VLQ: VLQ_Chromomagnetic.fr

File VLQ_Chromomagnetic.fr, 51.8 KB (added by buchkremer, 6 years ago)
Line 
1(***************************************************************************************************************)
2(******                       FeynRules mod-file for Model Independent searches of top partners           ******)
3(******                         X(5/3), T(2/3), B(-1/3) & Y(-4/3) with arbitrary couplings                ******)
4(******                                                                                                   ******)
5(******     Authors: M. Buchkremer, G. Cacciapaglia, A. Deandrea, L. Panizzi                              ******)
6(******                                                                                                   ******)
7(******                                                                                                   ******)
8(******                                                                                                   ******)
9(****** Choose whether Feynman gauge is desired.                                                          ******)
10(****** If set to False, unitary gauge is assumed.                                                        ******)
11(****** Feynman gauge is to be used for CalcHEP/CompHEP (calculation is 10-100 times faster) .            ******)
12(****** Feynman gauge is not supported in MadGraph and Sherpa.                                            ******)
13(****** Set FeynmanGauge = False for UFO outputs                                                          ******)
14(***************************************************************************************************************)
15
16(***************** This is the FeynRules model file for the gluon chromomagnetic coupling Qqg **********)
17
18M$ModelName = "VLQ_Chromomagnetic";
19
20
21M$Information = {Authors -> {"M. Buchkremer","G. Cacciapaglia","A. Deandrea","L. Panizzi"},
22             Version -> "1.2.5",
23             Date -> "10. 04. 2013",
24             Institutions -> {"Universite catholique de Louvain (CP3)", "Universite de Lyon (CNRS/IN2P3)","University of Southampton (School of Physics and Astronomy)"},
25             Emails -> {"mathieu.buchkremer@uclouvain.be", "g.cacciapaglia@ipnl.in2p3.fr","deandrea@ipnl.in2p3.fr", "l.panizzi@soton.ac.uk"}};
26
27
28(******* Index definitions ********)
29
30IndexRange[ Index[Generation] ] = Range[3]
31IndexRange[ Index[Colour] ] = NoUnfold[Range[3]]
32IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]]
33IndexRange[ Index[SU2W] ] = Unfold[Range[3]]
34IndexStyle[Colour, i]
35IndexStyle[Generation, f]
36IndexStyle[GenerationU, U]
37IndexStyle[GenerationD, D]
38IndexStyle[Gluon ,a]
39IndexStyle[SU2W ,k]
40
41(* Fixed parameter for the CKM sector (only one new vector-like partner) *)
42
43(******* Gauge parameters (for FeynArts) ********)
44
45GaugeXi[ V[1] ] = GaugeXi[A];
46GaugeXi[ V[2] ] = GaugeXi[Z];
47GaugeXi[ V[3] ] = GaugeXi[W];
48GaugeXi[ V[4] ] = GaugeXi[G];
49GaugeXi[ S[1] ] = 1;
50GaugeXi[ S[2] ] = GaugeXi[Z];
51GaugeXi[ S[3] ] = GaugeXi[W];
52GaugeXi[ U[1] ] = GaugeXi[A];
53GaugeXi[ U[2] ] = GaugeXi[Z];
54GaugeXi[ U[31] ] = GaugeXi[W];
55GaugeXi[ U[32] ] = GaugeXi[W];
56GaugeXi[ U[4] ] = GaugeXi[G];
57
58
59(****************  Parameters *************)
60
61M$Parameters = {
62
63  (* External parameters *)
64
65  \[Alpha]EWM1== {
66        ParameterType -> External,
67        BlockName -> SMINPUTS,
68        ParameterName -> aEWM1,
69        InteractionOrder -> {QED, -2},
70        Value -> 127.9,
71        Description -> "Inverse of the electroweak coupling constant"},
72
73  Gf == {
74        ParameterType -> External,
75        BlockName -> SMINPUTS,
76        TeX -> Subscript[G, f],
77        InteractionOrder -> {QED, 2},
78        Value -> 1.16600 * 10^(-5),
79        Description -> "Fermi constant"},
80
81  \[Alpha]S == {
82        ParameterType -> External,
83        BlockName -> SMINPUTS,
84        TeX -> Subscript[\[Alpha], s],
85        ParameterName -> aS,
86        InteractionOrder -> {QCD, 2},
87        Value -> 0.118,
88        Description -> "Strong coupling constant at the Z pole."},
89
90  ymdo == {
91        ParameterType -> External,
92        BlockName -> YUKAWA,
93        Value -> 5.04*10^(-3),
94        OrderBlock -> {1},
95        Description -> "Down Yukawa mass"},
96
97
98  ymup == {
99        ParameterType -> External,
100        BlockName -> YUKAWA,
101        Value -> 2.55*10^(-3),
102        OrderBlock -> {2},
103        Description -> "Up Yukawa mass"},
104
105  yms == {
106        ParameterType -> External,
107        BlockName -> YUKAWA,
108        Value -> 0.101,
109        OrderBlock -> {3},
110        Description -> "Strange Yukawa mass"},
111
112
113  ymc == {
114        ParameterType -> External,
115        BlockName -> YUKAWA,
116        Value -> 1.25,
117        OrderBlock -> {4},
118        Description -> "Charm Yukawa mass"},
119
120  ymb == {
121        ParameterType -> External,
122        BlockName -> YUKAWA,
123        Value -> 4.2,
124        OrderBlock -> {5},
125        Description -> "Bottom Yukawa mass"},
126
127  ymt == {
128        ParameterType -> External,
129        BlockName -> YUKAWA,
130        Value -> 174.3,
131        OrderBlock -> {6},
132        Description -> "Top Yukawa mass"},
133
134  yme == {
135        ParameterType -> External,
136        BlockName -> YUKAWA,
137        Value ->  5.11*10^(-4),
138        OrderBlock -> {11},
139        Description -> "Electron Yukawa mass"},
140
141  ymm == {
142        ParameterType -> External,
143        BlockName -> YUKAWA,
144        Value -> 0.10566,
145        OrderBlock -> {13},
146        Description -> "Muon Yukawa mass"},
147
148  ymtau == {
149        ParameterType -> External,
150        BlockName -> YUKAWA,
151        Value -> 1.777,
152        OrderBlock -> {15},
153        Description -> "Tau Yukawa mass"},
154
155  yx == {
156        ParameterType -> External,
157        BlockName -> YUKAWA,
158        ComplexParameter -> False,
159        Value -> 600,
160        Description -> "X mass"},
161
162  ytp == {
163        ParameterType -> External,
164        BlockName -> YUKAWA,
165        ComplexParameter -> False,
166        Value -> 600,
167        Description -> "T mass"},
168
169  ybp == {
170        ParameterType -> External,
171        BlockName -> YUKAWA,
172        ComplexParameter -> False,
173        Value -> 600,
174        Description -> "B mass"},
175
176  yy == {
177        ParameterType -> External,
178        BlockName -> YUKAWA,
179        ComplexParameter -> False,
180        Value -> 600,
181        Description -> "Y mass"},
182
183  KX == {
184        ParameterType -> External,
185        BlockName -> KAPPA,
186        ComplexParameter -> False,
187        Value -> 0,
188        Description -> "Kappa_X parameter"},
189
190  KT == {
191        ParameterType -> External,
192        BlockName -> KAPPA,
193        ComplexParameter -> False,
194        Value -> 0,
195        Description -> "Kappa_T parameter"},
196
197  KB == {
198        ParameterType -> External,
199        BlockName -> KAPPA,
200        ComplexParameter -> False,
201        Value -> 0,
202        Description -> "Kappa_B parameter"},
203
204  KY == {
205        ParameterType -> External,
206        BlockName -> KAPPA,
