MDMmodel: MDM.fr

File MDM.fr, 32.3 KB (added by Liang, 11 years ago)

the main model file

Line 
1(***************************************************************************************************************)
2(****** This is the FeynRules mod-file for the Minimal Dilaton Model(MDM) ******)
3(****** ******)
4(****** Authors: Junjie Cao, XiQing Hao, Zhaoxia Heng, Liangliang Shang, Yang Zhang ******)
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$ModelName = "Minimal Dilaton Model";
16
17M$Information = {
18 Authors -> {"Junjie Cao", "XiQing Hao", "Zhaoxia Heng", "Liangliang Shang", "Yang Zhang"},
19 Version -> "1.0.0",
20 Date -> "19. 6. 2014",
21 Institutions -> {"Henan Normal University, Center for High Energy Physics, Peking University", "Henan Normal University", "Henan Normal University", "Henan Normal University", "Institute of Theoretical Physics, Academia Sinica"},
22 Emails -> {"junjiec@itp.ac.cn", "haoxq@ihep.ac.cn", "zhaoxiaheng@gmail.com", "shlwell1988@gmail.com", "phyzhangyang@gmail.com"},
23 URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/SimpleExtensions"
24};
25
26FeynmanGauge = True;
27
28(* ************************** *)
29(* ***** vevs ***** *)
30(* ************************** *)
31M$vevs = { {Phi[2],vev}, {S, vevf} };
32
33(* ************************** *)
34(* ***** Gauge groups ***** *)
35(* ************************** *)
36M$GaugeGroups = {
37 U1Y == {
38 Abelian -> True,
39 CouplingConstant -> g1,
40 GaugeBoson -> B,
41 Charge -> Y
42 },
43 SU2L == {
44 Abelian -> False,
45 CouplingConstant -> gw,
46 GaugeBoson -> Wi,
47 StructureConstant -> Eps,
48 Representations -> {Ta,SU2D},
49 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
50 },
51 SU3C == {
52 Abelian -> False,
53 CouplingConstant -> gs,
54 GaugeBoson -> G,
55 StructureConstant -> f,
56 Representations -> {T,Colour},
57 SymmetricTensor -> dSUN
58 }
59};
60
61
62(* ************************** *)
63(* ***** Indices ***** *)
64(* ************************** *)
65
66IndexRange[Index[SU2W ]] = Unfold[Range[3]];
67IndexRange[Index[SU2D ]] = Unfold[Range[2]];
68IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
69IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
70IndexRange[Index[Generation]] = Range[3];
71
72IndexStyle[SU2W, j];
73IndexStyle[SU2D, k];
74IndexStyle[Gluon, a];
75IndexStyle[Colour, m];
76IndexStyle[Generation, f];
77
78
79(* ************************** *)
80(* *** Interaction orders *** *)
81(* *** (as used by mg5) *** *)
82(* ************************** *)
83
84M$InteractionOrderHierarchy = {
85 {QCD, 1},
86 {QED, 2}
87};
88
89
90(* ************************** *)
91(* **** Particle classes **** *)
92(* ************************** *)
93M$ClassesDescription = {
94
95(* Gauge bosons: physical vector fields *)
96 V[1] == {
97 ClassName -> A,
98 SelfConjugate -> True,
99 Mass -> 0,
100 Width -> 0,
101 ParticleName -> "a",
102 PDG -> 22,
103 PropagatorLabel -> "a",
104 PropagatorType -> W,
105 PropagatorArrow -> None,
106 FullName -> "Photon"
107 },
108 V[2] == {
109 ClassName -> Z,
110 SelfConjugate -> True,
111 Mass -> {MZ, 91.1876},
112 Width -> {WZ, 2.4952},
113 ParticleName -> "Z",
114 PDG -> 23,
115 PropagatorLabel -> "Z",
116 PropagatorType -> Sine,
117 PropagatorArrow -> None,
118 FullName -> "Z"
119 },
120 V[3] == {
121 ClassName -> W,
122 SelfConjugate -> False,
123 Mass -> {MW, Internal},
124 Width -> {WW, 2.085},
125 ParticleName -> "W+",
126 AntiParticleName -> "W-",
127 QuantumNumbers -> {Q -> 1},
128 PDG -> 24,
129 PropagatorLabel -> "W",
130 PropagatorType -> Sine,
131 PropagatorArrow -> Forward,
