HNLs: effective_HeavyN_Dirac.fr

File effective_HeavyN_Dirac.fr, 72.5 KB (added by ManuelGonzalezLopez, 3 years ago)

Model file for Dirac 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$ModelName = "effective_HeavyN_Dirac_v103";
15
16M$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 -> False,
265 Mass -> {Mnu, 0,0,0, {MassN4, Internal}},
266 Width -> {0, 0, 0, {WN, 0}},
267 QuantumNumbers -> {LeptonNumber -> 1},
268 PropagatorLabel -> {"v", "v1", "v2", "v3","N4"} ,
269 PropagatorType -> S,
270 PropagatorArrow -> Forward,
271 PDG -> {12000,14000,16000,18000},
272 ParticleName -> {"v1","v2","v3","N4"},
273 AntiParticleName -> {"v1~","v2~","v3~","N4~"},
274 FullName -> {"neutrino1", "neutrino2", "neutrino3","Heavy-neutrino"}
275 },
276
277 F[2] == {
278 ClassName -> l,
279 ClassMembers -> {e, mu, ta},
280 Indices -> {Index[Generation]},
281 FlavorIndex -> Generation,
282 SelfConjugate -> False,
283 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
284 Width -> 0,
285 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
286 PropagatorLabel -> {"l", "e", "mu", "ta"},
287 PropagatorType -> Straight,
288 PropagatorArrow -> Forward,
289 PDG -> {11, 13, 15},
290 ParticleName -> {"e-", "mu-", "ta-"},
291 AntiParticleName -> {"e+", "mu+", "ta+"},
292 FullName -> {"Electron", "Muon", "Tau"}
293 },
294 F[3] == {
295 ClassName -> uq,
296 ClassMembers -> {u, c, t},
297 Indices -> {Index[Generation], Index[Colour]},
298 FlavorIndex -> Generation,
299 SelfConjugate -> False,
300 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
301 Width -> {0, 0, {WT,1.50833649}},
302 QuantumNumbers -> {Q -> 2/3},
303 PropagatorLabel -> {"uq", "u", "c", "t"},
304 PropagatorType -> Straight,
305 PropagatorArrow -> Forward,
306 PDG -> {2, 4, 6},
307 ParticleName -> {"u", "c", "t" },
308 AntiParticleName -> {"u~", "c~", "t~"},
309 FullName -> {"u-quark", "c-quark", "t-quark"}
310 },
311 F[4] == {
312 ClassName -> dq,
313 ClassMembers -> {d, s, b},
314 Indices -> {Index[Generation], Index[Colour]},
315 FlavorIndex -> Generation,
316 SelfConjugate -> False,
317 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
318 Width -> 0,
319 QuantumNumbers -> {Q -> -1/3},
320 PropagatorLabel -> {"dq", "d", "s", "b"},
321 PropagatorType -> Straight,
322 PropagatorArrow -> Forward,
323 PDG -> {1,3,5},
324 ParticleName -> {"d", "s", "b" },
325 AntiParticleName -> {"d~", "s~", "b~"},
326 FullName -> {"d-quark", "s-quark", "b-quark"}
327 },
328
329(* Fermions: unphysical fields *)
330 F[11] == {
331 ClassName -> LL,
332 Unphysical -> True,
333 Indices -> {Index[SU2D], Index[Generation]},
334 FlavorIndex -> SU2D,
335 SelfConjugate -> False,
336 QuantumNumbers -> {Y -> -1/2},
337 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]] }
338 },
339 F[12] == {
340 ClassName -> lR,
341 Unphysical -> True,
342 Indices -> {Index[Generation]},
343 FlavorIndex -> Generation,
344 SelfConjugate -> False,
345 QuantumNumbers -> {Y -> -1},
346 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
347 },
348 F[13] == {
349 ClassName -> QL,
350 Unphysical -> True,
351 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
352 FlavorIndex -> SU2D,
353 SelfConjugate -> False,
354 QuantumNumbers -> {Y -> 1/6},
355 Definitions -> {
356 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
357 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
358 },
359 F[14] == {
360 ClassName -> uR,
361 Unphysical -> True,
362 Indices -> {Index[Generation], Index[Colour]},
363 FlavorIndex -> Generation,
364 SelfConjugate -> False,
365 QuantumNumbers -> {Y -> 2/3},
366 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
367 },
368 F[15] == {
369 ClassName -> dR,
370 Unphysical -> True,
371 Indices -> {Index[Generation], Index[Colour]},
372 FlavorIndex -> Generation,
373 SelfConjugate -> False,
374 QuantumNumbers -> {Y -> -1/3},
375 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
376 },
377 F[16] == {
378 ClassName -> NR,
379 Unphysical -> True,
380 Indices -> {Index[Heavynus]},
381 FlavorIndex -> Heavynus,
382 SelfConjugate -> False,
383 Definitions -> { NR[sp1_,ff_] :> Module[{sp2,ff2}, HEAVR[ff,ff2] ProjP[sp1,sp2] vl[sp2,ff2]] }
384 },
385 F[17] == {
386 ClassName -> NL,
387 Unphysical -> True,
388 Indices -> {Index[Heavynus]},
389 FlavorIndex -> Heavynus,
390 SelfConjugate -> False,
391 Definitions -> { NL[sp1_,ff_] :> Module[{sp2,ff2}, HEAV[ff,ff2] ProjM[sp1,sp2] vl[sp2,ff2]] }
392 },
393
394
395(* Higgs: physical scalars *)
396 S[1] == {
397 ClassName -> H,
398 SelfConjugate -> True,
399 Mass -> {MH,125.1},
400 Width -> {WH,0.00407},
401 PropagatorLabel -> "H",
402 PropagatorType -> D,
403 PropagatorArrow -> None,
404 PDG -> 25,
405 ParticleName -> "H",
406 FullName -> "H"
407 },
408
409(* Higgs: physical scalars *)
410 S[2] == {
411 ClassName -> G0,
412 SelfConjugate -> True,
413 Goldstone -> Z,
414 Mass -> {MZ, 91.1876},
415 Width -> {WZ, 2.4952},
416 PropagatorLabel -> "Go",
417 PropagatorType -> D,
418 PropagatorArrow -> None,
419 PDG -> 250,
420 ParticleName -> "G0",
421 FullName -> "G0"
422 },
423 S[3] == {
424 ClassName -> GP,
425 SelfConjugate -> False,
426 Goldstone -> W,
427 Mass -> {MW, Internal},
428 QuantumNumbers -> {Q -> 1},
429 Width -> {WW, 2.085},
430 PropagatorLabel -> "GP",
431 PropagatorType -> D,
432 PropagatorArrow -> None,
433 PDG -> 251,
434 ParticleName -> "G+",
435 AntiParticleName -> "G-",
436 FullName -> "GP"
437 },
438
439
440(* Pseudoscalar mesons *)
441 S[4] == {
442 ClassName -> K,
443 SelfConjugate -> False,
444 Mass -> {MK,0.493677},
445 QuantumNumbers -> {Q -> 1},
446 Width -> {WK,0},
447 PropagatorLabel -> "K",
448 PropagatorType -> D,
449 PropagatorArrow -> None,
450 PDG -> 321,
451 ParticleName -> "K+",
452 AntiParticleName -> "K-",
453 FullName -> "Charged Kaon"
454 },
455
456 S[5] == {
457 ClassName -> Pip,
458 SelfConjugate -> False,
459 Mass -> {MPip,0.13957},
460 QuantumNumbers -> {Q -> 1},
461 Width -> {WPip, 0},
462 PropagatorLabel -> "Pi",
463 PropagatorType -> D,
464 PropagatorArrow -> None,
465 PDG -> 211,
466 ParticleName -> "Pi+",
467 AntiParticleName -> "Pi-",
468 FullName -> "Charged Pion"
469 },
470
471 S[6] == {
472 ClassName -> Dd,
473 SelfConjugate -> False,
474 Mass -> {MDd,1.869},
475 QuantumNumbers -> {Q -> 1},
476 Width -> {WD, 0},
477 PropagatorLabel -> "Dd",
478 PropagatorType -> D,
479 PropagatorArrow -> None,
480 PDG -> 411,
481 ParticleName -> "D+",
482 AntiParticleName -> "D-",
483 FullName -> "Charged D"
484 },
485
486 S[13] == {
487 ClassName -> D0,
488 SelfConjugate -> False,
489 Mass -> {MD0,1.865},
490 QuantumNumbers -> {Q -> 0},
