HiggsCharacterisation: HiggsCharacterisation.fr

File HiggsCharacterisation.fr, 22.0 KB (added by mawatari, 12 years ago)

Main HC FR model file v3.4

Line 
1(*****************************************************************************************************)
2(* This is the FeynRules model file for the Higgs characterisation project *)
3(* *)
4(* It contains parts of existing FR model files: *)
5(* 1) HEFT, author: C. Duhr (https://feynrules.irmp.ucl.ac.be/wiki/HiggsEffectiveTheory) *)
6(* 2) Minimal Zprime, author: L. Basso (https://feynrules.irmp.ucl.ac.be/wiki/B-L-SM) *)
7(* 3) RS, author: P. de Aquino (https://feynrules.irmp.ucl.ac.be/wiki/RSmodel) *)
8(* *)
9(* Please contact K. Mawatari (kentarou.mawatari@vub.ac.be) for bugs and/or further information. *)
10(* *)
11(*****************************************************************************************************)
12
13
14(* ************************** *)
15(* ***** Information ***** *)
16(* ************************** *)
17
18M$ModelName = "HiggsCharac";
19
20M$Information = {
21 Authors -> {"P. de Aquino, K. Mawatari"},
22 Version -> "3.4",
23 Date -> "17. 10. 2013",
24 Institutions -> {"Vrije Universiteit Brussel"},
25 Emails -> {"kentarou.mawatari@vub.ac.be"},
26 URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/HiggsCharacterisation/",
27 References -> {"P. Artoisenet et al., arXiv:1306.6464"}
28};
29
30(* ************************** *)
31(* ***** Change log ***** *)
32(* ************************** *)
33
34(* 16.01.2013 v1.0 - released version. *)
35(* 04.04.2013 v1.1 - added the CP-odd Yukawa terms in the X0 Lagrangian. *)
36(* modified the X2 HD lagrangian to be proportional to 1/Lambda3. *)
37(* 15.04.2013 v2.0 - fixed a bug for the X2 lowest dimensional interactions with massive gauge bosons. *)
38(* parametrisation for X0 modified. *)
39(* 28.05.2013 v2.1 - fixed a bug for the X0 coupling to the massive vector bosons (SM couplings recovered). *)
40(* 27.06.2013 v3.0 - major update and version for the paper [arXiv:1306.6464]. *)
41(* 04.07.2013 v3.1 - fixed a bug in the gluon/photon gauge fixing term for X2. *)
42(* 20.07.2013 v3.2 - put the X width = 0.00407 GeV by HXSWG. *)
43(* introduced kqa, kqb, kla, and klb, instead of kfa and kfb. *)
44(* 24.07.2013 v3.3 - added the SM X0 self-interactions and the effective g-g-X0-X0 intereaction. *)
45(* 17.10.2013 v3.4 - redefined 'kHdw' as a complex. *)
46
47
48FeynmanGauge = False;
49
50(***** Setting for interaction order (as e.g. used by MadGraph 5) ******)
51
52M$InteractionOrderLimit = {
53 {QNP, 2}
54};
55
56M$InteractionOrderHierarchy = {
57 {QNP, 2}
58};
59
60
61(***** Particle classes list ******)
62
63M$ClassesDescription = {
64
65 S[1] == { ClassName -> X0,
66 SelfConjugate -> True,
67 Mass -> {MX0, 125.0},
68 Width -> {WX0, 0.00407},
69 ParticleName -> "X0",
70 PDG -> 5000000,
71 PropagatorLabel -> "X0",
72 PropagatorType -> D,
73 PropagatorArrow -> None,
74 FullName -> "X0"},
75
