B-L-SM: B-L_4.fr

File B-L_4.fr, 33.2 KB (added by WeiLiu, 4 years ago)

quantum number warning fixed

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$ModelName = "B-L-4";
16
17M$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(***this version take the neutrino mixing as external parameters******)
49(* ************************** *)
50(* ***** vevs ***** *)
51(* ************************** *)
52M$vevs = { {Phi[2],vev} };
53(************B-L***************)
54
55
56(************End***************)
57
58(* ************************** *)
59(* ***** Gauge groups ***** *)
60(* ************************** *)
61M$GaugeGroups = {
62(************B-L***************)
63 U1BL == {
64 Abelian -> True,
65 CouplingConstant -> g1p,
66 GaugeBoson -> Bp,
67 Charge -> BL
68 },
69(************End***************)
70 U1Y == {
71 Abelian -> True,
72 CouplingConstant -> g1,
73 GaugeBoson -> B,
74 Charge -> Y
75 },
76 SU2L == {
77 Abelian -> False,
78 CouplingConstant -> gw,
79 GaugeBoson -> Wi,
80 StructureConstant -> Eps,
81 Representations -> {Ta,SU2D},
82 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
83 },
84 SU3C == {
85 Abelian -> False,
86 CouplingConstant -> gs,
87 GaugeBoson -> G,
88 StructureConstant -> f,
89 Representations -> {T,Colour},
90 SymmetricTensor -> dSUN
91 }
92};
93
94
95(* ************************** *)
96(* ***** Indices ***** *)
97(* ************************** *)
98
99IndexRange[Index[SU2W ]] = Unfold[Range[3]];
100IndexRange[Index[SU2D ]] = Unfold[Range[2]];
101IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
102IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
103IndexRange[Index[Generation]] = Range[3];
104
105IndexStyle[SU2W, j];
106IndexStyle[SU2D, k];
107IndexStyle[Gluon, a];
108IndexStyle[Colour, m];
109IndexStyle[Generation, f];
110
111
112(* ************************** *)
113(* *** Interaction orders *** *)
114(* *** (as used by mg5) *** *)
115(* ************************** *)
116
117M$InteractionOrderHierarchy = {
118 {QCD, 1},
119 {QED, 2}
120};
121
122
123(* ************************** *)
124(* **** Particle classes **** *)
125(* ************************** *)
126M$ClassesDescription = {
127
128(* Gauge bosons: physical vector fields *)
129(* Gauge bosons: Q = 0 *)
130 V[1] == {
131 ClassName -> A,
132 SelfConjugate -> True,
133 Mass -> 0,
134 Width -> 0,
135 ParticleName -> "a",
136 PDG -> 22,
137 PropagatorLabel -> "a",
138 PropagatorType -> W,
139 PropagatorArrow -> None,
140 FullName -> "Photon"
141 },
142 V[2] == {
143 ClassName -> Z,
144 SelfConjugate -> True,
145 Mass -> {MZ, 91.1876},
146 Width -> {WZ, 2.4952},
147 ParticleName -> "Z",
148 PDG -> 23,
149 PropagatorLabel -> "Z",
150 PropagatorType -> Sine,
151 PropagatorArrow -> None,
152 FullName -> "Z"
153 },
154 V[3] == {
155 ClassName -> W,
156 SelfConjugate -> False,
157 Mass -> {MW, Internal},
158 Width -> {WW, 2.085},
159 ParticleName -> "W+",
160 AntiParticleName -> "W-",
161 QuantumNumbers -> {Q -> 1},
162 PDG -> 24,
163 PropagatorLabel -> "W",
164 PropagatorType -> Sine,
165 PropagatorArrow -> Forward,
166 FullName -> "W"
167 },
168 V[4] == {
169 ClassName -> G,
170 SelfConjugate -> True,
171 Indices -> {Index[Gluon]},
172 Mass -> 0,
173 Width -> 0,
174 ParticleName -> "g",
175 PDG -> 21,
176 PropagatorLabel -> "G",
177 PropagatorType -> C,
178 PropagatorArrow -> None,
179 FullName -> "G"
180 },
181
182(* Ghosts: related to physical gauge bosons *)
183 U[1] == {
184 ClassName -> ghA,
185 SelfConjugate -> False,
186 Ghost -> A,
187 QuantumNumbers -> {GhostNumber -> 1},
