VLQ_bsingletvl: BsingletVL.fr

File BsingletVL.fr, 30.5 KB (added by buchkremer, 6 years ago)
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1(***************************************************************************************************************)
2(******                       FeynRules mod-file for Model Independent searches of top partners           ******)
3(******                                      B(-1/3) singlet                                              ******)
4(******                                                                                                   ******)
5(******     Authors: M. Buchkremer, G. Cacciapaglia, A. Deandrea,L. Panizzi                               ******)
6(******                                                                                                   ******)
7(***************************************************************************************************************)
8
9M$ModelName = "BsingletVL";
10
11
12M$Information = {Authors -> {"M. Buchkremer","G. Cacciapaglia","A. Deandrea","L. Panizzi"},
13             Version -> "1.2.5",
14             Date -> "15. 04. 2014",
15             Institutions -> {"Universite catholique de Louvain (CP3)","Universite de Lyon (CNRS/IN2P3)","University of Southampton (School of Physics and Astronomy)"},
16             Emails -> {"mathieu.buchkremer@uclouvain.be", "g.cacciapaglia@ipnl.in2p3.fr","deandrea@ipnl.in2p3.fr", "l.panizzi@soton.ac.uk"},
17             References -> {"arXiv:1305.4172"}};
18
19
20(******* Index definitions ********)
21
22IndexRange[ Index[Generation] ] = Range[3]
23IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
24IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
25IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
26IndexStyle[Colour, i]
27IndexStyle[Generation, f]
28IndexStyle[Gluon ,a]
29IndexStyle[SU2W ,k]
30
31(******* Gauge parameters (for FeynArts) ********)
32
33GaugeXi[ V[1] ] = GaugeXi[A];
34GaugeXi[ V[2] ] = GaugeXi[Z];
35GaugeXi[ V[3] ] = GaugeXi[W];
36GaugeXi[ V[4] ] = GaugeXi[G];
37GaugeXi[ S[1] ] = 1;
38GaugeXi[ S[2] ] = GaugeXi[Z];
39GaugeXi[ S[3] ] = GaugeXi[W];
40GaugeXi[ U[1] ] = GaugeXi[A];
41GaugeXi[ U[2] ] = GaugeXi[Z];
42GaugeXi[ U[31] ] = GaugeXi[W];
43GaugeXi[ U[32] ] = GaugeXi[W];
44GaugeXi[ U[4] ] = GaugeXi[G];
45
46(****************  Parameters *************)
47
48M$Parameters = {
49
50  (* External parameters, SM *)
51
52  \[Alpha]EWM1== {
53        ParameterType -> External,
54        BlockName -> SMINPUTS,
55        ParameterName -> aEWM1,
56        InteractionOrder -> {QED, -2},
57        Value -> 127.9,
58        Description -> "Inverse of the electroweak coupling constant"},
59
60  Gf == {
61        ParameterType -> External,
62        BlockName -> SMINPUTS,
63        TeX -> Subscript[G, f],
64        InteractionOrder -> {QED, 2},
65        Value -> 1.16600 * 10^(-5),
66        Description -> "Fermi constant"},
67
68  \[Alpha]S == {
69        ParameterType -> External,
70        BlockName -> SMINPUTS,
71        TeX -> Subscript[\[Alpha], s],
72        ParameterName -> aS,
73        InteractionOrder -> {QCD, 2},
74        Value -> 0.118,
75        Description -> "Strong coupling constant at the Z pole."},
76
77  ymdo == {
78        ParameterType -> External,
79        BlockName -> YUKAWA,
80        Value -> 5.04*10^(-3),
81        OrderBlock -> {1},
82        Description -> "Down Yukawa mass"},
83
84  ymup == {
85        ParameterType -> External,
86        BlockName -> YUKAWA,
87        Value -> 2.55*10^(-3),
88        OrderBlock -> {2},
89        Description -> "Up Yukawa mass"},
90
91  yms == {
92        ParameterType -> External,
93        BlockName -> YUKAWA,
94        Value -> 0.101,
95        OrderBlock -> {3},
96        Description -> "Strange Yukawa mass"},
97
98  ymc == {
99        ParameterType -> External,
100        BlockName -> YUKAWA,
101        Value -> 1.25,
102        OrderBlock -> {4},
103        Description -> "Charm Yukawa mass"},
104
105  ymb == {
106        ParameterType -> External,
107        BlockName -> YUKAWA,
108        Value -> 4.2,
109        OrderBlock -> {5},
110        Description -> "Bottom Yukawa mass"},
111
112  ymt == {
113        ParameterType -> External,
114        BlockName -> YUKAWA,
115        Value -> 174.3,
116        OrderBlock -> {6},
117        Description -> "Top Yukawa mass"},
118