76 V[5] == { ClassName -> X1,
77 SelfConjugate -> True,
78 Mass -> {MX1, 125.0},
79 Width -> {WX1, 0.00407},
80 ParticleName -> "X1",
81 PDG -> 5000001,
82 PropagatorLabel -> "X1",
83 PropagatorType -> Sine,
84 PropagatorArrow -> None,
85 FullName -> "X1"},
86
87 T[1] == { ClassName -> X2,
88 SelfConjugate -> True,
89 Symmetric -> True,
90 Mass -> {MX2, 125.0},
91 Width -> {WX2,0.00407},
92 ParticleName -> "X2",
93 PDG -> 5000002,
94 PropagatorLabel -> "X2",
95 PropagatorArrow -> None,
96 FullName -> "X2"}
97
98};
99
100
101(* The loop coefficient from the HEFT model *)
102
103sert[x_] := 1+ 7/30 x + 2/21 x^2 + 26/525 x^3;
104serw[xw_, xt_] := 1 + xw * 66/235 +xw^2 * 228/1645 + xw^3 * 696/8225 +
105 xw^4 * 5248/90475 +xw^5 * 1280/29939+ xw^6 * 54528/1646645-
106 xt * 56/705 - xt^2 * 32/987;
107serp[x_] := 1 + x/3 + x^2 * 8/45 + x^3 * 4/35;
108
109
110(***** Parameter list ******)
111
112M$Parameters = {
113
114 Lambda == { ParameterType -> External,
115 Value -> 1000,
116 TeX -> \[CapitalLambda],
117 Description -> "cut-off scale"},
118
119 ca == { ParameterType -> External,
120 Value -> 1,
121 TeX -> Subscript[c,a],
122 Description -> "cosine of the scalar mixing between 0+ and 0-"},
123
124 sa == { ParameterType -> Internal,
125 Value -> Sqrt[1-ca^2],
126 TeX -> Subscript[s,a],
127 Description -> "sine of the scalar mixing between 0+ and 0-"},
128
129 kSM == { ParameterType -> External,
130 Value -> 1,
131 TeX -> Subscript[\[Kappa],SM],
132 Description -> "Hzz/Hww SM coupling parameter"},
133
134 kHtt == { ParameterType -> External,
135 Value -> 1,
136 TeX -> Subscript[\[Kappa],Htt],
137 Description -> "Htt coupling parameter"},
138
139 kAtt == { ParameterType -> External,
140 Value -> 1,
141 TeX -> Subscript[\[Kappa],Att],
142 Description -> "Att coupling parameter"},
143
144 kHbb == { ParameterType -> External,
145 Value -> 1,
146 TeX -> Subscript[\[Kappa],Hbb],
147 Description -> "Hbb coupling parameter"},
148
149 kAbb == { ParameterType -> External,
150 Value -> 1,
151 TeX -> Subscript[\[Kappa],Abb],
152 Description -> "Abb coupling parameter"},
153
154 kHll == { ParameterType -> External,
155 Value -> 1,
156 TeX -> Subscript[\[Kappa],Hll],
157 Description -> "Hll coupling parameter"},
158
159 kAll == { ParameterType -> External,
160 Value -> 1,
161 TeX -> Subscript[\[Kappa],All],
162 Description -> "All coupling parameter"},
163
164 kHaa == { ParameterType -> External,
165 Value -> 1,
166 InteractionOrder -> {QNP, 1},
167 TeX -> Subscript[\[Kappa],Haa],
168 Description -> "Haa coupling parameter"},
169
170 kAaa == { ParameterType -> External,
171 Value -> 1,
172 InteractionOrder -> {QNP, 1},
173 TeX -> Subscript[\[Kappa],Aaa],
174 Description -> "Aaa coupling parameter"},
175
176 kHza == { ParameterType -> External,
177 Value -> 1,
178 InteractionOrder -> {QNP, 1},
179 TeX -> Subscript[\[Kappa],Hza],
180 Description -> "Hza coupling parameter"},
181
182 kAza == { ParameterType -> External,
183 Value -> 1,
