HiggsCharacterisation: HC.fr

File HC.fr, 29.3 KB (added by mawatari, 10 years ago)

Main HC FR model file v4.1

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@lpsc.in2p3.fr) for bugs and/or further information. *)
10(* *)
11(*****************************************************************************************************)
12
13
14(* ************************** *)
15(* ***** Information ***** *)
16(* ************************** *)
17
18M$ModelName = "HC";
19
20M$Information = {
21 Authors -> {"K. Mawatari"},
22 Version -> "4.1",
23 Date -> "18.04.2016",
24 Institutions -> {"LPSC Grenoble"},
25 Emails -> {"kentarou.mawatari@lpsc.in2p3.fr"},
26 URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/HiggsCharacterisation/",
27 References -> {"P. Artoisenet et al., arXiv:1306.6464"}
28};
29
30
31(* ************************** *)
32(* ***** Change log ***** *)
33(* ************************** *)
34
35(* 16.01.2013 v1.0 - release version. *)
36(* 04.04.2013 v1.1 - added the CP-odd Yukawa terms in the X0 Lagrangian. *)
37(* modified the X2 HD lagrangian to be proportional to 1/Lambda3. *)
38(* 15.04.2013 v2.0 - fixed a bug for the X2 lowest dimensional interactions with massive gauge bosons. *)
39(* parametrisation for X0 modified. *)
40(* 28.05.2013 v2.1 - fixed a bug for the X0 coupling to the massive vector bosons (SM couplings recovered). *)
41(* 27.06.2013 v3.0 - major update and version for the paper [arXiv:1306.6464]. *)
42(* 04.07.2013 v3.1 - fixed a bug in the gluon/photon gauge fixing term for X2. *)
43(* 20.07.2013 v3.2 - put the X width = 0.00407 GeV by HXSWG. *)
44(* introduced kqa, kqb, kla, and klb, instead of kfa and kfb. *)
45(* 24.07.2013 v3.3 - added the SM X0 self-interactions and the effective g-g-X0-X0 intereaction. *)
46(* 17.10.2013 v3.4 - redefined 'kHdw' as a complex. *)
47(* 11.12.2013 v4.0 - based on FR2.0. *)
48(* fixed a sign of the AVV couplings. *)
49(* introduced kq3 for the X2 couplings to bottom and top. *)
50(* 18.04.2016 v4.1 - redefined LYukawaOdd in SM_HC.fr in terms of the Yukawa couplings. *)
51(* corrected the neutrino energy-momentum tensor for X2. *)
52(* added the X2-Z-A interaction. *)
53
54
55FeynmanGauge = False;
56
57(***** Setting for interaction order (as e.g. used by MadGraph 5) ******)
58
59M$InteractionOrderLimit = {
60 {QNP, 2}
61};
62
63M$InteractionOrderHierarchy = {
64 {QNP, 2}
65};
66
67
68(***** Particle classes list ******)
69
70M$ClassesDescription = {
71
72 S[1] == { ClassName -> X0,
73 SelfConjugate -> True,
74 Mass -> {MX0, 125.0},
75 Width -> {WX0, 0.00407},
76 ParticleName -> "X0",
77 PDG -> 5000000,
78 PropagatorLabel -> "X0",
79 PropagatorType -> D,
80 PropagatorArrow -> None,
81 FullName -> "X0"},
82
83 V[5] == { ClassName -> X1,
84 SelfConjugate -> True,
85 Mass -> {MX1, 125.0},
86 Width -> {WX1, 0.00407},
87 ParticleName -> "X1",
88 PDG -> 5000001,
89 PropagatorLabel -> "X1",
90 PropagatorType -> Sine,
91 PropagatorArrow -> None,
92 FullName -> "X1"},
93
94 T[1] == { ClassName -> X2,
95 SelfConjugate -> True,
96 Symmetric -> True,
97 Mass -> {MX2, 125.0},
98 Width -> {WX2,0.00407},
99 ParticleName -> "X2",
100 PDG -> 5000002,
101 PropagatorLabel -> "X2",
102 PropagatorArrow -> None,