132 FullName -> "W"
133 },
134 V[4] == {
135 ClassName -> G,
136 SelfConjugate -> True,
137 Indices -> {Index[Gluon]},
138 Mass -> 0,
139 Width -> 0,
140 ParticleName -> "g",
141 PDG -> 21,
142 PropagatorLabel -> "G",
143 PropagatorType -> C,
144 PropagatorArrow -> None,
145 FullName -> "G"
146 },
147
148(* Ghosts: related to physical gauge bosons *)
149 U[1] == {
150 ClassName -> ghA,
151 SelfConjugate -> False,
152 Ghost -> A,
153 QuantumNumbers -> {GhostNumber -> 1},
154 Mass -> 0,
155 Width -> 0,
156 PropagatorLabel -> "uA",
157 PropagatorType -> GhostDash,
158 PropagatorArrow -> Forward
159 },
160 U[2] == {
161 ClassName -> ghZ,
162 SelfConjugate -> False,
163 Ghost -> Z,
164 QuantumNumbers -> {GhostNumber -> 1},
165 Mass -> {MZ,91.1876},
166 Width -> {WZ, 2.4952},
167 PropagatorLabel -> "uZ",
168 PropagatorType -> GhostDash,
169 PropagatorArrow -> Forward
170 },
171 U[31] == {
172 ClassName -> ghWp,
173 SelfConjugate -> False,
174 Ghost -> W,
175 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
176 Mass -> {MW,Internal},
177 Width -> {WW, 2.085},
178 PropagatorLabel -> "uWp",
179 PropagatorType -> GhostDash,
180 PropagatorArrow -> Forward
181 },
182 U[32] == {
183 ClassName -> ghWm,
184 SelfConjugate -> False,
185 Ghost -> Wbar,
186 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
187 Mass -> {MW,Internal},
188 Width -> {WW, 2.085},
189 PropagatorLabel -> "uWm",
190 PropagatorType -> GhostDash,
191 PropagatorArrow -> Forward
192 },
193 U[4] == {
194 ClassName -> ghG,
195 SelfConjugate -> False,
196 Indices -> {Index[Gluon]},
197 Ghost -> G,
198 QuantumNumbers ->{GhostNumber -> 1},
199 Mass -> 0,
200 Width -> 0,
201 PropagatorLabel -> "uG",
202 PropagatorType -> GhostDash,
203 PropagatorArrow -> Forward
204 },
205
206(* Gauge bosons: unphysical vector fields *)
207 V[11] == {
208 ClassName -> B,
209 Unphysical -> True,
210 SelfConjugate -> True,
211 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
212 },
213 V[12] == {
214 ClassName -> Wi,
215 Unphysical -> True,
216 SelfConjugate -> True,
217 Indices -> {Index[SU2W]},
218 FlavorIndex -> SU2W,
219 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]}
220 },
221
222(* Ghosts: related to unphysical gauge bosons *)
223 U[11] == {
224 ClassName -> ghB,
225 Unphysical -> True,
226 SelfConjugate -> False,
227 Ghost -> B,
228 Definitions -> { ghB -> -sw ghZ + cw ghA}
229 },
230 U[12] == {
231 ClassName -> ghWi,
232 Unphysical -> True,
233 SelfConjugate -> False,
234 Ghost -> Wi,
235 Indices -> {Index[SU2W]},
236 FlavorIndex -> SU2W,
237 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
238 } ,
239
240(* Fermions: physical fields *)
241 F[1] == {
242 ClassName -> vl,
243 ClassMembers -> {ve,vm,vt},
244 Indices -> {Index[Generation]},
245 FlavorIndex -> Generation,
246 SelfConjugate -> False,
247 Mass -> 0,
248 Width -> 0,
249 QuantumNumbers -> {LeptonNumber -> 1},
250 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
251 PropagatorType -> S,
252 PropagatorArrow -> Forward,
253 PDG -> {12,14,16},
254 ParticleName -> {"ve","vm","vt"},
255 AntiParticleName -> {"ve~","vm~","vt~"},
256 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
257 },
258 F[2] == {
259 ClassName -> l,
260 ClassMembers -> {e, mu, ta},
261 Indices -> {Index[Generation]},
262 FlavorIndex -> Generation,
263 SelfConjugate -> False,
264 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
265 Width -> 0,
266 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
267 PropagatorLabel -> {"l", "e", "mu", "ta"},
268 PropagatorType -> Straight,
269 PropagatorArrow -> Forward,
270 PDG -> {11, 13, 15},
