B-L-SM: B-L-N_4.fr

File B-L-N_4.fr, 33.7 KB (added by WeiLiu, 3 years ago)

model file with automatic active-sterile neutrino mixing

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the B-L model ******)
3(****** ******)
4(****** Authors: Wei.Liu ******)
5(****** ******)
6(****** Choose whether Feynman gauge is desired. ******)
7(****** If set to False, unitary gauge is assumed. ****)
8(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
9(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
10(***************************************************************************************************************)
11
12(* ************************** *)
13(* ***** Information ***** *)
14(* ************************** *)
15M$ModelName = "B-L-N-4";
16
17M$Information = {
18 Authors -> {"Wei.Liu"},
19 Version -> "4.0.0",
20 Date -> "09. 12. 2019",
21 Institutions -> {"University College London"},
22 Emails -> {"wei.liu.16@ucl.ac.uk"},
23 URLs -> "http://feynrules.phys.ucl.ac.be"
24};
25
26FeynmanGauge = True;
27
28(* ************************** *)
29(* ***** NLO Variables ****** *)
30(******************************)
31
32FR$LoopSwitches = {{Gf, MW}};
33FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
34 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
35(************B-L***************)
36
37
38(************End***************)
39
40(* ************************** *)
41(* ***** Change log ***** *)
42(* ************************** *)
43
44(***v1.0,the ordinary version without NLO***)
45(***v2.1,change muh1 and muh2 to mu2h1 and mu2h2*****)
46(***v3.0,delete VEV blockname, and enter Neutrino mixing as internal parameters******)
47(***v4.0,rewrite accroding to my thesis, adding LGhBp, rewrite the LYukawa for the B-L part******)
48(* ************************** *)
49(* ***** vevs ***** *)
50(* ************************** *)
51M$vevs = { {Phi[2],vev} };
52(************B-L***************)
53
54
55(************End***************)
56
57(* ************************** *)
58(* ***** Gauge groups ***** *)
59(* ************************** *)
60M$GaugeGroups = {
61(************B-L***************)
62 U1BL == {
63 Abelian -> True,
64 CouplingConstant -> g1p,
65 GaugeBoson -> Bp,
66 Charge -> BL
67 },
68(************End***************)
69 U1Y == {
70 Abelian -> True,
71 CouplingConstant -> g1,
72 GaugeBoson -> B,
73 Charge -> Y
74 },
75 SU2L == {
76 Abelian -> False,
77 CouplingConstant -> gw,
78 GaugeBoson -> Wi,
79 StructureConstant -> Eps,
80 Representations -> {Ta,SU2D},
81 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
82 },
83 SU3C == {
84 Abelian -> False,
85 CouplingConstant -> gs,
86 GaugeBoson -> G,
87 StructureConstant -> f,
88 Representations -> {T,Colour},
89 SymmetricTensor -> dSUN
90 }
91};
92
93
94(* ************************** *)
95(* ***** Indices ***** *)
96(* ************************** *)
97
98IndexRange[Index[SU2W ]] = Unfold[Range[3]];
99IndexRange[Index[SU2D ]] = Unfold[Range[2]];
100IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
101IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
102IndexRange[Index[Generation]] = Range[3];
103
104IndexStyle[SU2W, j];
105IndexStyle[SU2D, k];
106IndexStyle[Gluon, a];
107IndexStyle[Colour, m];
108IndexStyle[Generation, f];
109
110
111(* ************************** *)
112(* *** Interaction orders *** *)
113(* *** (as used by mg5) *** *)
114(* ************************** *)
115
116M$InteractionOrderHierarchy = {
117 {QCD, 1},
118 {QED, 2}
119};
120
121
122(* ************************** *)
123(* **** Particle classes **** *)
124(* ************************** *)
125M$ClassesDescription = {
126
127(* Gauge bosons: physical vector fields *)
128(* Gauge bosons: Q = 0 *)
129 V[1] == {
130 ClassName -> A,
131 SelfConjugate -> True,
132 Mass -> 0,
133 Width -> 0,
134 ParticleName -> "a",
135 PDG -> 22,
136 PropagatorLabel -> "a",
