EWFF4DM: EWFF4DM.fr

File EWFF4DM.fr, 31.0 KB (added by AndrewCheek, 4 years ago)
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1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Standard model ******)
3(****** ******)
4(****** Authors: N. Christensen, C. Duhr, B. Fuks ******)
5(****** ******)
6(****** Choose whether Feynman gauge is desired. ******)
7(****** If set to False, unitary gauge is assumed. ****)
8(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
9(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
10(***************************************************************************************************************)
11
12(* ************************** *)
13(* ***** Information ***** *)
14(* ************************** *)
15M$ModelName = "Singlet Fermion coupling to photons EFT";
16
17M$Information = {
18 Authors -> {"A.Cheek", "Luca Pagani", "Ken Mimasu", "Chiara Arina"},
19 Version -> "1.0.0",
20 Date -> "16. 10. 2019",
21 Institutions -> {"Universite catholique de Louvain (CP3)"},
22 Emails -> {"andrew.cheek@uclouvain.be", "luca.pagani7@unibo.it", "ken.mimasu@uclouvain.be", "chiara.arina@uclouvain.be"},
23 URLs -> "NONE"
24};
25
26FeynmanGauge = True;
27
28(* ************************** *)
29(* ***** NLO Variables ****** *)
30(******************************)
31
32FR$LoopSwitches = {{Gf, MW}};
33FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
34 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
35
36(* ************************** *)
37(* ***** Change log ***** *)
38(* ************************** *)
39
40(* v1.4.6: NLO variable added. *)
41(* v1.4.5: Added widths for ghosts. *)
42(* v1.4.4: Changed widths of goldstone bosons to be the same as for the W and Z bosons *)
43(* v1.4.3: Updated conventions for the symmetric structure constants of SU3. *)
44(* v1.4.2: Set FeynmanGauge=True as default again. *)
45(* v1.4: Added SU(2) representation. *)
46(* -> Modification in the field declarations (doublets are added) *)
47(* -> Modification in the Lagrangian (much simpler). *)
48(* v1.3: Added yukawa couplings for all fermions for gauge invariance. *)
49(* Added yukawa couplings for 1st generation fermions to Massless.rst. *)
50(* Updated parameters to PDG 2010. *)
51(* v1.2: Set FeynmanGauge=True as default. *)
52(* Set Gluonic ghosts to be included in both gauges. *)
53(* v1.1: Fixed yukawa couplings in Feynman gauge. *)
54(* Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. *)
55(* Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. *)
56
57
58(* ************************** *)
59(* ***** Gauge groups ***** *)
60(* ************************** *)
61M$GaugeGroups = {
62 U1Y == {
63 Abelian -> True,
64 CouplingConstant -> g1,
65 GaugeBoson -> B,
66 Charge -> Y
67 },
68 SU2L == {
69 Abelian -> False,
70 CouplingConstant -> gw,
71 GaugeBoson -> Wi,
72 StructureConstant -> Eps,
73 Representations -> {Ta,SU2D},
74 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
75 },
76 SU3C == {
77 Abelian -> False,
78 CouplingConstant -> gs,
79 GaugeBoson -> G,
80 StructureConstant -> f,
81 Representations -> {T,Colour},
82 SymmetricTensor -> dSUN
83 }
84};
85
86
87(* ************************** *)
88(* ***** Indices ***** *)
89(* ************************** *)
90
91IndexRange[Index[SU2W ]] = Unfold[Range[3]];
92IndexRange[Index[SU2D ]] = Unfold[Range[2]];
93IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
94IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
95IndexRange[Index[Generation]] = Range[3];
96
97IndexStyle[SU2W, j];
