HEL: HEL.fr

File HEL.fr, 36.2 KB (added by Adam, 12 years ago)
Line 
1(* ************************** *)
2(* ***** Information ***** *)
3(* ************************** *)
4M$ModelName = "HEL";
5
6M$Information = {
7 Authors -> {"A. Alloul, B. Fuks, V. Sanz"},
8 Version -> "2.0",
9 Date -> "11. 03. 2014",
10 Institutions -> {"GRPHE Strasbourg / U. Haute Alsace", "CERN / IPHC Strasbourg / U. Strasbourg", "University of Sussex"},
11 Emails -> {"adam.alloul@iphc.cnrs.fr", "benjamin.fuks@iphc.cnrs.fr", "v.sanz@sussex.ac.uk"},
12 References -> "arXiv:1310.5150",
13 URLs -> "https://feynrules.irmp.ucl.ac.be/wiki/HEL"
14};
15
16FeynmanGauge = True;
17
18(* Change log *)
19 (* v1.1 (23.10.2013) BF: Fixing the coupling orders *)
20 (* v1.2 (24.10.2013) BF: Adding the SM gghh contribution in the large mtop limit *)
21 (* v2.0 (11.03.2014) BF: Adding the full SM + modifying the parameters cf. NP effects *)
22
23(* ************************** *)
24(* ***** Gauge groups ***** *)
25(* ************************** *)
26M$GaugeGroups = {
27 U1Y == {
28 Abelian -> True,
29 CouplingConstant -> g1,
30 GaugeBoson -> B,
31 Charge -> Y
32 },
33 SU2L == {
34 Abelian -> False,
35 CouplingConstant -> gw,
36 GaugeBoson -> Wi,
37 StructureConstant -> Eps,
38 Representations -> {Ta,SU2D},
39 Definitions -> {Ta[a_,b_,c_]->PauliSigma[a,b,c]/2, FSU2L[i_,j_,k_]:> I Eps[i,j,k]}
40 },
41 SU3C == {
42 Abelian -> False,
43 CouplingConstant -> gs,
44 GaugeBoson -> G,
45 StructureConstant -> f,
46 Representations -> {T,Colour},
47 SymmetricTensor -> dSUN
48 }
49};
50
51(* ************************** *)
52(* ***** Indices ***** *)
53(* ************************** *)
54IndexRange[Index[SU2W ]] = Unfold[Range[3]];
55IndexRange[Index[SU2D ]] = Unfold[Range[2]];
56IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
57IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
58IndexRange[Index[Generation]] = Range[3];
59IndexStyle[SU2W, j];
60IndexStyle[SU2D, k];
61IndexStyle[Gluon, a];
62IndexStyle[Colour, m];
63IndexStyle[Generation, f];
64
65
66(* ************************** *)
67(* ***** Orders ***** *)
68(* ************************** *)
69M$InteractionOrderHierarchy = { {QCD, 1}, {QED, 2}, {NP,1} };
70
71M$InteractionOrderLimit = { {QCD, 99}, {QED, 99} , {NP,1}};
72
73
74(* ************************** *)
75(* **** Particle classes **** *)
76(* ************************** *)
77M$ClassesDescription = {
78
79(* Gauge bosons: physical vector fields *)
80 V[1] == {
81 ClassName -> A,
82 SelfConjugate -> True,
83 Mass -> 0,
84 Width -> 0,
85 ParticleName -> "a",
86 PDG -> 22,
87 PropagatorLabel -> "a",
88 PropagatorType -> W,
89 PropagatorArrow -> None,
90 FullName -> "Photon"
91 },
92 V[2] == {
93 ClassName -> Z,
94 SelfConjugate -> True,
95 Mass -> {MZ, Internal},
96 Width -> {WZ, 2.4952},
97 ParticleName -> "Z",
98 PDG -> 23,
99 PropagatorLabel -> "Z",
100 PropagatorType -> Sine,
101 PropagatorArrow -> None,
102 FullName -> "Z"
103 },
104 V[3] == {
105 ClassName -> W,
106 SelfConjugate -> False,
107 Mass -> {MW, 80.385},
108 Width -> {WW, 2.085},
109 ParticleName -> "W+",
110 AntiParticleName -> "W-",
111 QuantumNumbers -> {Q -> 1},
112 PDG -> 24,
113 PropagatorLabel -> "W",
114 PropagatorType -> Sine,
115 PropagatorArrow -> Forward,
116 FullName -> "W"
117 },
118 V[4] == {
119 ClassName -> G,
120 SelfConjugate -> True,
121 Indices -> {Index[Gluon]},
122 Mass -> 0,
123 Width -> 0,
124 ParticleName -> "g",
125 PDG -> 21,
126 PropagatorLabel -> "G",
127 PropagatorType -> C,
128 PropagatorArrow -> None,
129 FullName -> "G"
130 },
131
132(* Ghosts: related to physical gauge bosons *)
133 U[1] == {
134 ClassName -> ghA,
135 SelfConjugate -> False,
136 Ghost -> A,
137 QuantumNumbers -> {GhostNumber -> 1},
138 Mass -> 0,
139 Width -> 0,
140 PropagatorLabel -> "uA",
141 PropagatorType -> GhostDash,
142 PropagatorArrow -> Forward
143 },
144 U[2] == {
145 ClassName -> ghZ,