188 Mass -> 0,
189 Width -> 0,
190 PropagatorLabel -> "uA",
191 PropagatorType -> GhostDash,
192 PropagatorArrow -> Forward
193 },
194 U[2] == {
195 ClassName -> ghZ,
196 SelfConjugate -> False,
197 Ghost -> Z,
198 QuantumNumbers -> {GhostNumber -> 1},
199 Mass -> {MZ,91.1876},
200 Width -> {WZ, 2.4952},
201 PropagatorLabel -> "uZ",
202 PropagatorType -> GhostDash,
203 PropagatorArrow -> Forward
204 },
205 U[31] == {
206 ClassName -> ghWp,
207 SelfConjugate -> False,
208 Ghost -> W,
209 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
210 Mass -> {MW,Internal},
211 Width -> {WW, 2.085},
212 PropagatorLabel -> "uWp",
213 PropagatorType -> GhostDash,
214 PropagatorArrow -> Forward
215 },
216 U[32] == {
217 ClassName -> ghWm,
218 SelfConjugate -> False,
219 Ghost -> Wbar,
220 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
221 Mass -> {MW,Internal},
222 Width -> {WW, 2.085},
223 PropagatorLabel -> "uWm",
224 PropagatorType -> GhostDash,
225 PropagatorArrow -> Forward
226 },
227 U[4] == {
228 ClassName -> ghG,
229 SelfConjugate -> False,
230 Indices -> {Index[Gluon]},
231 Ghost -> G,
232 PDG -> 82,
233 QuantumNumbers ->{GhostNumber -> 1},
234 Mass -> 0,
235 Width -> 0,
236 PropagatorLabel -> "uG",
237 PropagatorType -> GhostDash,
238 PropagatorArrow -> Forward
239 },
240(************B-L***************)
241 V[5] == {
242 ClassName -> Zp,
243 SelfConjugate -> True,
244 Indices -> {},
245 Mass -> {MZp, 1500},
246 Width -> {WZp, 80.00},
247 ParticleName -> "Zp",
248 PDG -> 9900032,
249 PropagatorLabel -> "Zp",
250 PropagatorType -> Sine,
251 PropagatorArrow -> None,
252 FullName -> "Zp"
253 },
254 V[6] == {
255 ClassName -> Bp,
256 SelfConjugate -> True,
257 Indices -> {},
258 Definitions -> {Bp[mu_] -> Zp[mu]},
259 Unphysical -> True
260 },
261
262 U[5] == {
263 ClassName -> ghZp,
264 SelfConjugate -> False,
265 Indices -> {},
266 Ghost -> Zp,
267 QuantumNumbers -> {GhostNumber -> 1},
268 Mass -> {MZp, Internal},
269 Width -> {WZp, 80.00},
270 PropagatorLabel -> "uZp",
271 PropagatorType -> GhostDash,
272 PropagatorArrow -> Forward
273 },
274 U[6] == {
275 ClassName -> ghBp,
276 SelfConjugate -> False,
277 Definitions -> {ghBp -> ghZp},
278 Indices -> {},
279 Unphysical -> True,
280 Ghost -> Bp
281 },
282
283(************End***************)
284
285(* Gauge bosons: unphysical vector fields *)
286 V[11] == {
287 ClassName -> B,
288 Unphysical -> True,
289 SelfConjugate -> True,
290 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
291 },
292 V[12] == {
293 ClassName -> Wi,
294 Unphysical -> True,
295 SelfConjugate -> True,
296 Indices -> {Index[SU2W]},
297 FlavorIndex -> SU2W,
298 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]}
299 },
300
301(* Ghosts: related to unphysical gauge bosons *)
302 U[11] == {
303 ClassName -> ghB,
304 Unphysical -> True,
305 SelfConjugate -> False,
306 Ghost -> B,
307 Definitions -> { ghB -> -sw ghZ + cw ghA}
308 },
309 U[12] == {
310 ClassName -> ghWi,
311 Unphysical -> True,
312 SelfConjugate -> False,
313 Ghost -> Wi,
314 Indices -> {Index[SU2W]},
315 FlavorIndex -> SU2W,
316 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
317 } ,
318
319(* Fermions: physical fields *)
320(************B-L******************)
321 F[1] == {
322 ClassName -> nL,
323 ClassMembers -> {nL1,nL2,nL3},
324 Indices -> {Index[Generation]},
325 FlavorIndex -> Generation,
326 SelfConjugate -> True,
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 Mass -> {MnH,{MnH1, 200.00},{MnH2, 200.00},{MnH3, 200.00}},
343 Width -> 10^(-13),