184 InteractionOrder -> {QNP, 1},
185 TeX -> Subscript[\[Kappa],Aza],
186 Description -> "Aza coupling parameter"},
187
188 kHgg == { ParameterType -> External,
189 Value -> 1,
190 InteractionOrder -> {QNP, 1},
191 TeX -> Subscript[\[Kappa],Hgg],
192 Description -> "Hgg coupling parameter"},
193
194 kAgg == { ParameterType -> External,
195 Value -> 1,
196 InteractionOrder -> {QNP, 1},
197 TeX -> Subscript[\[Kappa],Agg],
198 Description -> "Agg coupling parameter"},
199
200 kHzz == { ParameterType -> External,
201 Value -> 0,
202 InteractionOrder -> {QNP, 1},
203 TeX -> Subscript[\[Kappa],Hzz],
204 Description -> "Hzz coupling parameter"},
205
206 kAzz == { ParameterType -> External,
207 Value -> 0,
208 InteractionOrder -> {QNP, 1},
209 TeX -> Subscript[\[Kappa],Azz],
210 Description -> "Azz coupling parameter"},
211
212 kHww == { ParameterType -> External,
213 Value -> 0,
214 InteractionOrder -> {QNP, 1},
215 TeX -> Subscript[\[Kappa],Hww],
216 Description -> "Hww coupling parameter"},
217
218 kAww == { ParameterType -> External,
219 Value -> 0,
220 InteractionOrder -> {QNP, 1},
221 TeX -> Subscript[\[Kappa],Aww],
222 Description -> "Aww coupling parameter"},
223
224 kHda == { ParameterType -> External,
225 Value -> 0,
226 InteractionOrder -> {QNP, 1},
227 TeX -> Subscript[\[Kappa],Hda],
228 Description -> "Hda coupling parameter"},
229
230 kHdz == { ParameterType -> External,
231 Value -> 0,
232 InteractionOrder -> {QNP, 1},
233 TeX -> Subscript[\[Kappa],Hdz],
234 Description -> "Hdz coupling parameter"},
235
236 kHdwR == { ParameterType -> External,
237 ComplexParameter -> False,
238 Value -> 0,
239 TeX -> Subscript[\[Kappa],HdwR],
240 Description -> "Hdw coupling parameter (real part)"},
241
242 kHdwI == { ParameterType -> External,
243 ComplexParameter -> False,
244 Value -> 0,
245 TeX -> Subscript[\[Kappa],HdwI],
246 Description -> "Hdw coupling parameter (imaginary part)"},
247
248 kHdw == { ParameterType -> Internal,
249 ComplexParameter -> True,
250 Value -> {kHdwR+I*kHdwI},
251 InteractionOrder -> {QNP, 1},
252 TeX -> Subscript[\[Kappa],Hdw],
253 Description -> "Hdw coupling parameter"},
254
255 kHHgg == { ParameterType -> External,
256 Value -> 1,
257 InteractionOrder -> {QNP, 1},
258 TeX -> Subscript[\[Kappa],HHgg],
259 Description -> "HHgg coupling parameter"},
260
261 kAAgg == { ParameterType -> External,
262 Value -> 1,
263 InteractionOrder -> {QNP, 1},
264 TeX -> Subscript[\[Kappa],AAgg],
265 Description -> "AAgg coupling parameter"},
266
267 kqa == { ParameterType -> External,
268 Value -> 1,
269 InteractionOrder -> {QNP, 1},
270 TeX -> Subscript[\[Kappa],qqa],
271 Description -> "X1-qq vector coupling parameter"},
272
273 kqb == { ParameterType -> External,
274 Value -> 1,
275 InteractionOrder -> {QNP, 1},
276 TeX -> Subscript[\[Kappa],qqb],
277 Description -> "X1-qq axial-vector coupling parameter"},
278
279 kla == { ParameterType -> External,
280 Value -> 1,
281 InteractionOrder -> {QNP, 1},