119  yme == {
120        ParameterType -> External,
121        BlockName -> YUKAWA,
122        Value ->  5.11*10^(-4),
123        OrderBlock -> {11},
124        Description -> "Electron Yukawa mass"},
125
126  ymm == {
127        ParameterType -> External,
128        BlockName -> YUKAWA,
129        Value -> 0.10566,
130        OrderBlock -> {13},
131        Description -> "Muon Yukawa mass"},
132
133  ymtau == {
134        ParameterType -> External,
135        BlockName -> YUKAWA,
136        Value -> 1.777,
137        OrderBlock -> {15},
138        Description -> "Tau Yukawa mass"},
139
140  CKM == {
141        ParameterType -> External,
142        BlockName -> CKMBlock,
143        ComplexParameter -> False,
144       Indices -> {Index[Generation], Index[Generation]},
145       TensorClass -> CKM,
146       Unitary -> True,
147       Value -> {CKM[1,1] -> 0.97428,
148                 CKM[1,2] -> 0.2253,
149                 CKM[1,3] -> 0.00347,
150                 CKM[2,1] -> 0.2252,
151                 CKM[2,2] -> 0.97345,
152                 CKM[2,3] -> 0.0410,
153                 CKM[3,1] -> 0.00862,
154                 CKM[3,2] -> 0.0403,
155                 CKM[3,3] -> 0.999152},
156       Description -> "SM CKM Matrix"},
157
158  (* External parameters, VLQ *)
159
160  Gvl == {
161        TeX -> Subscript[g, VL],
162        ParameterType -> External,
163        BlockName -> Gvl,
164        ComplexParameter -> False,
165        Value ->  1,
166        Description -> "VL-VL-gauge factor multiplying SM coupling"},
167
168 gstar == {
169        ParameterType -> External,
170        BlockName -> Kappa,
171        ComplexParameter -> False,
172        Value -> 0.1,
173        Description -> "gstar"},
174
175 RL == {
176        ParameterType -> External,
177        BlockName -> Zeta,
178        ComplexParameter -> False,
179        Value -> 1,
180        Description -> "RL rate into light"},
181
182  KB == {
183        ParameterType -> Internal,
184        BlockName -> Kappa,
185        ComplexParameter -> False,
186        Value -> gstar,
187        Description -> "Kappa_B parameter"},
188
189  zetaBdL == {
190        ParameterType -> Internal,
191        BlockName -> Zeta,
192        ComplexParameter -> False,
193        Value -> RL/(1+RL),
194        Description -> "B-d mixing (left-handed)"},
195
196  zetaBsL == {
197        ParameterType -> Internal,
198        BlockName -> Zeta,
199        ComplexParameter -> False,
200        Value -> 0,
201        Description -> "B-s mixing (left-handed)"},
202
203  zetaBbL == {
204        ParameterType -> Internal,
205        BlockName -> Zeta,
206        ComplexParameter -> False,
207        Value -> 1/(1+RL),
208        Description -> "B-b mixing (left-handed)"},
209
210  zetaBdR == {
211        ParameterType -> Internal,
212        BlockName -> Zeta,
213        ComplexParameter -> False,
214        Value -> 0,
215        Description -> "B-d mixing (right-handed)"},
216
217  zetaBsR == {
218        ParameterType -> Internal,
219        BlockName -> Zeta,
220        ComplexParameter -> False,
221        Value -> 0,
222        Description -> "B-s mixing (right-handed)"},
223
224  zetaBbR == {
225        ParameterType -> Internal,
226        BlockName -> Zeta,
227        ComplexParameter -> False,
228        Value -> 0,
229        Description -> "B-b mixing (right-handed)"},
230
231
232   (* Internal Parameters, SM *)
233
234  \[Alpha]EW == {
235        ParameterType -> Internal,
236        Value -> 1/\[Alpha]EWM1,
237        TeX -> Subscript[\[Alpha], EW],
238        ParameterName -> aEW,
239        InteractionOrder -> {QED, 2},
240        Description -> "Electroweak coupling constant"},
241
242
243  MW == {
244        ParameterType -> Internal,
245        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
246        TeX  -> Subscript[M, W],
247        Description -> "W mass"},
248
249  sw2 == {
250        ParameterType -> Internal,
251        Value -> 1-(MW/MZ)^2,
252        Description -> "Squared Sin of the Weinberg angle"},
253
254   ee == {
255        TeX -> e,
256        ParameterType -> Internal,
257        Value -> Sqrt[4 Pi \[Alpha]EW],
258        InteractionOrder -> {QED, 1},
259        Description -> "Electric coupling constant"},
260
261   cw == {
262        TeX -> Subscript[c, w],
263        ParameterType -> Internal,
264        Value -> Sqrt[1 - sw2],
