B-L-SM: minimal_Zp.fr

File minimal_Zp.fr, 38.2 KB (added by Lorenzo Basso, 15 years ago)

Minimal Zp models FR file

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the minimal Zp models ******)
3(****** ******)
4(****** Author: L. Basso ******)
5(****** ******)
6(****** Choose whether Feynman gauge is desired. ******)
7(****** If set to False, unitary gauge is assumed. ****)
8(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
9(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
10(***************************************************************************************************************)
11
12M$ModelName = "minimal_Zp";
13
14
15M$Information = {Authors -> "L. Basso",
16 Version -> "2.0",
17 Date -> "09-06-2011",
18 Institutions -> {"University of Southampton", "RAL-PPD, Didcot, UK", "Albert-Ludwigs-UniversitÀt Freiburg"},
19 Emails -> {"lorenzo.basso@physik.uni-freiburg.de"},
20 References -> {"L.~Basso, G.M.~Pruna and S.~Moretti, \"A Renormalisation Group Equation Study of the Scalar Sector of the Minimal B-L Extension of the Standard Model,\", Phys.,Rev. D 82, 055018 (2010) [arXiv:1004.3039 [hep-ph]]", "L.~Basso, G.M.~Pruna and S.~Moretti, \"A Theoretical constraints on the couplings of non-exotic minimal Z' bosons,\", JHEP 1108 122 (2011) [arXiv:1106.4762 [hep-ph]]"},
21 URLs -> "http://feynrules.phys.ucl.ac.be/..."};
22
23FeynmanGauge = True;
24
25
26(******* Index definitions ********)
27
28IndexRange[ Index[Generation] ] = Range[3]
29
30IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
31
32IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
33
34IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
35
36
37IndexStyle[Colour, i]
38
39IndexStyle[Generation, f]
40
41IndexStyle[Gluon ,a]
42
43IndexStyle[SU2W ,k]
44
45
46
47(******* Gauge parameters (for FeynArts) ********)
48
49GaugeXi[ V[1] ] = GaugeXi[A];
50GaugeXi[ V[2] ] = GaugeXi[Z];
51GaugeXi[ V[3] ] = GaugeXi[W];
52GaugeXi[ V[4] ] = GaugeXi[G];
53GaugeXi[ V[7] ] = GaugeXi[Zp];
54GaugeXi[ S[1] ] = 1;
55GaugeXi[ S[2] ] = GaugeXi[Z];
56GaugeXi[ S[3] ] = GaugeXi[W];
57GaugeXi[ S[4] ] = 1;
58GaugeXi[ S[5] ] = GaugeXi[Zp];
59GaugeXi[ U[1] ] = GaugeXi[A];
60GaugeXi[ U[2] ] = GaugeXi[Z];
61GaugeXi[ U[31] ] = GaugeXi[W];
62GaugeXi[ U[32] ] = GaugeXi[W];
63GaugeXi[ U[4] ] = GaugeXi[G];
64GaugeXi[ U[7] ] = GaugeXi[Zp];
65
66
67(***** Setting for interaction order (as e.g. used by MadGraph 5) ******)
68
69M$InteractionOrderHierarchy = {
70 {QCD, 1},
71 {QED, 2}
72 };
73
74
75(**************** Parameters *************)
76
77M$Parameters = {
78
79 (* External parameters *)
80
81
82 \[Alpha]EWM1== {
83 ParameterType -> External,
84 BlockName -> BLINPUTS,
85 ParameterName -> aEWM1,
86 InteractionOrder -> {QED, -2},
87 Value -> 127.9,
88 Description -> "Inverse of the electroweak coupling constant at Z-pole"},
89
90 Gf == {
91 ParameterType -> External,
92 BlockName -> BLINPUTS,
93 InteractionOrder -> {QED, 2},
94 Value -> 1.16637 * 10^(-5),
95 Description -> "Fermi constant"},
96
97 \[Alpha]S == {
98 ParameterType -> External,
99 BlockName -> BLINPUTS,
100 TeX -> Subscript[\[Alpha], s],
101 ParameterName -> aS,
102 InteractionOrder -> {QCD, 2},
103 Value -> 0.1184,
104 Description -> "Strong coupling constant at the Z pole."},
105
106 MW == {
107 ParameterType -> External,
108 BlockName -> BLINPUTS,
109 Value -> 80.292,
110 Description -> "W mass"},
111
112 MZp == {
113 ParameterType -> External,
114 BlockName -> BLINPUTS,
115 Value -> 1500.00,
116 Description -> "Zp mass"},
117
118 g1p == {
119 ParameterType -> External,
120 BlockName -> BLINPUTS,
121 InteractionOrder -> {QED, 1},
122 Value -> 0.2,
123 Description -> "Zp coupling"},
124
125 gt == {
126 ParameterType -> External,
127 BlockName -> BLINPUTS,
128 InteractionOrder -> {QED, 1},
129 Value -> -0.1,
130 Description -> "Z-Zp mixing coupling"},
131
132 ymdo == {
133 ParameterType -> External,
134 BlockName -> YUKAWA,
135 Value -> 5.04*10^(-3),
136 OrderBlock -> {1},
137 Description -> "Down Yukawa mass"},
138
139
140 ymup == {
141 ParameterType -> External,
142 BlockName -> YUKAWA,
143 Value -> 2.55*10^(-3),
144 OrderBlock -> {2},
145 Description -> "Up Yukawa mass"},
146
147 yms == {
148 ParameterType -> External,
149 BlockName -> YUKAWA,
150 Value -> 0.101,
151 OrderBlock -> {3},
152 Description -> "Strange Yukawa mass"},
153
154 ymc == {
155 ParameterType -> External,
156 BlockName -> YUKAWA,
157 Value -> 1.27,
158 OrderBlock -> {4},
159 Description -> "Charm Yukawa mass"},
160
161 ymb == {
162 ParameterType -> External,