103 FullName -> "X2"}
104
105};
106
107
108(* The loop coefficient from the HEFT model *)
109
110sert[x_] := 1+ 7/30 x + 2/21 x^2 + 26/525 x^3;
111serw[xw_, xt_] := 1 + xw * 66/235 +xw^2 * 228/1645 + xw^3 * 696/8225 +
112 xw^4 * 5248/90475 +xw^5 * 1280/29939+ xw^6 * 54528/1646645-
113 xt * 56/705 - xt^2 * 32/987;
114serp[x_] := 1 + x/3 + x^2 * 8/45 + x^3 * 4/35;
115
116
117(***** Parameter list ******)
118
119M$Parameters = {
120
121 Lambda == { ParameterType -> External,
122 Value -> 1000,
123 TeX -> \[CapitalLambda],
124 Description -> "cut-off scale"},
125
126 ca == { ParameterType -> External,
127 Value -> 1,
128 TeX -> Subscript[c,a],
129 Description -> "cosine of the scalar mixing between 0+ and 0-"},
130
131 sa == { ParameterType -> Internal,
132 Value -> Sqrt[1-ca^2],
133 TeX -> Subscript[s,a],
134 Description -> "sine of the scalar mixing between 0+ and 0-"},
135
136 kSM == { ParameterType -> External,
137 Value -> 1,
138 TeX -> Subscript[\[Kappa],SM],
139 Description -> "Hzz/Hww SM coupling parameter"},
140
141 kHtt == { ParameterType -> External,
142 Value -> 1,
143 TeX -> Subscript[\[Kappa],Htt],
144 Description -> "Htt coupling parameter"},
145
146 kAtt == { ParameterType -> External,
147 Value -> 1,
148 TeX -> Subscript[\[Kappa],Att],
149 Description -> "Att coupling parameter"},
150
151 kHbb == { ParameterType -> External,
152 Value -> 1,
153 TeX -> Subscript[\[Kappa],Hbb],
154 Description -> "Hbb coupling parameter"},
155
156 kAbb == { ParameterType -> External,
157 Value -> 1,
158 TeX -> Subscript[\[Kappa],Abb],
159 Description -> "Abb coupling parameter"},
160
161 kHll == { ParameterType -> External,
162 Value -> 1,
163 TeX -> Subscript[\[Kappa],Hll],
164 Description -> "Hll coupling parameter"},
165
166 kAll == { ParameterType -> External,
167 Value -> 1,
168 TeX -> Subscript[\[Kappa],All],
169 Description -> "All coupling parameter"},
170
171 kHaa == { ParameterType -> External,
172 Value -> 1,
173 InteractionOrder -> {QNP, 1},
174 TeX -> Subscript[\[Kappa],Haa],
175 Description -> "Haa coupling parameter"},
176
177 kAaa == { ParameterType -> External,
178 Value -> 1,
179 InteractionOrder -> {QNP, 1},
180 TeX -> Subscript[\[Kappa],Aaa],
181 Description -> "Aaa coupling parameter"},
182
183 kHza == { ParameterType -> External,
184 Value -> 1,
185 InteractionOrder -> {QNP, 1},
186 TeX -> Subscript[\[Kappa],Hza],
187 Description -> "Hza coupling parameter"},
188
189 kAza == { ParameterType -> External,
190 Value -> 1,
191 InteractionOrder -> {QNP, 1},
192 TeX -> Subscript[\[Kappa],Aza],
193 Description -> "Aza coupling parameter"},
194
195 kHgg == { ParameterType -> External,
196 Value -> 1,
197 InteractionOrder -> {QNP, 1},
198 TeX -> Subscript[\[Kappa],Hgg],
199 Description -> "Hgg coupling parameter"},
200
201 kAgg == { ParameterType -> External,
202 Value -> 1,
203 InteractionOrder -> {QNP, 1},
204 TeX -> Subscript[\[Kappa],Agg],
205 Description -> "Agg coupling parameter"},
206
207 kHzz == { ParameterType -> External,
208 Value -> 0,
209 InteractionOrder -> {QNP, 1},
210 TeX -> Subscript[\[Kappa],Hzz],
211 Description -> "Hzz coupling parameter"},
212
213 kAzz == { ParameterType -> External,
214 Value -> 0,