265        Description -> "Cos of the Weinberg angle"}, 
266
267   sw == {
268        TeX -> Subscript[s, w],
269        ParameterType -> Internal,
270        Value -> Sqrt[sw2],
271        Description -> "Sin of the Weinberg angle"}, 
272
273   gw == {
274        TeX -> Subscript[g, w],
275        ParameterType -> Internal,
276        Value -> ee / sw,
277        InteractionOrder -> {QED, 1},
278        Description -> "Weak coupling constant"},
279
280   g1 == {
281        TeX -> Subscript[g, 1],
282        ParameterType -> Internal,
283        Value -> ee / cw,
284        InteractionOrder -> {QED, 1},
285        Description -> "U(1)Y coupling constant"},
286
287   gs == {
288        TeX -> Subscript[g, s],
289        ParameterType -> Internal,
290        Value -> Sqrt[4 Pi \[Alpha]S],
291        InteractionOrder -> {QCD, 1},
292        ParameterName -> G,
293        Description -> "Strong coupling constant"},
294
295   v == {
296        ParameterType -> Internal,
297        Value -> 2*MW*sw/ee,
298        InteractionOrder -> {QED, -1},
299        Description -> "Higgs VEV"},
300
301   \[Lambda] == {
302        ParameterType -> Internal,
303        Value -> MH^2/(2*v^2),
304        InteractionOrder -> {QED, 2},
305        ParameterName -> lam,
306        Description -> "Higgs quartic coupling"},
307
308   muH == {
309        ParameterType -> Internal,
310        Value -> Sqrt[v^2 \[Lambda]],
311        TeX -> \[Mu],
312        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
313
314   yl == {
315        TeX -> Superscript[y, l],
316        Indices -> {Index[Generation]},
317        AllowSummation -> True,
318        ParameterType -> Internal,
319        Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
320        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
321        InteractionOrder -> {QED, 1},
322        ComplexParameter -> False,
323        Description -> "Lepton Yukawa coupling"},
324
325   yu == {
326        TeX -> Superscript[y, u],
327        Indices -> {Index[Generation]},
328        AllowSummation -> True,
329        ParameterType -> Internal,
330        Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
331        ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
332        InteractionOrder -> {QED, 1},
333        ComplexParameter -> False,
334        Description -> "U-quark Yukawa coupling"},
335
336   yd == {
337        TeX -> Superscript[y, d],
338        Indices -> {Index[Generation]},
339        AllowSummation -> True,
340        ParameterType -> Internal,
341        Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
342        ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
343        InteractionOrder -> {QED, 1},
344        ComplexParameter -> False,
345        Description -> "D-quark Yukawa coupling"},
346
347
348   (************** Internal Parameters, VLQ **************)
349
350
351   (* B couplings *)
352
353  KBdLw == {
354        ParameterType -> Internal,
355        BlockName -> Kappa,
356        ComplexParameter -> False,
357        Value -> (ee/sw*Sqrt[zetaBdL])/Sqrt[2],
358        InteractionOrder -> {QED, 1},
359        Description -> "BdW coupling (left-handed)"},
360
361  KBsLw == {
362        ParameterType -> Internal,
363        BlockName -> Kappa,
364        ComplexParameter -> False,
365        Value -> (ee/sw*Sqrt[zetaBsL])/Sqrt[2],
366        InteractionOrder -> {QED, 1},
367        Description -> "BsW coupling (left-handed)"},
368
369  KBbLw == {
370        ParameterType -> Internal,
371        BlockName -> Kappa,
372        ComplexParameter -> False,
373        Value -> (gw*Sqrt[zetaBbL])/Sqrt[2],
374        InteractionOrder -> {QED, 1},
375        Description -> "BbW coupling (left-handed)"},
376
377  KBdRw == {
378        ParameterType -> Internal,
379        BlockName -> Kappa,
380        ComplexParameter -> False,
381        Value -> (ee/sw*Sqrt[zetaBdR])/Sqrt[2],
382        InteractionOrder -> {QED, 1},
383        Description -> "BdW coupling (right-handed)"},
384
385  KBsRw == {
386        ParameterType -> Internal,
387        BlockName -> Kappa,
388        ComplexParameter -> False,
389        Value -> (gw*Sqrt[zetaBsR])/Sqrt[2],
390        InteractionOrder -> {QED, 1},
391        Description -> "BsW coupling (right-handed)"},
392
393  KBbRw == {
394        ParameterType -> Internal,
395        BlockName -> Kappa,
