B-L-SM: B-L.fr

File B-L.fr, 33.9 KB (added by Lorenzo Basso, 15 years ago)

Pure B-L model FR file

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the pure B-L model ******)
3(****** ******)
4(****** Authors: L. Basso, G. M. Pruna ******)
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$ModelName = "B-L-FR";
13
14
15M$Information = {Authors -> {"L. Basso", "G. M. Pruna"},
16Version -> "1.1",
17 Date -> "27-10-2011",
18 Institutions -> {"University of Southampton, UK", "RAL-PPD, Didcot, UK", "Albert-Ludwigs-UniversitÀt Freiburg"},
19 Emails -> {"lorenzo.basso@physik.uni-freiburg.de", "Giovanni_Marco.Pruna@tu-dresden.de"},
20 References -> " L.~Basso, A.~Belyaev, S.~Moretti and C.~H.~Shepherd-Themistocleous, \"Phenomenology of the minimal B-L extension of the Standard model: Z' and neutrinos,\", Phys. Rev. D 80, 055030 (2009) [arXiv:0812.4313 [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(******* Gauge parameters (for FeynArts) ********)
46
47GaugeXi[ V[1] ] = GaugeXi[A];
48GaugeXi[ V[2] ] = GaugeXi[Z];
49GaugeXi[ V[3] ] = GaugeXi[W];
50GaugeXi[ V[4] ] = GaugeXi[G];
51GaugeXi[ V[7] ] = GaugeXi[Zp];
52GaugeXi[ S[1] ] = 1;
53GaugeXi[ S[2] ] = GaugeXi[Z];
54GaugeXi[ S[3] ] = GaugeXi[W];
55GaugeXi[ S[4] ] = 1;
56GaugeXi[ S[5] ] = GaugeXi[Zp];
57GaugeXi[ U[1] ] = GaugeXi[A];
58GaugeXi[ U[2] ] = GaugeXi[Z];
59GaugeXi[ U[31] ] = GaugeXi[W];
60GaugeXi[ U[32] ] = GaugeXi[W];
61GaugeXi[ U[4] ] = GaugeXi[G];
62GaugeXi[ U[7] ] = GaugeXi[Zp];
63
64(***** Setting for interaction order (as e.g. used by MadGraph 5) ******)
65
66M$InteractionOrderHierarchy = {
67 {QCD, 1},
68 {QED, 2}
69 };
70
71(**************** Parameters *************)
72
73M$Parameters = {
74
75 (* External parameters *)
76
77 \[Alpha]EWM1== {
78 ParameterType -> External,
79 BlockName -> BLINPUTS,
80 ParameterName -> aEWM1,
81 InteractionOrder -> {QED, -2},
82 Value -> 127.9,
83 Description -> "Inverse of the electroweak coupling constant at Z-pole"},
84
85 Gf == {
86 ParameterType -> External,
87 BlockName -> BLINPUTS,
88 InteractionOrder -> {QED, 2},
89 Value -> 1.16637 * 10^(-5),
90 Description -> "Fermi constant"},
91
92 \[Alpha]S == {
93 ParameterType -> External,
94 BlockName -> BLINPUTS,
95 TeX -> Subscript[\[Alpha], s],
96 ParameterName -> aS,
97 InteractionOrder -> {QCD, 2},
98 Value -> 0.1184,
99 Description -> "Strong coupling constant at the Z pole."},
100
101 g1p == {
102 ParameterType -> External,
103 BlockName -> BLINPUTS,
104 InteractionOrder -> {QED, 1},
105 Value -> 0.2,
106 Description -> "Zp coupling"},
107
108 MH1 == {
109 ParameterType -> External,
110 BlockName -> BLINPUTS,
111 Value -> 120.00,
112 Description -> "H1 mass"},
113
114 MH2 == {
115 ParameterType -> External,
116 BlockName -> BLINPUTS,
117 Value -> 450.00,
118 Description -> "H2 mass"},
119
120
121 Sa == {
122 ParameterType -> External,
123 BlockName -> BLINPUTS,
124 Value -> 0.01,
125 Description -> "Sine of Higgses mixing angle"},
126
127 ymdo == {
128 ParameterType -> External,
129 BlockName -> YUKAWA,
130 Value -> 5.04*10^(-3),
131 OrderBlock -> {1},
132 Description -> "Down Yukawa mass"},
133
134
135 ymup == {
136 ParameterType -> External,
137 BlockName -> YUKAWA,
138 Value -> 2.55*10^(-3),
139 OrderBlock -> {2},
140 Description -> "Up Yukawa mass"},
141
142
143 yms == {
144 ParameterType -> External,
145 BlockName -> YUKAWA,
146 Value -> 0.101,
147 OrderBlock -> {3},
148 Description -> "Strange Yukawa mass"},
149
150 ymc == {
151 ParameterType -> External,
152 BlockName -> YUKAWA,
153 Value -> 1.27,
154 OrderBlock -> {4},
155 Description -> "Charm Yukawa mass"},
156
157 ymb == {
158 ParameterType -> External,
159 BlockName -> YUKAWA,
160 Value -> 4.7,
161 OrderBlock -> {5},
162 Description -> "Bottom Yukawa mass"},
163
164 ymt == {
165 ParameterType -> External,
166 BlockName -> YUKAWA,
167 Value -> 172.0,
168 OrderBlock -> {6},
169 Description -> "Top Yukawa mass"},
170