271 ParticleName -> {"e-", "mu-", "ta-"},
272 AntiParticleName -> {"e+", "mu+", "ta+"},
273 FullName -> {"Electron", "Muon", "Tau"}
274 },
275 F[3] == {
276 ClassName -> dq,
277 ClassMembers -> {d, s, b},
278 Indices -> {Index[Generation], Index[Colour]},
279 FlavorIndex -> Generation,
280 SelfConjugate -> False,
281 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
282 Width -> 0,
283 QuantumNumbers -> {Q -> -1/3},
284 PropagatorLabel -> {"dq", "d", "s", "b"},
285 PropagatorType -> Straight,
286 PropagatorArrow -> Forward,
287 PDG -> {1,3,5},
288 ParticleName -> {"d", "s", "b" },
289 AntiParticleName -> {"d~", "s~", "b~"},
290 FullName -> {"d-quark", "s-quark", "b-quark"}
291 },
292
293(* new adding *)
294 F[4] == {
295 ClassName -> u,
296 Indices -> {Index[Colour]},
297 SelfConjugate -> False,
298 Mass -> {MU,2.55*^-3},
299 Width -> 0,
300 QuantumNumbers -> {Q -> 2/3},
301 PropagatorLabel -> {"u"},
302 PropagatorType -> Straight,
303 PropagatorArrow -> Forward,
304 PDG -> {2},
305 ParticleName -> {"u" },
306 AntiParticleName -> {"u~"},
307 FullName -> {"u-quark"}
308 },
309 F[5] == {
310 ClassName -> c,
311 Indices -> {Index[Colour]},
312 SelfConjugate -> False,
313 Mass -> {MC,1.27},
314 Width -> 0,
315 QuantumNumbers -> {Q -> 2/3},
316 PropagatorLabel -> {"c"},
317 PropagatorType -> Straight,
318 PropagatorArrow -> Forward,
319 PDG -> {4},
320 ParticleName -> {"c" },
321 AntiParticleName -> {"c~"},
322 FullName -> {"c-quark"}
323 },
324 F[6] == {
325 ClassName -> t,
326 Indices -> {Index[Colour]},
327 SelfConjugate -> False,
328 Mass -> {MT,172},
329 Width -> {WT,1.50833649},
330 QuantumNumbers -> {Q -> 2/3},
331 PropagatorLabel -> {"t"},
332 PropagatorType -> Straight,
333 PropagatorArrow -> Forward,
334 PDG -> {6},
335 ParticleName -> {"t" },
336 AntiParticleName -> {"t~"},
337 FullName -> {"t-quark"}
338 },
339 F[7] == {
340 ClassName -> tp,
341 Indices -> {Index[Colour]},
342 SelfConjugate -> False,
343 Mass -> {MTP,1670.3},
344 Width -> {WTP,37.8},
345 QuantumNumbers -> {Q -> 2/3},
346 PropagatorLabel -> {"tp"},
347 PropagatorType -> Straight,
348 PropagatorArrow -> Forward,
349 PDG -> {6000001},
350 ParticleName -> {"tp" },
351 AntiParticleName -> {"tp~"},
352 FullName -> {"tp-quark"}
353 },
354
355(* Fermions: unphysical fields *)
356 F[21] == {
357 ClassName -> LL,
358 Unphysical -> True,
359 Indices -> {Index[SU2D], Index[Generation]},
360 FlavorIndex -> SU2D,
361 SelfConjugate -> False,
362 QuantumNumbers -> {Y -> -1/2},
363 Definitions -> { LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] vl[sp2,ff]], LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]] }
364 },
365 F[22] == {
366 ClassName -> lR,
367 Unphysical -> True,
368 Indices -> {Index[Generation]},
369 FlavorIndex -> Generation,
370 SelfConjugate -> False,
371 QuantumNumbers -> {Y -> -1},
372 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
373 },
374(* QL modified *)
375 F[23] == {
376 ClassName -> QL,
377 Unphysical -> True,
378 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
379 FlavorIndex -> SU2D,
380 SelfConjugate -> False,
381 QuantumNumbers -> {Y -> 1/6},
382 Definitions -> {
383 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] u[sp2,cc] /; ff==1],
384 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] c[sp2,cc] /; ff==2],
385 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] ( cl t[sp2,cc] + sl tp[sp2,cc] ) /; ff==3],
386 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
387 },
388 F[31] == {
389 ClassName -> QLb,
390 Unphysical -> True,
391 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
