HELatNLO: HELatNLO.fr

File HELatNLO.fr, 25.6 KB (added by Ken Mimasu, 9 years ago)

FeynRules model file

Line 
1(* ************************** *)
2(* ***** Information ***** *)
3(* ************************** *)
4M$ModelName = "HELatNLO";
5
6M$Information = {
7 Authors -> {"B. Fuks"},
8 Version -> "0.1",
9 Date -> "05. 02. 2016",
10 Institutions -> {"LPTHE Paris / UPMC"},
11 Emails -> {"fuks@lpthe.jussieu.fr"},
12 References -> "",
13 URLs -> "https://feynrules.irmp.ucl.ac.be/wiki/SILH"
14};
15
16FeynmanGauge = True;
17
18(* Change log *)
19 (* v0.1 (05.02.2016) KM: *)
20
21
22(* ************************** *)
23(* ***** Gauge groups ***** *)
24(* ************************** *)
25M$GaugeGroups = {
26 U1Y == {
27 Abelian -> True,
28 CouplingConstant -> g1,
29 GaugeBoson -> B,
30 Charge -> Y
31 },
32 SU2L == {
33 Abelian -> False,
34 CouplingConstant -> gw,
35 GaugeBoson -> Wi,
36 StructureConstant -> Eps,
37 Representations -> {Ta,SU2D},
38 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
39 },
40 SU3C == {
41 Abelian -> False,
42 CouplingConstant -> gs,
43 GaugeBoson -> G,
44 StructureConstant -> f,
45 Representations -> {T,Colour},
46 SymmetricTensor -> dSUN
47 }
48};
49
50(* ************************** *)
51(* ***** Indices ***** *)
52(* ************************** *)
53IndexRange[Index[SU2W ]] = Unfold[Range[3]];
54IndexRange[Index[SU2D ]] = Unfold[Range[2]];
55IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
56IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
57IndexRange[Index[Generation]] = Range[3];
58IndexStyle[SU2W, j];
59IndexStyle[SU2D, k];
60IndexStyle[Gluon, a];
61IndexStyle[Colour, m];
62IndexStyle[Generation, f];
63
64
65(* ************************** *)
66(* ***** Orders ***** *)
67(* ************************** *)
68M$InteractionOrderHierarchy = { {QCD, 1}, {QED, 2}, {NP,2},{HIG,4},{HIW,6}};
69M$InteractionOrderLimit = { {QCD, 99}, {QED, 99} , {NP,1}, {HIG,1},{HIW,1}};
70
71
72(* ************************** *)
73(* **** Particle classes **** *)
74(* ************************** *)
75M$ClassesDescription = {
76
77(* Gauge bosons: physical vector fields *)
78 V[1] == {
79 ClassName -> A,
80 SelfConjugate -> True,
81 Mass -> 0,
82 Width -> 0,
83 ParticleName -> "a",
84 PDG -> 22,
85 PropagatorLabel -> "a",
86 PropagatorType -> W,
87 PropagatorArrow -> None,
88 FullName -> "Photon"
89 },
90 V[2] == {
91 ClassName -> Z,
92 SelfConjugate -> True,
93 Mass -> {MZ, 91.1876},
94 Width -> {WZ, 2.4952},
95 ParticleName -> "Z",
96 PDG -> 23,
97 PropagatorLabel -> "Z",
98 PropagatorType -> Sine,
99 PropagatorArrow -> None,
100 FullName -> "Z"
101 },
102 V[3] == {
103 ClassName -> W,
104 SelfConjugate -> False,
105 Mass -> {MW, Internal},
106 Width -> {WW, 2.085},
107 ParticleName -> "W+",
108 AntiParticleName -> "W-",
109 QuantumNumbers -> {Q -> 1},
110 PDG -> 24,
111 PropagatorLabel -> "W",
112 PropagatorType -> Sine,
113 PropagatorArrow -> Forward,
114 FullName -> "W"
115 },
116 V[4] == {
117 ClassName -> G,
118 SelfConjugate -> True,
119 Indices -> {Index[Gluon]},
120 Mass -> 0,
121 Width -> 0,
122 ParticleName -> "g",
123 PDG -> 21,
124 PropagatorLabel -> "G",
125 PropagatorType -> C,
126 PropagatorArrow -> None,
127 FullName -> "G"
128 },
129
130(* Ghosts: related to physical gauge bosons *)
131 U[1] == {
132 ClassName -> ghA,
