HiggsCharacterisation: HiggsCharacterization.fr

File HiggsCharacterization.fr, 20.4 KB (added by PriscilaAquino, 6 years ago)

Main FR model file v2.0.

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 Priscila de Aquino (paquino@vub.ac.be) for bugs and/or further information         *)
10(*                                                                                                   *)
11(* THE UFO FILE HAS BEEN MODIFIED BY HAND: COUPLINGS OF THE X2 TO THE PHOTONS MODIFIED TO            *)
12(* Ka AND INTERACTIONS BETWEEN RESONANCES REMOVED.                                                   *)
13(*                                                                                                   *)
14(*****************************************************************************************************)
15FeynmanGauge = False;
16
17M$ModelName = "Higgs_Characterization";
18M$Information = {
19  Authors      -> "P. de Aquino, K. Mawatari",
20  Version      -> "2.0",
21  Date         -> "15. 04. 2013"
22};
23
24(* ************************** *)
25(* *****  Gauge groups  ***** *)
26(* ************************** *)
27M$GaugeGroups = {
28    U11Y  == {
29    Abelian          -> True, 
30    CouplingConstant -> g1,
31    GaugeBoson       -> X1,
32    Charge           -> Y}
33    };
34
35(* The loop coefficient from the HEFT model *)
36
37sert[x_] := 1+ 7/30 x + 2/21 x^2 + 26/525 x^3;
38
39serw[xw_, xt_] := 1 + xw * 66/235 +xw^2 * 228/1645 + xw^3 * 696/8225 +
40            xw^4 * 5248/90475 +xw^5 * 1280/29939+ xw^6 * 54528/1646645-
41            xt * 56/705 - xt^2 * 32/987;
42
43serp[x_] := 1 + x/3 + x^2 * 8/45 + x^3 * 4/35;
44
45(***** Setting for interaction order (as e.g. used by MadGraph 5)  ******)
46
47M$InteractionOrderLimit = {
48     {QNP, 99}
49    };
50
51(***** Parameter list ******)
52
53M$Parameters = {
54
55kq == {
56            ParameterType -> External,
57            Value -> 1,
58            InteractionOrder -> {QNP, 1},
59            Description -> "Coupling with light quarks"},
60
61kg == {
62            ParameterType -> External,
63            Value -> 1,
64                InteractionOrder -> {QNP, 1},
65            Description -> "Coupling with gluons"},
66
67ka == {
68            ParameterType -> External,
69            Value -> 1,
70                InteractionOrder -> {QNP, 1},
71            Description -> "Coupling with photons"},
72               
73kv == {
74            ParameterType -> External,
75            Value -> 1,
76                InteractionOrder -> {QNP, 1},
77            Description -> "Coupling with vector boson"},
78
79kl == {
80            ParameterType -> External,
81            Value -> 1,
82                InteractionOrder -> {QNP, 1},
83            Description -> "Coupling with leptons"},
84
85ka1 == {
86            ParameterType -> External,
87            Value -> 0,
88                InteractionOrder -> {QNP, 1},
89            Description -> "Coupling with photons"},
90               
91       
92kg1 == {
93            ParameterType -> External,
94            Value -> 0,
95                InteractionOrder -> {QNP, 1},
96            Description -> "Coupling with gluons"},
97
98ka2 == {
99            ParameterType -> External,
100            Value -> 0,
101                InteractionOrder -> {QNP, 1},
102            Description -> "Coupling with photons"},
103               
104kg2 == {
105            ParameterType -> External,
106            Value -> 0,
107                InteractionOrder -> {QNP, 1},
108            Description -> "Coupling with gluons"},
109               
110               
111Lambda == {
112            ParameterType -> External,
113            Value -> 1000,
114            Description -> "Spin-2 effective scale"},
115