171 yme == {
172 ParameterType -> External,
173 BlockName -> YUKAWA,
174 Value -> 0.000511,
175 OrderBlock -> {11},
176 Description -> "Electron Yukawa mass"},
177
178 ymmu == {
179 ParameterType -> External,
180 BlockName -> YUKAWA,
181 Value -> 0.1057,
182 OrderBlock -> {13},
183 Description -> "Muon Yukawa mass"},
184
185 ymtau == {
186 ParameterType -> External,
187 BlockName -> YUKAWA,
188 Value -> 1.777,
189 OrderBlock -> {15},
190 Description -> "Tau Yukawa mass"},
191
192
193 sw2 == {
194 ParameterType -> External,
195 BlockName -> BLINPUTS,
196 Value -> 0.232,
197 Description -> "Squared Sin of the Weinberg angle"},
198
199
200 (* Internal Parameters *)
201
202 \[Alpha]EW == {
203 ParameterType -> Internal,
204 Value -> 1/\[Alpha]EWM1,
205 ParameterName -> aEW,
206 InteractionOrder -> {QED, 2},
207 Description -> "Electroweak coupling contant"},
208
209 sw == {
210 TeX -> Subscript[s, w],
211 ParameterType -> Internal,
212 Value -> Sqrt[sw2],
213 Description -> "Sin of the Weinberg angle"},
214
215
216 cw == {
217 TeX -> Subscript[c, w],
218 ParameterType -> Internal,
219 Value -> Sqrt[1 - sw^2],
220 Description -> "Cos of the Weinberg angle"},
221
222 MW == {
223 ParameterType -> Internal,
224 Value -> MZ * cw,
225 Description -> "W mass"},
226
227
228 ee == {
229 TeX -> e,
230 ParameterType -> Internal,
231 Value -> Sqrt[4 Pi \[Alpha]EW],
232 InteractionOrder -> {QED, 1},
233 Description -> "Electric coupling constant"},
234
235
236 gw == {
237 TeX -> Subscript[g, w],
238 ParameterType -> Internal,
239 Value -> ee / sw,
240 InteractionOrder -> {QED, 1},
241 Description -> "Weak coupling constant"},
242
243 g1 == {
244 TeX -> Subscript[g, 1],
245 ParameterType -> Internal,
246 Value -> ee / cw,
247 InteractionOrder -> {QED, 1},
248 Description -> "U(1)Y coupling constant"},
249
250 gs == {
251 TeX -> Subscript[g, s],
252 ParameterType -> Internal,
253 Value -> Sqrt[4 Pi \[Alpha]S],
254 InteractionOrder -> {QCD, 1},
255 ParameterName -> G,
256 Description -> "Strong coupling constant"},
257
258
259 v == {
260 ParameterType -> Internal,
261 BlockName -> VEV,
262 Value -> 2*MW*sw/ee,
263 InteractionOrder -> {QED, -1},
264 Description -> "H1 VEV"},
265
266 x == {
267 ParameterType -> Internal,
268 BlockName -> VEV,
269 Value -> MZp/(2*g1p),
270 InteractionOrder -> {QED, -1},
271 Description -> "H2 VEV"},
272
273
274 Ca == {
275 ParameterType -> Internal,
276 Value -> Sqrt[1-Sa^2],
277 ParameterName -> Ca,
278 Description -> "Cosine of Higgses mixing angle"},
279
280 yl == {
281 TeX -> Superscript[y, l],
282 Indices -> {Index[Generation]},
283 AllowSummation -> True,
284 ParameterType -> Internal,
285 Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymmu / v, yl[3] -> Sqrt[2] ymtau / v},
286 ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
287 InteractionOrder -> {QED, 1},
288 ComplexParameter -> False,
289 Description -> "Lepton Yukawa coupling"},
290
291 yu == {
292 Indices -> {Index[Generation]},
293 AllowSummation -> True,
294 AllowSummation -> True,
295 ParameterType -> Internal,
296 Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
297 ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
298 InteractionOrder -> {QED, 1},
299 ComplexParameter -> False,
300 Description -> "U-quark Yukawa coupling"},
301
302 yd == {
303 TeX -> Superscript[y, d],
304 Indices -> {Index[Generation]},
305 AllowSummation -> True,
306 ParameterType -> Internal,
307 Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
308 ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
309 InteractionOrder -> {QED, 1},
310 ComplexParameter -> False,
311 Description -> "D-quark Yukawa coupling"},
312
313 ynd == {
314 Indices -> {Index[Generation]},
315 AllowSummation -> True,
316 ParameterType -> Internal,
317 Value -> {ynd[1] -> Sqrt[2*MnL1*MnH1]/v,
318 ynd[2] -> Sqrt[2*MnL2*MnH2]/v,
319 ynd[3] -> Sqrt[2*MnL3*MnH3]/v},
320 ParameterName -> {ynd[1] -> ynd1, ynd[2] -> ynd2, ynd[3] -> ynd3},