282 TeX -> Subscript[\[Kappa],lla],
283 Description -> "X1-ll vector coupling parameter"},
284
285 klb == { ParameterType -> External,
286 Value -> 1,
287 InteractionOrder -> {QNP, 1},
288 TeX -> Subscript[\[Kappa],llb],
289 Description -> "X1-ll axial-vector coupling parameter"},
290
291 kw1 == { ParameterType -> External,
292 Value -> 1,
293 InteractionOrder -> {QNP, 1},
294 TeX -> Subscript[\[Kappa],w1],
295 Description -> "X1-WW coupling parameter 1"},
296
297 kw2 == { ParameterType -> External,
298 Value -> 1,
299 InteractionOrder -> {QNP, 1},
300 TeX -> Subscript[\[Kappa],w2],
301 Description -> "X1-WW coupling parameter 2"},
302
303 kw3 == { ParameterType -> External,
304 Value -> 0,
305 InteractionOrder -> {QNP, 1},
306 TeX -> Subscript[\[Kappa],w3],
307 Description -> "X1-WW coupling parameter 3"},
308
309 kw4 == { ParameterType -> External,
310 Value -> 0,
311 InteractionOrder -> {QNP, 1},
312 TeX -> Subscript[\[Kappa],w4],
313 Description -> "X1-WW coupling parameter 4"},
314
315 kw5 == { ParameterType -> External,
316 Value -> 0,
317 InteractionOrder -> {QNP, 1},
318 TeX -> Subscript[\[Kappa],w5],
319 Description -> "X1-WW coupling parameter 5"},
320
321 kz1 == { ParameterType -> External,
322 Value -> 0,
323 InteractionOrder -> {QNP, 1},
324 TeX -> Subscript[\[Kappa],z1],
325 Description -> "X1-ZZ coupling parameter 1"},
326
327 kz3 == { ParameterType -> External,
328 Value -> 1,
329 InteractionOrder -> {QNP, 1},
330 TeX -> Subscript[\[Kappa],z3],
331 Description -> "X1-ZZ coupling parameter 3"},
332
333 kz5 == { ParameterType -> External,
334 Value -> 0,
335 InteractionOrder -> {QNP, 1},
336 TeX -> Subscript[\[Kappa],z5],
337 Description -> "X1-ZZ coupling parameter 5"},
338
339 kq == { ParameterType -> External,
340 Value -> 1,
341 InteractionOrder -> {QNP, 1},
342 TeX -> Subscript[\[Kappa],q],
343 Description -> "X2-quark coupling parameter"},
344
345 kl == { ParameterType -> External,
346 Value -> 1,
347 InteractionOrder -> {QNP, 1},
348 TeX -> Subscript[\[Kappa],l],
349 Description -> "X2-lepton coupling parameter"},
350
351 kg == { ParameterType -> External,
352 Value -> 1,
353 InteractionOrder -> {QNP, 1},
354 TeX -> Subscript[\[Kappa],g],
355 Description -> "X2-gluon coupling parameter"},
356
357 ka == { ParameterType -> External,
358 Value -> 1,
359 InteractionOrder -> {QNP, 1},
360 TeX -> Subscript[\[Kappa],a],
361 Description -> "X2-photon coupling parameter"},
362
363 kz == { ParameterType -> External,
364 Value -> 1,
365 InteractionOrder -> {QNP, 1},
366 TeX -> Subscript[\[Kappa],z],
367 Description -> "X2-Z coupling parameter"},
368
369 kw == { ParameterType -> External,
370 Value -> 1,
371 InteractionOrder -> {QNP, 1},
372 TeX -> Subscript[\[Kappa],w],
373 Description -> "X2-W coupling parameter"},
374
375
376 gHaa == { ParameterType -> Internal,
377 Value -> -ee^2/(4*Pi)/(Pi*vev)*(-47/18), (* *serw[(MX0/2/MW)^2, (MX0/2/MT)^2], *)
378 TeX -> Subscript[g,Haa],
379 Description -> "Haa coupling"},