116ksm == {
117            ParameterType -> External,
118            Value -> 1,
119            InteractionOrder -> {QNP, 1},
120            Description -> "Lower dimensional operator switch"},
121
122GHaa == {TeX -> Subscript[g, Haa],
123       ParameterType -> Internal,
124       Value -> ee^2/4/Pi/(Pi*vev)*(47/18)*serw[(MX0/2/MW)^2, (MX0/2/MT)^2]},
125
126GAaa == {TeX -> Subscript[g, Aaa],
127       ParameterType -> Internal,
128       Value -> ee^2/4/Pi/(Pi*vev)},
129
130GHza == {TeX -> Subscript[g, Hza],
131       ParameterType -> Internal,
132       Value -> ee^2/4/Pi/(Pi*vev)},
133
134GAza == {TeX -> Subscript[g, Aza],
135       ParameterType -> Internal,
136       Value -> ee^2/4/Pi/(Pi*vev)},
137
138GHgg == {TeX -> Subscript[g, Hgg],
139       ParameterType -> Internal,
140       Value -> -gs^2/(4Pi(3Pi vev)) sert[(MX0/2/MT)^2] },
141
142GAgg == {TeX -> Subscript[g, Agg],
143       ParameterType -> Internal,
144       Value -> -gs^2/4/Pi/(2*Pi*vev)*serp[(MX0/2/MT)^2]},
145
146kHff == {TeX -> Subscript[k, Hf],
147       ParameterType -> External,
148           InteractionOrder -> {QNP, 1},
149       Value -> 1},
150
151kAff == {TeX -> Subscript[k, Af],
152       ParameterType -> External,
153           InteractionOrder -> {QNP, 1},
154       Value -> 1},
155
156kHaa == {TeX -> Subscript[k, Haa],
157       ParameterType -> External,
158           InteractionOrder -> {QNP, 1},
159       Value -> 1},
160
161kAaa == {TeX -> Subscript[k, Aaa],
162       ParameterType -> External,
163           InteractionOrder -> {QNP, 1},
164       Value -> 1},
165
166kHza == {TeX -> Subscript[k, Hza],
167       ParameterType -> External,
168           InteractionOrder -> {QNP, 1},
169       Value -> 1},
170
171kAza == {TeX -> Subscript[k, Aza],
172       ParameterType -> External,
173           InteractionOrder -> {QNP, 1},
174       Value -> 1},
175
176kHgg == {TeX -> Subscript[k, Hgg],
177       ParameterType -> External,
178           InteractionOrder -> {QNP, 1},
179       Value -> 1},
180
181kAgg == {TeX -> Subscript[k, Agg],
182       ParameterType -> External,
183           InteractionOrder -> {QNP, 1},
184       Value -> 1},
185           
186kHvv == {TeX -> Subscript[k, Hvv],
187       ParameterType -> External,
188           InteractionOrder -> {QNP, 1},
189       Value -> 0},
190
191kAvv == {TeX -> Subscript[k, Avv],
192       ParameterType -> External,
193           InteractionOrder -> {QNP, 1},
194       Value -> 0},
195
196afu == {
197            ParameterType -> Internal,
198            Value -> -gs/(2 cw)(1/2-4*sw2/3)},
199               
200bfu == {
201            ParameterType -> Internal,
202            Value -> -gs/(2 cw)(1/2)},
203               
204kfau == {
205            ParameterType -> External,
206            Value -> 1,
207            InteractionOrder -> {QNP, 1}},
208
209kfbu == {
210            ParameterType -> External,
211            Value -> 1,
212            InteractionOrder -> {QNP, 1}},
213
214afd == {
215            ParameterType -> Internal,
216            Value -> -gs/(2 cw)(-1/2+2*sw2/3)},
217               
218bfd == {
219            ParameterType -> Internal,
220            Value ->  -gs/(2 cw)(-1/2)},
221               
222kfad == {
223            ParameterType -> External,
224            Value -> 1,
225            InteractionOrder -> {QNP, 1}},
226
227kfbd == {
228            ParameterType -> External,
229            Value -> 1,
230            InteractionOrder -> {QNP, 1}},
231
232gwwz == {
233            ParameterType -> Internal,
234            Value -> -ee cw/sw,
235            Description -> "SM coupling"},
236
237kv1 == {
238            ParameterType -> External,
239            Value -> 0,
240            InteractionOrder -> {QNP, 1},