207        ComplexParameter -> False,
208        Value -> 0,
209        Description -> "Kappa_Y parameter"},
210
211  KG == {
212        ParameterType -> External,
213        BlockName -> KAPPA,
214        ComplexParameter -> False,
215        Value -> 0,
216        Description -> "Kappa_G parameter"},
217
218  xitpw == {
219        ParameterType -> External,
220        BlockName -> XI,
221        ComplexParameter -> False,
222        Value -> 0,
223        Description -> "Branching ratio of T in W"},
224
225  xitpz == {
226        ParameterType -> External,
227        BlockName -> XI,
228        ComplexParameter -> False,
229        Value -> 0,
230        Description -> "Branching ratio of T in Z"},
231
232  xitph == {
233        ParameterType -> External,
234        BlockName -> XI,
235        ComplexParameter -> False,
236        Value -> 0,
237        Description -> "Branching ratio of T in H"},
238
239  xibpw == {
240        ParameterType -> External,
241        BlockName -> XI,
242        ComplexParameter -> False,
243        Value -> 0,
244        Description -> "Branching ratio of B in W"},
245
246  xibpz == {
247        ParameterType -> External,
248        BlockName -> XI,
249        ComplexParameter -> False,
250        Value -> 0,
251        Description -> "Branching ratio of B in Z"},
252
253  xibph == {
254        ParameterType -> External,
255        BlockName -> XI,
256        ComplexParameter -> False,
257        Value -> 0,
258        Description -> "Branching ratio of B in H"},
259
260  zetauL == {
261        ParameterType -> External,
262        BlockName -> ZETA,
263        ComplexParameter -> False,
264        Value -> 0,
265        Description -> "T-u mixing (left-handed)"},
266
267  zetacL == {
268        ParameterType -> External,
269        BlockName -> ZETA,
270        ComplexParameter -> False,
271        Value -> 0,
272        Description -> "T-c mixing (left-handed)"},
273
274  zetatL == {
275        ParameterType -> External,
276        BlockName -> ZETA,
277        ComplexParameter -> False,
278        Value -> 0,
279        Description -> "T-t mixing (left-handed)"},
280
281  zetadL == {
282        ParameterType -> External,
283        BlockName -> ZETA,
284        ComplexParameter -> False,
285        Value -> 0,
286        Description -> "B-d mixing (left-handed)"},
287
288  zetasL == {
289        ParameterType -> External,
290        BlockName -> ZETA,
291        ComplexParameter -> False,
292        Value -> 0,
293        Description -> "B-s mixing (left-handed)"},
294
295  zetabL == {
296        ParameterType -> External,
297        BlockName -> ZETA,
298        ComplexParameter -> False,
299        Value -> 0,
300        Description -> "B-b mixing (left-handed)"},
301
302  zetauR == {
303        ParameterType -> External,
304        BlockName -> ZETA,
305        ComplexParameter -> False,
306        Value -> 0,
307        Description -> "T-u mixing (right-handed)"},
308
309  zetacR == {
310        ParameterType -> External,
311        BlockName -> ZETA,
312        ComplexParameter -> False,
313        Value -> 0,
314        Description -> "T-c mixing (right-handed)"},
315
316  zetatR == {
317        ParameterType -> External,
318        BlockName -> ZETA,
319        ComplexParameter -> False,
320        Value -> 0,
321        Description -> "T-t mixing (right-handed)"},
322
323  zetadR == {
324        ParameterType -> External,
325        BlockName -> ZETA,
326        ComplexParameter -> False,
327        Value -> 0,
328        Description -> "B-d mixing (right-handed)"},
329
330  zetasR == {
331        ParameterType -> External,
332        BlockName -> ZETA,
333        ComplexParameter -> False,
334        Value -> 0,
335        Description -> "B-s mixing (right-handed)"},
336
337  zetabR == {
338        ParameterType -> External,
339        BlockName -> ZETA,
340        ComplexParameter -> False,
341        Value -> 0,
342        Description -> "B-b mixing (right-handed)"},
343
344  CKM == {
345        ParameterType -> External,
346        BlockName -> CKMBlock,
347        ComplexParameter -> False,
348       Indices -> {Index[Generation], Index[Generation]},
349       TensorClass -> CKM,
350       Unitary -> True,
351       Value -> {CKM[1,1] -> 0.97428,
352                 CKM[1,2] -> 0.2253,
353                 CKM[1,3] -> 0.00347,
354                 CKM[2,1] -> 0.2252,
355                 CKM[2,2] -> 0.97345,
356                 CKM[2,3] -> 0.0410,
357                 CKM[3,1] -> 0.00862,
358                 CKM[3,2] -> 0.0403,
359                 CKM[3,3] -> 0.999152},
360       Description -> "SM CKM Matrix"},
361
362
363   (* Internal Parameters *)
364
365  \[Alpha]EW == {
366        ParameterType -> Internal,
367        Value -> 1/\[Alpha]EWM1,
368        TeX -> Subscript[\[Alpha], EW],
369        ParameterName -> aEW,
370        InteractionOrder -> {QED, 2},
371        Description -> "Electroweak coupling contant"},
372
373
374  MW == {
375        ParameterType -> Internal,
376        Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]],
377        TeX  -> Subscript[M, W],
378        Description -> "W mass"},
379
380  sw2 == {
381        ParameterType -> Internal,
382        Value -> 1-(MW/MZ)^2,
383        Description -> "Squared Sin of the Weinberg angle"},
384
385   ee == {
386        TeX -> e,
387        ParameterType -> Internal,
388        Value -> Sqrt[4 Pi \[Alpha]EW],
389        InteractionOrder -> {QED, 1},
390        Description -> "Electric coupling constant"},
391
392   cw == {
393        TeX -> Subscript[c, w],
394        ParameterType -> Internal,
395        Value -> Sqrt[1 - sw2],
396        Description -> "Cos of the Weinberg angle"}, 
397
398   sw == {
399        TeX -> Subscript[s, w],
400        ParameterType -> Internal,
401        Value -> Sqrt[sw2],
402        Description -> "Sin of the Weinberg angle"}, 
403
404   gw == {
405        TeX -> Subscript[g, w],
406        ParameterType -> Internal,
407        Value -> ee / sw,
408        InteractionOrder -> {QED, 1},
409        Description -> "Weak coupling constant"},
410
411   g1 == {
412        TeX -> Subscript[g, 1],
413        ParameterType -> Internal,
414        Value -> ee / cw,
415        InteractionOrder -> {QED, 1},
416        Description -> "U(1)Y coupling constant"},
417
418   gs == {
419        TeX -> Subscript[g, s],
420        ParameterType -> Internal,
421        Value -> Sqrt[4 Pi \[Alpha]S],
422        InteractionOrder -> {QCD, 1},
423        ParameterName -> G,
424        Description -> "Strong coupling constant"},
425
426   v == {
427        ParameterType -> Internal,
428        Value -> 2*MW*sw/ee,
429        InteractionOrder -> {QED, -1},
430        Description -> "Higgs VEV"},
431
432   \[Lambda] == {
433        ParameterType -> Internal,
434        Value -> MH^2/(2*v^2),
435        InteractionOrder -> {QED, 2},
436        ParameterName -> lam,
437        Description -> "Higgs quartic coupling"},
438
439   muH == {
440        ParameterType -> Internal,
441        Value -> Sqrt[v^2 \[Lambda]],
442        TeX -> \[Mu],
443        Description -> "Coefficient of the quadratic piece of the Higgs potential"},
444
445   yl == {
446        TeX -> Superscript[y, l],
447        Indices -> {Index[Generation]},
448        AllowSummation -> True,
449        ParameterType -> Internal,