321 InteractionOrder -> {QED, 1},
322 ComplexParameter -> False,
323 Description -> "Dirac neutrino Yukawa coupling"},
324
325 ynm == {
326 Indices -> {Index[Generation]},
327 AllowSummation -> True,
328 ParameterType -> Internal,
329 Value -> {ynm[1] -> (MnH1-MnL1)/Sqrt[2]/x,
330 ynm[2] -> (MnH2-MnL2)/Sqrt[2]/x,
331 ynm[3] -> (MnH3-MnL3)/Sqrt[2]/x},
332 ParameterName -> {ynm[1] -> ynm1, ynm[2] -> ynm2, ynm[3] -> ynm3},
333 InteractionOrder -> {QED, 1},
334 ComplexParameter -> False,
335 Description -> "Majorana neutrino Yukawa coupling"},
336
337 Mdd == {
338 Indices -> {Index[Generation]},
339 AllowSummation -> True,
340 ParameterType -> Internal,
341 Value -> {Mdd[1] -> ynd1*v/Sqrt[2],
342 Mdd[2] -> ynd2*v/Sqrt[2],
343 Mdd[3] -> ynd3*v/Sqrt[2]},
344 ParameterName -> {Mdd[1] -> Mdd1,
345 Mdd[2] -> Mdd2,
346 Mdd[3] -> Mdd3},
347 ComplexParameter -> False,
348 Description -> "Neutrino Dirac Mass"},
349
350 s12 == {
351 TeX -> Subscript[S\[Theta], 12],
352 ParameterType -> External,
353 BlockName -> CKMBLOCK,
354 Value -> 0.221,
355 Description -> "Sin(theta_12), PDG-94"},
356
357 s23 == {
358 TeX -> Subscript[S\[Theta], 23],
359 ParameterType -> External,
360 BlockName -> CKMBLOCK,
361 Value -> 0.040,
362 Description -> "Sin(theta_23), PDG-94"},
363
364 s13 == {
365 TeX -> Subscript[S\[Theta], 13],
366 ParameterType -> External,
367 BlockName -> CKMBLOCK,
368 Value -> 0.0035,
369 Description -> "Sin(theta_13), PDG-94"},
370
371 c12 == {
372 TeX -> Subscript[C\[Theta], 12],
373 ParameterType -> Internal,
374 BlockName -> CKMBLOCK,
375 Value -> Sqrt[1-s12^2],
376 Description -> "Cos(theta_12)"},
377
378 c23 == {
379 TeX -> Subscript[C\[Theta], 23],
380 ParameterType -> Internal,
381 BlockName -> CKMBLOCK,
382 Value -> Sqrt[1-s23^2],
383 Description -> "Cos(theta_23)"},
384
385 c13 == {
386 TeX -> Subscript[C\[Theta], 13],
387 ParameterType -> Internal,
388 BlockName -> CKMBLOCK,
389 Value -> Sqrt[1-s13^2],
390 Description -> "Cos(theta_13)"},
391
392 CKM == {
393 Indices -> {Index[Generation], Index[Generation]},
394 TensorClass -> CKM,
395 Unitary -> True,
396 Value -> {CKM[1,1] -> c12*c13,
397 CKM[1,2] -> s12*c13,
398 CKM[1,3] -> s13,
399 CKM[2,1] -> -s12*c23-c12*s23*s13,
400 CKM[2,2] -> c12*c23-s12*s23*s13,
401 CKM[2,3] -> s23*c13,
402 CKM[3,1] -> s12*s23-c12*c23*s13,
403 CKM[3,2] -> -c12*s23-s12*c23*s13,
404 CKM[3,3] -> c23*c13},
405 Description -> "CKM-Matrix"},
406
407 San == {
408 Indices -> {Index[Generation]},
409 AllowSummation -> True,
410 ParameterType -> Internal,
411 Value -> {San[1] -> -Sqrt[MnL1/(MnH1+MnL1)],
412 San[2] -> -Sin[ArcSin[2*Mdd2/Sqrt[4*Mdd2^2+(MnH2-MnL2)^2]]/2],
413 San[3] -> -Sin[ArcSin[2*Mdd3/Sqrt[4*Mdd3^2+(MnH3-MnL3)^2]]/2]},
414 ParameterName -> {San[1] -> San1, San[2] -> San2, San[3] -> San3},
415 ComplexParameter -> False,
416 Description -> "Sin-array of neutrino mass-eigenstates"},
417
418 Can == {
419 Indices -> {Index[Generation]},
420 AllowSummation -> True,
421 ParameterType -> Internal,
422 Value -> {Can[1] -> Sqrt[1-San1^2],
423 Can[2] -> Sqrt[1-San2^2],
424 Can[3] -> Sqrt[1-San3^2]},
425 ParameterName -> {Can[1] -> Can1, Can[2] -> Can2, Can[3] -> Can3},
426 ComplexParameter -> False,
427 Description -> "Cos-array of neutrino mass-eigenstates"},
428
429
430
431
432 \[Lambda]1 == {
433 ParameterType -> Internal,
434 Value -> MH1^2 /(2*v^2)*Ca^2 + MH2^2 /(2*v^2)*Sa^2,
435 ParameterName -> lam1,
436 InteractionOrder -> {QED, 2},
437 Description -> "Lambda 1"},
438
439 \[Lambda]2 == {
440 ParameterType -> Internal,
441 Value -> MH1^2 /(2*x^2)*Sa^2 + MH2^2 /(2*x^2)*Ca^2,
442 ParameterName -> lam2,
443 InteractionOrder -> {QED, 2},
444 Description -> "Lambda 2"},
445
446 \[Lambda]3 == {
447 ParameterType -> Internal,
448 Value -> (MH2^2 - MH1^2)/(x*v)*Sa*Ca,
449 ParameterName -> lam3,
450 InteractionOrder -> {QED, 2},
451 Description -> "Lambda 3, mixing parameter"},
452