380
381 gAaa == { ParameterType -> Internal,
382 Value -> -ee^2/(4*Pi)/(Pi*vev)*(4/3),
383 TeX -> Subscript[g,Aaa],
384 Description -> "Aaa coupling"},
385
386 gHza == { ParameterType -> Internal,
387 Value -> Sqrt[ee^2/(4*Pi)*Gf*MZ^2/(8*Sqrt[2]*Pi)]*(94*cw^2-13)/(9*Pi*vev),
388 TeX -> Subscript[g,Hza],
389 Description -> "Hza coupling"},
390
391 gAza == { ParameterType -> Internal,
392 Value -> -2*Sqrt[ee^2/(4*Pi)*Gf*MZ^2/(8*Sqrt[2]*Pi)]*(8*cw^2-5)/(3*Pi*vev),
393 TeX -> Subscript[g,Aza],
394 Description -> "Aza coupling"},
395
396 gHgg == { ParameterType -> Internal,
397 Value -> -gs^2/(4*Pi)/(3*Pi*vev), (* *sert[(MX0/2/MT)^2], *)
398 TeX -> Subscript[g,Hgg],
399 Description -> "Hgg coupling"},
400
401 gAgg == { ParameterType -> Internal,
402 Value -> -gs^2/(4*Pi)/(2*Pi*vev), (* *serp[(MX0/2/MT)^2], *)
403 TeX -> Subscript[g,Agg],
404 Description -> "Agg coupling"},
405
406 gHHgg == { ParameterType -> Internal,
407 Value -> gs^2/(4*Pi)/(3*Pi*vev^2),
408 TeX -> Subscript[g,HHgg],
409 Description -> "HHgg coupling"},
410
411 gAAgg == { ParameterType -> Internal,
412 Value -> gs^2/(4*Pi)/(2*Pi*vev^2),
413 TeX -> Subscript[g,AAgg],
414 Description -> "AAgg coupling"},
415
416 au == { ParameterType -> Internal,
417 Value -> ee/(2 sw cw)(1/2-4/3 sw2),
418 Tex -> Subscript[a,u],
419 Description -> "vector coupling for up-type quarks"},
420
421 bu == { ParameterType -> Internal,
422 Value -> ee/(2 sw cw)(1/2),
423 TeX -> Subscript[b,u],
424 Description -> "axial-vector coupling for up-type quarks"},
425
426 ad == { ParameterType -> Internal,
427 Value -> ee/(2 sw cw)(-1/2+2/3 sw2),
428 TeX -> Subscript[a,d],
429 Description -> "vector coupling for down-type quarks"},
430
431 bd == { ParameterType -> Internal,
432 Value -> ee/(2 sw cw)(-1/2),
433 TeX -> Subscript[b,d],
434 Description -> "axial-vector coupling for down-type quarks"},
435
436 an == { ParameterType -> Internal,
437 Value -> ee/(2 sw cw)(1/2),
438 Tex -> Subscript[a,n],
439 Description -> "vector coupling for neutrinos"},
440
441 bn == { ParameterType -> Internal,
442 Value -> ee/(2 sw cw)(1/2),
443 TeX -> Subscript[b,n],
444 Description -> "axial-vector coupling for neutrinos"},
445
446 al == { ParameterType -> Internal,
447 Value -> ee/(2 sw cw)(-1/2+2 sw2),
448 TeX -> Subscript[a,l],
449 Description -> "vector coupling for charged leptons"},
450
451 bl == { ParameterType -> Internal,
452 Value -> ee/(2 sw cw)(-1/2),
453 TeX -> Subscript[b,l],
454 Description -> "axial-vector coupling for charged leptons"},
455
456 gwwz == { ParameterType -> Internal,
457 Value -> -ee cw/sw,
458 TeX -> Subscript[g,wwz],
459 Description -> "WWZ coupling"}
460
461};
462
463
464(*****************************************************************************************)
465(**************************************** Lagrangian *************************************)
466(*****************************************************************************************)
467