137 PropagatorType -> W,
138 PropagatorArrow -> None,
139 FullName -> "Photon"
140 },
141 V[2] == {
142 ClassName -> Z,
143 SelfConjugate -> True,
144 Mass -> {MZ, 91.1876},
145 Width -> {WZ, 2.4952},
146 ParticleName -> "Z",
147 PDG -> 23,
148 PropagatorLabel -> "Z",
149 PropagatorType -> Sine,
150 PropagatorArrow -> None,
151 FullName -> "Z"
152 },
153 V[3] == {
154 ClassName -> W,
155 SelfConjugate -> False,
156 Mass -> {MW, Internal},
157 Width -> {WW, 2.085},
158 ParticleName -> "W+",
159 AntiParticleName -> "W-",
160 QuantumNumbers -> {Q -> 1},
161 PDG -> 24,
162 PropagatorLabel -> "W",
163 PropagatorType -> Sine,
164 PropagatorArrow -> Forward,
165 FullName -> "W"
166 },
167 V[4] == {
168 ClassName -> G,
169 SelfConjugate -> True,
170 Indices -> {Index[Gluon]},
171 Mass -> 0,
172 Width -> 0,
173 ParticleName -> "g",
174 PDG -> 21,
175 PropagatorLabel -> "G",
176 PropagatorType -> C,
177 PropagatorArrow -> None,
178 FullName -> "G"
179 },
180
181(* Ghosts: related to physical gauge bosons *)
182 U[1] == {
183 ClassName -> ghA,
184 SelfConjugate -> False,
185 Ghost -> A,
186 QuantumNumbers -> {GhostNumber -> 1},
187 Mass -> 0,
188 Width -> 0,
189 PropagatorLabel -> "uA",
190 PropagatorType -> GhostDash,
191 PropagatorArrow -> Forward
192 },
193 U[2] == {
194 ClassName -> ghZ,
195 SelfConjugate -> False,
196 Ghost -> Z,
197 QuantumNumbers -> {GhostNumber -> 1},
198 Mass -> {MZ,91.1876},
199 Width -> {WZ, 2.4952},
200 PropagatorLabel -> "uZ",
201 PropagatorType -> GhostDash,
202 PropagatorArrow -> Forward
203 },
204 U[31] == {
205 ClassName -> ghWp,
206 SelfConjugate -> False,
207 Ghost -> W,
208 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
209 Mass -> {MW,Internal},
210 Width -> {WW, 2.085},
211 PropagatorLabel -> "uWp",
212 PropagatorType -> GhostDash,
213 PropagatorArrow -> Forward
214 },
215 U[32] == {
216 ClassName -> ghWm,
217 SelfConjugate -> False,
218 Ghost -> Wbar,
219 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
220 Mass -> {MW,Internal},
221 Width -> {WW, 2.085},
222 PropagatorLabel -> "uWm",
223 PropagatorType -> GhostDash,
224 PropagatorArrow -> Forward
225 },
226 U[4] == {
227 ClassName -> ghG,
228 SelfConjugate -> False,
229 Indices -> {Index[Gluon]},
230 Ghost -> G,
231 PDG -> 82,
232 QuantumNumbers ->{GhostNumber -> 1},
233 Mass -> 0,
234 Width -> 0,
235 PropagatorLabel -> "uG",
236 PropagatorType -> GhostDash,
237 PropagatorArrow -> Forward
238 },
239(************B-L***************)
240 V[5] == {
241 ClassName -> Zp,
242 SelfConjugate -> True,
243 Indices -> {},
244 Mass -> {MZp, 1500},
245 Width -> {WZp, 80.00},
246 ParticleName -> "Zp",
247 PDG -> 9900032,
248 PropagatorLabel -> "Zp",
249 PropagatorType -> Sine,
250 PropagatorArrow -> None,
251 FullName -> "Zp"
252 },
253 V[6] == {
254 ClassName -> Bp,
255 SelfConjugate -> True,
256 Indices -> {},
257 Definitions -> {Bp[mu_] -> Zp[mu]},
258 Unphysical -> True
259 },
260
261 U[5] == {
262 ClassName -> ghZp,
263 SelfConjugate -> False,
264 Indices -> {},
265 Ghost -> Zp,
266 QuantumNumbers -> {GhostNumber -> 1},
267 Mass -> {MZp, Internal},
268 Width -> {WZp, 80.00},
269 PropagatorLabel -> "uZp",
270 PropagatorType -> GhostDash,
271 PropagatorArrow -> Forward
272 },
273 U[6] == {
274 ClassName -> ghBp,
275 SelfConjugate -> False,
276 Definitions -> {ghBp -> ghZp},
277 Indices -> {},
278 Unphysical -> True,
279 Ghost -> Bp
280 },
281
282(************End***************)
283
284(* Gauge bosons: unphysical vector fields *)
285 V[11] == {
286 ClassName -> B,
287 Unphysical -> True,
288 SelfConjugate -> True,
289 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
290 },
291 V[12] == {
292 ClassName -> Wi,
293 Unphysical -> True,
294 SelfConjugate -> True,
295 Indices -> {Index[SU2W]},
296 FlavorIndex -> SU2W,
297 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]}
298 },
299