215 InteractionOrder -> {QNP, 1},
216 TeX -> Subscript[\[Kappa],Azz],
217 Description -> "Azz coupling parameter"},
218
219 kHww == { ParameterType -> External,
220 Value -> 0,
221 InteractionOrder -> {QNP, 1},
222 TeX -> Subscript[\[Kappa],Hww],
223 Description -> "Hww coupling parameter"},
224
225 kAww == { ParameterType -> External,
226 Value -> 0,
227 InteractionOrder -> {QNP, 1},
228 TeX -> Subscript[\[Kappa],Aww],
229 Description -> "Aww coupling parameter"},
230
231 kHda == { ParameterType -> External,
232 Value -> 0,
233 InteractionOrder -> {QNP, 1},
234 TeX -> Subscript[\[Kappa],Hda],
235 Description -> "Hda coupling parameter"},
236
237 kHdz == { ParameterType -> External,
238 Value -> 0,
239 InteractionOrder -> {QNP, 1},
240 TeX -> Subscript[\[Kappa],Hdz],
241 Description -> "Hdz coupling parameter"},
242
243 kHdwR == { ParameterType -> External,
244 ComplexParameter -> False,
245 Value -> 0,
246 TeX -> Subscript[\[Kappa],HdwR],
247 Description -> "Hdw coupling parameter (real part)"},
248
249 kHdwI == { ParameterType -> External,
250 ComplexParameter -> False,
251 Value -> 0,
252 TeX -> Subscript[\[Kappa],HdwI],
253 Description -> "Hdw coupling parameter (imaginary part)"},
254
255 kHdw == { ParameterType -> Internal,
256 ComplexParameter -> True,
257 Value -> {kHdwR+I*kHdwI},
258 InteractionOrder -> {QNP, 1},
259 TeX -> Subscript[\[Kappa],Hdw],
260 Description -> "Hdw coupling parameter"},
261
262(*
263 kHwudLR == { ParameterType -> External,
264 ComplexParameter -> False,
265 Value -> 0,
266 TeX -> Subscript[\[Kappa],HwudLR],
267 Description -> "HwudL coupling parameter (real part)"},
268
269 kHwudLI == { ParameterType -> External,
270 ComplexParameter -> False,
271 Value -> 0,
272 TeX -> Subscript[\[Kappa],HwudLI],
273 Description -> "HwudL coupling parameter (imaginary part)"},
274
275 kHwudL == { ParameterType -> Internal,
276 ComplexParameter -> True,
277 Value -> {kHwudLR+I*kHwudLI},
278 InteractionOrder -> {QNP, 1},
279 TeX -> Subscript[\[Kappa],HwudL],
280 Description -> "HwudL coupling parameter"},
281
282 kHwudRR == { ParameterType -> External,
283 ComplexParameter -> False,
284 Value -> 0,
285 TeX -> Subscript[\[Kappa],HwudRR],
286 Description -> "HwudR coupling parameter (real part)"},
287
288 kHwudRI == { ParameterType -> External,
289 ComplexParameter -> False,
290 Value -> 0,
291 TeX -> Subscript[\[Kappa],HwudRI],
292 Description -> "HwudR coupling parameter (imaginary part)"},
293
294 kHwudR == { ParameterType -> Internal,
295 ComplexParameter -> True,
296 Value -> {kHwudRR+I*kHwudRI},
297 InteractionOrder -> {QNP, 1},
298 TeX -> Subscript[\[Kappa],HwudR],
299 Description -> "HwudR coupling parameter"},
300
301 kHwllR == { ParameterType -> External,
302 ComplexParameter -> False,
303 Value -> 0,
304 TeX -> Subscript[\[Kappa],HwllR],
305 Description -> "Hwll coupling parameter (real part)"},
306
307 kHwllI == { ParameterType -> External,
308 ComplexParameter -> False,
309 Value -> 0,
310 TeX -> Subscript[\[Kappa],HwllI],
311 Description -> "Hwll coupling parameter (imaginary part)"},
312
313 kHwll == { ParameterType -> Internal,
314 ComplexParameter -> True,
315 Value -> {kHwllR+I*kHwllI},
316 InteractionOrder -> {QNP, 1},