468(****************************************** Spin-0 ***************************************)
469
470L0v := (-1/4 ( ca kHaa gHaa FS[A,mu,nu] FS[A,mu,nu] + sa kAaa gAaa FS[A,mu,nu] Dual[FS][A,mu,nu] ) -
471 1/2 ( ca kHza gHza FS[Z,mu,nu] FS[A,mu,nu] + sa kAza gAza FS[Z,mu,nu] Dual[FS][A,mu,nu] ) -
472 1/4 ( ca kHgg gHgg FS[G,mu,nu,a] FS[G,mu,nu,a] + sa kAgg gAgg FS[G,mu,nu,a] Dual[FS][G,mu,nu,a] ) -
473 1/4/Lambda ( ca kHzz FS[Z,mu,nu] FS[Z,mu,nu] + sa kAzz FS[Z,mu,nu] Dual[FS][Z,mu,nu] ) -
474 1/2/Lambda ( ca kHww FS[Wbar,mu,nu] FS[W,mu,nu] + sa kAww FS[Wbar,mu,nu] Dual[FS][W,mu,nu] ) -
475 1 /Lambda ( ca kHda Z[nu] del[FS[A,mu,nu],mu] +
476 ca kHdz Z[nu] del[FS[Z,mu,nu],mu] +
477 ca ( kHdw Wbar[nu] del[FS[W,mu,nu],mu] + HC[kHdw Wbar[nu] del[FS[W,mu,nu],mu]] ) ) ) X0;
478
479L0v6 := -1/8 ( ca kHHgg gHHgg FS[G,mu,nu,a] FS[G,mu,nu,a] +
480 +sa kAAgg gAAgg FS[G,mu,nu,a] Dual[FS][G,mu,nu,a] ) X0 X0;
481
482
483(****************************************** Spin-1 ***************************************)
484
485L1f := ( kqa au uqbar[s,n,i].Ga[mu,s,t].uq[t,n,i] +
486 kqa ad dqbar[s,n,i].Ga[mu,s,t].dq[t,n,i] +
487 kla an vlbar[s,n] .Ga[mu,s,t].vl[t,n] +
488 kla al lbar[s,n] .Ga[mu,s,t]. l[t,n] -
489 kqb bu uqbar[s,n,i].Ga[mu,s,t].Ga[5,t,u].uq[u,n,i] -
490 kqb bd dqbar[s,n,i].Ga[mu,s,t].Ga[5,t,u].dq[u,n,i] -
491 klb bn vlbar[s,n] .Ga[mu,s,t].Ga[5,t,u].vl[u,n] -
492 klb bl lbar[s,n] .Ga[mu,s,t].Ga[5,t,u]. l[u,n] ) X1[mu];
493
494L1w := I kw1 gwwz ( FS[Wbar,mu,nu] W[mu] - FS[W,mu,nu] Wbar[mu] ) X1[nu] +
495 I kw2 gwwz Wbar[mu] W[nu] FS[X1,mu,nu] -
496 kw3 Wbar[mu] W[nu] ( del[X1[nu],mu] + del[X1[mu],nu] ) +
497 I kw4 Wbar[mu] W[nu] Dual[FS][X1,mu,nu] -
498 kw5 Eps[mu,nu,rho,sig] ( Wbar[mu] del[W[nu],rho] - del[Wbar[mu],rho] W[nu] ) X1[sig];
499
500L1z := - kz1 FS[Z,mu,nu] Z[mu] X1[nu] -
501 kz3 X1[mu] del[Z[mu],nu] Z[nu] -
502 kz5 Eps[mu,nu,rho,sig] X1[mu] Z[nu] del[Z[sig],rho];
503
504L1 := L1f + L1w + L1z;
505
506
507(****************************************** Spin-2 ***************************************)
508
509(*** Defining the cov derivatives ***)
510
511covdelU[field_, mu_] :=
512 Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
513 - I ee/cw 4/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
514
515covdelD[field_, mu_] :=
516 Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
517 + I ee/cw 2/3 B[mu]/2 ProjP.field - I ee/cw/3 B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
518
519covdelE[field_, mu_] :=
520 Module[{j, a}, del[field, mu]
521 + I ee/cw 2 B[mu]/2 ProjP.field + I ee/cw B[mu]/2 ProjM.field + I ee/sw/2 ProjM.field Wi[mu,3]];
522
523covdelN[field_, mu_] :=
524 Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
525
526
527(*** Defining the energy-momentum tensor T[mu,nu] ***)
528
529(* Fermions *)
530
531TFq[mu_,nu_] := (-ME[mu,nu] (I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho]
532 + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho]
533
534 + ee/sw/Sqrt[2] (uqbar.Ga[rho].ProjM.CKM.dq W[rho] + dqbar.Ga[rho].ProjM.HC[CKM].uq Wbar[rho]) )
