v*Sqrt[2] (
766 mv3 Cos[theta13] Sin[theta23] (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]) +
767 mv1 (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23]) (Ve Cos[theta12] Cos[theta13] +
768 Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
769 Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) +
770 mv2 (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]) (Ve Cos[theta13] Sin[theta12] +
771 Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
772 Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
773 gPhiR[3,1] -> -Sqrt[2]/v*(mv1 (Sin[theta12] Sin[theta23] - Cos[theta12] Cos[theta23] Sin[theta13])),
774 gPhiR[3,2] -> -Sqrt[2]/v*(mv2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23])),
775 gPhiR[3,3] -> -Sqrt[2]/v*(mv3 Cos[theta13] Cos[theta23]),
776 gPhiR[3,4] -> (mtr/v*Sqrt[2])*(-1/2 Vtt (3 Ve^2 + 3 Vm^2 + 3 Vtt^2 - 2)) -
777 2/v*Sqrt[2] (
778 mv3 Cos[theta13] Cos[theta23] (Vtt Cos[theta13] Cos[theta23] + Ve Sin[theta13] + Vm Cos[theta13] Sin[theta23]) +
779 mv1 (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) (Ve Cos[theta12] Cos[theta13] +
780 Vtt (-Cos[theta12] Cos[theta23] Sin[theta13] + Sin[theta12] Sin[theta23]) +
781 Vm (-Cos[theta23] Sin[theta12] - Cos[theta12] Sin[theta13] Sin[theta23])) +
782 mv2 (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) (Ve Cos[theta13] Sin[theta12] +
783 Vtt (-Cos[theta23] Sin[theta12] Sin[theta13] - Cos[theta12] Sin[theta23]) +
784 Vm (Cos[theta12] Cos[theta23] - Sin[theta12] Sin[theta13] Sin[theta23]))),
785 gPhiR[4,1] -> mtr/v*( (Ve^2 + Vm^2 + Vtt^2 - 2) (Sin[theta12] (Vtt Sin[theta23] - Vm Cos[theta23]) +
786 Cos[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
787 gPhiR[4,2] -> mtr/v*( (Ve^2 + Vm^2 + Vtt^2 - 2) (Cos[theta12] (Vm Cos[theta23] - Vtt Sin[theta23]) +
788 Sin[theta12] (Ve Cos[theta13] - Sin[theta13] (Vtt Cos[theta23] + Vm Sin[theta23])))),
789 gPhiR[4,3] -> mtr/v*( (Ve^2 + Vm^2 + Vtt^2 - 2) (Ve Sin[theta13] + Cos[theta13] (Vtt Cos[theta23] + Vm Sin[theta23]))),
790 gPhiR[4,4] -> 0 },
791 Description -> "gPhiR-Matrix"}
792
793
794
795
796}
797
798
799(************** Gauge Groups ******************)
800
801M$GaugeGroups = {
802
803 U1Y == {
804 Abelian -> True,
805 GaugeBoson -> B,
806 Charge -> Y,
807 CouplingConstant -> g1},
808
809 SU2L == {
810 Abelian -> False,
811 GaugeBoson -> Wi,
812 StructureConstant -> Eps,
813 CouplingConstant -> gw},
814
815 SU3C == {
816 Abelian -> False,
817 GaugeBoson -> G,
818 StructureConstant -> f,
819 SymmetricTensor -> dSUN,
820 Representations -> {T, Colour},
821 CouplingConstant -> gs}
822}
823
824(********* Particle Classes **********)
825
826M$ClassesDescription = {
827
828(********** Fermions ************)
829 (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
830 F[1] == {
831 ClassName -> vl,
832 ClassMembers -> {v1,v2,v3,tr0},
833 FlavorIndex -> LeptonGeneration,
834 SelfConjugate -> True,
835 Indices -> {Index[LeptonGeneration]},
836 Mass -> {Mv, {Mv1, 0}, {Mv2, 0}, {Mv3, 0}, {Mtr0, 100.8}},
837 Width -> {0, 0, 0, {Wtr0, 0.1}},
838 PropagatorLabel -> {"v", "v1", "v2", "v3","tr0"} ,
839 PropagatorType -> S,
840 PropagatorArrow -> Forward,
841 PDG -> {8000012,8000014,8000016,8000018},
842 FullName -> {"nu1", "nu2", "nu3", "Sigma0"} },
