GeneralU1: U1XGeneric.fr

File U1XGeneric.fr, 39.8 KB (added by ArindamDas, 5 years ago)
Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the generic U(1)_X model ******)
3(***************************************************************************************************************)
4(****** Contains three massive Majorana neutrinos and a scalar. All the SM particles and new scalar are ********)
5(***** charged under the new gauge U(1)X. Heavy neutrino masses MNi and mixing parameters VlNi between ********)
6(**** heavy mass eigenstate and flavour eigenstates are considered as independent parameter. ********)
7(***************************************************************************************************************)
8(****** Contact Authors: Sanjoy Mandal, Arindam Das ******)
9(***************************************************************************************************************)
10(****** Choose whether Feynman gauge is desired. ******)
11(****** If set to False, unitary gauge is assumed. ****)
12(****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
13(****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
14(***************************************************************************************************************)
15
16(* ************************** *)
17(* ***** Information ***** *)
18(* ************************** *)
19M$ModelName = "U1XGeneric";
20
21M$Information = {
22 Authors -> {"Sanjoy Mandal", "Arindam Das"},
23 Version -> "1.1.0",
24 Date -> "28. 01. 2022",
25 Institutions -> {"Korea Institute of Advanced Study, Seoul 02455”, "Hokkaido University, Sapporo 060-0817, Japan"},
26 Emails -> {"mandal.sanjoy10@gmail.com", "dasarindamphysics@gmail.com"},
27 URLs -> "http://feynrules.phys.ucl.ac.be"
28};
29
30FeynmanGauge = True;
31
32(* ************************** *)
33(* ***** NLO Variables ****** *)
34(******************************)
35
36FR$LoopSwitches = {{Gf, MW}};
37FR$RmDblExt = { ymb -> MB, ymc -> MC, ymdo -> MD, yme -> Me,
38 ymm -> MMU, yms -> MS, ymt -> MT, ymtau -> MTA, ymup -> MU};
39
40
41(* ************************** *)
42(* ***** vevs ***** *)
43(* ************************** *)
44M$vevs = { {Phi[2],vev} };
45
46(* ************************** *)
47(* ***** Gauge groups ***** *)
48(* ************************** *)
49M$GaugeGroups = {
50 U1BL == {
51 Abelian -> True,
52 GaugeBoson -> Bp,
53 Charge -> BL,
54 CouplingConstant -> g1p},
55
56 U1Y == {
57 Abelian -> True,
58 CouplingConstant -> g1,
59 GaugeBoson -> B,
60 Charge -> Y
61 },
62 SU2L == {
63 Abelian -> False,
64 CouplingConstant -> gw,
65 GaugeBoson -> Wi,
66 StructureConstant -> Eps,
67 Representations -> {Ta,SU2D},
68 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
69 },
70 SU3C == {
71 Abelian -> False,
72 CouplingConstant -> gs,
73 GaugeBoson -> G,
74 StructureConstant -> f,
75 Representations -> {T,Colour},
76 SymmetricTensor -> dSUN
77 }
78};
79
80
81(* ************************** *)
82(* ***** Indices ***** *)
83(* ************************** *)
84
85IndexRange[Index[SU2W ]] = Unfold[Range[3]];
86IndexRange[Index[SU2D ]] = Unfold[Range[2]];
87IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
88IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
89IndexRange[Index[Generation]] = Range[3];
90
91IndexStyle[SU2W, j];
92IndexStyle[SU2D, k];
93IndexStyle[Gluon, a];
94IndexStyle[Colour, m];
95IndexStyle[Generation, f];
96
97
98(* ************************** *)
99(* *** Interaction orders *** *)
100(* *** (as used by mg5) *** *)
101(* ************************** *)
102
103M$InteractionOrderHierarchy = {
104 {QCD, 1},
105 {QED, 2}
106};
107
108
109(* ************************** *)
110(* **** Particle classes **** *)
111(* ************************** *)
112M$ClassesDescription = {
113
114(* Gauge bosons: physical vector fields *)
115 V[1] == {
116 ClassName -> A,
117 SelfConjugate -> True,
118 Mass -> 0,
119 Width -> 0,
120 ParticleName -> "a",
121 PDG -> 22,
122 PropagatorLabel -> "a",
123 PropagatorType -> W,
124 PropagatorArrow -> None,
125 FullName -> "Photon"
126 },
127 V[2] == {
128 ClassName -> Z,
129 SelfConjugate -> True,
130 Mass -> {MZ, 91.1876},
131 Width -> {WZ, 2.4952},
132 ParticleName -> "Z",
133 PDG -> 23,
134 PropagatorLabel -> "Z",
135 PropagatorType -> Sine,
136 PropagatorArrow -> None,
137 FullName -> "Z"
138 },
139 V[3] == {
140 ClassName -> W,
141 SelfConjugate -> False,
142 Mass -> {MW, 80.379},
143 Width -> {WW, 2.085},
144 ParticleName -> "W+",
145 AntiParticleName -> "W-",