241            Description -> "Couplings of spin-1 to X"},
242
243kv2 == {
244            ParameterType -> External,
245            Value -> 0,
246            InteractionOrder -> {QNP, 1},
247            Description -> "Couplings of spin-1 to X"},
248
249kv3 == {
250            ParameterType -> External,
251            Value -> 0,
252            InteractionOrder -> {QNP, 1},
253            Description -> "Couplings of spin-1 to X"},
254
255kv4 == {
256            ParameterType -> External,
257            Value -> 0,
258            InteractionOrder -> {QNP, 1},
259            Description -> "Couplings of spin-1 to X"},
260
261kv5 == {
262            ParameterType -> External,
263            Value -> 0,
264            InteractionOrder -> {QNP, 1},
265            Description -> "Couplings of spin-1 to X"},
266
267
268(*tha == {Value -> 2.88,
269          TeX -> Subscript[\[Theta], a],
270          Description -> "Scalar mixing angle"},*)
271
272ca == {ParameterType -> External,
273          Value -> 1,
274          TeX -> Subscript[c,a],
275          InteractionOrder -> {QNP, 0},
276          Description -> "Cos of the scalar mixing angle"},
277
278sa == {ParameterType -> Internal,
279          Value -> Sqrt[1-ca^2],
280          TeX -> Subscript[s,a],
281          InteractionOrder -> {QNP, 0},
282          Description -> "Sin of the scalar mixing angle"}
283};
284
285
286(***** Particle classes list ******)
287
288M$ClassesDescription = {
289 V[7] == {
290        ClassName -> X1,
291        SelfConjugate -> True,
292        Indices -> {},
293        Mass -> {MX1, 125.0},
294        Width -> {WX1, 0.07567860},
295        PropagatorLabel -> "X1",
296        ParticleName -> "X1",
297        PropagatorType -> Sine,
298        PropagatorArrow -> None,
299        PDG -> 5000002,
300        FullName -> "X1"},
301               
302(*V[8] == {
303        ClassName -> X1p,
304        SelfConjugate -> True,
305        Indices -> {},
306        Mass -> {MX1p, 125.0},
307        Width -> {WX1p, 0.07567860},
308        PropagatorLabel -> "X1p",
309        ParticleName -> "X1p",
310        PropagatorType -> Sine,
311        PropagatorArrow -> None,
312        PDG -> 5000003,
313        FullName -> "X1m"},*)
314
315 S[3] == {
316   ClassName -> X0x,
317   SelfConjugate -> True,
318   Mass -> {MX0,125},
319   Width -> {WX0, 0.07567860},
320   PDG -> 5000001,
321   ParticleName -> "X0"},
322
323
324T[1] == {
325     ClassName -> X2,
326     SelfConjugate -> True,
327     ParticleName ->"X2",
328     PDG -> 5000004,
329     Symmetric -> True,
330     Mass -> {MX2, 125.0},
331     Width -> {WX2,0.07567860}} 
332         
333         };
334
335(**************************************** Lagrangian *************************************)
336(*****************************************************************************************)
337
338(* Spin-0 ********************************************************************************)
339(*****************************************************************************************)
340
341LG0:= - 1/4 (  ca kHgg GHgg FS[G, mu, nu, b] FS[G, mu, nu, b] +
342                sa kAgg GAgg FS[G, mu, nu, b] Dual[FS][G, mu, nu, b]) X0x -
343        1/4 (  ca kHaa GHaa (del[A[nu], mu] - del[A[mu], nu])(del[A[nu], mu] - del[A[mu], nu]) +
344                sa kAaa GAaa (del[A[nu], mu] - del[A[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[A[sig], rho]-del[A[rho], sig])) X0x -
345        1/4 (  ca kHza GHza (del[Z[nu], mu] - del[Z[mu], nu])(del[A[nu], mu] - del[A[mu], nu]) +
346                                sa kAza GAza (del[Z[nu], mu] - del[Z[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[A[sig], rho]-del[A[rho], sig])) X0x -
347        1/4(  ca kHvv ((del[Z[nu], mu] - del[Z[mu], nu])(del[Z[nu], mu] - del[Z[mu], nu]) +