843
844 (* Leptons (electron): I_3 = -1/2, Q = -1 *)
845 F[2] == {
846 ClassName -> l,
847 ClassMembers -> {e, m, tt,trm},
848 FlavorIndex -> LeptonGeneration,
849 SelfConjugate -> False,
850 Indices -> {Index[LeptonGeneration]},
851 Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}, {Mtrch, 101}},
852 Width -> {0, 0, {Wtau, 0.1}, {Wtrch, 0.1}},
853 QuantumNumbers -> {Q -> -1},
854 PropagatorLabel -> {"l", "e", "m", "tt", "tr-"},
855 PropagatorType -> Straight,
856 ParticleName -> {"e-", "m-", "tt-", "tr-"},
857 AntiParticleName -> {"e+", "m+", "tt+", "tr+"},
858 PropagatorArrow -> Forward,
859 PDG -> {11, 13, 15,8000020},
860 FullName -> {"Electron", "Muon", "Tau", "Sigma-"} },
861
862 (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
863 F[3] == {
864 ClassMembers -> {u, c, t},
865 ClassName -> uq,
866 FlavorIndex -> Generation,
867 SelfConjugate -> False,
868 Indices -> {Index[Generation], Index[Colour]},
869 Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 174.3}},
870 Width -> {0, {WC, 0.1}, {WT, 1.50833649}},
871 QuantumNumbers -> {Q -> 2/3},
872 PropagatorLabel -> {"uq", "u", "c", "t"},
873 PropagatorType -> Straight,
874 PropagatorArrow -> Forward,
875 PDG -> {2, 4, 6},
876 FullName -> {"u-quark", "c-quark", "t-quark"}},
877
878 (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
879 F[4] == {
880 ClassMembers -> {d, s, b},
881 ClassName -> dq,
882 FlavorIndex -> Generation,
883 SelfConjugate -> False,
884 Indices -> {Index[Generation], Index[Colour]},
885 Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.104}, {MB, 4.7}},
886 Width -> {0, 0, {WB, 0.1}},
887 QuantumNumbers -> {Q -> -1/3},
888 PropagatorLabel -> {"dq", "d", "s", "b"},
889 PropagatorType -> Straight,
890 PropagatorArrow -> Forward,
891 PDG -> {1,3,5},
892 FullName -> {"d-quark", "s-quark", "b-quark"} },
893
894(********** Ghosts **********)
895 U[1] == {
896 ClassName -> ghA,
897 SelfConjugate -> False,
898 Indices -> {},
899 Ghost -> A,
900 Mass -> 0,
901 QuantumNumbers -> {GhostNumber -> 1},
902 PropagatorLabel -> uA,
903 PropagatorType -> GhostDash,
904 PropagatorArrow -> Forward},
905
906 U[2] == {
907 ClassName -> ghZ,
908 SelfConjugate -> False,
909 Indices -> {},
910 Mass -> {MZ, 91.188},
911 Ghost -> Z,
912 QuantumNumbers -> {GhostNumber -> 1},
913 PropagatorLabel -> uZ,
914 PropagatorType -> GhostDash,
915 PropagatorArrow -> Forward},
916
917 U[31] == {
918 ClassName -> ghWp,
919 SelfConjugate -> False,
920 Indices -> {},
921 Mass -> {MW, Internal},
922 Ghost -> W,
923 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
924 PropagatorLabel -> uWp,
925 PropagatorType -> GhostDash,
926 PropagatorArrow -> Forward},
927
928 U[32] == {
929 ClassName -> ghWm,
930 SelfConjugate -> False,
931 Indices -> {},
932 Mass -> {MW, Internal},
933 Ghost -> Wbar,
934 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
935 PropagatorLabel -> uWm,
936 PropagatorType -> GhostDash,
937 PropagatorArrow -> Forward},
938
939 U[4] == {
940 ClassName -> ghG,
941 SelfConjugate -> False,
942 Indices -> {Index[Gluon]},
943 Ghost -> G,
944 Mass -> 0,
945 QuantumNumbers -> {GhostNumber -> 1},
946 PropagatorLabel -> uG,
947 PropagatorType -> GhostDash,
948 PropagatorArrow -> Forward},
949
950 U[5] == {