133 SelfConjugate -> False,
134 Ghost -> A,
135 QuantumNumbers -> {GhostNumber -> 1},
136 Mass -> 0,
137 Width -> 0,
138 PropagatorLabel -> "uA",
139 PropagatorType -> GhostDash,
140 PropagatorArrow -> Forward
141 },
142 U[2] == {
143 ClassName -> ghZ,
144 SelfConjugate -> False,
145 Ghost -> Z,
146 QuantumNumbers -> {GhostNumber -> 1},
147 Mass -> {MZ, 91.1876},
148 Width -> {WZ, 2.4952},
149 PropagatorLabel -> "uZ",
150 PropagatorType -> GhostDash,
151 PropagatorArrow -> Forward
152 },
153 U[31] == {
154 ClassName -> ghWp,
155 SelfConjugate -> False,
156 Ghost -> W,
157 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
158 Mass -> {MW,Internal},
159 Width -> {WW, 2.085},
160 PropagatorLabel -> "uWp",
161 PropagatorType -> GhostDash,
162 PropagatorArrow -> Forward
163 },
164 U[32] == {
165 ClassName -> ghWm,
166 SelfConjugate -> False,
167 Ghost -> Wbar,
168 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
169 Mass -> {MW,Internal},
170 Width -> {WW, 2.085},
171 PropagatorLabel -> "uWm",
172 PropagatorType -> GhostDash,
173 PropagatorArrow -> Forward
174 },
175 U[4] == {
176 ClassName -> ghG,
177 SelfConjugate -> False,
178 Indices -> {Index[Gluon]},
179 Ghost -> G,
180 PDG -> 82,
181 QuantumNumbers ->{GhostNumber -> 1},
182 Mass -> 0,
183 Width -> 0,
184 PropagatorLabel -> "uG",
185 PropagatorType -> GhostDash,
186 PropagatorArrow -> Forward
187 },
188
189(* Gauge bosons: unphysical vector fields *)
190 V[11] == {
191 ClassName -> B,
192 Unphysical -> True,
193 SelfConjugate -> True,
194 Definitions -> { B[mu_] -> -sw Z[mu] + cw A[mu]}
195 },
196 V[12] == {
197 ClassName -> Wi,
198 Unphysical -> True,
199 SelfConjugate -> True,
200 Indices -> {Index[SU2W]},
201 FlavorIndex -> SU2W,
202 Definitions -> {
203 Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2],
204 Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]),
205 Wi[mu_,3] -> cw Z[mu] + sw A[mu]}
206 },
207
208(* Ghosts: related to unphysical gauge bosons *)
209 U[11] == {
210 ClassName -> ghB,
211 Unphysical -> True,
212 SelfConjugate -> False,
213 Ghost -> B,
214 Definitions -> { ghB -> -sw ghZ + cw ghA}
215 },
216 U[12] == {
217 ClassName -> ghWi,
218 Unphysical -> True,
219 SelfConjugate -> False,
220 Ghost -> Wi,
221 Indices -> {Index[SU2W]},
222 FlavorIndex -> SU2W,
223 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
224 } ,
225
226(* Fermions: physical fields *)
227 F[1] == {
228 ClassName -> vl,
229 ClassMembers -> {ve,vm,vt},
230 Indices -> {Index[Generation]},
231 FlavorIndex -> Generation,
232 SelfConjugate -> False,
233 Mass -> 0,
234 Width -> 0,
235 QuantumNumbers -> {LeptonNumber -> 1},
236 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
237 PropagatorType -> S,
238 PropagatorArrow -> Forward,
239 PDG -> {12,14,16},
240 ParticleName -> {"ve","vm","vt"},
241 AntiParticleName -> {"ve~","vm~","vt~"},
242 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
243 },
244 F[2] == {
245 ClassName -> l,
246 ClassMembers -> {e, mu, ta},
247 Indices -> {Index[Generation]},
248 FlavorIndex -> Generation,
249 SelfConjugate -> False,
250 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
251 Width -> 0,
252 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
253 PropagatorLabel -> {"l", "e", "mu", "ta"},
254 PropagatorType -> Straight,
255 PropagatorArrow -> Forward,