300(* Ghosts: related to unphysical gauge bosons *)
301 U[11] == {
302 ClassName -> ghB,
303 Unphysical -> True,
304 SelfConjugate -> False,
305 Ghost -> B,
306 Definitions -> { ghB -> -sw ghZ + cw ghA}
307 },
308 U[12] == {
309 ClassName -> ghWi,
310 Unphysical -> True,
311 SelfConjugate -> False,
312 Ghost -> Wi,
313 Indices -> {Index[SU2W]},
314 FlavorIndex -> SU2W,
315 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
316 } ,
317
318(* Fermions: physical fields *)
319(************B-L******************)
320 F[1] == {
321 ClassName -> nL,
322 ClassMembers -> {nL1,nL2,nL3},
323 Indices -> {Index[Generation]},
324 FlavorIndex -> Generation,
325 SelfConjugate -> True,
326 QuantumNumbers -> {},
327 Mass -> {MnL,{MnL1, 10^(-9)},{MnL2, 10^(-9)},{MnL3, 10^(-9)}},
328 Width -> 0,
329 PropagatorLabel -> {"nL", "nul1", "nul2", "nul3"} ,
330 PropagatorType -> S,
331 PropagatorArrow -> Forward,
332 PDG -> {12,14,16},
333 ParticleName -> {"n1","n2","n3"},
334 FullName -> {"Light neutrino 1", "Light neutrino 2", "Light neutrino 3"}
335 },
336 F[16] == {
337 ClassName -> nH,
338 ClassMembers -> {nH1, nH2, nH3},
339 Indices -> {Index[Generation]},
340 FlavorIndex -> Generation,
341 SelfConjugate -> True,
342 QuantumNumbers -> {},
343 Mass -> {MnH,{MnH1, 200.00},{MnH2, 200.00},{MnH3, 200.00}},
344 Width -> 10^(-13),
345 PropagatorLabel -> {"nH","nuh1","nuh2","nuh3"},
346 PropagatorType -> Straight,
347 PropagatorArrow -> Forward,
348 PDG -> {9910012, 9910014, 9910016},
349 ParticleName -> {"nH1","nH2","nH3"},
350 FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"}
351 },
352 (* unphysical *)
353 F[17] == {
354 ClassName -> nF,
355 ClassMembers -> {nF1,nF2,nF3},
356 Indices -> {Index[Generation]},
357 FlavorIndex -> Generation,
358 SelfConjugate -> True,
359 Unphysical -> True,
360 Definitions -> {nF[sp_,ff_] -> Can[ff] nL[sp,ff]-San[ff] nH[sp,ff]}
361 },
362 (* unphysical *)
363 F[18] == {
364 ClassName -> nR,
365 ClassMembers -> {nR1,nR2,nR3},
366 Indices -> {Index[Generation]},
367 FlavorIndex -> Generation,
368 SelfConjugate -> True,
369 Unphysical -> True,
370 Definitions -> {nR[sp_,ff_] -> San[ff] nL[sp,ff]+Can[ff] nH[sp,ff]}
371 },
372
373 (* Flavour-eigenstate neutrino: unphysical *)
374 (* Righthanded flavor neutrino: unphysical *)
375 F[20] == {
376 ClassName -> VR,
377 Unphysical -> True,
378 Indices -> {Index[Generation]},
379 QuantumNumbers -> {Y -> 0, BL -> -1},
380 FlavorIndex -> Generation,
381 SelfConjugate -> False,
382 Definitions -> { VR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] nR[sp2,ff]]}
383 },
384(***************END******************)
385
386 F[2] == {
387 ClassName -> l,
388 ClassMembers -> {e, mu, ta},
389 Indices -> {Index[Generation]},
390 FlavorIndex -> Generation,
391 SelfConjugate -> False,
392 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
393 Width -> 0,
394 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
395 PropagatorLabel -> {"l", "e", "mu", "ta"},
396 PropagatorType -> Straight,
397 PropagatorArrow -> Forward,
398 PDG -> {11, 13, 15},
399 ParticleName -> {"e-", "mu-", "ta-"},
400 AntiParticleName -> {"e+", "mu+", "ta+"},
401 FullName -> {"Electron", "Muon", "Tau"}
402 },
403 (* Quarks (u): I_3 = +1/2, Q = +2/3, BL=1/3 *)
404 F[3] == {
405 ClassName -> uq,
406 ClassMembers -> {u, c, t},
407 Indices -> {Index[Generation], Index[Colour]},
408 FlavorIndex -> Generation,
409 SelfConjugate -> False,
410 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
411 Width -> {0, 0, {WT,1.50833649}},
412 QuantumNumbers -> {Q -> 2/3},
413 PropagatorLabel -> {"uq", "u", "c", "t"},
414 PropagatorType -> Straight,
415 PropagatorArrow -> Forward,
416 PDG -> {2, 4, 6},
417 ParticleName -> {"u", "c", "t" },
418 AntiParticleName -> {"u~", "c~", "t~"},
419 FullName -> {"u-quark", "c-quark", "t-quark"}
420 },
421 (* Quarks (d): I_3 = -1/2, Q = -1/3, BL=1/3 *)