348                     (del[Wbar[nu], mu] - del[Wbar[mu], nu])(del[W[nu], mu] - del[W[mu], nu])) +
349                sa kAvv ((del[Z[nu], mu] - del[Z[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[Z[sig], rho] - del[Z[rho], sig]) +
350                      (del[Wbar[nu], mu] - del[Wbar[mu], nu])(1/2)Eps[mu,nu,rho,sig](del[W[sig], rho] - del[W[rho], sig]))) X0x;
351
352
353(*****************************************************************************************)
354
355(* RS ************************************************************************************)
356(*****************************************************************************************)
357
358
359(********************** Gravitational Coupling ******************************************)
360(********************** Defining the cov derivatives *************************************)
361
362covdelU[field_, mu_] :=
363  Module[{j, a},   del[field, mu] - I gs G[mu, a] T[a].field
364                 - 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]];
365
366covdelD[field_, mu_] :=
367  Module[{j, a}, del[field, mu] - I gs G[mu, a] T[a].field
368                 + 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]];
369
370covdelE[field_, mu_] :=
371  Module[{j, a},  del[field, mu]
372                 + 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]];
373
374(* Version 2.0 => fixed a sign problem and a factor 2 missing in the above derivative *)
375
376covdelN[field_, mu_] :=
377  Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
378
379(******************** Defining the field strenght tensors:********************************)
380
381FG[mu_,nu_,a1_,a2_,a3_] := del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3];
382
383FA[mu_,nu_] := del[B[nu], mu] - del[B[mu], nu];
384
385FW[mu_,nu_,i1_,i2_,i3_] := del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + ee/sw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3];
386
387(******************* Defining the energy-momentum tensor T[mu,nu] ************************)
388
389(* Gauge bosons *)
390
391TG[mu_,nu_]:= ( - ME[mu,nu]. (-1/4 (-kv) FA[rho, sig] FA[rho,sig] - 1/4 (-kv)FW[rho,sig,i1,i2,i3] FW[rho,sig, i1,i4,i5] - 1/4 (-kg)FG[rho,sig,a1,a2,a3] FG[rho,sig, a1,a4,a5])
392                - (-kv)FA[mu,rho] FA[nu,rho] - (-kv)FW[mu,rho,i1,i2,i3] FW[nu,rho, i1,i4,i5] - (-kg) FG[mu,rho,a1,a2,a3] FG[nu,rho, a1,a2,a3]);
393(* Fermions *)
394
395TF[mu_,nu_] := (-ME[mu,nu] ((-kq) (I uqbar.(Ga[rho].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].uq, rho]
396                          + I dqbar.(Ga[rho].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].dq, rho])
397                          +(-kl)(+ I vlbar.(Ga[rho].covdelN[vl, rho]) -1/2 del[I vlbar.Ga[rho].vl, rho]
398                          + I lbar.(Ga[rho].covdelE[l, rho]  ) -1/2 del[I lbar.Ga[rho].l, rho])
399                         
400                          + ee/sw/Sqrt[2] ((-kq) uqbar.Ga[rho].ProjM.CKM.dq W[rho] + (-kq) dqbar.Ga[rho].ProjM.HC[CKM].uq Wbar[rho]
401                                         + (-kl) vlbar.Ga[rho].ProjM.l W[rho] + (-kq) lbar.Ga[rho].ProjM.vl Wbar[rho]) )
402               + ( (-kq) (I/2  uqbar.Ga[mu].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].uq, mu]
403                    + I/2  uqbar.Ga[nu].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].uq, nu]                   
404                    + I/2  dqbar.Ga[mu].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].dq, mu]
405                    + I/2  dqbar.Ga[nu].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].dq, nu])+
406                    (-kl) (I/2  vlbar.Ga[mu].covdelN[vl, nu] - 1/4 I del[vlbar.Ga[nu].vl, mu]
