VLQ_bsingletvl: BsingletVL.fr

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