146 QuantumNumbers -> {Q -> 1},
147 PDG -> 24,
148 PropagatorLabel -> "W",
149 PropagatorType -> Sine,
150 PropagatorArrow -> Forward,
151 FullName -> "W"
152 },
153 V[4] == {
154 ClassName -> G,
155 SelfConjugate -> True,
156 Indices -> {Index[Gluon]},
157 Mass -> 0,
158 Width -> 0,
159 ParticleName -> "g",
160 PDG -> 21,
161 PropagatorLabel -> "G",
162 PropagatorType -> C,
163 PropagatorArrow -> None,
164 FullName -> "G"
165 },
166V[5] == {
167 ClassName -> Zp,
168 SelfConjugate -> True,
169 Indices -> {},
170 Mass -> {MZp, 3000},
171 Width -> {WZp, 1.0},
172 PropagatorLabel -> "Zp",
173 PropagatorType -> Sine,
174 PropagatorArrow -> None,
175 PDG -> 9900032,
176 FullName -> "Zp" },
177
178(* Ghosts: related to physical gauge bosons *)
179 U[1] == {
180 ClassName -> ghA,
181 SelfConjugate -> False,
182 Ghost -> A,
183 QuantumNumbers -> {GhostNumber -> 1},
184 Mass -> 0,
185 Width -> 0,
186 PropagatorLabel -> "uA",
187 PropagatorType -> GhostDash,
188 PropagatorArrow -> Forward
189 },
190 U[2] == {
191 ClassName -> ghZ,
192 SelfConjugate -> False,
193 Ghost -> Z,
194 QuantumNumbers -> {GhostNumber -> 1},
195 Mass -> {MZ,91.1876},
196 Width -> {WZ, 2.4952},
197 PropagatorLabel -> "uZ",
198 PropagatorType -> GhostDash,
199 PropagatorArrow -> Forward
200 },
201 U[31] == {
202 ClassName -> ghWp,
203 SelfConjugate -> False,
204 Ghost -> W,
205 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
206 Mass -> {MW,80.379},
207 Width -> {WW, 2.085},
208 PropagatorLabel -> "uWp",
209 PropagatorType -> GhostDash,
210 PropagatorArrow -> Forward
211 },
212 U[32] == {
213 ClassName -> ghWm,
214 SelfConjugate -> False,
215 Ghost -> Wbar,
216 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
217 Mass -> {MW,80.379},
218 Width -> {WW, 2.085},
219 PropagatorLabel -> "uWm",
220 PropagatorType -> GhostDash,
221 PropagatorArrow -> Forward
222 },
223 U[4] == {
224 ClassName -> ghG,
225 SelfConjugate -> False,
226 Indices -> {Index[Gluon]},
227 Ghost -> G,
228 PDG -> 82,
229 QuantumNumbers ->{GhostNumber -> 1},
230 Mass -> 0,
231 Width -> 0,
232 PropagatorLabel -> "uG",
233 PropagatorType -> GhostDash,
234 PropagatorArrow -> Forward
235 },
236 U[5] == {
237 ClassName -> ghZp,
238 SelfConjugate -> False,
239 Indices -> {},
240 Mass -> {MZp, 3000},
241 Width -> {WZp, 1.0},
242 Ghost -> Zp,
243 QuantumNumbers -> {GhostNumber -> 1},
244 PropagatorLabel -> uZp,
245 PropagatorType -> GhostDash,
246 PropagatorArrow -> Forward},
247
248
249(* Gauge bosons: unphysical vector fields *)
250 V[11] == {
251 ClassName -> B,
252 Unphysical -> True,
253 SelfConjugate -> True,
254 Definitions -> { B[mu_] -> cw A[mu] - sw*Cp Z[mu] + sw*Sp Zp[mu]}
255 },
256 V[12] == {
257 ClassName -> Wi,
258 Unphysical -> True,
259 SelfConjugate -> True,
260 Indices -> {Index[SU2W]},
261 FlavorIndex -> SU2W,
262 Definitions -> { Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]), Wi[mu_,3] -> sw A[mu] + cw*Cp Z[mu] - cw*Sp Zp[mu]}
263 },
264 V[13] == {
265 ClassName -> Bp,
266 SelfConjugate -> True,
267 Definitions -> {Bp[mu_] -> Sp Z[mu] + Cp Zp[mu]},
268 Indices -> {},
269 Unphysical -> True},
270
271(* Ghosts: related to unphysical gauge bosons *)
272 U[11] == {
273 ClassName -> ghB,
274 Unphysical -> True,
275 SelfConjugate -> False,
276 Ghost -> B,
277 Definitions -> { ghB -> -sw*Cp ghZ + cw ghA + sw*Sp ghZp }
278 },
279 U[12] == {
280 ClassName -> ghWi,
281 Unphysical -> True,
282 SelfConjugate -> False,
283 Ghost -> Wi,
284 Indices -> {Index[SU2W]},
285 FlavorIndex -> SU2W,
286 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw*Cp ghZ + sw ghA - cw*Sp ghZp }
287 } ,
288 U[13] == {
289 ClassName -> ghBp,
290 SelfConjugate -> False,
291 Definitions -> {ghBp -> Sp ghZ + Cp ghZp },
292 Indices -> {},
293 Unphysical -> True,
294 Ghost -> Bp},
295
296(* Fermions: physical fields *)
297 F[1] == {
298 ClassName -> nL,
299 ClassMembers -> {nL1,nL2,nL3},
300 Indices -> {Index[Generation]},
301 FlavorIndex -> Generation,
302 SelfConjugate -> True,
303 QuantumNumbers -> {},
304 Mass -> {MnL,{MnL1, 0},{MnL2, 0},{MnL3, 0}},
305 Width -> 0,
306 PropagatorLabel -> {"nL", "nul1", "nul2", "nul3"} ,
307 PropagatorType -> S,
308 PropagatorArrow -> Forward,
309 PDG -> {1200,1400,1600},
310 ParticleName -> {"v1","v2","v3"},
311 FullName -> {"Light neutrino 1", "Light neutrino 2", "Light neutrino 3"}
312 },
313 F[16] == {
314 ClassName -> nH,
315 ClassMembers -> {N1, N2, N3},
316 Indices -> {Index[Generation]},
317 FlavorIndex -> Generation,