146 SelfConjugate -> False,
147 Ghost -> Z,
148 QuantumNumbers -> {GhostNumber -> 1},
149 Mass -> {MZ,Internal},
150 Width -> {WZ, 2.4952},
151 PropagatorLabel -> "uZ",
152 PropagatorType -> GhostDash,
153 PropagatorArrow -> Forward
154 },
155 U[31] == {
156 ClassName -> ghWp,
157 SelfConjugate -> False,
158 Ghost -> W,
159 QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
160 Mass -> {MW,80.385},
161 Width -> {WW, 2.085},
162 PropagatorLabel -> "uWp",
163 PropagatorType -> GhostDash,
164 PropagatorArrow -> Forward
165 },
166 U[32] == {
167 ClassName -> ghWm,
168 SelfConjugate -> False,
169 Ghost -> Wbar,
170 QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
171 Mass -> {MW,80.385},
172 Width -> {WW, 2.085},
173 PropagatorLabel -> "uWm",
174 PropagatorType -> GhostDash,
175 PropagatorArrow -> Forward
176 },
177 U[4] == {
178 ClassName -> ghG,
179 SelfConjugate -> False,
180 Indices -> {Index[Gluon]},
181 Ghost -> G,
182 PDG -> 82,
183 QuantumNumbers ->{GhostNumber -> 1},
184 Mass -> 0,
185 Width -> 0,
186 PropagatorLabel -> "uG",
187 PropagatorType -> GhostDash,
188 PropagatorArrow -> Forward
189 },
190
191(* Gauge bosons: unphysical vector fields *)
192 V[11] == {
193 ClassName -> B,
194 Unphysical -> True,
195 SelfConjugate -> True,
196 Definitions -> { B[mu_] -> -sw Z[mu]+cw A[mu]}
197 },
198 V[12] == {
199 ClassName -> Wi,
200 Unphysical -> True,
201 SelfConjugate -> True,
202 Indices -> {Index[SU2W]},
203 FlavorIndex -> SU2W,
204 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]}
205 },
206
207(* Ghosts: related to unphysical gauge bosons *)
208 U[11] == {
209 ClassName -> ghB,
210 Unphysical -> True,
211 SelfConjugate -> False,
212 Ghost -> B,
213 Definitions -> { ghB -> -sw ghZ + cw ghA}
214 },
215 U[12] == {
216 ClassName -> ghWi,
217 Unphysical -> True,
218 SelfConjugate -> False,
219 Ghost -> Wi,
220 Indices -> {Index[SU2W]},
221 FlavorIndex -> SU2W,
222 Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[3] -> cw ghZ+sw ghA}
223 } ,
224
225(* Fermions: physical fields *)
226 F[1] == {
227 ClassName -> vl,
228 ClassMembers -> {ve,vm,vt},
229 Indices -> {Index[Generation]},
230 FlavorIndex -> Generation,
231 SelfConjugate -> False,
232 Mass -> 0,
233 Width -> 0,
234 QuantumNumbers -> {LeptonNumber -> 1},
235 PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
236 PropagatorType -> S,
237 PropagatorArrow -> Forward,
238 PDG -> {12,14,16},
239 ParticleName -> {"ve","vm","vt"},
240 AntiParticleName -> {"ve~","vm~","vt~"},
241 FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
242 },
243 F[2] == {
244 ClassName -> l,
245 ClassMembers -> {e, mu, ta},
246 Indices -> {Index[Generation]},
247 FlavorIndex -> Generation,
248 SelfConjugate -> False,
249 Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
250 Width -> 0,
251 QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
252 PropagatorLabel -> {"l", "e", "mu", "ta"},
253 PropagatorType -> Straight,
254 PropagatorArrow -> Forward,
255 PDG -> {11, 13, 15},
256 ParticleName -> {"e-", "mu-", "ta-"},
257 AntiParticleName -> {"e+", "mu+", "ta+"},
258 FullName -> {"Electron", "Muon", "Tau"}
259 },
260 F[3] == {
261 ClassName -> uq,
262 ClassMembers -> {u, c, t},
263 Indices -> {Index[Generation], Index[Colour]},
264 FlavorIndex -> Generation,
265 SelfConjugate -> False,
266 Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
267 Width -> {0, 0, {WT,1.50833649}},
268 QuantumNumbers -> {Q -> 2/3},
269 PropagatorLabel -> {"uq", "u", "c", "t"},
270 PropagatorType -> Straight,
271 PropagatorArrow -> Forward,
272 PDG -> {2, 4, 6},
273 ParticleName -> {"u", "c", "t" },
274 AntiParticleName -> {"u~", "c~", "t~"},
275 FullName -> {"u-quark", "c-quark", "t-quark"}
276 },
277 F[4] == {
278 ClassName -> dq,
279 ClassMembers -> {d, s, b},
280 Indices -> {Index[Generation], Index[Colour]},
281 FlavorIndex -> Generation,
282 SelfConjugate -> False,