491 Width -> {WD0,0},
492 PropagatorLabel -> "D0",
493 PropagatorType -> D,
494 PropagatorArrow -> None,
495 PDG -> 421,
496 ParticleName -> "D0",
497 AntiParticleName -> "D0bar",
498 FullName -> "Neutral D"
499 },
500
501 S[7] == {
502 ClassName -> Pi0,
503 SelfConjugate -> True,
504 Mass -> {MPi0,0.13498},
505 Width -> {WPi0, 0},
506 PropagatorLabel -> "Pi0",
507 PropagatorType -> D,
508 PropagatorArrow -> None,
509 PDG -> 111,
510 ParticleName -> "Pi0",
511 FullName -> "Neutral Pion"
512 },
513
514 S[12] == {
515 ClassName -> K0,
516 SelfConjugate -> False,
517 Mass -> {MK0,0.497611},
518 QuantumNumbers -> {Q -> 0},
519 Width -> {WK0,0},
520 PropagatorLabel -> "K0",
521 PropagatorType -> D,
522 PropagatorArrow -> None,
523 PDG -> 311,
524 ParticleName -> "K0",
525 AntiParticleName -> "K0bar",
526 FullName -> "Neutral Kaon"
527 },
528
529 S[8] == {
530 ClassName -> Eta,
531 SelfConjugate -> True,
532 Mass -> {Meta,0.54786},
533 Width -> {Weta, 0},
534 PropagatorLabel -> "eta",
535 PropagatorType -> D,
536 PropagatorArrow -> None,
537 PDG -> 221,
538 ParticleName -> "Eta",
539 FullName -> "Eta"
540 },
541
542 S[9] == {
543 ClassName -> Etap,
544 SelfConjugate -> True,
545 Mass -> {Metap,0.9578},
546 Width -> {Wetap, 0},
547 PropagatorLabel -> "etap",
548 PropagatorType -> D,
549 PropagatorArrow -> None,
550 PDG -> 331,
551 ParticleName -> "Etap",
552 FullName -> "Eta Prime"
553 },
554
555 S[10] == {
556 ClassName -> Ds,
557 SelfConjugate -> False,
558 Mass -> {MDs,1.9683},
559 QuantumNumbers -> {Q -> 1},
560 Width -> {WDs, 0},
561 PropagatorLabel -> "Ds",
562 PropagatorType -> D,
563 PropagatorArrow -> None,
564 PDG -> 431,
565 ParticleName -> "Ds+",
566 AntiParticleName -> "Ds-",
567 FullName -> "Charged Ds"
568 },
569
570 S[15] == {
571 ClassName -> Bu,
572 SelfConjugate -> False,
573 Mass -> {MBu,5.279},
574 QuantumNumbers -> {Q -> 1},
575 Width -> {WBu, 0},
576 PropagatorLabel -> "Bu",
577 PropagatorType -> D,
578 PropagatorArrow -> None,
579 PDG -> 521,
580 ParticleName -> "B+",
581 AntiParticleName -> "B-",
582 FullName -> "Charged B"
583 },
584
585 S[16] == {
586 ClassName -> Bc,
587 SelfConjugate -> False,
588 Mass -> {MBc,6.275},
589 QuantumNumbers -> {Q -> 1},
590 Width -> {WBc, 0},
591 PropagatorLabel -> "Bc",
592 PropagatorType -> D,
593 PropagatorArrow -> None,
594 PDG -> 541,
595 ParticleName -> "Bc+",
596 AntiParticleName -> "Bc-",
597 FullName -> "Charged Bc"
598 },
599
600 S[17] == {
601 ClassName -> B0,
602 SelfConjugate -> False,
603 Mass -> {MB0,5.280},
604 QuantumNumbers -> {Q -> 0},
605 Width -> {WB0,0},
606 PropagatorLabel -> "B0",
607 PropagatorType -> D,
608 PropagatorArrow -> None,
609 PDG -> 511,
610 ParticleName -> "B0",
611 AntiParticleName -> "B0bar",
612 FullName -> "Neutral B"
613 },
614
615 S[18] == {
616 ClassName -> B0s,
617 SelfConjugate -> False,
618 Mass -> {MB0s,5.367},
619 QuantumNumbers -> {Q -> 0},
620 Width -> {WB0s,0},
621 PropagatorLabel -> "B0s",
622 PropagatorType -> D,
623 PropagatorArrow -> None,
624 PDG -> 531,
625 ParticleName -> "B0s",
626 AntiParticleName -> "B0sbar",
627 FullName -> "Neutral Bs"
628 },
629
630(* Higgs: unphysical scalars *)
631 S[11] == {
632 ClassName -> Phi,
633 Unphysical -> True,
634 Indices -> {Index[SU2D]},
635 FlavorIndex -> SU2D,
636 SelfConjugate -> False,
637 QuantumNumbers -> {Y -> 1/2},
638 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
639 },
640
641(* Vector mesons *)
642
643
644 V[21] == {
645 ClassName -> rho0,
646 SelfConjugate -> True,
647 Mass -> {Mrho0, 0.77526},
648 Width -> {Wrho0, 0.1478},
649 ParticleName -> "rho0",
650 PDG -> 113,
651 PropagatorLabel -> "rho0",
652 PropagatorType -> Sine,
653 PropagatorArrow -> None,
654 FullName -> "rho 0"
655 },
656
657 V[22] == {
658 ClassName -> rho,
659 SelfConjugate -> False,
660 Mass -> {Mrho, 0.77511},
661 Width -> {Wrho, 0.1491},
662 ParticleName -> "rho+",
663 AntiParticleName -> "rho-",
664 QuantumNumbers -> {Q -> 1},
665 PDG -> 213,
666 PropagatorLabel -> "rho",
667 PropagatorType -> Sine,
668 PropagatorArrow -> Forward,
669 FullName -> "charged rho"
670 },
671
672
673 V[23] == {
674 ClassName -> omega,
675 SelfConjugate -> True,
676 Mass -> {Mom, 0.78265},
677 Width -> {Wom, 0.00849},
678 ParticleName -> "omega",
679 PDG -> 223,
680 PropagatorLabel -> "omega",
681 PropagatorType -> Sine,
682 PropagatorArrow -> None,
683 FullName -> "Omega"
684 },
685
686 V[24] == {
687 ClassName -> Kstar,
688 SelfConjugate -> False,
689 Mass -> {MKstar, 0.8917},
690 Width -> {WKstar, 0.0508},
691 ParticleName -> "Kstar+",
692 AntiParticleName -> "Kstar-",
693 QuantumNumbers -> {Q -> 1},
694 PDG -> 323,
695 PropagatorLabel -> "Kstar",
696 PropagatorType -> Sine,
697 PropagatorArrow -> Forward,
698 FullName -> "Charged Kstar"
699 },
700
701 V[25] == {
702 ClassName -> phimeson,
703 SelfConjugate -> True,
704 Mass -> {Mphi, 1.019461},
705 Width -> {Wphi, 0.004249},
706 ParticleName -> "phimeson",
707 PDG -> 333,
708 PropagatorLabel -> "phi",
709 PropagatorType -> Sine,
710 PropagatorArrow -> Forward,
711 FullName -> "phi meson"
712 },
713
714 V[26] == {
715 ClassName -> Bstar,
716 SelfConjugate -> False,
717 Mass -> {MBstar, 5.3247},
718 Width -> {WBstar, 0},
719 ParticleName -> "Bstar+",
720 AntiParticleName -> "Bstar-",
721 QuantumNumbers -> {Q -> 1},
722 PDG -> 523,
723 PropagatorLabel -> "Bstar",
724 PropagatorType -> Sine,
725 PropagatorArrow -> Forward,
726 FullName -> "Charged Bstar"
727 }
728
729};
730
731
732
733(* ************************** *)
734(* ***** Gauge ***** *)
735(* ***** Parameters ***** *)
736(* ***** (FeynArts) ***** *)
737(* ************************** *)
738
739GaugeXi[ V[1] ] = GaugeXi[A];
740GaugeXi[ V[2] ] = GaugeXi[Z];
741GaugeXi[ V[3] ] = GaugeXi[W];
742GaugeXi[ V[4] ] = GaugeXi[G];
743GaugeXi[ S[1] ] = 1;
744GaugeXi[ S[2] ] = GaugeXi[Z];
745GaugeXi[ S[3] ] = GaugeXi[W];
746GaugeXi[ U[1] ] = GaugeXi[A];
747GaugeXi[ U[2] ] = GaugeXi[Z];
748GaugeXi[ U[31] ] = GaugeXi[W];
749GaugeXi[ U[32] ] = GaugeXi[W];
750GaugeXi[ U[4] ] = GaugeXi[G];
751
752
753(* ************************** *)
754(* ***** Parameters ***** *)
755(* ************************** *)
756M$Parameters = {
757
758 (* External parameters *)
759 aEWM1 == {
760 ParameterType -> External,
761 BlockName -> SMINPUTS,
762 OrderBlock -> 1,
763 Value -> 127.9,
764 InteractionOrder -> {QED,-2},
765 Description -> "Inverse of the EW coupling constant at the Z pole"
766 },
767 Gf == {
768 ParameterType -> External,
769 BlockName -> SMINPUTS,
770 OrderBlock -> 2,
771 Value -> 1.16637*^-5,
772 InteractionOrder -> {QED,2},
773 TeX -> Subscript[G,f],