317 TeX -> Subscript[\[Kappa],Hwll],
318 Description -> "Hwll coupling parameter"},
319*)
320
321 kHHgg == { ParameterType -> External,
322 Value -> 1,
323 InteractionOrder -> {QNP, 1},
324 TeX -> Subscript[\[Kappa],HHgg],
325 Description -> "HHgg coupling parameter"},
326
327 kAAgg == { ParameterType -> External,
328 Value -> 1,
329 InteractionOrder -> {QNP, 1},
330 TeX -> Subscript[\[Kappa],AAgg],
331 Description -> "AAgg coupling parameter"},
332
333 kqa == { ParameterType -> External,
334 Value -> 1,
335 InteractionOrder -> {QNP, 1},
336 TeX -> Subscript[\[Kappa],qqa],
337 Description -> "X1-qq vector coupling parameter"},
338
339 kqb == { ParameterType -> External,
340 Value -> 1,
341 InteractionOrder -> {QNP, 1},
342 TeX -> Subscript[\[Kappa],qqb],
343 Description -> "X1-qq axial-vector coupling parameter"},
344
345 kla == { ParameterType -> External,
346 Value -> 1,
347 InteractionOrder -> {QNP, 1},
348 TeX -> Subscript[\[Kappa],lla],
349 Description -> "X1-ll vector coupling parameter"},
350
351 klb == { ParameterType -> External,
352 Value -> 1,
353 InteractionOrder -> {QNP, 1},
354 TeX -> Subscript[\[Kappa],llb],
355 Description -> "X1-ll axial-vector coupling parameter"},
356
357 kw1 == { ParameterType -> External,
358 Value -> 1,
359 InteractionOrder -> {QNP, 1},
360 TeX -> Subscript[\[Kappa],w1],
361 Description -> "X1-WW coupling parameter 1"},
362
363 kw2 == { ParameterType -> External,
364 Value -> 1,
365 InteractionOrder -> {QNP, 1},
366 TeX -> Subscript[\[Kappa],w2],
367 Description -> "X1-WW coupling parameter 2"},
368
369 kw3 == { ParameterType -> External,
370 Value -> 0,
371 InteractionOrder -> {QNP, 1},
372 TeX -> Subscript[\[Kappa],w3],
373 Description -> "X1-WW coupling parameter 3"},
374
375 kw4 == { ParameterType -> External,
376 Value -> 0,
377 InteractionOrder -> {QNP, 1},
378 TeX -> Subscript[\[Kappa],w4],
379 Description -> "X1-WW coupling parameter 4"},
380
381 kw5 == { ParameterType -> External,
382 Value -> 0,
383 InteractionOrder -> {QNP, 1},
384 TeX -> Subscript[\[Kappa],w5],
385 Description -> "X1-WW coupling parameter 5"},
386
387 kz1 == { ParameterType -> External,
388 Value -> 0,
389 InteractionOrder -> {QNP, 1},
390 TeX -> Subscript[\[Kappa],z1],
391 Description -> "X1-ZZ coupling parameter 1"},
392
393 kz3 == { ParameterType -> External,
394 Value -> 1,
395 InteractionOrder -> {QNP, 1},
396 TeX -> Subscript[\[Kappa],z3],
397 Description -> "X1-ZZ coupling parameter 3"},
398
399 kz5 == { ParameterType -> External,
400 Value -> 0,
401 InteractionOrder -> {QNP, 1},
402 TeX -> Subscript[\[Kappa],z5],
403 Description -> "X1-ZZ coupling parameter 5"},
404
405 kq == { ParameterType -> External,
406 Value -> 1,
407 InteractionOrder -> {QNP, 1},
408 TeX -> Subscript[\[Kappa],q],
409 Description -> "X2-light quark coupling parameter"},
410
411 kq3 == { ParameterType -> External,
412 Value -> 1,
413 InteractionOrder -> {QNP, 1},
414 TeX -> Subscript[\[Kappa],q3],
415 Description -> "X2-3rd generation quark coupling parameter"},
416
417 kl == { ParameterType -> External,
418 Value -> 1,
419 InteractionOrder -> {QNP, 1},
420 TeX -> Subscript[\[Kappa],l],
421 Description -> "X2-lepton coupling parameter"},
422