256 PDG -> {11, 13, 15},
257 ParticleName -> {"e-", "mu-", "ta-"},
258 AntiParticleName -> {"e+", "mu+", "ta+"},
259 FullName -> {"Electron", "Muon", "Tau"}
260 },
261 F[3] == {
262 ClassName -> uq,
263 ClassMembers -> {u, c, t},
264 Indices -> {Index[Generation], Index[Colour]},
265 FlavorIndex -> Generation,
266 SelfConjugate -> False,
267 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
268 Width -> {0, 0, {WT,1.50833649}},
269 QuantumNumbers -> {Q -> 2/3},
270 PropagatorLabel -> {"uq", "u", "c", "t"},
271 PropagatorType -> Straight,
272 PropagatorArrow -> Forward,
273 PDG -> {2, 4, 6},
274 ParticleName -> {"u", "c", "t" },
275 AntiParticleName -> {"u~", "c~", "t~"},
276 FullName -> {"u-quark", "c-quark", "t-quark"}
277 },
278 F[4] == {
279 ClassName -> dq,
280 ClassMembers -> {d, s, b},
281 Indices -> {Index[Generation], Index[Colour]},
282 FlavorIndex -> Generation,
283 SelfConjugate -> False,
284 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
285 Width -> 0,
286 QuantumNumbers -> {Q -> -1/3},
287 PropagatorLabel -> {"dq", "d", "s", "b"},
288 PropagatorType -> Straight,
289 PropagatorArrow -> Forward,
290 PDG -> {1,3,5},
291 ParticleName -> {"d", "s", "b" },
292 AntiParticleName -> {"d~", "s~", "b~"},
293 FullName -> {"d-quark", "s-quark", "b-quark"}
294 },
295
296(* Fermions: unphysical fields *)
297 F[11] == {
298 ClassName -> LL,
299 Unphysical -> True,
300 Indices -> {Index[SU2D], Index[Generation]},
301 FlavorIndex -> SU2D,
302 SelfConjugate -> False,
303 QuantumNumbers -> {Y -> -1/2},
304 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]] }
305 },
306 F[12] == {
307 ClassName -> lR,
308 Unphysical -> True,
309 Indices -> {Index[Generation]},
310 FlavorIndex -> Generation,
311 SelfConjugate -> False,
312 QuantumNumbers -> {Y -> -1},
313 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
314 },
315 F[13] == {
316 ClassName -> QL,
317 Unphysical -> True,
318 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
319 FlavorIndex -> SU2D,
320 SelfConjugate -> False,
321 QuantumNumbers -> {Y -> 1/6},
322 Definitions -> {
323 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
324 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
325 },
326 F[14] == {
327 ClassName -> uR,
328 Unphysical -> True,
329 Indices -> {Index[Generation], Index[Colour]},
330 FlavorIndex -> Generation,
331 SelfConjugate -> False,
332 QuantumNumbers -> {Y -> 2/3},
333 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
334 },
335 F[15] == {
336 ClassName -> dR,
337 Unphysical -> True,
338 Indices -> {Index[Generation], Index[Colour]},
339 FlavorIndex -> Generation,
340 SelfConjugate -> False,
341 QuantumNumbers -> {Y -> -1/3},
342 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
343 },
344
345(* Higgs: physical scalars *)
346 S[1] == {
347 ClassName -> H,
348 SelfConjugate -> True,
349 Mass -> {MH,125},
350 Width -> {WH,0.00407},
351 PropagatorLabel -> "H",
352 PropagatorType -> D,
353 PropagatorArrow -> None,
354 PDG -> 25,
355 ParticleName -> "H",
356 FullName -> "H"
357 },
358
359(* Higgs: physical scalars *)
360 S[2] == {
361 ClassName -> G0,
362 SelfConjugate -> True,
363 Goldstone -> Z,
364 Mass -> {MZ, 91.1876},
365 Width -> {WZ, 2.4952},
366 PropagatorLabel -> "Go",
367 PropagatorType -> D,
368 PropagatorArrow -> None,