453 mu2H1 == {
454 ParameterType -> Internal,
455 Value -> - \[Lambda]1 * v^2 - \[Lambda]3 /2 * x^2,
456 TeX -> m^2,
457 Description -> "Coefficient of the quadratic piece of the H1 potential"},
458
459 mu2H2 == {
460 ParameterType -> Internal,
461 Value -> - \[Lambda]3 /2 * v^2 - \[Lambda]2 * x^2,
462 TeX -> \[Mu]^2,
463 Description -> "Coefficient of the quadratic piece of the H2 potential"}
464
465}
466
467(************** Gauge Groups ******************)
468
469M$GaugeGroups = {
470
471 U1BL == {
472 Abelian -> True,
473 GaugeBoson -> Bp,
474 Charge -> BL,
475 CouplingConstant -> g1p},
476
477 U1Y == {
478 Abelian -> True,
479 GaugeBoson -> B,
480 Charge -> Y,
481 CouplingConstant -> g1},
482
483 SU2L == {
484 Abelian -> False,
485 GaugeBoson -> Wi,
486 StructureConstant -> Eps,
487 CouplingConstant -> gw},
488
489 SU3C == {
490 Abelian -> False,
491 GaugeBoson -> G,
492 StructureConstant -> f,
493 SymmetricTensor -> dSUN,
494 Representations -> {T, Colour},
495 CouplingConstant -> gs}
496}
497
498(********* Particle Classes **********)
499
500M$ClassesDescription = {
501
502(********** Fermions ************)
503
504 (* Mass-Eigenstate light neutrino: Q = 0, BL= -1 *)
505
506 F[11] == {
507 ClassName -> nL,
508 ClassMembers -> {nL1, nL2, nL3},
509 FlavorIndex -> Generation,
510 SelfConjugate -> True,
511 Indices -> {Index[Generation]},
512 Mass -> {MnL, {MnL1, 10^(-9)}, {MnL2, 10^(-9)}, {MnL3, 10^(-9)}},
513 Width -> 0,
514 PropagatorLabel -> {"nL", "nul1", "nul2", "nul3"},
515 PropagatorType -> Straight,
516 ParticleName -> {"n1", "n2", "n3"},
517 PropagatorArrow -> Forward,
518 PDG -> {12, 14, 16},
519 FullName -> {"Light neutrino 1", "Light neutrino 2", "Light neutrino 3"} },
520
521 (* Mass-Eigenstate heavy neutrino: Q = 0, BL= -1 *)
522
523 F[12] == {
524 ClassName -> nH,
525 ClassMembers -> {nH1, nH2, nH3},
526 FlavorIndex -> Generation,
527 SelfConjugate -> True,
528 Indices -> {Index[Generation]},
529 Mass -> {MnH, {MnH1, 200.00}, {MnH2, 200.00}, {MnH3, 200.00}},
530 Width -> 10^(-13),
531 PropagatorLabel -> {"nH", "nuh1", "nuh2", "nuh3"},
532 PropagatorType -> Straight,
533 ParticleName -> {"~n1", "~n2", "~n3"},
534 PropagatorArrow -> Forward,
535 PDG -> {9910012, 9910014, 9910016},
536 FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"} },
537
538 (* Left-handed neutrino: unphysical *)
539 F[13] == {
540 ClassName -> nF,
541 ClassMembers -> {nF1,nF2,nF3},
542 FlavorIndex -> Generation,
543 SelfConjugate -> True,
544 Indices -> {Index[Generation]},
545 Unphysical -> True,
546 Definitions -> {nF[s_,i_] -> Can[i] nL[s,i]-San[i] nH[s,i]},
547 FullName -> {"Majorana LH component of Dirac neutrino 1",
548 "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} },
549
550 (* Right-handed neutrino: unphysical *)
551 F[14] == {
552 ClassName -> nR,
553 ClassMembers -> {nR1,nR2,nR3},
554 FlavorIndex -> Generation,
555 SelfConjugate -> True,
556 Indices -> {Index[Generation]},
557 Unphysical -> True,
558 Definitions -> {nR[s_,i_] -> San[i] nL[s,i]+Can[i] nH[s,i]},
559 FullName -> {"Majorana LH component of Dirac neutrino 1", "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} },
560
561
562 (* Flavour-eigenstate neutrino: unphysical *)
563 F[15] == {
564 ClassName -> vl,
565 ClassMembers -> {vle,vlm,vlt},
566 FlavorIndex -> Generation,
567 SelfConjugate -> False,
568 Indices -> {Index[Generation]},
569 QuantumNumbers -> {Q -> 0, LeptonNumber -> 1, BarionLepton -> -1},
570 Unphysical -> True,
571 Definitions -> {vl[s_,i_] -> left[nF[s,i]]+right[nR[s,i]]},
572 ParticleName -> {"nue", "num", "nut"},
573 AntiParticleName -> {"nue-bar", "num-bar", "nut-bar"},
574 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
575
576
577 (* Leptons (electron): I_3 = -1/2, Q = -1, BL= -1 *)
578 F[2] == {
579 ClassName -> l,
580 ClassMembers -> {e, m, tt},
581 FlavorIndex -> Generation,
582 SelfConjugate -> False,
583 Indices -> {Index[Generation]},