774 Description -> "Fermi constant"
775 },
776 aS == {
777 ParameterType -> External,
778 BlockName -> SMINPUTS,
779 OrderBlock -> 3,
780 Value -> 0.1184,
781 InteractionOrder -> {QCD,2},
782 TeX -> Subscript[\[Alpha],s],
783 Description -> "Strong coupling constant at the Z pole"
784 },
785 ymdo == {
786 ParameterType -> External,
787 BlockName -> YUKAWA,
788 OrderBlock -> 1,
789 Value -> 5.04*^-3,
790 Description -> "Down Yukawa mass"
791 },
792 ymup == {
793 ParameterType -> External,
794 BlockName -> YUKAWA,
795 OrderBlock -> 2,
796 Value -> 2.55*^-3,
797 Description -> "Up Yukawa mass"
798 },
799 yms == {
800 ParameterType -> External,
801 BlockName -> YUKAWA,
802 OrderBlock -> 3,
803 Value -> 0.101,
804 Description -> "Strange Yukawa mass"
805 },
806 ymc == {
807 ParameterType -> External,
808 BlockName -> YUKAWA,
809 OrderBlock -> 4,
810 Value -> 1.27,
811 Description -> "Charm Yukawa mass"
812 },
813 ymb == {
814 ParameterType -> External,
815 BlockName -> YUKAWA,
816 OrderBlock -> 5,
817 Value -> 4.7,
818 Description -> "Bottom Yukawa mass"
819 },
820 ymt == {
821 ParameterType -> External,
822 BlockName -> YUKAWA,
823 OrderBlock -> 6,
824 Value -> 172,
825 Description -> "Top Yukawa mass"
826 },
827 yme == {
828 ParameterType -> External,
829 BlockName -> YUKAWA,
830 OrderBlock -> 11,
831 Value -> 5.11*^-4,
832 Description -> "Electron Yukawa mass"
833 },
834 ymm == {
835 ParameterType -> External,
836 BlockName -> YUKAWA,
837 OrderBlock -> 13,
838 Value -> 0.10566,
839 Description -> "Muon Yukawa mass"
840 },
841 ymtau == {
842 ParameterType -> External,
843 BlockName -> YUKAWA,
844 OrderBlock -> 15,
845 Value -> 1.777,
846 Description -> "Tau Yukawa mass"
847 },
848 modthetae == {
849 ParameterType -> External,
850 BlockName -> YUKAWA,
851 OrderBlock -> 16,
852 Value -> 0.00001,
853 Description -> "Heavy-nu-electron mixing modulus"
854 },
855 argthetae == {
856 ParameterType -> External,
857 BlockName -> YUKAWA,
858 OrderBlock -> 17,
859 Value -> 0,
860 Description -> "Heavy-nu-electron mixing argument (degrees)"
861 },
862 thetae == {
863 ParameterType -> Internal,
864 BlockName -> YUKAWA,
865 Value -> modthetae*Exp[I*Pi/180*argthetae],
866 Description -> "Heavy-nu-electron mixing"
867 },
868 modthetamu == {
869 ParameterType -> External,
870 BlockName -> YUKAWA,
871 OrderBlock -> 18,
872 Value -> 0.00001,
873 Description -> "Heavy-nu-muon mixing modulus"
874 },
875 argthetamu == {
876 ParameterType -> External,
877 BlockName -> YUKAWA,
878 OrderBlock -> 19,
879 Value -> 0,
880 Description -> "Heavy-nu-muon mixing argument (degrees)"
881 },
882 thetamu == {
883 ParameterType -> Internal,
884 BlockName -> YUKAWA,
885 Value -> modthetamu*Exp[I*Pi/180*argthetamu],
886 Description -> "Heavy-nu-muon mixing"
887 },
888 modthetatau == {
889 ParameterType -> External,
890 BlockName -> YUKAWA,
891 OrderBlock -> 20,
892 Value -> 0.00001,
893 Description -> "Heavy-nu-tau mixing modulus"
894 },
895 argthetatau == {
896 ParameterType -> External,
897 BlockName -> YUKAWA,
898 OrderBlock -> 21,
899 Value -> 0,
900 Description -> "Heavy-nu-tau mixing argument (degrees)"
901 },
902 thetatau == {
903 ParameterType -> Internal,
904 BlockName -> YUKAWA,
905 Value -> modthetatau*Exp[I*Pi/180*argthetatau],
906 Description -> "Heavy-nu-tau mixing"
907 },
908 MN4 == {
909 ParameterType -> External,
910 BlockName -> YUKAWA,
911 OrderBlock -> 22,
912 Value -> 1.0,
913 Description -> "Majorana mass for N4 in GeV"
914 },
915
916 cabi == {
917 ParameterType -> External,
918 BlockName -> CKMBLOCK,
919 OrderBlock -> 1,
920 Value -> 0.227736,
921 TeX -> Subscript[\[Theta], c],
922 Description -> "Cabibbo angle"
923 },
924
925 th13 == {
926 ParameterType -> External,
927 ComplexParameter -> False,
928 BlockName -> CKMBLOCK,
929 OrderBlock -> 2,
930 Value -> 0.003508,
931 TeX -> Subscript[\[Theta], 13],
932 Description -> "CKM Theta 13"
933 },
934
935 th23 == {
936 ParameterType -> External,
937 ComplexParameter -> False,
938 BlockName -> CKMBLOCK,
939 OrderBlock -> 3,
940 Value -> 0.041539,
941 TeX -> Subscript[\[Theta], 23],
942 Description -> "CKM theta 23"
943 },
944
945 del13 == {
946 ParameterType -> External,
947 ComplexParameter -> False,
948 BlockName -> CKMBLOCK,
949 OrderBlock -> 4,
950 Value -> 1.20,
951 TeX -> Subscript[\[Delta], 13],
952 Description -> "CKM delta 13"
953 },
954
955 MassN4 == {
956 ParameterType -> Internal,
957 Value -> MN4,
958 Description -> "Heavy mass"
959 },
960
961 fK == {
962 ParameterType -> External,
963 BlockName -> MESONBLOCK,
964 OrderBlock -> 2,
965 Value -> 0.1556,
966 Description -> "Kaon decay constant"
967 },
968
969 fpi == {
970 ParameterType -> External,
971 BlockName -> MESONBLOCK,
972 OrderBlock -> 3,
973 Value -> 0.1302,
974 Description -> "Pion decay constant"
975 },
976
977 feta == {
978 ParameterType -> External,
979 BlockName -> MESONBLOCK,
980 OrderBlock -> 4,
981 Value -> 0.08159,
982 Description -> "Eta decay constant"
983 },
984
985 fetap == {
986 ParameterType -> External,
987 BlockName -> MESONBLOCK,
988 OrderBlock -> 5,
989 Value -> -0.0946,
990 Description -> "Eta prime decay constant"
991 },
992
993 fD == {
994 ParameterType -> External,
995 BlockName -> MESONBLOCK,
996 OrderBlock -> 6,
997 Value -> 0.212,
998 Description -> "D decay constant"
999 },
1000
1001 frho == {
1002 ParameterType -> External,
1003 BlockName -> MESONBLOCK,
1004 OrderBlock -> 7,
1005 Value -> 0.17,
1006 Description -> "rho decay constant"
1007 },
1008
1009 fKstar == {
1010 ParameterType -> External,
1011 BlockName -> MESONBLOCK,
1012 OrderBlock -> 34,
1013 Value -> 0.177,
1014 Description -> "Kstar decay constant"
1015 },
1016
1017 fDs == {
1018 ParameterType -> External,
1019 BlockName -> MESONBLOCK,
1020 OrderBlock -> 8,
1021 Value -> 0.249,
1022 Description -> "Ds decay constant"
1023 },
1024
1025 fomega == {
1026 ParameterType -> External,
1027 BlockName -> MESONBLOCK,
1028 OrderBlock -> 9,
1029 Value -> 0.155,
1030 Description -> "omega decay constant"
1031 },
1032
1033 fphi == {
1034 ParameterType -> External,
1035 BlockName -> MESONBLOCK,
1036 OrderBlock -> 10,
1037 Value -> 0.232,
1038 Description -> "phi decay constant"
1039 },
1040
1041 fB == {
1042 ParameterType -> External,
1043 BlockName -> MESONBLOCK,
1044 OrderBlock -> 11,
1045 Value -> 0.190,
1046 ComplexParameter -> False,
1047 Description -> "B decay constant"
1048 },
1049
1050 fBs == {
1051 ParameterType -> External,
1052 BlockName -> MESONBLOCK,
1053 OrderBlock -> 12,
1054 Value -> 0.230,
1055 ComplexParameter -> False,
1056 Description -> "Bs decay constant"