98IndexStyle[SU2D, k];
99IndexStyle[Gluon, a];
100IndexStyle[Colour, m];
101IndexStyle[Generation, f];
102
103
104(* ************************** *)
105(* *** Interaction orders *** *)
106(* *** (as used by mg5) *** *)
107(* ************************** *)
108
109M$InteractionOrderHierarchy = {
110 {NP, 1},
111 {QCD, 2},
112 {QED, 4}
113};
114
115(* ************************** *)
116(* **** Particle classes **** *)
117(* ************************** *)
118M$ClassesDescription = {
119
120(* Gauge bosons: physical vector fields *)
121 V[1] == {
122 ClassName -> A,
123 SelfConjugate -> True,
124 Mass -> 0,
125 Width -> 0,
126 ParticleName -> "a",
127 PDG -> 22,
128 PropagatorLabel -> "a",
129 PropagatorType -> W,
130 PropagatorArrow -> None,
131 FullName -> "Photon"
132 },
133 V[2] == {
134 ClassName -> Z,
135 SelfConjugate -> True,
136 Mass -> {MZ, 91.1876},
137 Width -> {WZ, 2.4952},
138 ParticleName -> "Z",
139 PDG -> 23,
140 PropagatorLabel -> "Z",
141 PropagatorType -> Sine,
142 PropagatorArrow -> None,
143 FullName -> "Z"
144 },
145 V[3] == {
146 ClassName -> W,
147 SelfConjugate -> False,
148 Mass -> {MW, 79.8244},
149 Width -> {WW, 2.085},
150 ParticleName -> "W+",
151 AntiParticleName -> "W-",
152 QuantumNumbers -> {Q -> 1},
153 PDG -> 24,
154 PropagatorLabel -> "W",
155 PropagatorType -> Sine,
156 PropagatorArrow -> Forward,
157 FullName -> "W"
158 },
159 V[4] == {
160 ClassName -> G,
161 SelfConjugate -> True,
162 Indices -> {Index[Gluon]},
163 Mass -> 0,
164 Width -> 0,
165 ParticleName -> "g",
166 PDG -> 21,
167 PropagatorLabel -> "G",
168 PropagatorType -> C,
169 PropagatorArrow -> None,
170 FullName -> "G"
171 },
172 (* Ghosts: related to physical gauge bosons *)
173 U[1] == {
174 ClassName -> ghA,
175 SelfConjugate -> False,
176 Ghost -> A,
177 QuantumNumbers -> {GhostNumber -> 1},
178 Mass -> 0,
179 Width -> 0,
180 PropagatorLabel -> "uA",
181 PropagatorType -> GhostDash,
182 PropagatorArrow -> Forward
183 },
184 U[2] == {
185 ClassName -> ghZ,
186 SelfConjugate -> False,
187 Ghost -> Z,
188 QuantumNumbers -> {GhostNumber -> 1},
189 Mass -> {MZ, 91.1876},
190 Width -> {WZ, 2.4952},
191 PropagatorLabel -> "uZ",
192 PropagatorType -> GhostDash,
193 PropagatorArrow -> Forward
194 },
195 U[31] == {
196 ClassName -> ghWp,
197 SelfConjugate -> False,
198 Ghost -> W,
199 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
200 Mass -> {MW, 79.8244},
201 Width -> {WW, 2.085},
202 PropagatorLabel -> "uWp",
203 PropagatorType -> GhostDash,
204 PropagatorArrow -> Forward
205 },
206 U[32] == {
207 ClassName -> ghWm,
208 SelfConjugate -> False,
209 Ghost -> Wbar,
210 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
211 Mass -> {MW, 79.8244},
212 Width -> {WW, 2.085},
213 PropagatorLabel -> "uWm",
214 PropagatorType -> GhostDash,
215 PropagatorArrow -> Forward
216 },
217 U[4] == {
218 ClassName -> ghG,
219 SelfConjugate -> False,
220 Indices -> {Index[Gluon]},
221 Ghost -> G,
222 QuantumNumbers ->{GhostNumber -> 1},
223 Mass -> 0,
224 Width -> 0,
225 PropagatorLabel -> "uG",
226 PropagatorType -> GhostDash,
227 PropagatorArrow -> Forward
228 },
229
230(* Gauge bosons: unphysical vector fields *)
231 V[11] == {
232 ClassName -> B,
233 Unphysical -> True,
234 SelfConjugate -> True,
235 Definitions -> {
236 B[mu_] ->(cw*A[mu] + sw*Z[mu])
237 }
238 },
239 V[12] == {
240 ClassName -> Wi,
241 Unphysical -> True,
242 SelfConjugate -> True,
243 Indices -> {Index[SU2W]},
244 FlavorIndex -> SU2W,
245 Definitions -> {
246 Wi[mu_,1] -> ( Wbar[mu] + W[mu] )/Sqrt[2],
