HNLs: effective_HeavyN_Majorana.fr

File effective_HeavyN_Majorana.fr, 72.1 KB (added by ManuelGonzalezLopez, 4 years ago)

Model file for Majorana neutrinos.

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file used for Majorana neutrinos in: ******)
3(****** GeV-scale neutrinos: interactions with mesons and DUNE sensitivity, arXiv:2007.03701 ******)
4(****** ******)
5(****** Authors: "P. Coloma", "E. Fernandez-Martinez", "M. Gonzalez-Lopez", "J. Hernandez-Garcia" ******)
6(****** ******)
7(****** Note: Unitary gauge is assumed (FeynmanGauge = False) ******)
8(****** since Feynman gauge is not supported in MadGraph. ******)
9(***************************************************************************************************************)
10
11(* ************************** *)
12(* ***** Information ***** *)
13(* ************************** *)
14M$ModelName = "effective_HeavyN_Majorana_v103";
15
16M$Information = {
17 Authors -> {"P. Coloma", "E. Fernandez-Martinez", "M. Gonzalez-Lopez", "J. Hernandez-Garcia"},
18 Version -> "1.0.0",
19 Date -> "06. 06. 2020",
20 Institutions -> {"Instituto de Fisica Corpuscular, Universidad de Valencia & CSIC, and Instituto de Fisica Teorica UAM/CSIC", "Departamento de Fisica Teorica & Instituto de Fisica Teorica, Universidad Autonoma de Madrid & CSIC", "Departamento de Fisica Teorica & Instituto de Fisica Teorica, Universidad Autonoma de Madrid & CSIC", "Institute for Theoretical Physics, ELTE Eotvos Lorand University"},
21 Emails -> {"pilar.coloma@ift.csic.es", "enrique.fernandez-martinez@uam.es", "manuel.gonzalezl@uam.es", "josu.hernandez@ttk.elte.hu"},
22 URLs -> "https://arxiv.org/abs/2007.03701"
23};
24
25FeynmanGauge = False;
26
27(* Add mesons and remove quarks from the Lagrangian. Change to False for a high-energy description in terms of quarks and without mesons. *)
28Mesons = True;
29
30(* ************************** *)
31(* ***** NLO Variables ****** *)
32(******************************)
33
34FR$LoopSwitches = {{Gf, MW}};
35FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
36 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU, MN4 -> MassN4};
37
38
39(* ************************** *)
40(* ***** vevs ***** *)
41(* ************************** *)
42M$vevs = { {Phi[2],vev} };
43
44(* ************************** *)
45(* ***** Gauge groups ***** *)
46(* ************************** *)
47M$GaugeGroups = {
48 U1Y == {
49 Abelian -> True,
50 CouplingConstant -> g1,
51 GaugeBoson -> B,
52 Charge -> Y
53 },
54 SU2L == {
55 Abelian -> False,
56 CouplingConstant -> gw,
57 GaugeBoson -> Wi,
58 StructureConstant -> Eps,
59 Representations -> {Ta,SU2D},
60 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
61 },
62 SU3C == {
63 Abelian -> False,
64 CouplingConstant -> gs,
65 GaugeBoson -> G,
66 StructureConstant -> f,
67 Representations -> {T,Colour},
68 SymmetricTensor -> dSUN
69 }
70};
71
72
73(* ************************** *)
74(* ***** Indices ***** *)
75(* ************************** *)
76
77IndexRange[Index[SU2W ]] = Unfold[Range[3]];
78IndexRange[Index[SU2D ]] = Unfold[Range[2]];
79IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
80IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
81IndexRange[Index[Generation]] = Range[3];
82IndexRange[Index[Neutrinos ]] = Range[4];
83IndexRange[Index[Heavynus ]] = Range[1];
84
85
86IndexStyle[SU2W, j];
87IndexStyle[SU2D, k];
88IndexStyle[Gluon, a];
89IndexStyle[Colour, m];
90IndexStyle[Generation, f];
91IndexStyle[Neutrinos, n];
92IndexStyle[Heavynus, r];
93
94
95(* ************************** *)
96(* *** Interaction orders *** *)
97(* *** (as used by mg5) *** *)
98(* ************************** *)
99
100M$InteractionOrderHierarchy = {
101 {QCD, 1},
102 {QED, 2}
103};
104
105
106(* ************************** *)
107(* **** Particle classes **** *)
108(* ************************** *)
109M$ClassesDescription = {
110
111(* Gauge bosons: physical vector fields *)
112 V[1] == {
113 ClassName -> A,
114 SelfConjugate -> True,
115 Mass -> 0,
116 Width -> 0,
117 ParticleName -> "a",
118 PDG -> 22,
119 PropagatorLabel -> "a",
120 PropagatorType -> W,
121 PropagatorArrow -> None,
122 FullName -> "Photon"
123 },
124 V[2] == {
125 ClassName -> Z,
126 SelfConjugate -> True,
127 Mass -> {MZ, 91.1876},
128 Width -> {WZ, 2.4952},
129 ParticleName -> "Z",
130 PDG -> 23,
131 PropagatorLabel -> "Z",
132 PropagatorType -> Sine,
133 PropagatorArrow -> None,
134 FullName -> "Z"
135 },
136 V[3] == {
137 ClassName -> W,
138 SelfConjugate -> False,
139 Mass -> {MW, Internal},
140 Width -> {WW, 2.085},
141 ParticleName -> "W+",
142 AntiParticleName -> "W-",
143 QuantumNumbers -> {Q -> 1},
144 PDG -> 24,
145 PropagatorLabel -> "W",
146 PropagatorType -> Sine,
147 PropagatorArrow -> Forward,
148 FullName -> "W"
149 },
150 V[4] == {
151 ClassName -> G,
152 SelfConjugate -> True,
153 Indices -> {Index[Gluon]},
154 Mass -> 0,
155 Width -> 0,
156 ParticleName -> "g",
157 PDG -> 21,
158 PropagatorLabel -> "G",
159 PropagatorType -> C,
160 PropagatorArrow -> None,
161 FullName -> "G"
162 },
163
164(* Ghosts: related to physical gauge bosons *)
165 U[1] == {
166 ClassName -> ghA,
167 SelfConjugate -> False,
168 Ghost -> A,
169 QuantumNumbers -> {GhostNumber -> 1},
170 Mass -> 0,
171 Width -> 0,
172 PropagatorLabel -> "uA",
173 PropagatorType -> GhostDash,
174 PropagatorArrow -> Forward
175 },
176 U[2] == {
177 ClassName -> ghZ,
178 SelfConjugate -> False,
179 Ghost -> Z,
180 QuantumNumbers -> {GhostNumber -> 1},
181 Mass -> {MZ,91.1876},
182 Width -> {WZ, 2.4952},
183 PropagatorLabel -> "uZ",
184 PropagatorType -> GhostDash,
185 PropagatorArrow -> Forward
186 },
187 U[31] == {
188 ClassName -> ghWp,
189 SelfConjugate -> False,
190 Ghost -> W,
191 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
192 Mass -> {MW,Internal},
193 Width -> {WW, 2.085},
194 PropagatorLabel -> "uWp",
195 PropagatorType -> GhostDash,
196 PropagatorArrow -> Forward
197 },
198 U[32] == {
199 ClassName -> ghWm,
200 SelfConjugate -> False,
201 Ghost -> Wbar,
202 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
203 Mass -> {MW,Internal},
204 Width -> {WW, 2.085},
205 PropagatorLabel -> "uWm",
206 PropagatorType -> GhostDash,
207 PropagatorArrow -> Forward
208 },
209 U[4] == {
210 ClassName -> ghG,
211 SelfConjugate -> False,
212 Indices -> {Index[Gluon]},
213 Ghost -> G,
214 PDG -> 82,
215 QuantumNumbers ->{GhostNumber -> 1},
216 Mass -> 0,
217 Width -> 0,
218 PropagatorLabel -> "uG",
219 PropagatorType -> GhostDash,
220 PropagatorArrow -> Forward
221 },
222
223(* Gauge bosons: unphysical vector fields *)
224 V[11] == {
225 ClassName -> B,
226 Unphysical -> True,
227 SelfConjugate -> True,
228 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
229 },
230 V[12] == {
231 ClassName -> Wi,
232 Unphysical -> True,
233 SelfConjugate -> True,
234 Indices -> {Index[SU2W]},
235 FlavorIndex -> SU2W,
236 Definitions -> { Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3] -> cw Z[mu] + sw A[mu]}
237 },
238
239(* Ghosts: related to unphysical gauge bosons *)
240 U[11] == {
241 ClassName -> ghB,
242 Unphysical -> True,
243 SelfConjugate -> False,
244 Ghost -> B,
245 Definitions -> { ghB -> -sw ghZ + cw ghA}
246 },
247 U[12] == {
248 ClassName -> ghWi,
249 Unphysical -> True,
250 SelfConjugate -> False,
251 Ghost -> Wi,
252 Indices -> {Index[SU2W]},
253 FlavorIndex -> SU2W,
254 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
255 } ,
256
257(* Fermions: physical fields *)
258(* Note that technically these are neutrino mass eigenstates and as such we gave them different labels and codes than to the flavour eigenstates. *)
259 F[1] == {
260 ClassName -> vl,
261 ClassMembers -> {v1,v2,v3,N4},
262 Indices -> {Index[Neutrinos]},
263 FlavorIndex -> Neutrinos,
264 SelfConjugate -> True,
265 Mass -> {Mnu, 0,0,0, {MassN4, Internal}},
266 Width -> {0, 0, 0, {WN, 0}},
267 PropagatorLabel -> {"v", "v1", "v2", "v3","N4"} ,
268 PropagatorType -> S,
269 PropagatorArrow -> Forward,
270 PDG -> {12000,14000,16000,18000},
271 ParticleName -> {"v1","v2","v3","N4"},
272 AntiParticleName -> {"v1~","v2~","v3~","N4~"},
273 FullName -> {"neutrino1", "neutrino2", "neutrino3","Heavy-neutrino"}
274 },
275
276 F[2] == {
277 ClassName -> l,
278 ClassMembers -> {e, mu, ta},
279 Indices -> {Index[Generation]},
280 FlavorIndex -> Generation,
281 SelfConjugate -> False,
282 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
283 Width -> 0,
284 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