423 kg == { ParameterType -> External,
424 Value -> 1,
425 InteractionOrder -> {QNP, 1},
426 TeX -> Subscript[\[Kappa],g],
427 Description -> "X2-gluon coupling parameter"},
428
429 ka == { ParameterType -> External,
430 Value -> 1,
431 InteractionOrder -> {QNP, 1},
432 TeX -> Subscript[\[Kappa],a],
433 Description -> "X2-photon coupling parameter"},
434
435 kz == { ParameterType -> External,
436 Value -> 1,
437 InteractionOrder -> {QNP, 1},
438 TeX -> Subscript[\[Kappa],z],
439 Description -> "X2-Z coupling parameter"},
440
441 kw == { ParameterType -> External,
442 Value -> 1,
443 InteractionOrder -> {QNP, 1},
444 TeX -> Subscript[\[Kappa],w],
445 Description -> "X2-W coupling parameter"},
446
447 kza == { ParameterType -> External,
448 Value -> 0,
449 InteractionOrder -> {QNP, 1},
450 TeX -> Subscript[\[Kappa],za],
451 Description -> "X2-Z-A coupling parameter"},
452
453
454 gHaa == { ParameterType -> Internal,
455 Value -> ee^2/(4*Pi)/(Pi*vev)*(47/18), (* *serw[(MX0/2/MW)^2, (MX0/2/MT)^2], *)
456 TeX -> Subscript[g,Haa],
457 Description -> "Haa coupling"},
458
459 gAaa == { ParameterType -> Internal,
460 Value -> ee^2/(4*Pi)/(Pi*vev)*(4/3),
461 TeX -> Subscript[g,Aaa],
462 Description -> "Aaa coupling"},
463
464 gHza == { ParameterType -> Internal,
465 Value -> Sqrt[ee^2/(4*Pi)*Gf*MZ^2/(8*Sqrt[2]*Pi)]*(94*cw^2-13)/(9*Pi*vev),
466 TeX -> Subscript[g,Hza],
467 Description -> "Hza coupling"},
468
469 gAza == { ParameterType -> Internal,
470 Value -> 2*Sqrt[ee^2/(4*Pi)*Gf*MZ^2/(8*Sqrt[2]*Pi)]*(8*cw^2-5)/(3*Pi*vev),
471 TeX -> Subscript[g,Aza],
472 Description -> "Aza coupling"},
473
474 gHgg == { ParameterType -> Internal,
475 Value -> -gs^2/(4*Pi)/(3*Pi*vev), (* *sert[(MX0/2/MT)^2], *)
476 TeX -> Subscript[g,Hgg],
477 Description -> "Hgg coupling"},
478
479 gAgg == { ParameterType -> Internal,
480 Value -> gs^2/(4*Pi)/(2*Pi*vev), (* *serp[(MX0/2/MT)^2], *)
481 TeX -> Subscript[g,Agg],
482 Description -> "Agg coupling"},
483
484 gHHgg == { ParameterType -> Internal,
485 Value -> gs^2/(4*Pi)/(3*Pi*vev^2),
486 TeX -> Subscript[g,HHgg],
487 Description -> "HHgg coupling"},
488
489 gAAgg == { ParameterType -> Internal,
490 Value -> gs^2/(4*Pi)/(2*Pi*vev^2),
491 TeX -> Subscript[g,AAgg],
492 Description -> "AAgg coupling"},
493
494 au == { ParameterType -> Internal,
495 Value -> ee/(2 sw cw)(1/2-4/3 sw2),
496 Tex -> Subscript[a,u],
497 Description -> "vector coupling for up-type quarks"},
498
499 bu == { ParameterType -> Internal,
500 Value -> ee/(2 sw cw)(1/2),
501 TeX -> Subscript[b,u],
502 Description -> "axial-vector coupling for up-type quarks"},
503
504 ad == { ParameterType -> Internal,
505 Value -> ee/(2 sw cw)(-1/2+2/3 sw2),
506 TeX -> Subscript[a,d],
507 Description -> "vector coupling for down-type quarks"},
508
509 bd == { ParameterType -> Internal,
510 Value -> ee/(2 sw cw)(-1/2),
511 TeX -> Subscript[b,d],
512 Description -> "axial-vector coupling for down-type quarks"},
513
514 an == { ParameterType -> Internal,
515 Value -> ee/(2 sw cw)(1/2),
516 Tex -> Subscript[a,n],
517 Description -> "vector coupling for neutrinos"},
518
519 bn == { ParameterType -> Internal,
520 Value -> ee/(2 sw cw)(1/2),
521 TeX -> Subscript[b,n],