247 Wi[mu_,2] -> ( Wbar[mu] - W[mu] )/(I*Sqrt[2]),
248 Wi[mu_,3] -> ( sw*A[mu] - cw*Z[mu] )
249 }
250 },
251
252(* Ghosts: related to unphysical gauge bosons *)
253 U[11] == {
254 ClassName -> ghB,
255 Unphysical -> True,
256 SelfConjugate -> False,
257 Ghost -> B,
258 Definitions -> { ghB -> -sw ghZ + cw ghA }
259 },
260 U[12] == {
261 ClassName -> ghWi,
262 Unphysical -> True,
263 SelfConjugate -> False,
264 Ghost -> Wi,
265 Indices -> {Index[SU2W]},
266 FlavorIndex -> SU2W,
267 Definitions -> { ghWi[1] -> (ghWp + ghWm)/Sqrt[2],
268 ghWi[2] -> (ghWm - ghWp)/(I*Sqrt[2]),
269 ghWi[3] -> cw ghZ + sw ghA }
270 } ,
271
272(* Fermions: physical fields *)
273 F[1] == {
274 ClassName -> vl,
275 ClassMembers -> {ve, vm, vt},
276 Indices -> {Index[Generation]},
277 FlavorIndex -> Generation,
278 SelfConjugate -> False,
279 Mass -> 0,
280 Width -> 0,
281 QuantumNumbers -> {LeptonNumber -> 1},
282 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
283 PropagatorType -> S,
284 PropagatorArrow -> Forward,
285 PDG -> {12,14,16},
286 ParticleName -> {"ve","vm","vt"},
287 AntiParticleName -> {"ve~","vm~","vt~"},
288 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
289 },
290 F[2] == {
291 ClassName -> l,
292 ClassMembers -> {e, mu, ta},
293 Indices -> {Index[Generation]},
294 FlavorIndex -> Generation,
295 SelfConjugate -> False,
296 Mass -> {Ml, {Me,5.11*^-4}, {MM,0.10566}, {MTA,1.777}},
297 Width -> 0,
298 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
299 PropagatorLabel -> {"l", "e", "mu", "ta"},
300 PropagatorType -> Straight,
301 PropagatorArrow -> Forward,
302 PDG -> {11, 13, 15},
303 ParticleName -> {"e-", "mu-", "ta-"},
304 AntiParticleName -> {"e+", "mu+", "ta+"},
305 FullName -> {"Electron", "Muon", "Tau"}
306 },
307 F[3] == {
308 ClassName -> uq,
309 ClassMembers -> {u, c, t},
310 Indices -> {Index[Generation], Index[Colour]},
311 FlavorIndex -> Generation,
312 SelfConjugate -> False,
313 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
314 Width -> {0, 0, {WT,1.50833649}},
315 QuantumNumbers -> {Q -> 2/3},
316 PropagatorLabel -> {"uq", "u", "c", "t"},
317 PropagatorType -> Straight,
318 PropagatorArrow -> Forward,
319 PDG -> {2, 4, 6},
320 ParticleName -> {"u", "c", "t" },
321 AntiParticleName -> {"u~", "c~", "t~"},
322 FullName -> {"u-quark", "c-quark", "t-quark"}
323 },
324 F[4] == {
325 ClassName -> dq,
326 ClassMembers -> {d, s, b},
327 Indices -> {Index[Generation], Index[Colour]},
328 FlavorIndex -> Generation,
329 SelfConjugate -> False,
330 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
331 Width -> 0,
332 QuantumNumbers -> {Q -> -1/3},
333 PropagatorLabel -> {"dq", "d", "s", "b"},
334 PropagatorType -> Straight,
335 PropagatorArrow -> Forward,
336 PDG -> {1,3,5},
337 ParticleName -> {"d", "s", "b" },
338 AntiParticleName -> {"d~", "s~", "b~"},
339 FullName -> {"d-quark", "s-quark", "b-quark"}
340 },
341
342(* Fermions: unphysical fields *)
343 F[11] == {
344 ClassName -> LL,
345 Unphysical -> True,
346 Indices -> {Index[SU2D], Index[Generation]},
347 FlavorIndex -> SU2D,
348 SelfConjugate -> False,
349 QuantumNumbers -> {Y -> -1/2},
350 Definitions -> {
351 LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] vl[sp2,ff]],
352 LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]]
353 }
354 },
355 F[12] == {
356 ClassName -> lR,
357 Unphysical -> True,
358 Indices -> {Index[Generation]},
359 FlavorIndex -> Generation,
360 SelfConjugate -> False,
361 QuantumNumbers -> {Y -> -1},
362 Definitions -> {
363 lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]]