285 PropagatorLabel -> {"l", "e", "mu", "ta"},
286 PropagatorType -> Straight,
287 PropagatorArrow -> Forward,
288 PDG -> {11, 13, 15},
289 ParticleName -> {"e-", "mu-", "ta-"},
290 AntiParticleName -> {"e+", "mu+", "ta+"},
291 FullName -> {"Electron", "Muon", "Tau"}
292 },
293 F[3] == {
294 ClassName -> uq,
295 ClassMembers -> {u, c, t},
296 Indices -> {Index[Generation], Index[Colour]},
297 FlavorIndex -> Generation,
298 SelfConjugate -> False,
299 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
300 Width -> {0, 0, {WT,1.50833649}},
301 QuantumNumbers -> {Q -> 2/3},
302 PropagatorLabel -> {"uq", "u", "c", "t"},
303 PropagatorType -> Straight,
304 PropagatorArrow -> Forward,
305 PDG -> {2, 4, 6},
306 ParticleName -> {"u", "c", "t" },
307 AntiParticleName -> {"u~", "c~", "t~"},
308 FullName -> {"u-quark", "c-quark", "t-quark"}
309 },
310 F[4] == {
311 ClassName -> dq,
312 ClassMembers -> {d, s, b},
313 Indices -> {Index[Generation], Index[Colour]},
314 FlavorIndex -> Generation,
315 SelfConjugate -> False,
316 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
317 Width -> 0,
318 QuantumNumbers -> {Q -> -1/3},
319 PropagatorLabel -> {"dq", "d", "s", "b"},
320 PropagatorType -> Straight,
321 PropagatorArrow -> Forward,
322 PDG -> {1,3,5},
323 ParticleName -> {"d", "s", "b" },
324 AntiParticleName -> {"d~", "s~", "b~"},
325 FullName -> {"d-quark", "s-quark", "b-quark"}
326 },
327
328(* Fermions: unphysical fields *)
329 F[11] == {
330 ClassName -> LL,
331 Unphysical -> True,
332 Indices -> {Index[SU2D], Index[Generation]},
333 FlavorIndex -> SU2D,
334 SelfConjugate -> False,
335 QuantumNumbers -> {Y -> -1/2},
336 Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNS[ff,ff2] ProjM[sp1,sp2] vl[sp2,ff2]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
337 },
338 F[12] == {
339 ClassName -> lR,
340 Unphysical -> True,
341 Indices -> {Index[Generation]},
342 FlavorIndex -> Generation,
343 SelfConjugate -> False,
344 QuantumNumbers -> {Y -> -1},
345 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
346 },
347 F[13] == {
348 ClassName -> QL,
349 Unphysical -> True,
350 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
351 FlavorIndex -> SU2D,
352 SelfConjugate -> False,
353 QuantumNumbers -> {Y -> 1/6},
354 Definitions -> {
355 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
356 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
357 },
358 F[14] == {
359 ClassName -> uR,
360 Unphysical -> True,
361 Indices -> {Index[Generation], Index[Colour]},
362 FlavorIndex -> Generation,
363 SelfConjugate -> False,
364 QuantumNumbers -> {Y -> 2/3},
365 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
366 },
367 F[15] == {
368 ClassName -> dR,
369 Unphysical -> True,
370 Indices -> {Index[Generation], Index[Colour]},
371 FlavorIndex -> Generation,
372 SelfConjugate -> False,
373 QuantumNumbers -> {Y -> -1/3},
374 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
375 },
376 F[16] == {
377 ClassName -> NR,
378 Unphysical -> True,
379 Indices -> {Index[Heavynus]},
380 FlavorIndex -> Heavynus,
381 SelfConjugate -> True,
382 Definitions -> { NR[sp1_,ff_] :> Module[{sp2,ff2}, HEAV[ff,ff2] ProjP[sp1,sp2] vl[sp2,ff2]] }
383 },
384 F[17] == {
385 ClassName -> NRc,
386 Unphysical -> True,
387 Indices -> {Index[Heavynus]},
388 FlavorIndex -> Heavynus,
389 SelfConjugate -> True,
390 Definitions -> { NRc[sp1_,ff_] :> Module[{sp2,ff2}, HEAV[ff,ff2] ProjM[sp1,sp2] vl[sp2,ff2]] }
391 },
392
393
394(* Higgs: physical scalars *)
395 S[1] == {
396 ClassName -> H,
397 SelfConjugate -> True,
398 Mass -> {MH,125.1},
399 Width -> {WH,0.00407},
400 PropagatorLabel -> "H",
401 PropagatorType -> D,
402 PropagatorArrow -> None,
403 PDG -> 25,
404 ParticleName -> "H",
405 FullName -> "H"
406 },
407
408(* Higgs: physical scalars *)
409 S[2] == {
410 ClassName -> G0,
411 SelfConjugate -> True,
412 Goldstone -> Z,
413 Mass -> {MZ, 91.1876},
414 Width -> {WZ, 2.4952},
415 PropagatorLabel -> "Go",
416 PropagatorType -> D,
417 PropagatorArrow -> None,
418 PDG -> 250,
419 ParticleName -> "G0",
420 FullName -> "G0"
421 },
422 S[3] == {
423 ClassName -> GP,
424 SelfConjugate -> False,
425 Goldstone -> W,
426 Mass -> {MW, Internal},
427 QuantumNumbers -> {Q -> 1},
428 Width -> {WW, 2.085},
429 PropagatorLabel -> "GP",
430 PropagatorType -> D,
431 PropagatorArrow -> None,
432 PDG -> 251,
433 ParticleName -> "G+",
434 AntiParticleName -> "G-",
435 FullName -> "GP"
436 },
437
438
439(* Pseudoscalar mesons *)
440 S[4] == {
441 ClassName -> K,
442 SelfConjugate -> False,
443 Mass -> {MK,0.493677},
444 QuantumNumbers -> {Q -> 1},
445 Width -> {WK,0},
446 PropagatorLabel -> "K",
447 PropagatorType -> D,
448 PropagatorArrow -> None,
449 PDG -> 321,
450 ParticleName -> "K+",
451 AntiParticleName -> "K-",
452 FullName -> "Charged Kaon"
453 },
454
455 S[5] == {
456 ClassName -> Pip,
457 SelfConjugate -> False,
458 Mass -> {MPip,0.13957},
459 QuantumNumbers -> {Q -> 1},
460 Width -> {WPip, 0},
461 PropagatorLabel -> "Pi",
462 PropagatorType -> D,
463 PropagatorArrow -> None,
464 PDG -> 211,
465 ParticleName -> "Pi+",
466 AntiParticleName -> "Pi-",
467 FullName -> "Charged Pion"
468 },
469
470 S[6] == {
471 ClassName -> Dd,
472 SelfConjugate -> False,
473 Mass -> {MDd,1.869},
474 QuantumNumbers -> {Q -> 1},
475 Width -> {WD, 0},
476 PropagatorLabel -> "Dd",
477 PropagatorType -> D,
478 PropagatorArrow -> None,
479 PDG -> 411,
480 ParticleName -> "D+",
481 AntiParticleName -> "D-",
482 FullName -> "Charged D"
483 },
484
485 S[13] == {
486 ClassName -> D0,
487 SelfConjugate -> False,
488 Mass -> {MD0,1.865},
489 QuantumNumbers -> {Q -> 0},
490 Width -> {WD0,0},
491 PropagatorLabel -> "D0",
492 PropagatorType -> D,
493 PropagatorArrow -> None,
494 PDG -> 421,
495 ParticleName -> "D0",
496 AntiParticleName -> "D0bar",
497 FullName -> "Neutral D"
498 },
499
500 S[7] == {
501 ClassName -> Pi0,
502 SelfConjugate -> True,
503 Mass -> {MPi0,0.13498},
504 Width -> {WPi0, 0},
505 PropagatorLabel -> "Pi0",
506 PropagatorType -> D,
507 PropagatorArrow -> None,
508 PDG -> 111,
509 ParticleName -> "Pi0",
510 FullName -> "Neutral Pion"
511 },
512
513 S[12] == {
514 ClassName -> K0,
515 SelfConjugate -> False,
516 Mass -> {MK0,0.497611},
517 QuantumNumbers -> {Q -> 0},
518 Width -> {WK0,0},
519 PropagatorLabel -> "K0",
520 PropagatorType -> D,
521 PropagatorArrow -> None,
522 PDG -> 311,
523 ParticleName -> "K0",
524 AntiParticleName -> "K0bar",
525 FullName -> "Neutral Kaon"
526 },
527
528 S[8] == {
529 ClassName -> Eta,
530 SelfConjugate -> True,
531 Mass -> {Meta,0.54786},
532 Width -> {Weta, 0},
533 PropagatorLabel -> "eta",
534 PropagatorType -> D,
535 PropagatorArrow -> None,
536 PDG -> 221,
537 ParticleName -> "Eta",
538 FullName -> "Eta"
539 },
540
541 S[9] == {
542 ClassName -> Etap,
543 SelfConjugate -> True,
544 Mass -> {Metap,0.9578},
545 Width -> {Wetap, 0},
546 PropagatorLabel -> "etap",
547 PropagatorType -> D,
548 PropagatorArrow -> None,
549 PDG -> 331,
550 ParticleName -> "Etap",
551 FullName -> "Eta Prime"
552 },
553
554 S[10] == {
555 ClassName -> Ds,
556 SelfConjugate -> False,
557 Mass -> {MDs,1.9683},
558 QuantumNumbers -> {Q -> 1},
559 Width -> {WDs, 0},
560 PropagatorLabel -> "Ds",
561 PropagatorType -> D,
562 PropagatorArrow -> None,
563 PDG -> 431,
564 ParticleName -> "Ds+",
565 AntiParticleName -> "Ds-",
566 FullName -> "Charged Ds"
567 },
568
569 S[15] == {
570 ClassName -> Bu,
571 SelfConjugate -> False,
572 Mass -> {MBu,5.279},
573 QuantumNumbers -> {Q -> 1},
574 Width -> {WBu, 0},
575 PropagatorLabel -> "Bu",
576 PropagatorType -> D,
577 PropagatorArrow -> None,
578 PDG -> 521,
579 ParticleName -> "B+",
580 AntiParticleName -> "B-",
581 FullName -> "Charged B"
582 },
583
584 S[16] == {
585 ClassName -> Bc,
586 SelfConjugate -> False,
587 Mass -> {MBc,6.275},
588 QuantumNumbers -> {Q -> 1},
589 Width -> {WBc, 0},
590 PropagatorLabel -> "Bc",
591 PropagatorType -> D,
592 PropagatorArrow -> None,
593 PDG -> 541,
594 ParticleName -> "Bc+",
595 AntiParticleName -> "Bc-",
596 FullName -> "Charged Bc"
597 },
598
599 S[17] == {
600 ClassName -> B0,
601 SelfConjugate -> False,
602 Mass -> {MB0,5.280},
603 QuantumNumbers -> {Q -> 0},
604 Width -> {WB0,0},
605 PropagatorLabel -> "B0",
606 PropagatorType -> D,
607 PropagatorArrow -> None,
608 PDG -> 511,
609 ParticleName -> "B0",
610 AntiParticleName -> "B0bar",
611 FullName -> "Neutral B"
612 },
613
614 S[18] == {
615 ClassName -> B0s,