369 PDG -> 250,
370 ParticleName -> "G0",
371 FullName -> "G0"
372 },
373 S[3] == {
374 ClassName -> GP,
375 SelfConjugate -> False,
376 Goldstone -> W,
377 Mass -> {MW, Internal},
378 QuantumNumbers -> {Q -> 1},
379 Width -> {WW, 2.085},
380 PropagatorLabel -> "GP",
381 PropagatorType -> D,
382 PropagatorArrow -> None,
383 PDG -> 251,
384 ParticleName -> "G+",
385 AntiParticleName -> "G-",
386 FullName -> "GP"
387 },
388
389(* Higgs: unphysical scalars *)
390 S[11] == {
391 ClassName -> Phi,
392 Unphysical -> True,
393 Indices -> {Index[SU2D]},
394 FlavorIndex -> SU2D,
395 SelfConjugate -> False,
396 QuantumNumbers -> {Y -> 1/2},
397 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
398 }
399};
400
401
402(* ************************** *)
403(* ***** Gauge ***** *)
404(* ***** Parameters ***** *)
405(* ***** (FeynArts) ***** *)
406(* ************************** *)
407
408GaugeXi[ V[1] ] = GaugeXi[A];
409GaugeXi[ V[2] ] = GaugeXi[Z];
410GaugeXi[ V[3] ] = GaugeXi[W];
411GaugeXi[ V[4] ] = GaugeXi[G];
412GaugeXi[ S[1] ] = 1;
413GaugeXi[ S[2] ] = GaugeXi[Z];
414GaugeXi[ S[3] ] = GaugeXi[W];
415GaugeXi[ U[1] ] = GaugeXi[A];
416GaugeXi[ U[2] ] = GaugeXi[Z];
417GaugeXi[ U[31] ] = GaugeXi[W];
418GaugeXi[ U[32] ] = GaugeXi[W];
419GaugeXi[ U[4] ] = GaugeXi[G];
420
421
422(* ************************** *)
423(* ***** Parameters ***** *)
424(* ************************** *)
425(* The loop coefficients *)
426sert[x_] := 1+ 7/30 x + 2/21 x^2 + 26/525 x^3;
427serw[xw_, xt_] := 1 + xw * 66/235 +xw^2 * 228/1645 + xw^3 * 696/8225 +
428 xw^4 * 5248/90475 +xw^5 * 1280/29939+ xw^6 * 54528/1646645-
429 xt * 56/705 - xt^2 * 32/987;
430
431M$Parameters = {
432 (* New physics parameters *)
433 NPl == { TeX -> \[CapitalLambda], ParameterType -> External, Value -> 1000, BlockName -> NEWCOUP, OrderBlock -> 0 },
434 cWW == { TeX -> Subscript[C,W], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 1 , InteractionOrder -> {{NP,1},{QED,-1}} },
435 cHW == { TeX -> Subscript[C,HW], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 2 , InteractionOrder -> {{NP,1},{QED,-1}} },
436 cB == { TeX -> Subscript[C,B], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 3, InteractionOrder -> {{NP,1},{QED,-1}} },
437
438 cHB == { TeX -> Subscript[C,HB],
439 ParameterType -> External,
440 Value -> 0.1,
441 BlockName -> NEWCOUP, OrderBlock -> 4,
442 InteractionOrder -> {{NP,1},{QED,-1}} },
443
444 cBB == { TeX -> Subscript[C,BB],
445 ParameterType -> External,
446 Value -> 0.1,
447 BlockName -> NEWCOUP, OrderBlock -> 5,
448 InteractionOrder -> {{NP,1},{QED,-1}} },
449
450 AH == { TeX->Subscript[A,H], ParameterType->Internal, Value -> ee^2/4/Pi/(Pi*vev)*(47/18)(*serw[(MH/2/MW)^2, (MH/2/MT)^2] comment to be consitent with hza*), InteractionOrder -> {HIW, 1}},
451 gZAH == { (*TeX->Subscript[g,ZAH], *)
452ParameterType->Internal,
453Value -> Sqrt[aEW Gf MZ^2/(8 Pi Sqrt[2])](94 cw2-13)/(9 Pi vev),
454InteractionOrder -> {HIW, 1}},
455 GH == { TeX->Subscript[G,H], ParameterType->Internal, Value -> -gs^2/(4Pi(3Pi vev)) (*sert[(MH/2/MT)^2]*), InteractionOrder -> {HIG, 1}},
456
457 (* External parameters *)
458
459 aEWM1 == {
460 ParameterType -> External,
461 BlockName -> SMINPUTS,
462 OrderBlock -> 1,
463 Value -> 127.9,
464 InteractionOrder -> {QED,-2},
465 Description -> "Inverse of the EW coupling constant at the Z pole"