163 BlockName -> YUKAWA,
164 Value -> 4.7,
165 OrderBlock -> {5},
166 Description -> "Bottom Yukawa mass"},
167
168 ymt == {
169 ParameterType -> External,
170 BlockName -> YUKAWA,
171 Value -> 172.0,
172 OrderBlock -> {6},
173 Description -> "Top Yukawa mass"},
174
175 yme == {
176 ParameterType -> External,
177 BlockName -> YUKAWA,
178 Value -> 0.000511,
179 OrderBlock -> {11},
180 Description -> "Electron Yukawa mass"},
181
182 ymmu == {
183 ParameterType -> External,
184 BlockName -> YUKAWA,
185 Value -> 0.1057,
186 OrderBlock -> {13},
187 Description -> "Muon Yukawa mass"},
188
189 ymtau == {
190 ParameterType -> External,
191 BlockName -> YUKAWA,
192 Value -> 1.777,
193 OrderBlock -> {15},
194 Description -> "Tau Yukawa mass"},
195
196 MH1 == {
197 ParameterType -> External,
198 BlockName -> BLINPUTS,
199 Value -> 120.00,
200 Description -> "H1 mass"},
201
202 MH2 == {
203 ParameterType -> External,
204 BlockName -> BLINPUTS,
205 Value -> 450.00,
206 Description -> "H2 mass"},
207
208
209 Sa == {
210 ParameterType -> External,
211 BlockName -> BLINPUTS,
212 Value -> 0.1,
213 Description -> "Sine of Higgses mixing angle"},
214
215 sw2 == {
216 ParameterType -> External,
217 BlockName -> BLINPUTS,
218 Value -> 0.232,
219 Description -> "Squared Sin of the Weinberg angle"},
220
221
222
223 (* Internal Parameters *)
224
225 \[Alpha]EW == {
226 ParameterType -> Internal,
227 Value -> 1/\[Alpha]EWM1,
228 TeX -> Subscript[\[Alpha], EW],
229 ParameterName -> aEW,
230 InteractionOrder -> {QED, 2},
231 Description -> "Electroweak coupling contant"},
232
233
234 ee == {
235 TeX -> e,
236 ParameterType -> Internal,
237 Value -> Sqrt[4 Pi \[Alpha]EW],
238 InteractionOrder -> {QED, 1},
239 Description -> "Electric coupling constant"},
240
241 cw == {
242 TeX -> Subscript[c, w],
243 ParameterType -> Internal,
244 Value -> Sqrt[1 - sw2],
245 Description -> "Cos of the Weinberg angle"},
246
247 sw == {
248 TeX -> Subscript[s, w],
249 ParameterType -> Internal,
250 Value -> Sqrt[sw2],
251 Description -> "Sin of the Weinberg angle"},
252
253 gw == {
254 TeX -> Subscript[g, w],
255 ParameterType -> Internal,
256 Value -> ee / sw,
257 Definitions -> {gw -> ee / sw},
258 InteractionOrder -> {QED, 1},
259 Description -> "Weak coupling constant"},
260
261 g1 == {
262 TeX -> Subscript[g, 1],
263 ParameterType -> Internal,
264 Value -> ee / cw,
265 Definitions -> {g1 -> ee / cw},
266 InteractionOrder -> {QED, 1},
267 Description -> "U(1)Y coupling constant"},
268
269 gs == {
270 TeX -> Subscript[g, s],
271 ParameterType -> Internal,
272 Value -> Sqrt[4 Pi \[Alpha]S],
273 InteractionOrder -> {QCD, 1},
274 ParameterName -> G,
275 Description -> "Strong coupling constant"},
276
277 v == {
278 ParameterType -> Internal,
279 BlockName -> VEV,
280 Value -> 2*MW*sw/ee,
281 InteractionOrder -> {QED, -1},
282 Description -> "H1 VEV"},
283
284
285 x == {
286 ParameterType -> Internal,
287 BlockName -> VEV,
288 Value -> MZp/(2*g1p)*Sqrt[1-gt^2*v^2/(4*MZp^2-v^2*(gw^2+g1^2))],
289 InteractionOrder -> {QED, -1},
290 Description -> "H2 VEV"},
291
292
293 Ca == {
294 ParameterType -> Internal,
295 Value -> Sqrt[1-Sa^2],
296 ParameterName -> Ca,
297 Description -> "Cosine of Higgses mixing angle"},
298
299
300 yl == {
301 TeX -> Superscript[y, l],
302 Indices -> {Index[Generation]},
303 AllowSummation -> True,
304 ParameterType -> Internal,
305 Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymmu / v, yl[3] -> Sqrt[2] ymtau / v},
306 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
307 InteractionOrder -> {QED, 1},
308 ComplexParameter -> False,
309 Description -> "Lepton Yukawa coupling"},
310
311 yu == {
312 Indices -> {Index[Generation]},
313 AllowSummation -> True,
314 AllowSummation -> True,
315 ParameterType -> Internal,
316 Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
317 ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
318 InteractionOrder -> {QED, 1},
319 ComplexParameter -> False,
320 Description -> "U-quark Yukawa coupling"},
321
322 yd == {
323 TeX -> Superscript[y, d],
324 Indices -> {Index[Generation]},
325 AllowSummation -> True,
326 ParameterType -> Internal,
327 Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
328 ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
329 InteractionOrder -> {QED, 1},
330 ComplexParameter -> False,
331 Description -> "D-quark Yukawa coupling"},
332
333 ynd == {
334 Indices -> {Index[Generation]},
335 AllowSummation -> True,
336 ParameterType -> Internal,
337 Value -> {ynd[1] -> Sqrt[2*MnL1*MnH1]/v,
338 ynd[2] -> Sqrt[2*MnL2*MnH2]/v,