392 FlavorIndex -> SU2D,
393 SelfConjugate -> False,
394 QuantumNumbers -> {Y -> 1/6},
395 Definitions -> {
396 QLb[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp2,sp1] ubar[sp2,cc] /; ff==1],
397 QLb[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp2,sp1] cbar[sp2,cc] /; ff==2],
398 QLb[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjP[sp2,sp1] ( cl tbar[sp2,cc] + sl tpbar[sp2,cc] ) /; ff==3],
399 QLb[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, Conjugate[ CKM[ff,ff2] ] ProjP[sp2,sp1] dqbar[sp2,ff2,cc]] }
400 },
401(* uR modified *)
402 F[24] == {
403 ClassName -> uR,
404 Unphysical -> True,
405 Indices -> {Index[Generation], Index[Colour]},
406 FlavorIndex -> Generation,
407 SelfConjugate -> False,
408 QuantumNumbers -> {Y -> 2/3},
409 Definitions -> {
410 uR[sp1_,1,cc_] :> Module [ {sp2}, ProjP[sp1,sp2] u[sp2,cc]],
411 uR[sp1_,2,cc_] :> Module [ {sp2}, ProjP[sp1,sp2] c[sp2,cc]],
412 uR[sp1_,3,cc_] :> Module [ {sp2}, ProjP[sp1,sp2] ( cr t[sp2,cc] + sr tp[sp2,cc] )] }
413 },
414 F[32] == {
415 ClassName -> uRb,
416 Unphysical -> True,
417 Indices -> {Index[Generation], Index[Colour]},
418 FlavorIndex -> Generation,
419 SelfConjugate -> False,
420 QuantumNumbers -> {Y -> 2/3},
421 Definitions -> {
422 uRb[sp1_,1,cc_] :> Module [ {sp2}, ProjM[sp2,sp1] ubar[sp2,cc]],
423 uRb[sp1_,2,cc_] :> Module [ {sp2}, ProjM[sp2,sp1] cbar[sp2,cc]],
424 uRb[sp1_,3,cc_] :> Module [ {sp2}, ProjM[sp2,sp1] ( cr tbar[sp2,cc] + sr tpbar[sp2,cc] )] }
425 },
426 F[25] == {
427 ClassName -> dR,
428 Unphysical -> True,
429 Indices -> {Index[Generation], Index[Colour]},
430 FlavorIndex -> Generation,
431 SelfConjugate -> False,
432 QuantumNumbers -> {Y -> -1/3},
433 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
434 },
435
436(* new adding *)
437 F[26] == {
438 ClassName -> TR,
439 Unphysical -> True,
440 Indices -> {Index[Colour]},
441 SelfConjugate -> False,
442 QuantumNumbers -> {Y -> 2/3},
443 Definitions -> { TR[sp1_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] ( -sr t[sp2,cc] + cr tp[sp2,cc] )] }
444 },
445 F[27] == {
446 ClassName -> TL,
447 Unphysical -> True,
448 Indices -> {Index[Colour]},
449 SelfConjugate -> False,
450 QuantumNumbers -> {Y -> 2/3},
451 Definitions -> { TL[sp1_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] ( -sl t[sp2,cc] + cl tp[sp2,cc] )] }
452 },
453
454(* Higgs: physical scalars *)
455 S[1] == {
456 ClassName -> h,
457 SelfConjugate -> True,
458 Mass -> {Mh,125},
459 Width -> {Wh,0.00407},
460 PropagatorLabel -> "h",
461 PropagatorType -> D,
462 PropagatorArrow -> None,
463 PDG -> 25,
464 ParticleName -> "h",
465 FullName -> "h"
466 },
467
468(* Higgs: physical scalars *)
469 S[2] == {
470 ClassName -> G0,
471 SelfConjugate -> True,
472 Goldstone -> Z,
473 Mass -> {MZ, 91.1876},
474 Width -> {WZ, 2.4952},
475 PropagatorLabel -> "Go",
476 PropagatorType -> D,
477 PropagatorArrow -> None,
478 PDG -> 250,
479 ParticleName -> "G0",
480 FullName -> "G0"
481 },
482 S[3] == {
483 ClassName -> GP,
484 SelfConjugate -> False,
485 Goldstone -> W,
486 Mass -> {MW, Internal},
487 QuantumNumbers -> {Q -> 1},
488 Width -> {WW, 2.085},
489 PropagatorLabel -> "GP",
490 PropagatorType -> D,
491 PropagatorArrow -> None,
492 PDG -> 251,
493 ParticleName -> "G+",
494 AntiParticleName -> "G-",
495 FullName -> "GP"
496 },
497(* new adding *)
498 S[21] == {
499 ClassName -> sDM,
500 SelfConjugate -> True,
501 Mass -> {MsDM, 173.2},
502 Width -> {WsDM,1},
503 PropagatorLabel -> "sDM",
504 PropagatorType -> D,
505 PropagatorArrow -> None,
506 PDG -> 6000011,
507 ParticleName -> "sDM",
508 FullName -> "the dilaton particle"