951 ClassName -> ghWi,
952 Unphysical -> True,
953 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
954 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
955 ghWi[3] -> cw ghZ + sw ghA},
956 SelfConjugate -> False,
957 Ghost -> Wi,
958 Indices -> {Index[SU2W]},
959 FlavorIndex -> SU2W},
960
961 U[6] == {
962 ClassName -> ghB,
963 SelfConjugate -> False,
964 Definitions -> {ghB -> -sw ghZ + cw ghA},
965 Indices -> {},
966 Ghost -> B,
967 Unphysical -> True},
968
969(************ Gauge Bosons ***************)
970 (* Gauge bosons: Q = 0 *)
971 V[1] == {
972 ClassName -> A,
973 SelfConjugate -> True,
974 Indices -> {},
975 Mass -> 0,
976 Width -> 0,
977 PropagatorLabel -> "a",
978 PropagatorType -> W,
979 PropagatorArrow -> None,
980 PDG -> 22,
981 FullName -> "Photon" },
982
983 V[2] == {
984 ClassName -> Z,
985 SelfConjugate -> True,
986 Indices -> {},
987 Mass -> {MZ, 91.188},
988 Width -> {WZ, 2.44140351},
989 PropagatorLabel -> "Z",
990 PropagatorType -> Sine,
991 PropagatorArrow -> None,
992 PDG -> 23,
993 FullName -> "Z" },
994
995 (* Gauge bosons: Q = -1 *)
996 V[3] == {
997 ClassName -> W,
998 SelfConjugate -> False,
999 Indices -> {},
1000 Mass -> {MW, Internal},
1001 Width -> {WW, 2.04759951},
1002 QuantumNumbers -> {Q -> 1},
1003 PropagatorLabel -> "W",
1004 PropagatorType -> Sine,
1005 PropagatorArrow -> Forward,
1006 ParticleName ->"W+",
1007 AntiParticleName ->"W-",
1008 PDG -> 24,
1009 FullName -> "W" },
1010
1011V[4] == {
1012 ClassName -> G,
1013 SelfConjugate -> True,
1014 Indices -> {Index[Gluon]},
1015 Mass -> 0,
1016 Width -> 0,
1017 PropagatorLabel -> G,
1018 PropagatorType -> C,
1019 PropagatorArrow -> None,
1020 PDG -> 21,
1021 FullName -> "G" },
1022
1023V[5] == {
1024 ClassName -> Wi,
1025 Unphysical -> True,
1026 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
1027 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
1028 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
1029 SelfConjugate -> True,
1030 Indices -> {Index[SU2W]},
1031 FlavorIndex -> SU2W,
1032 Mass -> 0,
1033 PDG -> {1,2,3}},
1034
1035V[6] == {
1036 ClassName -> B,
1037 SelfConjugate -> True,
1038 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
1039 Indices -> {},
1040 Mass -> 0,
1041 Unphysical -> True},
1042
1043
1044(************ Scalar Fields **********)
1045 (* physical Higgs: Q = 0 *)
1046 S[1] == {
1047 ClassName -> H,
1048 SelfConjugate -> True,
1049 Mass -> {MH, 120},
1050 Width -> {WH, 0.00575308848},
1051 PropagatorLabel -> "H",
1052 PropagatorType -> D,
1053 PropagatorArrow -> None,
1054 PDG -> 25,
1055 TeXParticleName -> "\\phi",
1056 TeXClassName -> "\\phi",
1057 FullName -> "H" },
1058
1059S[2] == {
1060 ClassName -> phi,
1061 SelfConjugate -> True,
1062 Mass -> {MZ, 91.188},
1063 Width -> Wphi,
1064 PropagatorLabel -> "Phi",
1065 PropagatorType -> D,
1066 PropagatorArrow -> None,
1067 ParticleName ->"phi0",
1068 PDG -> 250,
1069 FullName -> "Phi",
1070 Goldstone -> Z },
1071
1072S[3] == {
1073 ClassName -> phi2,
1074 SelfConjugate -> False,
1075 Mass -> {MW, Internal},
1076 Width -> Wphi2,
1077 PropagatorLabel -> "Phi2",
1078 PropagatorType -> D,
1079 PropagatorArrow -> None,
1080 ParticleName ->"phi+",
1081 AntiParticleName ->"phi-",
1082 PDG -> 251,