283 Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
284 Width -> 0,
285 QuantumNumbers -> {Q -> -1/3},
286 PropagatorLabel -> {"dq", "d", "s", "b"},
287 PropagatorType -> Straight,
288 PropagatorArrow -> Forward,
289 PDG -> {1,3,5},
290 ParticleName -> {"d", "s", "b" },
291 AntiParticleName -> {"d~", "s~", "b~"},
292 FullName -> {"d-quark", "s-quark", "b-quark"}
293 },
294
295(* Fermions: unphysical fields *)
296 F[11] == {
297 ClassName -> LL,
298 Unphysical -> True,
299 Indices -> {Index[SU2D], Index[Generation]},
300 FlavorIndex -> SU2D,
301 SelfConjugate -> False,
302 QuantumNumbers -> {Y -> -1/2},
303 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]] }
304 },
305 F[12] == {
306 ClassName -> lR,
307 Unphysical -> True,
308 Indices -> {Index[Generation]},
309 FlavorIndex -> Generation,
310 SelfConjugate -> False,
311 QuantumNumbers -> {Y -> -1},
312 Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
313 },
314 F[13] == {
315 ClassName -> QL,
316 Unphysical -> True,
317 Indices -> {Index[SU2D], Index[Generation], Index[Colour]},
318 FlavorIndex -> SU2D,
319 SelfConjugate -> False,
320 QuantumNumbers -> {Y -> 1/6},
321 Definitions -> {
322 QL[sp1_,1,ff_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] uq[sp2,ff,cc]],
323 QL[sp1_,2,ff_,cc_] :> Module[{sp2,ff2}, CKM[ff,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]] }
324 },
325 F[14] == {
326 ClassName -> uR,
327 Unphysical -> True,
328 Indices -> {Index[Generation], Index[Colour]},
329 FlavorIndex -> Generation,
330 SelfConjugate -> False,
331 QuantumNumbers -> {Y -> 2/3},
332 Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
333 },
334 F[15] == {
335 ClassName -> dR,
336 Unphysical -> True,
337 Indices -> {Index[Generation], Index[Colour]},
338 FlavorIndex -> Generation,
339 SelfConjugate -> False,
340 QuantumNumbers -> {Y -> -1/3},
341 Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
342 },
343
344(* Higgs: physical scalars *)
345 S[1] == {
346 ClassName -> H,
347 SelfConjugate -> True,
348 Mass -> {MH,125},
349 Width -> {WH,0.00407},
350 PropagatorLabel -> "H",
351 PropagatorType -> D,
352 PropagatorArrow -> None,
353 PDG -> 25,
354 ParticleName -> "H",
355 FullName -> "H"
356 },
357
358(* Higgs: physical scalars *)
359 S[2] == {
360 ClassName -> G0,
361 SelfConjugate -> True,
362 Goldstone -> Z,
363 Mass -> {MZ, Internal},
364 Width -> {WZ, 2.4952},
365 PropagatorLabel -> "Go",
366 PropagatorType -> D,
367 PropagatorArrow -> None,
368 PDG -> 250,
369 ParticleName -> "G0",
370 FullName -> "G0"
371 },
372 S[3] == {
373 ClassName -> GP,
374 SelfConjugate -> False,
375 Goldstone -> W,
376 Mass -> {MW, 80.385},
377 QuantumNumbers -> {Q -> 1},
378 Width -> {WW, 2.085},
379 PropagatorLabel -> "GP",
380 PropagatorType -> D,
381 PropagatorArrow -> None,
382 PDG -> 251,
383 ParticleName -> "G+",
384 AntiParticleName -> "G-",
385 FullName -> "GP"
386 },
387
388(* Higgs: unphysical scalars *)
389 S[11] == {
390 ClassName -> Phi,
391 Unphysical -> True,
392 Indices -> {Index[SU2D]},
393 FlavorIndex -> SU2D,
394 SelfConjugate -> False,
395 QuantumNumbers -> {Y -> 1/2},
396 Definitions -> { Phi[1] -> -I GP, Phi[2] -> (vev + H + I G0)/Sqrt[2] }
397 }
398};
399
400
401(* ************************** *)
402(* ***** Gauge ***** *)
403(* ***** Parameters ***** *)
404(* ***** (FeynArts) ***** *)
405(* ************************** *)
406
407GaugeXi[ V[1] ] = GaugeXi[A];
408GaugeXi[ V[2] ] = GaugeXi[Z];
409GaugeXi[ V[3] ] = GaugeXi[W];
410GaugeXi[ V[4] ] = GaugeXi[G];
411GaugeXi[ S[1] ] = 1;
412GaugeXi[ S[2] ] = GaugeXi[Z];
413GaugeXi[ S[3] ] = GaugeXi[W];
414GaugeXi[ U[1] ] = GaugeXi[A];
415GaugeXi[ U[2] ] = GaugeXi[Z];
416GaugeXi[ U[31] ] = GaugeXi[W];
417GaugeXi[ U[32] ] = GaugeXi[W];
418GaugeXi[ U[4] ] = GaugeXi[G];
419
420
421(* ************************** *)
422(* ***** Parameters ***** *)
423(* ************************** *)
424(* The loop coefficients *)