407                    + I/2  vlbar.Ga[nu].covdelN[vl, mu] - 1/4 I del[vlbar.Ga[mu].vl, nu]                   
408                    + I/2  lbar.Ga[mu].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].l, mu]
409                    + I/2  lbar.Ga[nu].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].l, nu])  )
410
411                + ee/sw/2/Sqrt[2] ((-kq)(uqbar.Ga[mu].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[nu]
412                              + uqbar.Ga[nu].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].ProjM.HC[CKM].uq Wbar[mu])
413                              + (-kl)(vlbar.Ga[mu].ProjM.l W[nu] + lbar.Ga[mu].ProjM.vl Wbar[nu]
414                              + vlbar.Ga[nu].ProjM.l W[mu] + lbar.Ga[nu].ProjM.vl Wbar[mu])));
415
416TFAxial[mu_,nu_] := (-ME[mu,nu] ((-kq)(I uqbar.(Ga[rho].Ga[5].covdelU[uq, rho]) -1/2 del[I uqbar.Ga[rho].Ga[5].uq, rho]
417                          + I dqbar.(Ga[rho].Ga[5].covdelD[dq, rho]) -1/2 del[I dqbar.Ga[rho].Ga[5].dq, rho])
418                          + (-kl)( I vtbar.(Ga[rho].Ga[5].covdelN[vt, rho]) -1/2 del[I vtbar.Ga[rho].Ga[5].vt, rho]
419                          + I lbar.(Ga[rho].Ga[5].covdelE[l, rho]  ) -1/2 del[I lbar.Ga[rho].Ga[5].l, rho])
420                         
421                          + ee/sw/Sqrt[2] (-kq uqbar.Ga[rho].Ga[5].ProjM.CKM.dq W[rho] + (-kq) dqbar.Ga[rho].Ga[5].ProjM.HC[CKM].uq Wbar[rho]
422                                         + (-kl) vtbar.Ga[rho].Ga[5].ProjM.l W[rho] + (-kl) lbar.Ga[rho].Ga[5].ProjM.vt Wbar[rho]) )
423               + ((-kq)(I/2  uqbar.Ga[mu].Ga[5].covdelU[uq, nu] - 1/4 I del[uqbar.Ga[nu].Ga[5].uq, mu]
424                    + I/2  uqbar.Ga[nu].Ga[5].covdelU[uq, mu] - 1/4 I del[uqbar.Ga[mu].Ga[5].uq, nu]                   
425                    + I/2  dqbar.Ga[mu].Ga[5].covdelD[dq, nu] - 1/4 I del[dqbar.Ga[nu].Ga[5].dq, mu]
426                    + I/2  dqbar.Ga[nu].Ga[5].covdelD[dq, mu] - 1/4 I del[dqbar.Ga[mu].Ga[5].dq, nu])
427                    + (-kl) (I/2  vtbar.Ga[mu].Ga[5].covdelN[vt, nu] - 1/4 I del[vtbar.Ga[nu].Ga[5].vt, mu]
428                    + I/2  vtbar.Ga[nu].Ga[5].covdelN[vt, mu] - 1/4 I del[vtbar.Ga[mu].Ga[5].vt, nu]                   
429                    + I/2  lbar.Ga[mu].Ga[5].covdelE[l, nu] - 1/4 I del[lbar.Ga[nu].Ga[5].l, mu]
430                    + I/2  lbar.Ga[nu].Ga[5].covdelE[l, mu] - 1/4 I del[lbar.Ga[mu].Ga[5].l, nu]))
431
432                + ee/sw/2/Sqrt[2] ((-kq) (uqbar.Ga[mu].Ga[5].ProjM.CKM.dq W[nu] + dqbar.Ga[mu].Ga[5].ProjM.HC[CKM].uq Wbar[nu]
433                              + uqbar.Ga[nu].Ga[5].ProjM.CKM.dq W[mu] + dqbar.Ga[nu].Ga[5].ProjM.HC[CKM].uq Wbar[mu])
434                              +(-kl) (vtbar.Ga[mu].Ga[5].ProjM.l W[nu] + lbar.Ga[mu].Ga[5].ProjM.vt Wbar[nu]
435                              + vtbar.Ga[nu].Ga[5].ProjM.l W[mu] + lbar.Ga[nu].Ga[5].ProjM.vt Wbar[mu])));
436
437
438(* Definitions for Higgs and Yukawa *)
439 
440TH[mu_, nu_]  := Block[{ii,mu, feynmangaugerules},
441  feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
442 
443  ExpandIndices[-ME[mu,nu].(DC[PhiHbar[ii],rho] DC[PhiH[ii],rho])+DC[PhiHbar[ii],mu] DC[PhiH[ii],nu]+DC[PhiHbar[ii],nu] DC[PhiH[ii],mu], FlavorExpand->{SU2D,SU2W}]/.feynmangaugerules
444 ];
445
446(* Yukawa *)
447
448TYuk := Block[{sp,ii,jj,cc,ff1,ff2,ff3,yuk,feynmangaugerules},
449  feynmangaugerules = If[Not[FeynmanGauge], {G0|GP|GPbar ->0}, {}];
450 
451  yuk = ExpandIndices[
452   -yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] PhiH[ii] -
453    yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] PhiH[ii] -
454    yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] PhiHbar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
455  yuk = yuk /. { CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