584 Mass -> {Ml, {ME, 0.000511}, {MM, 0.1057}, {MTA, 1.777}},
585 Width -> 0,
586 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1, BarionLepton -> -1},
587 PropagatorLabel -> {"l", "e", "m", "tt"},
588 PropagatorType -> Straight,
589 ParticleName -> {"e", "m", "l"},
590 AntiParticleName -> {"E", "M", "L"},
591 PropagatorArrow -> Forward,
592 PDG -> {11, 13, 15},
593 FullName -> {"Electron", "Muon", "Tau"} },
594
595 (* Quarks (u): I_3 = +1/2, Q = +2/3, BL=1/3 *)
596 F[3] == {
597 ClassMembers -> {u, c, t},
598 ClassName -> uq,
599 FlavorIndex -> Generation,
600 SelfConjugate -> False,
601 Indices -> {Index[Generation], Index[Colour]},
602 Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.27}, {MT, 172.0}},
603 Width -> {0, 0, {WT, 1.50833649}},
604 QuantumNumbers -> {Q -> 2/3, BarionLepton -> 1/3},
605 PropagatorLabel -> {"uq", "u", "c", "t"},
606 ParticleName -> {"u", "c", "t"},
607 AntiParticleName -> {"U", "C", "T"},
608 PropagatorType -> Straight,
609 PropagatorArrow -> Forward,
610 PDG -> {2, 4, 6},
611 FullName -> {"u-quark", "c-quark", "t-quark"}},
612
613 (* Quarks (d): I_3 = -1/2, Q = -1/3, BL=1/3 *)
614 F[4] == {
615 ClassMembers -> {d, s, b},
616 ClassName -> dq,
617 FlavorIndex -> Generation,
618 SelfConjugate -> False,
619 Indices -> {Index[Generation], Index[Colour]},
620 Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}},
621 Width -> 0,
622 QuantumNumbers -> {Q -> -1/3, BarionLepton -> 1/3},
623 ParticleName -> {"d", "s", "b"},
624 AntiParticleName -> {"D", "S", "B"},
625 PropagatorLabel -> {"dq", "d", "s", "b"},
626 PropagatorType -> Straight,
627 PropagatorArrow -> Forward,
628 PDG -> {1,3,5},
629 FullName -> {"d-quark", "s-quark", "b-quark"} },
630
631
632(********** Ghosts **********)
633 U[1] == {
634 ClassName -> ghA,
635 SelfConjugate -> False,
636 Indices -> {},
637 Ghost -> A,
638 Mass -> 0,
639 QuantumNumbers -> {GhostNumber -> 1},
640 PropagatorLabel -> uA,
641 PropagatorType -> GhostDash,
642 PropagatorArrow -> Forward},
643
644 U[2] == {
645 ClassName -> ghZ,
646 SelfConjugate -> False,
647 Indices -> {},
648 Mass -> {MZ, Internal},
649 Ghost -> Z,
650 QuantumNumbers -> {GhostNumber -> 1},
651 PropagatorLabel -> uZ,
652 PropagatorType -> GhostDash,
653 PropagatorArrow -> Forward},
654
655 U[31] == {
656 ClassName -> ghWp,
657 SelfConjugate -> False,
658 Indices -> {},
659 Mass -> {MW, Internal},
660 Ghost -> W,
661 QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
662 PropagatorLabel -> uWp,
663 PropagatorType -> GhostDash,
664 PropagatorArrow -> Forward},
665
666 U[32] == {
667 ClassName -> ghWm,
668 SelfConjugate -> False,
669 Indices -> {},
670 Mass -> {MW, Internal},
671 Ghost -> Wbar,
672 QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
673 PropagatorLabel -> uWm,
674 PropagatorType -> GhostDash,
675 PropagatorArrow -> Forward},
676
677 U[4] == {
678 ClassName -> ghG,
679 SelfConjugate -> False,
680 Indices -> {Index[Gluon]},
681 Ghost -> G,
682 Mass -> 0,
683 QuantumNumbers -> {GhostNumber -> 1},
684 PropagatorLabel -> uG,
685 PropagatorType -> GhostDash,
686 PropagatorArrow -> Forward},
687
688 U[5] == {
689 ClassName -> ghWi,
690 Unphysical -> True,
691 Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
692 ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
693 ghWi[3] -> cw ghZ + sw ghA},
694 SelfConjugate -> False,
695 Indices -> {Index[SU2W]},
696 FlavorIndex -> SU2W,
697 Ghost -> Wi},
698
699 U[6] == {
700 ClassName -> ghB,
701 SelfConjugate -> False,
702 Definitions -> {ghB -> -sw ghZ + cw ghA},
703 Indices -> {},
704 Unphysical -> True,
705 Ghost -> B},
706
707 U[7] == {
708 ClassName -> ghZp,
709 SelfConjugate -> False,
710 Indices -> {},
711 Mass -> {MZp, Internal},
712 Ghost -> Zp,
713 QuantumNumbers -> {GhostNumber -> 1},
714 PropagatorLabel -> uZp,
715 PropagatorType -> GhostDash,
716 PropagatorArrow -> Forward},
717
718 U[8] == {
719 ClassName -> ghBp,
