B-L-SM: B-L.fr

File B-L.fr, 33.9 KB (added by L.Basso, 6 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