509 },
510
511(* Higgs part: unphysical scalars *)
512(* new adding *)
513 S[31] == {
514 ClassName -> S,
515 Unphysical -> True,
516 SelfConjugate -> True,
517 Definitions -> { S -> vevf + h ss + sDM cs}
518 },
519(* Phi modified *)
520 S[11] == {
521 ClassName -> Phi,
522 Unphysical -> True,
523 Indices -> {Index[SU2D]},
524 FlavorIndex -> SU2D,
525 SelfConjugate -> False,
526 QuantumNumbers -> {Y -> 1/2},
527 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + h cs - sDM ss + I G0)/Sqrt[2] }
528 }
529};
530
531
532(* ************************** *)
533(* ***** Gauge ***** *)
534(* ***** Parameters ***** *)
535(* ***** (FeynArts) ***** *)
536(* ************************** *)
537
538GaugeXi[ V[1] ] = GaugeXi[A];
539GaugeXi[ V[2] ] = GaugeXi[Z];
540GaugeXi[ V[3] ] = GaugeXi[W];
541GaugeXi[ V[4] ] = GaugeXi[G];
542GaugeXi[ S[1] ] = 1;
543GaugeXi[ S[2] ] = GaugeXi[Z];
544GaugeXi[ S[3] ] = GaugeXi[W];
545GaugeXi[ U[1] ] = GaugeXi[A];
546GaugeXi[ U[2] ] = GaugeXi[Z];
547GaugeXi[ U[31] ] = GaugeXi[W];
548GaugeXi[ U[32] ] = GaugeXi[W];
549GaugeXi[ U[4] ] = GaugeXi[G];
550
551
552(* ************************** *)
553(* ***** Parameters ***** *)
554(* ************************** *)
555M$Parameters = {
556
557 (* External parameters *)
558 aEWM1 == {
559 ParameterType -> External,
560 BlockName -> SMINPUTS,
561 OrderBlock -> 1,
562 Value -> 127.9,
563 InteractionOrder -> {QED,-2},
564 Description -> "Inverse of the EW coupling constant at the Z pole"
565 },
566 Gf == {
567 ParameterType -> External,
568 BlockName -> SMINPUTS,
569 OrderBlock -> 2,
570 Value -> 1.16637*^-5,
571 InteractionOrder -> {QED,2},
572 TeX -> Subscript[G,f],
573 Description -> "Fermi constant"
574 },
575 aS == {
576 ParameterType -> External,
577 BlockName -> SMINPUTS,
578 OrderBlock -> 3,
579 Value -> 0.1184,
580 InteractionOrder -> {QCD,2},
581 TeX -> Subscript[\[Alpha],s],
582 Description -> "Strong coupling constant at the Z pole"
583 },
584 ymdo == {
585 ParameterType -> External,
586 BlockName -> YUKAWA,
587 OrderBlock -> 1,
588 Value -> 5.04*^-3,
589 Description -> "Down Yukawa mass"
590 },
591 ymup == {
592 ParameterType -> External,
593 BlockName -> YUKAWA,
594 OrderBlock -> 2,
595 Value -> 2.55*^-3,
596 Description -> "Up Yukawa mass"
597 },
598 yms == {
599 ParameterType -> External,
600 BlockName -> YUKAWA,
601 OrderBlock -> 3,
602 Value -> 0.101,
603 Description -> "Strange Yukawa mass"
604 },
605 ymc == {
606 ParameterType -> External,
607 BlockName -> YUKAWA,
608 OrderBlock -> 4,
609 Value -> 1.27,
610 Description -> "Charm Yukawa mass"
611 },
612 ymb == {
613 ParameterType -> External,
614 BlockName -> YUKAWA,
615 OrderBlock -> 5,
616 Value -> 4.7,
617 Description -> "Bottom Yukawa mass"
618 },
619 yme == {
620 ParameterType -> External,
621 BlockName -> YUKAWA,
622 OrderBlock -> 11,
623 Value -> 5.11*^-4,
624 Description -> "Electron Yukawa mass"
625 },
626 ymm == {
627 ParameterType -> External,
628 BlockName -> YUKAWA,
629 OrderBlock -> 13,
630 Value -> 0.10566,
631 Description -> "Muon Yukawa mass"
632 },
633 ymtau == {
634 ParameterType -> External,
635 BlockName -> YUKAWA,
636 OrderBlock -> 15,
637 Value -> 1.777,
638 Description -> "Tau Yukawa mass"
639 },
640 cabi == {
641 ParameterType -> External,
642 BlockName -> CKMBLOCK,
643 OrderBlock -> 1,
644 Value -> 0.227736,
645 TeX -> Subscript[\[Theta], c],
646 Description -> "Cabibbo angle"
647 },
648
649 (* Internal Parameters *)
650 aEW == {
651 ParameterType -> Internal,
652 Value -> 1/aEWM1,
653 InteractionOrder -> {QED,2},
654 TeX -> Subscript[\[Alpha], EW],