364 }
365 },
366 F[13] == {
367 ClassName -> QL,
368 Unphysical -> True,
369 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
370 FlavorIndex -> SU2D,
371 SelfConjugate -> False,
372 QuantumNumbers -> {Y -> 1/6},
373 Definitions -> {
374 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
375 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2},
376 CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]
377 ]
378 }
379 },
380 F[14] == {
381 ClassName -> uR,
382 Unphysical -> True,
383 Indices -> {Index[Generation], Index[Colour]},
384 FlavorIndex -> Generation,
385 SelfConjugate -> False,
386 QuantumNumbers -> {Y -> 2/3},
387 Definitions -> {
388 uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]]
389 }
390 },
391 F[15] == {
392 ClassName -> dR,
393 Unphysical -> True,
394 Indices -> {Index[Generation], Index[Colour]},
395 FlavorIndex -> Generation,
396 SelfConjugate -> False,
397 QuantumNumbers -> {Y -> -1/3},
398 Definitions -> {
399 dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]]
400 }
401 },
402
403(* Fermionic DM candidates *)
404 F[16] == {
405 ClassName -> Chi,
406 SelfConjugate -> True,
407 Mass -> {MChi, 10.},
408 PropagatorLabel -> "X" ,
409 PropagatorType -> Straight,
410 PDG -> {9990},
411 Width -> 0,
412 ParticleName -> {"Chi"},
413 FullName -> {"Dark Majorana fermion singlet"}
414 },
415
416 F[17] == {
417 ClassName -> Psi,
418 SelfConjugate -> False,
419 Mass -> {MPsi, 10.},
420 PropagatorLabel -> "Psi" ,
421 PropagatorType -> Straight,
422 PDG -> {9991},
423 Width -> 0,
424 ParticleName -> {"Psi"},
425 FullName -> {"Dark Dirac fermion singlet"}
426 },
427
428(* Higgs: physical scalars *)
429 S[1] == {
430 ClassName -> H,
431 SelfConjugate -> True,
432 Mass -> {MH,125},
433 Width -> {WH,0.00575308848},
434 PropagatorLabel -> "H",
435 PropagatorType -> D,
436 PropagatorArrow -> None,
437 PDG -> 25,
438 ParticleName -> "H",
439 FullName -> "H"
440 },
441
442(* Higgs: physical scalars *)
443 S[2] == {
444 ClassName -> G0,
445 SelfConjugate -> True,
446 Goldstone -> Z,
447 Mass -> {MZ, 91.1876},
448 Width -> {WZ, 2.4952},
449 PropagatorLabel -> "Go",
450 PropagatorType -> D,
451 PropagatorArrow -> None,
452 PDG -> 250,
453 ParticleName -> "G0",
454 FullName -> "G0"
455 },
456 S[3] == {
457 ClassName -> GP,
458 SelfConjugate -> False,
459 Goldstone -> W,
460 Mass -> {MW, 79.8244},
461 QuantumNumbers -> {Q -> 1},
462 Width -> {WW, 2.085},
463 PropagatorLabel -> "GP",
464 PropagatorType -> D,
465 PropagatorArrow -> None,
466 PDG -> 251,
467 ParticleName -> "G+",
468 AntiParticleName -> "G-",
469 FullName -> "GP"
470 },
471
472(* Higgs: unphysical scalars *)
473 S[11] == {
474 ClassName -> Phi,
475 Unphysical -> True,
476 Indices -> {Index[SU2D]},
477 FlavorIndex -> SU2D,
478 SelfConjugate -> False,
479 QuantumNumbers -> {Y -> 1/2},
480 Definitions -> {
481 Phi[1] -> -I GP,
482 (* Canonical normalisation of Higgs and G0 fields *)
483 Phi[2] -> ( vev + H + I G0 )/Sqrt[2]
484 }
485 }
486};
487
488
489(* ************************** *)
490(* ***** Gauge ***** *)
491(* ***** Parameters ***** *)
492(* ***** (FeynArts) ***** *)
493(* ************************** *)
494
495GaugeXi[ V[1] ] = GaugeXi[A];
496GaugeXi[ V[2] ] = GaugeXi[Z];
497GaugeXi[ V[3] ] = GaugeXi[W];
498GaugeXi[ V[4] ] = GaugeXi[G];
499GaugeXi[ S[1] ] = 1;
500GaugeXi[ S[2] ] = GaugeXi[Z];
501GaugeXi[ S[3] ] = GaugeXi[W];
502GaugeXi[ U[1] ] = GaugeXi[A];
503GaugeXi[ U[2] ] = GaugeXi[Z];
504GaugeXi[ U[31] ] = GaugeXi[W];
505GaugeXi[ U[32] ] = GaugeXi[W];