422 F[4] == {
423 ClassName -> dq,
424 ClassMembers -> {d, s, b},
425 Indices -> {Index[Generation], Index[Colour]},
426 FlavorIndex -> Generation,
427 SelfConjugate -> False,
428 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
429 Width -> 0,
430 QuantumNumbers -> {Q -> -1/3},
431 PropagatorLabel -> {"dq", "d", "s", "b"},
432 PropagatorType -> Straight,
433 PropagatorArrow -> Forward,
434 PDG -> {1,3,5},
435 ParticleName -> {"d", "s", "b" },
436 AntiParticleName -> {"d~", "s~", "b~"},
437 FullName -> {"d-quark", "s-quark", "b-quark"}
438 },
439
440(* Fermions: unphysical fields *)
441 F[11] == {
442 ClassName -> LL,
443 Unphysical -> True,
444 Indices -> {Index[SU2D], Index[Generation]},
445 FlavorIndex -> SU2D,
446 SelfConjugate -> False,
447 QuantumNumbers -> {Y -> -1/2, BL -> -1},
448 Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] nF[sp2,ff]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
449 },
450 F[12] == {
451 ClassName -> lR,
452 Unphysical -> True,
453 Indices -> {Index[Generation]},
454 FlavorIndex -> Generation,
455 SelfConjugate -> False,
456 QuantumNumbers -> {Y -> -1, BL -> -1},
457 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
458 },
459 F[13] == {
460 ClassName -> QL,
461 Unphysical -> True,
462 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
463 FlavorIndex -> SU2D,
464 SelfConjugate -> False,
465 QuantumNumbers -> {Y -> 1/6, BL -> 1/3},
466 Definitions -> {
467 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
468 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
469 },
470 F[14] == {
471 ClassName -> uR,
472 Unphysical -> True,
473 Indices -> {Index[Generation], Index[Colour]},
474 FlavorIndex -> Generation,
475 SelfConjugate -> False,
476 QuantumNumbers -> {Y -> 2/3, BL -> 1/3},
477 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
478 },
479 F[15] == {
480 ClassName -> dR,
481 Unphysical -> True,
482 Indices -> {Index[Generation], Index[Colour]},
483 FlavorIndex -> Generation,
484 SelfConjugate -> False,
485 QuantumNumbers -> {Y -> -1/3, BL -> 1/3},
486 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
487 },
488
489(* Higgs: physical scalars *)
490 S[1] == {
491 ClassName -> H1,
492 SelfConjugate -> True,
493 Mass -> {MH1,125},
494 Width -> {WH1,0.00407},
495 PropagatorLabel -> "H1",
496 PropagatorType -> D,
497 PropagatorArrow -> None,
498 PDG -> 9900025,
499 ParticleName -> "H1",
500 FullName -> "H1"
501 },
502
503(* Higgs: physical scalars *)
504(**********phi(phi0)****************)
505 S[2] == {
506 ClassName -> G0,
507 SelfConjugate -> True,
508 Goldstone -> Z,
509 Mass -> {MZ, 91.1876},
510 Width -> {WZ, 2.4952},
511 PropagatorLabel -> "Go",
512 PropagatorType -> D,
513 PropagatorArrow -> None,
514 PDG -> 250,
515 ParticleName -> "G0",
516 FullName -> "G0"
517 },
518(************phi2*******************)
519 S[3] == {
520 ClassName -> GP,
521 SelfConjugate -> False,
522 Goldstone -> W,
523 Mass -> {MW, Internal},
524 QuantumNumbers -> {Q -> 1},
525 Width -> {WW, 2.085},
526 PropagatorLabel -> "GP",
527 PropagatorType -> D,
528 PropagatorArrow -> None,
529 PDG -> 251,
530 ParticleName -> "G+",
531 AntiParticleName -> "G-",
532 FullName -> "GP"
533 },
534 (***************B-L*****************)
535(* Higgs: unphysical scalars *)
536 S[11] == {
537 ClassName -> Phi,
538 Unphysical -> True,
539 Indices -> {Index[SU2D]},
540 FlavorIndex -> SU2D,
541 SelfConjugate -> False,
542 QuantumNumbers -> {Y -> 1/2, BL -> 0},
543 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + Ca*H1 + Sa*H2 + I G0)/Sqrt[2] }
544 },
545 S[12] == {
546 ClassName -> Xi,
547 Unphysical -> True,
548 SelfConjugate -> False,
549 QuantumNumbers -> {Y -> 0, BL -> 2},
550 Definitions -> { Xi -> (xev - Sa*H1 + Ca*H2 + I phip)/Sqrt[2]
551 }
552 },
553 S[4] == {
554 ClassName -> H2,
555 SelfConjugate -> True,
556 Mass -> {MH2, Internal},