655 Description -> "Electroweak coupling contant"
656 },
657 MW == {
658 ParameterType -> Internal,
659 Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
660 TeX -> Subscript[M,W],
661 Description -> "W mass"
662 },
663 sw2 == {
664 ParameterType -> Internal,
665 Value -> 1-(MW/MZ)^2,
666 Description -> "Squared Sin of the Weinberg angle"
667 },
668 ee == {
669 ParameterType -> Internal,
670 Value -> Sqrt[4 Pi aEW],
671 InteractionOrder -> {QED,1},
672 TeX -> e,
673 Description -> "Electric coupling constant"
674 },
675 cw == {
676 ParameterType -> Internal,
677 Value -> Sqrt[1-sw2],
678 TeX -> Subscript[c,w],
679 Description -> "Cosine of the Weinberg angle"
680 },
681 sw == {
682 ParameterType -> Internal,
683 Value -> Sqrt[sw2],
684 TeX -> Subscript[s,w],
685 Description -> "Sine of the Weinberg angle"
686 },
687 gw == {
688 ParameterType -> Internal,
689 Definitions -> {gw->ee/sw},
690 InteractionOrder -> {QED,1},
691 TeX -> Subscript[g,w],
692 Description -> "Weak coupling constant at the Z pole"
693 },
694 g1 == {
695 ParameterType -> Internal,
696 Definitions -> {g1->ee/cw},
697 InteractionOrder -> {QED,1},
698 TeX -> Subscript[g,1],
699 Description -> "U(1)Y coupling constant at the Z pole"
700 },
701 gs == {
702 ParameterType -> Internal,
703 Value -> Sqrt[4 Pi aS],
704 InteractionOrder -> {QCD,1},
705 TeX -> Subscript[g,s],
706 ParameterName -> G,
707 Description -> "Strong coupling constant at the Z pole"
708 },
709 vev == {
710 ParameterType -> Internal,
711 Value -> 2*MW*sw/ee,
712 InteractionOrder -> {QED,-1},
713 Description -> "Higgs vacuum expectation value"
714 },
715 yl == {
716 ParameterType -> Internal,
717 Indices -> {Index[Generation], Index[Generation]},
718 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
719 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
720 InteractionOrder -> {QED, 1},
721 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
722 TeX -> Superscript[y, l],
723 Description -> "Lepton Yukawa couplings"
724 },
725 yd == {
726 ParameterType -> Internal,
727 Indices -> {Index[Generation], Index[Generation]},
728 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
729 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
730 InteractionOrder -> {QED, 1},
731 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
732 TeX -> Superscript[y, d],
733 Description -> "Down-type Yukawa couplings"
734 },
735(* N. B. : only Cabibbo mixing! *)
736 CKM == {
737 ParameterType -> Internal,
738 Indices -> {Index[Generation], Index[Generation]},
739 Unitary -> True,
740 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
741 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
742 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
743 TeX -> Superscript[V,CKM],
744 Description -> "CKM-Matrix"},
745
746(* new add *)
747 eta == {
748 ParameterType -> External,
749 BlockName -> MDMINPUTS,
750 OrderBlock -> 1,
751 Value -> 0.33,
752 TeX -> \[Eta],
753 Description -> "The ratio of the two scalar vacuum expectation values in the MDM"
754 },
755 ts == {
756 ParameterType -> External,
757 BlockName -> MDMINPUTS,
758 OrderBlock -> 2,
759 Value -> -0.23,
760 Tex -> Subscript[tan\[Theta],S],
761 Description -> "The tangent value of the mixing angle \[Theta]_S between the new Scalar S and the unphysical Higgs scalar Phi[2]"
762 },
763 sl == {
764 ParameterType -> External,
765 BlockName -> MDMINPUTS,
766 OrderBlock -> 3,
767 Value -> 0.12,
768 Tex -> Subscript[sin\[Theta],L],
769 Description -> "The sine value of the mixing angle \[Theta]_L between top quark and its partner"
770 },
771
772 vevf == {