1057 },
1058
1059 fBc == {
1060 ParameterType -> External,
1061 BlockName -> MESONBLOCK,
1062 OrderBlock -> 13,
1063 Value -> 0.190,
1064 ComplexParameter -> False,
1065 Description -> "Bc decay constant"
1066 },
1067
1068
1069 (* Internal Parameters *)
1070 aEW == {
1071 ParameterType -> Internal,
1072 Value -> 1/aEWM1,
1073 InteractionOrder -> {QED,2},
1074 TeX -> Subscript[\[Alpha], EW],
1075 Description -> "Electroweak coupling contant"
1076 },
1077 MW == {
1078 ParameterType -> Internal,
1079 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-3.14/Sqrt[2]*aEW/Gf*MZ^2]],
1080 TeX -> Subscript[M,W],
1081 Description -> "W mass"
1082 },
1083 sw2 == {
1084 ParameterType -> Internal,
1085 Value -> 1-(MW/MZ)^2,
1086 Description -> "Squared Sin of the Weinberg angle"
1087 },
1088 ee == {
1089 ParameterType -> Internal,
1090 Value -> Sqrt[4 3.14 aEW],
1091 InteractionOrder -> {QED,1},
1092 TeX -> e,
1093 Description -> "Electric coupling constant"
1094 },
1095 cw == {
1096 ParameterType -> Internal,
1097 Value -> Sqrt[1-sw2],
1098 TeX -> Subscript[c,w],
1099 Description -> "Cosine of the Weinberg angle"
1100 },
1101 sw == {
1102 ParameterType -> Internal,
1103 Value -> Sqrt[sw2],
1104 TeX -> Subscript[s,w],
1105 Description -> "Sine of the Weinberg angle"
1106 },
1107 gw == {
1108 ParameterType -> Internal,
1109 Definitions -> {gw->ee/sw},
1110 InteractionOrder -> {QED,1},
1111 TeX -> Subscript[g,w],
1112 Description -> "Weak coupling constant at the Z pole"
1113 },
1114 g1 == {
1115 ParameterType -> Internal,
1116 Definitions -> {g1->ee/cw},
1117 InteractionOrder -> {QED,1},
1118 TeX -> Subscript[g,1],
1119 Description -> "U(1)Y coupling constant at the Z pole"
1120 },
1121 gs == {
1122 ParameterType -> Internal,
1123 Value -> Sqrt[4 3.14 aS],
1124 InteractionOrder -> {QCD,1},
1125 TeX -> Subscript[g,s],
1126 ParameterName -> G,
1127 Description -> "Strong coupling constant at the Z pole"
1128 },
1129 vev == {
1130 ParameterType -> Internal,
1131 Value -> 2*MW*sw/ee,
1132 InteractionOrder -> {QED,-1},
1133 Description -> "Higgs vacuum expectation value"
1134 },
1135 lam == {
1136 ParameterType -> Internal,
1137 Value -> MH^2/(2*vev^2),
1138 InteractionOrder -> {QED, 2},
1139 Description -> "Higgs quartic coupling"
1140 },
1141 muH == {
1142 ParameterType -> Internal,
1143 Value -> Sqrt[vev^2 lam],
1144 TeX -> \[Mu],
1145 Description -> "Coefficient of the quadratic piece of the Higgs potential"
1146 },
1147 thetatot == {
1148 ParameterType -> Internal,
1149 Value -> Sqrt[thetae*Conjugate[thetae]+thetamu*Conjugate[thetamu]+thetatau*Conjugate[thetatau]],
1150 TeX -> \[Theta],
1151 Description -> "Heavy-active mixing"
1152 },
1153 thetas == {
1154 ParameterType -> Internal,
1155 Value -> thetae+thetamu+thetatau,
1156 TeX -> Subscript[\[Theta],s],
1157 Description -> "Heavy-active mixing sum"
1158 },
1159 r == {
1160 ParameterType -> Internal,
1161 Value -> 1/Sqrt[1+thetatot^2],
1162 Description -> "useful ratio"
1163 },
1164 yN == {
1165 ParameterType -> Internal,
1166 Indices -> {Index[Generation], Index[Heavynus]},
1167 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},
1168 InteractionOrder -> {QED, 1},
1169 ParameterName -> {yN[1,1] -> yNe, yN[2,1] -> yNmu, yN[3,1] -> yNtau},
1170 TeX -> Superscript[y, N],
1171 Description -> "Heavy nu Yukawa couplings"
1172 },
1173 numass == {
1174 ParameterType -> Internal,
1175 Indices -> {Index[Neutrinos], Index[Neutrinos]},
1176 Value -> {numass[4,4] :> MN4, numass[ii_,jj_] :> 0},
1177 InteractionOrder -> {QED, 0},
1178 ParameterName -> {numass[1,1] :> mnu1, numass[2,2] :> mnu2, numass[3,3] :> mnu3, numass[4,4] :> mnu4},
1179 TeX -> Superscript[m, nu],
1180 Description -> "Neutrino mass"
1181 },
1182
1183 (** Form factors for K0 to Pi+ decays: linear parametrization **)
1184
1185 avq2K0Pi == {
1186 ParameterType -> Internal,
1187 Indices -> {Index[Neutrinos], Index[Generation]},
1188 Value -> {avq2K0Pi[ii_,ll_] ->
1189 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],
1190 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]]},
1191 Description -> "Average momentum transfer in K0 to Pi decays"
1192 },
1193
1194 fplusK0Pi == {
1195 ParameterType -> Internal,
1196 Indices -> {Index[Neutrinos], Index[Generation]},
1197 Value -> {fplusK0Pi[ii_,ll_] -> 0.9749*(1+0.0282*avq2K0Pi[ii,ll]/MPip^2)},
1198 Description -> "Average f+ form factor in K0 to Pi+ decays"
1199 },
1200
1201 f0K0Pi == {
1202 ParameterType -> Internal,
1203 Indices -> {Index[Neutrinos], Index[Generation]},
1204 Value -> {f0K0Pi[ii_,ll_] -> 0.9749*(1+0.0138*avq2K0Pi[ii,ll]/MPip^2)},
1205 Description -> "Average f0 form factor in K0 to Pi+ decays"
1206 },
1207
1208 fminusK0Pi == {
1209 ParameterType -> Internal,
1210 Indices -> {Index[Neutrinos], Index[Generation]},
1211 Value -> {fminusK0Pi[ii_,ll_] -> (MPip^2-MK0^2)*(f0K0Pi[ii,ll]-fplusK0Pi[ii,ll])/avq2K0Pi[ii,ll]},
1212 Description -> "Average f- form factor in K0 to Pi+ decays"
1213 },
1214
1215(** Form factors for K+ to Pi0 decays: linear parametrization **)
1216
1217 avq2KPi0 == {
1218 ParameterType -> Internal,
1219 Indices -> {Index[Neutrinos], Index[Generation]},
1220 Value -> {avq2KPi0[ii_,ll_] ->
1221 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],
1222 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]]},
1223 Description -> "Average momentum transfer in K+ to Pi0 decays"
1224 },
1225
1226 fplusKPi0 == {
1227 ParameterType -> Internal,
1228 Indices -> {Index[Neutrinos], Index[Generation]},
1229 Value -> {fplusKPi0[ii_,ll_] -> 0.9749*(1+0.0297*avq2KPi0[ii,ll]/MPip^2)},
1230 Description -> "Average f+ form factor in K+ to Pi0 decays"
1231 },
1232
1233 f0KPi0 == {
1234 ParameterType -> Internal,
1235 Indices -> {Index[Neutrinos], Index[Generation]},
1236 Value -> {f0KPi0[ii_,ll_] -> 0.9749*(1+0.0195*avq2KPi0[ii,ll]/MPip^2)},
1237 Description -> "Average f0 form factor in K+ to Pi0 decays"
1238 },
1239
1240 fminusKPi0 == {
1241 ParameterType -> Internal,
1242 Indices -> {Index[Neutrinos], Index[Generation]},
1243 Value -> {fminusKPi0[ii_,ll_] -> (MPi0^2-MK^2)*(f0KPi0[ii,ll]-fplusKPi0[ii,ll])/avq2KPi0[ii,ll]},
1244 Description -> "Average f- form factor in K+ to Pi0 decays"
1245 },
1246
1247(** Form factors for D to K decays: pole parametrization **)
1248
1249 avq2DK == {
1250 ParameterType -> Internal,
1251 Indices -> {Index[Neutrinos], Index[Generation]},
1252 Value -> {avq2DK[ii_,ll_] ->
1253 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],
1254 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]]},
1255 Description -> "Average momentum transfer in D to K decays"