557 Width -> {WH2, 10},
558 PropagatorLabel -> "H2",
559 PropagatorType -> D,
560 PropagatorArrow -> None,
561 PDG -> 9900026,
562 ParticleName -> "H2",
563 FullName -> "H2"
564 },
565 S[5] == {
566 ClassName -> phip,
567 SelfConjugate -> True,
568 Goldstone -> Zp,
569 Mass -> {MZp, Internal},
570 Width -> Wphip,
571 PropagatorLabel -> "Phip",
572 PropagatorType -> D,
573 PropagatorArrow -> None,
574 PDG -> 9900252,
575 ParticleName -> "phi0p",
576 FullName -> "Phip"
577 }
578};
579 (***************END*****************)
580
581(* ************************** *)
582(* ***** Gauge ***** *)
583(* ***** Parameters ***** *)
584(* ***** (FeynArts) ***** *)
585(* ************************** *)
586
587GaugeXi[ V[1] ] = GaugeXi[A];
588GaugeXi[ V[2] ] = GaugeXi[Z];
589GaugeXi[ V[3] ] = GaugeXi[W];
590GaugeXi[ V[4] ] = GaugeXi[G];
591GaugeXi[ S[1] ] = 1;
592GaugeXi[ S[2] ] = GaugeXi[Z];
593GaugeXi[ S[3] ] = GaugeXi[W];
594GaugeXi[ U[1] ] = GaugeXi[A];
595GaugeXi[ U[2] ] = GaugeXi[Z];
596GaugeXi[ U[31] ] = GaugeXi[W];
597GaugeXi[ U[32] ] = GaugeXi[W];
598GaugeXi[ U[4] ] = GaugeXi[G];
599(***************B-L*****************)
600GaugeXi[ V[5] ] = GaugeXi[Zp];
601GaugeXi[ S[4] ] = 1;
602GaugeXi[ S[5] ] = GaugeXi[Zp];
603GaugeXi[ U[5] ] = GaugeXi[Zp];
604(***************END*****************)
605
606(* ************************** *)
607(* ***** Parameters ***** *)
608(* ************************** *)
609M$Parameters = {
610
611 (* External parameters *)
612 aEWM1 == {
613 ParameterType -> External,
614 BlockName -> SMINPUTS,
615 OrderBlock -> 1,
616 Value -> 127.9,
617 InteractionOrder -> {QED,-2},
618 Description -> "Inverse of the EW coupling constant at the Z pole"
619 },
620 Gf == {
621 ParameterType -> External,
622 BlockName -> SMINPUTS,
623 OrderBlock -> 2,
624 Value -> 1.16637*^-5,
625 InteractionOrder -> {QED,2},
626 TeX -> Subscript[G,f],
627 Description -> "Fermi constant"
628 },
629 aS == {
630 ParameterType -> External,
631 BlockName -> SMINPUTS,
632 OrderBlock -> 3,
633 Value -> 0.1184,
634 InteractionOrder -> {QCD,2},
635 TeX -> Subscript[\[Alpha],s],
636 Description -> "Strong coupling constant at the Z pole"
637 },
638 ymdo == {
639 ParameterType -> External,
640 BlockName -> YUKAWA,
641 OrderBlock -> 1,
642 Value -> 5.04*^-3,
643 Description -> "Down Yukawa mass"
644 },
645 ymup == {
646 ParameterType -> External,
647 BlockName -> YUKAWA,
648 OrderBlock -> 2,
649 Value -> 2.55*^-3,
650 Description -> "Up Yukawa mass"
651 },
652 yms == {
653 ParameterType -> External,
654 BlockName -> YUKAWA,
655 OrderBlock -> 3,
656 Value -> 0.101,
657 Description -> "Strange Yukawa mass"
658 },
659 ymc == {
660 ParameterType -> External,
661 BlockName -> YUKAWA,
662 OrderBlock -> 4,
663 Value -> 1.27,
664 Description -> "Charm Yukawa mass"
665 },
666 ymb == {
667 ParameterType -> External,
668 BlockName -> YUKAWA,
669 OrderBlock -> 5,
670 Value -> 4.7,
671 Description -> "Bottom Yukawa mass"
672 },
673 ymt == {
674 ParameterType -> External,
675 BlockName -> YUKAWA,
676 OrderBlock -> 6,
677 Value -> 172,
678 Description -> "Top Yukawa mass"
679 },
680 yme == {
681 ParameterType -> External,
682 BlockName -> YUKAWA,
683 OrderBlock -> 11,
684 Value -> 5.11*^-4,
685 Description -> "Electron Yukawa mass"
686 },
687 ymm == {
688 ParameterType -> External,
689 BlockName -> YUKAWA,
690 OrderBlock -> 13,
691 Value -> 0.10566,
692 Description -> "Muon Yukawa mass"
693 },
694 ymtau == {
695 ParameterType -> External,
696 BlockName -> YUKAWA,
697 OrderBlock -> 15,
698 Value -> 1.777,
699 Description -> "Tau Yukawa mass"
700 },
701 cabi == {
702 ParameterType -> External,
703 BlockName -> CKMBLOCK,
704 OrderBlock -> 1,
705 Value -> 0.227736,
706 TeX -> Subscript[\[Theta], c],
707 Description -> "Cabibbo angle"
708 },
709 (***************B-L*****************)
710 g1p == {
711 ParameterType -> External,