506GaugeXi[ U[4] ] = GaugeXi[G];
507
508
509(* ************************** *)
510(* ***** Parameters ***** *)
511(* ************************** *)
512M$Parameters = {
513
514 (* External parameters *)
515 Gf == {
516 ParameterType -> External,
517 BlockName -> SMINPUTS,
518 OrderBlock -> 2,
519 Value -> 1.16637*^-5,
520 InteractionOrder -> {QED,2},
521 TeX -> Subscript[G,f],
522 Description -> "Fermi constant"
523 },
524 Mreno == {
525 ParameterType -> External,
526 BlockName -> Renor,
527 Value -> 555,
528 TeX -> Subscript[M,reno],
529 Description -> "scale for the renormalisation of dim6 op"
530 },
531 aS == {
532 ParameterType -> External,
533 BlockName -> SMINPUTS,
534 OrderBlock -> 3,
535 Value -> 0.1184,
536 InteractionOrder -> {QCD,2},
537 TeX -> Subscript[\[Alpha],s],
538 Description -> "Strong coupling constant at the Z pole"
539 },
540 ymdo == {
541 ParameterType -> External,
542 BlockName -> YUKAWA,
543 OrderBlock -> 1,
544 Value -> 5.04*^-3,
545 Description -> "Down Yukawa mass"
546 },
547 ymup == {
548 ParameterType -> External,
549 BlockName -> YUKAWA,
550 OrderBlock -> 2,
551 Value -> 2.55*^-3,
552 Description -> "Up Yukawa mass"
553 },
554 yms == {
555 ParameterType -> External,
556 BlockName -> YUKAWA,
557 OrderBlock -> 3,
558 Value -> 0.101,
559 Description -> "Strange Yukawa mass"
560 },
561 ymc == {
562 ParameterType -> External,
563 BlockName -> YUKAWA,
564 OrderBlock -> 4,
565 Value -> 1.27,
566 Description -> "Charm Yukawa mass"
567 },
568 ymb == {
569 ParameterType -> External,
570 BlockName -> YUKAWA,
571 OrderBlock -> 5,
572 Value -> 4.7,
573 Description -> "Bottom Yukawa mass"
574 },
575 ymt == {
576 ParameterType -> External,
577 BlockName -> YUKAWA,
578 OrderBlock -> 6,
579 Value -> 172,
580 Description -> "Top Yukawa mass"
581 },
582 yme == {
583 ParameterType -> External,
584 BlockName -> YUKAWA,
585 OrderBlock -> 11,
586 Value -> 5.11*^-4,
587 Description -> "Electron Yukawa mass"
588 },
589 ymm == {
590 ParameterType -> External,
591 BlockName -> YUKAWA,
592 OrderBlock -> 13,
593 Value -> 0.10566,
594 Description -> "Muon Yukawa mass"
595 },
596 ymtau == {
597 ParameterType -> External,
598 BlockName -> YUKAWA,
599 OrderBlock -> 15,
600 Value -> 1.777,
601 Description -> "Tau Yukawa mass"
602 },
603 cabi == {
604 ParameterType -> External,
605 BlockName -> CKMBLOCK,
606 OrderBlock -> 1,
607 Value -> 0.227736,
608 TeX -> Subscript[\[Theta], c],
609 Description -> "Cabibbo angle"
610 },
611 (* External parameters *)
612 Lambda == {
613 ParameterType -> External,
614 BlockName -> LDARK,
615 OrderBlock -> 1,
616 Value -> 100000.,
617 InteractionOrder -> {NP, -1},
618 TeX -> \[CapitalLambda],
619 Description -> "EFT cutoff"
620 },
621
622 CAn == {
623 ParameterType -> External,
624 BlockName -> LDARK,
625 OrderBlock -> 2,
626 InteractionOrder -> {QED,1},
627 Value -> 1.,
628 TeX -> Subscript[C,An],
629 Description -> "Anapole coupling"
630 },
631 CBan == {
632 ParameterType -> External,
633 BlockName -> LDARK,
634 OrderBlock -> 3,
635 InteractionOrder -> {QED,1},
636 Value -> 1.,
637 TeX -> Subscript[C,Ban],
638 Description -> "Banapole coupling"
639 },
640
641 CMag == {
642 ParameterType -> External,
643 BlockName -> LDARK,
644 OrderBlock -> 4,
645 InteractionOrder -> {QED,1},
646 Value -> 1.,
647 TeX -> Subscript[C,Mag],
648 Description -> "Magnetic dipole coupling"
649 },
650
651 CBmag == {
652 ParameterType -> External,
653 BlockName -> LDARK,
654 OrderBlock -> 5,
655 InteractionOrder -> {QED,1},
656 Value -> 1.,
657 TeX -> Subscript[C,Bmag],