450        Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymm / v, yl[3] -> Sqrt[2] ymtau / v},
451        ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau},
452        InteractionOrder -> {QED, 1},
453        ComplexParameter -> False,
454        Description -> "Lepton Yukawa coupling"},
455
456   yu == {
457        TeX -> Superscript[y, u],
458        Indices -> {Index[Generation]},
459        AllowSummation -> True,
460        ParameterType -> Internal,
461        Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v},
462        ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt},
463        InteractionOrder -> {QED, 1},
464        ComplexParameter -> False,
465        Description -> "U-quark Yukawa coupling"},
466
467   yd == {
468        TeX -> Superscript[y, d],
469        Indices -> {Index[Generation]},
470        AllowSummation -> True,
471        ParameterType -> Internal,
472        Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v},
473        ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb},
474        InteractionOrder -> {QED, 1},
475        ComplexParameter -> False,
476        Description -> "D-quark Yukawa coupling"},
477
478  gamma0tpw == {
479        ParameterType -> Internal,
480        BlockName -> WIDTH,
481        ComplexParameter -> False,
482        Value -> (1-MW^2/MTP^2)*(1+MW^2/MTP^2-2*MW^4/MTP^4),
483        Description -> "T partial width for T>Wq (massless q)"},
484
485  gamma0tpz == {
486        ParameterType -> Internal,
487        BlockName -> WIDTH,
488        ComplexParameter -> False,
489        Value -> 1/2*(1-MZ^2/MTP^2)*(1+MZ^2/MTP^2-2*MZ^4/MTP^4),
490        Description -> "T partial width for T>Zq (massless q)"},
491
492  gamma0tph == {
493        ParameterType -> Internal,
494        BlockName -> WIDTH,
495        ComplexParameter -> False,
496        Value -> 1/2*(1-MH^2/MTP^2)^2,
497        Description -> "T partial width for T>Hq (massless q)"},
498
499
500  gamma0bpw == {
501        ParameterType -> Internal,
502        BlockName -> WIDTH,
503        ComplexParameter -> False,
504        Value -> (1-MW^2/MBP^2)*(1+MW^2/MBP^2-2*MW^4/MBP^4),
505        Description -> "B partial width for B>Wq (massless q)"},
506
507
508  gamma0bpz == {
509        ParameterType -> Internal,
510        BlockName -> WIDTH,
511        ComplexParameter -> False,
512        Value -> 1/2*(1-MZ^2/MBP^2)*(1+MZ^2/MBP^2-2*MZ^4/MBP^4),
513        Description -> "B partial width for B>Zq (massless q)"},
514
515
516  gamma0bph == {
517        ParameterType -> Internal,
518        BlockName -> WIDTH,
519        ComplexParameter -> False,
520        Value -> 1/2*(1-MH^2/MBP^2)^2,
521        Description -> "B partial width for B>Hq (massless q)"},
522
523
524  gamma0xw == {
525        ParameterType -> Internal,
526        BlockName -> WIDTH,
527        ComplexParameter -> False,
528        Value -> (1-MW^2/MX^2)*(1+MW^2/MX^2-2*MW^4/MX^4),
529        Description -> "X partial width for X>Wq (massless q)"},
530
531
532  gamma0yw == {
533        ParameterType -> Internal,
534        BlockName -> WIDTH,
535        ComplexParameter -> False,
536        Value -> (1-MW^2/MY^2)*(1+MW^2/MY^2-2*MW^4/MY^4),
537        Description -> "Y partial width for Y>Wq (massless q)"},
538
539
540fuL == {ParameterType -> External,
541        BlockName -> GLUON,
542        ComplexParameter -> False,
543        Description -> "T-u-g LH coupling",
544       Value -> 0},
545
546fuR == {ParameterType -> External,
547        BlockName -> GLUON,
548        ComplexParameter -> False,
549        Description -> "T-u-g RH coupling",
550       Value -> 0},
551
552fcL == {ParameterType -> External,
553        BlockName -> GLUON,
554        ComplexParameter -> False,
555        Description -> "T-c-g LH coupling",
556       Value -> 0},
557
558fcR == {ParameterType -> External,
559        BlockName -> GLUON,
560        ComplexParameter -> False,
561        Description -> "T-c-g RH coupling",
562       Value -> 0},
563
564ftL == {ParameterType -> External,
565        BlockName -> GLUON,
566        ComplexParameter -> False,
567        Description -> "T-t-g LH coupling",
568       Value -> 0},
569
570ftR == {ParameterType -> External,
571        BlockName -> GLUON,
572        ComplexParameter -> False,
573        Description -> "T-t-g RH coupling",
574       Value -> 0},
575
576fdL == {ParameterType -> External,
577        BlockName -> GLUON,
578        ComplexParameter -> False,
579        Description -> "B-d-g LH coupling",
580       Value -> 0},
581
582fdR == {ParameterType -> External,
583        BlockName -> GLUON,
584        ComplexParameter -> False,
585        Description -> "B-d-g RH coupling",
586       Value -> 0},
587
588fsL == {ParameterType -> External,
589        BlockName -> GLUON,
590        ComplexParameter -> False,
591        Description -> "B-s-g LH coupling",
592       Value -> 0},
593
594fsR == {ParameterType -> External,
595        BlockName -> GLUON,
596        ComplexParameter -> False,
597        Description -> "B-s-g RH coupling",
598       Value -> 0},
599
600fbL == {ParameterType -> External,
601        BlockName -> GLUON,
602        ComplexParameter -> False,
603        Description -> "B-b-g LH coupling",
604       Value -> 0},
605
606fbR == {ParameterType -> External,
607        BlockName -> GLUON,
608        ComplexParameter -> False,
609        Description -> "B-b-g RH coupling",
610       Value -> 0},
611
612Lambda == {ParameterType -> External,
613        BlockName -> GLUON,
614        ComplexParameter -> False,
615        Description -> "NP scale of the chromomagnetic D=6 operator",
616       Value -> 600},
617
618  KXuL == {
619        ParameterType -> Internal,
620        BlockName -> KAPPA,
621        ComplexParameter -> False,
622        Value -> (ee/sw*Sqrt[zetauL/gamma0xw])/Sqrt[2],
623        InteractionOrder -> {QED, 1},
624        Description -> "XuW coupling (left-handed)"},
625
626  KXuR == {
627        ParameterType -> Internal,
628        BlockName -> KAPPA,
629        ComplexParameter -> False,
630        Value -> (ee/sw*Sqrt[zetauR/gamma0xw])/Sqrt[2],
631        InteractionOrder -> {QED, 1},
632        Description -> "XuW coupling (right-handed)"},
633
634  KXcL == {
635        ParameterType -> Internal,
636        BlockName -> KAPPA,
637        ComplexParameter -> False,
638        Value -> (ee/sw*Sqrt[zetacL/gamma0xw])/Sqrt[2],
639        InteractionOrder -> {QED, 1},
640        Description -> "XcW coupling (left-handed)"},
641
642
643  KXcR == {
644        ParameterType -> Internal,
645        BlockName -> KAPPA,
646        ComplexParameter -> False,
647        Value -> (ee/sw*Sqrt[zetacR/gamma0xw])/Sqrt[2],
648        InteractionOrder -> {QED, 1},
649        Description -> "XcW coupling (right-handed)"},
650
651
652  KXtL == {
653        ParameterType -> Internal,
654        BlockName -> KAPPA,
655        ComplexParameter -> False,
656        Value -> (ee/sw*Sqrt[zetatL/gamma0xw])/Sqrt[2],
657        InteractionOrder -> {QED, 1},
658        Description -> "XtW coupling (left-handed)"},
659
660
661  KXtR == {
662        ParameterType -> Internal,
663        BlockName -> KAPPA,
664        ComplexParameter -> False,
665        Value -> (ee/sw*Sqrt[zetatR/gamma0xw])/Sqrt[2],
666        InteractionOrder -> {QED, 1},
667        Description -> "XtW coupling (right-handed)"},
668