339 ynd[3] -> Sqrt[2*MnL3*MnH3]/v},
340 ParameterName -> {ynd[1] -> ynd1,
341 ynd[2] -> ynd2,
342 ynd[3] -> ynd3},
343 InteractionOrder -> {QED, 1},
344 ComplexParameter -> False,
345 Description -> "Dirac neutrino Yukawa coupling"},
346
347 ynm == {
348 Indices -> {Index[Generation]},
349 AllowSummation -> True,
350 ParameterType -> Internal,
351 Value -> {ynm[1] -> (MnH1-MnL1)/Sqrt[2]/x,
352 ynm[2] -> (MnH2-MnL2)/Sqrt[2]/x,
353 ynm[3] -> (MnH3-MnL3)/Sqrt[2]/x},
354 ParameterName -> {ynm[1] -> ynm1, ynm[2] -> ynm2, ynm[3] -> ynm3},
355 InteractionOrder -> {QED, 1},
356 ComplexParameter -> False,
357 Description -> "Majorana neutrino Yukawa coupling"},
358
359 Mdd == {
360 Indices -> {Index[Generation]},
361 AllowSummation -> True,
362 ParameterType -> Internal,
363 Value -> {Mdd[1] -> ynd1*v/Sqrt[2],
364 Mdd[2] -> ynd2*v/Sqrt[2],
365 Mdd[3] -> ynd3*v/Sqrt[2]},
366 ParameterName -> {Mdd[1] -> Mdd1, Mdd[2] -> Mdd2, Mdd[3] -> Mdd3},
367 ComplexParameter -> False,
368 Description -> "Neutrino Dirac Mass"},
369
370 s12 == {
371 TeX -> Subscript[S\[Theta], 12],
372 ParameterType -> External,
373 BlockName -> CKMBLOCK,
374 Value -> 0.221,
375 Description -> "Sin(theta_12), PDG-94"},
376
377 s23 == {
378 TeX -> Subscript[S\[Theta], 23],
379 ParameterType -> External,
380 BlockName -> CKMBLOCK,
381 Value -> 0.040,
382 Description -> "Sin(theta_23), PDG-94"},
383
384 s13 == {
385 TeX -> Subscript[S\[Theta], 13],
386 ParameterType -> External,
387 BlockName -> CKMBLOCK,
388 Value -> 0.0035,
389 Description -> "Sin(theta_13), PDG-94"},
390
391 c12 == {
392 TeX -> Subscript[C\[Theta], 12],
393 ParameterType -> Internal,
394 BlockName -> CKMBLOCK,
395 Value -> Sqrt[1-s12^2],
396 Description -> "Cos(theta_12)"},
397
398 c23 == {
399 TeX -> Subscript[C\[Theta], 23],
400 ParameterType -> Internal,
401 BlockName -> CKMBLOCK,
402 Value -> Sqrt[1-s23^2],
403 Description -> "Cos(theta_23)"},
404
405 c13 == {
406 TeX -> Subscript[C\[Theta], 13],
407 ParameterType -> Internal,
408 BlockName -> CKMBLOCK,
409 Value -> Sqrt[1-s13^2],
410 Description -> "Cos(theta_13)"},
411
412 CKM == {
413 Indices -> {Index[Generation], Index[Generation]},
414 TensorClass -> CKM,
415 Unitary -> True,
416 Value -> {CKM[1,1] -> c12*c13,
417 CKM[1,2] -> s12*c13,
418 CKM[1,3] -> s13,
419 CKM[2,1] -> -s12*c23-c12*s23*s13,
420 CKM[2,2] -> c12*c23-s12*s23*s13,
421 CKM[2,3] -> s23*c13,
422 CKM[3,1] -> s12*s23-c12*c23*s13,
423 CKM[3,2] -> -c12*s23-s12*c23*s13,
424 CKM[3,3] -> c23*c13},
425 Description -> "CKM-Matrix"},
426
427 San == {
428 Indices -> {Index[Generation]},
429 AllowSummation -> True,
430 ParameterType -> Internal,
431 Value -> {San[1] -> Sin[ArcSin[-2*Mdd1/Sqrt[4*Mdd1^2+(MnH1-MnL1)^2]]/2],
432 San[2] -> Sin[ArcSin[-2*Mdd2/Sqrt[4*Mdd2^2+(MnH2-MnL2)^2]]/2],
433 San[3] -> Sin[ArcSin[-2*Mdd3/Sqrt[4*Mdd3^2+(MnH3-MnL3)^2]]/2]},
434 ParameterName -> {San[1] -> San1, San[2] -> San2, San[3] -> San3},
435 ComplexParameter -> False,
436 Description -> "Sin-array of neutrino mass-eigenstates"},
437
438 Can == {
439 Indices -> {Index[Generation]},
440 AllowSummation -> True,
441 ParameterType -> Internal,
442 Value -> {Can[1] -> Sqrt[1-San1^2],
443 Can[2] -> Sqrt[1-San2^2],
444 Can[3] -> Sqrt[1-San3^2]},
445 Definitions -> {Can[1]*San1-> Sa2n1/2,
446 Can[2]*San2-> Sa2n2/2,
447 Can[3]*San3-> Sa2n3/2,
448 Can[1]^2 -San1^2-> Ca2n1,
449 Can[2]^2 -San2^2-> Ca2n2,
450 Can[3]^2 -San3^2-> Ca2n3},
451 ParameterName -> {Can[1] -> Can1, Can[2] -> Can2, Can[3] -> Can3},
452 ComplexParameter -> False,
453 Description -> "Cos-array of neutrino mass-eigenstates"},
454
455
456
457 \[Lambda]1 == {
458 ParameterType -> Internal,
459 Value -> MH1^2 /(2*v^2)*Ca^2 + MH2^2 /(2*v^2)*Sa^2,
460 ParameterName -> lam1,
461 InteractionOrder -> {QED, 2},
462 Description -> "Lambda 1"},
463
464 \[Lambda]2 == {
465 ParameterType -> Internal,
466 Value -> MH1^2 /(2*x^2)*Sa^2 + MH2^2 /(2*x^2)*Ca^2,
467 ParameterName -> lam2,
468 InteractionOrder -> {QED, 2},
469 Description -> "Lambda 2"},
470
471 \[Lambda]3 == {
472 ParameterType -> Internal,
473 Value -> (MH2^2 - MH1^2)/(x*v)*Sa*Ca,
474 ParameterName -> lam3,
475 InteractionOrder -> {QED, 2},
476 Description -> "Lambda 3, mixing parameter"},
477
478 mu2H1 == {
479 ParameterType -> Internal,
480 Value -> - \[Lambda]1 * v^2 - \[Lambda]3 /2 * x^2,
481 TeX -> m^2,
482 Description -> "Coefficient of the quadratic piece of the H1 potential"},
483
484 mu2H2 == {
485 ParameterType -> Internal,
486 Value -> - \[Lambda]3 /2 * v^2 - \[Lambda]2 * x^2,
487 TeX -> \[Mu]^2,