466 },
467 Gf == {
468 ParameterType -> External,
469 BlockName -> SMINPUTS,
470 OrderBlock -> 2,
471 Value -> 1.16637*^-5,
472 InteractionOrder -> {QED,2},
473 TeX -> Subscript[G,f],
474 Description -> "Fermi constant"
475 },
476 aS == {
477 ParameterType -> External,
478 BlockName -> SMINPUTS,
479 OrderBlock -> 3,
480 Value -> 0.1184,
481 InteractionOrder -> {QCD,2},
482 TeX -> Subscript[\[Alpha],s],
483 Description -> "Strong coupling constant at the Z pole"
484 },
485 ymdo == {
486 ParameterType -> External,
487 BlockName -> YUKAWA,
488 OrderBlock -> 1,
489 Value -> 5.04*^-3,
490 Description -> "Down Yukawa mass"
491 },
492 ymup == {
493 ParameterType -> External,
494 BlockName -> YUKAWA,
495 OrderBlock -> 2,
496 Value -> 2.55*^-3,
497 Description -> "Up Yukawa mass"
498 },
499 yms == {
500 ParameterType -> External,
501 BlockName -> YUKAWA,
502 OrderBlock -> 3,
503 Value -> 0.101,
504 Description -> "Strange Yukawa mass"
505 },
506 ymc == {
507 ParameterType -> External,
508 BlockName -> YUKAWA,
509 OrderBlock -> 4,
510 Value -> 1.27,
511 Description -> "Charm Yukawa mass"
512 },
513 ymb == {
514 ParameterType -> External,
515 BlockName -> YUKAWA,
516 OrderBlock -> 5,
517 Value -> 4.7,
518 Description -> "Bottom Yukawa mass"
519 },
520 ymt == {
521 ParameterType -> External,
522 BlockName -> YUKAWA,
523 OrderBlock -> 6,
524 Value -> 172,
525 Description -> "Top Yukawa mass"
526 },
527 yme == {
528 ParameterType -> External,
529 BlockName -> YUKAWA,
530 OrderBlock -> 11,
531 Value -> 5.11*^-4,
532 Description -> "Electron Yukawa mass"
533 },
534 ymm == {
535 ParameterType -> External,
536 BlockName -> YUKAWA,
537 OrderBlock -> 13,
538 Value -> 0.10566,
539 Description -> "Muon Yukawa mass"
540 },
541 ymtau == {
542 ParameterType -> External,
543 BlockName -> YUKAWA,
544 OrderBlock -> 15,
545 Value -> 1.777,
546 Description -> "Tau Yukawa mass"
547 },
548 cabi == {
549 ParameterType -> External,
550 BlockName -> CKMBLOCK,
551 OrderBlock -> 1,
552 Value -> 0.227736,
553 TeX -> Subscript[\[Theta], c],
554 Description -> "Cabibbo angle"
555 },
556
557 (* Internal Parameters *)
558 aEW == {
559 ParameterType -> Internal,
560 Value -> 1/aEWM1,
561 InteractionOrder -> {QED,2},
562 TeX -> Subscript[\[Alpha], EW],
563 Description -> "Electroweak coupling constant"
564 },
565
566 vev == {
567 ParameterType -> Internal,
568 Value -> Sqrt[1/(Sqrt[2] Gf)],
569 InteractionOrder -> {QED,-1},
570 Description -> "Higgs vacuum expectation value"
571 },
572
573 ee == {
574 ParameterType -> Internal,
575 Value -> Sqrt[4 Pi aEW] (1+cWW Pi aEW vev^2/2 /NPl^2 ),
576 InteractionOrder -> {QED,1},
577 TeX -> e,
578 Description -> "Electric coupling constant"
579 },
580
581 cw2 == {
582 ParameterType -> Internal,
583 Value ->(MZ^2*(8*NPl^2 - 4*cB*ee^2*vev^2) + 4*MZ*Sqrt[(MZ - ee*vev)*(MZ + ee*vev)]*(2*NPl^2 + cB*ee^2*vev^2) - ee^2*vev^2*(8*NPl^2 + cWW*ee^2*vev^2))/ (16*MZ*NPl^2*Sqrt[(MZ - ee*vev)*(MZ + ee*vev)])
584 },
585
586 cw == {
587 ParameterType -> Internal,
588 Value -> Sqrt[cw2],
589 TeX -> Subscript[c,w],
590 Description -> "Cosine of the Weinberg angle"
591 },
592 sw2 == {
593 ParameterType -> Internal,
594 Value -> 1-(cw)^2,
595 Description -> "Squared Sin of the Weinberg angle"
596 },
597
598 sw == {
599 ParameterType -> Internal,