658 Description -> "B-Magnetic dipole coupling"
659 },
660
661 CElec == {
662 ParameterType -> External,
663 BlockName -> LDARK,
664 OrderBlock -> 6,
665 InteractionOrder -> {QED,1},
666 Value -> 1.,
667 TeX -> Subscript[C,Elec],
668 Description -> "Electric dipole coupling"
669 },
670
671 CBelec == {
672 ParameterType -> External,
673 BlockName -> LDARK,
674 OrderBlock -> 7,
675 InteractionOrder -> {QED,1},
676 Value -> 1.,
677 TeX -> Subscript[C,Belec],
678 Description -> "B-Electric dipole coupling"
679 },
680 Ccr == {
681 ParameterType -> External,
682 BlockName -> LDARK,
683 OrderBlock -> 8,
684 InteractionOrder -> {QED,1},
685 Value -> 1.,
686 TeX -> Subscript[C,CR],
687 Description -> "Charge-Radius coupling"
688 },
689
690 CBcr == {
691 ParameterType -> External,
692 BlockName -> LDARK,
693 OrderBlock -> 9,
694 InteractionOrder -> {QED,1},
695 Value -> 1.,
696 TeX -> Subscript[C,Bcr],
697 Description -> "B Charge-Radius coupling"
698 },
699
700 CDan == {
701 ParameterType -> External,
702 BlockName -> LDARK,
703 OrderBlock -> 10,
704 InteractionOrder -> {QED,1},
705 Value -> 1.,
706 TeX -> Subscript[C,Dan],
707 Description -> "Anapole coupling to Dirac DM"
708 },
709 CBdan == {
710 ParameterType -> External,
711 BlockName -> LDARK,
712 OrderBlock -> 11,
713 InteractionOrder -> {QED,1},
714 Value -> 1.,
715 TeX -> Subscript[C,Bdan],
716 Description -> "Banapole coupling to Dirac"
717 },
718
719
720 (* Internal Parameters *)
721 (* SM inputs *)
722 (* EW parameters *)
723 vev == {
724 ParameterType -> Internal,
725 Value -> (
726 Sqrt[ 1/(Sqrt[2]*Gf) ]
727 ),
728 TeX -> v,
729 InteractionOrder -> {QED,-1},
730 Description -> "Higgs vacuum expectation value in terms of Gf in the SM"
731 },
732
733 cw == {
734 ParameterType -> Internal,
735 Value -> MW/MZ ,
736 TeX -> Subscript[c,w],
737 Description -> "Cosine of the Weinberg angle in terms of inputs in the SM"
738 },
739
740 sw == {
741 ParameterType -> Internal,
742 Value -> ( Sqrt[1 - (MW/MZ)^2] ),
743 TeX -> Subscript[s,w],
744 Description -> "Sine of the Weinberg angle in terms of inputs in the SM"
745 },
746
747 ee == {
748 ParameterType -> Internal,
749 Value -> 2*MW*sw/vev,
750 InteractionOrder -> {QED,1},
751 TeX -> e,
752 Description -> "Electric coupling constant in terms of inputs in the SM"
753 },
754
755 gw == {
756 ParameterType -> Internal,
757 Definitions -> {
758 gw -> ee/sw
759 },
760 InteractionOrder -> {QED,1},
761 TeX -> Subscript[g,w],
762 Description -> "Weak coupling constant at the Z pole"
763 },
764
765 g1 == {
766 ParameterType -> Internal,
767 Definitions -> {
768 g1 -> ee/cw
769 },
770 InteractionOrder -> {QED,1},
771 TeX -> Subscript[g,1],
772 Description -> "U(1)Y coupling constant at the Z pole"
773 },
774
775 gs == {
776 ParameterType -> Internal,
777 Value -> Sqrt[4 Pi aS],
778 InteractionOrder -> {QCD,1},
779 TeX -> Subscript[g,s],
780 ParameterName -> G,
781 Description -> "Strong coupling constant at the Z pole"
782 },
783
784 aEW == {
785 ParameterType -> Internal,
786 Value -> ee^2/(4*Pi),
787 InteractionOrder -> {QED,2},
788 TeX -> Subscript[\[Alpha], EW],
789 Description -> "Electroweak fine structure constant"
790 },
791
792 aEWM1 == {
793 ParameterType -> Internal,
794 OrderBlock -> 1,
795 Value -> 1/aEW,
796 InteractionOrder -> {QED,-2},
797 Description -> "Inverse of the EW coupling constant at the Z pole"
798 },
799
800 lam == {
801 ParameterType -> Internal,
802 Definitions -> {
803 lam -> (MH^2)/(2*vev^2)
804 },
805 InteractionOrder -> {QED, 2},