773 ParameterType -> Internal,
774 Value -> vev/eta,
775 InteractionOrder -> {QED,-1},
776 Description -> "The new scalar vacuum expectation value in the MDM"
777 },
778 ss == {
779 ParameterType -> Internal,
780 Value -> ts / Sqrt[1 + ts^2],
781 Tex -> Subscript[sin\[Theta],S],
782 Description -> "The sine value of \[Theta]_S"
783 },
784 cs == {
785 ParameterType -> Internal,
786 Value -> 1 / Sqrt[1 + ts^2],
787 Tex -> Subscript[cos\[Theta],S],
788 Description -> "The cosine value of \[Theta]_S"
789 },
790 cl == {
791 ParameterType -> Internal,
792 Value -> Sqrt[1 - sl^2],
793 Tex -> Subscript[cos\[Theta],L],
794 Description -> "The cosine value of \[Theta]_L"
795 },
796 sr == {
797 ParameterType -> Internal,
798 Value -> MT sl / (MTP cl),
799 Tex -> Subscript[sin\[Theta],R],
800 Description -> "The sine value of the mixing angle \[Theta]_R between top quark and its partner"
801 },
802 cr == {
803 ParameterType -> Internal,
804 Value -> 1,
805 Tex -> Subscript[cos\[Theta],L],
806 Description -> "The cosine value of \[Theta]_R fixed to 1"
807 },
808 dkappa == {
809 ParameterType -> Internal,
810 Value -> Abs[Mh^2 - MsDM^2] / vev^2 Abs[eta ts] / (1 + ts^2),
811 TeX -> \[Kappa],
812 InteractionOrder -> {QED,2},
813 Description -> "Coefficient of quartic couplings of the new scalar S and the unphical Higgs scalar Phi"
814 },
815 dlamh == {
816 ParameterType -> Internal,
817 Value -> Abs[Mh^2 - MsDM^2] / vev^2 (Abs[(Mh^2 + MsDM^2) / (Mh^2 - MsDM^2)] + Abs[2 cs ss]/(2 cs ss) (cs^2 - ss^2)),
818 TeX -> Subscript[\[Lambda],H],
819 InteractionOrder -> {QED,2},
820 Description -> "Coefficient of quartic self-couplings of the unphical Higgs scalar Phi"
821 },
822 dlams == {
823 ParameterType -> Internal,
824 Value -> 3 Abs[Mh^2 - MsDM^2] / (2 vevf^2) (Abs[(Mh^2 + MsDM^2) / (Mh^2 - MsDM^2)] - Abs[2 cs ss]/(2 cs ss) (cs^2 - ss^2)),
825 TeX -> Subscript[\[Lambda],S],
826 InteractionOrder -> {QED,2},
827 Description -> "Coefficient of quartic self-couplings of the new scalar S in the MDM"
828 },
829 muS2 == {
830 ParameterType -> Internal,
831 Value -> - dlams / 6 vevf^2 - dkappa vev^2 / 2,
832 Tex -> Superscript[Subscript[m, S],2],
833 Description -> "Coefficient of the quadratic piece of the new scalar S"
834 },
835(* muH modified*)
836 muH2 == {
837 ParameterType -> Internal,
838 Value -> - dkappa vevf^2 / 2 - dlamh vev^2 / 4,
839 TeX -> Superscript[Subscript[m, H],2],
840 Description -> "Coefficient of the quadratic piece of the unphysical Higgs scalar"
841 },
842(* modified ymt *)
843 ymt == {
844 ParameterType -> Internal,
845 Value -> MT / cl,
846 Description -> "Modified top Yukawa mass in the MDM"
847 },
848 yu == {
849 ParameterType -> Internal,
850 Indices -> {Index[Generation], Index[Generation]},
851 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
852 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
853 InteractionOrder -> {QED, 1},
854 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
855 TeX -> Superscript[y, u],
856 Description -> "Up-type Yukawa couplings"
857 },
858 yp == {
859 ParameterType -> Internal,
860 Value -> Sqrt[2] / vev MTP sl,
861 InteractionOrder -> {QED, 1},
862 ParameterName -> yp,
863 Tex -> Superscript[y, \[Prime]],
864 Description -> "new Yukawa Couplings of the top quark partner in the MDM"
865 },
866 Mdltn == {
867 ParameterType -> Internal,
868 Value -> MTP cl,
869 Description -> "Coefficient of couplings of the top quark partner and the new scalar"
870 }
871
872};
873
874(* ************************** *)
875(* ***** Lagrangian ***** *)
876(* ************************** *)
877
878LGauge := Block[{mu,nu,ii,aa},