616 SelfConjugate -> False,
617 Mass -> {MB0s,5.367},
618 QuantumNumbers -> {Q -> 0},
619 Width -> {WB0s,0},
620 PropagatorLabel -> "B0s",
621 PropagatorType -> D,
622 PropagatorArrow -> None,
623 PDG -> 531,
624 ParticleName -> "B0s",
625 AntiParticleName -> "B0sbar",
626 FullName -> "Neutral Bs"
627 },
628
629(* Higgs: unphysical scalars *)
630 S[11] == {
631 ClassName -> Phi,
632 Unphysical -> True,
633 Indices -> {Index[SU2D]},
634 FlavorIndex -> SU2D,
635 SelfConjugate -> False,
636 QuantumNumbers -> {Y -> 1/2},
637 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
638 },
639
640(* Vector mesons *)
641
642
643 V[21] == {
644 ClassName -> rho0,
645 SelfConjugate -> True,
646 Mass -> {Mrho0, 0.77526},
647 Width -> {Wrho0, 0.1478},
648 ParticleName -> "rho0",
649 PDG -> 113,
650 PropagatorLabel -> "rho0",
651 PropagatorType -> Sine,
652 PropagatorArrow -> None,
653 FullName -> "rho 0"
654 },
655
656 V[22] == {
657 ClassName -> rho,
658 SelfConjugate -> False,
659 Mass -> {Mrho, 0.77511},
660 Width -> {Wrho, 0.1491},
661 ParticleName -> "rho+",
662 AntiParticleName -> "rho-",
663 QuantumNumbers -> {Q -> 1},
664 PDG -> 213,
665 PropagatorLabel -> "rho",
666 PropagatorType -> Sine,
667 PropagatorArrow -> Forward,
668 FullName -> "charged rho"
669 },
670
671
672 V[23] == {
673 ClassName -> omega,
674 SelfConjugate -> True,
675 Mass -> {Mom, 0.78265},
676 Width -> {Wom, 0.00849},
677 ParticleName -> "omega",
678 PDG -> 223,
679 PropagatorLabel -> "omega",
680 PropagatorType -> Sine,
681 PropagatorArrow -> None,
682 FullName -> "Omega"
683 },
684
685 V[24] == {
686 ClassName -> Kstar,
687 SelfConjugate -> False,
688 Mass -> {MKstar, 0.8917},
689 Width -> {WKstar, 0.0508},
690 ParticleName -> "Kstar+",
691 AntiParticleName -> "Kstar-",
692 QuantumNumbers -> {Q -> 1},
693 PDG -> 323,
694 PropagatorLabel -> "Kstar",
695 PropagatorType -> Sine,
696 PropagatorArrow -> Forward,
697 FullName -> "Charged Kstar"
698 },
699
700 V[25] == {
701 ClassName -> phimeson,
702 SelfConjugate -> True,
703 Mass -> {Mphi, 1.019461},
704 Width -> {Wphi, 0.004249},
705 ParticleName -> "phimeson",
706 PDG -> 333,
707 PropagatorLabel -> "phi",
708 PropagatorType -> Sine,
709 PropagatorArrow -> Forward,
710 FullName -> "phi meson"
711 },
712
713 V[26] == {
714 ClassName -> Bstar,
715 SelfConjugate -> False,
716 Mass -> {MBstar, 5.3247},
717 Width -> {WBstar, 0},
718 ParticleName -> "Bstar+",
719 AntiParticleName -> "Bstar-",
720 QuantumNumbers -> {Q -> 1},
721 PDG -> 523,
722 PropagatorLabel -> "Bstar",
723 PropagatorType -> Sine,
724 PropagatorArrow -> Forward,
725 FullName -> "Charged Bstar"
726 }
727
728};
729
730
731
732(* ************************** *)
733(* ***** Gauge ***** *)
734(* ***** Parameters ***** *)
735(* ***** (FeynArts) ***** *)
736(* ************************** *)
737
738GaugeXi[ V[1] ] = GaugeXi[A];
739GaugeXi[ V[2] ] = GaugeXi[Z];
740GaugeXi[ V[3] ] = GaugeXi[W];
741GaugeXi[ V[4] ] = GaugeXi[G];
742GaugeXi[ S[1] ] = 1;
743GaugeXi[ S[2] ] = GaugeXi[Z];
744GaugeXi[ S[3] ] = GaugeXi[W];
745GaugeXi[ U[1] ] = GaugeXi[A];
746GaugeXi[ U[2] ] = GaugeXi[Z];
747GaugeXi[ U[31] ] = GaugeXi[W];
748GaugeXi[ U[32] ] = GaugeXi[W];
749GaugeXi[ U[4] ] = GaugeXi[G];
750
751
752(* ************************** *)
753(* ***** Parameters ***** *)
754(* ************************** *)
755M$Parameters = {
756
757 (* External parameters *)
758 aEWM1 == {
759 ParameterType -> External,
760 BlockName -> SMINPUTS,
761 OrderBlock -> 1,
762 Value -> 127.9,
763 InteractionOrder -> {QED,-2},
764 Description -> "Inverse of the EW coupling constant at the Z pole"
765 },
766 Gf == {
767 ParameterType -> External,
768 BlockName -> SMINPUTS,
769 OrderBlock -> 2,
770 Value -> 1.16637*^-5,
771 InteractionOrder -> {QED,2},
772 TeX -> Subscript[G,f],
773 Description -> "Fermi constant"
774 },
775 aS == {
776 ParameterType -> External,
777 BlockName -> SMINPUTS,
778 OrderBlock -> 3,
779 Value -> 0.1184,
780 InteractionOrder -> {QCD,2},
781 TeX -> Subscript[\[Alpha],s],
782 Description -> "Strong coupling constant at the Z pole"
783 },
784 ymdo == {
785 ParameterType -> External,
786 BlockName -> YUKAWA,
787 OrderBlock -> 1,
788 Value -> 5.04*^-3,
789 Description -> "Down Yukawa mass"
790 },
791 ymup == {
792 ParameterType -> External,
793 BlockName -> YUKAWA,
794 OrderBlock -> 2,
795 Value -> 2.55*^-3,
796 Description -> "Up Yukawa mass"
797 },
798 yms == {
799 ParameterType -> External,
800 BlockName -> YUKAWA,
801 OrderBlock -> 3,
802 Value -> 0.101,
803 Description -> "Strange Yukawa mass"
804 },
805 ymc == {
806 ParameterType -> External,
807 BlockName -> YUKAWA,
808 OrderBlock -> 4,
809 Value -> 1.27,
810 Description -> "Charm Yukawa mass"
811 },
812 ymb == {
813 ParameterType -> External,
814 BlockName -> YUKAWA,
815 OrderBlock -> 5,
816 Value -> 4.7,
817 Description -> "Bottom Yukawa mass"
818 },
819 ymt == {
820 ParameterType -> External,
821 BlockName -> YUKAWA,
822 OrderBlock -> 6,
823 Value -> 172,
824 Description -> "Top Yukawa mass"
825 },
826 yme == {
827 ParameterType -> External,
828 BlockName -> YUKAWA,
829 OrderBlock -> 11,
830 Value -> 5.11*^-4,
831 Description -> "Electron Yukawa mass"
832 },
833 ymm == {
834 ParameterType -> External,
835 BlockName -> YUKAWA,
836 OrderBlock -> 13,
837 Value -> 0.10566,
838 Description -> "Muon Yukawa mass"
839 },
840 ymtau == {
841 ParameterType -> External,
842 BlockName -> YUKAWA,
843 OrderBlock -> 15,
844 Value -> 1.777,
845 Description -> "Tau Yukawa mass"
846 },
847 modthetae == {
848 ParameterType -> External,
849 BlockName -> YUKAWA,
850 OrderBlock -> 16,
851 Value -> 0.00001,
852 Description -> "Heavy-nu-electron mixing modulus"
853 },
854 argthetae == {
855 ParameterType -> External,
856 BlockName -> YUKAWA,
857 OrderBlock -> 17,
858 Value -> 0,
859 Description -> "Heavy-nu-electron mixing argument (degrees)"
860 },
861 thetae == {
862 ParameterType -> Internal,
863 BlockName -> YUKAWA,
864 Value -> modthetae*Exp[I*Pi/180*argthetae],
865 Description -> "Heavy-nu-electron mixing"
866 },
867 modthetamu == {
868 ParameterType -> External,
869 BlockName -> YUKAWA,
870 OrderBlock -> 18,
871 Value -> 0.00001,
872 Description -> "Heavy-nu-muon mixing modulus"
873 },
874 argthetamu == {
875 ParameterType -> External,
876 BlockName -> YUKAWA,
877 OrderBlock -> 19,
878 Value -> 0,
879 Description -> "Heavy-nu-muon mixing argument (degrees)"
880 },
881 thetamu == {
882 ParameterType -> Internal,
883 BlockName -> YUKAWA,
884 Value -> modthetamu*Exp[I*Pi/180*argthetamu],
885 Description -> "Heavy-nu-muon mixing"
886 },
887 modthetatau == {
888 ParameterType -> External,
889 BlockName -> YUKAWA,
890 OrderBlock -> 20,
891 Value -> 0.00001,
892 Description -> "Heavy-nu-tau mixing modulus"
893 },
894 argthetatau == {
895 ParameterType -> External,
896 BlockName -> YUKAWA,
897 OrderBlock -> 21,
898 Value -> 0,
899 Description -> "Heavy-nu-tau mixing argument (degrees)"
900 },
901 thetatau == {
902 ParameterType -> Internal,
903 BlockName -> YUKAWA,
904 Value -> modthetatau*Exp[I*Pi/180*argthetatau],
905 Description -> "Heavy-nu-tau mixing"
906 },
907 MN4 == {
908 ParameterType -> External,
909 BlockName -> YUKAWA,
910 OrderBlock -> 22,
911 Value -> 1.0,
912 Description -> "Majorana mass for N4 in GeV"
913 },
914
915 cabi == {
916 ParameterType -> External,
917 BlockName -> CKMBLOCK,
918 OrderBlock -> 1,
919 Value -> 0.227736,
920 TeX -> Subscript[\[Theta], c],
921 Description -> "Cabibbo angle"
922 },
923
924 th13 == {
925 ParameterType -> External,
926 ComplexParameter -> False,
927 BlockName -> CKMBLOCK,
928 OrderBlock -> 2,
929 Value -> 0.003508,
930 TeX -> Subscript[\[Theta], 13],
931 Description -> "CKM Theta 13"
932 },
933
934 th23 == {
935 ParameterType -> External,
936 ComplexParameter -> False,
937 BlockName -> CKMBLOCK,
938 OrderBlock -> 3,
939 Value -> 0.041539,
940 TeX -> Subscript[\[Theta], 23],
941 Description -> "CKM theta 23"
942 },
943
944 del13 == {
945 ParameterType -> External,
946 ComplexParameter -> False,
947 BlockName -> CKMBLOCK,
948 OrderBlock -> 4,
949 Value -> 1.20,
950 TeX -> Subscript[\[Delta], 13],
951 Description -> "CKM delta 13"
952 },
953
954 MassN4 == {
955 ParameterType -> Internal,
956 Value -> MN4,
957 Description -> "Heavy mass"
958 },
959
960 fK == {
961 ParameterType -> External,
962 BlockName -> MESONBLOCK,
963 OrderBlock -> 2,
964 Value -> 0.1556,
965 Description -> "Kaon decay constant"
966 },
967
968 fpi == {
969 ParameterType -> External,