396        ComplexParameter -> False,
397        Value -> (gw*Sqrt[zetaBbR])/Sqrt[2],
398        InteractionOrder -> {QED, 1},
399        Description -> "BbW coupling (right-handed)"},
400
401  KBdLz == {
402        ParameterType -> Internal,
403        BlockName -> Kappa,
404        ComplexParameter -> False,
405        Value -> (gw*Sqrt[zetaBdL])/2/cw,
406        InteractionOrder -> {QED, 1},
407        Description -> "BdZ coupling (left-handed)"},
408
409  KBsLz == {
410        ParameterType -> Internal,
411        BlockName -> Kappa,
412        ComplexParameter -> False,
413        Value -> (gw*Sqrt[zetaBsL])/2/cw,
414        InteractionOrder -> {QED, 1},
415        Description -> "BsZ coupling (left-handed)"},
416
417  KBbLz == {
418        ParameterType -> Internal,
419        BlockName -> Kappa,
420        ComplexParameter -> False,
421        Value -> (gw*Sqrt[zetaBbL])/2/cw,
422        InteractionOrder -> {QED, 1},
423        Description -> "BbZ coupling (left-handed)"},
424
425  KBdRz == {
426        ParameterType -> Internal,
427        BlockName -> Kappa,
428        ComplexParameter -> False,
429        Value -> (gw*Sqrt[zetaBdR])/2/cw,
430        InteractionOrder -> {QED, 1},
431        Description -> "BdZ coupling (right-handed)"},
432
433  KBsRz == {
434        ParameterType -> Internal,
435        BlockName -> Kappa,
436        ComplexParameter -> False,
437        Value -> (gw*Sqrt[zetaBsR])/2/cw,
438        InteractionOrder -> {QED, 1},
439        Description -> "BsZ coupling (right-handed)"},
440
441  KBbRz == {
442        ParameterType -> Internal,
443        BlockName -> Kappa,
444        ComplexParameter -> False,
445        Value -> (gw*Sqrt[zetaBbR])/2/cw,
446        InteractionOrder -> {QED, 1},
447        Description -> "BbZ coupling (right-handed)"},
448
449  KBdLh == {
450        ParameterType -> Internal,
451        BlockName -> Kappa,
452        ComplexParameter -> False,
453        Value -> (Sqrt[zetaBdL]),
454        InteractionOrder -> {QED, 0},
455        Description -> "BdH coupling (left-handed)"},
456
457  KBsLh == {
458        ParameterType -> Internal,
459        BlockName -> Kappa,
460        ComplexParameter -> False,
461        Value -> (Sqrt[zetaBsL]),
462        InteractionOrder -> {QED, 0},
463        Description -> "BsH coupling (left-handed)"},
464
465  KBbLh == {
466        ParameterType -> Internal,
467        BlockName -> Kappa,
468        ComplexParameter -> False,
469        Value -> (Sqrt[zetaBbL]),
470        InteractionOrder -> {QED, 0},
471        Description -> "BbH coupling (left-handed)"},
472
473  KBdRh == {
474        ParameterType -> Internal,
475        BlockName -> Kappa,
476        ComplexParameter -> False,
477        Value -> (Sqrt[zetaBdR]),
478        InteractionOrder -> {QED, 0},
479        Description -> "BdH coupling (right-handed)"},
480
481  KBsRh == {
482        ParameterType -> Internal,
483        BlockName -> Kappa,
484        ComplexParameter -> False,
485        Value -> (Sqrt[zetaBsR]),
486        InteractionOrder -> {QED, 0},
487        Description -> "BsH coupling (right-handed)"},
488
489  KBbRh == {
490        ParameterType -> Internal,
491        BlockName -> Kappa,
492        ComplexParameter -> False,
493        Value -> (Sqrt[zetaBbR]),
494        InteractionOrder -> {QED, 0},
495        Description -> "BbH coupling (right-handed)"}
496
497}
498
499 
500(************** Gauge Groups ******************)
501
502M$GaugeGroups = {
503
504  U1Y == {
505        Abelian -> True,
506        GaugeBoson -> B,
507        Charge -> Y,
508        CouplingConstant -> g1},
509
510  SU2L == {
511        Abelian -> False,
512        GaugeBoson -> Wi,
513        StructureConstant -> Eps,
514        CouplingConstant -> gw},
515
516  SU3C == {
517        Abelian -> False,
518        GaugeBoson -> G,
519        StructureConstant -> f,
520        SymmetricTensor -> dSUN,
521        Representations -> {T, Colour},
522        CouplingConstant -> gs}
523}
524
525(********* Particle Classes **********)
526
527M$ClassesDescription = {
528
529(********** Fermions ************)
530        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
531  F[1] == {
532        ClassName -> vl,
533        ClassMembers -> {ve,vm,vt},
534        FlavorIndex -> Generation,
535        SelfConjugate -> False,
536        Indices -> {Index[Generation]},
537        Mass -> 0,