879 ExpandIndices[-1/4 FS[B,mu,nu] FS[B,mu,nu] - 1/4 FS[Wi,mu,nu,ii] FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa], FlavorExpand->SU2W]];
880
881(* LFermions modified *)
882LFermions := Block[{mu,ii,cc,sp1,sp2,ff},
883 ExpandIndices[I*(
884 Ga[mu,sp1,sp2] QLb[sp1, ii, ff, cc].DC[QL[sp2, ii, ff, cc], mu] + Ga[mu,sp1,sp2] LLbar[sp1, ii, ff].DC[LL[sp2, ii, ff], mu] + Ga[mu,sp1,sp2] uRb[sp1, ff, cc].DC[uR[sp2, ff, cc], mu] + Ga[mu,sp1,sp2] dRbar[sp1, ff, cc].DC[dR[sp2, ff, cc], mu] + Ga[mu,sp1,sp2] lRbar[sp1, ff].DC[lR[sp2, ff], mu])]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
885
886(* new adding *)
887LFermionsDM := Block[{mu,sp,cc},
888 ExpandIndices[ I TLbar.Ga[mu].DC[TL, mu] + I TLbar.Ga[mu].DC[TR, mu] + I TRbar.Ga[mu].DC[TL, mu] + I TRbar.Ga[mu].DC[TR, mu] - Mdltn / vevf S ( TLbar[sp,cc].TL[sp,cc] + TLbar[sp,cc].TR[sp,cc] + TRbar[sp,cc].TL[sp,cc] + TRbar[sp,cc].TR[sp,cc] ) ,
889 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
890
891(* LHiggs modified *)
892LHiggs := Block[{ii,jj,mu, feynmangaugerules},
893 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
894
895 ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] - 1 / 2 del[S,mu] del[S,mu] - muS2 / 2 S^2 - dlams / 24 S^4 - dkappa / 2 S^2 Phibar[ii] Phi[ii] - muH2 Phibar[ii] Phi[ii] - dlamh / 4 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
896 ];
897
898(* LYukawa modified *)
899LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
900 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
901
902 yuk = ExpandIndices[
903 -yd[ff2, ff3] CKM[ff1, ff2] QLb[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
904 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
905 yu[ff1, ff2] QLb[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj]
906 -Conjugate[yd[ff2, ff3]] Conjugate[CKM[ff1, ff2]] dRbar [sp, ff3, cc].QL [sp, ii, ff1, cc] Phibar[ii] -
907 Conjugate[yl[ff1, ff3]] lRbar[sp, ff3].LL [sp, ii, ff1]. Phibar[ii] -
908 Conjugate[yu[ff1, ff2]] uRb[sp, ff2, cc].QL [sp, ii, ff1, cc] Phi[jj] Conjugate[Eps[ii, jj]]];
909 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
910 yuk/.feynmangaugerules
911 ];
912
913(* new adding *)
914LYukawaDM := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
915 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
916
917 yuk = ExpandIndices[
918 -yp QLb[sp, ii, 3, cc].TR [sp, cc] Phibar[jj] Eps[ii, jj]
919 -Conjugate[yp] TRbar[sp, cc].QL [sp, ii, 3, cc] Phi[jj] Conjugate[Eps[ii, jj]], FlavorExpand -> SU2D];
920 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
921 yuk/.feynmangaugerules
922 ];
923
924LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
925 (* Pure gauge piece *)
926 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
927 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
928 LGhs = -ghGbar.del[DC[ghG,mu],mu];
929
930 (* Scalar pieces: see Peskin pages 739-742 *)
931 (* phi1 and phi2 are the real degrees of freedom of GP *)
932 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
933 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
934 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
935 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
936 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
937 doublet0 = {0, vev/Sqrt[2]};
938 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}];
939 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
940 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
941
942ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
943
944LMDM:= LGauge + LFermions + LFermionsDM + LHiggs + LYukawa + LYukawaDM + LGhost;