669
670  KYdL == {
671        ParameterType -> Internal,
672        BlockName -> KAPPA,
673        ComplexParameter -> False,
674        Value -> (ee/sw*Sqrt[zetadL/gamma0yw])/Sqrt[2],
675        InteractionOrder -> {QED, 1},
676        Description -> "YdW coupling (left-handed)"},
677
678
679  KYdR == {
680        ParameterType -> Internal,
681        BlockName -> KAPPA,
682        ComplexParameter -> False,
683        Value -> (ee/sw*Sqrt[zetadR/gamma0yw])/Sqrt[2],
684        InteractionOrder -> {QED, 1},
685        Description -> "YdW coupling (right-handed)"},
686
687
688  KYsL == {
689        ParameterType -> Internal,
690        BlockName -> KAPPA,
691        ComplexParameter -> False,
692        Value -> (ee/sw*Sqrt[zetasL/gamma0yw])/Sqrt[2],
693        InteractionOrder -> {QED, 1},
694        Description -> "YsW coupling (left-handed)"},
695
696
697  KYsR == {
698        ParameterType -> Internal,
699        BlockName -> KAPPA,
700        ComplexParameter -> False,
701        Value -> (ee/sw*Sqrt[zetasR/gamma0yw])/Sqrt[2],
702        InteractionOrder -> {QED, 1},
703        Description -> "YsW coupling (right-handed)"},
704
705
706  KYbL == {
707        ParameterType -> Internal,
708        BlockName -> KAPPA,
709        ComplexParameter -> False,
710        Value -> (ee/sw*Sqrt[zetabL/gamma0yw])/Sqrt[2],
711        InteractionOrder -> {QED, 1},
712        Description -> "YbW coupling (left-handed)"},
713
714
715  KYbR == {
716        ParameterType -> Internal,
717        BlockName -> KAPPA,
718        ComplexParameter -> False,
719        Value -> (ee/sw*Sqrt[zetabR/gamma0yw])/Sqrt[2],
720        InteractionOrder -> {QED, 1},
721        Description -> "YbW coupling (right-handed)"},
722
723
724  KTuLw == {
725        ParameterType -> Internal,
726        BlockName -> KAPPA,
727        ComplexParameter -> False,
728        Value -> (ee/sw*Sqrt[zetauL*xitpw/gamma0tpw])/Sqrt[2],
729        InteractionOrder -> {QED, 1},
730        Description -> "TuW coupling (left-handed)"},
731
732
733  KTuRw == {
734        ParameterType -> Internal,
735        BlockName -> KAPPA,
736        ComplexParameter -> False,
737        Value -> (ee/sw*Sqrt[zetauR*xitpw/gamma0tpw])/Sqrt[2],
738        InteractionOrder -> {QED, 1},
739        Description -> "TuW coupling (right-handed)"},
740
741
742  KTcLw == {
743        ParameterType -> Internal,
744        BlockName -> KAPPA,
745        ComplexParameter -> False,
746        Value -> (ee/sw*Sqrt[zetacL*xitpw/gamma0tpw])/Sqrt[2],
747        InteractionOrder -> {QED, 1},
748        Description -> "TcW coupling (left-handed)"},
749
750
751  KTcRw == {
752        ParameterType -> Internal,
753        BlockName -> KAPPA,
754        ComplexParameter -> False,
755        Value -> (ee/sw*Sqrt[zetacR*xitpw/gamma0tpw])/Sqrt[2],
756        InteractionOrder -> {QED, 1},
757        Description -> "TcW coupling (right-handed)"},
758
759
760  KTtLw == {
761        ParameterType -> Internal,
762        BlockName -> KAPPA,
763        ComplexParameter -> False,
764        Value -> (ee/sw*Sqrt[zetatL*xitpw/gamma0tpw])/Sqrt[2],
765        InteractionOrder -> {QED, 1},
766        Description -> "TtW coupling (left-handed)"},
767
768
769  KTtRw == {
770        ParameterType -> Internal,
771        BlockName -> KAPPA,
772        ComplexParameter -> False,
773        Value -> (ee/sw*Sqrt[zetatR*xitpw/gamma0tpw])/Sqrt[2],
774        InteractionOrder -> {QED, 1},
775        Description -> "TtW coupling (right-handed)"},
776
777
778  KTuLz == {
779        ParameterType -> Internal,
780        BlockName -> KAPPA,
781        ComplexParameter -> False,
782        Value -> (ee/sw*Sqrt[zetauL*xitpz/gamma0tpz])/2/cw,
783        InteractionOrder -> {QED, 1},
784        Description -> "TuZ coupling (left-handed)"},
785
786
787  KTuRz == {
788        ParameterType -> Internal,
789        BlockName -> KAPPA,
790        ComplexParameter -> False,
791        Value -> (ee/sw*Sqrt[zetauR*xitpz/gamma0tpz])/2/cw,
792        InteractionOrder -> {QED, 1},
793        Description -> "TuZ coupling (right-handed)"},
794
795
796  KTcLz == {
797        ParameterType -> Internal,
798        BlockName -> KAPPA,
799        ComplexParameter -> False,
800        Value -> (ee/sw*Sqrt[zetacL*xitpz/gamma0tpz])/2/cw,
801        InteractionOrder -> {QED, 1},
802        Description -> "TcZ coupling (left-handed)"},
803
804
805  KTcRz == {
806        ParameterType -> Internal,
807        BlockName -> KAPPA,
808        ComplexParameter -> False,
809        Value -> (ee/sw*Sqrt[zetacR*xitpz/gamma0tpz])/2/cw,
810        InteractionOrder -> {QED, 1},
811        Description -> "TcZ coupling (right-handed)"},
812
813
814  KTtLz == {
815        ParameterType -> Internal,
816        BlockName -> KAPPA,
817        ComplexParameter -> False,
818        Value -> (ee/sw*Sqrt[zetatL*xitpz/gamma0tpz])/2/cw,
819        InteractionOrder -> {QED, 1},
820        Description -> "TtZ coupling (left-handed)"},
821
822
823  KTtRz == {
824        ParameterType -> Internal,
825        BlockName -> KAPPA,
826        ComplexParameter -> False,
827        Value -> (ee/sw*Sqrt[zetatR*xitpz/gamma0tpz])/2/cw,
828        InteractionOrder -> {QED, 1},
829        Description -> "TtZ coupling (right-handed)"},
830
831
832  KTuLh == {
833        ParameterType -> Internal,
834        BlockName -> KAPPA,
835        ComplexParameter -> False,
836        Value -> (Sqrt[zetauL*xitph/gamma0tph]),
837        InteractionOrder -> {QED, 0},
838        Description -> "TuH coupling (left-handed)"},
839
840  KTuRh == {
841        ParameterType -> Internal,
842        BlockName -> KAPPA,
843        ComplexParameter -> False,
844        Value -> (Sqrt[zetauR*xitph/gamma0tph]),
845        InteractionOrder -> {QED, 0},
846        Description -> "TuH coupling (right-handed)"},
847
848
849  KTcLh == {
850        ParameterType -> Internal,
851        BlockName -> KAPPA,
852        ComplexParameter -> False,
853        Value -> (Sqrt[zetacL*xitph/gamma0tph]),
854        InteractionOrder -> {QED, 0},
855        Description -> "TcH coupling (left-handed)"},
856
857
858  KTcRh == {
859        ParameterType -> Internal,
860        BlockName -> KAPPA,
861        ComplexParameter -> False,
862        Value -> (Sqrt[zetacR*xitph/gamma0tph]),
863        InteractionOrder -> {QED, 0},
864        Description -> "TcH coupling (right-handed)"},
865
866
867  KTtLh == {
868        ParameterType -> Internal,
869        BlockName -> KAPPA,
870        ComplexParameter -> False,
871        Value -> (Sqrt[zetatL*xitph/gamma0tph]),
872        InteractionOrder -> {QED, 0},
873        Description -> "TtH coupling (left-handed)"},
874
875
876  KTtRh == {
877        ParameterType -> Internal,
878        BlockName -> KAPPA,
879        ComplexParameter -> False,
880        Value -> (Sqrt[zetatR*xitph/gamma0tph]),
881        InteractionOrder -> {QED, 0},
882        Description -> "TtH coupling (right-handed)"},
883
884
885  KBdLw == {
886        ParameterType -> Internal,
887        BlockName -> KAPPA,
888        ComplexParameter -> False,
889        Value -> (ee/sw*Sqrt[zetadL*xibpw/gamma0bpw])/Sqrt[2],
890        InteractionOrder -> {QED, 1},
891        Description -> "BdW coupling (left-handed)"},
892
893
894  KBdRw == {
895        ParameterType -> Internal,
896        BlockName -> KAPPA,
897        ComplexParameter -> False,