425sert[x_] := 1+ 7/30 x + 2/21 x^2 + 26/525 x^3;
426serw[xw_, xt_] := 1 + xw * 66/235 +xw^2 * 228/1645 + xw^3 * 696/8225 +
427 xw^4 * 5248/90475 +xw^5 * 1280/29939+ xw^6 * 54528/1646645-
428 xt * 56/705 - xt^2 * 32/987;
429
430M$Parameters = {
431 (* New physics parameters *)
432 cH == { TeX -> Subscript[C,H], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 1 , InteractionOrder -> {NP,1} },
433 cT == { TeX -> Subscript[C,T], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 2 , InteractionOrder -> {NP,1} },
434 c6 == { TeX -> Subscript[C,6], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 3 , InteractionOrder -> {NP,1} },
435 cu == { TeX -> Subscript[C,u], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 4 , InteractionOrder -> {NP,1} },
436 cd == { TeX -> Subscript[C,d], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 5 , InteractionOrder -> {NP,1} },
437 cl == { TeX -> Subscript[C,l], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 6 , InteractionOrder -> {NP,1} },
438 cWW == { TeX -> Subscript[C,W], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 7 , InteractionOrder -> {NP,1} },
439 cB == { TeX -> Subscript[C,B], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 8 , InteractionOrder -> {NP,1} },
440 cHW == { TeX -> Subscript[C,HW], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 9 , InteractionOrder -> {NP,1} },
441 cHB == { TeX -> Subscript[C,HB], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 10, InteractionOrder -> {NP,1} },
442 cA == { TeX -> Subscript[C,\[Gamma]], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 11, InteractionOrder -> {NP,1} },
443 cG == { TeX -> Subscript[C,g] , ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 12, InteractionOrder -> {NP,1} },
444 cHQ == { TeX -> Subscript[C,Hq], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 13, InteractionOrder -> {NP,1} },
445 cpHQ== { TeX -> Subscript[C',Hq], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 14, InteractionOrder -> {NP,1} },
446 cHu == { TeX -> Subscript[C,Hu], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 15, InteractionOrder -> {NP,1} },
447 cHd == { TeX -> Subscript[C,Hd], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 16, InteractionOrder -> {NP,1} },
448 cHud== { TeX -> Subscript[C,Hud], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 17, InteractionOrder -> {NP,1} },
449 cHL == { TeX -> Subscript[C,Hl], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 18, InteractionOrder -> {NP,1} },
450 cpHL== { TeX -> Subscript[C',Hl], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 19, InteractionOrder -> {NP,1} },
451 cHe == { TeX -> Subscript[C,He], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 20, InteractionOrder -> {NP,1} },
452 cuB == { TeX -> Subscript[C,uB], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 21, InteractionOrder -> {NP,1} },
453 cuW == { TeX -> Subscript[C,uW], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 22, InteractionOrder -> {NP,1} },
454 cuG == { TeX -> Subscript[C,uG], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 23, InteractionOrder -> {NP,1} },
455 cdB == { TeX -> Subscript[C,dB], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 24, InteractionOrder -> {NP,1} },
456 cdW == { TeX -> Subscript[C,dW], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 25, InteractionOrder -> {NP,1} },
457 cdG == { TeX -> Subscript[C,dG], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 26, InteractionOrder -> {NP,1} },
458 clB == { TeX -> Subscript[C,lB], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 27, InteractionOrder -> {NP,1} },
459 clW == { TeX -> Subscript[C,lW], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 28, InteractionOrder -> {NP,1} },
460 c3W == { TeX -> Subscript[C,3W], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 29, InteractionOrder -> {NP,1} },