538        Width -> 0,
539        QuantumNumbers -> {LeptonNumber -> 1},
540        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
541        PropagatorType -> S,
542        PropagatorArrow -> Forward,
543        PDG -> {12,14,16},
544        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
545
546        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
547  F[2] == {
548        ClassName -> l,
549        ClassMembers -> {e, m, tt},
550        FlavorIndex -> Generation,
551        SelfConjugate -> False,
552        Indices -> {Index[Generation]},
553        Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
554        Width -> 0,
555        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
556        PropagatorLabel -> {"l", "e", "m", "tt"},
557        PropagatorType -> Straight,
558        ParticleName -> {"e-", "m-", "tt-"},
559        AntiParticleName -> {"e+", "m+", "tt+"},
560        PropagatorArrow -> Forward,
561        PDG -> {11, 13, 15},
562        FullName -> {"Electron", "Muon", "Tau"} },
563
564        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
565  F[3] == {
566        ClassMembers -> {u, c, t},
567        ClassName -> uq,
568        FlavorIndex -> Generation,
569        SelfConjugate -> False,
570        Indices -> {Index[Generation], Index[Colour]},
571        Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.40}, {MT, 174.3}},
572        Width -> {0, 0, {WT, 1.51013490}},
573        QuantumNumbers -> {Q -> 2/3},
574        PropagatorLabel -> {"uq", "u", "c", "t"},
575        PropagatorType -> Straight,
576        PropagatorArrow -> Forward,
577        PDG -> {2, 4, 6},
578        FullName -> {"u-quark", "c-quark", "t-quark"}},
579
580        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
581  F[4] == {
582        ClassMembers -> {d, s, b},
583        ClassName -> dq,
584        FlavorIndex -> Generation,
585        SelfConjugate -> False,
586        Indices -> {Index[Generation], Index[Colour]},
587        Mass -> {Md, {MD,  5.04*10^(-3)}, {MS, 0.101}, {MB, 4.2}},
588        Width -> 0,
589        QuantumNumbers -> {Q -> -1/3},
590        PropagatorLabel -> {"dq", "d", "s", "b"},
591        PropagatorType -> Straight,
592        PropagatorArrow -> Forward,
593        PDG -> {1,3,5},
594        FullName -> {"d-quark", "s-quark", "b-quark"} },
595
596
597        (* VLQ Quarks B, Q=-1/3 *)
598  F[7] == {
599        ClassName -> bpq,
600        ClassMembers -> {bp},
601        SelfConjugate -> False,
602        Indices -> {Index[Colour]},
603        Mass -> {{MQ,1000}},
604        Width -> {{WBP, 1}},
605        QuantumNumbers -> {Q -> -1/3},
606        PropagatorLabel -> {"bp"},
607        PropagatorType -> Straight,
608        PropagatorArrow -> Forward,
609        PDG -> {6000007},
610        FullName -> {"B-quark"}},
611
612
613(********** Ghosts **********)
614        U[1] == {
615       ClassName -> ghA,
616       SelfConjugate -> False,
617       Indices -> {},
618       Ghost -> A,
619       Mass -> 0,
620       QuantumNumbers -> {GhostNumber -> 1},
621       PropagatorLabel -> uA,
622       PropagatorType -> GhostDash,
623       PropagatorArrow -> Forward},
624
625        U[2] == {
626       ClassName -> ghZ,
627       SelfConjugate -> False,
628       Indices -> {},
629       Mass -> {MZ, 91.1876},
630       Ghost -> Z,
631       QuantumNumbers -> {GhostNumber -> 1},
632       PropagatorLabel -> uZ,
633       PropagatorType -> GhostDash,
634       PropagatorArrow -> Forward},
635
636        U[31] == {
637       ClassName -> ghWp,
638       SelfConjugate -> False,
639       Indices -> {},
640       Mass -> {MW, Internal},
641       Ghost -> W,
642       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
643       PropagatorLabel -> uWp,
644       PropagatorType -> GhostDash,
645       PropagatorArrow -> Forward},
646
647   U[32] == {
648       ClassName -> ghWm,
649       SelfConjugate -> False,
650       Indices -> {},
651       Mass -> {MW, Internal},
652       Ghost -> Wbar,
653       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
654       PropagatorLabel -> uWm,
655       PropagatorType -> GhostDash,
656       PropagatorArrow -> Forward},
657
658        U[4] == {
659       ClassName -> ghG,
660       SelfConjugate -> False,
661       Indices -> {Index[Gluon]},
662       Ghost -> G,
663       Mass -> 0,