898        Value -> (ee/sw*Sqrt[zetadR*xibpw/gamma0bpw])/Sqrt[2],
899        InteractionOrder -> {QED, 1},
900        Description -> "BdW coupling (right-handed)"},
901
902
903  KBsLw == {
904        ParameterType -> Internal,
905        BlockName -> KAPPA,
906        ComplexParameter -> False,
907        Value -> (ee/sw*Sqrt[zetasL*xibpw/gamma0bpw])/Sqrt[2],
908        InteractionOrder -> {QED, 1},
909        Description -> "BsW coupling (left-handed)"},
910
911
912  KBsRw == {
913        ParameterType -> Internal,
914        BlockName -> KAPPA,
915        ComplexParameter -> False,
916        Value -> (gw*Sqrt[zetasR*xibpw/gamma0bpw])/Sqrt[2],
917        InteractionOrder -> {QED, 1},
918        Description -> "BsW coupling (right-handed)"},
919
920
921  KBbLw == {
922        ParameterType -> Internal,
923        BlockName -> KAPPA,
924        ComplexParameter -> False,
925        Value -> (gw*Sqrt[zetabL*xibpw/gamma0bpw])/Sqrt[2],
926        InteractionOrder -> {QED, 1},
927        Description -> "BbW coupling (left-handed)"},
928
929
930  KBbRw == {
931        ParameterType -> Internal,
932        BlockName -> KAPPA,
933        ComplexParameter -> False,
934        Value -> (gw*Sqrt[zetabR*xibpw/gamma0bpw])/Sqrt[2],
935        InteractionOrder -> {QED, 1},
936        Description -> "BbW coupling (right-handed)"},
937
938
939  KBdLz == {
940        ParameterType -> Internal,
941        BlockName -> KAPPA,
942        ComplexParameter -> False,
943        Value -> (gw*Sqrt[zetadL*xibpz/gamma0bpz])/2/cw,
944        InteractionOrder -> {QED, 1},
945        Description -> "BdZ coupling (left-handed)"},
946
947
948  KBdRz == {
949        ParameterType -> Internal,
950        BlockName -> KAPPA,
951        ComplexParameter -> False,
952        Value -> (gw*Sqrt[zetadR*xibpz/gamma0bpz])/2/cw,
953        InteractionOrder -> {QED, 1},
954        Description -> "BdZ coupling (right-handed)"},
955
956
957  KBsLz == {
958        ParameterType -> Internal,
959        BlockName -> KAPPA,
960        ComplexParameter -> False,
961        Value -> (gw*Sqrt[zetasL*xibpz/gamma0bpz])/2/cw,
962        InteractionOrder -> {QED, 1},
963        Description -> "BsZ coupling (left-handed)"},
964
965
966  KBsRz == {
967        ParameterType -> Internal,
968        BlockName -> KAPPA,
969        ComplexParameter -> False,
970        Value -> (gw*Sqrt[zetasR*xibpz/gamma0bpz])/2/cw,
971        InteractionOrder -> {QED, 1},
972        Description -> "BsZ coupling (right-handed)"},
973
974
975  KBbLz == {
976        ParameterType -> Internal,
977        BlockName -> KAPPA,
978        ComplexParameter -> False,
979        Value -> (gw*Sqrt[zetabL*xibpz/gamma0bpz])/2/cw,
980        InteractionOrder -> {QED, 1},
981        Description -> "BbZ coupling (left-handed)"},
982
983
984  KBbRz == {
985        ParameterType -> Internal,
986        BlockName -> KAPPA,
987        ComplexParameter -> False,
988        Value -> (gw*Sqrt[zetabR*xibpz/gamma0bpz])/2/cw,
989        InteractionOrder -> {QED, 1},
990        Description -> "BbZ coupling (right-handed)"},
991
992
993  KBdLh == {
994        ParameterType -> Internal,
995        BlockName -> KAPPA,
996        ComplexParameter -> False,
997        Value -> (Sqrt[zetadL*xibph/gamma0bph]),
998        InteractionOrder -> {QED, 0},
999        Description -> "BdH coupling (left-handed)"},
1000
1001
1002  KBdRh == {
1003        ParameterType -> Internal,
1004        BlockName -> KAPPA,
1005        ComplexParameter -> False,
1006        Value -> (Sqrt[zetadR*xibph/gamma0bph]),
1007        InteractionOrder -> {QED, 0},
1008        Description -> "BdH coupling (right-handed)"},
1009
1010
1011  KBsLh == {
1012        ParameterType -> Internal,
1013        BlockName -> KAPPA,
1014        ComplexParameter -> False,
1015        Value -> (Sqrt[zetasL*xibph/gamma0bph]),
1016        InteractionOrder -> {QED, 0},
1017        Description -> "BsH coupling (left-handed)"},
1018
1019
1020  KBsRh == {
1021        ParameterType -> Internal,
1022        BlockName -> KAPPA,
1023        ComplexParameter -> False,
1024        Value -> (Sqrt[zetasR*xibph/gamma0bph]),
1025        InteractionOrder -> {QED, 0},
1026        Description -> "BsH coupling (right-handed)"},
1027
1028
1029  KBbLh == {
1030        ParameterType -> Internal,
1031        BlockName -> KAPPA,
1032        ComplexParameter -> False,
1033        Value -> (Sqrt[zetabL*xibph/gamma0bph]),
1034        InteractionOrder -> {QED, 0},
1035        Description -> "BbH coupling (left-handed)"},
1036
1037
1038  KBbRh == {
1039        ParameterType -> Internal,
1040        BlockName -> KAPPA,
1041        ComplexParameter -> False,
1042        Value -> (Sqrt[zetabR*xibph/gamma0bph]),
1043        InteractionOrder -> {QED, 0},
1044        Description -> "BbH coupling (right-handed)"}}
1045
1046(************** Gauge Groups ******************)
1047
1048M$GaugeGroups = {
1049
1050  U1Y == {
1051        Abelian -> True,
1052        GaugeBoson -> B,
1053        Charge -> Y,
1054        CouplingConstant -> g1},
1055
1056  SU2L == {
1057        Abelian -> False,
1058        GaugeBoson -> Wi,
1059        StructureConstant -> Eps,
1060        CouplingConstant -> gw},
1061
1062  SU3C == {
1063        Abelian -> False,
1064        GaugeBoson -> G,
1065        StructureConstant -> f,
1066        SymmetricTensor -> dSUN,
1067        Representations -> {T, Colour},
1068        CouplingConstant -> gs}
1069}
1070
1071(********* Particle Classes **********)
1072
1073M$ClassesDescription = {
1074
1075(********** Fermions ************)
1076        (* Leptons (neutrino): I_3 = +1/2, Q = 0 *)
1077  F[1] == {
1078        ClassName -> vl,
1079        ClassMembers -> {ve,vm,vt},
1080        FlavorIndex -> Generation,
1081        SelfConjugate -> False,
1082        Indices -> {Index[Generation]},
1083        Mass -> 0,
1084        Width -> 0,
1085        QuantumNumbers -> {LeptonNumber -> 1},
1086        PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
1087        PropagatorType -> S,
1088        PropagatorArrow -> Forward,
1089        PDG -> {12,14,16},
1090        FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} },
1091
1092        (* Leptons (electron): I_3 = -1/2, Q = -1 *)
1093  F[2] == {
1094        ClassName -> l,
1095        ClassMembers -> {e, m, tt},
1096        FlavorIndex -> Generation,
1097        SelfConjugate -> False,
1098        Indices -> {Index[Generation]},
1099        Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}},
1100        Width -> 0,
1101        QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
1102        PropagatorLabel -> {"l", "e", "m", "tt"},
1103        PropagatorType -> Straight,
1104        ParticleName -> {"e-", "m-", "tt-"},
1105        AntiParticleName -> {"e+", "m+", "tt+"},
1106        PropagatorArrow -> Forward,
1107        PDG -> {11, 13, 15},
1108        FullName -> {"Electron", "Muon", "Tau"} },
1109
1110        (* Quarks (u): I_3 = +1/2, Q = +2/3 *)
1111  F[3] == {
1112        ClassMembers -> {u, c, t},
1113        ClassName -> uq,
1114        FlavorIndex -> Generation,
1115        SelfConjugate -> False,
1116        Indices -> {Index[Generation], Index[Colour]},
1117        Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.40}, {MT, 174.3}},
1118        Width -> {0, 0, {WT, 1.51013490}},
1119        QuantumNumbers -> {Q -> 2/3},