600 Value -> Sqrt[sw2],
601 TeX -> Subscript[s,w],
602 Description -> "Sine of the Weinberg angle"
603 },
604
605 MW == {
606 ParameterType -> Internal,
607 Value -> (ee*vev)/(2*sw) ,
608 TeX -> Subscript[M,W],
609 Description -> "W mass"
610 },
611 gw == {
612 ParameterType -> Internal,
613 Definitions -> {gw->ee/sw/(1 + ( cWW ee^2/sw^2 vev^2)/(8 NPl^2))},
614 InteractionOrder -> {QED,1},
615 TeX -> Subscript[g,w],
616 Description -> "Weak coupling constant at the Z pole"
617 },
618 g1 == {
619 ParameterType -> Internal,
620 Definitions -> {g1->1/(1 + (cBB ee^2 vev^2)/(4 NPl^2 cw^2) )ee/cw},
621 InteractionOrder -> {QED,1},
622 TeX -> Subscript[g,1],
623 Description -> "U(1)Y coupling constant at the Z pole"
624 },
625 gs == {
626 ParameterType -> Internal,
627 Value -> Sqrt[4 Pi aS],
628 InteractionOrder -> {QCD,1},
629 TeX -> Subscript[g,s],
630 ParameterName -> G,
631 Description -> "Strong coupling constant at the Z pole"
632 },
633 lam == {
634 ParameterType -> Internal,
635 Value -> MH^2/(2*vev^2),
636 InteractionOrder -> {QED, 2},
637 Description -> "Higgs quartic coupling"
638 },
639 muH == {
640 ParameterType -> Internal,
641 Value -> Sqrt[vev^2 lam],
642 TeX -> \[Mu],
643 Description -> "Coefficient of the quadratic piece of the Higgs potential"
644 },
645 yl == {
646 ParameterType -> Internal,
647 Indices -> {Index[Generation], Index[Generation]},
648 Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
649 Value -> {yl[1,1] -> Sqrt[2] yme / vev, yl[2,2] -> Sqrt[2] ymm / vev, yl[3,3] -> Sqrt[2] ymtau / vev},
650 InteractionOrder -> {QED, 1},
651 ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
652 TeX -> Superscript[y, l],
653 Description -> "Lepton Yukawa couplings"
654 },
655 yu == {
656 ParameterType -> Internal,
657 Indices -> {Index[Generation], Index[Generation]},
658 Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
659 Value -> {yu[1,1] -> Sqrt[2] ymup/vev, yu[2,2] -> Sqrt[2] ymc/vev, yu[3,3] -> Sqrt[2] ymt/vev},
660 InteractionOrder -> {QED, 1},
661 ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
662 TeX -> Superscript[y, u],
663 Description -> "Up-type Yukawa couplings"
664 },
665 yd == {
666 ParameterType -> Internal,
667 Indices -> {Index[Generation], Index[Generation]},
668 Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
669 Value -> {yd[1,1] -> Sqrt[2] ymdo/vev, yd[2,2] -> Sqrt[2] yms/vev, yd[3,3] -> Sqrt[2] ymb/vev},
670 InteractionOrder -> {QED, 1},
671 ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
672 TeX -> Superscript[y, d],
673 Description -> "Down-type Yukawa couplings"
674 },
675(* N. B. : only Cabibbo mixing! *)
676 CKM == {
677 ParameterType -> Internal,
678 Indices -> {Index[Generation], Index[Generation]},
679 Unitary -> True,
680 Value -> {CKM[1,1] -> Cos[cabi], CKM[1,2] -> Sin[cabi], CKM[1,3] -> 0,
681 CKM[2,1] -> -Sin[cabi], CKM[2,2] -> Cos[cabi], CKM[2,3] -> 0,
682 CKM[3,1] -> 0, CKM[3,2] -> 0, CKM[3,3] -> 1},
683 TeX -> Superscript[V,CKM],
684 Description -> "CKM-Matrix"}
685
686};
687
688(* ************************** *)
689(* ***** Lagrangian ***** *)
690(* ************************** *)
691
692
693LGauge := Block[{mu,nu,ii,aa},
694 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]];
695
696LFermions := Block[{mu},
697 ExpandIndices[I*(