1256 },
1257
1258 tplusDK == {
1259 ParameterType -> Internal,
1260 Value -> (MDd+MK)^2,
1261 Description -> "t+ factor in the pole parametrization"
1262 },
1263
1264 t0DK == {
1265 ParameterType -> Internal,
1266 Value -> (MDd+MK)*(Sqrt[MK]-Sqrt[MDd])^2,
1267 Description -> "t0 factor in the pole parametrization"
1268 },
1269
1270 zDK == {
1271 ParameterType -> Internal,
1272 Indices -> {Index[Neutrinos], Index[Generation]},
1273 Value -> {zDK[ii_,ll_] -> (Sqrt[tplusDK-avq2DK[ii,ll]]-Sqrt[tplusDK-t0DK])/(Sqrt[tplusDK-avq2DK[ii,ll]]+Sqrt[tplusDK-t0DK])},
1274 Description -> "z factor in the pole parametrization"
1275 },
1276
1277 z0DK == {
1278 ParameterType -> Internal,
1279 Value -> (Sqrt[tplusDK]-Sqrt[tplusDK-t0DK])/(Sqrt[tplusDK]+Sqrt[tplusDK-t0DK]),
1280 Description -> "z0 factor in the pole parametrization"
1281 },
1282
1283 fplusDK == {
1284 ParameterType -> Internal,
1285 Indices -> {Index[Neutrinos], Index[Generation]},
1286 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])},
1287 Description -> "Average f+ form factor in D to K decays"
1288 },
1289
1290 f0DK == {
1291 ParameterType -> Internal,
1292 Indices -> {Index[Neutrinos], Index[Generation]},
1293 Value -> {f0DK[ii_,ll_] -> (0.7647-2.084*(zDK[ii,ll]-z0DK)*(1+0.5*(zDK[ii,ll]+z0DK)))},
1294 Description -> "Average f0 form factor in D to K decays"
1295 },
1296
1297 fminusDK == {
1298 ParameterType -> Internal,
1299 Indices -> {Index[Neutrinos], Index[Generation]},
1300 Value -> {fminusDK[ii_,ll_] -> (MK^2-MDd^2)/avq2DK[ii,ll]*(f0DK[ii,ll]-fplusDK[ii,ll])},
1301 Description -> "Average f- form factor in D to K decays"
1302 },
1303
1304(** Form factors for B+ to Pi0 decays: FLAG review **)
1305
1306 avq2BPi0 == {
1307 ParameterType -> Internal,
1308 Indices -> {Index[Neutrinos], Index[Generation]},
1309 Value -> {avq2BPi0[ii_,ll_] ->
1310 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],
1311 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],
1312 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]]]},
1313 Description -> "Average momentum transfer in B+ to Pi0 decays"
1314 },
1315
1316 tplusBPi0 == {
1317 ParameterType -> Internal,
1318 Value -> (MBu + MPi0)^2,
1319 Description -> "t+ factor"
1320 },
1321
1322 t0BPi0 == {
1323 ParameterType -> Internal,
1324 Value -> (MBu + MPi0)*(Sqrt[MPi0]-Sqrt[MBu])^2,
1325 Description -> "t0 factor"
1326 },
1327
1328 zBPi0 == {
1329 ParameterType -> Internal,
1330 Indices -> {Index[Neutrinos], Index[Generation]},
1331 Value -> {zBPi0[ii_,ll_] -> (Sqrt[tplusBPi0-avq2BPi0[ii,ll]]-Sqrt[tplusBPi0-t0BPi0])/(Sqrt[tplusBPi0-avq2BPi0[ii,ll]]+Sqrt[tplusBPi0-t0BPi0])},
1332 Description -> "z factor"
1333 },
1334
1335 z0BPi0 == {
1336 ParameterType -> Internal,
1337 Value -> (Sqrt[tplusBPi0]-Sqrt[tplusBPi0-t0BPi0])/(Sqrt[tplusBPi0]+Sqrt[tplusBPi0-t0BPi0]),
1338 Description -> "z0 factor"
1339 },
1340
1341 fplusBPi0 == {
1342 ParameterType -> Internal,
1343 Indices -> {Index[Neutrinos], Index[Generation]},
1344 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)},
1345 Description -> "Average f+ form factor in B+ to Pi0 decays"
1346 },
1347
1348 f0BPi0 == {
1349 ParameterType -> Internal,
1350 Indices -> {Index[Neutrinos], Index[Generation]},
1351 Value -> {f0BPi0[ii_,ll_] -> (1.2527548*zBPi0[ii,ll]^2 - 1.61*zBPi0[ii,ll] + 0.490)},
1352 Description -> "Average f0 form factor in B+ to Pi0 decays"
1353 },
1354
1355 fminusBPi0 == {
1356 ParameterType -> Internal,
1357 Indices -> {Index[Neutrinos], Index[Generation]},
1358 Value -> {fminusBPi0[ii_,ll_] -> (MPi0^2-MBu^2)/avq2BPi0[ii,ll]*(f0BPi0[ii,ll]-fplusBPi0[ii,ll])},
1359 Description -> "Average f- form factor in B+ to Pi0 decays"
1360 },
1361
1362(** Form factors for B0 to Pi+ decays: FLAG review **)
1363
1364 avq2B0Pi == {
1365 ParameterType -> Internal,
1366 Indices -> {Index[Neutrinos], Index[Generation]},
1367 Value -> {avq2B0Pi[ii_,ll_] ->
1368 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],
1369 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],
1370 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]]]},
1371 Description -> "Average momentum transfer in B0 to Pi+ decays"
1372 },
1373
1374 tplusB0Pi == {
1375 ParameterType -> Internal,
1376 Value -> (MB0 + MPip)^2,
1377 Description -> "t+ factor"
1378 },
1379
1380 t0B0Pi == {
1381 ParameterType -> Internal,
1382 Value -> (MB0 + MPip)*(Sqrt[MPip]-Sqrt[MB0])^2,
1383 Description -> "t0 factor"
1384 },
1385
1386 zB0Pi == {
1387 ParameterType -> Internal,
1388 Indices -> {Index[Neutrinos], Index[Generation]},
1389 Value -> {zB0Pi[ii_,ll_] -> (Sqrt[tplusB0Pi-avq2B0Pi[ii,ll]]-Sqrt[tplusB0Pi-t0B0Pi])/(Sqrt[tplusB0Pi-avq2B0Pi[ii,ll]]+Sqrt[tplusB0Pi-t0B0Pi])},
1390 Description -> "z factor"
1391 },
1392
1393 z0B0Pi == {
1394 ParameterType -> Internal,
1395 Value -> (Sqrt[tplusB0Pi]-Sqrt[tplusB0Pi-t0B0Pi])/(Sqrt[tplusB0Pi]+Sqrt[tplusB0Pi-t0B0Pi]),
1396 Description -> "z0 factor"
1397 },
1398
1399 fplusB0Pi == {
1400 ParameterType -> Internal,
1401 Indices -> {Index[Neutrinos], Index[Generation]},
1402 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)},
1403 Description -> "Average f+ form factor in B0 to Pi+ decays"
1404 },
1405
1406 f0B0Pi == {
1407 ParameterType -> Internal,
1408 Indices -> {Index[Neutrinos], Index[Generation]},
1409 Value -> {f0B0Pi[ii_,ll_] -> (1.268691923*zB0Pi[ii,ll]^2 - 1.61*zB0Pi[ii,ll] + 0.490)},
1410 Description -> "Average f0 form factor in B0 to Pi+ decays"
1411 },
1412
1413 fminusB0Pi == {
1414 ParameterType -> Internal,
1415 Indices -> {Index[Neutrinos], Index[Generation]},
1416 Value -> {fminusB0Pi[ii_,ll_] -> (MPip^2-MB0^2)/avq2B0Pi[ii,ll]*(f0B0Pi[ii,ll]-fplusB0Pi[ii,ll])},
1417 Description -> "Average f- form factor in B0 to Pi+ decays"
1418 },
1419
1420 (** Form factors for B+ to D0 decays: FLAG review **)
1421
1422 avq2BD0 == {
1423 ParameterType -> Internal,
1424 Indices -> {Index[Neutrinos], Index[Generation]},
1425 Value -> {avq2BD0[ii_,ll_] ->
1426 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],
1427 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],
1428 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]]]},
1429 Description -> "Average momentum transfer in B+ to D0 decays"
1430 },
1431
1432 tplusBD0 == {
1433 ParameterType -> Internal,
1434 Value -> (MBu + MD0)^2,
1435 Description -> "t+ factor"
1436 },
1437
1438 t0BD0 == {
1439 ParameterType -> Internal,
1440 Value -> (MBu + MD0)*(Sqrt[MD0]-Sqrt[MBu])^2,
1441 Description -> "t0 factor"
1442 },
1443
1444 zBD0 == {
1445 ParameterType -> Internal,
1446 Indices -> {Index[Neutrinos], Index[Generation]},