720 SelfConjugate -> False,
721 Definitions -> {ghBp -> ghZp},
722 Indices -> {},
723 Unphysical -> True,
724 Ghost -> Bp},
725
726(************ Gauge Bosons ***************)
727 (* Gauge bosons: Q = 0 *)
728 V[1] == {
729 ClassName -> A,
730 SelfConjugate -> True,
731 Indices -> {},
732 Mass -> 0,
733 Width -> 0,
734 PropagatorLabel -> "a",
735 PropagatorType -> W,
736 PropagatorArrow -> None,
737 PDG -> 22,
738 FullName -> "Photon" },
739
740 V[2] == {
741 ClassName -> Z,
742 SelfConjugate -> True,
743 Indices -> {},
744 Mass -> {MZ, 91.188},
745 Width -> {WZ, 2.4952},
746 PropagatorLabel -> "Z",
747 PropagatorType -> Sine,
748 PropagatorArrow -> None,
749 PDG -> 23,
750 FullName -> "Z" },
751
752 (* Gauge bosons: Q = -1 *)
753 V[3] == {
754 ClassName -> W,
755 SelfConjugate -> False,
756 Indices -> {},
757 Mass -> {MW, Internal},
758 Width -> {WW, 2.085},
759 QuantumNumbers -> {Q -> 1},
760 PropagatorLabel -> "W",
761 PropagatorType -> Sine,
762 PropagatorArrow -> Forward,
763 ParticleName ->"W+",
764 AntiParticleName ->"W-",
765 PDG -> 24,
766 FullName -> "W" },
767
768V[4] == {
769 ClassName -> G,
770 SelfConjugate -> True,
771 Indices -> {Index[Gluon]},
772 Mass -> 0,
773 Width -> 0,
774 PropagatorLabel -> G,
775 PropagatorType -> C,
776 PropagatorArrow -> None,
777 PDG -> 21,
778 FullName -> "G" },
779
780V[5] == {
781 ClassName -> Wi,
782 Unphysical -> True,
783 Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
784 Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
785 Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
786 SelfConjugate -> True,
787 Indices -> {Index[SU2W]},
788 FlavorIndex -> SU2W,
789 Mass -> 0,
790 PDG -> {1,2,3}},
791
792V[6] == {
793 ClassName -> B,
794 SelfConjugate -> True,
795 Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
796 Indices -> {},
797 Mass -> 0,
798 Unphysical -> True},
799
800V[7] == {
801 ClassName -> Zp,
802 SelfConjugate -> True,
803 Indices -> {},
804 Mass -> {MZp, 1500},
805 Width -> {WZp, 80.00},
806 PropagatorLabel -> "Zp",
807 PropagatorType -> Sine,
808 PropagatorArrow -> None,
809 PDG -> 9900032,
810 FullName -> "Zp" },
811
812V[8] == {
813 ClassName -> Bp,
814 SelfConjugate -> True,
815 Definitions -> {Bp[mu_] -> Zp[mu]},
816 Indices -> {},
817 Unphysical -> True},
818
819
820(************ Scalar Fields **********)
821 (* physical Higgs: Q = 0 *)
822 S[1] == {
823 ClassName -> H1,
824 SelfConjugate -> True,
825 Mass -> {MH1, Internal},
826 Width -> {WH1, 1.5},
827 PropagatorLabel -> "H1",
828 PropagatorType -> D,
829 PropagatorArrow -> None,
830 PDG -> 9900025,
831 FullName -> "H1" },
832
833 S[2] == {
834 ClassName -> phi,
835 SelfConjugate -> True,
836 Mass -> {MZ, Internal},
837 Width -> Wphi,
838 PropagatorLabel -> "Phi",
839 PropagatorType -> D,
840 PropagatorArrow -> None,
841 ParticleName ->"phi0",
842 PDG -> 9900250,
843 FullName -> "Phi",
844 Goldstone -> Z },
845
846 S[3] == {
847 ClassName -> phi2,
848 SelfConjugate -> False,
849 Mass -> {MW, Internal},
850 Width -> Wphi2,
851 PropagatorLabel -> "Phi2",
852 PropagatorType -> D,
853 PropagatorArrow -> None,
854 ParticleName ->"phi+",
855 AntiParticleName ->"phi-",
856 PDG -> 9900251,
857 FullName -> "Phi2",
858 Goldstone -> W,
859 QuantumNumbers -> {Q -> 1}},
860
861 S[4] == {
862 ClassName -> H2,
863 SelfConjugate -> True,
864 Mass -> {MH2, Internal},
865 Width -> {WH2, 10},
866 PropagatorLabel -> "H2",
867 PropagatorType -> D,
868 PropagatorArrow -> None,
869 PDG -> 9900026,
870 FullName -> "H2" },
871
872 S[5] == {
873 ClassName -> phip,
874 SelfConjugate -> True,
875 Mass -> {MZp, Internal},
876 Width -> Wphip,
877 PropagatorLabel -> "Phip",
878 PropagatorType -> D,
879 PropagatorArrow -> None,
880 ParticleName ->"phi0p",
881 PDG -> 9900252,
882 FullName -> "Phip",
883 Goldstone -> Zp }
884
885}
886
887
888(*****************************************************************************************)
889
890(* SM Lagrangian *)