318 SelfConjugate -> True,
319 QuantumNumbers -> {},
320 Mass -> {MnH,{MN1, 200.00},{MN2, 400.00},{MN3, 600.00}},
321 Width -> {{WN1,1},{WN2,1},{WN3,1}},
322 PropagatorLabel -> {"nH","nuh1","nuh2","nuh3"},
323 PropagatorType -> Straight,
324 PropagatorArrow -> Forward,
325 PDG -> {9910012, 9910014, 9910016},
326 ParticleName -> {"N1","N2","N3"},
327 FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"}
328 },
329 (* unphysical *)
330 F[17] == {
331 ClassName -> nuF,
332 ClassMembers -> {nuF1,nuF2,nuF3},
333 Indices -> {Index[Generation]},
334 FlavorIndex -> Generation,
335 SelfConjugate -> True,
336 Unphysical -> True,
337 Definitions -> {nuF[sp_,ff_] -> Module[{ff2}, UPMNS[ff,ff2] nL[sp,ff2] + Sm[ff,ff2] nH[sp,ff2]]}
338 },
339 (* unphysical *)
340 F[18] == {
341 ClassName -> nuH,
342 ClassMembers -> {nuH1,nuH2,nuH3},
343 Indices -> {Index[Generation]},
344 FlavorIndex -> Generation,
345 SelfConjugate -> True,
346 Unphysical -> True,
347 Definitions -> {nuH[sp_,ff_] -> Module[{ff2}, Conjugate[Tm[ff,ff2]] nL[sp,ff2] + Conjugate[VV[ff,ff2]] nH[sp,ff2]]}
348 },
349
350 F[19] == {
351 ClassName -> nuHp,
352 ClassMembers -> {nuHp1,nuHp2,nuHp3},
353 Indices -> {Index[Generation]},
354 FlavorIndex -> Generation,
355 SelfConjugate -> True,
356 Unphysical -> True,
357 Definitions -> {nuHp[sp_,ff_] -> Module[{ff2}, Tm[ff,ff2] nL[sp,ff2] + VV[ff,ff2] nH[sp,ff2]]}
358 },
359
360 (* Flavour-eigenstate neutrino: unphysical *)
361 (* Righthanded flavor neutrino: unphysical *)
362 F[20] == {
363 ClassName -> NR,
364 Unphysical -> True,
365 Indices -> {Index[Generation]},
366 QuantumNumbers -> {Y -> 0, BL -> -xPhi},
367 FlavorIndex -> Generation,
368 SelfConjugate -> False,
369 Definitions -> { NR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] nuH[sp2,ff]]}
370 },
371
372 F[21] == {
373 ClassName -> NRc,
374 Unphysical -> True,
375 Indices -> {Index[Generation]},
376 QuantumNumbers -> {Y -> 0, BL -> xPhi},
377 FlavorIndex -> Generation,
378 SelfConjugate -> False,
379 Definitions -> { NRc[sp1_,ff_] :> Module[{sp2}, ProjM[sp1,sp2] nuHp[sp2,ff]]}
380 },
381
382 F[2] == {
383 ClassName -> l,
384 ClassMembers -> {e, mu, ta},
385 Indices -> {Index[Generation]},
386 FlavorIndex -> Generation,
387 SelfConjugate -> False,
388 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
389 Width -> 0,
390 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
391 PropagatorLabel -> {"l", "e", "mu", "ta"},
392 PropagatorType -> Straight,
393 PropagatorArrow -> Forward,
394 PDG -> {11, 13, 15},
395 ParticleName -> {"e-", "mu-", "ta-"},
396 AntiParticleName -> {"e+", "mu+", "ta+"},
397 FullName -> {"Electron", "Muon", "Tau"}
398 },
399 F[3] == {
400 ClassName -> uq,
401 ClassMembers -> {u, c, t},
402 Indices -> {Index[Generation], Index[Colour]},
403 FlavorIndex -> Generation,
404 SelfConjugate -> False,
405 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
406 Width -> {0, 0, {WT,1.50833649}},
407 QuantumNumbers -> {Q -> 2/3},
408 PropagatorLabel -> {"uq", "u", "c", "t"},
409 PropagatorType -> Straight,
410 PropagatorArrow -> Forward,
411 PDG -> {2, 4, 6},
412 ParticleName -> {"u", "c", "t" },
413 AntiParticleName -> {"u~", "c~", "t~"},
414 FullName -> {"u-quark", "c-quark", "t-quark"}
415 },
416 F[4] == {
417 ClassName -> dq,
418 ClassMembers -> {d, s, b},
419 Indices -> {Index[Generation], Index[Colour]},
420 FlavorIndex -> Generation,
421 SelfConjugate -> False,
422 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
423 Width -> 0,
424 QuantumNumbers -> {Q -> -1/3},
425 PropagatorLabel -> {"dq", "d", "s", "b"},
426 PropagatorType -> Straight,
427 PropagatorArrow -> Forward,
428 PDG -> {1,3,5},
429 ParticleName -> {"d", "s", "b" },
430 AntiParticleName -> {"d~", "s~", "b~"},
431 FullName -> {"d-quark", "s-quark", "b-quark"}
432 },
433
434(* Fermions: unphysical fields *)
435 F[11] == {
436 ClassName -> LL,
437 Unphysical -> True,
438 Indices -> {Index[SU2D], Index[Generation]},
439 FlavorIndex -> SU2D,
440 SelfConjugate -> False,
441 QuantumNumbers -> {Y -> -1/2, BL -> -(1/2)*xH-xPhi },
442 Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] nuF[sp2,ff]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
443 },
444
445 F[12] == {
446 ClassName -> lR,
447 Unphysical -> True,
448 Indices -> {Index[Generation]},
449 FlavorIndex -> Generation,
450 SelfConjugate -> False,
451 QuantumNumbers -> {Y -> -1, BL -> -xH-xPhi},
452 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
453 },
454 F[13] == {