1447 Value -> {zBD0[ii_,ll_] -> (Sqrt[tplusBD0-avq2BD0[ii,ll]]-Sqrt[tplusBD0-t0BD0])/(Sqrt[tplusBD0-avq2BD0[ii,ll]]+Sqrt[tplusBD0-t0BD0])},
1448 Description -> "z factor"
1449 },
1450
1451 z0BD0 == {
1452 ParameterType -> Internal,
1453 Value -> (Sqrt[tplusBD0]-Sqrt[tplusBD0-t0BD0])/(Sqrt[tplusBD0]+Sqrt[tplusBD0-t0BD0]),
1454 Description -> "z0 factor"
1455 },
1456
1457 fplusBD0 == {
1458 ParameterType -> Internal,
1459 Indices -> {Index[Neutrinos], Index[Generation]},
1460 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)},
1461 Description -> "Average f+ form factor in B+ to D0 decays"
1462 },
1463
1464 f0BD0 == {
1465 ParameterType -> Internal,
1466 Indices -> {Index[Neutrinos], Index[Generation]},
1467 Value -> {f0BD0[ii_,ll_] -> (33.2166*zBD0[ii,ll]^2 - 2.45*zBD0[ii,ll] + 0.794)},
1468 Description -> "Average f0 form factor in B+ to D0 decays"
1469 },
1470
1471 fminusBD0 == {
1472 ParameterType -> Internal,
1473 Indices -> {Index[Neutrinos], Index[Generation]},
1474 Value -> {fminusBD0[ii_,ll_] -> (MD0^2-MBu^2)/avq2BD0[ii,ll]*(f0BD0[ii,ll]-fplusBD0[ii,ll])},
1475 Description -> "Average f- form factor in B+ to D0 decays"
1476 },
1477
1478 (** Form factors for B0 to D+ decays: FLAG review **)
1479
1480 avq2B0D == {
1481 ParameterType -> Internal,
1482 Indices -> {Index[Neutrinos], Index[Generation]},
1483 Value -> {avq2B0D[ii_,ll_] ->
1484 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],
1485 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],
1486 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]]]},
1487 Description -> "Average momentum transfer in B0 to D+ decays"
1488 },
1489
1490 tplusB0D == {
1491 ParameterType -> Internal,
1492 Value -> (MB0 + MDd)^2,
1493 Description -> "t+ factor"
1494 },
1495
1496 t0B0D == {
1497 ParameterType -> Internal,
1498 Value -> (MB0 + MDd)*(Sqrt[MDd]-Sqrt[MB0])^2,
1499 Description -> "t0 factor"
1500 },
1501
1502 zB0D == {
1503 ParameterType -> Internal,
1504 Indices -> {Index[Neutrinos], Index[Generation]},
1505 Value -> {zB0D[ii_,ll_] -> (Sqrt[tplusB0D-avq2B0D[ii,ll]]-Sqrt[tplusB0D-t0B0D])/(Sqrt[tplusB0D-avq2B0D[ii,ll]]+Sqrt[tplusB0D-t0B0D])},
1506 Description -> "z factor"
1507 },
1508
1509 z0B0D == {
1510 ParameterType -> Internal,
1511 Value -> (Sqrt[tplusB0D]-Sqrt[tplusB0D-t0B0D])/(Sqrt[tplusB0D]+Sqrt[tplusB0D-t0B0D]),
1512 Description -> "z0 factor"
1513 },
1514
1515 fplusB0D == {
1516 ParameterType -> Internal,
1517 Indices -> {Index[Neutrinos], Index[Generation]},
1518 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)},
1519 Description -> "Average f+ form factor in B0 to D+ decays"
1520 },
1521
1522 f0B0D == {
1523 ParameterType -> Internal,
1524 Indices -> {Index[Neutrinos], Index[Generation]},
1525 Value -> {f0B0D[ii_,ll_] -> (33.5115*zB0D[ii,ll]^2 - 2.45*zB0D[ii,ll] + 0.794)},
1526 Description -> "Average f0 form factor in B0 to D+ decays"
1527 },
1528
1529 fminusB0D == {
1530 ParameterType -> Internal,
1531 Indices -> {Index[Neutrinos], Index[Generation]},
1532 Value -> {fminusB0D[ii_,ll_] -> (MDd^2-MB0^2)/avq2B0D[ii,ll]*(f0B0D[ii,ll]-fplusB0D[ii,ll])},
1533 Description -> "Average f- form factor in B0 to D+ decays"
1534 },
1535
1536 (** Form factors for B0s to Ds+ decays: FLAG review **)
1537
1538 avq2B0sDs == {
1539 ParameterType -> Internal,
1540 Indices -> {Index[Neutrinos], Index[Generation]},
1541 Value -> {avq2B0sDs[ii_,ll_] ->
1542 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],
1543 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],
1544 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]]]},
1545 Description -> "Average momentum transfer in B0s to Ds+ decays"
1546 },
1547
1548 tplusB0sDs == {
1549 ParameterType -> Internal,
1550 Value -> (MB0s + MDs)^2,
1551 Description -> "t+ factor"
1552 },
1553
1554 t0B0sDs == {
1555 ParameterType -> Internal,
1556 Value -> (MB0s + MDs)*(Sqrt[MDs]-Sqrt[MB0s])^2,
1557 Description -> "t0 factor"
1558 },
1559
1560 zB0sDs == {
1561 ParameterType -> Internal,
1562 Indices -> {Index[Neutrinos], Index[Generation]},
1563 Value -> {zB0sDs[ii_,ll_] -> (Sqrt[tplusB0sDs-avq2B0sDs[ii,ll]]-Sqrt[tplusB0sDs-t0B0sDs])/(Sqrt[tplusB0sDs-avq2B0sDs[ii,ll]]+Sqrt[tplusB0sDs-t0B0sDs])},
1564 Description -> "z factor"
1565 },
1566
1567 z0B0sDs == {
1568 ParameterType -> Internal,
1569 Value -> (Sqrt[tplusB0sDs]-Sqrt[tplusB0sDs-t0B0sDs])/(Sqrt[tplusB0sDs]+Sqrt[tplusB0sDs-t0B0sDs]),
1570 Description -> "z0 factor"
1571 },
1572
1573 fplusB0sDs == {
1574 ParameterType -> Internal,
1575 Indices -> {Index[Neutrinos], Index[Generation]},
1576 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)},
1577 Description -> "Average f+ form factor in B0s to Ds+ decays"
1578 },
1579
1580 f0B0sDs == {
1581 ParameterType -> Internal,
1582 Indices -> {Index[Neutrinos], Index[Generation]},
1583 Value -> {f0B0sDs[ii_,ll_] -> (39.1988*zB0sDs[ii,ll]^2 - 2.45*zB0sDs[ii,ll] + 0.794)},
1584 Description -> "Average f0 form factor in B0s to Ds+ decays"
1585 },
1586
1587 fminusB0sDs == {
1588 ParameterType -> Internal,
1589 Indices -> {Index[Neutrinos], Index[Generation]},
1590 Value -> {fminusB0sDs[ii_,ll_] -> (MDs^2-MB0s^2)/avq2B0sDs[ii,ll]*(f0B0sDs[ii,ll]-fplusB0sDs[ii,ll])},
1591 Description -> "Average f- form factor in B0s to Ds+ decays"
1592 },
1593
1594 (** Form factors for B0s to K+ decays: FLAG review **)
1595
1596 avq2B0sK == {
1597 ParameterType -> Internal,
1598 Indices -> {Index[Neutrinos], Index[Generation]},
1599 Value -> {avq2B0sK[ii_,ll_] ->
1600 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],
1601 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],
1602 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]]]},
1603 Description -> "Average momentum transfer in B0s to K+ decays"
1604 },
1605
1606 tplusB0sK == {
1607 ParameterType -> Internal,
1608 Value -> (MB0s + MK)^2,
1609 Description -> "t+ factor"
1610 },
1611
1612 t0B0sK == {
1613 ParameterType -> Internal,
1614 Value -> (MB0s + MK)*(Sqrt[MK]-Sqrt[MB0s])^2,
1615 Description -> "t0 factor"
1616 },
1617
1618 zB0sK == {
1619 ParameterType -> Internal,
1620 Indices -> {Index[Neutrinos], Index[Generation]},
1621 Value -> {zB0sK[ii_,ll_] -> (Sqrt[tplusB0sK-avq2B0sK[ii,ll]]-Sqrt[tplusB0sK-t0B0sK])/(Sqrt[tplusB0sK-avq2B0sK[ii,ll]]+Sqrt[tplusB0sK-t0B0sK])},
1622 Description -> "z factor"
1623 },
1624
1625 z0B0sK == {
1626 ParameterType -> Internal,
1627 Value -> (Sqrt[tplusB0sK]-Sqrt[tplusB0sK-t0B0sK])/(Sqrt[tplusB0sK]+Sqrt[tplusB0sK-t0B0sK]),
1628 Description -> "z0 factor"
1629 },
1630
1631 fplusB0sK == {
1632 ParameterType -> Internal,
1633 Indices -> {Index[Neutrinos], Index[Generation]},