891
892(******************** Gauge F^2 Lagrangian terms*************************)
893(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
894 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
895 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
896
897 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[Bp[nu], mu] - del[Bp[mu], nu])^2 -
898
899 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
900 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
901
902
903(********************* Fermion Lagrangian terms*************************)
904(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
905 LFermions := Module[{Lkin, LQCD, LEWleft, LEWright},
906
907 Lkin = I uqbar.Ga[mu].del[uq, mu] +
908 I dqbar.Ga[mu].del[dq, mu] +
909 I lbar.Ga[mu].del[l, mu] +
910 I left[anti[vl]].Ga[mu].del[left[vl],mu] +
911 I right[anti[vl]].Ga[mu].del[right[vl],mu];
912
913 LQCD = gs (uqbar.Ga[mu].T[a].uq +
914 dqbar.Ga[mu].T[a].dq)G[mu, a];
915
916 LBright =
917 -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*)
918 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*)
919 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*)
920
921 LBleft =
922 -ee/cw B[mu]/2 left[anti[vl]].Ga[mu].ProjM.vl - (*Y_LL=-1*)
923 ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*)
924 ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*)
925 ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*)
926
927 LWleft = ee/sw/2(
928 left[anti[vl]].Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
929 lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*)
930
931 Sqrt[2] left[anti[vl]].Ga[mu].ProjM.l W[mu] +
932 Sqrt[2] lbar.Ga[mu].ProjM.left[vl] Wbar[mu]+
933
934 uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*)
935 dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*)
936
937 Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
938 Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
939 );
940
941 LBpright =
942 - g1p Bp[mu] anti[vl].Ga[mu].ProjP.right[vl] - (*BL_vlR=-1*)
943 g1p Bp[mu] lbar.Ga[mu].ProjP.l + (*BL_lR=-1*)
944 g1p/3 Bp[mu] uqbar.Ga[mu].ProjP.uq + (*BL_uR=1/3*)
945 g1p/3 Bp[mu] dqbar.Ga[mu].ProjP.dq; (*BL_dR=1/3*)
946
947 LBpleft =
948 - g1p Bp[mu] anti[vl].Ga[mu].ProjM.left[vl] - (*BL_vlL=-1*)
949 g1p Bp[mu] lbar.Ga[mu].ProjM.l + (*BL_lL=-1*)
950 g1p/3 Bp[mu] uqbar.Ga[mu].ProjM.uq + (*BL_uL=1/3*)
951 g1p/3 Bp[mu] dqbar.Ga[mu].ProjM.dq (*BL_dL=1/3*)
952 ;
953
954 Lkin + LQCD + LBright + LBleft + LWleft + LBpright + LBpleft ];
955
956(******************** Higgs Lagrangian terms****************************)
957 Phi := If[FeynmanGauge, {-I phi2, (v + Ca*H1+Sa*H2 + I phi)/Sqrt[2]}, {0, (v + Ca*H1+Sa*H2)/Sqrt[2]}];
958 Phibar := If[FeynmanGauge, {I phi2bar, (v + Ca*H1+Sa*H2 - I phi)/Sqrt[2]} ,{0, (v + Ca*H1+Sa*H2)/Sqrt[2]}];
959
960 Chi := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 + I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}];
961 Chibar := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 - I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}];
962
963 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphichi, Dcp, Dcpbar},
964
965 PMVec = Table[PauliSigma[i], {i, 3}];
966 Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
967
968 (*Y_phi=1/2*)
969 Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
970 Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
971
972 (*BL_phi=2*)
973 Dcp[f_, mu_] := I del[f, mu] + 2*g1p Bp[mu] f ;
974 Dcpbar[f_, mu_] := -I del[f, mu] + 2*g1p Bp[mu] f ;
975
976 Vphichi[Phi_, Phibar_, Chi_, Chibar_] := mu2H1 Phibar.Phi + mu2H2 Chibar.Chi +
977 \[Lambda]1 (Phibar.Phi)^2 + \[Lambda]2 (Chibar.Chi)^2 + \[Lambda]3 (Phibar.Phi)*(Chibar.Chi);
978
979 (Dcbar[Phibar, mu]).Dc[Phi, mu] + (Dcpbar[Chibar, mu]).Dcp[Chi, mu] - Vphichi[Phi, Phibar, Chi, Chibar]
980
981 ];
982
983
984(*************** Yukawa Lagrangian***********************)