344 PropagatorLabel -> {"nH","nuh1","nuh2","nuh3"},
345 PropagatorType -> Straight,
346 PropagatorArrow -> Forward,
347 PDG -> {9910012, 9910014, 9910016},
348 ParticleName -> {"nH1","nH2","nH3"},
349 FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"}
350 },
351 (* unphysical *)
352 F[17] == {
353 ClassName -> nF,
354 ClassMembers -> {nF1,nF2,nF3},
355 Indices -> {Index[Generation]},
356 FlavorIndex -> Generation,
357 SelfConjugate -> True,
358 Unphysical -> True,
359 Definitions -> {nF[sp_,ff_] -> Can[ff] nL[sp,ff]-San[ff] nH[sp,ff]}
360 },
361 (* unphysical *)
362 F[18] == {
363 ClassName -> nR,
364 ClassMembers -> {nR1,nR2,nR3},
365 Indices -> {Index[Generation]},
366 FlavorIndex -> Generation,
367 SelfConjugate -> True,
368 Unphysical -> True,
369 Definitions -> {nR[sp_,ff_] -> San[ff] nL[sp,ff]+Can[ff] nH[sp,ff]}
370 },
371
372 (* Flavour-eigenstate neutrino: unphysical *)
373 (* Righthanded flavor neutrino: unphysical *)
374 F[20] == {
375 ClassName -> VR,
376 Unphysical -> True,
377 Indices -> {Index[Generation]},
378 QuantumNumbers -> {Y -> 0, BL -> -1, LeptonNumber -> 1},
379 FlavorIndex -> Generation,
380 SelfConjugate -> False,
381 Definitions -> { VR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] nR[sp2,ff]]}
382 },
383(***************END******************)
384
385 F[2] == {
386 ClassName -> l,
387 ClassMembers -> {e, mu, ta},
388 Indices -> {Index[Generation]},
389 FlavorIndex -> Generation,
390 SelfConjugate -> False,
391 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
392 Width -> 0,
393 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
394 PropagatorLabel -> {"l", "e", "mu", "ta"},
395 PropagatorType -> Straight,
396 PropagatorArrow -> Forward,
397 PDG -> {11, 13, 15},
398 ParticleName -> {"e-", "mu-", "ta-"},
399 AntiParticleName -> {"e+", "mu+", "ta+"},
400 FullName -> {"Electron", "Muon", "Tau"}
401 },
402 (* Quarks (u): I_3 = +1/2, Q = +2/3, BL=1/3 *)
403 F[3] == {
404 ClassName -> uq,
405 ClassMembers -> {u, c, t},
406 Indices -> {Index[Generation], Index[Colour]},
407 FlavorIndex -> Generation,
408 SelfConjugate -> False,
409 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
410 Width -> {0, 0, {WT,1.50833649}},
411 QuantumNumbers -> {Q -> 2/3},
412 PropagatorLabel -> {"uq", "u", "c", "t"},
413 PropagatorType -> Straight,
414 PropagatorArrow -> Forward,
415 PDG -> {2, 4, 6},
416 ParticleName -> {"u", "c", "t" },
417 AntiParticleName -> {"u~", "c~", "t~"},
418 FullName -> {"u-quark", "c-quark", "t-quark"}
419 },
420 (* Quarks (d): I_3 = -1/2, Q = -1/3, BL=1/3 *)
421 F[4] == {
422 ClassName -> dq,
423 ClassMembers -> {d, s, b},
424 Indices -> {Index[Generation], Index[Colour]},
425 FlavorIndex -> Generation,
426 SelfConjugate -> False,
427 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
428 Width -> 0,
429 QuantumNumbers -> {Q -> -1/3},
430 PropagatorLabel -> {"dq", "d", "s", "b"},
431 PropagatorType -> Straight,
432 PropagatorArrow -> Forward,
433 PDG -> {1,3,5},
434 ParticleName -> {"d", "s", "b" },
435 AntiParticleName -> {"d~", "s~", "b~"},
436 FullName -> {"d-quark", "s-quark", "b-quark"}
437 },
438
439(* Fermions: unphysical fields *)
440 F[11] == {
441 ClassName -> LL,
442 Unphysical -> True,
443 Indices -> {Index[SU2D], Index[Generation]},
444 FlavorIndex -> SU2D,
445 SelfConjugate -> False,
446 QuantumNumbers -> {Y -> -1/2, BL -> -1},
447 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]] }
448 },
449 F[12] == {
450 ClassName -> lR,
451 Unphysical -> True,
452 Indices -> {Index[Generation]},