461 c3G == { TeX -> Subscript[C,3G], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 30, InteractionOrder -> {NP,1} },
462 c2W == { TeX -> Subscript[C,2W], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 31, InteractionOrder -> {NP,1} },
463 c2B == { TeX -> Subscript[C,2B], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 32, InteractionOrder -> {NP,1} },
464 c2G == { TeX -> Subscript[C,2G], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 33, InteractionOrder -> {NP,1} },
465 tcHW== { TeX -> Subscript[OverTilde[C],HW], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 34 , InteractionOrder -> {NP,1}},
466 tcHB== { TeX -> Subscript[OverTilde[C],HB], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 35 , InteractionOrder -> {NP,1}},
467 tcG == { TeX -> Subscript[OverTilde[C],G], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 36 , InteractionOrder -> {NP,1}},
468 tcA == { TeX -> Subscript[OverTilde[C],A], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 37 , InteractionOrder -> {NP,1}},
469 tc3W== { TeX -> Subscript[OverTilde[C],3W], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 38 , InteractionOrder -> {NP,1}},
470 tc3G== { TeX -> Subscript[OverTilde[C],3G], ParameterType -> External, Value -> 0.1, BlockName -> NEWCOUP, OrderBlock -> 39 , InteractionOrder -> {NP,1}},
471 dum == { TeX -> "", ParameterType -> Internal, Definition -> {dum->1}, InteractionOrder -> {QED,1}},
472
473 (* External parameters *)
474 aEWM1 == {
475 ParameterType -> External,
476 BlockName -> SMINPUTS,
477 OrderBlock -> 1,
478 Value -> 127.9,
479 InteractionOrder -> {QED,-2},
480 Description -> "Inverse of the EW coupling constant at the Z pole"
481 },
482 Gf == {
483 ParameterType -> External,
484 BlockName -> SMINPUTS,
485 OrderBlock -> 2,
486 Value -> 1.16637*^-5,
487 InteractionOrder -> {QED,2},
488 TeX -> Subscript[G,f],
489 Description -> "Fermi constant"
490 },
491 aS == {
492 ParameterType -> External,
493 BlockName -> SMINPUTS,
494 OrderBlock -> 3,
495 Value -> 0.1184,
496 InteractionOrder -> {QCD,2},
497 TeX -> Subscript[\[Alpha],s],
498 Description -> "Strong coupling constant at the Z pole"
499 },
500 ymdo == {
501 ParameterType -> External,
502 BlockName -> YUKAWA,
503 OrderBlock -> 1,
504 Value -> 5.04*^-3,
505 Description -> "Down Yukawa mass"
506 },
507 ymup == {
508 ParameterType -> External,
509 BlockName -> YUKAWA,
510 OrderBlock -> 2,
511 Value -> 2.55*^-3,
512 Description -> "Up Yukawa mass"
513 },
514 yms == {
515 ParameterType -> External,
516 BlockName -> YUKAWA,
517 OrderBlock -> 3,
518 Value -> 0.101,
519 Description -> "Strange Yukawa mass"
520 },
521 ymc == {
522 ParameterType -> External,
523 BlockName -> YUKAWA,
524 OrderBlock -> 4,
525 Value -> 1.27,
526 Description -> "Charm Yukawa mass"
527 },
528 ymb == {
529 ParameterType -> External,
530 BlockName -> YUKAWA,
531 OrderBlock -> 5,
532 Value -> 4.7,
533 Description -> "Bottom Yukawa mass"
534 },
535 ymt == {
536 ParameterType -> External,
537 BlockName -> YUKAWA,
538 OrderBlock -> 6,
539 Value -> 172,
540 Description -> "Top Yukawa mass"
541 },
542 yme == {
543 ParameterType -> External,
544 BlockName -> YUKAWA,
545 OrderBlock -> 11,
546 Value -> 5.11*^-4,
547 Description -> "Electron Yukawa mass"
548 },
549 ymm == {
550 ParameterType -> External,
551 BlockName -> YUKAWA,
552 OrderBlock -> 13,
553 Value -> 0.10566,
554 Description -> "Muon Yukawa mass"
555 },
556 ymtau == {
557 ParameterType -> External,
558 BlockName -> YUKAWA,
559 OrderBlock -> 15,
560 Value -> 1.777,
561 Description -> "Tau Yukawa mass"
562 },
563 cabi == {
564 ParameterType -> External,
565 BlockName -> CKMBLOCK,
566 OrderBlock -> 1,
567 Value -> 0.227736,
568 TeX -> Subscript[\[Theta], c],
569 Description -> "Cabibbo angle"
570 },
571
572 (* Internal Parameters *)
573 aEW == {
574 ParameterType -> Internal,
575 Value -> 1/aEWM1,
576 InteractionOrder -> {QED,2},