985(*NOTE: Neutrino states have been expanded on the LH/RH components and the LH mass terms have been changed signs*)
986
987LYuk := If[FeynmanGauge,
988
989 Module[{s,r,n,m,i}, -
990 yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) -
991 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] -
992
993 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*)
994 yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)
995
996 - yl[n] Can[n] anti[nL][s,n].ProjP[s,r].l[r,n] (-I phi2)
997 + yl[n] San[n] anti[nH][s,n].ProjP[s,r].l[r,n] (-I phi2)
998
999 - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] +
1000 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]+
1001 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]-
1002
1003 ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (Ca*H1+Sa*H2 - I phi)/Sqrt[2]
1004
1005 - ynd[n] San[n] lbar[s,n].ProjP[s,r].nL[r,n] (I phi2bar) +
1006 ynd[n] Can[n] lbar[s,n].ProjP[s,r].nH[r,n] (I phi2bar) +
1007
1008
1009 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]-
1010 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]-
1011
1012 ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (-Sa*H1+Ca*H2 + I phip)/Sqrt[2]
1013
1014
1015 ],
1016
1017 Module[{s,r,n,m,i}, -
1018 yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2] -
1019 yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2]
1020
1021 - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2] +
1022 ynd[n] San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]+
1023 ynd[n] San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]-
1024
1025 ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (Ca*H1+Sa*H2)/Sqrt[2]+
1026
1027
1028
1029 ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]-
1030 ynm[n] Can[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]-
1031
1032 ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (-Sa*H1+Ca*H2)/Sqrt[2]
1033
1034 ]
1035 ];
1036
1037LYukawa := LYuk + HC[LYuk];
1038
1039
1040
1041(**************Ghost terms**************************)
1042(* Now we need the ghost terms which are of the form: *)
1043(* - g * antighost * d_BRST G *)
1044(* where d_BRST G is BRST transform of the gauge fixing function. *)
1045
1046LGhost := If[FeynmanGauge,
1047 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB, dBRSTBp, LGhostBp},
1048
1049 (***********First the pure gauge piece.**********************)
1050 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1051 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1052
1053 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
1054 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
1055
1056 dBRSTB[mu_] := cw/ee del[ghB, mu];
1057 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
1058
1059 dBRSTBp[mu_] := 1/g1p del[ghBp, mu];
1060 LGhostBp := - g1p ghBpbar.del[dBRSTBp[mu],mu];
1061
1062 (***********Next the piece from the scalar field.************)
1063 LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) +
1064 I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) -
1065 ee/(2*sw) MW ( ( (v+Ca*H1+Sa*H2) + I phi) ghWpbar.ghWp +
1066 ( (v+Ca*H1+Sa*H2) - I phi) ghWmbar.ghWm ) -
1067 I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
1068 ee/(2*sw*cw) MZ (v+Ca*H1+Sa*H2) ghZbar.ghZ -
1069
1070 2*g1p MZp (x-Sa*H1+Ca*H2) ghZpbar.ghZp ;
1071
1072
1073 (***********Now add the pieces together.********************)
1074 LGhostG + LGhostWi + LGhostB + LGhostphi + LGhostBp ]
1075
1076,
1077
1078 (*If unitary gauge, only include the gluonic ghost.*)
1079 Block[{dBRSTG,LGhostG},
1080
1081 (***********First the pure gauge piece.**********************)
1082 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1083 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1084
1085 (***********Now add the pieces together.********************)
1086 LGhostG]
1087
1088];
1089
1090(*********Total B-L Lagrangian*******)
1091LBL := LGauge + LHiggs + LFermions + LYukawa + LGhost;
1092
1093