970 BlockName -> MESONBLOCK,
971 OrderBlock -> 3,
972 Value -> 0.1302,
973 Description -> "Pion decay constant"
974 },
975
976 feta == {
977 ParameterType -> External,
978 BlockName -> MESONBLOCK,
979 OrderBlock -> 4,
980 Value -> 0.08159,
981 Description -> "Eta decay constant"
982 },
983
984 fetap == {
985 ParameterType -> External,
986 BlockName -> MESONBLOCK,
987 OrderBlock -> 5,
988 Value -> -0.0946,
989 Description -> "Eta prime decay constant"
990 },
991
992 fD == {
993 ParameterType -> External,
994 BlockName -> MESONBLOCK,
995 OrderBlock -> 6,
996 Value -> 0.212,
997 Description -> "D decay constant"
998 },
999
1000 frho == {
1001 ParameterType -> External,
1002 BlockName -> MESONBLOCK,
1003 OrderBlock -> 7,
1004 Value -> 0.17,
1005 Description -> "rho decay constant"
1006 },
1007
1008 fKstar == {
1009 ParameterType -> External,
1010 BlockName -> MESONBLOCK,
1011 OrderBlock -> 34,
1012 Value -> 0.177,
1013 Description -> "Kstar decay constant"
1014 },
1015
1016 fDs == {
1017 ParameterType -> External,
1018 BlockName -> MESONBLOCK,
1019 OrderBlock -> 8,
1020 Value -> 0.249,
1021 Description -> "Ds decay constant"
1022 },
1023
1024 fomega == {
1025 ParameterType -> External,
1026 BlockName -> MESONBLOCK,
1027 OrderBlock -> 9,
1028 Value -> 0.155,
1029 Description -> "omega decay constant"
1030 },
1031
1032 fphi == {
1033 ParameterType -> External,
1034 BlockName -> MESONBLOCK,
1035 OrderBlock -> 10,
1036 Value -> 0.232,
1037 Description -> "phi decay constant"
1038 },
1039
1040 fB == {
1041 ParameterType -> External,
1042 BlockName -> MESONBLOCK,
1043 OrderBlock -> 11,
1044 Value -> 0.190,
1045 ComplexParameter -> False,
1046 Description -> "B decay constant"
1047 },
1048
1049 fBs == {
1050 ParameterType -> External,
1051 BlockName -> MESONBLOCK,
1052 OrderBlock -> 12,
1053 Value -> 0.230,
1054 ComplexParameter -> False,
1055 Description -> "Bs decay constant"
1056 },
1057
1058 fBc == {
1059 ParameterType -> External,
1060 BlockName -> MESONBLOCK,
1061 OrderBlock -> 13,
1062 Value -> 0.190,
1063 ComplexParameter -> False,
1064 Description -> "Bc decay constant"
1065 },
1066
1067
1068 (* Internal Parameters *)
1069 aEW == {
1070 ParameterType -> Internal,
1071 Value -> 1/aEWM1,
1072 InteractionOrder -> {QED,2},
1073 TeX -> Subscript[\[Alpha], EW],
1074 Description -> "Electroweak coupling contant"
1075 },
1076 MW == {
1077 ParameterType -> Internal,
1078 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-3.14/Sqrt[2]*aEW/Gf*MZ^2]],
1079 TeX -> Subscript[M,W],
1080 Description -> "W mass"
1081 },
1082 sw2 == {
1083 ParameterType -> Internal,
1084 Value -> 1-(MW/MZ)^2,
1085 Description -> "Squared Sin of the Weinberg angle"
1086 },
1087 ee == {
1088 ParameterType -> Internal,
1089 Value -> Sqrt[4 3.14 aEW],
1090 InteractionOrder -> {QED,1},
1091 TeX -> e,
1092 Description -> "Electric coupling constant"
1093 },
1094 cw == {
1095 ParameterType -> Internal,
1096 Value -> Sqrt[1-sw2],
1097 TeX -> Subscript[c,w],
1098 Description -> "Cosine of the Weinberg angle"
1099 },
1100 sw == {
1101 ParameterType -> Internal,
1102 Value -> Sqrt[sw2],
1103 TeX -> Subscript[s,w],
1104 Description -> "Sine of the Weinberg angle"
1105 },
1106 gw == {
1107 ParameterType -> Internal,
1108 Definitions -> {gw->ee/sw},
1109 InteractionOrder -> {QED,1},
1110 TeX -> Subscript[g,w],
1111 Description -> "Weak coupling constant at the Z pole"
1112 },
1113 g1 == {
1114 ParameterType -> Internal,
1115 Definitions -> {g1->ee/cw},
1116 InteractionOrder -> {QED,1},
1117 TeX -> Subscript[g,1],
1118 Description -> "U(1)Y coupling constant at the Z pole"
1119 },
1120 gs == {
1121 ParameterType -> Internal,
1122 Value -> Sqrt[4 3.14 aS],
1123 InteractionOrder -> {QCD,1},
1124 TeX -> Subscript[g,s],
1125 ParameterName -> G,
1126 Description -> "Strong coupling constant at the Z pole"
1127 },
1128 vev == {
1129 ParameterType -> Internal,
1130 Value -> 2*MW*sw/ee,
1131 InteractionOrder -> {QED,-1},
1132 Description -> "Higgs vacuum expectation value"
1133 },
1134 lam == {
1135 ParameterType -> Internal,
1136 Value -> MH^2/(2*vev^2),
1137 InteractionOrder -> {QED, 2},
1138 Description -> "Higgs quartic coupling"
1139 },
1140 muH == {
1141 ParameterType -> Internal,
1142 Value -> Sqrt[vev^2 lam],
1143 TeX -> \[Mu],
1144 Description -> "Coefficient of the quadratic piece of the Higgs potential"
1145 },
1146 thetatot == {
1147 ParameterType -> Internal,
1148 Value -> Sqrt[thetae*Conjugate[thetae]+thetamu*Conjugate[thetamu]+thetatau*Conjugate[thetatau]],
1149 TeX -> \[Theta],
1150 Description -> "Heavy-active mixing"
1151 },
1152 thetas == {
1153 ParameterType -> Internal,
1154 Value -> thetae+thetamu+thetatau,
1155 TeX -> Subscript[\[Theta],s],
1156 Description -> "Heavy-active mixing sum"
1157 },
1158 r == {
1159 ParameterType -> Internal,
1160 Value -> 1/Sqrt[1+4*thetatot^2],
1161 Description -> "useful ratio"
1162 },
1163 yN == {
1164 ParameterType -> Internal,
1165 Indices -> {Index[Generation], Index[Heavynus]},
1166 Value -> {yN[1,1] -> Sqrt[2] Conjugate[thetae] MN4 /vev, yN[2,1] -> Sqrt[2] Conjugate[thetamu] MN4 /vev, yN[3,1] -> Sqrt[2] Conjugate[thetatau] MN4 /vev},
1167 InteractionOrder -> {QED, 1},
1168 ParameterName -> {yN[1,1] -> yNe, yN[2,1] -> yNmu, yN[3,1] -> yNtau},
1169 TeX -> Superscript[y, N],
1170 Description -> "Heavy nu Yukawa couplings"
1171 },
1172 numass == {
1173 ParameterType -> Internal,
1174 Indices -> {Index[Neutrinos], Index[Neutrinos]},
1175 Value -> {numass[3,3] :> 0.5*MN4*Abs[1-1/r], numass[4,4] :> 0.5*MN4*Abs[1+1/r], numass[ii_,jj_] :> 0},
1176 InteractionOrder -> {QED, 0},
1177 ParameterName -> {numass[1,1] -> mnu1, numass[2,2] -> mnu2, numass[3,3] -> mnu3, numass[4,4] -> mnu4},
1178 TeX -> Superscript[m, nu],
1179 Description -> "Neutrino mass"
1180 },
1181
1182 (** Form factors for K0 to Pi+ decays: linear parametrization **)
1183
1184 avq2K0Pi == {
1185 ParameterType -> Internal,
1186 Indices -> {Index[Neutrinos], Index[Generation]},
1187 Value -> {avq2K0Pi[ii_,ll_] ->
1188 If[ll==1, -1.7232*numass[ii,ii]^3 + 1.08186*numass[ii,ii]^2 + 0.0973741*numass[ii,ii] + 0.0331474*KroneckerDelta[ii,ii],
1189 If[ll==2, -3.15565*numass[ii,ii]^3 + 1.70749*numass[ii,ii]^2 + 0.0668773*numass[ii,ii] + 0.052815*KroneckerDelta[ii,ii], 10^-90]]},
1190 Description -> "Average momentum transfer in K0 to Pi decays"
1191 },
1192
1193 fplusK0Pi == {
1194 ParameterType -> Internal,
1195 Indices -> {Index[Neutrinos], Index[Generation]},
1196 Value -> {fplusK0Pi[ii_,ll_] -> 0.9749*(1+0.0282*avq2K0Pi[ii,ll]/MPip^2)},
1197 Description -> "Average f+ form factor in K0 to Pi+ decays"
1198 },
1199
1200 f0K0Pi == {
1201 ParameterType -> Internal,
1202 Indices -> {Index[Neutrinos], Index[Generation]},
1203 Value -> {f0K0Pi[ii_,ll_] -> 0.9749*(1+0.0138*avq2K0Pi[ii,ll]/MPip^2)},
1204 Description -> "Average f0 form factor in K0 to Pi+ decays"
1205 },
1206
1207 fminusK0Pi == {
1208 ParameterType -> Internal,
1209 Indices -> {Index[Neutrinos], Index[Generation]},
1210 Value -> {fminusK0Pi[ii_,ll_] -> (MPip^2-MK0^2)*(f0K0Pi[ii,ll]-fplusK0Pi[ii,ll])/avq2K0Pi[ii,ll]},
1211 Description -> "Average f- form factor in K0 to Pi+ decays"
1212 },
1213
1214(** Form factors for K+ to Pi0 decays: linear parametrization **)
1215
1216 avq2KPi0 == {
1217 ParameterType -> Internal,
1218 Indices -> {Index[Neutrinos], Index[Generation]},
1219 Value -> {avq2KPi0[ii_,ll_] ->
1220 If[ll==1, -1.80782*numass[ii,ii]^3 + 1.10701*numass[ii,ii]^2 + 0.0998414*numass[ii,ii] + 0.0329829*KroneckerDelta[ii,ii],
1221 If[ll==2, -3.22495*numass[ii,ii]^3 + 1.71265*numass[ii,ii]^2 + 0.0698265*numass[ii,ii] + 0.052995*KroneckerDelta[ii,ii], 10^-90]]},
1222 Description -> "Average momentum transfer in K+ to Pi0 decays"
1223 },
1224
1225 fplusKPi0 == {
1226 ParameterType -> Internal,
1227 Indices -> {Index[Neutrinos], Index[Generation]},
1228 Value -> {fplusKPi0[ii_,ll_] -> 0.9749*(1+0.0297*avq2KPi0[ii,ll]/MPip^2)},
1229 Description -> "Average f+ form factor in K+ to Pi0 decays"
1230 },
1231
1232 f0KPi0 == {
1233 ParameterType -> Internal,
1234 Indices -> {Index[Neutrinos], Index[Generation]},
1235 Value -> {f0KPi0[ii_,ll_] -> 0.9749*(1+0.0195*avq2KPi0[ii,ll]/MPip^2)},
1236 Description -> "Average f0 form factor in K+ to Pi0 decays"
1237 },
1238
1239 fminusKPi0 == {
1240 ParameterType -> Internal,
1241 Indices -> {Index[Neutrinos], Index[Generation]},
1242 Value -> {fminusKPi0[ii_,ll_] -> (MPi0^2-MK^2)*(f0KPi0[ii,ll]-fplusKPi0[ii,ll])/avq2KPi0[ii,ll]},