664       QuantumNumbers -> {GhostNumber -> 1},
665       PropagatorLabel -> uG,
666       PropagatorType -> GhostDash,
667       PropagatorArrow -> Forward},
668
669        U[5] == {
670        ClassName -> ghWi,
671        Unphysical -> True,
672        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
673                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
674                        ghWi[3] -> cw ghZ + sw ghA},
675        SelfConjugate -> False,
676        Ghost -> Wi,
677        Indices -> {Index[SU2W]},
678        FlavorIndex -> SU2W},
679
680        U[6] == {
681        ClassName -> ghB,
682        SelfConjugate -> False,
683        Definitions -> {ghB -> -sw ghZ + cw ghA},
684        Indices -> {},
685        Ghost -> B,
686        Unphysical -> True},
687
688(************ Gauge Bosons ***************)
689        (* Gauge bosons: Q = 0 *)
690  V[1] == {
691        ClassName -> A,
692        SelfConjugate -> True,
693        Indices -> {},
694        Mass -> 0,
695        Width -> 0,
696        PropagatorLabel -> "a",
697        PropagatorType -> W,
698        PropagatorArrow -> None,
699        PDG -> 22,
700        FullName -> "Photon" },
701
702  V[2] == {
703        ClassName -> Z,
704        SelfConjugate -> True,
705        Indices -> {},
706        Mass -> {MZ, 91.1876},
707        Width -> {WZ, 2.44639985},
708        PropagatorLabel -> "Z",
709        PropagatorType -> Sine,
710        PropagatorArrow -> None,
711        PDG -> 23,
712        FullName -> "Z" },
713
714        (* Gauge bosons: Q = -1 *)
715  V[3] == {
716        ClassName -> W,
717        SelfConjugate -> False,
718        Indices -> {},
719        Mass -> {MW, Internal},
720        Width -> {WW, 2.03535570},
721        QuantumNumbers -> {Q -> 1},
722        PropagatorLabel -> "W",
723        PropagatorType -> Sine,
724        PropagatorArrow -> Forward,
725        ParticleName ->"W+",
726        AntiParticleName ->"W-",
727        PDG -> 24,
728        FullName -> "W" },
729
730V[4] == {
731        ClassName -> G,
732        SelfConjugate -> True,
733        Indices -> {Index[Gluon]},
734        Mass -> 0,
735        Width -> 0,
736        PropagatorLabel -> G,
737        PropagatorType -> C,
738        PropagatorArrow -> None,
739        PDG -> 21,
740        FullName -> "G" },
741
742V[5] == {
743        ClassName -> Wi,
744        Unphysical -> True,
745        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
746                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
747                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
748        SelfConjugate -> True,
749        Indices -> {Index[SU2W]},
750        FlavorIndex -> SU2W,
751        Mass -> 0,
752        PDG -> {1,2,3}},
753
754V[6] == {
755        ClassName -> B,
756        SelfConjugate -> True,
757        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
758        Indices -> {},
759        Mass -> 0,
760        Unphysical -> True},
761
762
763(************ Scalar Fields **********)
764        (* physical Higgs: Q = 0 *)
765  S[1] == {
766        ClassName -> H,
767        SelfConjugate -> True,
768        Mass -> {MH, 125},
769        Width -> {WH, 0.00679485838},
770        PropagatorLabel -> "H",
771        PropagatorType -> D,
772        PropagatorArrow -> None,
773        PDG -> 25,
774        TeXParticleName -> "\\phi",
775        TeXClassName -> "\\phi",
776        FullName -> "H" },
777
778S[2] == {
779        ClassName -> phi,
780        SelfConjugate -> True,
781        Mass -> {MZ, 91.5445065},
782        Width -> Wphi,
783        PropagatorLabel -> "Phi",
784        PropagatorType -> D,
785        PropagatorArrow -> None,
786        ParticleName ->"phi0",
787        PDG -> 250,
788        FullName -> "Phi",
789        Goldstone -> Z },
790
791S[3] == {
792        ClassName -> phi2,
793        SelfConjugate -> False,
794        Mass -> {MW, Internal},
795        Width -> Wphi2,
796        PropagatorLabel -> "Phi2",
797        PropagatorType -> D,
798        PropagatorArrow -> None,
799        ParticleName ->"phi+",
800        AntiParticleName ->"phi-",
801        PDG -> 251,
802        FullName -> "Phi2",
803        TeXClassName -> "\\phi^+",
804        TeXParticleName -> "\\phi^+",
805        TeXAntiParticleName -> "\\phi^-",
806        Goldstone -> W,
807        QuantumNumbers -> {Q -> 1}}
808}
809
810