488 Description -> "Coefficient of the quadratic piece of the H2 potential"},
489
490
491 Sp2num == {
492 ParameterType -> Internal,
493 Value -> 2*gt*Sqrt[(ee/sw)^2+(ee/cw)^2]},
494
495 Cp2num == {
496 ParameterType -> Internal,
497 Value -> gt^2+16*(x/v)^2*g1p^2-(ee/sw)^2-(ee/cw)^2},
498
499 Sp == {
500 AllowSummation -> True,
501 ParameterType -> Internal,
502 Value -> Sin[ArcSin[Sp2num/Sqrt[Sp2num^2+Cp2num^2]]/2],
503 ComplexParameter -> False,
504 Description -> "Sin-array of neutrino mass-eigenstates"},
505
506 Cp == {
507 AllowSummation -> True,
508 ParameterType -> Internal,
509 Value -> Sqrt[1-Sp^2],
510 ComplexParameter -> False,
511 Description -> "Cos-array of neutrino mass-eigenstates"},
512
513
514 Cn == {
515 ParameterType -> Internal,
516 ComplexParameter -> False,
517 Value -> (ee/sw)^2+(ee/cw)^2+gt^2+16*(x/v)^2*g1p^2},
518
519 Dn == {
520 ParameterType -> Internal,
521 ComplexParameter -> False,
522 Value -> 64*((ee/sw)^2+(ee/cw)^2)*g1p^2*v^2*x^2},
523
524
525 MZ == {
526 ParameterType -> Internal,
527 Value -> Sqrt[(Cn*v^2-Sqrt[-Dn+v^4*Cn^2])/8],
528 Description -> "Z mass"},
529
530 S2gNum == {
531 ParameterType -> Internal,
532 ComplexParameter -> False,
533 Value -> 8*x/v*gt*g1p},
534
535 C2gNum == {
536 ParameterType -> Internal,
537 ComplexParameter -> False,
538 Value -> (ee/sw)^2+(ee/cw)^2+gt^2-16*(x/v)^2*g1p^2},
539
540
541 sg == {
542 ParameterType -> Internal,
543 ComplexParameter -> False,
544 Value -> Sin[ArcSin[-S2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2],
545 Description -> "cosine of Z-Zp goldostone mixing angle"},
546
547 cg == {
548 ParameterType -> Internal,
549 ComplexParameter -> False,
550 Value -> Sqrt[1-sg^2],
551 Description -> "sine of Z-Zp goldstone mixing angle"}
552(* Value -> Cos[ArcCos[-C2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2], *)
553}
554
555(************** Gauge Groups ******************)
556
557M$GaugeGroups = {
558
559 U1BL == {
560 Abelian -> True,
561 GaugeBoson -> Bp,
562 Charge -> BL,
563 CouplingConstant -> g1p},
564
565 U1Y == {
566 Abelian -> True,
567 GaugeBoson -> B,
568 Charge -> Y,
569 CouplingConstant -> g1},
570
571 SU2L == {
572 Abelian -> False,
573 GaugeBoson -> Wi,
574 StructureConstant -> Eps,
575 CouplingConstant -> gw},
576
577 SU3C == {
578 Abelian -> False,
579 GaugeBoson -> G,
580 StructureConstant -> f,
581 SymmetricTensor -> dSUN,
582 Representations -> {T, Colour},
583 CouplingConstant -> gs}
584}
585
586(********* Particle Classes **********)
587
588M$ClassesDescription = {
589
590(********** Fermions ************)
591
592 (* Mass-Eigenstate light neutrino: Q = 0, BL= -1 *)
593
594 F[11] == {
595 ClassName -> nL,
596 ClassMembers -> {nL1, nL2, nL3},
597 FlavorIndex -> Generation,
598 SelfConjugate -> True,
599 Indices -> {Index[Generation]},
600 Mass -> {MnL, {MnL1, 10^(-9)}, {MnL2, 10^(-9)}, {MnL3, 10^(-9)}},
601 Width -> 0,
602 PropagatorLabel -> {"nL", "nul1", "nul2", "nul3"},
603 PropagatorType -> Straight,
604 ParticleName -> {"n1", "n2", "n3"},
605 PropagatorArrow -> Forward,
606 PDG -> {12, 14, 16},
607 FullName -> {"Light neutrino 1", "Light neutrino 2", "Light neutrino 3"} },
608
609 (* Mass-Eigenstate heavy neutrino: Q = 0, BL= -1 *)
610
611 F[12] == {
612 ClassName -> nH,
613 ClassMembers -> {nH1, nH2, nH3},
614 FlavorIndex -> Generation,
615 SelfConjugate -> True,
616 Indices -> {Index[Generation]},
617 Mass -> {MnH, {MnH1, 200.00}, {MnH2, 200.00}, {MnH3, 200.00}},
618 Width -> 10^(-13),
619 PropagatorLabel -> {"nH", "nuh1", "nuh2", "nuh3"},
620 PropagatorType -> Straight,
621 ParticleName -> {"~n1", "~n2", "~n3"},
622 PropagatorArrow -> Forward,
623 PDG -> {9100012, 9100014, 9100016},
624 FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"} },
625
626 (* Left-handed neutrino: unphysical *)
627 F[13] == {
628 ClassName -> nF,
629 ClassMembers -> {nF1,nF2,nF3},
630 FlavorIndex -> Generation,
631 SelfConjugate -> True,
632 Indices -> {Index[Generation]},
633 Unphysical -> True,
634 Definitions -> {nF[s_,i_] -> Can[i] nL[s,i]-San[i] nH[s,i]},
635 FullName -> {"Majorana LH component of Dirac neutrino 1",
636 "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} },
637
638 (* Right-handed neutrino: unphysical *)
639 F[14] == {
640 ClassName -> nR,
641 ClassMembers -> {nR1,nR2,nR3},
642 FlavorIndex -> Generation,
643 SelfConjugate -> True,
644 Indices -> {Index[Generation]},
645 Unphysical -> True,
646 Definitions -> {nR[s_,i_] -> San[i] nL[s,i]+Can[i] nH[s,i]},
647 FullName -> {"Majorana LH component of Dirac neutrino 1", "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} },