1243 Description -> "Average f- form factor in K+ to Pi0 decays"
1244 },
1245
1246(** Form factors for D to K decays: pole parametrization **)
1247
1248 avq2DK == {
1249 ParameterType -> Internal,
1250 Indices -> {Index[Neutrinos], Index[Generation]},
1251 Value -> {avq2DK[ii_,ll_] ->
1252 If[ll==1, -0.364268*numass[ii,ii]^3 + 0.932086*numass[ii,ii]^2 + 0.381641*numass[ii,ii] + 0.538848*KroneckerDelta[ii,ii],
1253 If[ll==2, -0.337128*numass[ii,ii]^3 + 0.94568*numass[ii,ii]^2 + 0.368498*numass[ii,ii] + 0.568881*KroneckerDelta[ii,ii], 10^-90]]},
1254 Description -> "Average momentum transfer in D to K decays"
1255 },
1256
1257 tplusDK == {
1258 ParameterType -> Internal,
1259 Value -> (MDd+MK)^2,
1260 Description -> "t+ factor in the pole parametrization"
1261 },
1262
1263 t0DK == {
1264 ParameterType -> Internal,
1265 Value -> (MDd+MK)*(Sqrt[MK]-Sqrt[MDd])^2,
1266 Description -> "t0 factor in the pole parametrization"
1267 },
1268
1269 zDK == {
1270 ParameterType -> Internal,
1271 Indices -> {Index[Neutrinos], Index[Generation]},
1272 Value -> {zDK[ii_,ll_] -> (Sqrt[tplusDK-avq2DK[ii,ll]]-Sqrt[tplusDK-t0DK])/(Sqrt[tplusDK-avq2DK[ii,ll]]+Sqrt[tplusDK-t0DK])},
1273 Description -> "z factor in the pole parametrization"
1274 },
1275
1276 z0DK == {
1277 ParameterType -> Internal,
1278 Value -> (Sqrt[tplusDK]-Sqrt[tplusDK-t0DK])/(Sqrt[tplusDK]+Sqrt[tplusDK-t0DK]),
1279 Description -> "z0 factor in the pole parametrization"
1280 },
1281
1282 fplusDK == {
1283 ParameterType -> Internal,
1284 Indices -> {Index[Neutrinos], Index[Generation]},
1285 Value -> {fplusDK[ii_,ll_] -> (0.7647-0.066*(zDK[ii,ll]-z0DK)*(1+0.5*(zDK[ii,ll]+z0DK)))/(1-0.22*avq2DK[ii,ll])},
1286 Description -> "Average f+ form factor in D to K decays"
1287 },
1288
1289 f0DK == {
1290 ParameterType -> Internal,
1291 Indices -> {Index[Neutrinos], Index[Generation]},
1292 Value -> {f0DK[ii_,ll_] -> (0.7647-2.084*(zDK[ii,ll]-z0DK)*(1+0.5*(zDK[ii,ll]+z0DK)))},
1293 Description -> "Average f0 form factor in D to K decays"
1294 },
1295
1296 fminusDK == {
1297 ParameterType -> Internal,
1298 Indices -> {Index[Neutrinos], Index[Generation]},
1299 Value -> {fminusDK[ii_,ll_] -> (MK^2-MDd^2)/avq2DK[ii,ll]*(f0DK[ii,ll]-fplusDK[ii,ll])},
1300 Description -> "Average f- form factor in D to K decays"
1301 },
1302
1303(** Form factors for B+ to Pi0 decays: FLAG review **)
1304
1305 avq2BPi0 == {
1306 ParameterType -> Internal,
1307 Indices -> {Index[Neutrinos], Index[Generation]},
1308 Value -> {avq2BPi0[ii_,ll_] ->
1309 If[ll==1, -0.0747182*numass[ii,ii]^3 + 0.757551*numass[ii,ii]^2 + 1.43992*numass[ii,ii] + 9.05607*KroneckerDelta[ii,ii],
1310 If[ll==2, -0.0692688*numass[ii,ii]^3 + 0.731411*numass[ii,ii]^2 + 1.47166*numass[ii,ii] + 9.08105*KroneckerDelta[ii,ii],
1311 If[ll==3, -0.163478*numass[ii,ii]^3 + 1.45186*numass[ii,ii]^2 + 0.790463*numass[ii,ii] + 13.5051*KroneckerDelta[ii,ii],10^-90]]]},
1312 Description -> "Average momentum transfer in B+ to Pi0 decays"
1313 },
1314
1315 tplusBPi0 == {
1316 ParameterType -> Internal,
1317 Value -> (MBu + MPi0)^2,
1318 Description -> "t+ factor"
1319 },
1320
1321 t0BPi0 == {
1322 ParameterType -> Internal,
1323 Value -> (MBu + MPi0)*(Sqrt[MPi0]-Sqrt[MBu])^2,
1324 Description -> "t0 factor"
1325 },
1326
1327 zBPi0 == {
1328 ParameterType -> Internal,
1329 Indices -> {Index[Neutrinos], Index[Generation]},
1330 Value -> {zBPi0[ii_,ll_] -> (Sqrt[tplusBPi0-avq2BPi0[ii,ll]]-Sqrt[tplusBPi0-t0BPi0])/(Sqrt[tplusBPi0-avq2BPi0[ii,ll]]+Sqrt[tplusBPi0-t0BPi0])},
1331 Description -> "z factor"
1332 },
1333
1334 z0BPi0 == {
1335 ParameterType -> Internal,
1336 Value -> (Sqrt[tplusBPi0]-Sqrt[tplusBPi0-t0BPi0])/(Sqrt[tplusBPi0]+Sqrt[tplusBPi0-t0BPi0]),
1337 Description -> "z0 factor"
1338 },
1339
1340 fplusBPi0 == {
1341 ParameterType -> Internal,
1342 Indices -> {Index[Neutrinos], Index[Generation]},
1343 Value -> {fplusBPi0[ii_,ll_] -> (1/(1-avq2BPi0[ii,ll]/MBstar^2))*(-0.68*(zBPi0[ii,ll]-1/3(zBPi0[ii,ll]^3))-0.86*((zBPi0[ii,ll]^3)2/3 + zBPi0[ii,ll]^2) + 0.404)},
1344 Description -> "Average f+ form factor in B+ to Pi0 decays"
1345 },
1346
1347 f0BPi0 == {
1348 ParameterType -> Internal,
1349 Indices -> {Index[Neutrinos], Index[Generation]},
1350 Value -> {f0BPi0[ii_,ll_] -> (1.2527548*zBPi0[ii,ll]^2 - 1.61*zBPi0[ii,ll] + 0.490)},
1351 Description -> "Average f0 form factor in B+ to Pi0 decays"
1352 },
1353
1354 fminusBPi0 == {
1355 ParameterType -> Internal,
1356 Indices -> {Index[Neutrinos], Index[Generation]},
1357 Value -> {fminusBPi0[ii_,ll_] -> (MPi0^2-MBu^2)/avq2BPi0[ii,ll]*(f0BPi0[ii,ll]-fplusBPi0[ii,ll])},
1358 Description -> "Average f- form factor in B+ to Pi0 decays"
1359 },
1360
1361(** Form factors for B0 to Pi+ decays: FLAG review **)
1362
1363 avq2B0Pi == {
1364 ParameterType -> Internal,
1365 Indices -> {Index[Neutrinos], Index[Generation]},
1366 Value -> {avq2B0Pi[ii_,ll_] ->
1367 If[ll==1, -0.0738527*numass[ii,ii]^3 + 0.750683*numass[ii,ii]^2 + 1.45882*numass[ii,ii] + 9.01069*KroneckerDelta[ii,ii],
1368 If[ll==2, -0.0695186*numass[ii,ii]^3 + 0.731836*numass[ii,ii]^2 + 1.47827*numass[ii,ii] + 9.0398*KroneckerDelta[ii,ii],
1369 If[ll==3, -0.164163*numass[ii,ii]^3 + 1.45367*numass[ii,ii]^2 + 0.794287*numass[ii,ii] + 13.4752*KroneckerDelta[ii,ii], 10^-90]]]},
1370 Description -> "Average momentum transfer in B0 to Pi+ decays"
1371 },
1372
1373 tplusB0Pi == {
1374 ParameterType -> Internal,
1375 Value -> (MB0 + MPip)^2,
1376 Description -> "t+ factor"
1377 },
1378
1379 t0B0Pi == {
1380 ParameterType -> Internal,
1381 Value -> (MB0 + MPip)*(Sqrt[MPip]-Sqrt[MB0])^2,
1382 Description -> "t0 factor"
1383 },
1384
1385 zB0Pi == {
1386 ParameterType -> Internal,
1387 Indices -> {Index[Neutrinos], Index[Generation]},
1388 Value -> {zB0Pi[ii_,ll_] -> (Sqrt[tplusB0Pi-avq2B0Pi[ii,ll]]-Sqrt[tplusB0Pi-t0B0Pi])/(Sqrt[tplusB0Pi-avq2B0Pi[ii,ll]]+Sqrt[tplusB0Pi-t0B0Pi])},
1389 Description -> "z factor"
1390 },
1391
1392 z0B0Pi == {
1393 ParameterType -> Internal,
1394 Value -> (Sqrt[tplusB0Pi]-Sqrt[tplusB0Pi-t0B0Pi])/(Sqrt[tplusB0Pi]+Sqrt[tplusB0Pi-t0B0Pi]),
1395 Description -> "z0 factor"
1396 },
1397
1398 fplusB0Pi == {
1399 ParameterType -> Internal,
1400 Indices -> {Index[Neutrinos], Index[Generation]},
1401 Value -> {fplusB0Pi[ii_,ll_] -> (1/(1-avq2B0Pi[ii,ll]/MBstar^2))*(-0.68*(zB0Pi[ii,ll]-zB0Pi[ii,ll]^3/3)-0.86*((2 zB0Pi[ii,ll]^3)/3 + zB0Pi[ii,ll]^2) + 0.404)},
1402 Description -> "Average f+ form factor in B0 to Pi+ decays"
1403 },
1404
1405 f0B0Pi == {
1406 ParameterType -> Internal,
1407 Indices -> {Index[Neutrinos], Index[Generation]},
1408 Value -> {f0B0Pi[ii_,ll_] -> (1.268691923*zB0Pi[ii,ll]^2 - 1.61*zB0Pi[ii,ll] + 0.490)},
1409 Description -> "Average f0 form factor in B0 to Pi+ decays"
1410 },
1411
1412 fminusB0Pi == {
1413 ParameterType -> Internal,
1414 Indices -> {Index[Neutrinos], Index[Generation]},
1415 Value -> {fminusB0Pi[ii_,ll_] -> (MPip^2-MB0^2)/avq2B0Pi[ii,ll]*(f0B0Pi[ii,ll]-fplusB0Pi[ii,ll])},
1416 Description -> "Average f- form factor in B0 to Pi+ decays"
1417 },
1418
1419 (** Form factors for B+ to D0 decays: FLAG review **)
1420
1421 avq2BD0 == {
1422 ParameterType -> Internal,
1423 Indices -> {Index[Neutrinos], Index[Generation]},
1424 Value -> {avq2BD0[ii_,ll_] ->
1425 If[ll==1, -0.0756751*numass[ii,ii]^3 + 0.619874*numass[ii,ii]^2 + 1.06348*numass[ii,ii] + 3.82403*KroneckerDelta[ii,ii],
1426 If[ll==2, -0.0614*numass[ii,ii]^3 + 0.580972*numass[ii,ii]^2 + 1.08624*numass[ii,ii] + 3.85694*KroneckerDelta[ii,ii],
1427 If[ll==3, -0.49004*numass[ii,ii]^3 + 2.19813*numass[ii,ii]^2 + 0.420447*numass[ii,ii] + 7.22909*KroneckerDelta[ii,ii],10^-90]]]},
1428 Description -> "Average momentum transfer in B+ to D0 decays"
1429 },
1430
1431 tplusBD0 == {
1432 ParameterType -> Internal,
1433 Value -> (MBu + MD0)^2,
1434 Description -> "t+ factor"
1435 },
1436
1437 t0BD0 == {
1438 ParameterType -> Internal,
1439 Value -> (MBu + MD0)*(Sqrt[MD0]-Sqrt[MBu])^2,
1440 Description -> "t0 factor"
1441 },
1442
1443 zBD0 == {
1444 ParameterType -> Internal,
1445 Indices -> {Index[Neutrinos], Index[Generation]},
1446 Value -> {zBD0[ii_,ll_] -> (Sqrt[tplusBD0-avq2BD0[ii,ll]]-Sqrt[tplusBD0-t0BD0])/(Sqrt[tplusBD0-avq2BD0[ii,ll]]+Sqrt[tplusBD0-t0BD0])},
1447 Description -> "z factor"
1448 },
1449
1450 z0BD0 == {
1451 ParameterType -> Internal,
1452 Value -> (Sqrt[tplusBD0]-Sqrt[tplusBD0-t0BD0])/(Sqrt[tplusBD0]+Sqrt[tplusBD0-t0BD0]),
1453 Description -> "z0 factor"
1454 },
1455
1456 fplusBD0 == {