712 BlockName -> BLINPUTS,
713 InteractionOrder -> {QED, 1},
714 TeX -> Subscript[g,1p],
715 Value -> 0.2,
716 Description -> "U(1)Y B-L coupling coustant at the Zp pole"
717 },
718 MH2 == {
719 ParameterType -> External,
720 BlockName -> BLINPUTS,
721 Value -> 450.00,
722 Description -> "H2 mass"
723 },
724 Sa == {
725 ParameterType -> External,
726 BlockName -> BLINPUTS,
727 Value -> 0.1,
728 Description -> "Sine of Higgses mixing angle"
729 },
730 (*********************neutrino mixing********************)
731 San == {
732 ParameterType -> Internal,
733 BlockName -> BLINPUTS,
734 Indices -> {Index[Generation]},
735 AllowSummation -> True,
736 Value -> {San[1] ->-Sqrt[MnL1/(MnH1+MnL1)],
737 San[2] -> -Sin[ArcSin[2*Mdd2/Sqrt[4*Mdd2^2+(MnH2-MnL2)^2]]/2],
738 San[3] -> -Sin[ArcSin[2*Mdd3/Sqrt[4*Mdd3^2+(MnH3-MnL3)^2]]/2]
739 },
740 ComplexParameter -> False,
741 ParameterName -> {San[1] -> San1, San[2] -> San2, San[3] -> San3},
742 Description -> "Sin-array of neutrino mass-eigenstates"
743 },
744 (***************END*****************)
745 (* Internal Parameters *)
746 Mdd == {
747 Indices -> {Index[Generation]},
748 AllowSummation -> True,
749 ParameterType -> Internal,
750 Value -> {Mdd[1] -> ynd1*vev/Sqrt[2],
751 Mdd[2] -> ynd2*vev/Sqrt[2],
752 Mdd[3] -> ynd3*vev/Sqrt[2]},
753 ParameterName -> {Mdd[1] -> Mdd1,
754 Mdd[2] -> Mdd2,
755 Mdd[3] -> Mdd3},
756 ComplexParameter -> False,
757 Description -> "Neutrino Dirac Mass"
758 },
759 aEW == {
760 ParameterType -> Internal,
761 Value -> 1/aEWM1,
762 InteractionOrder -> {QED,2},
763 TeX -> Subscript[\[Alpha], EW],
764 Description -> "Electroweak coupling contant"
765 },
766 MW == {
767 ParameterType -> Internal,
768 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
769 TeX -> Subscript[M,W],
770 Description -> "W mass"
771 },
772 sw2 == {
773 ParameterType -> Internal,
774 Value -> 1-(MW/MZ)^2,
775 Description -> "Squared Sin of the Weinberg angle"
776 },
777 ee == {
778 ParameterType -> Internal,
779 Value -> Sqrt[4 Pi aEW],
780 InteractionOrder -> {QED,1},
781 TeX -> e,
782 Description -> "Electric coupling constant"
783 },
784 cw == {
785 ParameterType -> Internal,
786 Value -> Sqrt[1-sw2],
787 TeX -> Subscript[c,w],
788 Description -> "Cosine of the Weinberg angle"
789 },
790 sw == {
791 ParameterType -> Internal,
792 Value -> Sqrt[sw2],
793 TeX -> Subscript[s,w],
794 Description -> "Sine of the Weinberg angle"
795 },
796 gw == {
797 ParameterType -> Internal,
798 Definitions -> {gw->ee/sw},
799 InteractionOrder -> {QED,1},
800 TeX -> Subscript[g,w],
801 Description -> "Weak coupling constant at the Z pole"
802 },
803 g1 == {
804 ParameterType -> Internal,
805 Definitions -> {g1->ee/cw},
806 InteractionOrder -> {QED,1},
807 TeX -> Subscript[g,1],
808 Description -> "U(1)Y coupling constant at the Z pole"
809 },
810 gs == {
811 ParameterType -> Internal,
812 Value -> Sqrt[4 Pi aS],
813 InteractionOrder -> {QCD,1},
814 TeX -> Subscript[g,s],
815 ParameterName -> G,
816 Description -> "Strong coupling constant at the Z pole"
817 },
818 vev == {
819 ParameterType -> Internal,
820 Value -> 2*MW*sw/ee,
821 InteractionOrder -> {QED,-1},
822 Description -> "Higgs vacuum expectation value"
823 },
824 (****************lightneutrino**************)
825 (*****************B-L********************)
826 xev == {
827 ParameterType -> Internal,
828 Value -> MZp/(2*g1p),
829 InteractionOrder -> {QED, -1},
830 Description -> "H2 VEV"
831 },
832 Ca == {
833 ParameterType -> Internal,
834 Value -> Sqrt[1-Sa^2],
835 ParameterName -> Ca,
836 Description -> "Cosine of Higgses mixing angle"
837 },
838 (*************neutrino mass terms********)
839 ynd == {
840 ParameterType -> Internal,
841 Indices -> {Index[Generation]},
842 AllowSummation -> True,
843 Value -> {ynd[1] -> Sqrt[2*MnH1*MnL1]/vev,
844 ynd[2] -> Sqrt[2*MnH2*MnL2]/vev,
845 ynd[3] -> Sqrt[2*MnH3*MnL3]/vev