455 ClassName -> QL,
456 Unphysical -> True,
457 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
458 FlavorIndex -> SU2D,
459 SelfConjugate -> False,
460 QuantumNumbers -> {Y -> 1/6, BL -> (1/6)*xH+(1/3)*xPhi},
461 Definitions -> {
462 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
463 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
464 },
465 F[14] == {
466 ClassName -> uR,
467 Unphysical -> True,
468 Indices -> {Index[Generation], Index[Colour]},
469 FlavorIndex -> Generation,
470 SelfConjugate -> False,
471 QuantumNumbers -> {Y -> 2/3, BL -> (2/3)*xH+(1/3)*xPhi},
472 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
473 },
474 F[15] == {
475 ClassName -> dR,
476 Unphysical -> True,
477 Indices -> {Index[Generation], Index[Colour]},
478 FlavorIndex -> Generation,
479 SelfConjugate -> False,
480 QuantumNumbers -> {Y -> -1/3, BL -> -(1/3)*xH+(1/3)*xPhi},
481 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
482 },
483
484
485
486(* Higgs: physical scalars *)
487 S[1] == {
488 ClassName -> H1,
489 SelfConjugate -> True,
490 Mass -> {MH1,125.18},
491 Width -> {WH1,0.00407},
492 PropagatorLabel -> "H1",
493 PropagatorType -> D,
494 PropagatorArrow -> None,
495 PDG -> 25,
496 ParticleName -> "H1",
497 FullName -> "H1"
498 },
499
500(* Higgs: physical scalars *)
501 S[2] == {
502 ClassName -> G0,
503 SelfConjugate -> True,
504 Goldstone -> Z,
505 Mass -> {MZ, 91.1876},
506 Width -> {WZ, 2.4952},
507 PropagatorLabel -> "Go",
508 PropagatorType -> D,
509 PropagatorArrow -> None,
510 PDG -> 250,
511 ParticleName -> "G0",
512 FullName -> "G0"
513 },
514 S[3] == {
515 ClassName -> GP,
516 SelfConjugate -> False,
517 Goldstone -> W,
518 Mass -> {MW, 80.379},
519 QuantumNumbers -> {Q -> 1},
520 Width -> {WW, 2.085},
521 PropagatorLabel -> "GP",
522 PropagatorType -> D,
523 PropagatorArrow -> None,
524 PDG -> 251,
525 ParticleName -> "G+",
526 AntiParticleName -> "G-",
527 FullName -> "GP"
528 },
529 S[4] == {
530 ClassName -> H2,
531 SelfConjugate -> True,
532 Mass -> {MH2, 450},
533 Width -> {WH2, 1.0},
534 PropagatorLabel -> "H2",
535 PropagatorType -> D,
536 PropagatorArrow -> None,
537 PDG -> 9900035,
538 FullName -> "H2" },
539 S[5] == {
540 ClassName -> phiZp,
541 SelfConjugate -> True,
542 Mass -> {MZp, 3000},
543 Width -> {WZp, 1.0},
544 PropagatorLabel -> "phiZp",
545 PropagatorType -> D,
546 PropagatorArrow -> None,
547 ParticleName ->"phiZp",
548 PDG -> 9900252,
549 FullName -> "PhiZp",
550 Goldstone -> Zp },
551
552 S[6] == {
553 ClassName -> GZ,
554 Unphysical -> True,
555 Definitions -> {GZ -> cg G0 - sg phiZp},
556 SelfConjugate -> True},
557
558 S[7] == {
559 ClassName -> GZp,
560 Unphysical -> True,
561 Definitions -> {GZp -> sg G0 + cg phiZp},
562 SelfConjugate -> True},
563
564(* Higgs: unphysical scalars *)
565 S[11] == {
566 ClassName -> Phi,
567 Unphysical -> True,
568 Indices -> {Index[SU2D]},
569 FlavorIndex -> SU2D,
570 SelfConjugate -> False,
571 QuantumNumbers -> {Y -> 1/2, BL -> xH/2},
572 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + Ca*H1+Sa*H2 + I GZ)/Sqrt[2] }
573 },
574 S[12] == {
575 ClassName -> Chi,
576 Unphysical -> True,
577 Indices -> {},
578 SelfConjugate -> False,
579 QuantumNumbers -> {Y -> 0, BL -> 2*xPhi},
580 Definitions -> { Chi -> (x -Sa*H1+Ca*H2 + I GZp)/Sqrt[2] }
581 }
582};
583
584
585(* ************************** *)
586(* ***** Gauge ***** *)
587(* ***** Parameters ***** *)
588(* ***** (FeynArts) ***** *)
589(* ************************** *)
590
591GaugeXi[ V[1] ] = GaugeXi[A];
592GaugeXi[ V[2] ] = GaugeXi[Z];
593GaugeXi[ V[3] ] = GaugeXi[W];
594GaugeXi[ V[4] ] = GaugeXi[G];
595GaugeXi[ V[5] ] = GaugeXi[Zp];
596GaugeXi[ S[1] ] = 1;
597GaugeXi[ S[2] ] = GaugeXi[Z];
598GaugeXi[ S[3] ] = GaugeXi[W];
599GaugeXi[ S[4] ] = 1;
600GaugeXi[ S[5] ] = GaugeXi[Zp];
601GaugeXi[ U[1] ] = GaugeXi[A];
602GaugeXi[ U[2] ] = GaugeXi[Z];
603GaugeXi[ U[31] ] = GaugeXi[W];
604GaugeXi[ U[32] ] = GaugeXi[W];
605GaugeXi[ U[4] ] = GaugeXi[G];
606GaugeXi[ U[5] ] = GaugeXi[Zp];
607
608
609(* ************************** *)
610(* ***** Parameters ***** *)
611(* ************************** *)
612M$Parameters = {
613
614 (* External parameters *)
615 aEWM1 == {
616 ParameterType -> External,
617 BlockName -> SMINPUTS,
618 OrderBlock -> 1,
619 Value -> 127.9,
620 InteractionOrder -> {QED,-2},
621 Description -> "Inverse of the EW coupling constant at the Z pole"
622 },
623 Gf == {
624 ParameterType -> External,
625 BlockName -> SMINPUTS,
626 OrderBlock -> 2,