1457 ParameterType -> Internal,
1458 Indices -> {Index[Neutrinos], Index[Generation]},
1459 Value -> {fplusBD0[ii_,ll_] -> (1/(1-avq2BD0[ii,ll]/MBstar^2))*(-7.11*(zBD0[ii,ll]-1/3(zBD0[ii,ll]^3)) + 66*((zBD0[ii,ll]^3)2/3 + zBD0[ii,ll]^2) + 0.909)},
1460 Description -> "Average f+ form factor in B+ to D0 decays"
1461 },
1462
1463 f0BD0 == {
1464 ParameterType -> Internal,
1465 Indices -> {Index[Neutrinos], Index[Generation]},
1466 Value -> {f0BD0[ii_,ll_] -> (33.2166*zBD0[ii,ll]^2 - 2.45*zBD0[ii,ll] + 0.794)},
1467 Description -> "Average f0 form factor in B+ to D0 decays"
1468 },
1469
1470 fminusBD0 == {
1471 ParameterType -> Internal,
1472 Indices -> {Index[Neutrinos], Index[Generation]},
1473 Value -> {fminusBD0[ii_,ll_] -> (MD0^2-MBu^2)/avq2BD0[ii,ll]*(f0BD0[ii,ll]-fplusBD0[ii,ll])},
1474 Description -> "Average f- form factor in B+ to D0 decays"
1475 },
1476
1477 (** Form factors for B0 to D+ decays: FLAG review **)
1478
1479 avq2B0D == {
1480 ParameterType -> Internal,
1481 Indices -> {Index[Neutrinos], Index[Generation]},
1482 Value -> {avq2B0D[ii_,ll_] ->
1483 If[ll==1, -0.0759024*numass[ii,ii]^3 + 0.620479*numass[ii,ii]^2 + 1.06255*numass[ii,ii] + 3.81359*KroneckerDelta[ii,ii],
1484 If[ll==2, -0.0616034*numass[ii,ii]^3 + 0.58158*numass[ii,ii]^2 + 1.08525*numass[ii,ii] + 3.84654*KroneckerDelta[ii,ii],
1485 If[ll==3, -0.492883*numass[ii,ii]^3 + 2.20311*numass[ii,ii]^2 + 0.419677*numass[ii,ii] + 7.2176*KroneckerDelta[ii,ii],10^-90]]]},
1486 Description -> "Average momentum transfer in B0 to D+ decays"
1487 },
1488
1489 tplusB0D == {
1490 ParameterType -> Internal,
1491 Value -> (MB0 + MDd)^2,
1492 Description -> "t+ factor"
1493 },
1494
1495 t0B0D == {
1496 ParameterType -> Internal,
1497 Value -> (MB0 + MDd)*(Sqrt[MDd]-Sqrt[MB0])^2,
1498 Description -> "t0 factor"
1499 },
1500
1501 zB0D == {
1502 ParameterType -> Internal,
1503 Indices -> {Index[Neutrinos], Index[Generation]},
1504 Value -> {zB0D[ii_,ll_] -> (Sqrt[tplusB0D-avq2B0D[ii,ll]]-Sqrt[tplusB0D-t0B0D])/(Sqrt[tplusB0D-avq2B0D[ii,ll]]+Sqrt[tplusB0D-t0B0D])},
1505 Description -> "z factor"
1506 },
1507
1508 z0B0D == {
1509 ParameterType -> Internal,
1510 Value -> (Sqrt[tplusB0D]-Sqrt[tplusB0D-t0B0D])/(Sqrt[tplusB0D]+Sqrt[tplusB0D-t0B0D]),
1511 Description -> "z0 factor"
1512 },
1513
1514 fplusB0D == {
1515 ParameterType -> Internal,
1516 Indices -> {Index[Neutrinos], Index[Generation]},
1517 Value -> {fplusB0D[ii_,ll_] -> (1/(1-avq2B0D[ii,ll]/MBstar^2))*(-7.11*(zB0D[ii,ll]-1/3(zB0D[ii,ll]^3)) + 66*((zB0D[ii,ll]^3)2/3 + zB0D[ii,ll]^2) + 0.909)},
1518 Description -> "Average f+ form factor in B0 to D+ decays"
1519 },
1520
1521 f0B0D == {
1522 ParameterType -> Internal,
1523 Indices -> {Index[Neutrinos], Index[Generation]},
1524 Value -> {f0B0D[ii_,ll_] -> (33.5115*zB0D[ii,ll]^2 - 2.45*zB0D[ii,ll] + 0.794)},
1525 Description -> "Average f0 form factor in B0 to D+ decays"
1526 },
1527
1528 fminusB0D == {
1529 ParameterType -> Internal,
1530 Indices -> {Index[Neutrinos], Index[Generation]},
1531 Value -> {fminusB0D[ii_,ll_] -> (MDd^2-MB0^2)/avq2B0D[ii,ll]*(f0B0D[ii,ll]-fplusB0D[ii,ll])},
1532 Description -> "Average f- form factor in B0 to D+ decays"
1533 },
1534
1535 (** Form factors for B0s to Ds+ decays: FLAG review **)
1536
1537 avq2B0sDs == {
1538 ParameterType -> Internal,
1539 Indices -> {Index[Neutrinos], Index[Generation]},
1540 Value -> {avq2B0sDs[ii_,ll_] ->
1541 If[ll==1, -0.0767788*numass[ii,ii]^3 + 0.621995*numass[ii,ii]^2 + 1.06724*numass[ii,ii] + 3.76534*KroneckerDelta[ii,ii],
1542 If[ll==2, -0.0624231*numass[ii,ii]^3 + 0.583268*numass[ii,ii]^2 + 1.08928*numass[ii,ii] + 3.79888*KroneckerDelta[ii,ii],
1543 If[ll==3, -0.505219*numass[ii,ii]^3 + 2.2248*numass[ii,ii]^2 + 0.418473*numass[ii,ii] + 7.17705*KroneckerDelta[ii,ii],10^-90]]]},
1544 Description -> "Average momentum transfer in B0s to Ds+ decays"
1545 },
1546
1547 tplusB0sDs == {
1548 ParameterType -> Internal,
1549 Value -> (MB0s + MDs)^2,
1550 Description -> "t+ factor"
1551 },
1552
1553 t0B0sDs == {
1554 ParameterType -> Internal,
1555 Value -> (MB0s + MDs)*(Sqrt[MDs]-Sqrt[MB0s])^2,
1556 Description -> "t0 factor"
1557 },
1558
1559 zB0sDs == {
1560 ParameterType -> Internal,
1561 Indices -> {Index[Neutrinos], Index[Generation]},
1562 Value -> {zB0sDs[ii_,ll_] -> (Sqrt[tplusB0sDs-avq2B0sDs[ii,ll]]-Sqrt[tplusB0sDs-t0B0sDs])/(Sqrt[tplusB0sDs-avq2B0sDs[ii,ll]]+Sqrt[tplusB0sDs-t0B0sDs])},
1563 Description -> "z factor"
1564 },
1565
1566 z0B0sDs == {
1567 ParameterType -> Internal,
1568 Value -> (Sqrt[tplusB0sDs]-Sqrt[tplusB0sDs-t0B0sDs])/(Sqrt[tplusB0sDs]+Sqrt[tplusB0sDs-t0B0sDs]),
1569 Description -> "z0 factor"
1570 },
1571
1572 fplusB0sDs == {
1573 ParameterType -> Internal,
1574 Indices -> {Index[Neutrinos], Index[Generation]},
1575 Value -> {fplusB0sDs[ii_,ll_] -> (1/(1-avq2B0sDs[ii,ll]/MBstar^2))*(-7.11*(zB0sDs[ii,ll]-1/3(zB0sDs[ii,ll]^3)) + 66*((zB0sDs[ii,ll]^3)2/3 + zB0sDs[ii,ll]^2) + 0.909)},
1576 Description -> "Average f+ form factor in B0s to Ds+ decays"
1577 },
1578
1579 f0B0sDs == {
1580 ParameterType -> Internal,
1581 Indices -> {Index[Neutrinos], Index[Generation]},
1582 Value -> {f0B0sDs[ii_,ll_] -> (39.1988*zB0sDs[ii,ll]^2 - 2.45*zB0sDs[ii,ll] + 0.794)},
1583 Description -> "Average f0 form factor in B0s to Ds+ decays"
1584 },
1585
1586 fminusB0sDs == {
1587 ParameterType -> Internal,
1588 Indices -> {Index[Neutrinos], Index[Generation]},
1589 Value -> {fminusB0sDs[ii_,ll_] -> (MDs^2-MB0s^2)/avq2B0sDs[ii,ll]*(f0B0sDs[ii,ll]-fplusB0sDs[ii,ll])},
1590 Description -> "Average f- form factor in B0s to Ds+ decays"
1591 },
1592
1593 (** Form factors for B0s to K+ decays: FLAG review **)
1594
1595 avq2B0sK == {
1596 ParameterType -> Internal,
1597 Indices -> {Index[Neutrinos], Index[Generation]},
1598 Value -> {avq2B0sK[ii_,ll_] ->
1599 If[ll==1, -0.0305836*numass[ii,ii]^3 + 0.431928*numass[ii,ii]^2 + 1.84666*numass[ii,ii] + 7.82438*KroneckerDelta[ii,ii],
1600 If[ll==2, -0.0223321*numass[ii,ii]^3 + 0.3961*numass[ii,ii]^2 + 1.87998*numass[ii,ii] + 7.86105*KroneckerDelta[ii,ii],
1601 If[ll==3, -0.111798*numass[ii,ii]^3 + 1.23898*numass[ii,ii]^2 + 0.905063*numass[ii,ii] + 12.2134*KroneckerDelta[ii,ii],10^-90]]]},
1602 Description -> "Average momentum transfer in B0s to K+ decays"
1603 },
1604
1605 tplusB0sK == {
1606 ParameterType -> Internal,
1607 Value -> (MB0s + MK)^2,
1608 Description -> "t+ factor"
1609 },
1610
1611 t0B0sK == {
1612 ParameterType -> Internal,
1613 Value -> (MB0s + MK)*(Sqrt[MK]-Sqrt[MB0s])^2,
1614 Description -> "t0 factor"
1615 },
1616
1617 zB0sK == {
1618 ParameterType -> Internal,
1619 Indices -> {Index[Neutrinos], Index[Generation]},
1620 Value -> {zB0sK[ii_,ll_] -> (Sqrt[tplusB0sK-avq2B0sK[ii,ll]]-Sqrt[tplusB0sK-t0B0sK])/(Sqrt[tplusB0sK-avq2B0sK[ii,ll]]+Sqrt[tplusB0sK-t0B0sK])},
1621 Description -> "z factor"
1622 },
1623
1624 z0B0sK == {
1625 ParameterType -> Internal,
1626 Value -> (Sqrt[tplusB0sK]-Sqrt[tplusB0sK-t0B0sK])/(Sqrt[tplusB0sK]+Sqrt[tplusB0sK-t0B0sK]),
1627 Description -> "z0 factor"
1628 },
1629
1630 fplusB0sK == {
1631 ParameterType -> Internal,
1632 Indices -> {Index[Neutrinos], Index[Generation]},
1633 Value -> {fplusB0sK[ii_,ll_] -> (1/(1-avq2B0sK[ii,ll]/MBstar^2))*(-0.672*(zB0sK[ii,ll]+1/4*zB0sK[ii,ll]^4) + 0.07*(zB0sK[ii,ll]^2 - 1/2*zB0sK[ii,ll]^4) + 1.34*(3/4*zB0sK[ii,ll]^4 + zB0sK[ii,ll]^3) + 0.374)},
1634 Description -> "Average f+ form factor in B0s to K+ decays"
1635 },
1636
1637 f0B0sK == {
1638 ParameterType -> Internal,
1639 Indices -> {Index[Neutrinos], Index[Generation]},
1640 Value -> {f0B0sK[ii_,ll_] -> (14.0162*zB0sK[ii,ll]^3 + 0.24*zB0sK[ii,ll]^2 + 0.089*zB0sK[ii,ll] + 0.2203)},
1641 Description -> "Average f0 form factor in B0s to K+ decays"
1642 },
1643
1644 fminusB0sK == {
1645 ParameterType -> Internal,
1646 Indices -> {Index[Neutrinos], Index[Generation]},
1647 Value -> {fminusB0sK[ii_,ll_] -> (MK^2-MB0s^2)/avq2B0sK[ii,ll]*(f0B0sK[ii,ll]-fplusB0sK[ii,ll])},
1648 Description -> "Average f- form factor in B0s to K+ decays"
1649 },
1650
1651 yl == {
1652 ParameterType -> Internal,
1653 Indices -> {Index[Generation], Index[Generation]},
1654 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1655 Value -> {yl[1,1] -> Sqrt[2] yme /vev, yl[2,2] -> Sqrt[2] ymm /vev, yl[3,3] -> Sqrt[2] ymtau /vev},
1656 InteractionOrder -> {QED, 1},
1657 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
1658 TeX -> Superscript[y, l],
1659 Description -> "Lepton Yukawa couplings"
1660 },
1661 yu == {