846 },
847 InteractionOrder -> {QED, 1},
848 ComplexParameter -> False,
849 ParameterName -> {ynd[1] -> ynd1, ynd[2] -> ynd2, ynd[3] -> ynd3},
850 Description -> "Dirac neutrino Yukawa coupling"
851 },
852
853 ynm == {
854 ParameterType -> Internal,
855 Indices -> {Index[Generation]},
856 AllowSummation -> True,
857 Value -> {ynm[1] -> (MnH1-MnL1)/Sqrt[2]/xev,
858 ynm[2] -> (MnH2-MnL2)/Sqrt[2]/xev,
859 ynm[3] -> (MnH3-MnL3)/Sqrt[2]/xev},
860 InteractionOrder -> {QED, 1},
861 ComplexParameter -> False,
862 ParameterName -> {ynm[1] -> ynm1, ynm[2] -> ynm2, ynm[3] -> ynm3},
863 Description -> "Majorana neutrino Yukawa coupling"
864 },
865
866 Can == {
867 ParameterType -> Internal,
868 Indices -> {Index[Generation]},
869 AllowSummation -> True,
870 Value -> {Can[1] -> Sqrt[1-San1^2],
871 Can[2] -> Sqrt[1-San2^2],
872 Can[3] -> Sqrt[1-San3^2]},
873 ComplexParameter -> False,
874 ParameterName -> {Can[1] -> Can1, Can[2] -> Can2, Can[3] -> Can3},
875 Description -> "Cos-array of neutrino mass-eigenstates"
876 },
877
878
879 (**************Higgs Potential*******************)
880 lam1 == {
881 ParameterType -> Internal,
882 Value -> MH1^2/(2*vev^2)*Ca^2 + MH2^2 /(2*vev^2)*Sa^2,
883 ParameterName -> lam1,
884 InteractionOrder -> {QED, 2},
885 Description -> "Higgs quartic coupling piece for H1"
886 },
887 lam2 == {
888 ParameterType -> Internal,
889 Value -> MH1^2 /(2*xev^2)*Sa^2 + MH2^2 /(2*xev^2)*Ca^2,
890 ParameterName -> lam2,
891 InteractionOrder -> {QED,2},
892 Description -> "Higgs quartic coupling piece for H2"
893 },
894 lam3 == {
895 ParameterType -> Internal,
896 Value -> (MH2^2 - MH1^2)/(xev*vev)*Sa*Ca,
897 ParameterName -> lam3,
898 InteractionOrder -> {QED, 2},
899 Description -> "Mixing part"
900 },
901 mu2H1 == {
902 ParameterType -> Internal,
903 Value -> -lam1 * vev^2 - lam3 /2 * xev^2,
904 TeX -> \[Mu],
905 Description -> "Coefficient of the quadratic piece of the H1 potential"
906 },
907 mu2H2 == {
908 ParameterType -> Internal,
909 Value -> -lam3 /2 * vev^2 - lam2 * xev^2,
910 TeX -> \[Mu]prime,
911 Description -> "Coefficient of the quadratic piece of the H2 potential"
912 },
913 (******************END*********************)
914 yl == {
915 ParameterType -> Internal,
916 Indices -> {Index[Generation], Index[Generation]},
917 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
918 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
919 InteractionOrder -> {QED, 1},
920 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
921 TeX -> Superscript[y, l],
922 Description -> "Lepton Yukawa couplings"
923 },
924 yu == {
925 ParameterType -> Internal,
926 Indices -> {Index[Generation], Index[Generation]},
927 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
928 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
929 InteractionOrder -> {QED, 1},
930 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
931 TeX -> Superscript[y, u],
932 Description -> "Up-type Yukawa couplings"
933 },
934 yd == {
935 ParameterType -> Internal,
936 Indices -> {Index[Generation], Index[Generation]},
937 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
938 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
939 InteractionOrder -> {QED, 1},
940 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
941 TeX -> Superscript[y, d],
942 Description -> "Down-type Yukawa couplings"
943 },
944(* N. B. : only Cabibbo mixing! *)
945 CKM == {
946 ParameterType -> Internal,
947 Indices -> {Index[Generation], Index[Generation]},
948 Unitary -> True,
949 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
950 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
951 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
952 TeX -> Superscript[V,CKM],
953 Description -> "CKM-Matrix"}
954};
955
956(* ************************** *)
957(* ***** Lagrangian ***** *)