1120        PropagatorLabel -> {"uq", "u", "c", "t"},
1121        PropagatorType -> Straight,
1122        PropagatorArrow -> Forward,
1123        PDG -> {2, 4, 6},
1124        FullName -> {"u-quark", "c-quark", "t-quark"}},
1125
1126        (* Quarks (d): I_3 = -1/2, Q = -1/3 *)
1127  F[4] == {
1128        ClassMembers -> {d, s, b},
1129        ClassName -> dq,
1130        FlavorIndex -> Generation,
1131        SelfConjugate -> False,
1132        Indices -> {Index[Generation], Index[Colour]},
1133        Mass -> {Md, {MD,  5.04*10^(-3)}, {MS, 0.101}, {MB, 4.2}},
1134        Width -> 0,
1135        QuantumNumbers -> {Q -> -1/3},
1136        PropagatorLabel -> {"dq", "d", "s", "b"},
1137        PropagatorType -> Straight,
1138        PropagatorArrow -> Forward,
1139        PDG -> {1,3,5},
1140        FullName -> {"d-quark", "s-quark", "b-quark"} },
1141
1142        (* VLQ Quarks X *)
1143  F[5] == {
1144        ClassMembers -> {x},
1145        ClassName -> xq,
1146        SelfConjugate -> False,
1147        Indices -> {Index[Colour]},
1148        Mass -> {{MX,600}},
1149        Width -> {{WX, 1}},
1150        QuantumNumbers -> {Q -> 5/3},
1151        PropagatorLabel -> {"x"},
1152        PropagatorType -> Straight,
1153        PropagatorArrow -> Forward,
1154        PDG -> {6000008},
1155        FullName -> {"X-quark"}},
1156
1157        (* VLQ Quarks T *)
1158  F[6] == {
1159        ClassName -> tpq,
1160        ClassMembers -> {tp},
1161        SelfConjugate -> False,
1162        Indices -> {Index[Colour]},
1163        Mass -> {{MTP,600}},
1164        Width -> {{WTP, 1}},
1165        QuantumNumbers -> {Q -> 2/3},
1166        PropagatorLabel -> {"tp"},
1167        PropagatorType -> Straight,
1168        PropagatorArrow -> Forward,
1169        PDG -> {6000006},
1170        FullName -> {"T-quark"}},
1171
1172        (* VLQ Quarks B *)
1173  F[7] == {
1174        ClassName -> bpq,
1175        ClassMembers -> {bp},
1176        SelfConjugate -> False,
1177        Indices -> {Index[Colour]},
1178        Mass -> {{MBP,600}},
1179        Width -> {{WBP, 1}},
1180        QuantumNumbers -> {Q -> -1/3},
1181        PropagatorLabel -> {"bp"},
1182        PropagatorType -> Straight,
1183        PropagatorArrow -> Forward,
1184        PDG -> {6000005},
1185        FullName -> {"B-quark"}},
1186
1187        (* VLQ Quarks Y *)
1188  F[8] == {
1189        ClassMembers -> {y},
1190        ClassName -> yq,
1191        SelfConjugate -> False,
1192        Indices -> {Index[Colour]},
1193        Mass -> {{MY,600}},
1194        Width -> {{WY, 1}},
1195        QuantumNumbers -> {Q -> -4/3},
1196        PropagatorLabel -> {"y"},
1197        PropagatorType -> Straight,
1198        PropagatorArrow -> Forward,
1199        PDG -> {6000007},
1200        FullName -> {"Y-quark"}},
1201
1202(********** Ghosts **********)
1203        U[1] == {
1204       ClassName -> ghA,
1205       SelfConjugate -> False,
1206       Indices -> {},
1207       Ghost -> A,
1208       Mass -> 0,
1209       QuantumNumbers -> {GhostNumber -> 1},
1210       PropagatorLabel -> uA,
1211       PropagatorType -> GhostDash,
1212       PropagatorArrow -> Forward},
1213
1214        U[2] == {
1215       ClassName -> ghZ,
1216       SelfConjugate -> False,
1217       Indices -> {},
1218       Mass -> {MZ, 91.1876},
1219       Ghost -> Z,
1220       QuantumNumbers -> {GhostNumber -> 1},
1221       PropagatorLabel -> uZ,
1222       PropagatorType -> GhostDash,
1223       PropagatorArrow -> Forward},
1224
1225        U[31] == {
1226       ClassName -> ghWp,
1227       SelfConjugate -> False,
1228       Indices -> {},
1229       Mass -> {MW, Internal},
1230       Ghost -> W,
1231       QuantumNumbers -> {Q-> 1, GhostNumber -> 1},
1232       PropagatorLabel -> uWp,
1233       PropagatorType -> GhostDash,
1234       PropagatorArrow -> Forward},
1235
1236   U[32] == {
1237       ClassName -> ghWm,
1238       SelfConjugate -> False,
1239       Indices -> {},
1240       Mass -> {MW, Internal},
1241       Ghost -> Wbar,
1242       QuantumNumbers -> {Q-> -1, GhostNumber -> 1},
1243       PropagatorLabel -> uWm,
1244       PropagatorType -> GhostDash,
1245       PropagatorArrow -> Forward},
1246
1247        U[4] == {
1248       ClassName -> ghG,
1249       SelfConjugate -> False,
1250       Indices -> {Index[Gluon]},
1251       Ghost -> G,
1252       Mass -> 0,
1253       QuantumNumbers -> {GhostNumber -> 1},
1254       PropagatorLabel -> uG,
1255       PropagatorType -> GhostDash,
1256       PropagatorArrow -> Forward},
1257
1258        U[5] == {
1259        ClassName -> ghWi,
1260        Unphysical -> True,
1261        Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
1262                        ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I,
1263                        ghWi[3] -> cw ghZ + sw ghA},
1264        SelfConjugate -> False,
1265        Ghost -> Wi,
1266        Indices -> {Index[SU2W]},
1267        FlavorIndex -> SU2W},
1268
1269        U[6] == {
1270        ClassName -> ghB,
1271        SelfConjugate -> False,
1272        Definitions -> {ghB -> -sw ghZ + cw ghA},
1273        Indices -> {},
1274        Ghost -> B,
1275        Unphysical -> True},
1276
1277(************ Gauge Bosons ***************)
1278        (* Gauge bosons: Q = 0 *)
1279  V[1] == {
1280        ClassName -> A,
1281        SelfConjugate -> True,
1282        Indices -> {},
1283        Mass -> 0,
1284        Width -> 0,
1285        PropagatorLabel -> "a",
1286        PropagatorType -> W,
1287        PropagatorArrow -> None,
1288        PDG -> 22,
1289        FullName -> "Photon" },
1290
1291  V[2] == {
1292        ClassName -> Z,
1293        SelfConjugate -> True,
1294        Indices -> {},
1295        Mass -> {MZ, 91.1876},
1296        Width -> {WZ, 2.44639985},
1297        PropagatorLabel -> "Z",
1298        PropagatorType -> Sine,
1299        PropagatorArrow -> None,
1300        PDG -> 23,
1301        FullName -> "Z" },
1302
1303        (* Gauge bosons: Q = -1 *)
1304  V[3] == {
1305        ClassName -> W,
1306        SelfConjugate -> False,
1307        Indices -> {},
1308        Mass -> {MW, Internal},
1309        Width -> {WW, 2.03535570},
1310        QuantumNumbers -> {Q -> 1},
1311        PropagatorLabel -> "W",
1312        PropagatorType -> Sine,
1313        PropagatorArrow -> Forward,
1314        ParticleName ->"W+",
1315        AntiParticleName ->"W-",
1316        PDG -> 24,
1317        FullName -> "W" },
1318
1319V[4] == {
1320        ClassName -> G,
1321        SelfConjugate -> True,
1322        Indices -> {Index[Gluon]},
1323        Mass -> 0,
1324        Width -> 0,
1325        PropagatorLabel -> G,
1326        PropagatorType -> C,
1327        PropagatorArrow -> None,
1328        PDG -> 21,
1329        FullName -> "G" },
1330
1331V[5] == {
1332        ClassName -> Wi,
1333        Unphysical -> True,
1334        Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2],
1335                        Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I,
1336                        Wi[mu_, 3] -> cw Z[mu] + sw A[mu]},
1337        SelfConjugate -> True,
1338        Indices -> {Index[SU2W]},
1339        FlavorIndex -> SU2W,
1340        Mass -> 0,
1341        PDG -> {1,2,3}},
1342
1343V[6] == {
1344        ClassName -> B,
1345        SelfConjugate -> True,
1346        Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]},