522 Description -> "axial-vector coupling for neutrinos"},
523
524 al == { ParameterType -> Internal,
525 Value -> ee/(2 sw cw)(-1/2+2 sw2),
526 TeX -> Subscript[a,l],
527 Description -> "vector coupling for charged leptons"},
528
529 bl == { ParameterType -> Internal,
530 Value -> ee/(2 sw cw)(-1/2),
531 TeX -> Subscript[b,l],
532 Description -> "axial-vector coupling for charged leptons"},
533
534 gwwz == { ParameterType -> Internal,
535 Value -> -ee cw/sw,
536 TeX -> Subscript[g,wwz],
537 Description -> "WWZ coupling"}
538
539};
540
541
542(*****************************************************************************************)
543(**************************************** Lagrangian *************************************)
544(*****************************************************************************************)
545
546(****************************************** Spin-0 ***************************************)
547
548L0v := (-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] ) -
549 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] ) -
550 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] ) -
551 1/4/Lambda ( ca kHzz FS[Z,mu,nu] FS[Z,mu,nu] + sa kAzz FS[Z,mu,nu] Dual[FS][Z,mu,nu] ) -
552 1/2/Lambda ( ca kHww FS[Wbar,mu,nu] FS[W,mu,nu] + sa kAww FS[Wbar,mu,nu] Dual[FS][W,mu,nu] ) -
553 1 /Lambda ( ca kHda Z[nu] del[FS[A,mu,nu],mu] +
554 ca kHdz Z[nu] del[FS[Z,mu,nu],mu] +
555 ca ( kHdw Wbar[nu] del[FS[W,mu,nu],mu] + HC[kHdw Wbar[nu] del[FS[W,mu,nu],mu]] ) ) ) X0;
556
557(*
558L0vff := -1/Lambda ca ( kHwudL CKM[i,j] uqbar[s,i,a].Ga[mu,s,t].ProjM[t,u].dq[u,j,a] +
559 kHwudR uqbar.Ga[mu].ProjP.dq +
560 kHwll vlbar.Ga[mu].ProjM.l ) W[mu] X0;
561*)
562
563L0v6 := -1/8 ( ca kHHgg gHHgg FS[G,mu,nu,a] FS[G,mu,nu,a] +
564 +sa kAAgg gAAgg FS[G,mu,nu,a] Dual[FS][G,mu,nu,a] ) X0 X0;
565
566
567(****************************************** Spin-1 ***************************************)
568
569L1f := ( kqa au uqbar[s,n,i].Ga[mu,s,t].uq[t,n,i] +
570 kqa ad dqbar[s,n,i].Ga[mu,s,t].dq[t,n,i] +
571 kla an vlbar[s,n] .Ga[mu,s,t].vl[t,n] +
572 kla al lbar[s,n] .Ga[mu,s,t]. l[t,n] -
573 kqb bu uqbar[s,n,i].Ga[mu,s,t].Ga[5,t,u].uq[u,n,i] -
574 kqb bd dqbar[s,n,i].Ga[mu,s,t].Ga[5,t,u].dq[u,n,i] -
575 klb bn vlbar[s,n] .Ga[mu,s,t].Ga[5,t,u].vl[u,n] -
576 klb bl lbar[s,n] .Ga[mu,s,t].Ga[5,t,u]. l[u,n] ) X1[mu];
577
578L1w := I kw1 gwwz ( FS[Wbar,mu,nu] W[mu] - FS[W,mu,nu] Wbar[mu] ) X1[nu] +
579 I kw2 gwwz Wbar[mu] W[nu] FS[X1,mu,nu] -
580 kw3 Wbar[mu] W[nu] ( del[X1[nu],mu] + del[X1[mu],nu] ) +
581 I kw4 Wbar[mu] W[nu] Dual[FS][X1,mu,nu] -
582 kw5 Eps[mu,nu,rho,sig] ( Wbar[mu] del[W[nu],rho] - del[Wbar[mu],rho] W[nu] ) X1[sig];
583
584L1z := - kz1 FS[Z,mu,nu] Z[mu] X1[nu] -
585 kz3 X1[mu] del[Z[mu],nu] Z[nu] -
586 kz5 Eps[mu,nu,rho,sig] X1[mu] Z[nu] del[Z[sig],rho];
587
588L1 := L1f + L1w + L1z;
589
590
591(****************************************** Spin-2 ***************************************)
592
593(*** Defining the cov derivatives ***)
594
595covdelU[field_, mu_] :=
596 Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
597 - 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]];
598
599covdelD[field_, mu_] :=
600 Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