1662 ParameterType -> Internal,
1663 Indices -> {Index[Generation], Index[Generation]},
1664 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1665 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
1666 InteractionOrder -> {QED, 1},
1667 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
1668 TeX -> Superscript[y, u],
1669 Description -> "Up-type Yukawa couplings"
1670 },
1671 yd == {
1672 ParameterType -> Internal,
1673 Indices -> {Index[Generation], Index[Generation]},
1674 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1675 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
1676 InteractionOrder -> {QED, 1},
1677 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
1678 TeX -> Superscript[y, d],
1679 Description -> "Down-type Yukawa couplings"
1680 },
1681
1682 CKM == {
1683 ParameterType -> Internal,
1684 Indices -> {Index[Generation], Index[Generation]},
1685 Unitary -> True,
1686 Value -> {CKM[1,1] -> Cos[cabi] Cos[th13], CKM[1,2] -> Sin[cabi] Cos[th13], CKM[1,3] -> Sin[th13] Exp[-I del13],
1687 CKM[2,1] -> -Sin[cabi] Cos[th23] - Cos[cabi] Sin[th23] Sin[th13] Exp[I del13], CKM[2,2] -> Cos[cabi] Cos[th23] - Sin[cabi] Sin[th23] Sin[th13] Exp[I del13], CKM[2,3] -> Sin[th23] Cos[th13],
1688 CKM[3,1] -> Sin[cabi] Sin[th23] - Cos[cabi] Cos[th23] Sin[th13] Exp[I del13], CKM[3,2] -> -Cos[cabi] Sin[th23] - Sin[cabi] Cos[th23] Sin[th13] Exp[I del13], CKM[3,3] -> Cos[th23] Cos[th13]},
1689 TeX -> Superscript[V,CKM],
1690 Description -> "CKM-Matrix"},
1691
1692 HEAV == {
1693 ParameterType -> Internal,
1694 Indices -> {Index[Heavynus],Index[Neutrinos]},
1695 Value -> {HEAV[1,1] -> 0, HEAV[1,2] -> 0, HEAV[1,3] -> I*Sqrt[(1-r)/2], HEAV[1,4] -> Sqrt[(1+r)/2]},
1696TeX -> Superscript[U,n],
1697ComplexParameter -> True,
1698 Description -> "Mass eigenstate component of right-handed nu"},
1699
1700
1701 PMNS == {
1702 ParameterType -> Internal,
1703 Indices -> {Index[Generation], Index[Neutrinos]},
1704 Unitary -> False,
1705 Value -> {PMNS[1,1] -> If[thetae == thetamu && thetamu == thetatau, 1/Sqrt[2], (thetatau-thetamu)/Sqrt[3*thetatot^2-thetas*Conjugate[thetas]]],
1706 PMNS[1,2] -> If[thetae == thetamu && thetamu == thetatau, -1/Sqrt[6], (thetas*Conjugate[thetae]-thetatot^2)/(thetatot*Sqrt[3*thetatot^2-thetas*Conjugate[thetas]])],
1707 PMNS[1,3] -> If[thetae == thetamu && thetamu == thetatau, -I*Sqrt[(1+r)/6], -I*Conjugate[thetae]*Sqrt[(1+r)/2]/thetatot],
1708 PMNS[1,4] -> If[thetae == thetamu && thetamu == thetatau, Sqrt[(1-r)/6], Sqrt[2/(1+r)]*r*Conjugate[thetae]],
1709 PMNS[2,1] -> If[thetae == thetamu && thetamu == thetatau, -1/Sqrt[2], (thetae-thetatau)/Sqrt[3*thetatot^2-thetas*Conjugate[thetas]]],
1710 PMNS[2,2] -> If[thetae == thetamu && thetamu == thetatau, -1/Sqrt[6], (thetas*Conjugate[thetamu]-thetatot^2)/(thetatot*Sqrt[3*thetatot^2-thetas*Conjugate[thetas]])],
1711 PMNS[2,3] -> If[thetae == thetamu && thetamu == thetatau, -I*Sqrt[(1+r)/6], -I*Conjugate[thetamu]*Sqrt[(1+r)/2]/thetatot],
1712 PMNS[2,4] -> If[thetae == thetamu && thetamu == thetatau, Sqrt[(1-r)/6], Sqrt[2/(1+r)]*r*Conjugate[thetamu]],
1713 PMNS[3,1] -> If[thetae == thetamu && thetamu == thetatau, 0, (thetamu-thetae)/Sqrt[3*thetatot^2-thetas*Conjugate[thetas]]],
1714 PMNS[3,2] -> If[thetae == thetamu && thetamu == thetatau, Sqrt[2/3], (thetas*Conjugate[thetatau]-thetatot^2)/(thetatot*Sqrt[3*thetatot^2-thetas*Conjugate[thetas]])],
1715 PMNS[3,3] -> If[thetae == thetamu && thetamu == thetatau, -I*Sqrt[(1+r)/6], -I*Conjugate[thetatau]*Sqrt[(1+r)/2]/thetatot],
1716 PMNS[3,4] -> If[thetae == thetamu && thetamu == thetatau, Sqrt[(1-r)/6], Sqrt[2/(1+r)]*r*Conjugate[thetatau]]},
1717 TeX -> Superscript[U,PMNS],
1718 ComplexParameter -> True,
1719 Description -> "PMNS-Matrix"}
1720};
1721
1722
1723
1724(* ************************** *)
1725(* ***** Lagrangian ***** *)
1726(* For consistency we do not *)
1727(* add quarks with mesons *)
1728(* ************************** *)
1729
1730LGauge := Block[{mu,nu,ii,aa},
1731 ExpandIndices[-1/4 FS[B,mu,nu] FS[B,mu,nu] - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa], FlavorExpand->SU2W]];
1732
1733LQuarks := Block[{mu},
1734 ExpandIndices[I*(
1735 QLbar.Ga[mu].DC[QL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu]),
1736 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c], PMNS[b_,a_] Conjugate[PMNS[c_,a_]]->IndexDelta[b,c], HEAV[b_,a_] Conjugate[HEAV[c_,a_]]->IndexDelta[b,c], PMNS[a_,b_] Conjugate[PMNS[a_,c_]] ->IndexDelta[b,c] - HEAV[1,b] Conjugate[HEAV[1,c]]}];
1737
1738LFermions := Block[{mu},
1739 ExpandIndices[I*(
1740 LLbar.Ga[mu].DC[LL, mu] + lRbar.Ga[mu].DC[lR, mu] + NRcbar.Ga[mu].DC[NRc, mu] ),
1741 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c], PMNS[b_,a_] Conjugate[PMNS[c_,a_]]->IndexDelta[b,c], HEAV[b_,a_] Conjugate[HEAV[c_,a_]]->IndexDelta[b,c], PMNS[a_,b_] Conjugate[PMNS[a_,c_]] ->IndexDelta[b,c] - HEAV[1,b] Conjugate[HEAV[1,c]]}];
1742
1743LHiggs := Block[{ii,mu, feynmangaugerules},
1744 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
1745 ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
1746 ];
1747
1748LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
1749 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
1750
1751 yuk = ExpandIndices[
1752 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
1753 yl[ff1, ff3] LLbar[sp, ii, ff1].lR[sp, ff3] Phi[ii] -
1754 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj] - yN[ff1, ff2] LLbar[sp, ii, ff1].NR[sp, ff2] Phibar[jj] Eps[ii, jj] - MN4/2 NRcbar[sp,ff1].NR[sp,ff1] , FlavorExpand -> SU2D];
1755 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c], PMNS[b_,a_] Conjugate[PMNS[c_,a_]]->IndexDelta[b,c], HEAV[b_,a_] Conjugate[HEAV[c_,a_]]->IndexDelta[b,c], PMNS[a_,b_] Conjugate[PMNS[a_,c_]] ->IndexDelta[b,c] - HEAV[1,b] Conjugate[HEAV[1,c]]};
1756 yuk+HC[yuk]/.feynmangaugerules
1757 ];
1758
1759LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
1760 (* Pure gauge piece *)
1761 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
1762 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
1763 LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
1764
1765(***********************************)
1766(*** Meson interactions ***)
1767(***********************************)
1768
1769(*LHadr := Block[{mu,nu,ii,jj,kk,ff1,ff2,ff3,ff4,ff5,yhad},*)
1770LHadr := Block[{mu,nu,ii,jj,kk,ff1,ff2,ff3,yhad},
1771 yhad = ExpandIndices[
1772
1773(*** Charged pseudoscalars ***)
1774
1775(*K*)
1776
17771/2 DC[Kbar,mu] DC[K,mu] - MK^2/2 Kbar K
1778+ Sum[I*Sqrt[2]*Gf*fK*CKM[1,2] Kbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1],{ff1,1,4},{ff2,1,3}]
1779- Sum[I*Sqrt[2]*Gf*fK*CKM[1,2] Kbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1],{ff1,3,4},{ff2,1,3}]
1780
1781(* Pi *)
1782
1783+ 1/2 DC[Pipbar,mu] DC[Pip,mu] - MPip^2/2 Pipbar Pip
1784+ Sum[I*Sqrt[2]*Gf*fpi*CKM[1,1] Pipbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
1785- Sum[I*Sqrt[2]*Gf*fpi*CKM[1,1] Pipbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,3,4},{ff2,1,3}]
1786
1787(*D*)
1788
1789+ 1/2 DC[Ddbar,mu] DC[Dd,mu] - MDd^2/2 Ddbar Dd
1790+ Sum[I*Sqrt[2]*Gf*fD*CKM[2,1] Ddbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
1791- Sum[I*Sqrt[2]*Gf*fD*CKM[2,1] Ddbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,3,4},{ff2,1,3}]
1792
1793(*Ds*)
1794
1795+ 1/2 DC[Dsbar,mu] DC[Ds,mu] - MDs^2/2 Dsbar Ds
1796+ Sum[I*Sqrt[2]*Gf*fDs*CKM[2,2] Dsbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
1797- Sum[I*Sqrt[2]*Gf*fDs*CKM[2,2] Dsbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,3,4},{ff2,1,3}]
1798
1799(*B*)
1800
1801+ 1/2 DC[Bubar,mu] DC[Bu,mu] - MBu^2/2 Bubar Bu
1802+ Sum[I*Sqrt[2]*Gf*fB*CKM[1,3] Bubar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
1803- Sum[I*Sqrt[2]*Gf*fB*CKM[1,3] Bubar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,3,4},{ff2,1,3}]
1804
1805(*Bc*)
1806
1807+ 1/2 DC[Bcbar,mu] DC[Bc,mu] - MBc^2/2 Bcbar Bc
1808+ Sum[I*Sqrt[2]*Gf*fBc*CKM[2,3] Bcbar PMNS[ff2,ff1] yl[ff2,ff2] vev/Sqrt[2] lbar[ii, ff2].ProjM[ii,jj].vl[jj, ff1] ,{ff1,1,4},{ff2,1,3}]
1809- Sum[I*Sqrt[2]*Gf*fBc*CKM[2,3] Bcbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii, ff2].ProjP[ii,jj].vl[jj, ff1] ,{ff1,3,4},{ff2,1,3}]
1810
1811(*** Neutral pseudoscalars ***)
1812
1813(* pi0 *)
1814
1815+ 1/4 DC[Pi0,mu] DC[Pi0,mu] - MPi0^2/4 Pi0 Pi0
1816- Sum[I/2*Gf*fpi Pi0 Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff2,ff2] vlbar[ii, ff1].ProjP[ii,jj].vl[jj, ff2] ,{ff1,1,4},{ff2,3,4},{ff3,1,3}]