811(*****************************************************************************************)
812
813(* SM Lagrangian *)
814
815(******************** Gauge F^2 Lagrangian terms*************************)
816(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
817 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
818                                        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
819       
820        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
821       
822        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
823                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
824
825
826(********************* Fermion Lagrangian terms*************************)
827(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
828 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
829
830    Lkin = I uqbar.Ga[mu].del[uq, mu] +
831        I dqbar.Ga[mu].del[dq, mu] +
832        I lbar.Ga[mu].del[l, mu] +
833        I vlbar.Ga[mu].del[vl, mu];
834
835    LQCD = gs (uqbar.Ga[mu].T[a].uq +
836        dqbar.Ga[mu].T[a].dq)G[mu, a];
837
838    LBright =
839       -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
840        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
841        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
842
843    LBleft =
844       -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
845        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
846        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
847        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
848       
849    LWleft = ee/sw/2(
850        vlbar.Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
851        lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
852       
853        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
854        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
855       
856        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
857        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
858       
859        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
860        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
861        );
862
863    Lkin + LQCD + LBright + LBleft + LWleft];
864
865
866(** Note : Modifications to the SM W and Z currents should be considered here above **)
867
868(******************** Higgs Lagrangian terms****************************)
869 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
870 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
871 
872
873   
874 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
875   
876    PMVec = Table[PauliSigma[i], {i, 3}];   
877    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
878
879        (*Y_phi=1*)
880    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
881    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
882    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
883
884    (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
885   
886
887(*************** Yukawa Lagrangian***********************)
888LYuk := If[FeynmanGauge,
889
890      Module[{s,r,n,m,i},                                                                 -
891              yd[m] CKM[n,m]     uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2)              -
892              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2]   -
893         
894              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2]   + (*This sign from eps matrix*)       
895              yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)    -
896       
897              yl[n]              vlbar[s,n].ProjP[s,r].l[r,n]      (-I phi2)              -
898              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H +I phi)/Sqrt[2]
899           ],
900           
901           Module[{s,r,n,m,i},                                                    -
902              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
903              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
904              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]
905           ]
906         ];
907
908LYukawa := LYuk + HC[LYuk];
909
910(** Note : Modifications to the SM H currents should be considered here above **)
911
912(**************Ghost terms**************************)