1347        Indices -> {},
1348        Mass -> 0,
1349        Unphysical -> True},
1350
1351
1352(************ Scalar Fields **********)
1353        (* physical Higgs: Q = 0 *)
1354  S[1] == {
1355        ClassName -> H,
1356        SelfConjugate -> True,
1357        Mass -> {MH, 120},
1358        Width -> {WH, 0.00679485838},
1359        PropagatorLabel -> "H",
1360        PropagatorType -> D,
1361        PropagatorArrow -> None,
1362        PDG -> 25,
1363        TeXParticleName -> "\\phi",
1364        TeXClassName -> "\\phi",
1365        FullName -> "H" },
1366
1367S[2] == {
1368        ClassName -> phi,
1369        SelfConjugate -> True,
1370        Mass -> {MZ, 91.5445065},
1371        Width -> Wphi,
1372        PropagatorLabel -> "Phi",
1373        PropagatorType -> D,
1374        PropagatorArrow -> None,
1375        ParticleName ->"phi0",
1376        PDG -> 250,
1377        FullName -> "Phi",
1378        Goldstone -> Z },
1379
1380S[3] == {
1381        ClassName -> phi2,
1382        SelfConjugate -> False,
1383        Mass -> {MW, Internal},
1384        Width -> Wphi2,
1385        PropagatorLabel -> "Phi2",
1386        PropagatorType -> D,
1387        PropagatorArrow -> None,
1388        ParticleName ->"phi+",
1389        AntiParticleName ->"phi-",
1390        PDG -> 251,
1391        FullName -> "Phi2",
1392        TeXClassName -> "\\phi^+",
1393        TeXParticleName -> "\\phi^+",
1394        TeXAntiParticleName -> "\\phi^-",
1395        Goldstone -> W,
1396        QuantumNumbers -> {Q -> 1}}
1397}
1398
1399
1400
1401
1402(*****************************************************************************************)
1403
1404(* SM Lagrangian *)
1405
1406(******************** Gauge F^2 Lagrangian terms*************************)
1407(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1408 LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])*
1409                                        (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) -
1410       
1411        1/4 (del[B[nu], mu] - del[B[mu], nu])^2 -
1412       
1413        1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])*
1414                 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]);
1415
1416
1417(********************* Fermion Lagrangian terms*************************)
1418(*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*)
1419 LFermions = Module[{Lkin, LQCD, LEWleft, LEWright},
1420
1421    Lkin = I uqbar.Ga[mu].del[uq, mu] +
1422        I dqbar.Ga[mu].del[dq, mu] +
1423        I lbar.Ga[mu].del[l, mu] +
1424        I vlbar.Ga[mu].del[vl, mu];
1425
1426    LQCD = gs (uqbar.Ga[mu].T[a].uq +
1427        dqbar.Ga[mu].T[a].dq)G[mu, a];
1428
1429    LBright =
1430       -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l +           (*Y_lR=-2*)
1431        4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq -       (*Y_uR=4/3*)
1432        2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq;        (*Y_dR=-2/3*)
1433
1434    LBleft =
1435       -ee/cw B[mu]/2 vlbar.Ga[mu].ProjM.vl -          (*Y_LL=-1*)
1436        ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l  +           (*Y_LL=-1*)
1437        ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq +        (*Y_QL=1/3*)
1438        ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ;        (*Y_QL=1/3*)
1439       
1440    LWleft = ee/sw/2(
1441        vlbar.Ga[mu].ProjM.vl Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
1442        lbar.Ga[mu].ProjM.l Wi[mu, 3] +                (*         ( 0  -1 )*)
1443       
1444        Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] +
1445        Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+
1446       
1447        uqbar.Ga[mu].ProjM.uq Wi[mu, 3] -              (*sigma3 = ( 1   0 )*)
1448        dqbar.Ga[mu].ProjM.dq Wi[mu, 3] +              (*         ( 0  -1 )*)
1449       
1450        Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] +
1451        Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu]
1452        );
1453
1454    Lkin + LQCD + LBright + LBleft + LWleft];
1455
1456
1457(** Note : future modifications to the SM W and Z currents should be considered here above **)
1458
1459(******************** Higgs Lagrangian terms****************************)
1460 Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}];
1461 Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}];
1462 
1463
1464   
1465 LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi},
1466   
1467    PMVec = Table[PauliSigma[i], {i, 3}];   
1468    Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]};
1469
1470        (*Y_phi=1*)
1471    Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f;
1472    Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec);
1473    Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2;
1474
1475    (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]];
1476   
1477
1478(*************** Yukawa Lagrangian***********************)
1479LYuk := If[FeynmanGauge,
1480
1481      Module[{s,r,n,m,i},                                                                 -
1482              yd[m] CKM[n,m]     uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2)              -
1483              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2]   -
1484         
1485              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H -I phi)/Sqrt[2]   + (*This sign from eps matrix*)       
1486              yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar)    -
1487       
1488              yl[n]              vlbar[s,n].ProjP[s,r].l[r,n]      (-I phi2)              -
1489              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H +I phi)/Sqrt[2]
1490           ],
1491           
1492           Module[{s,r,n,m,i},                                                    -
1493              yd[n]              dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2]  -
1494              yu[n]              uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2]  -
1495              yl[n]               lbar[s,n].ProjP[s,r].l[r,n]      (v+H)/Sqrt[2]
1496           ]
1497         ];
1498
1499LYukawa := LYuk + HC[LYuk];
1500
1501(** Note : future modifications to the SM H currents should be considered here above **)
1502
1503(**************Ghost terms**************************)
1504(* Now we need the ghost terms which are of the form:             *)
1505(* - g * antighost * d_BRST G                                     *)
1506(* where d_BRST G is BRST transform of the gauge fixing function. *)
1507
1508LGhost := If[FeynmanGauge,
1509                Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB},
1510               
1511        (***********First the pure gauge piece.**********************) 
1512        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1513                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1514       
1515        dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
1516                LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];   
1517       
1518        dBRSTB[mu_] := cw/ee del[ghB, mu];
1519                LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
1520       
1521        (***********Next the piece from the scalar field.************)
1522        LGhostphi := -   ee/(2*sw*cw) MW ( - I phi2    ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA )  +