958(* ************************** *)
959
960LGauge := Block[{mu,nu,ii,aa},
961 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]
962(*************B-L*******************)
963 -1/4 FS[Bp,mu,nu] FS[Bp,mu,nu],
964(*************END********************)
965 FlavorExpand->SU2W]];
966
967LFermions := Block[{mu},
968 ExpandIndices[I*(
969 QLbar.Ga[mu].DC[QL, mu] + LLbar.Ga[mu].DC[LL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu] + lRbar.Ga[mu].DC[lR, mu]
970(**********B-L*********************)
971 + VRbar.Ga[mu].DC[VR,mu]
972(***********END********************)
973),
974 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
975
976LHiggs := Block[{ii,mu, feynmangaugerules},
977 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar|phip ->0}, {}];
978
979 ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] - mu2H1 Phibar[ii] Phi[ii] - lam1 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]
980(*******************B-L****************************)
981+ DC[Xibar,mu] DC[Xi,mu]
982- mu2H2 Xibar Xi
983- lam2 Xibar Xi Xibar Xi
984- lam3 Phibar[ii]Phi[ii] Xibar Xi
985(*******************END****************************)
986 , FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
987 ];
988
989LYukawaSM := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
990 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar|phip ->0}, {}];
991
992 yuk = ExpandIndices[
993 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
994 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
995 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj]
996 , FlavorExpand -> SU2D];
997 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
998 yuk+HC[yuk]/.feynmangaugerules
999 ];
1000(**********************B-L***************************)
1001LYukawaBL := Block[{ff1,sp,ii,feynmangaugerules},
1002 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar|phip ->0}, {}];
1003
1004 yun = ExpandIndices[
1005 -ynd[ff1] LLbar[sp,ii,ff1].VR[sp,ff1]Phibar[jj]Eps[ii, jj]
1006 -ynm[ff1] nRbar[sp,ff1].VR[sp,ff1] Xi
1007 , FlavorExpand -> SU2D];
1008 yun+HC[yun]/.feynmangaugerules
1009 ];
1010LYukawa := LYukawaSM + LYukawaBL;
1011Lmaj :=-ynm[ff1] nRbar[sp,ff1].VR[sp,ff1] Xi
1012Lnew :=-ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n]Xi
1013(**********************END***************************)
1014(*******************Eqn.(2.44) from 1106.4691******************************)
1015(*****************B-L is an abelian group, DC->del, https://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost**********)
1016LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,LGhBp, LGhphiBL, mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
1017 (* Pure gauge piece *)
1018 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
1019 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
1020 LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
1021(******************B-L***********************)
1022 LGhBp = - ghBpbar.del[del[ghBp, mu],mu];
1023 LGhphiBL = -2*g1p MZp (xev-Sa*H1+Ca*H2) ghZpbar.ghZp;
1024(**********************END***************************)
1025 (* Scalar pieces: see Peskin pages 739-742 *)
1026 (* phi1 and phi2 are the real degrees of freedom of GP *)
1027 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
1028 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
1029 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
1030 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
1031 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
1032 doublet0 = {0, vev/Sqrt[2]};
1033 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}];
1034 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
1035 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
1036
1037ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi + LGhBp + LGhphiBL ,0], FlavorExpand->SU2W]];
1038LBL:= LGauge + LFermions + LHiggs + LYukawa + LGhost;