627 Value -> 1.16637*^-5,
628 InteractionOrder -> {QED,2},
629 TeX -> Subscript[G,f],
630 Description -> "Fermi constant"
631 },
632 aS == {
633 ParameterType -> External,
634 BlockName -> SMINPUTS,
635 OrderBlock -> 3,
636 Value -> 0.1184,
637 InteractionOrder -> {QCD,2},
638 TeX -> Subscript[\[Alpha],s],
639 Description -> "Strong coupling constant at the Z pole"
640 },
641
642
643 xH == {
644 ParameterType -> External,
645 BlockName -> BLINPUTS,
646 Value -> 1,
647 Description -> "xH parameter"},
648
649 xPhi == {
650 ParameterType -> External,
651 BlockName -> BLINPUTS,
652 Value -> 1,
653 Description -> "xPhi parameter"},
654
655
656 g1p == {
657 ParameterType -> External,
658 BlockName -> BLINPUTS,
659 InteractionOrder -> {QED, 1},
660 Value -> 0.2,
661 Description -> "Zp coupling"},
662
663 g1pp == {
664 ParameterType -> Internal,
665 BlockName -> BLINPUTS,
666 InteractionOrder -> {QED, 1},
667 Value -> g1p*xPhi,
668 Description -> "effective-Zp coupling"},
669
670
671 gt == {
672 ParameterType -> Internal,
673 BlockName -> BLINPUTS,
674 InteractionOrder -> {QED, 1},
675 Value -> g1p*xH,
676 Description -> "Z-Zp mixing coupling"},
677
678
679 Sa == {
680 ParameterType -> External,
681 BlockName -> BLINPUTS,
682 Value -> 0.01,
683 Description -> "Sine of Higgses mixing angle"},
684
685 Ca == {
686 ParameterType -> Internal,
687 Value -> Sqrt[1-Sa^2],
688 ParameterName -> Ca,
689 Description -> "Cosine of Higgses mixing angle"},
690
691 ymdo == {
692 ParameterType -> External,
693 BlockName -> YUKAWA,
694 OrderBlock -> 1,
695 Value -> 5.04*^-3,
696 Description -> "Down Yukawa mass"
697 },
698 ymup == {
699 ParameterType -> External,
700 BlockName -> YUKAWA,
701 OrderBlock -> 2,
702 Value -> 2.55*^-3,
703 Description -> "Up Yukawa mass"
704 },
705 yms == {
706 ParameterType -> External,
707 BlockName -> YUKAWA,
708 OrderBlock -> 3,
709 Value -> 0.101,
710 Description -> "Strange Yukawa mass"
711 },
712 ymc == {
713 ParameterType -> External,
714 BlockName -> YUKAWA,
715 OrderBlock -> 4,
716 Value -> 1.27,
717 Description -> "Charm Yukawa mass"
718 },
719 ymb == {
720 ParameterType -> External,
721 BlockName -> YUKAWA,
722 OrderBlock -> 5,
723 Value -> 4.7,
724 Description -> "Bottom Yukawa mass"
725 },
726 ymt == {
727 ParameterType -> External,
728 BlockName -> YUKAWA,
729 OrderBlock -> 6,
730 Value -> 172,
731 Description -> "Top Yukawa mass"
732 },
733 yme == {
734 ParameterType -> External,
735 BlockName -> YUKAWA,
736 OrderBlock -> 11,
737 Value -> 5.11*^-4,
738 Description -> "Electron Yukawa mass"
739 },
740 ymm == {
741 ParameterType -> External,
742 BlockName -> YUKAWA,
743 OrderBlock -> 13,
744 Value -> 0.10566,
745 Description -> "Muon Yukawa mass"
746 },
747 ymtau == {
748 ParameterType -> External,
749 BlockName -> YUKAWA,
750 OrderBlock -> 15,
751 Value -> 1.777,
752 Description -> "Tau Yukawa mass"
753 },
754 cabi == {
755 ParameterType -> External,
756 BlockName -> CKMBLOCK,
757 OrderBlock -> 1,
758 Value -> 0.227736,
759 TeX -> Subscript[\[Theta], c],
760 Description -> "Cabibbo angle"
761 },
762
763 (* Internal Parameters *)
764 aEW == {
765 ParameterType -> Internal,
766 Value -> 1/aEWM1,
767 InteractionOrder -> {QED,2},
768 TeX -> Subscript[\[Alpha], EW],
769 Description -> "Electroweak coupling contant"
770 },
771
772 sw2 == {
773 ParameterType -> Internal,
774 Value -> 0.231,
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
819 vev == {
820 ParameterType -> Internal,
821 BlockName -> VEV,
822 Value -> 2*MW*sw/ee,
823 InteractionOrder -> {QED,-1},
824 Description -> "SM Higgs vacuum expectation value"
825 },
826
827 x == {
828 ParameterType -> Internal,
829 BlockName -> VEV,
830 Value -> MZp/(2*g1pp)*Sqrt[1-gt^2*vev^2/(4*MZp^2-vev^2*(gw^2+g1^2))],
831 InteractionOrder -> {QED, -1},
832 Description -> "Non SM Higgs VEV"},
833
834
835 \[Lambda]1 == {
836 ParameterType -> Internal,
837 Value -> MH1^2 /(2*vev^2)*Ca^2 + MH2^2 /(2*vev^2)*Sa^2,
838 ParameterName -> lam1,
839 InteractionOrder -> {QED, 2},
840 Description -> "Lambda 1"},
841
842 \[Lambda]2 == {
843 ParameterType -> Internal,
844 Value -> MH1^2 /(2*x^2)*Sa^2 + MH2^2 /(2*x^2)*Ca^2,
845 ParameterName -> lam2,
846 InteractionOrder -> {QED, 2},
847 Description -> "Lambda 2"},
848
849 \[Lambda]3 == {
850 ParameterType -> Internal,
851 Value -> (MH2^2 - MH1^2)/(x*vev)*Sa*Ca,
852 ParameterName -> lam3,
853 InteractionOrder -> {QED, 2},
854 Description -> "Lambda 3, mixing parameter"},
855
856 mu2H1 == {