1083 FullName -> "Phi2",
1084 TeXClassName -> "\\phi^+",
1085 TeXParticleName -> "\\phi^+",
1086 TeXAntiParticleName -> "\\phi^-",
1087 Goldstone -> W,
1088 QuantumNumbers -> {Q -> 1}}
1089}
1090
1091
1092
1093
1094(*****************************************************************************************)
1095
1096(* SM + type III seesaw Lagrangian *)
1097
1098(******************** Gauge F^2 Lagrangian terms*************************)
1099(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1100 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
1101 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
1102
1103 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
1104
1105 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
1106 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
1107
1108
1109(********************* Fermion Lagrangian terms*************************)
1110(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1111 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
1112
1113 Lkin = I uqbar.Ga[mu].del[uq, mu] +
1114 I dqbar.Ga[mu].del[dq, mu] +
1115 I lbar.Ga[mu].del[l, mu] +
1116 I/2 vlbar.Ga[mu].del[vl, mu];
1117
1118 LQCD = gs (uqbar.Ga[mu].T[a].uq +
1119 dqbar.Ga[mu].T[a].dq)G[mu, a];
1120
1121 LBright =
1122 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.gNCR.l +
1123 -2ee*cw B[mu]/2 lbar.Ga[mu].ProjP.l +
1124 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
1125 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
1126
1127 LBleft =
1128 -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.gNCnu.vl +
1129 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjM.gNCL.l +
1130 -2ee*cw B[mu]/2 lbar.Ga[mu].ProjM.l +
1131 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
1132 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
1133
1134 LWleft = Module[{s,r,p,n,m,i},
1135 ee/sw/2(
1136
1137 vlbar[s,n].Ga[mu,s,p].ProjM[p,r].gNCnu[n,m].vl[r,m] Wi[mu, 3] +
1138 + 2 lbar[s,n].Ga[mu,s,p].ProjM[p,r].gNCL[n,m].l[r,m] Wi[mu, 3] +
1139 - 2*sw^2 lbar[s,n].Ga[mu,s,p].ProjM[p,r].l[r,n] Wi[mu, 3] +
1140 + 2 lbar[s,n].Ga[mu,s,p].ProjP[p,r].gNCR[n,m].l[r,m] Wi[mu, 3] +
1141 - 2*sw^2 lbar[s,n].Ga[mu,s,p].ProjP[p,r].l[r,n] Wi[mu, 3] +
1142
1143 Sqrt[2] vlbar[s,n].Ga[mu,s,p].ProjM[p,r].gCCL[m,n].l[r,m] W[mu] +
1144 Sqrt[2] lbar[s,n].Ga[mu,s,p].ProjM[p,r].gCCL[n,m].vl[r,m] Wbar[mu]+
1145 2 vlbar[s,n].Ga[mu,s,p].ProjP[p,r].gCCR[m,n].l[r,m] W[mu] +
1146 2 lbar[s,n].Ga[mu,s,p].ProjP[p,r].gCCR[n,m].vl[r,m] Wbar[mu]+
1147
1148 uqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].uq[r,n,i] Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
1149 dqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].dq[r,n,i] Wi[mu, 3] + (* ( 0 -1 )*)
1150
1151 Sqrt[2] uqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].CKM[n,m].dq[r,m,i] W[mu] +
1152 Sqrt[2] dqbar[s,n,i].Ga[mu,s,p].ProjM[p,r].Conjugate[CKM[m,n]].uq[r,m,i] Wbar[mu]
1153 )];
1154
1155 Lkin + LQCD + LBright + LBleft + LWleft];
1156
1157(******************** Higgs Lagrangian terms****************************)
1158 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
1159 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
1160
1161
1162
1163 LHiggs := Block[{PMvec, WVec, Dc, Dcbar, Vphi},
1164