1634 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)},
1635 Description -> "Average f+ form factor in B0s to K+ decays"
1636 },
1637
1638 f0B0sK == {
1639 ParameterType -> Internal,
1640 Indices -> {Index[Neutrinos], Index[Generation]},
1641 Value -> {f0B0sK[ii_,ll_] -> (14.0162*zB0sK[ii,ll]^3 + 0.24*zB0sK[ii,ll]^2 + 0.089*zB0sK[ii,ll] + 0.2203)},
1642 Description -> "Average f0 form factor in B0s to K+ decays"
1643 },
1644
1645 fminusB0sK == {
1646 ParameterType -> Internal,
1647 Indices -> {Index[Neutrinos], Index[Generation]},
1648 Value -> {fminusB0sK[ii_,ll_] -> (MK^2-MB0s^2)/avq2B0sK[ii,ll]*(f0B0sK[ii,ll]-fplusB0sK[ii,ll])},
1649 Description -> "Average f- form factor in B0s to K+ decays"
1650 },
1651
1652 yl == {
1653 ParameterType -> Internal,
1654 Indices -> {Index[Generation], Index[Generation]},
1655 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1656 Value -> {yl[1,1] -> Sqrt[2] yme /vev, yl[2,2] -> Sqrt[2] ymm /vev, yl[3,3] -> Sqrt[2] ymtau /vev},
1657 InteractionOrder -> {QED, 1},
1658 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
1659 TeX -> Superscript[y, l],
1660 Description -> "Lepton Yukawa couplings"
1661 },
1662 yu == {
1663 ParameterType -> Internal,
1664 Indices -> {Index[Generation], Index[Generation]},
1665 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1666 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
1667 InteractionOrder -> {QED, 1},
1668 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
1669 TeX -> Superscript[y, u],
1670 Description -> "Up-type Yukawa couplings"
1671 },
1672 yd == {
1673 ParameterType -> Internal,
1674 Indices -> {Index[Generation], Index[Generation]},
1675 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
1676 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
1677 InteractionOrder -> {QED, 1},
1678 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
1679 TeX -> Superscript[y, d],
1680 Description -> "Down-type Yukawa couplings"
1681 },
1682
1683 CKM == {
1684 ParameterType -> Internal,
1685 Indices -> {Index[Generation], Index[Generation]},
1686 Unitary -> True,
1687 Value -> {CKM[1,1] -> Cos[cabi] Cos[th13], CKM[1,2] -> Sin[cabi] Cos[th13], CKM[1,3] -> Sin[th13] Exp[-I del13],
1688 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],
1689 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]},
1690 TeX -> Superscript[V,CKM],
1691 Description -> "CKM-Matrix"},
1692
1693 HEAV == {
1694 ParameterType -> Internal,
1695 Indices -> {Index[Heavynus],Index[Neutrinos]},
1696 Value -> {HEAV[1,1] -> -Conjugate[thetae]/r,
1697 HEAV[1,2] -> -Conjugate[thetamu]/r,
1698 HEAV[1,3] -> -Conjugate[thetatau]/r,
1699 HEAV[1,4] -> 1/r},
1700 TeX -> Superscript[UL,n],
1701 ComplexParameter -> True,
1702 Description -> "Mass eigenstate component of right-handed nu"},
1703
1704 HEAVR == {
1705 ParameterType -> Internal,
1706 Indices -> {Index[Heavynus],Index[Neutrinos]},
1707 Value -> {HEAVR[1,1] -> 0,
1708 HEAVR[1,2] -> 0,
1709 HEAVR[1,3] -> 0,
1710 HEAVR[1,4] -> 1},
1711 TeX -> Superscript[UR,n],
1712 ComplexParameter -> True,
1713 Description -> "Mass eigenstate component of right-handed nu"},
1714
1715
1716 PMNS == {
1717 ParameterType -> Internal,
1718 Indices -> {Index[Generation], Index[Neutrinos]},
1719 Unitary -> False,
1720 Value -> {PMNS[1,1] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 1, 1-thetae*Conjugate[thetae]*(r-1)/r/thetatot^2],
1721 PMNS[1,2] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -thetae*Conjugate[thetamu]*(r-1)/r/thetatot^2],
1722 PMNS[1,3] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -thetae*Conjugate[thetatau]*(r-1)/r/thetatot^2],
1723 PMNS[1,4] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, thetae/r],
1724 PMNS[2,1] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -Conjugate[thetae]*thetamu*(r-1)/r/thetatot^2],
1725 PMNS[2,2] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 1, 1-thetamu*Conjugate[thetamu]*(r-1)/r/thetatot^2],
1726 PMNS[2,3] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -thetamu*Conjugate[thetatau]*(r-1)/r/thetatot^2],
1727 PMNS[2,4] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, thetamu/r],
1728 PMNS[3,1] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -Conjugate[thetae]*thetatau*(r-1)/r/thetatot^2],
1729 PMNS[3,2] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, -Conjugate[thetamu]*thetatau*(r-1)/r/thetatot^2],
1730 PMNS[3,3] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 1, 1-thetatau*Conjugate[thetatau]*(r-1)/r/thetatot^2],
1731 PMNS[3,4] -> If[thetae == 0 && thetamu == 0 && thetatau == 0, 0, thetatau/r]},
1732 TeX -> Superscript[U,PMNS],
1733 TeX -> Superscript[U,PMNS],
1734 ComplexParameter -> True,
1735 Description -> "PMNS-Matrix"}
1736};
1737
1738
1739
1740(* ************************** *)
1741(* ***** Lagrangian ***** *)
1742(* For consistency we do not *)
1743(* add quarks with mesons *)
1744(* ************************** *)
1745
1746LGauge := Block[{mu,nu,ii,aa},
1747 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]];
1748
1749LQuarks := Block[{mu},
1750 ExpandIndices[I*(
1751 QLbar.Ga[mu].DC[QL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu]),
1752 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]]}];
1753
1754LFermions := Block[{mu},
1755 ExpandIndices[I*(
1756 LLbar.Ga[mu].DC[LL, mu] + lRbar.Ga[mu].DC[lR, mu] + NLbar.Ga[mu].DC[NL, mu] + NRbar.Ga[mu].DC[NR, mu] ),
1757 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]]}];
1758
1759LHiggs := Block[{ii,mu, feynmangaugerules},
1760 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
1761 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
1762 ];
1763
1764LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
1765 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
1766
1767 yuk = ExpandIndices[
1768 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
1769 yl[ff1, ff3] LLbar[sp, ii, ff1].lR[sp, ff3] Phi[ii] -
1770 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 NLbar[sp,ff1].NR[sp,ff1] , FlavorExpand -> SU2D];
1771 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]]};
1772 yuk+HC[yuk]/.feynmangaugerules
1773 ];
1774
1775LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
1776 (* Pure gauge piece *)
1777 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
1778 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
1779 LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
1780
1781(***********************************)
1782(*** Meson interactions ***)
1783(***********************************)
1784
1785(*LHadr := Block[{mu,nu,ii,jj,kk,ff1,ff2,ff3,ff4,ff5,yhad},*)