648
649
650 (* Flavour-eigenstate neutrino: unphysical *)
651 F[15] == {
652 ClassName -> vl,
653 ClassMembers -> {vle,vlm,vlt},
654 FlavorIndex -> Generation,
655 SelfConjugate -> False,
656 Indices -> {Index[Generation]},
657 QuantumNumbers -> {Q -> 0, LeptonNumber -> 1, BarionLepton -> -1},
658 Unphysical -> True,
659 Definitions -> {vl[s_,i_] -> left[nF[s,i]]+right[nR[s,i]]},
660 ParticleName -> {"nue", "num", "nut"},
661 AntiParticleName -> {"nue-bar", "num-bar", "nut-bar"},
662 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
663
664
665 (* Leptons (electron): I_3 = -1/2, Q = -1, BL= -1 *)
666 F[2] == {
667 ClassName -> l,
668 ClassMembers -> {e, m, tt},
669 FlavorIndex -> Generation,
670 SelfConjugate -> False,
671 Indices -> {Index[Generation]},
672 Mass -> {Ml, {ME, 0.000511}, {MM, 0.1057}, {MTA, 1.777}},
673 Width -> 0,
674 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1, BarionLepton -> -1},
675 PropagatorLabel -> {"l", "e", "m", "tt"},
676 PropagatorType -> Straight,
677 ParticleName -> {"e", "m", "l"},
678 AntiParticleName -> {"E", "M", "L"},
679 PropagatorArrow -> Forward,
680 PDG -> {11, 13, 15},
681 FullName -> {"Electron", "Muon", "Tau"} },
682
683 (* Quarks (u): I_3 = +1/2, Q = +2/3, BL=1/3 *)
684 F[3] == {
685 ClassMembers -> {u, c, t},
686 ClassName -> uq,
687 FlavorIndex -> Generation,
688 SelfConjugate -> False,
689 Indices -> {Index[Generation], Index[Colour]},
690 Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.27}, {MT, 172.0}},
691 Width -> {0, 0, {WT, 1.50833649}},
692 QuantumNumbers -> {Q -> 2/3, BarionLepton -> 1/3},
693 PropagatorLabel -> {"uq", "u", "c", "t"},
694 ParticleName -> {"u", "c", "t"},
695 AntiParticleName -> {"U", "C", "T"},
696 PropagatorType -> Straight,
697 PropagatorArrow -> Forward,
698 PDG -> {2, 4, 6},
699 FullName -> {"u-quark", "c-quark", "t-quark"}},
700
701 (* Quarks (d): I_3 = -1/2, Q = -1/3, BL=1/3 *)
702 F[4] == {
703 ClassMembers -> {d, s, b},
704 ClassName -> dq,
705 FlavorIndex -> Generation,
706 SelfConjugate -> False,
707 Indices -> {Index[Generation], Index[Colour]},
708 Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
709 Width -> 0,
710 QuantumNumbers -> {Q -> -1/3, BarionLepton -> 1/3},
711 ParticleName -> {"d", "s", "b"},
712 AntiParticleName -> {"D", "S", "B"},
713 PropagatorLabel -> {"dq", "d", "s", "b"},
714 PropagatorType -> Straight,
715 PropagatorArrow -> Forward,
716 PDG -> {1,3,5},
717 FullName -> {"d-quark", "s-quark", "b-quark"} },
718
719
720(********** Ghosts **********)
721 U[1] == {
722 ClassName -> ghA,
723 SelfConjugate -> False,
724 Indices -> {},
725 Ghost -> A,
726 Mass -> 0,
727 QuantumNumbers -> {GhostNumber -> 1},
728 PropagatorLabel -> uA,
729 PropagatorType -> GhostDash,
730 PropagatorArrow -> Forward},
731
732 U[2] == {
733 ClassName -> ghZ,
734 SelfConjugate -> False,
735 Indices -> {},
736 Mass -> {MZ, Internal},
737 Ghost -> Z,
738 QuantumNumbers -> {GhostNumber -> 1},
739 PropagatorLabel -> uZ,
740 PropagatorType -> GhostDash,
741 PropagatorArrow -> Forward},
742
743 U[31] == {
744 ClassName -> ghWp,
745 SelfConjugate -> False,
746 Indices -> {},
747 Mass -> {MW, Internal},
748 Ghost -> W,
749 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
750 PropagatorLabel -> uWp,
751 PropagatorType -> GhostDash,
752 PropagatorArrow -> Forward},
753
754 U[32] == {
755 ClassName -> ghWm,
756 SelfConjugate -> False,
757 Indices -> {},
758 Mass -> {MW, Internal},
759 Ghost -> Wbar,
760 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
761 PropagatorLabel -> uWm,
762 PropagatorType -> GhostDash,
763 PropagatorArrow -> Forward},
764
765 U[4] == {
766 ClassName -> ghG,
767 SelfConjugate -> False,
768 Indices -> {Index[Gluon]},
769 Ghost -> G,
770 Mass -> 0,
771 QuantumNumbers -> {GhostNumber -> 1},
772 PropagatorLabel -> uG,
773 PropagatorType -> GhostDash,
774 PropagatorArrow -> Forward},
775
776 U[5] == {
777 ClassName -> ghWi,
778 Unphysical -> True,
779 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
780 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
781 ghWi[3] -> cw*Cp ghZ + sw ghA - cw*Sp ghZp},
782 SelfConjugate -> False,
783 Indices -> {Index[SU2W]},
784 FlavorIndex -> SU2W,
785 Ghost -> Wi},
786
787 U[6] == {
788 ClassName -> ghB,
789 SelfConjugate -> False,
790 Definitions -> {ghB -> -sw*Cp ghZ + cw ghA + sw*Sp ghZp},
791 Indices -> {},
792 Unphysical -> True,
793 Ghost -> B},
794
795 U[7] == {
796 ClassName -> ghZp,
797 SelfConjugate -> False,
798 Indices -> {},
799 Mass -> {MZp, Internal},
800 Ghost -> Zp,