453 FlavorIndex -> Generation,
454 SelfConjugate -> False,
455 QuantumNumbers -> {Y -> -1, BL -> -1},
456 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
457 },
458 F[13] == {
459 ClassName -> QL,
460 Unphysical -> True,
461 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
462 FlavorIndex -> SU2D,
463 SelfConjugate -> False,
464 QuantumNumbers -> {Y -> 1/6, BL -> 1/3},
465 Definitions -> {
466 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
467 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
468 },
469 F[14] == {
470 ClassName -> uR,
471 Unphysical -> True,
472 Indices -> {Index[Generation], Index[Colour]},
473 FlavorIndex -> Generation,
474 SelfConjugate -> False,
475 QuantumNumbers -> {Y -> 2/3, BL -> 1/3},
476 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
477 },
478 F[15] == {
479 ClassName -> dR,
480 Unphysical -> True,
481 Indices -> {Index[Generation], Index[Colour]},
482 FlavorIndex -> Generation,
483 SelfConjugate -> False,
484 QuantumNumbers -> {Y -> -1/3, BL -> 1/3},
485 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
486 },
487
488(* Higgs: physical scalars *)
489 S[1] == {
490 ClassName -> H1,
491 SelfConjugate -> True,
492 Mass -> {MH1,125},
493 Width -> {WH1,0.00407},
494 PropagatorLabel -> "H1",
495 PropagatorType -> D,
496 PropagatorArrow -> None,
497 PDG -> 9900025,
498 ParticleName -> "H1",
499 FullName -> "H1"
500 },
501
502(* Higgs: physical scalars *)
503(**********phi(phi0)****************)
504 S[2] == {
505 ClassName -> G0,
506 SelfConjugate -> True,
507 Goldstone -> Z,
508 Mass -> {MZ, 91.1876},
509 Width -> {WZ, 2.4952},
510 PropagatorLabel -> "Go",
511 PropagatorType -> D,
512 PropagatorArrow -> None,
513 PDG -> 250,
514 ParticleName -> "G0",
515 FullName -> "G0"
516 },
517(************phi2*******************)
518 S[3] == {
519 ClassName -> GP,
520 SelfConjugate -> False,
521 Goldstone -> W,
522 Mass -> {MW, Internal},
523 QuantumNumbers -> {Q -> 1},
524 Width -> {WW, 2.085},
525 PropagatorLabel -> "GP",
526 PropagatorType -> D,
527 PropagatorArrow -> None,
528 PDG -> 251,
529 ParticleName -> "G+",
530 AntiParticleName -> "G-",
531 FullName -> "GP"
532 },
533 (***************B-L*****************)
534(* Higgs: unphysical scalars *)
535 S[11] == {
536 ClassName -> Phi,
537 Unphysical -> True,
538 Indices -> {Index[SU2D]},
539 FlavorIndex -> SU2D,
540 SelfConjugate -> False,
541 QuantumNumbers -> {Y -> 1/2, BL -> 0},
542 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + Ca*H1 + Sa*H2 + I G0)/Sqrt[2] }
543 },
544 S[12] == {
545 ClassName -> Xi,
546 Unphysical -> True,
547 SelfConjugate -> False,
548 QuantumNumbers -> {Y -> 0, BL -> 2},
549 Definitions -> { Xi -> (xev - Sa*H1 + Ca*H2 + I phip)/Sqrt[2]
550 }
551 },
552 S[4] == {
553 ClassName -> H2,
554 SelfConjugate -> True,
555 Mass -> {MH2, Internal},
556 Width -> {WH2, 10},
557 PropagatorLabel -> "H2",
558 PropagatorType -> D,
559 PropagatorArrow -> None,
560 PDG -> 9900026,
561 ParticleName -> "H2",
562 FullName -> "H2"
563 },
564 S[5] == {
565 ClassName -> phip,
566 SelfConjugate -> True,
567 Goldstone -> Zp,
568 Mass -> {MZp, Internal},
569 Width -> Wphip,
570 PropagatorLabel -> "Phip",
571 PropagatorType -> D,
572 PropagatorArrow -> None,
573 PDG -> 9900252,
574 ParticleName -> "phi0p",
575 FullName -> "Phip"
576 }
577};
578 (***************END*****************)
579
580(* ************************** *)
581(* ***** Gauge ***** *)
582(* ***** Parameters ***** *)
583(* ***** (FeynArts) ***** *)
584(* ************************** *)
585