577 TeX -> Subscript[\[Alpha], EW],
578 Description -> "Electroweak coupling contant"
579 },
580 ee == {
581 ParameterType -> Internal,
582 Value -> Sqrt[4 Pi aEW],
583 InteractionOrder -> {QED,1},
584 TeX -> e,
585 Description -> "Electric coupling constant"
586 },
587 vev == {
588 ParameterType -> Internal,
589 Value -> Sqrt[1/(Sqrt[2] Gf)],
590 InteractionOrder -> {QED,-1},
591 Description -> "Higgs vacuum expectation value"
592 },
593 sw == {
594 ParameterType -> Internal,
595 Value -> ee*vev/(2*MW),
596 TeX -> Subscript[s,w],
597 Description -> "Sine of the Weinberg angle"
598 },
599 cw == {
600 ParameterType -> Internal,
601 Value -> Sqrt[1-sw^2],
602 TeX -> Subscript[c,w],
603 Description -> "Cosine of the Weinberg angle"
604 },
605 gw == {
606 ParameterType -> Internal,
607 Definitions -> {gw->ee/sw},
608 InteractionOrder -> {QED,1},
609 TeX -> Subscript[g,w],
610 Description -> "Weak coupling constant at the Z pole"
611 },
612 g1 == {
613 ParameterType -> Internal,
614 Definitions -> {g1->ee/cw},
615 InteractionOrder -> {QED,1},
616 TeX -> Subscript[g,1],
617 Description -> "U(1)Y coupling constant at the Z pole"
618 },
619 MZ == {
620 ParameterType -> Internal,
621 Value -> Sqrt[gw^2 vev^2/(4 cw^2) (1-cT+8 cA sw^4/cw^2)],
622 TeX -> Subscript[M,Z],
623 Description -> "Z mass"
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 Definitions -> {lam->MH^2/(2 vev^2)*(1-13/8*c6+cH)},
636 InteractionOrder -> {QED, 2},
637 Description -> "Higgs quartic coupling"
638 },
639 muH == {
640 ParameterType -> Internal,
641 Definitions -> {muH->(1+c6/4) Sqrt[lam vev^2]},
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 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], InteractionOrder -> {QED, 2}},
686 GH == { TeX->Subscript[G,H], ParameterType->Internal, Value -> -gs^2/(4Pi(3Pi vev)) (*sert[(MH/2/MT)^2]*), InteractionOrder -> {QCD, 2}}
687};
688
689(* ************************** *)
690(* ***** Lagrangian ***** *)
691(* ************************** *)
692
693
694LGauge := Block[{mu,nu,ii,aa},
695 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]];
696
697LFermions := Block[{mu},
698 ExpandIndices[I*(
699 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]),
700 FlavorExpand->{SU2W,SU2D}]/.{CKM[a_,b_] Conjugate[CKM[a_,c_]]->IndexDelta[b,c], CKM[b_,a_] Conjugate[CKM[c_,a_]]->IndexDelta[b,c]}];
701
702LHiggs := Block[{ii,mu, feynmangaugerules},
703 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
704
705 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
706 ];
707
708LYukawa := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
709 feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
710
711 yuk = ExpandIndices[
712 -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] -
713 yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] -
714 yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
715 yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
716 yuk+HC[yuk]/.feynmangaugerules
717 ];
718
719LGhost := Block[{LGh1,LGhw,LGhs,LGhphi,mu, generators,gh,ghbar,Vectorize,phi1,phi2,togoldstones,doublet,doublet0},
720 (* Pure gauge piece *)
721 LGh1 = -ghBbar.del[DC[ghB,mu],mu];
722 LGhw = -ghWibar.del[DC[ghWi,mu],mu];
723 LGhs = -ghGbar.del[DC[ghG,mu],mu];
724
725 (* Scalar pieces: see Peskin pages 739-742 *)
726 (* phi1 and phi2 are the real degrees of freedom of GP *)
727 (* Vectorize transforms a doublet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
728 gh = {ghB, ghWi[1], ghWi[2], ghWi[3]};
729 ghbar = {ghBbar, ghWibar[1], ghWibar[2], ghWibar[3]};
730 generators = {-I/2 g1 IdentityMatrix[2], -I/2 gw PauliSigma[1], -I/2 gw PauliSigma[2], -I/2 gw PauliSigma[3]};
731 doublet = Expand[{(-I phi1 - phi2)/Sqrt[2], Phi[2]} /. MR$Definitions /. vev -> 0];
732 doublet0 = {0, vev/Sqrt[2]};
733 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}];