801 QuantumNumbers -> {GhostNumber -> 1},
802 PropagatorLabel -> uZp,
803 PropagatorType -> GhostDash,
804 PropagatorArrow -> Forward},
805
806 U[8] == {
807 ClassName -> ghBp,
808 SelfConjugate -> False,
809 Definitions -> {ghBp -> Sp ghZ + Cp ghZp},
810 Indices -> {},
811 Unphysical -> True,
812 Ghost -> Bp},
813
814(************ Gauge Bosons ***************)
815 (* Gauge bosons: Q = 0 *)
816 V[1] == {
817 ClassName -> A,
818 SelfConjugate -> True,
819 Indices -> {},
820 Mass -> 0,
821 Width -> 0,
822 PropagatorLabel -> "a",
823 PropagatorType -> W,
824 PropagatorArrow -> None,
825 PDG -> 22,
826 FullName -> "Photon" },
827
828 V[2] == {
829 ClassName -> Z,
830 SelfConjugate -> True,
831 Indices -> {},
832 Mass -> {MZ, Internal},
833 Width -> {WZ, 2.4952},
834 PropagatorLabel -> "Z",
835 PropagatorType -> Sine,
836 PropagatorArrow -> None,
837 PDG -> 23,
838 FullName -> "Z" },
839
840 (* Gauge bosons: Q = -1 *)
841 V[3] == {
842 ClassName -> W,
843 SelfConjugate -> False,
844 Indices -> {},
845 Mass -> {MW, Internal},
846 Width -> {WW, 2.085},
847 QuantumNumbers -> {Q -> 1},
848 PropagatorLabel -> "W",
849 PropagatorType -> Sine,
850 PropagatorArrow -> Forward,
851 ParticleName ->"W+",
852 AntiParticleName ->"W-",
853 PDG -> 24,
854 FullName -> "W" },
855
856V[4] == {
857 ClassName -> G,
858 SelfConjugate -> True,
859 Indices -> {Index[Gluon]},
860 Mass -> 0,
861 Width -> 0,
862 PropagatorLabel -> G,
863 PropagatorType -> C,
864 PropagatorArrow -> None,
865 PDG -> 21,
866 FullName -> "G" },
867
868V[5] == {
869 ClassName -> Wi,
870 Unphysical -> True,
871 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
872 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
873 Wi[mu_, 3] -> sw A[mu] + cw*Cp Z[mu] - cw*Sp Zp[mu]},
874 SelfConjugate -> True,
875 Indices -> {Index[SU2W]},
876 FlavorIndex -> SU2W,
877 Mass -> 0,
878 PDG -> {1,2,3}},
879
880V[6] == {
881 ClassName -> B,
882 SelfConjugate -> True,
883 Definitions -> {B[mu_] -> cw A[mu] - sw*Cp Z[mu] + sw*Sp Zp[mu]},
884 Indices -> {},
885 Mass -> 0,
886 Unphysical -> True},
887
888V[7] == {
889 ClassName -> Zp,
890 SelfConjugate -> True,
891 Indices -> {},
892 Mass -> {MZp, Internal},
893 Width -> {WZp, 80.00},
894 PropagatorLabel -> "Zp",
895 PropagatorType -> Sine,
896 PropagatorArrow -> None,
897 PDG -> 9900032,
898 FullName -> "Zp" },
899
900V[8] == {
901 ClassName -> Bp,
902 SelfConjugate -> True,
903 Definitions -> {Bp[mu_] -> Sp Z[mu] + Cp Zp[mu]},
904 Indices -> {},
905 Unphysical -> True},
906
907
908(************ Scalar Fields **********)
909 (* physical Higgs: Q = 0 *)
910 S[1] == {
911 ClassName -> H1,
912 SelfConjugate -> True,
913 Mass -> {MH1, Internal},
914 Width -> {WH1, 1.5},
915 PropagatorLabel -> "H1",
916 PropagatorType -> D,
917 PropagatorArrow -> None,
918 PDG -> 9900025,
919 FullName -> "H1" },
920
921 S[2] == {
922 ClassName -> phiZ,
923 SelfConjugate -> True,
924 Mass -> {MZ, Internal},
925 Width -> Wphi,
926 PropagatorLabel -> "PhiZ",
927 PropagatorType -> D,
928 PropagatorArrow -> None,
929 ParticleName ->"phiZ",
930 PDG -> 9900250,
931 FullName -> "PhiZ",
932 Goldstone -> Z },
933
934 S[3] == {
935 ClassName -> phi2,
936 SelfConjugate -> False,
937 Mass -> {MW, Internal},
938 Width -> Wphi2,
939 PropagatorLabel -> "Phi2",
940 PropagatorType -> D,
941 PropagatorArrow -> None,
942 ParticleName ->"phi+",
943 AntiParticleName ->"phi-",
944 PDG -> 9900251,
945 FullName -> "Phi2",
946 Goldstone -> W,
947 QuantumNumbers -> {Q -> 1}},
948
949 S[4] == {
950 ClassName -> H2,
951 SelfConjugate -> True,
952 Mass -> {MH2, Internal},
953 Width -> {WH2, 10},
954 PropagatorLabel -> "H2",
955 PropagatorType -> D,
956 PropagatorArrow -> None,
957 PDG -> 9900026,
958 FullName -> "H2" },
959
960 S[5] == {
961 ClassName -> phiZp,
962 SelfConjugate -> True,
963 Mass -> {MZp, Internal},
964 Width -> WphiZp,
965 PropagatorLabel -> "PhiZp",
966 PropagatorType -> D,
967 PropagatorArrow -> None,
968 ParticleName ->"phiZp",
969 PDG -> 9900252,
970 FullName -> "PhiZp",
971 Goldstone -> Zp },
972
973 S[6] == {
974 ClassName -> phi,
975 Unphysical -> True,
976 Definitions -> {phi -> cg phiZ - sg phiZp},
977 SelfConjugate -> True},
978
979 S[7] == {
980 ClassName -> phip,
981 Unphysical -> True,
982 Definitions -> {phip -> sg phiZ + cg phiZp},
983 SelfConjugate -> True},
984
985 S[8] == {
986 ClassName -> phic,
987 Unphysical -> True,
988 Definitions -> {phic[1] -> (phi2 + phi2bar)/Sqrt[2],
989 phic[2] -> (phi2bar - phi2)/Sqrt[2]/I},
990 SelfConjugate -> False}
991
992}
993
994