586GaugeXi[ V[1] ] = GaugeXi[A];
587GaugeXi[ V[2] ] = GaugeXi[Z];
588GaugeXi[ V[3] ] = GaugeXi[W];
589GaugeXi[ V[4] ] = GaugeXi[G];
590GaugeXi[ S[1] ] = 1;
591GaugeXi[ S[2] ] = GaugeXi[Z];
592GaugeXi[ S[3] ] = GaugeXi[W];
593GaugeXi[ U[1] ] = GaugeXi[A];
594GaugeXi[ U[2] ] = GaugeXi[Z];
595GaugeXi[ U[31] ] = GaugeXi[W];
596GaugeXi[ U[32] ] = GaugeXi[W];
597GaugeXi[ U[4] ] = GaugeXi[G];
598(***************B-L*****************)
599GaugeXi[ V[5] ] = GaugeXi[Zp];
600GaugeXi[ S[4] ] = 1;
601GaugeXi[ S[5] ] = GaugeXi[Zp];
602GaugeXi[ U[5] ] = GaugeXi[Zp];
603(***************END*****************)
604
605(* ************************** *)
606(* ***** Parameters ***** *)
607(* ************************** *)
608M$Parameters = {
609
610 (* External parameters *)
611 aEWM1 == {
612 ParameterType -> External,
613 BlockName -> SMINPUTS,
614 OrderBlock -> 1,
615 Value -> 127.9,
616 InteractionOrder -> {QED,-2},
617 Description -> "Inverse of the EW coupling constant at the Z pole"
618 },
619 Gf == {
620 ParameterType -> External,
621 BlockName -> SMINPUTS,
622 OrderBlock -> 2,
623 Value -> 1.16637*^-5,
624 InteractionOrder -> {QED,2},
625 TeX -> Subscript[G,f],
626 Description -> "Fermi constant"
627 },
628 aS == {
629 ParameterType -> External,
630 BlockName -> SMINPUTS,
631 OrderBlock -> 3,
632 Value -> 0.1184,
633 InteractionOrder -> {QCD,2},
634 TeX -> Subscript[\[Alpha],s],
635 Description -> "Strong coupling constant at the Z pole"
636 },
637 ymdo == {
638 ParameterType -> External,
639 BlockName -> YUKAWA,
640 OrderBlock -> 1,
641 Value -> 5.04*^-3,
642 Description -> "Down Yukawa mass"
643 },
644 ymup == {
645 ParameterType -> External,
646 BlockName -> YUKAWA,
647 OrderBlock -> 2,
648 Value -> 2.55*^-3,
649 Description -> "Up Yukawa mass"
650 },
651 yms == {
652 ParameterType -> External,
653 BlockName -> YUKAWA,
654 OrderBlock -> 3,
655 Value -> 0.101,
656 Description -> "Strange Yukawa mass"
657 },
658 ymc == {
659 ParameterType -> External,
660 BlockName -> YUKAWA,
661 OrderBlock -> 4,
662 Value -> 1.27,
663 Description -> "Charm Yukawa mass"
664 },
665 ymb == {
666 ParameterType -> External,
667 BlockName -> YUKAWA,
668 OrderBlock -> 5,
669 Value -> 4.7,
670 Description -> "Bottom Yukawa mass"
671 },
672 ymt == {
673 ParameterType -> External,
674 BlockName -> YUKAWA,
675 OrderBlock -> 6,
676 Value -> 172,
677 Description -> "Top Yukawa mass"
678 },
679 yme == {
680 ParameterType -> External,
681 BlockName -> YUKAWA,
682 OrderBlock -> 11,
683 Value -> 5.11*^-4,
684 Description -> "Electron Yukawa mass"
685 },
686 ymm == {
687 ParameterType -> External,
688 BlockName -> YUKAWA,
689 OrderBlock -> 13,
690 Value -> 0.10566,
691 Description -> "Muon Yukawa mass"
692 },
693 ymtau == {
694 ParameterType -> External,
695 BlockName -> YUKAWA,
696 OrderBlock -> 15,
697 Value -> 1.777,
698 Description -> "Tau Yukawa mass"
699 },
700 cabi == {
701 ParameterType -> External,
702 BlockName -> CKMBLOCK,
703 OrderBlock -> 1,
704 Value -> 0.227736,
705 TeX -> Subscript[\[Theta], c],
706 Description -> "Cabibbo angle"
707 },
708 (***************B-L*****************)
709 g1p == {
710 ParameterType -> External,
711 BlockName -> BLINPUTS,
712 InteractionOrder -> {QED, 1},
713 TeX -> Subscript[g,1p],
714 Value -> 0.2,
715 Description -> "U(1)Y B-L coupling coustant at the Zp pole"
716 },
717 MH2 == {
718 ParameterType -> External,
719 BlockName -> BLINPUTS,
720 Value -> 450.00,
721 Description -> "H2 mass"
722 },
723 Sa == {
724 ParameterType -> External,
725 BlockName -> BLINPUTS,