535 + ( I/2 uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu]
536 + I/2 uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu]
537 + I/2 dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu]
538 + I/2 dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu] )
539
540 + ee/sw/2/Sqrt[2] (uqbar.Ga[mu].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[nu]
541 + uqbar.Ga[nu].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].ProjM.HC[CKM].uq Wbar[mu] ));
542
543TFl[mu_,nu_] := (-ME[mu,nu] (I vlbar.(Ga[rho].covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].vl, rho]
544 + I lbar.(Ga[rho].covdelE[l, rho] ) -1/2 del[I lbar.Ga[rho].l, rho]
545
546 + ee/sw/Sqrt[2] ( vlbar.Ga[rho].ProjM.l W[rho] + lbar.Ga[rho].ProjM.vl Wbar[rho]) )
547 + ( I/2 vlbar.Ga[mu].covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].vl, mu]
548 + I/2 vlbar.Ga[nu].covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].vl, nu]
549 + I/2 lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu]
550 + I/2 lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu] )
551
552 + ee/sw/2/Sqrt[2] (vlbar.Ga[mu].ProjM.l W[nu] + lbar.Ga[mu].ProjM.vl Wbar[nu]
553 + vlbar.Ga[nu].ProjM.l W[mu] + lbar.Ga[nu].ProjM.vl Wbar[mu]));
554
555(* Yukawa *)
556
557TYq[mu_,nu_] := -ME[mu,nu] ( - MT tbar.t - MB bbar.b );
558TYl[mu_,nu_] := -ME[mu,nu] ( - MTA tabar.ta );
559
560(* Gauge bosons *)
561
562TGg[mu_,nu_] := -ME[mu,nu] (-1/4 FS[G,rho,sig,a] FS[G,rho,sig,a]) - FS[G,mu,rho,a] FS[G,nu,rho,a];
563TGa[mu_,nu_] := -ME[mu,nu] (-1/4 FS[A,rho,sig] FS[A,rho,sig]) - FS[A,mu,rho] FS[A,nu,rho];
564TGz[mu_,nu_] := -ME[mu,nu] (-1/4 FS[Z,rho,sig] FS[Z,rho,sig] + 1/2 MZ^2 Z[rho] Z[rho]) -
565 (FS[Z,mu,rho] FS[Z,nu,rho] - MZ^2 Z[mu] Z[nu]);
566TGw[mu_,nu_] := -ME[mu,nu] (-1/2 FS[Wbar,rho,sig] FS[W,rho,sig] + MW^2 Wbar[rho] W[rho]) -
567 (FS[Wbar,mu,rho] FS[W,nu,rho] - MW^2 Wbar[mu] W[nu] + FS[Wbar,nu,rho] FS[W,mu,rho] - MW^2 Wbar[nu] W[mu]);
568
569(* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators *)
570(* and unitary gauge for massive gauge boson propagators. *)
571
572TGFg[mu_,nu_]:= -ME[mu,nu].( del[del[G[sig, a1], sig], rho].G[rho, a1] +
573 1/2 del[G[rho, a1], rho].del[G[sig, a1], sig] ) +
574 del[del[G[rho, a1], rho], mu].G[nu, a1] + del[del[G[rho, a1], rho], nu].G[mu, a1];
575
576TGFa[mu_,nu_]:= -ME[mu,nu].( del[del[A[sig], sig], rho].A[rho] +
577 1/2 del[A[rho], rho].del[A[sig], sig] ) +
578 del[del[A[rho], rho], mu].A[nu] + del[del[A[rho], rho], nu].A[mu];
579
580(*** Writing the lagrangian ***)
581
582L2f := -1/Lambda ( kq (TFq[mu,nu]+TYq[mu,nu]) + kl (TFl[mu,nu]+TYl[mu,nu]) ) X2[mu,nu];
583L2v := -1/Lambda ( kg (TGg[mu,nu]+TGFg[mu,nu]) +
584 ka (TGa[mu,nu]+TGFa[mu,nu]) +
585 kz TGz[mu,nu] +
586 kw TGw[mu,nu] ) X2[mu,nu];
587
588L2 := L2f + L2v;
589
590(*****************************************************************************************)
591
592LagHC:= LSM + L0v + L1 + L2 + L0v6;