995(*****************************************************************************************)
996
997(* mZp Lagrangian *)
998
999(******************** Gauge F^2 Lagrangian terms*************************)
1000(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1001 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
1002 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
1003
1004 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[Bp[nu], mu] - del[Bp[mu], nu])^2 -
1005
1006 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
1007 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
1008
1009
1010(********************* Fermion Lagrangian terms*************************)
1011(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1012 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
1013
1014 Lkin = I uqbar.Ga[mu].del[uq, mu] +
1015 I dqbar.Ga[mu].del[dq, mu] +
1016 I lbar.Ga[mu].del[l, mu] +
1017 I left[anti[vl]].Ga[mu].del[left[vl],mu] +
1018 I right[anti[vl]].Ga[mu].del[right[vl],mu];
1019
1020 LQCD = gs (uqbar.Ga[mu].T[a].uq +
1021 dqbar.Ga[mu].T[a].dq)G[mu, a];
1022
1023 LBright =
1024 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
1025 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
1026 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
1027
1028 LBleft =
1029 -ee/cw B[mu]/2 left[anti[vl]].Ga[mu].ProjM.vl - (*Y_LL=-1*)
1030 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
1031 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
1032 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
1033
1034 LWleft = ee/sw/2(
1035 left[anti[vl]].Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
1036 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
1037
1038 Sqrt[2] left[anti[vl]].Ga[mu].ProjM.l W[mu] +
1039 Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
1040
1041 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
1042 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
1043
1044 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
1045 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
1046 );
1047
1048 LBpright =
1049 - g1p Bp[mu] right[anti[vl]].Ga[mu].ProjP.vl + (*Y_vlR=0, BL_vlR=-1*)
1050 (-1*gt -g1p) Bp[mu] lbar.Ga[mu].ProjP.l + (*Y_lR=-1, BL_lR=-1*)
1051 (2/3*gt + g1p/3) Bp[mu] uqbar.Ga[mu].ProjP.uq + (*Y_uR=2/3, BL_uR=1/3*)
1052 (-1/3*gt + g1p/3) Bp[mu] dqbar.Ga[mu].ProjP.dq; (*Y_dR=-1/3, BL_dR=1/3*)
1053
1054 LBpleft =
1055 - (gt/2 + g1p) Bp[mu] left[anti[vl]].Ga[mu].ProjM.vl - (*Y_lL=-1/2, BL_vlL=-1*)
1056 (gt/2 + g1p) Bp[mu] lbar.Ga[mu].ProjM.l + (*Y_lL=-1/2, BL_lL=-1*)
1057 (gt/3/2 + g1p/3) Bp[mu] uqbar.Ga[mu].ProjM.uq + (*Y_qL=1/6, BL_uL=1/3*)
1058 (gt/3/2 + g1p/3) Bp[mu] dqbar.Ga[mu].ProjM.dq (*Y_qL=1/6, BL_dL=1/3*)
1059 ;
1060
1061 Lkin + LQCD + LBright + LBleft + LWleft + LBpright + LBpleft ];
1062
1063(******************** Higgs Lagrangian terms****************************)
1064 Phi := If[FeynmanGauge, {-I phi2, (v + Ca*H1+Sa*H2 + I phi)/Sqrt[2]}, {0, (v + Ca*H1+Sa*H2)/Sqrt[2]}];
1065 Phibar := If[FeynmanGauge, {I phi2bar, (v + Ca*H1+Sa*H2 - I phi)/Sqrt[2]} ,{0, (v + Ca*H1+Sa*H2)/Sqrt[2]}];
1066
1067 Chi := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 + I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}];
1068 Chibar := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 - I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}];
1069
1070 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphichi, Dcp, Dcpbar},
1071
1072 PMVec = Table[PauliSigma[i], {i, 3}];
1073 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1074
1075 (*Y_phi=1/2*)
1076 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + gt/2 Bp[mu] f + ee/sw/2 (Wvec[mu].PMVec).f;
1077 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + gt/2 Bp[mu] f + ee/sw/2 f.(Wvec[mu].PMVec);
1078
1079 (*BL_phi=2*)
1080 Dcp[f_, mu_] := I del[f, mu] + 2*g1p Bp[mu] f ;
1081 Dcpbar[f_, mu_] := -I del[f, mu] + 2*g1p Bp[mu] f ;
1082
1083 Vphichi[Phi_, Phibar_, Chi_, Chibar_] := mu2H1 Phibar.Phi + mu2H2 Chibar.Chi +
1084 \[Lambda]1 (Phibar.Phi)^2 + \[Lambda]2 (Chibar.Chi)^2 + \[Lambda]3 (Phibar.Phi)*(Chibar.Chi);
1085
1086 (Dcbar[Phibar, mu]).Dc[Phi, mu] + (Dcpbar[Chibar, mu]).Dcp[Chi, mu] - Vphichi[Phi, Phibar, Chi, Chibar]
1087
1088 ];
1089
1090
1091
1092(*************** Yukawa Lagrangian***********************)
1093(*NOTE: Neutrino states have been expanded on the LH/RH components and the LH mass terms have been changed signs*)
1094
1095LYuk := If[FeynmanGauge,
1096
1097 Module[{s,r,n,m,i}, -
1098 yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