726 Value -> 0.1,
727 Description -> "Sine of Higgses mixing angle"
728 },
729 (*********************neutrino mixing********************)
730 San == {
731 ParameterType -> Internal,
732 BlockName -> BLINPUTS,
733 Indices -> {Index[Generation]},
734 AllowSummation -> True,
735 Value -> {San[1] -> 0.01,
736 San[2] -> 0.01,
737 San[3] -> 0.01
738 },
739 ComplexParameter -> False,
740 ParameterName -> {San[1] -> San1, San[2] -> San2, San[3] -> San3},
741 Description -> "Sin-array of neutrino mass-eigenstates"
742 },
743 (***************END*****************)
744 (* Internal Parameters *)
745 aEW == {
746 ParameterType -> Internal,
747 Value -> 1/aEWM1,
748 InteractionOrder -> {QED,2},
749 TeX -> Subscript[\[Alpha], EW],
750 Description -> "Electroweak coupling contant"
751 },
752 MW == {
753 ParameterType -> Internal,
754 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
755 TeX -> Subscript[M,W],
756 Description -> "W mass"
757 },
758 sw2 == {
759 ParameterType -> Internal,
760 Value -> 1-(MW/MZ)^2,
761 Description -> "Squared Sin of the Weinberg angle"
762 },
763 ee == {
764 ParameterType -> Internal,
765 Value -> Sqrt[4 Pi aEW],
766 InteractionOrder -> {QED,1},
767 TeX -> e,
768 Description -> "Electric coupling constant"
769 },
770 cw == {
771 ParameterType -> Internal,
772 Value -> Sqrt[1-sw2],
773 TeX -> Subscript[c,w],
774 Description -> "Cosine of the Weinberg angle"
775 },
776 sw == {
777 ParameterType -> Internal,
778 Value -> Sqrt[sw2],
779 TeX -> Subscript[s,w],
780 Description -> "Sine of the Weinberg angle"
781 },
782 gw == {
783 ParameterType -> Internal,
784 Definitions -> {gw->ee/sw},
785 InteractionOrder -> {QED,1},
786 TeX -> Subscript[g,w],
787 Description -> "Weak coupling constant at the Z pole"
788 },
789 g1 == {
790 ParameterType -> Internal,
791 Definitions -> {g1->ee/cw},
792 InteractionOrder -> {QED,1},
793 TeX -> Subscript[g,1],
794 Description -> "U(1)Y coupling constant at the Z pole"
795 },
796 gs == {
797 ParameterType -> Internal,
798 Value -> Sqrt[4 Pi aS],
799 InteractionOrder -> {QCD,1},
800 TeX -> Subscript[g,s],
801 ParameterName -> G,
802 Description -> "Strong coupling constant at the Z pole"
803 },
804 vev == {
805 ParameterType -> Internal,
806 Value -> 2*MW*sw/ee,
807 InteractionOrder -> {QED,-1},
808 Description -> "Higgs vacuum expectation value"
809 },
810 (****************lightneutrino**************)
811 (*****************B-L********************)
812 xev == {
813 ParameterType -> Internal,
814 Value -> MZp/(2*g1p),
815 InteractionOrder -> {QED, -1},
816 Description -> "H2 VEV"
817 },
818 Ca == {
819 ParameterType -> Internal,
820 Value -> Sqrt[1-Sa^2],
821 ParameterName -> Ca,
822 Description -> "Cosine of Higgses mixing angle"
823 },
824 (*************neutrino mass terms********)
825 ynd == {
826 ParameterType -> Internal,
827 Indices -> {Index[Generation]},
828 AllowSummation -> True,
829 Value -> {ynd[1] -> Sqrt[2*MnH1*MnL1]/vev,
830 ynd[2] -> Sqrt[2*MnH2*MnL2]/vev,
831 ynd[3] -> Sqrt[2*MnH3*MnL3]/vev
832 },
833 InteractionOrder -> {QED, 1},
834 ComplexParameter -> False,
835 ParameterName -> {ynd[1] -> ynd1, ynd[2] -> ynd2, ynd[3] -> ynd3},
836 Description -> "Dirac neutrino Yukawa coupling"
837 },
838
839 ynm == {
840 ParameterType -> Internal,
841 Indices -> {Index[Generation]},
842 AllowSummation -> True,
843 Value -> {ynm[1] -> (MnH1-MnL1)/Sqrt[2]/xev,
844 ynm[2] -> (MnH2-MnL2)/Sqrt[2]/xev,
845 ynm[3] -> (MnH3-MnL3)/Sqrt[2]/xev},
846 InteractionOrder -> {QED, 1},
847 ComplexParameter -> False,