734 togoldstones := {phi1 -> (GP + GPbar)/Sqrt[2], phi2 -> (-GP + GPbar)/(I Sqrt[2])};
735 LGhphi=Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].doublet0].Vectorize[generators[[lll]].(doublet+doublet0)],{kkk,4},{lll,4}]] /.togoldstones;
736
737ExpandIndices[ LGhs + If[FeynmanGauge, LGh1 + LGhw + LGhphi,0], FlavorExpand->SU2W]];
738
739LSM:= LGauge + LFermions + LHiggs + LYukawa + LGhost;
740
741Wvec[mu_,nu_,ii_,jj_]:= Module[{aa},Ta[aa,ii,jj] FS[Wi,mu,nu,aa]];
742
743LSILH := Block[{ii,jj,kk, ff1,ff2,ff3, cc, sp,mu,nu, LHSelf, LHFermions, LHGauge},
744 LHSelf = ExpandIndices[
745 cH/(2 vev^2) del[Phibar[ii] Phi[ii],mu] del[Phibar[jj] Phi[jj],mu] +
746 cT/(2 vev^2) ( Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]) (Phibar[jj] DC[Phi[jj],mu] - DC[Phibar[jj],mu] Phi[jj]) -
747 c6 lam / vev^2 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj] Phibar[kk] Phi[kk],
748 FlavorExpand->{SU2W,SU2D}];
749
750 LHFermions = ExpandIndices[
751 -cu/vev^2 yu[ff1,ff2] Phibar[ii] Phi[ii] QLbar[sp,jj,ff1,cc].uR[sp,ff2,cc] Phibar[kk] Eps[jj,kk] -
752 cd/vev^2 yd[ff2,ff3] CKM[ff1,ff2] Phibar[ii] Phi[ii] QLbar[sp,jj,ff1,cc].dR[sp,ff3,cc] Phi[jj] -
753 cl/vev^2 yl[ff1,ff2] Phibar[ii] Phi[ii] LLbar[sp,jj,ff1].lR[sp,ff2] Phi[jj],
754 FlavorExpand->{SU2W,SU2D}]/. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
755
756 LHGauge = ExpandIndices[
757 I cWW gw / MW^2 DC[Wvec[mu,nu,ii,jj],nu] (Phibar[ii] DC[Phi[jj],mu] - DC[Phibar[ii],mu] Phi[jj]) +
758 I cB g1 / (2 MW^2) del[FS[B,mu,nu],nu] (Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]) +
759 2 I cHW gw / MW^2 Wvec[mu,nu,ii,jj] DC[Phibar[ii],mu] DC[Phi[jj],nu] +
760 I cHB g1 / MW^2 FS[B,mu,nu] DC[Phibar[ii],mu] DC[Phi[ii],nu] +
761 cA g1^2 / MW^2 Phibar[ii] Phi[ii] FS[B,mu,nu] FS[B,mu,nu] +
762 cG dum^2 gs^2 / MW^2 Phibar[ii] Phi[ii] FS[G,mu,nu,jj] FS[G,mu,nu,jj],
763 FlavorExpand->{SU2W,SU2D}];
764
765 Return[LHSelf + LHFermions + HC[LHFermions] + LHGauge];
766];
767
768LF1 := Block[{LFQL, LFQR, LFLL, LFLR, ii,jj,kk,ll,sp1,sp2,ff,cc,mu},
769 LFQL = ExpandIndices[
770 I cHQ / vev^2 QLbar.Ga[mu].QL ( Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]) +
771 4 I cpHQ / vev^2 Ta[aa,ii,jj] Ta[aa,kk,ll] Ga[mu,sp1,sp2] QLbar[sp1,ii,ff,cc].QL[sp2,jj,ff,cc] ( Phibar[kk] DC[Phi[ll],mu] - DC[Phibar[kk],mu] Phi[ll]),
772 FlavorExpand->{SU2W,SU2D}];
773
774 LFQR = ExpandIndices[
775 I cHu / (2 vev^2) uRbar.Ga[mu].uR ( Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]) +
776 I cHd / (2 vev^2) dRbar.Ga[mu].dR ( Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]) +
777 I cHud / vev^2 Eps[ii,jj] uRbar.Ga[mu].dR ( Phi[jj] DC[Phi[ii],mu] - DC[Phi[jj],mu] Phi[ii]),
778 FlavorExpand->{SU2W,SU2D}];
779
780 LFLL = ExpandIndices[
781 I cHL / vev^2 LLbar.Ga[mu].LL ( Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]) +
782 4 I cpHL / vev^2 Ta[aa,ii,jj] Ta[aa,kk,ll] Ga[mu,sp1,sp2] LLbar[sp1,ii,ff].LL[sp2,jj,ff] ( Phibar[kk] DC[Phi[ll],mu] - DC[Phibar[kk],mu] Phi[ll]),
783 FlavorExpand->{SU2W,SU2D}];
784
785 LFLR = ExpandIndices[
786 I cHe / (2 vev^2) lRbar.Ga[mu].lR ( Phibar[ii] DC[Phi[ii],mu] - DC[Phibar[ii],mu] Phi[ii]),
787 FlavorExpand->{SU2W,SU2D}];
788
789 Return[LFQL + LFQR + HC[LFQR] + LFLL + LFLR];
790];
791
792LF2 := Block[{LFu, LFd, LFl, sp1,sp2,sp3, mu,nu, ff1,ff2, ii,jj,kk,ll, cc},
793 LFu = ExpandIndices[
794 I cuB g1/(2 MW^2) (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yu[ff1,ff2] QLbar[sp1,jj,ff1,cc].uR[sp2,ff2,cc] Phibar[kk] Eps[jj,kk] FS[B,mu,nu] +
795 I cuW gw/MW^2 Ta[ii,jj,ll] (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yu[ff1,ff2] QLbar[sp1,jj,ff1,cc].uR[sp2,ff2,cc] Phibar[kk] Eps[ll,kk] FS[Wi,mu,nu,ii] +
796 I cuG gs/MW^2 T[ii,cc1,cc] (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yu[ff1,ff2] QLbar[sp1,jj,ff1,cc1].uR[sp2,ff2,cc] Phibar[kk] Eps[jj,kk] FS[G,mu,nu,ii],
797 FlavorExpand->{SU2W,SU2D}];
798
799 LFd = ExpandIndices[