601 + 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]];
602
603covdelE[field_, mu_] :=
604 Module[{j, a}, del[field, mu]
605 + 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]];
606
607covdelN[field_, mu_] :=
608 Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
609
610
611(*** Defining the energy-momentum tensor T[mu,nu] ***)
612
613(* Fermions *)
614
615(* TFq[mu_,nu_] := (-ME[mu,nu] (I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho]
616 + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho]
617 + ee/sw/Sqrt[2] (uqbar.Ga[rho].ProjM.CKM.dq W[rho] + dqbar.Ga[rho].ProjM.HC[CKM].uq Wbar[rho]) )
618 + ( I/2 uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu]
619 + I/2 uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu]
620 + I/2 dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu]
621 + I/2 dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu] )
622 + ee/sw/2/Sqrt[2] (uqbar.Ga[mu].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[nu]
623 + uqbar.Ga[nu].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].ProjM.HC[CKM].uq Wbar[mu] )); *)
624
625TFq[mu_,nu_] := (-ME[mu,nu] ( I ubar.(Ga[rho].covdelU[u, rho]) -1/2 del[I ubar.Ga[rho].u, rho]
626 + I dbar.(Ga[rho].covdelD[d, rho]) -1/2 del[I dbar.Ga[rho].d, rho]
627 + ee/sw/Sqrt[2] ( Cos[cabi] ubar.Ga[rho].ProjM.d W[rho]
628 + Sin[cabi] ubar.Ga[rho].ProjM.s W[rho]
629 + Cos[cabi] dbar.Ga[rho].ProjM.u Wbar[rho]
630 + Sin[cabi] sbar.Ga[rho].ProjM.u Wbar[rho] ) )
631 +( I/2 ubar.Ga[mu].covdelU[u, nu] - 1/4 I del[ubar.Ga[nu].u, mu]
632 + I/2 ubar.Ga[nu].covdelU[u, mu] - 1/4 I del[ubar.Ga[mu].u, nu]
633 + I/2 dbar.Ga[mu].covdelD[d, nu] - 1/4 I del[dbar.Ga[nu].d, mu]
634 + I/2 dbar.Ga[nu].covdelD[d, mu] - 1/4 I del[dbar.Ga[mu].d, nu] )
635 +ee/sw/2/Sqrt[2] ( Cos[cabi] ubar.Ga[mu].ProjM.d W[nu]
636 + Cos[cabi] ubar.Ga[nu].ProjM.d W[mu]
637 + Sin[cabi] ubar.Ga[mu].ProjM.s W[nu]
638 + Sin[cabi] ubar.Ga[nu].ProjM.s W[mu]
639 + Cos[cabi] dbar.Ga[mu].ProjM.u Wbar[nu]
640 + Cos[cabi] dbar.Ga[nu].ProjM.u Wbar[mu]
641 + Sin[cabi] sbar.Ga[mu].ProjM.u Wbar[nu]
642 + Sin[cabi] sbar.Ga[nu].ProjM.u Wbar[mu] ) )+
643 (-ME[mu,nu] ( I cbar.(Ga[rho].covdelU[c, rho]) -1/2 del[I cbar.Ga[rho].c, rho]
644 + I sbar.(Ga[rho].covdelD[s, rho]) -1/2 del[I sbar.Ga[rho].s, rho]
645 + ee/sw/Sqrt[2] ( Cos[cabi] cbar.Ga[rho].ProjM.s W[rho]
646 - Sin[cabi] cbar.Ga[rho].ProjM.d W[rho]
647 + Cos[cabi] sbar.Ga[rho].ProjM.c Wbar[rho]
648 - Sin[cabi] dbar.Ga[rho].ProjM.c Wbar[rho] ) )
649 +( I/2 cbar.Ga[mu].covdelU[c, nu] - 1/4 I del[cbar.Ga[nu].c, mu]
650 + I/2 cbar.Ga[nu].covdelU[c, mu] - 1/4 I del[cbar.Ga[mu].c, nu]
651 + I/2 sbar.Ga[mu].covdelD[s, nu] - 1/4 I del[sbar.Ga[nu].s, mu]
652 + I/2 sbar.Ga[nu].covdelD[s, mu] - 1/4 I del[sbar.Ga[mu].s, nu] )
653 +ee/sw/2/Sqrt[2] ( Cos[cabi] cbar.Ga[mu].ProjM.s W[nu]
654 + Cos[cabi] cbar.Ga[nu].ProjM.s W[mu]
655 - Sin[cabi] cbar.Ga[mu].ProjM.d W[nu]
656 - Sin[cabi] cbar.Ga[nu].ProjM.d W[mu]
657 + Cos[cabi] sbar.Ga[mu].ProjM.c Wbar[nu]
658 + Cos[cabi] sbar.Ga[nu].ProjM.c Wbar[mu]
659 - Sin[cabi] dbar.Ga[mu].ProjM.c Wbar[nu]
660 - Sin[cabi] dbar.Ga[nu].ProjM.c Wbar[mu] ) );
661
662TFq3[mu_,nu_] := (-ME[mu,nu] ( I tbar.(Ga[rho].covdelU[t, rho]) -1/2 del[I tbar.Ga[rho].t, rho]