848 ParameterName -> {ynm[1] -> ynm1, ynm[2] -> ynm2, ynm[3] -> ynm3},
849 Description -> "Majorana neutrino Yukawa coupling"
850 },
851
852 Can == {
853 ParameterType -> Internal,
854 Indices -> {Index[Generation]},
855 AllowSummation -> True,
856 Value -> {Can[1] -> Sqrt[1-San1^2],
857 Can[2] -> Sqrt[1-San2^2],
858 Can[3] -> Sqrt[1-San3^2]},
859 ComplexParameter -> False,
860 ParameterName -> {Can[1] -> Can1, Can[2] -> Can2, Can[3] -> Can3},
861 Description -> "Cos-array of neutrino mass-eigenstates"
862 },
863
864
865 (**************Higgs Potential*******************)
866 lam1 == {
867 ParameterType -> Internal,
868 Value -> MH1^2/(2*vev^2)*Ca^2 + MH2^2 /(2*vev^2)*Sa^2,
869 ParameterName -> lam1,
870 InteractionOrder -> {QED, 2},
871 Description -> "Higgs quartic coupling piece for H1"
872 },
873 lam2 == {
874 ParameterType -> Internal,
875 Value -> MH1^2 /(2*xev^2)*Sa^2 + MH2^2 /(2*xev^2)*Ca^2,
876 ParameterName -> lam2,
877 InteractionOrder -> {QED,2},
878 Description -> "Higgs quartic coupling piece for H2"
879 },
880 lam3 == {
881 ParameterType -> Internal,
882 Value -> (MH2^2 - MH1^2)/(xev*vev)*Sa*Ca,
883 ParameterName -> lam3,
884 InteractionOrder -> {QED, 2},
885 Description -> "Mixing part"
886 },
887 mu2H1 == {
888 ParameterType -> Internal,
889 Value -> -lam1 * vev^2 - lam3 /2 * xev^2,
890 TeX -> \[Mu],
891 Description -> "Coefficient of the quadratic piece of the H1 potential"
892 },
893 mu2H2 == {
894 ParameterType -> Internal,
895 Value -> -lam3 /2 * vev^2 - lam2 * xev^2,
896 TeX -> \[Mu]prime,
897 Description -> "Coefficient of the quadratic piece of the H2 potential"
898 },
899 (******************END*********************)
900 yl == {
901 ParameterType -> Internal,
902 Indices -> {Index[Generation], Index[Generation]},
903 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
904 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
905 InteractionOrder -> {QED, 1},
906 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
907 TeX -> Superscript[y, l],
908 Description -> "Lepton Yukawa couplings"
909 },
910 yu == {
911 ParameterType -> Internal,
912 Indices -> {Index[Generation], Index[Generation]},
913 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
914 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
915 InteractionOrder -> {QED, 1},
916 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
917 TeX -> Superscript[y, u],
918 Description -> "Up-type Yukawa couplings"
919 },
920 yd == {
921 ParameterType -> Internal,
922 Indices -> {Index[Generation], Index[Generation]},
923 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
924 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
925 InteractionOrder -> {QED, 1},
926 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
927 TeX -> Superscript[y, d],
928 Description -> "Down-type Yukawa couplings"
929 },
930(* N. B. : only Cabibbo mixing! *)
931 CKM == {
932 ParameterType -> Internal,
933 Indices -> {Index[Generation], Index[Generation]},
934 Unitary -> True,
935 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
936 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
937 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
938 TeX -> Superscript[V,CKM],
939 Description -> "CKM-Matrix"}
940};
941
942(* ************************** *)
943(* ***** Lagrangian ***** *)
944(* ************************** *)
945
946LGauge := Block[{mu,nu,ii,aa},
947 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]
948(*************B-L*******************)
949 -1/4 FS[Bp,mu,nu] FS[Bp,mu,nu],