806 Description -> "Higgs quartic coupling"
807 },
808
809 muH == {
810 ParameterType -> Internal,
811 Definitions -> { muH -> MH/Sqrt[2] },
812 TeX -> \[Mu],
813 Description -> "Mass parameter of the Higgs potential in terms of inputs in the SM"
814 },
815
816 yl == {
817 ParameterType -> Internal,
818 Indices -> {Index[Generation], Index[Generation]},
819 Definitions -> {
820 yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j),
821 yl[1,1] -> Sqrt[2] yme / vev ,
822 yl[2,2] -> Sqrt[2] ymm / vev ,
823 yl[3,3] -> Sqrt[2] ymtau/ vev
824 },
825 InteractionOrder -> {QED, 1},
826 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
827 TeX -> Superscript[y, l],
828 Description -> "Lepton Yukawa couplings"
829 },
830
831 yu == {
832 ParameterType -> Internal,
833 Indices -> {Index[Generation], Index[Generation]},
834 Definitions -> {
835 yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j),
836 yu[1,1] -> Sqrt[2] ymup/ vev,
837 yu[2,2] -> Sqrt[2] ymc / vev,
838 yu[3,3] -> Sqrt[2] ymt / vev
839 },
840 InteractionOrder -> {QED, 1},
841 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
842 TeX -> Superscript[y, u],
843 Description -> "Up-type Yukawa couplings"
844 },
845
846 yd == {
847 ParameterType -> Internal,
848 Indices -> {Index[Generation], Index[Generation]},
849 Definitions -> {
850 yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j),
851 yd[1,1] -> Sqrt[2] ymdo/ vev,
852 yd[2,2] -> Sqrt[2] yms / vev,
853 yd[3,3] -> Sqrt[2] ymb / vev
854 },
855 InteractionOrder -> {QED, 1},
856 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
857 TeX -> Superscript[y, d],
858 Description -> "Down-type Yukawa couplings"
859 },
860
861(* N. B. : only Cabibbo mixing! *)
862 CKM == {
863 ParameterType -> Internal,
864 Indices -> {Index[Generation], Index[Generation]},
865 Unitary -> True,
866 Value -> {
867 CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
868 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
869 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1
870 },
871 TeX -> Superscript[V,CKM],
872 Description -> "CKM-Matrix"}
873};
874
875
876(* ************************** *)
877(* ***** Lagrangian ***** *)
878(* ************************** *)
879
880ckm = {Conjugate[CKM[i_, j_]] -> IndexDelta[i, j], CKM[i_, j_] -> IndexDelta[i, j]};
881
882ExpandFunc[a_, subs___] := (
883 ( ExpandIndices[a, FlavorExpand -> True] /. Flatten[List[subs]] ) // Expand
884 (* // ReplaceAll[#, Power[Lambda, i_Integer] :> 0 /; i < -2] &
885 // Series[#, {Lambda, Infinity , 2}] & // Normal *)
886)
887
888LGauge := Module[{mu,nu,ii,aa},
889
890Print["--- Expanding LGauge ---"];
891
892 Map[ExpandFunc, {
893 - 1/4 FS[B,mu,nu] FS[B,mu,nu],
894 - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii],
895 - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa]
896 }
897 ] // Total
898
899];
900
901
902LFermions := Module[{mu},
903
904Print["--- Expanding LFermions ---"];
905
906 Map[ExpandFunc[#, {}] &, {
907 I*QLbar.Ga[mu].DC[QL, mu],
908 I*LLbar.Ga[mu].DC[LL, mu],
909 I*uRbar.Ga[mu].DC[uR, mu],
910 I*dRbar.Ga[mu].DC[dR, mu],
911 I*lRbar.Ga[mu].DC[lR, mu]
912 }
913 ] // Total
914
915];
916
917
918LHiggs := Module[{ii,jj,mu,feynmangaugerules},
919
920Print["--- Expanding LHiggs ---"];
921
922 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
923
924 Map[ExpandFunc[#, feynmangaugerules] &, {
925 DC[Phibar[ii],mu] DC[Phi[ii],mu] ,
926 muH^2 Phibar[ii] Phi[ii],
927 - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]
928 }
929 ] // Total
930
931];
932
933