1165 PMvec = Table[PauliSigma[i], {i, 3}];
1166 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1167
1168 (*Y_phi=1*)
1169 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMvec).f;
1170 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMvec);
1171
1172 Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
1173
1174 (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
1175
1176
1177(*************** Yukawa Lagrangian***********************)
1178LYuk := If[FeynmanGauge,
1179
1180 Module[{s,r,n,m,i}, -
1181 yd[n] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
1182 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] -
1183
1184 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2] + (*This sign from eps matrix*)
1185 yu[n] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) -
1186
1187 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v)/Sqrt[2] -
1188 gHlR[n,m] lbar[s,n].ProjP[s,r].l[r,m] (H) -
1189 gHnuR[n,m] vlbar[s,n].ProjP[s,r].vl[r,m] (H)/Sqrt[2] -
1190 getalR[n,m] lbar[s,n].ProjP[s,r].l[r,m] (I phi) -
1191 getanuR[n,m] vlbar[s,n].ProjP[s,r].vl[r,m] (I phi)/Sqrt[2] -
1192 gPhiR[n,m] lbar[s,n].ProjP[s,r].vl[r,m] (I phi2bar) - (* Different convention in phi2 definition compared to paper *)
1193 gPhiL[n,m] lbar[s,n].ProjM[s,r].vl[r,m] (I phi2bar) (* Different convention in phi2 definition compared to paper *)
1194 ],
1195
1196 Module[{s,r,n,m,i}, -
1197 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] -
1198 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] -
1199 yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v)/Sqrt[2] -
1200 gHlR[n,m] lbar[s,n].ProjP[s,r].l[r,m] (H) -
1201 gHnuR[n,m] vlbar[s,n].ProjP[s,r].vl[r,m] (H)/Sqrt[2]
1202 ]
1203 ];
1204
1205LYukawa := LYuk + HC[LYuk];
1206
1207(****************** Majorana Masses *********************)
1208
1209LMasses= - mtr/2 tr0bar.tr0 - mtrm trmbar.trm
1210
1211
1212(**************Ghost terms**************************)
1213(* Now we need the ghost terms which are of the form: *)
1214(* - g * antighost * d_BRST G *)
1215(* where d_BRST G is BRST transform of the gauge fixing function. *)
1216
1217LGhost := If[FeynmanGauge,
1218 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
1219
1220 (***********First the pure gauge piece.**********************)
1221 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1222 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1223
1224 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
1225 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
1226
1227 dBRSTB[mu_] := cw/ee del[ghB, mu];
1228 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
1229
1230 (***********Next the piece from the scalar field.************)
1231 LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
1232 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
1233 ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) -
1234 I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
1235 ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
1236
1237
1238 (***********Now add the pieces together.********************)
1239 LGhostG + LGhostWi + LGhostB + LGhostphi]
1240
1241, 0];
1242
1243(*********Total Lagrangian*******)
1244LTypeIII := LGauge + LHiggs + LFermions + LYukawa + LGhost + LMasses
1245
1246