698 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]),
699 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
700
701LHiggs := Block[{ii,mu, feynmangaugerules},
702 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
703
704 ExpandIndices[DC[Phibar[ii],mu] DC[Phi[ii],mu] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
705 ];
706
707LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
708 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
709
710 yuk = ExpandIndices[
711 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
712 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
713 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
714 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
715 yuk+HC[yuk]/.feynmangaugerules
716 ];
717
718LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
719 (* Pure gauge piece *)
720 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
721 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
722 LGhs = -ghGbar.del[DC[ghG,mu],mu];
723
724 (* Scalar pieces: see Peskin pages 739-742 *)
725 (* phi1 and phi2 are the real degrees of freedom of GP *)
726 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
727 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
728 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
729 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
730 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
731 doublet0 = {0, vev/Sqrt[2]};
732 Vectorize[{a_, b_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]]}/.{Im[_]->0, Re[num_]->num}];
733 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
734 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
735
736ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
737
738LSM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;
739
740Wvec[mu_,nu_,ii_,jj_]:= Module[{aa},Ta[aa,ii,jj] FS[Wi,mu,nu,aa]];
741
742LSILH := Block[{ii,jj,mu,nu, OW, OB, OHW, OHBi, OBB},
743
744 OW = I cWW gw/2 (Phibar[ii] DC[Phi[jj],mu] - DC[Phibar[ii],mu] Phi[jj]) DC[Wvec[mu,nu,ii,jj],nu];
745 OB = I cB g1/2 (Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]) del[FS[B,mu,nu],nu];
746 OHW= I cHW gw DC[Phibar[ii],mu] DC[Phi[jj],nu] Wvec[mu,nu,ii,jj];
747 OHB= I cHB g1 DC[Phibar[ii],mu] DC[Phi[ii],nu] FS[B,mu,nu];
748 OBB= cBB g1^2/4 Phibar[ii] Phi[ii] FS[B,mu,nu] FS[B,mu,nu];
749
750 1/NPl^2 (OW+OB+OHB+OHW+OBB)
751];
752
753RedefineSMP[lag_]:=Block[{mylag},
754 mylag := ExpandIndices[lag,FlavorExpand->{SU2D,SU2W}];
755 (* Field redefinitions *)
756 mylag = mylag/. {A[mu_] :> A[mu] (1 + ( cBB g1^2 cw^2 vev^2)/(4 NPl^2)) -
757 Z[mu] ((2* cB*cw^2*g1^2 + (2*cBB*cw^2*g1^2 - (1-cw^2) cWW*gw^2)*sw^2)*vev^2)/(8*cw*NPl^2*sw),
758 Z[mu_] :> Z[mu] (1 + ( cWW gw^2 vev^2)/(8 NPl^2) + (cB g1^2 vev^2)/(4 NPl^2) + (cBB g1^2 sw^2 vev^2)/(4 NPl^2)) -
759 A[mu] ((2* cB *cw^2*g1^2 0 + (2*cBB*cw^2*g1^2 - cw^2 cWW*gw^2)*sw^2)*vev^2)/(8*cw*NPl^2*sw),
760 W[mu_] -> W[mu] (1 + (cWW gw^2 vev^2)/(8 NPl^2)),
761 Wbar[mu_] -> Wbar[mu] (1 + (cWW gw^2 vev^2)/(8 NPl^2))}//.MR$Definitions(*for g1 before series and the other ???*);
762 (Normal[Series[#,{NPl,Infinity,2}]]&)/@ mylag
763];
764
765LLOPP := -1/4 GH FS[G, mu, nu, b] FS[G, mu, nu, b] H (1-0*H/(2 vev)) - 1/4 AH FS[A, mu, nu] FS[A, mu, nu] H- 1/2 gZAH FS[Z, mu, nu] FS[A, mu, nu] H;
766
767Lag:=RedefineSMP[LSM+LSILH] + LLOPP;
768
769