934LYukawa := Module[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
935
936Print["--- Expanding LYukawa ---"];
937
938 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
939
940 yuk = Map[ExpandFunc[#, feynmangaugerules] &, {
941 - yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc] dR[sp, ff3, cc] Phi[ii],
942 - yl[ff1, ff3] LLbar[sp, ii, ff1] lR[sp, ff3] Phi[ii],
943 - yu[ff1, ff2] QLbar[sp, ii, ff1, cc] uR[sp, ff2, cc] Phibar[jj] Eps[ii, jj]
944 }
945 ] // Total;
946
947 yuk+HC[yuk]
948
949];
950
951
952LGhost := Module[ {LGh1,LGhw,LGhs,LGhphi,mu,generators,gh,ghbar,
953 Vectorize,phi1,phi2,togoldstones,doublet,doublet0,ii},
954
955Print["--- Expanding LGhost ---"];
956
957 (* Pure gauge piece *)
958 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
959 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
960 LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
961
962 (* Scalar pieces: see Peskin pages 739-742 *)
963 (* phi1 and phi2 are the real degrees of freedom of GP *)
964 (* Vectorize transforms a doublet in a vector in the phi-basis, *)
965 (* i.e. the basis of real degrees of freedom *)
966 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
967 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
968
969 generators = { -I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1],
970 -I/2 gw PauliSigma[2] , -I/2 gw PauliSigma[3]};
971
972 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
973 doublet0 = {0, vev/Sqrt[2]};
974 Vectorize[{a_, b_}]:= Simplify[
975 {Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]],
976 Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]
977 }/.{Im[_]->0, Re[num_]->num}
978 ];
979
980 togoldstones := {phi1 -> ( GP + GPbar )/Sqrt[2],
981 phi2 -> (-GP + GPbar )/(I Sqrt[2])};
982
983 LGhphi = Plus@@Flatten[Table[
984 - ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0]
985 . Vectorize[generators[[lll]].(doublet+doublet0)],
986 {kkk,4}, {lll,4}
987 ]]/.togoldstones;
988
989 ExpandIndices[
990 LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi, 0]
991 , FlavorExpand->SU2W
992 ]
993
994]// Expand ;
995
996(* Full Lagrangian *)
997LSM := LGauge + LFermions + LHiggs + LYukawa + LGhost;
998
999Lkin := I/2 Chibar.Ga[mu].del[Chi, mu]\
1000 - 1/2 MChi Chibar.Chi\
1001 + I Psibar.Ga[mu].del[Psi,mu]\
1002 - MPsi Psibar.Psi;
1003
1004Lan := cw(CAn/Lambda^2) (1/2) Chibar.Ga[mu].Ga[5].Chi.del[FS[A, mu, nu],nu]
1005
1006Lban := (CBan/Lambda^2) (1/2) Chibar.Ga[mu].Ga[5].Chi.del[FS[B, mu, nu],nu]
1007
1008Lmag := cw(CMag/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Psi.FS[A, mu, nu] - cw(CMag/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Psi.FS[A, mu, nu]
1009
1010LBmag := (CBmag/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Psi.FS[B, mu, nu] - (CBmag/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Psi.FS[B, mu, nu]
1011
1012Lelec := cw I (CElec/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Ga[5].Psi.FS[A, mu, nu] - cw I (CElec/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Ga[5].Psi.FS[A, mu, nu]
1013
1014LBelec := I (CBelec/Lambda) (I/4) Psibar.Ga[mu].Ga[nu].Ga[5].Psi.FS[B, mu, nu] - I (CBelec/Lambda) (I/4) Psibar.Ga[nu].Ga[mu].Ga[5].Psi.FS[B, mu, nu]
1015
1016LCR := cw (Ccr/Lambda^2) Psibar.Ga[mu].Psi.del[FS[A, mu, nu], nu]
1017
1018LBcr := (CBcr/Lambda^2) Psibar.Ga[mu].Psi.del[FS[B, mu, nu], nu]
1019
1020LAndirac := cw(CDan/Lambda^2) Psibar.Ga[mu].Ga[5].Psi.del[FS[A, mu, nu],nu]
1021
1022LBandirac := (CBdan/Lambda^2) Psibar.Ga[mu].Ga[5].Psi.del[FS[B, mu, nu],nu]