913(* Now we need the ghost terms which are of the form:             *)
914(* - g * antighost * d_BRST G                                     *)
915(* where d_BRST G is BRST transform of the gauge fixing function. *)
916
917LGhost := If[FeynmanGauge,
918                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
919               
920        (***********First the pure gauge piece.**********************) 
921        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
922                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
923       
924        dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
925                LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];   
926       
927        dBRSTB[mu_] := cw/ee del[ghB, mu];
928                LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
929       
930        (***********Next the piece from the scalar field.************)
931        LGhostphi := -   ee/(2*sw*cw) MW ( - I phi2    ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA )  +
932                        I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA )    ) -
933                        ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm   ) -
934                        I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
935                        ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
936                       
937                       
938        (***********Now add the pieces together.********************)
939        LGhostG + LGhostWi + LGhostB + LGhostphi]
940
941,
942
943        (*If unitary gauge, only include the gluonic ghost.*)
944                Block[{dBRSTG,LGhostG},
945               
946        (***********First the pure gauge piece.**********************) 
947        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
948                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];                 
949                       
950        (***********Now add the pieces together.********************)
951        LGhostG]
952
953];
954               
955(*********SM Lagrangian*******)         
956LSM := LGauge + LHiggs + LFermions + LYukawa  + LGhost;
957
958
959(*********VLQ Lagrangians*******)
960(** We assume that the physical and mass eigenstates match for vector-like quarks **)
961               
962(*********LB, EW interactions*******)
963
964LBW :=
965+KB*KBdLw*(bpbar.Wbar[mu].Ga[mu].ProjM.u)+KB*KBdRw*(bpbar.Wbar[mu].Ga[mu].ProjP.u)+KB*KBdLw*(ubar.W[mu].Ga[mu].ProjM.bp)+KB*KBdRw*(ubar.W[mu].Ga[mu].ProjP.bp)+KB*KBsLw*(bpbar.Wbar[mu].Ga[mu].ProjM.c)+KB*KBsRw*(bpbar.Wbar[mu].Ga[mu].ProjP.c)+KB*KBsLw*(cbar.W[mu].Ga[mu].ProjM.bp)+KB*KBsRw*(cbar.W[mu].Ga[mu].ProjP.bp)+KB*KBbLw*(bpbar.Wbar[mu].Ga[mu].ProjM.t)+KB*KBbRw*(bpbar.Wbar[mu].Ga[mu].ProjP.t)+KB*KBbLw*(tbar.W[mu].Ga[mu].ProjM.bp)+KB*KBbRw*(tbar.W[mu].Ga[mu].ProjP.bp);
966
967LBZ :=+KB*KBdLz*(bpbar.Z[mu].Ga[mu].ProjM.d)+KB*KBdRz*(bpbar.Z[mu].Ga[mu].ProjP.d)+KB*KBdLz*(dbar.Z[mu].Ga[mu].ProjM.bp)+KB*KBdRz*(dbar.Z[mu].Ga[mu].ProjP.bp)+KB*KBsLz*(bpbar.Z[mu].Ga[mu].ProjM.s)+KB*KBsRz*(bpbar.Z[mu].Ga[mu].ProjP.s)+KB*KBsLz*(sbar.Z[mu].Ga[mu].ProjM.bp)+KB*KBsRz*(sbar.Z[mu].Ga[mu].ProjP.bp)+KB*KBbLz*(bpbar.Z[mu].Ga[mu].ProjM.b)+KB*KBbRz*(bpbar.Z[mu].Ga[mu].ProjP.b)+KB*KBbLz*(bbar.Z[mu].Ga[mu].ProjM.bp)+KB*KBbRz*(bbar.Z[mu].Ga[mu].ProjP.bp);
968
969LBH:=-KB*MQ*KBdLh*(bpbar.H.ProjP.d)/v-KB*MQ*KBdLh*(dbar.H.ProjM.bp)/v-KB*MQ*KBdRh*(bpbar.H.ProjM.d)/v-KB*MQ*KBdRh*(dbar.H.ProjP.bp)/v-KB*MQ*KBsLh*(bpbar.H.ProjP.s)/v-KB*MQ*KBsLh*(sbar.H.ProjM.bp)/v-KB*MQ*KBsRh*(bpbar.H.ProjM.s)/v-KB*MQ*KBsRh*(sbar.H.ProjP.bp)/v-KB*MQ*KBbLh*(bpbar.H.ProjP.b)/v-KB*MQ*KBbLh*(bbar.H.ProjM.bp)/v-KB*MQ*KBbRh*(bpbar.H.ProjM.b)/v-KB*MQ*KBbRh*(bbar.H.ProjP.bp)/v;
970
971
972
973(*********B-gauge interaction*******)
974
975    LBVL = Gvl*ee/cw/3 B[mu]/2 bpbar.Ga[mu].bp;        (*Y_QL=1/3*)
976       
977    LWVL = Gvl*ee/sw/2(bpbar.Ga[mu].bp Wi[mu,3])
978
979
980(*********Kinetic, mass & QCD lagrangians for VLQ*******)
981
982LBK := I bpbar.Ga[mu].del[bp, mu];
983
984LBM := -MQ.bpbar.bp;
985
986LBG :=  gs (bpbar.Ga[mu].T[a].bp)G[mu, a];
987
988LBK := I bpbar.Ga[mu].del[bp, mu];
989
990LBM := -MQ.bpbar.bp;
991
992LBG :=  gs (bpbar.Ga[mu].T[a].bp)G[mu, a];
993
994
995LB := LBW + LBZ + LBH + LBK + LBM + LBG;
996
997LVLQ := LB + LBVL + LWVL;
998
999
1000
1001(*********Total Lagrangian*******)
1002
1003L := LSM + LVLQ;
1004
1005