857 ParameterType -> Internal,
858 Value -> \[Lambda]1 * vev^2 + \[Lambda]3 /2 * x^2,
859 TeX -> m^2,
860 Description -> "Coefficient of the quadratic piece of the H1 potential"},
861
862 mu2H2 == {
863 ParameterType -> Internal,
864 Value -> \[Lambda]3 /2 * vev^2 + \[Lambda]2 * x^2,
865 TeX -> \[Mu]^2,
866 Description -> "Coefficient of the quadratic piece of the H2 potential"},
867
868 Sp2num == {
869 ParameterType -> Internal,
870 Value -> 2*gt*Sqrt[(ee/sw)^2+(ee/cw)^2]},
871
872 Cp2num == {
873 ParameterType -> Internal,
874 Value -> gt^2+16*(x/vev)^2*(g1pp)^2-(ee/sw)^2-(ee/cw)^2},
875
876 Sp == {
877 ParameterType -> Internal,
878 Value -> Sin[ArcSin[Sp2num/Sqrt[Sp2num^2+Cp2num^2]]/2],
879 ComplexParameter -> False,
880 Description -> "sine mixing Zp-Z"},
881
882 Cp == {
883 ParameterType -> Internal,
884 Value -> Sqrt[1-Sp^2],
885 ComplexParameter -> False,
886 Description -> "cosine mixing Zp-Z"},
887
888 Cn == {
889 ParameterType -> Internal,
890 ComplexParameter -> False,
891 Value -> (ee/sw)^2+(ee/cw)^2+gt^2+16*(x/vev)^2*(g1pp)^2},
892
893 Dn == {
894 ParameterType -> Internal,
895 ComplexParameter -> False,
896 Value -> 64*((ee/sw)^2+(ee/cw)^2)*(g1pp)^2*vev^2*x^2},
897
898
899(* MZ == {
900 ParameterType -> Internal,
901 Value -> Sqrt[(Cn*vev^2-Sqrt[-Dn+vev^4*Cn^2])/8],
902 Description -> "Z mass"}, *)
903
904 S2gNum == {
905 ParameterType -> Internal,
906 ComplexParameter -> False,
907 Value -> 8*x/vev*gt*(g1pp)},
908
909 C2gNum == {
910 ParameterType -> Internal,
911 ComplexParameter -> False,
912 Value -> (ee/sw)^2+(ee/cw)^2+gt^2-16*(x/vev)^2*(g1pp)^2},
913
914
915 sg == {
916 ParameterType -> Internal,
917 ComplexParameter -> False,
918 Value -> Sin[ArcSin[-S2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2],
919 Description -> "cosine of Z-Zp goldostone mixing angle"},
920 cg == {
921 ParameterType -> Internal,
922 ComplexParameter -> False,
923 Value -> Sqrt[1-sg^2],
924 Description -> "sine of Z-Zp goldstone mixing angle"},
925
926
927 yl == {
928 ParameterType -> Internal,
929 Indices -> {Index[Generation], Index[Generation]},
930 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
931 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
932 InteractionOrder -> {QED, 1},
933 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
934 TeX -> Superscript[y, l],
935 Description -> "Lepton Yukawa couplings"
936 },
937 yu == {
938 ParameterType -> Internal,
939 Indices -> {Index[Generation], Index[Generation]},
940 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
941 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
942 InteractionOrder -> {QED, 1},
943 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
944 TeX -> Superscript[y, u],
945 Description -> "Up-type Yukawa couplings"
946 },
947 yd == {
948 ParameterType -> Internal,
949 Indices -> {Index[Generation], Index[Generation]},
950 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
951 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
952 InteractionOrder -> {QED, 1},
953 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
954 TeX -> Superscript[y, d],
955 Description -> "Down-type Yukawa couplings"
956 },
957
958(* Cabibbo mixing! *)
959 CKM == {
960 ParameterType -> Internal,
961 Indices -> {Index[Generation], Index[Generation]},
962 Unitary -> True,
963 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
964 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
965 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
966 TeX -> Superscript[V,CKM],
967 Description -> "CKM-Matrix"},
968
969 (* ***** RHN parameters ***** *)
970
971 VeN1 == {
972 ParameterType -> External,
973 BlockName -> NUMIXING,
974 OrderBlock -> 1,
975 Value -> 0.001,
976 ComplexParameter -> False,
977 TeX -> Subscript[V,eN1],
978 Description -> "Mixing between ve flavor/gauge state and N1 mass state"
979 },
980
981 VeN2 == {
982 ParameterType -> External,
983 BlockName -> NUMIXING,
984 OrderBlock -> 2,
985 Value -> 0.0,
986 ComplexParameter -> False,
987 TeX -> Subscript[V,eN2],
988 Description -> "Mixing between ve flavor/gauge state and N2 mass state"
989 },
990
991 VeN3 == {
992 ParameterType -> External,
993 BlockName -> NUMIXING,
994 OrderBlock -> 3,
995 Value -> 0.0,
996 ComplexParameter -> False,
997 TeX -> Subscript[V,eN3],
998 Description -> "Mixing between ve flavor/gauge state and N3 mass state"
999 },
1000
1001 VmuN1 == {
1002 ParameterType -> External,
1003 BlockName -> NUMIXING,
1004 OrderBlock -> 4,
1005 Value -> 0.0,