1817+ Sum[I/2*Gf*fpi Pi0 Conjugate[PMNS[ff3,ff1]] PMNS[ff3,ff2] numass[ff1,ff1] vlbar[ii, ff1].ProjM[ii,jj].vl[jj, ff2] ,{ff1,3,4},{ff2,1,4},{ff3,1,3}]
1818
1819(* eta *)
1820
1821+ 1/4 DC[Etabar,mu] DC[Eta,mu] - Meta^2/4 Eta Eta
1822- Sum[I/2*Gf*feta Eta Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff2,ff2] vlbar[ii, ff1].ProjP[ii,jj].vl[jj, ff2] ,{ff1,1,4},{ff2,3,4},{ff3,1,3}]
1823+ Sum[I/2*Gf*feta Eta Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff1,ff1] vlbar[ii, ff1].ProjM[ii,jj].vl[jj, ff2] ,{ff1,1,4},{ff2,1,4},{ff3,1,3}]
1824
1825(* eta^' *)
1826
1827+ 1/4 DC[Etapbar,mu] DC[Etap,mu] - Metap^2/4 Etap Etap
1828- Sum[I/2*Gf*fetap Etap Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff2,ff2] vlbar[ii, ff1].ProjP[ii,jj].vl[jj, ff2] ,{ff1,1,4},{ff2,3,4},{ff3,1,3}]
1829+ Sum[I/2*Gf*fetap Etap Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] numass[ff1,ff1] vlbar[ii, ff1].ProjM[ii,jj].vl[jj, ff2] ,{ff1,3,4},{ff2,1,4},{ff3,1,3}]
1830
1831(*** Neutral vector mesons ***)
1832
1833(* rho0 *)
1834
1835-1/8 FS[rho0,mu,nu] FS[rho0,mu,nu] + Mrho0^2/4 rho0[mu] rho0[mu]
1836- Sum[1/2*Gf*frho*(1-2*sw^2) rho0[mu] Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] vlbar[ii, ff1].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk, ff2] ,{ff1,1,4},{ff2,1,4},{ff3,1,3}]
1837
1838(* omega *)
1839
1840-1/8 FS[omega,mu,nu] FS[omega,mu,nu] + Mom^2/4 omega[mu] omega[mu]
1841+ Sum[1/2*Gf*fomega*(2/3*sw^2) omega[mu] Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] vlbar[ii,ff1].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff2] ,{ff1,1,4},{ff2,1,4},{ff3,1,3}]
1842
1843(* phi *)
1844
1845-1/8 FS[phimeson,mu,nu] FS[phimeson,mu,nu] + Mphi^2/4 phimeson[mu] phimeson[mu]
1846+ Sum[1/2*Sqrt[2]*Gf*fphi*(1/2 - 2/3*sw^2) phimeson[mu] Conjugate[PMNS[ff3,ff1]]PMNS[ff3,ff2] vlbar[ii,ff1].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff2] ,{ff1,1,4},{ff2,1,4},{ff3,1,3}]
1847
1848(*** Charged vector mesons ***)
1849
1850(* Rho *)
1851
1852-1/4 FS[rhobar,mu,nu] FS[rho,mu,nu] + Mrho^2/2 rhobar[mu] rho[mu]
1853- Sum[Sqrt[2]*Gf*frho*CKM[1,1] PMNS[ff2,ff1] lbar[ii, ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] rhobar[mu] ,{ff1,1,4},{ff2,1,3}]
1854
1855(* Kstar *)
1856
1857-1/4 FS[Kstarbar,mu,nu] FS[Kstar,mu,nu] + MKstar^2/2 Kstarbar[mu] Kstar[mu]
1858- Sum[Sqrt[2]*Gf*fKstar*CKM[1,2] PMNS[ff2,ff1] lbar[ii, ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] Kstarbar[mu] ,{ff1,1,4},{ff2,1,3}]
1859
1860(*** Semileptonic decays: ***)
1861
1862(* K -> pi0 l nu and K0 -> pip l nu *)
1863
1864+ 1/2 DC[K0bar,mu] DC[K0,mu] - MK0^2/2 K0bar K0
1865
1866-Sum[2*Sqrt[2]*Gf*CKM[1,2]*fplusK0Pi[ff1,ff2]*I del[Pipbar,mu] K0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
1867+Sum[Sqrt[2]*Gf*CKM[1,2]*(fplusK0Pi[ff1,ff2] - fminusK0Pi[ff1,ff2])*vev/Sqrt[2] Pipbar K0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
1868-Sum[Sqrt[2]*Gf*CKM[1,2]*(fplusK0Pi[ff1,ff2] - fminusK0Pi[ff1,ff2]) Pipbar K0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,3,4},{ff2,1,2}]
1869
1870-Sum[2*Gf*CKM[1,2]*fplusKPi0[ff1,ff2]*I del[Pi0,mu] Kbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
1871+Sum[Gf*CKM[1,2]*(fplusKPi0[ff1,ff2] - fminusKPi0[ff1,ff2])*vev/Sqrt[2] Pi0 Kbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
1872-Sum[Gf*CKM[1,2]*(fplusKPi0[ff1,ff2] - fminusKPi0[ff1,ff2]) Pi0 Kbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1],{ff1,3,4},{ff2,1,2}]
1873
1874(* D -> K0 l nu and D0 -> K l nu *)
1875
1876+ 1/2 DC[D0bar,mu] DC[D0,mu] - MD0^2/2 D0bar D0
1877
1878-Sum[2*Sqrt[2]*Gf*CKM[2,2]*fplusDK[ff1,ff2]*I del[Kbar,mu] D0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
1879+Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2] - fminusDK[ff1,ff2])*vev/Sqrt[2] Kbar D0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
1880-Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2] - fminusDK[ff1,ff2]) Kbar D0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1],{ff1,3,4},{ff2,1,2}]
1881
1882-Sum[2*Sqrt[2]*Gf*CKM[2,2]*fplusDK[ff1,ff2]*I del[K0bar,mu] Ddbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1],{ff1,1,4},{ff2,1,2}]
1883+Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2]-fminusDK[ff1,ff2])*vev/Sqrt[2] K0bar Ddbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1],{ff1,1,4},{ff2,1,2}]
1884-Sum[Sqrt[2]*Gf*CKM[2,2]*(fplusDK[ff1,ff2]-fminusDK[ff1,ff2]) K0bar Ddbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1],{ff1,3,4},{ff2,1,2}]
1885
1886(* B+ -> pi0 l nu and B0 -> pi+ l nu *)
1887
1888+ 1/2 DC[B0bar,mu] DC[B0,mu] - MB0^2/2 B0bar B0
1889
1890-Sum[2*Gf*CKM[1,3]*fplusBPi0[ff1,ff2]*I del[Pi0,mu] Bubar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
1891+Sum[Gf*CKM[1,3]*(fplusBPi0[ff1,ff2] - fminusBPi0[ff1,ff2])*vev/Sqrt[2] Pi0 Bubar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
1892-Sum[Gf*CKM[1,3]*(fplusBPi0[ff1,ff2] - fminusBPi0[ff1,ff2]) Pi0 Bubar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,3,4},{ff2,1,3}]
1893
1894-Sum[2*Sqrt[2]*Gf*CKM[1,3]*fplusB0Pi[ff1,ff2]*I del[Pipbar,mu] B0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
1895+Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0Pi[ff1,ff2] - fminusB0Pi[ff1,ff2])*vev/Sqrt[2] Pipbar B0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
1896-Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0Pi[ff1,ff2] - fminusB0Pi[ff1,ff2]) Pipbar B0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,3,4},{ff2,1,3}]
1897
1898(* B+ -> D0 l nu, B0 -> D+ l nu and B0s -> Ds+ l nu *)
1899
1900-Sum[2*Sqrt[2]*Gf*CKM[2,3]*fplusBD0[ff1,ff2]*I del[D0bar,mu] Bubar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
1901+Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusBD0[ff1,ff2]-fminusBD0[ff1,ff2])*vev/Sqrt[2] D0bar Bubar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
1902-Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusBD0[ff1,ff2]-fminusBD0[ff1,ff2]) D0bar Bubar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,3,4},{ff2,1,3}]
1903
1904-Sum[2*Sqrt[2]*Gf*CKM[2,3]fplusB0D[ff1,ff2]*I del[Ddbar,mu] B0bar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
1905+Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0D[ff1,ff2] - fminusB0D[ff1,ff2])*vev/Sqrt[2] Ddbar B0bar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
1906-Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0D[ff1,ff2] - fminusB0D[ff1,ff2]) Ddbar B0bar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,3,4},{ff2,1,3}]
1907
1908+ 1/2 DC[B0sbar,mu] DC[B0s,mu] - MB0s^2/2 B0sbar B0s
1909
1910-Sum[2*Sqrt[2]*Gf*CKM[2,3]*fplusB0sDs[ff1,ff2]*I del[Dsbar,mu] B0sbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
1911+Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0sDs[ff1,ff2] - fminusB0sDs[ff1,ff2])*vev/Sqrt[2] Dsbar B0sbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
1912-Sum[Sqrt[2]*Gf*CKM[2,3]*(fplusB0sDs[ff1,ff2] - fminusB0sDs[ff1,ff2]) Dsbar B0sbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,3,4},{ff2,1,3}]
1913
1914(* B0s -> K+ l nu *)
1915
1916-Sum[2*Sqrt[2]*Gf*CKM[1,3]*fplusB0sK[ff1,ff2]*I del[Kbar,mu] B0sbar PMNS[ff2,ff1] lbar[ii,ff2].Ga[mu,ii,jj].ProjM[jj,kk].vl[kk,ff1] ,{ff1,1,4},{ff2,1,3}]
1917+Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0sK[ff1,ff2] - fminusB0sK[ff1,ff2])*vev/Sqrt[2] Kbar B0sbar PMNS[ff2,ff1] yl[ff2,ff2] lbar[ii,ff2].ProjM[ii,jj].vl[jj,ff1] ,{ff1,1,4},{ff2,1,3}]
1918-Sum[Sqrt[2]*Gf*CKM[1,3]*(fplusB0sK[ff1,ff2] - fminusB0sK[ff1,ff2]) Kbar B0sbar PMNS[ff2,ff1] numass[ff1,ff1] lbar[ii,ff2].ProjP[ii,jj].vl[jj,ff1] ,{ff1,3,4},{ff2,1,3}]
1919
1920
1921
1922, FlavorExpand->{SU2D,SU2W}];
1923yhad+HC[yhad]
1924 ];
1925
1926
1927 (* Scalar pieces: see Peskin pages 739-742 *)
1928 (* phi1 and phi2 are the real degrees of freedom of GP *)
1929 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
1930 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
1931 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
1932 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
1933 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
1934 doublet0 = {0, vev/Sqrt[2]};
1935 Vectorize[{a_, b_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]}/.{Im[_]->0, Re[num_]->num}];
1936 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
1937 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
1938
1939ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
1940
1941LagHeavyN:= LGauge + LFermions + LHiggs + LYukawa + LGhost + If[Mesons,LHadr,LQuarks];