VLQ: VLQ_Chromomagnetic.fr

File VLQ_Chromomagnetic.fr, 51.8 KB (added by Mathieu Buchkremer, 11 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