800 I cdB g1/(2 MW^2) (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yd[ff2,ff3] CKM[ff1,ff2] QLbar[sp1,jj,ff1,cc].dR[sp2,ff3,cc] Phi[jj] FS[B,mu,nu] +
801 I cdW gw/MW^2 Ta[ii,jj,ll] (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yd[ff2,ff3] CKM[ff1,ff2] QLbar[sp1,jj,ff1,cc].dR[sp2,ff3,cc] Phi[ll] FS[Wi,mu,nu,ii] +
802 I cdG gs/MW^2 T[ii,cc1,cc] (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yd[ff2,ff3] CKM[ff1,ff2] QLbar[sp1,jj,ff1,cc1].dR[sp2,ff3,cc] Phi[jj] FS[G,mu,nu,ii],
803 FlavorExpand->{SU2W,SU2D}];
804
805 LFl = ExpandIndices[
806 I clB g1/(2 MW^2) (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yl[ff1,ff2] LLbar[sp1,jj,ff1].lR[sp2,ff2] Phi[jj] FS[B,mu,nu] +
807 I clW gw/MW^2 Ta[ii,jj,ll] (Ga[mu,sp1,sp3] Ga[nu,sp3,sp2] - Ga[nu,sp1,sp3] Ga[mu,sp3,sp2] ) yl[ff1,ff2] LLbar[sp1,jj,ff1].lR[sp2,ff2] Phi[ll] FS[Wi,mu,nu,ii],
808 FlavorExpand->{SU2W,SU2D}];
809
810 Return[LFu + LFd + LFl + HC[LFu + LFd + LFl]];
811];
812
813LBosons := Block[{LWWW, LGGG, LWW, LBB, LGG, ii,jj,kk,mu,nu,ro},
814 LWWW = ExpandIndices[-I c3W/MW^2 gw^3 FSU2L[ii,jj,kk] FS[Wi,mu,nu,ii] FS[Wi,nu,ro,jj] FS[Wi,ro,mu,kk], FlavorExpand->{SU2D,SU2W}];
815 LGGG = -I c3G/MW^2 gs^3 FSU3C[ii,jj,kk] FS[G,mu,nu,ii] FS[G,nu,ro,jj] FS[G,ro,mu,kk];
816
817 LWW = ExpandIndices[ c2W/MW^2 DC[FS[Wi,mu,nu,ii],mu] DC[FS[Wi,ro,nu,ii],ro], FlavorExpand->{SU2D,SU2W}];
818 LBB = ExpandIndices[ c2B/MW^2 del[FS[B,mu,nu],mu] del[FS[B,ro,nu],ro], FlavorExpand->{SU2D,SU2W}];
819 LGG = c2G/MW^2 DC[FS[G,mu,nu,ii],mu] DC[FS[G,ro,nu,ii],ro];
820
821 Return[LWWW + LGGG + LWW + LGG + LBB];
822];
823
824LCP := Block[{LHV, LVVV, ii,jj,kk,aa,mu,nu,ro,rop,mup, outlag},
825 LHV = ExpandIndices[
826 I Eps[mu,nu,ro,sig] tcHW gw/MW^2 Ta[aa,ii,jj] DC[Phibar[ii],mu] DC[Phi[jj],nu] FS[Wi,ro,sig,aa] +
827 I/2 Eps[mu,nu,ro,sig] tcHB g1/MW^2 DC[Phibar[ii],mu] DC[Phi[ii],nu] FS[B,ro,sig] +
828 1/2 Eps[mu,nu,ro,sig] tcA g1^2/MW^2 Phibar[ii] Phi[ii] FS[B,mu,nu] FS[B,ro,sig] +
829 1/2 Eps[mu,nu,ro,sig] dum^2 tcG gs^2/MW^2 Phibar[ii] Phi[ii] FS[G,mu,nu,aa] FS[G,ro,sig,aa],
830 FlavorExpand->{SU2W,SU2D}];
831
832 LVVV= ExpandIndices[
833 -I/2 Eps[ro,mu,rop,mup] tc3W gw^3/MW^2 FSU2L[ii,jj,kk] FS[Wi,mu,nu,ii] FS[Wi,nu,ro,jj] FS[Wi,rop,mup,kk] +
834 -I/2 Eps[ro,mu,rop,mup] tc3G gs^3/MW^2 FSU3C[ii,jj,kk] FS[G,mu,nu,ii] FS[G,nu,ro,jj] FS[G,rop,mup,kk],
835 FlavorExpand->{SU2W,SU2D}];
836
837 outlag = OptimizeIndex[LHV+LVVV]/.Eps[args__] :> Signature[{args}] Eps[Sequence @@ Sort[{args}]];
838 outlag=outlag /. del[a_, m1_] del[a_, m2_] Eps[n1___, m1_, n2___, m2_, n3___] :> 0;
839
840 Return[ outlag ];
841];
842
843LLOPP := -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;
844
845RemoveL2[exp_]:= Block[{tmp=Expand[exp]},
846 tmp=If[Length[tmp]===1,{tmp}, List@@tmp];
847 tmp = Select[tmp, (PRIVATE`GetIntOrder[#]/.{QCD->1, QED->1, PRIVATE`GetIntOrder[__] -> 1}) =!= NP^2 &];
848 tmp = Select[tmp, (PRIVATE`GetIntOrder[#]/.{QCD->1, QED->1, PRIVATE`GetIntOrder[__] -> 1}) =!= NP^3 &];
849 tmp = Select[tmp, (PRIVATE`GetIntOrder[#]/.{QCD->1, QED->1, PRIVATE`GetIntOrder[__] -> 1}) =!= NP^4 &];
850 tmp = Select[tmp, (PRIVATE`GetIntOrder[#]/.{QCD->1, QED->1, PRIVATE`GetIntOrder[__] -> 1}) =!= NP^5 &];
851 tmp = Select[tmp, (PRIVATE`GetIntOrder[#]/.{QCD->1, QED->1, PRIVATE`GetIntOrder[__] -> 1}) =!= NP^6 &];
852 Return[Plus@@tmp];
853];
854
855LagHEL := Block[{lagtmp},
856 lagtmp = {LF1+LF2+LSILH+LBosons+LCP+LSM};
857 lagtmp = RemoveL2[#/.H->H (1- cH/2)] &/@ lagtmp;
858 lagtmp = RemoveL2[#/.G[inds__] :> G[inds] (1 + cG dum^2 gs^2 vev^2/MW^2)] &/@ lagtmp;
859 lagtmp = RemoveL2[#/.Z[mu_] :> Z[mu] (1 + cA ee^2 (1 - cw^2) vev^2/(cw^2 MW^2))] &/@ lagtmp;
860 lagtmp = RemoveL2[#/.A[mu_] :> A[mu] (1 + cA ee^2 vev^2/MW^2) - 2 Z[mu] cA sw ee^2 vev^2/(cw MW^2)] &/@ lagtmp;
861 lagtmp = lagtmp/.Conjugate[CKM[a_, b_]]*CKM[a_, c_]->IndexDelta[b, c];
862 lagtmp = OptimizeIndex/@lagtmp;
863 Return[(Plus@@lagtmp)+LLOPP];
864];
865
866