1099 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] -
1100
1101 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2 -I phi)/Sqrt[2] + (*This sign from eps matrix*)
1102 yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)
1103
1104 - yl[n] Can[n] anti[nL][s,n].ProjP[s,r].l[r,n] (-I phi2)
1105 + yl[n] San[n] anti[nH][s,n].ProjP[s,r].l[r,n] (-I phi2)
1106
1107 - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] +
1108 ynd[n] San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]+
1109 ynd[n] San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]-
1110
1111 ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]
1112
1113 - ynd[n] San[n] lbar[s,n].ProjP[s,r].nL[r,n] (I phi2bar) +
1114 ynd[n] Can[n] lbar[s,n].ProjP[s,r].nH[r,n] (I phi2bar) +
1115
1116 ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]-
1117 ynm[n] Can[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]-
1118
1119 ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]
1120
1121
1122 ],
1123
1124 Module[{s,r,n,m,i}, -
1125 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2] -
1126 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2]
1127
1128 - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2] +
1129 ynd[n] San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]+
1130 ynd[n] San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]-
1131
1132 ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]+
1133
1134
1135
1136 ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]-
1137 ynm[n] Can[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]-
1138
1139 ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]
1140
1141 ]
1142 ];
1143
1144LYukawa := LYuk + HC[LYuk];
1145
1146
1147
1148(**************Ghost terms**************************)
1149(* Now we need the ghost terms which are of the form: *)
1150(* - g * antighost * d_BRST G *)
1151(* where d_BRST G is BRST transform of the gauge fixing function. *)
1152
1153LGhost := If[FeynmanGauge,
1154 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB, dBRSTBp, LGhostBp},
1155
1156 (***********First the pure gauge piece.**********************)
1157 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1158 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1159
1160 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
1161 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
1162
1163 dBRSTB[mu_] := cw/ee del[ghB, mu];
1164 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
1165
1166 dBRSTBp[mu_] := 1/g1p del[ghBp, mu];
1167 LGhostBp := - g1p ghBpbar.del[dBRSTBp[mu],mu];
1168
1169 (***********Next the piece from the scalar field.************)
1170 LGhostphi :=
1171 (*- ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
1172 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
1173 ee/(2*sw) MW ( ( (v+Ca*H1+Sa*H2) + I phi) ghWpbar.ghWp +
1174 ( (v+Ca*H1+Sa*H2) - I phi) ghWmbar.ghWm ) -
1175 I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
1176 ee/(2*sw*cw) MZ (v+Ca*H1+Sa*H2) ghZbar.ghZ *)
1177
11781/4*gw*v (-gw*(v+Ca*H1+Sa*H2) ghWibar[1].ghWi[1] +g1 phic[2] ghWibar[1].ghB +gw phic[2] ghWibar[1].ghWi[3] -gw phi ghWibar[1].ghWi[2] + gt phic[2] ghWibar[1].ghBp) +
11791/4*gw*v (-gw*(v+Ca*H1+Sa*H2) ghWibar[2].ghWi[2] -g1 phic[1] ghWibar[2].ghB -gw phic[1] ghWibar[2].ghWi[3] +gw phi ghWibar[2].ghWi[1] -gt phic[1] ghWibar[2].ghBp) +
11801/4*gw*v (g1*(v+Ca*H1+Sa*H2) ghWibar[3].ghB -gw*(v+Ca*H1+Sa*H2) ghWibar[3].ghWi[3] +gw phic[1] ghWibar[3].ghWi[2]
1181-gw phic[2] ghWibar[3].ghWi[1] +gt (v+Ca*H1+Sa*H2) ghWibar[3].ghBp ) +
11821/4*g1*v (-g1*(v+Ca*H1+Sa*H2) ghBbar.ghB +gw*(v+Ca*H1+Sa*H2) ghBbar.ghWi[3] -gw phic[1] ghBbar.ghWi[2] +gw phic[2] ghBbar.ghWi[1] -gt*(v+Ca*H1+Sa*H2) ghBbar.ghBp) +
11831/4*gt*v (-g1*(v+Ca*H1+Sa*H2) ghBpbar.ghB +gw*(v+Ca*H1+Sa*H2) ghBpbar.ghWi[3] -gw phic[1] ghBpbar.ghWi[2] +gw phic[2] ghBpbar.ghWi[1] -gt (v+Ca*H1+Sa*H2) ghBpbar.ghBp) -
11844*g1p^2*x*(x-Sa*H1+Ca*H2) ghBpbar.ghBp
1185;
1186
1187 (***********Now add the pieces together.********************)
1188 LGhostG + LGhostWi + LGhostB + LGhostphi + LGhostBp ]
1189
1190,
1191
1192 (*If unitary gauge, only include the gluonic ghost.*)
1193 Block[{dBRSTG,LGhostG},
1194
1195 (***********First the pure gauge piece.**********************)
1196 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1197 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1198
1199 (***********Now add the pieces together.********************)
1200 LGhostG]
1201
1202];
1203
1204(*********Total SM Lagrangian*******)
1205LmZp := LGauge + LHiggs + LFermions + LYukawa + LGhost;