1523                        I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA )    ) -
1524                        ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm   ) -
1525                        I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) -
1526                        ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ;
1527                       
1528                       
1529        (***********Now add the pieces together.********************)
1530        LGhostG + LGhostWi + LGhostB + LGhostphi]
1531
1532,
1533
1534        (*If unitary gauge, only include the gluonic ghost.*)
1535                Block[{dBRSTG,LGhostG},
1536               
1537        (***********First the pure gauge piece.**********************) 
1538        dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1539                LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];                 
1540                       
1541        (***********Now add the pieces together.********************)
1542        LGhostG]
1543
1544];
1545               
1546(*********SM Lagrangian*******)         
1547LSM := LGauge + LHiggs + LFermions + LYukawa  + LGhost;
1548
1549
1550(*********VLQ Lagrangians*******)
1551(** We here assume that the physical and mass eigenstates match for the vector-like quarks **)
1552               
1553(*********LT, EW interactions*******)
1554
1555LTW :=
1556+KT*KTuLw*(tpbar.W[mu].Ga[mu].ProjM.d)+KT*KTuRw*(tpbar.W[mu].Ga[mu].ProjP.d)+KT*KTuLw*(dbar.Wbar[mu].Ga[mu].ProjM.tp)+KT*KTuRw*(dbar.Wbar[mu].Ga[mu].ProjP.tp)+KT*KTcLw*(tpbar.W[mu].Ga[mu].ProjM.s)+KT*KTcRw*(tpbar.W[mu].Ga[mu].ProjP.s)+KT*KTcLw*(sbar.Wbar[mu].Ga[mu].ProjM.tp)+KT*KTcRw*(sbar.Wbar[mu].Ga[mu].ProjP.tp)+KT*KTtLw*(tpbar.W[mu].Ga[mu].ProjM.b)+KT*KTtRw*(tpbar.W[mu].Ga[mu].ProjP.b)+KT*KTtLw*(bbar.Wbar[mu].Ga[mu].ProjM.tp)+KT*KTtRw*(bbar.Wbar[mu].Ga[mu].ProjP.tp);
1557
1558LTZ :=+KT*KTuLz*(tpbar.Z[mu].Ga[mu].ProjM.u)+KT*KTuRz*(tpbar.Z[mu].Ga[mu].ProjP.u)+KT*KTuLz*(ubar.Z[mu].Ga[mu].ProjM.tp)+KT*KTuRz*(ubar.Z[mu].Ga[mu].ProjP.tp)+KT*KTcLz*(tpbar.Z[mu].Ga[mu].ProjM.c)+KT*KTcRz*(tpbar.Z[mu].Ga[mu].ProjP.c)+KT*KTcLz*(cbar.Z[mu].Ga[mu].ProjM.tp)+KT*KTcRz*(cbar.Z[mu].Ga[mu].ProjP.tp)+KT*KTtLz*(tpbar.Z[mu].Ga[mu].ProjM.t)+KT*KTtRz*(tpbar.Z[mu].Ga[mu].ProjP.t)+KT*KTtLz*(tbar.Z[mu].Ga[mu].ProjM.tp)+KT*KTtRz*(tbar.Z[mu].Ga[mu].ProjP.tp);
1559
1560LTH:=-KT*MTP*KTuLh*(tpbar.H.ProjP.u)/v-KT*MTP*KTuLh*(ubar.H.ProjM.tp)/v-KT*MTP*KTuRh*(tpbar.H.ProjM.u)/v-KT*MTP*KTuRh*(ubar.H.ProjP.tp)/v-KT*MTP*KTcLh*(tpbar.H.ProjP.c)/v-KT*MTP*KTcLh*(cbar.H.ProjM.tp)/v-KT*MTP*KTcRh*(tpbar.H.ProjM.c)/v-KT*MTP*KTcRh*(cbar.H.ProjP.tp)/v-KT*MTP*KTtLh*(tpbar.H.ProjP.t)/v-KT*MTP*KTtLh*(tbar.H.ProjM.tp)/v-KT*MTP*KTtRh*(tpbar.H.ProjM.t)/v-KT*MTP*KTtRh*(tbar.H.ProjP.tp)/v;
1561
1562
1563(*********LB, EW interactions*******)
1564
1565LBW :=+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);
1566
1567LBZ := +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);
1568
1569LBH:=-KB*MBP*KBdLh*(bpbar.H.ProjP.d)/v-KB*MBP*KBdLh*(dbar.H.ProjM.bp)/v-KB*MBP*KBdRh*(bpbar.H.ProjM.d)/v-KB*MBP*KBdRh*(dbar.H.ProjP.bp)/v-KB*MBP*KBsLh*(bpbar.H.ProjP.s)/v-KB*MBP*KBsLh*(sbar.H.ProjM.bp)/v-KB*MBP*KBsRh*(bpbar.H.ProjM.s)/v-KB*MBP*KBsRh*(sbar.H.ProjP.bp)/v-KB*MBP*KBbLh*(bpbar.H.ProjP.b)/v-KB*MBP*KBbLh*(bbar.H.ProjM.bp)/v-KB*MBP*KBbRh*(bpbar.H.ProjM.b)/v-KB*MBP*KBbRh*(bbar.H.ProjP.bp)/v;
1570
1571(*********LX, EW interactions*******)
1572
1573
1574LXW :=
1575KX*KXuL*(xbar.W[mu].Ga[mu].ProjM.u)+KX*KXuR*(xbar.W[mu].Ga[mu].ProjP.u)+KX*KXuL*(ubar.Wbar[mu].Ga[mu].ProjM.x)+KX*KXuR*(ubar.Wbar[mu].Ga[mu].ProjP.x)+KX*KXcL*(xbar.W[mu].Ga[mu].ProjM.c)+KX*KXcR*(xbar.W[mu].Ga[mu].ProjP.c)+KX*KXcL*(cbar.Wbar[mu].Ga[mu].ProjM.x)+KX*KXcR*(cbar.Wbar[mu].Ga[mu].ProjP.x)+KX*KXtL*(xbar.W[mu].Ga[mu].ProjM.t)+KX*KXtR*(xbar.W[mu].Ga[mu].ProjP.t)+KX*KXtL*(tbar.Wbar[mu].Ga[mu].ProjM.x)+KX*KXtR*(tbar.Wbar[mu].Ga[mu].ProjP.x);
1576
1577
1578
1579(*********LY, EW interactions*******)
1580
1581LYW :=
1582+KY*KYdL*(ybar.Wbar[mu].Ga[mu].ProjM.d)+KY*KYdR*(ybar.Wbar[mu].Ga[mu].ProjP.d)+KY*KYdL*(dbar.W[mu].Ga[mu].ProjM.y)+KY*KYdR*(dbar.W[mu].Ga[mu].ProjP.y)+KY*KYsL*(ybar.Wbar[mu].Ga[mu].ProjM.s)+KY*KYsR*(ybar.Wbar[mu].Ga[mu].ProjP.s)+KY*KYsL*(sbar.W[mu].Ga[mu].ProjM.y)+KY*KYsR*(sbar.W[mu].Ga[mu].ProjP.y)+KY*KYbL*(ybar.Wbar[mu].Ga[mu].ProjM.b)+KY*KYbR*(ybar.Wbar[mu].Ga[mu].ProjP.b)+KY*KYbL*(bbar.W[mu].Ga[mu].ProjM.y)+KY*KYbR*(bbar.W[mu].Ga[mu].ProjP.y);
1583
1584
1585(*********Kinetic, mass & QCD lagrangians for VLQ*******)
1586
1587LTK := I tpbar.Ga[mu].del[tp, mu];
1588LBK := I bpbar.Ga[mu].del[bp, mu];
1589LXK := I xbar.Ga[mu].del[x, mu];
1590LYK := I ybar.Ga[mu].del[y, mu];
1591
1592LTM := -MTP.tpbar.tp;
1593LBM := -MBP.bpbar.bp;
1594LXM := -MX.xbar.x;
1595LYM := -MY.ybar.y;
1596
1597
1598LTG :=  gs (tpbar.Ga[mu].T[a].tp)G[mu, a];
1599LBG :=  gs (bpbar.Ga[mu].T[a].bp)G[mu, a];
1600LXG :=  gs (xbar.Ga[mu].T[a].x)G[mu, a];
1601LYG :=  gs (ybar.Ga[mu].T[a].y)G[mu, a];
1602
1603LTA :=  2*ee/3 (tpbar.Ga[mu].tp)A[mu];
1604LBA :=  -1*ee/3 (bpbar.Ga[mu].bp)A[mu];
1605LXA :=  5*ee/3 (xbar.Ga[mu].x)A[mu];
1606LYA :=  -4*ee/3 (ybar.Ga[mu].y)A[mu]; 
1607
1608LT := LTW + LTZ + LTH + LTK + LTM + LTG +LTA ;
1609LB := LBW + LBZ + LBH + LBK + LBM + LBG +LBA ;
1610LX := LXW + LXK + LXM + LXG + LXA ;
1611LY := LYW + LYK + LYM + LYG + LYA ;
1612
1613LVLQ := LT + LB + LX + LY;
1614
1615
1616(*********Gluon-VLQ chromomagnetic Lagrangian*******)
1617
1618
1619Sigma[mu_,nu_]:=I/2*(Ga[mu].Ga[nu]-Ga[nu].Ga[mu]);
1620
1621
1622LChromoT := KT*KG*gs*v/2/Lambda/Lambda*Module[{a, s, r, i, j, t, u, mu, nu},uqbar[r, 1, i].tp[s, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fuR*ProjP[u, r] + fuL*ProjM[u, r]) FS[G, mu, nu, a] + tpbar[r, i].uq[s, 1, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fuR*ProjP[u, r] + fuL*ProjM[u, r]) FS[G, mu, nu, a] + uqbar[r, 2, i].tp[s, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fcR*ProjP[u, r] + fcL*ProjM[u, r]) FS[G, mu, nu, a] + tpbar[r, i].uq[s, 2, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fcR*ProjP[u, r] + fcL*ProjM[u, r]) FS[G, mu, nu, a] + uqbar[r, 3, i].tp[s, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (ftR*ProjP[u, r] + ftL*ProjM[u, r]) FS[G, mu, nu, a] + tpbar[r, i].uq[s, 3, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (ftR*ProjP[u, r] + ftL*ProjM[u, r]) FS[G, mu, nu, a]];
1623
1624LChromoB := KB*KG*gs*v/2/Lambda/Lambda*Module[{a, s, r, i, j, t, u, mu, nu},dqbar[r, 1, i].bp[s, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fdR*ProjP[u, r] + fdL*ProjM[u, r]) FS[G, mu, nu, a] + bpbar[r, i].dq[s, 1, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fdR*ProjP[u, r] + fdL*ProjM[u, r]) FS[G, mu, nu, a] + dqbar[r, 2, i].bp[s, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fsR*ProjP[u, r] + fsL*ProjM[u, r]) FS[G, mu, nu, a] + bpbar[r, i].dq[s, 2, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fsR*ProjP[u, r] + fsL*ProjM[u, r]) FS[G, mu, nu, a] + dqbar[r, 3, i].bp[s, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fbR*ProjP[u, r] + fbL*ProjM[u, r]) FS[G, mu, nu, a] + bpbar[r, i].dq[s, 3, j] T[a, i,j] (I/2*(Ga[mu, s, t].Ga[nu, t, u] - Ga[nu, s, t].Ga[mu, t, u])) (fbR*ProjP[u, r] + fbL*ProjM[u, r]) FS[G, mu, nu, a]];
1625
1626
1627
1628(*********Total Lagrangian*******)
1629
1630LAn := LChromoT + LChromoB;
1631
1632L := LSM + LVLQ + LAn;
1633
1634