1006 ComplexParameter -> False,
1007 TeX -> Subscript[V,muN1],
1008 Description -> "Mixing between vm flavor/gauge state and N1 mass state"
1009 },
1010
1011 VmuN2 == {
1012 ParameterType -> External,
1013 BlockName -> NUMIXING,
1014 OrderBlock -> 5,
1015 Value -> 0.001,
1016 ComplexParameter -> False,
1017 TeX -> Subscript[V,muN2],
1018 Description -> "Mixing between vm flavor/gauge state and N2 mass state"
1019 },
1020
1021 VmuN3 == {
1022 ParameterType -> External,
1023 BlockName -> NUMIXING,
1024 OrderBlock -> 6,
1025 Value -> 0.0,
1026 ComplexParameter -> False,
1027 TeX -> Subscript[V,muN3],
1028 Description -> "Mixing between vm flavor/gauge state and N3 mass state"
1029 },
1030
1031 VtaN1 == {
1032 ParameterType -> External,
1033 BlockName -> NUMIXING,
1034 OrderBlock -> 7,
1035 Value -> 0.0,
1036 ComplexParameter -> False,
1037 TeX -> Subscript[V,taN1],
1038 Description -> "Mixing between vt flavor/gauge state and N1 mass state"
1039 },
1040
1041 VtaN2 == {
1042 ParameterType -> External,
1043 BlockName -> NUMIXING,
1044 OrderBlock -> 8,
1045 Value -> 0.0,
1046 ComplexParameter -> False,
1047 TeX -> Subscript[V,taN2],
1048 Description -> "Mixing between vt flavor/gauge state and N2 mass state"
1049 },
1050
1051 VtaN3 == {
1052 ParameterType -> External,
1053 BlockName -> NUMIXING,
1054 OrderBlock -> 9,
1055 Value -> 0.001,
1056 ComplexParameter -> False,
1057 TeX -> Subscript[V,taN3],
1058 Description -> "Mixing between vt flavor/gauge state and N3 mass state"
1059 },
1060
1061Sm == {
1062 ParameterType -> Internal,
1063 Indices -> {Index[Generation], Index[Generation]},
1064 Value -> {Sm[1,1] -> VeN1, Sm[1,2] -> VeN2, Sm[1,3] -> VeN3,
1065 Sm[2,1] -> VmuN1, Sm[2,2] -> VmuN2, Sm[2,3] -> VmuN3,
1066 Sm[3,1] -> VtaN1, Sm[3,2] -> VtaN2, Sm[3,3] -> VtaN3},
1067 TeX -> Superscript[S,m],
1068 Description -> "S-Matrix"},
1069
1070
1071UPMNS == {
1072 ParameterType -> Internal,
1073 Indices -> {Index[Generation], Index[Generation]},
1074 Value -> {UPMNS[1,1] -> 1, UPMNS[1,2] -> 0, UPMNS[1,3] -> 0,
1075 UPMNS[2,1] -> 0, UPMNS[2,2] -> 1, UPMNS[2,3] -> 0,
1076 UPMNS[3,1] -> 0, UPMNS[3,2] -> 0, UPMNS[3,3] -> 1},
1077 ComplexParameter -> True,
1078 ParameterName -> {UPMNS[1,1]->U11, UPMNS[1,2]->U12, UPMNS[1,3]->U13, UPMNS[2,1]->U21, UPMNS[2,2]->U22, UPMNS[2,3]->U23, UPMNS[3,1]->U31, UPMNS[3,2]->U32, UPMNS[3,3]->U33},
1079 TeX -> Superscript[U,PMNS],
1080 Description -> "PMNS-Matrix"},
1081
1082
1083Tm == {
1084 ParameterType -> Internal,
1085 Indices -> {Index[Generation], Index[Generation]},
1086 Value -> {Tm[1,1] -> -VeN1, Tm[1,2] -> -VmuN1, Tm[1,3] -> -VtaN1,
1087 Tm[2,1] -> -VeN2, Tm[2,2] -> -VmuN2, Tm[2,3] -> -VtaN2,
1088 Tm[3,1] -> -VeN3, Tm[3,2] -> -VmuN3, Tm[3,3] -> -VtaN3},
1089 TeX -> Superscript[T,m],
1090 Description -> "T-Matrix"},
1091
1092
1093VV == {
1094 ParameterType -> External,
1095 Indices -> {Index[Generation], Index[Generation]},
1096 BlockName -> VV,
1097 Value -> {VV[1,1] -> 1, VV[1,2] -> 0, VV[1,3] -> 0,
1098 VV[2,1] -> 0, VV[2,2] -> 1, VV[2,3] -> 0,
1099 VV[3,1] -> 0, VV[3,2] -> 0, VV[3,3] -> 1},
1100 ComplexParameter -> True,
1101 TeX -> Superscript[V,V],
1102 Description -> "V-Matrix"},
1103
1104 ynd == {
1105 ParameterType -> Internal,
1106 Indices -> {Index[Generation], Index[Generation]},
1107 Value -> {ynd[1,1] -> Sqrt[2] VeN1 MN1/(vev) , ynd[1,2] -> 0, ynd[1,3] -> 0,
1108 ynd[2,1] -> 0, ynd[2,2] -> Sqrt[2] VmuN2 MN2/(vev), ynd[2,3] -> 0,
1109 ynd[3,1] -> 0, ynd[3,2] -> 0, ynd[3,3] -> Sqrt[2] VtaN3 MN3/(vev)},
1110 TeX -> Superscript[y,nd],
1111 InteractionOrder -> {QED,1},
1112 Description -> "ynd-Matrix"},
1113
1114 ynm == {
1115 ComplexParameter -> False,
1116 ParameterType -> Internal,
1117 Indices -> {Index[Generation], Index[Generation]},
1118 Value -> {ynm[1, 1] -> MN1/(Sqrt[2]*x), ynm[1, 2] -> 0.0, ynm[1, 3] -> 0.0,
1119 ynm[2, 1] -> 0.0, ynm[2, 2] -> MN2/(Sqrt[2]*x), ynm[2, 3] -> 0.0,
1120 ynm[3, 1] -> 0.0, ynm[3, 2] -> 0.0, ynm[3, 3] -> MN3/(Sqrt[2]*x) },
1121 InteractionOrder -> {QED,1},
1122 Description -> "Majorana yukawa",
1123 TeX -> Subscript[y, MN]
1124 }
1125
1126};
1127
1128(* ************************** *)
1129(* ***** Lagrangian ***** *)
1130(* ************************** *)
1131
1132(* Kinetic terms for SM gauge fields and U(1)X gauge field Bp *)
1133
1134LGauge := Block[{mu,nu,ii,aa},
1135 ExpandIndices[-1/4 FS[B,mu,nu] FS[B,mu,nu] -1/4 FS[Bp,mu,nu] FS[Bp,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]];
1136