663 + I bbar.(Ga[rho].covdelD[b, rho]) -1/2 del[I bbar.Ga[rho].b, rho]
664 + ee/sw/Sqrt[2] ( tbar.Ga[rho].ProjM.b W[rho]
665 + bbar.Ga[rho].ProjM.t Wbar[rho]) )
666 +( I/2 tbar.Ga[mu].covdelU[t, nu] - 1/4 I del[tbar.Ga[nu].t, mu]
667 + I/2 tbar.Ga[nu].covdelU[t, mu] - 1/4 I del[tbar.Ga[mu].t, nu]
668 + I/2 bbar.Ga[mu].covdelD[b, nu] - 1/4 I del[bbar.Ga[nu].b, mu]
669 + I/2 bbar.Ga[nu].covdelD[b, mu] - 1/4 I del[bbar.Ga[mu].b, nu] )
670 +ee/sw/2/Sqrt[2] ( tbar.Ga[mu].ProjM.b W[nu]
671 + tbar.Ga[nu].ProjM.b W[mu]
672 + bbar.Ga[mu].ProjM.t Wbar[nu]
673 + bbar.Ga[nu].ProjM.t Wbar[mu] ) );
674
675TFl[mu_,nu_] := (-ME[mu,nu] ( I vlbar.(Ga[rho].ProjM.covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].ProjM.vl, rho]
676 + I lbar.(Ga[rho].covdelE[l, rho]) -1/2 del[I lbar.Ga[rho].l, rho]
677 + ee/sw/Sqrt[2] ( vlbar.Ga[rho].ProjM.l W[rho]
678 + lbar.Ga[rho].ProjM.vl Wbar[rho]) )
679 +( I/2 vlbar.Ga[mu].ProjM.covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].ProjM.vl, mu]
680 + I/2 vlbar.Ga[nu].ProjM.covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].ProjM.vl, nu]
681 + I/2 lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu]
682 + I/2 lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu] )
683 +ee/sw/2/Sqrt[2] ( vlbar.Ga[mu].ProjM.l W[nu]
684 + lbar.Ga[mu].ProjM.vl Wbar[nu]
685 + vlbar.Ga[nu].ProjM.l W[mu]
686 + lbar.Ga[nu].ProjM.vl Wbar[mu] ) );
687
688(* Yukawa *)
689
690TYq[mu_,nu_] := -ME[mu,nu] ( - MT tbar.t - MB bbar.b );
691TYl[mu_,nu_] := -ME[mu,nu] ( - MTA tabar.ta );
692
693(* Gauge bosons *)
694
695TGg[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];
696TGa[mu_,nu_] := -ME[mu,nu] (-1/4 FS[A,rho,sig] FS[A,rho,sig]) - FS[A,mu,rho] FS[A,nu,rho];
697TGz[mu_,nu_] := -ME[mu,nu] (-1/4 FS[Z,rho,sig] FS[Z,rho,sig] + 1/2 MZ^2 Z[rho] Z[rho]) -
698 (FS[Z,mu,rho] FS[Z,nu,rho] - MZ^2 Z[mu] Z[nu]);
699TGw[mu_,nu_] := -ME[mu,nu] (-1/2 FS[Wbar,rho,sig] FS[W,rho,sig] + MW^2 Wbar[rho] W[rho]) -
700 (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]);
701TGza[mu_,nu_] := -ME[mu,nu] (-1/2 FS[Z,rho,sig] FS[A,rho,sig]) -
702 (FS[Z,mu,rho] FS[A,nu,rho] + FS[Z,nu,rho] FS[A,mu,rho]);
703
704(* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators *)
705(* and unitary gauge for massive gauge boson propagators. *)
706
707TGFg[mu_,nu_]:= -ME[mu,nu].( del[del[G[sig, a1], sig], rho].G[rho, a1] +
708 1/2 del[G[rho, a1], rho].del[G[sig, a1], sig] ) +
709 del[del[G[rho, a1], rho], mu].G[nu, a1] + del[del[G[rho, a1], rho], nu].G[mu, a1];
710
711TGFa[mu_,nu_]:= -ME[mu,nu].( del[del[A[sig], sig], rho].A[rho] +
712 1/2 del[A[rho], rho].del[A[sig], sig] ) +
713 del[del[A[rho], rho], mu].A[nu] + del[del[A[rho], rho], nu].A[mu];
714
715(*** Writing the lagrangian ***)
716
717L2f := -1/Lambda ( kq TFq[mu,nu] + kq3 (TFq3[mu,nu]+TYq[mu,nu]) + kl (TFl[mu,nu]+TYl[mu,nu]) ) X2[mu,nu];
718L2v := -1/Lambda ( kg (TGg[mu,nu]+TGFg[mu,nu]) +
719 ka (TGa[mu,nu]+TGFa[mu,nu]) +
720 kz TGz[mu,nu] +
721 kw TGw[mu,nu] +
722 kza TGza[mu,nu] ) X2[mu,nu];
723
724L2 := L2f + L2v;
725
726(*****************************************************************************************)
727
728LagHC:= LSM + L0v + L1 + L2 + L0v6;