1786LHadr := Block[{mu,nu,ii,jj,kk,ff1,ff2,ff3,yhad},
1787 yhad = ExpandIndices[
1788
1789(*** Charged pseudoscalars ***)
1790
1791(*K*)
1792
17931/2 DC[Kbar,mu] DC[K,mu] - MK^2/2 Kbar K
1794+ 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}]
1795- 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],{ff1,4,4},{ff2,1,3}]
1796
1797(* Pi *)
1798
1799+ 1/2 DC[Pipbar,mu] DC[Pip,mu] - MPip^2/2 Pipbar Pip
1800+ 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}]
1801- 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] ,{ff1,4,4},{ff2,1,3}]
1802
1803(*D*)
1804
1805+ 1/2 DC[Ddbar,mu] DC[Dd,mu] - MDd^2/2 Ddbar Dd
1806+ 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}]
1807- 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] ,{ff1,4,4},{ff2,1,3}]
1808
1809(*Ds*)
1810
1811+ 1/2 DC[Dsbar,mu] DC[Ds,mu] - MDs^2/2 Dsbar Ds
1812+ 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}]
1813- 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] ,{ff1,4,4},{ff2,1,3}]
1814
1815(*B*)
1816
1817+ 1/2 DC[Bubar,mu] DC[Bu,mu] - MBu^2/2 Bubar Bu
1818+ 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}]
1819- 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] ,{ff1,4,4},{ff2,1,3}]
1820
1821(*Bc*)
1822
1823+ 1/2 DC[Bcbar,mu] DC[Bc,mu] - MBc^2/2 Bcbar Bc
1824+ 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}]
1825- 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] ,{ff1,4,4},{ff2,1,3}]
1826
1827(*** Neutral pseudoscalars ***)
1828
1829(* pi0 *)
1830
1831- 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},{ff2,4,4},{ff3,1,3}]
1832+ 1/4 DC[Pi0,mu] DC[Pi0,mu] - MPi0^2/4 Pi0 Pi0
1833+ 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] ,{ff1,4,4},{ff2,1,4},{ff3,1,3}]
1834
1835(* eta *)
1836
1837+ 1/4 DC[Etabar,mu] DC[Eta,mu] - Meta^2/4 Eta Eta
1838- 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},{ff2,4,4},{ff3,1,3}]
1839+ 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] ,{ff1,4,4},{ff2,1,4},{ff3,1,3}]
1840
1841(* eta^' *)
1842
1843+ 1/4 DC[Etapbar,mu] DC[Etap,mu] - Metap^2/4 Etap Etap
1844- 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},{ff2,4,4},{ff3,1,3}]
1845+ 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] ,{ff1,4,4},{ff2,1,4},{ff3,1,3}]
1846
1847(*** Neutral vector mesons ***)
1848
1849(* rho0 *)
1850
1851-1/8 FS[rho0,mu,nu] FS[rho0,mu,nu] + Mrho0^2/4 rho0[mu] rho0[mu]
1852- 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}]
1853
1854(* omega *)
1855
1856-1/8 FS[omega,mu,nu] FS[omega,mu,nu] + Mom^2/4 omega[mu] omega[mu]
1857+ 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}]
1858
1859(* phi *)
1860
1861-1/8 FS[phimeson,mu,nu] FS[phimeson,mu,nu] + Mphi^2/4 phimeson[mu] phimeson[mu]
1862+ 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}]
1863
1864(*** Charged vector mesons ***)
1865
1866(* Rho *)
1867
1868-1/4 FS[rhobar,mu,nu] FS[rho,mu,nu] + Mrho^2/2 rhobar[mu] rho[mu]
1869- 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}]
1870
1871(* Kstar *)
1872
1873-1/4 FS[Kstarbar,mu,nu] FS[Kstar,mu,nu] + MKstar^2/2 Kstarbar[mu] Kstar[mu]
1874- 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}]
1875
1876(*** Semileptonic decays: ***)
1877
1878(* K -> pi0 l nu and K0 -> pip l nu *)
1879
1880+ 1/2 DC[K0bar,mu] DC[K0,mu] - MK0^2/2 K0bar K0
1881
1882-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}]
1883+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}]
1884-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] ,{ff1,4,4},{ff2,1,2}]
1885
1886-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}]
1887+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}]
1888-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],{ff1,4,4},{ff2,1,2}]
1889
1890(* D -> K0 l nu and D0 -> K l nu *)
1891
1892+ 1/2 DC[D0bar,mu] DC[D0,mu] - MD0^2/2 D0bar D0
1893
1894-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}]
1895+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}]
1896-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],{ff1,4,4},{ff2,1,2}]
1897
1898-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}]
1899+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}]
1900-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],{ff1,4,4},{ff2,1,2}]
1901
1902(* B+ -> pi0 l nu and B0 -> pi+ l nu *)
1903
1904+ 1/2 DC[B0bar,mu] DC[B0,mu] - MB0^2/2 B0bar B0
1905
1906-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}]
1907+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}]
1908-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] ,{ff1,4,4},{ff2,1,3}]
1909
1910-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}]
1911+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}]
1912-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] ,{ff1,4,4},{ff2,1,3}]
1913
1914(* B+ -> D0 l nu, B0 -> D+ l nu and B0s -> Ds+ l nu *)
1915
1916-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}]
1917+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}]
1918-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] ,{ff1,4,4},{ff2,1,3}]
1919
1920-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}]
1921+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}]
1922-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] ,{ff1,4,4},{ff2,1,3}]
1923
1924+ 1/2 DC[B0sbar,mu] DC[B0s,mu] - MB0s^2/2 B0sbar B0s
1925
1926-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}]
1927+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}]
1928-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] ,{ff1,4,4},{ff2,1,3}]
1929
1930(* B0s -> K+ l nu *)
1931
1932-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}]
1933+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}]
1934-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] ,{ff1,4,4},{ff2,1,3}]
1935
1936
1937
1938, FlavorExpand->{SU2D,SU2W}];
1939yhad+HC[yhad]
1940 ];
1941
1942
1943 (* Scalar pieces: see Peskin pages 739-742 *)
1944 (* phi1 and phi2 are the real degrees of freedom of GP *)
1945 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
1946 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
1947 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
1948 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
1949 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
1950 doublet0 = {0, vev/Sqrt[2]};
1951 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}];
1952 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
1953 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
1954
1955ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
1956
1957LagHeavyN:= LGauge + LFermions + LHiggs + LYukawa + LGhost + If[Mesons,LHadr,LQuarks];