1137(* Note that as we redefine LL in presence of light and heavy neutrino mixing, the term LLbar.Ga[mu].DC[LL, mu] contains all the new mixing dependent charged and neutral current interactions such as N-l-W, N-vl-Z, N-N-Z *)
1138
1139LFermions := Block[{mu},
1140 ExpandIndices[I*(
1141 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] ),
1142 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
1143
1144(* Most general Higgs potential with SM Higgs doublet and new scalar Chi *)
1145
1146LHiggs := Block[{ii,mu, feynmangaugerules},
1147 feynmangaugerules = If[Not[FeynmanGauge], {GZ|GP|GPbar|GZp ->0}, {}];
1148
1149 ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] + (DC[Chibar, mu]).DC[Chi, mu] + mu2H1 Phibar[ii] Phi[ii] + mu2H2 Chibar.Chi - \[Lambda]1 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj]-\[Lambda]2 (Chibar.Chi)^2 -
1150 \[Lambda]3 (Phibar[ii] Phi[ii])*(Chibar.Chi), FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
1151 ];
1152
1153(* SM Yukawa *)
1154LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
1155 feynmangaugerules = If[Not[FeynmanGauge], {GZ|GP|GPbar|GZp ->0}, {}];
1156
1157 yuk = ExpandIndices[
1158 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
1159 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] - yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj] , FlavorExpand -> SU2D];
1160 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
1161 yuk+HC[yuk]/.feynmangaugerules
1162 ];
1163
1164(* ************************** *)
1165(* ***** RHN Lagrangian ***** *)
1166(* ************************** *)
1167
1168LFermionsNR := Block[{mu},
1169 ExpandIndices[I*( NRbar.Ga[mu].DC[NR,mu] ),
1170 FlavorExpand->{SU2W,SU2D}]];
1171
1172(* LYukawaNR contains all the Higgs interactions such as vl-vl-H, vl-N-H, N-N-H *)
1173LYukawaNR := Block[{ff1,ff2,sp,ii,yun,feynmangaugerules},
1174 feynmangaugerules = If[Not[FeynmanGauge], {GZ|GP|GPbar|GZp ->0}, {}];
1175 yun = ExpandIndices[
1176 -ynd[ff1,ff2] LLbar[sp,ii,ff1].NR[sp,ff2] Phibar[jj] Eps[ii, jj] - ynm[ff1,ff2]/2 NRcbar[sp,ff1].NR[sp,ff2] Chi, FlavorExpand -> SU2D];
1177 yun+HC[yun]/.feynmangaugerules
1178 ];
1179
1180LGhost := If[FeynmanGauge,
1181 Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB, dBRSTBp, LGhostBp},
1182
1183 (***********First the pure gauge piece.**********************)
1184 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1185 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1186
1187 dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ];
1188 LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu];
1189
1190 dBRSTB[mu_] := cw/ee del[ghB, mu];
1191 LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu];
1192
1193 dBRSTBp[mu_] := 1/g1pp del[ghBp, mu];
1194 LGhostBp := - g1pp ghBpbar.del[dBRSTBp[mu],mu];
1195
1196 (***********Next the piece from the scalar field.************)
1197 LGhostphi :=
1198(1/4*gw*vev (-gw*(vev +Ca*H1+Sa*H2) ghWibar[1].ghWi[1] + g1 phi2 ghWibar[1].ghB +gw phi2 ghWibar[1].ghWi[3] -gw GZ ghWibar[1].ghWi[2] + gt phi2 ghWibar[1].ghBp) +
11991/4*gw*vev (-gw*(vev +Ca*H1+Sa*H2) ghWibar[2].ghWi[2] - g1 phi1 ghWibar[2].ghB -gw phi1 ghWibar[2].ghWi[3] +gw GZ ghWibar[2].ghWi[1] -gt phi1 ghWibar[2].ghBp) +
12001/4*gw*vev (g1*(vev +Ca*H1+Sa*H2) ghWibar[3].ghB -gw*(vev +Ca*H1+Sa*H2) ghWibar[3].ghWi[3] +gw phi1 ghWibar[3].ghWi[2]
1201-gw phi2 ghWibar[3].ghWi[1] +gt (vev +Ca*H1+Sa*H2) ghWibar[3].ghBp ) +
12021/4*g1*vev (-g1*(vev +Ca*H1+Sa*H2) ghBbar.ghB +gw*(vev +Ca*H1+Sa*H2) ghBbar.ghWi[3] -gw phi1 ghBbar.ghWi[2] +gw phi2 ghBbar.ghWi[1] -gt*(vev +Ca*H1+Sa*H2) ghBbar.ghBp) +
12031/4*gt*vev (-g1*(vev +Ca*H1+Sa*H2) ghBpbar.ghB +gw*(vev +Ca*H1+Sa*H2) ghBpbar.ghWi[3] -gw phi1 ghBpbar.ghWi[2] +gw phi2 ghBpbar.ghWi[1] -gt (vev +Ca*H1+Sa*H2) ghBpbar.ghBp) -
12044*g1pp^2*x*(x-Sa*H1+Ca*H2) ghBpbar.ghBp) /.{phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])}
1205;
1206
1207 (***********Now add the pieces together.********************)
1208 LGhostG + LGhostWi + LGhostB + LGhostphi + LGhostBp ],
1209 (*If unitary gauge, only include the gluonic ghost.*)
1210 Block[{dBRSTG,LGhostG},
1211 (***********First the pure gauge piece.**********************)
1212 dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]];
1213 LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu];
1214 (***********Now add the pieces together.********************)
1215 LGhostG]
1216];
1217
1218
1219LRHN := LFermionsNR + LYukawaNR;
1220
1221LSM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;
1222Lfull := LSM+LRHN;