950(*************END********************)
951 FlavorExpand->SU2W]];
952
953LFermions := Block[{mu},
954 ExpandIndices[I*(
955 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]
956(**********B-L*********************)
957 + VRbar.Ga[mu].DC[VR,mu]
958(***********END********************)
959),
960 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
961
962LHiggs := Block[{ii,mu, feynmangaugerules},
963 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar|phip ->0}, {}];
964
965 ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] - mu2H1 Phibar[ii] Phi[ii] - lam1 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]
966(*******************B-L****************************)
967+ DC[Xibar,mu] DC[Xi,mu]
968- mu2H2 Xibar Xi
969- lam2 Xibar Xi Xibar Xi
970- lam3 Phibar[ii]Phi[ii] Xibar Xi
971(*******************END****************************)
972 , FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
973 ];
974
975LYukawaSM := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
976 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar|phip ->0}, {}];
977
978 yuk = ExpandIndices[
979 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
980 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
981 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj]
982 , FlavorExpand -> SU2D];
983 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
984 yuk+HC[yuk]/.feynmangaugerules
985 ];
986(**********************B-L***************************)
987LYukawaBL := Block[{ff1,sp,ii,feynmangaugerules},
988 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar|phip ->0}, {}];
989
990 yun = ExpandIndices[
991 -ynd[ff1] LLbar[sp,ii,ff1].VR[sp,ff1]Phibar[jj]Eps[ii, jj]
992 -ynm[ff1] nRbar[sp,ff1].VR[sp,ff1] Xi
993 , FlavorExpand -> SU2D];
994 yun+HC[yun]/.feynmangaugerules
995 ];
996LYukawa := LYukawaSM + LYukawaBL;
997Lmaj :=-ynm[ff1] nRbar[sp,ff1].VR[sp,ff1] Xi
998Lnew :=-ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n]Xi
999(**********************END***************************)
1000(*******************Eqn.(2.44) from 1106.4691******************************)
1001(*****************B-L is an abelian group, DC->del, https://en.wikipedia.org/wiki/Faddeev%E2%80%93Popov_ghost**********)
1002LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,LGhBp, LGhphiBL, mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
1003 (* Pure gauge piece *)
1004 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
1005 LGhw = -ghWibar[ii].del[DC[ghWi[ii],mu],mu];
1006 LGhs = -ghGbar[ii].del[DC[ghG[ii],mu],mu];
1007(******************B-L***********************)
1008 LGhBp = - ghBpbar.del[del[ghBp, mu],mu];
1009 LGhphiBL = -2*g1p MZp (xev-Sa*H1+Ca*H2) ghZpbar.ghZp;
1010(**********************END***************************)
1011 (* Scalar pieces: see Peskin pages 739-742 *)
1012 (* phi1 and phi2 are the real degrees of freedom of GP *)
1013 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
1014 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
1015 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
1016 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
1017 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
1018 doublet0 = {0, vev/Sqrt[2]};
1019 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}];
1020 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
1021 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
1022
1023ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi + LGhBp + LGhphiBL ,0], FlavorExpand->SU2W]];
1024LBL:= LGauge + LFermions + LHiggs + LYukawa + LGhost;