456  yuk+HC[yuk]/.feynmangaugerules
457 ];
458
459TY[mu_,nu_] := -ME[mu,nu](TYuk + HC[TYuk]);
460
461
462(* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators and unitary gauge for massive gauge boson propagators. *)
463
464TGF[mu_, nu_]:= (-ME[mu,nu].( (-kg)del[del[G[sig, a1], sig], rho].G[rho, a1] + (-ka)del[del[A[sig], sig], rho].A[rho] +
465                                1/2 (-kg)del[G[rho, a1], rho].del[G[rho, a1], rho] + 1/2 (-ka)del[A[rho], rho].del[A[rho], rho])
466                        + ((-kg)del[del[G[rho, a1], rho], mu].G[nu, a1] + (-ka)del[del[A[rho], rho], mu].A[nu] +(-kg)
467                                                   del[del[G[rho, a1], rho], nu].G[mu, a1] + (-ka)del[del[A[rho], rho], nu].A[mu] ));
468
469(*******************************  Writing the lagrangian *********************************)
470
471LagG := 1/Lambda (X2[mu,nu] (TG[mu,nu] + TGF[mu,nu])); (*ka,kg,kv are defined with TG[mu,nu]*)
472LagF := 1/Lambda(X2[mu,nu] TF[mu,nu]);
473LagHY := -kq/Lambda(X2[mu,nu] TY[mu,nu]) -kv/Lambda(X2[mu,nu] TH[mu,nu]);
474LagRS := LagG + LagF + LagHY;
475
476(********** Beta implementation of the 2+ (higher dimensional) and 2- resonance ***********)
477
478TA2m[mu_, nu_] := (-del[del[(-1/4 FA[rho, sig] FA[rho, sig]), mu], nu]);
479TA2mAxial[mu_, nu_] := (-del[del[(-1/8 FA[rho, sig] Eps[rho, sig, alpha, beta] FA[alpha, beta]), mu], nu]);
480
481TW2m[mu_, nu_] := (-del[del[(-1/4 FW[rho, sig, i1, i2, i3] FW[rho, sig, i1, i4, i5]), mu], nu]);
482TW2mAxial[mu_, nu_] := (-del[del[(-1/8 FW[rho, sig, i1, i2, i3] Eps[rho, sig, alpha, beta] FW[alpha, beta, i1, i4, i5]), mu], nu]);
483
484TG2m[mu_, nu_] := (-del[del[(-1/4 FG[rho, sig, a1, a2, a3] FG[rho, sig, a1, a4, a5]),mu],nu]);
485TG2mAxial[mu_, nu_] := (-del[del[(-1/8 FG[rho, sig, a1, a2, a3] Eps[rho, sig, alpha, beta] FG[alpha, beta, a1, a4, a5]), mu], nu]);
486
487LG2m := X2[mu,nu] (-ka2/Lambda^3 TA2mAxial[mu,nu] -kv2/Lambda^3 TW2mAxial[mu,nu] -kg2/Lambda^3 TG2mAxial[mu,nu]);
488LGHD := X2[mu,nu] (-ka1/Lambda^3 TA2m[mu,nu] -kv1/Lambda^3 TW2m[mu,nu] -kg1/Lambda^3 TG2m[mu,nu]);
489
490(*****************************************************************************************)
491(* Spin-1 - vector and pseudo-vector *****************************************************)
492(*****************************************************************************************)
493               
494(* Defining one arbitrary coupling of the spin-1 with W+ W- *)
495
496                LBprightPsVec =
497                        kfbu bfu X1[mu] uqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjP[x,r].uq[r,n,i] +
498                        kfbd bfd X1[mu] dqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjP[x,r].dq[r,n,i];
499       
500                LBpleftPsVec =
501                        kfbu bfu X1[mu] uqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjM[x,r].uq[r,n,i] +
502                        kfbd bfd X1[mu] dqbar[s,n,i].Ga[mu,s,v].Ga[5,v,x].ProjM[x,r].dq[r,n,i];
503
504                LBprightVec =
505                        kfau afu X1[mu] uqbar[s,n,i].Ga[mu,s,v].ProjP[v,r].uq[r,n,i] +
506                        kfad afd X1[mu] dqbar[s,n,i].Ga[mu,s,v].ProjP[v,r].dq[r,n,i];
507       
508                LBpleftVec =
509                        kfau afu X1[mu] uqbar[s,n,i].Ga[mu,s,v].ProjM[v,r].uq[r,n,i] +
510                        kfad afd X1[mu] dqbar[s,n,i].Ga[mu,s,v].ProjM[v,r].dq[r,n,i];
511
512
513LF= LBprightVec + LBpleftVec + LBprightPsVec + LBpleftPsVec;
514 
515
516LWW=( I kv1 gwwz(del[Wbar[nu], mu] - del[Wbar[mu], nu]) W[mu] X1[nu] - I kv1 gwwz Wbar[mu] X1[nu] (del[W[nu], mu] - del[W[mu], nu])
517    +I kv2 gwwz Wbar[mu]W[nu]FS[X1,mu,nu]
518        -kv3 Wbar[mu]W[nu](del[X1[nu],mu]+del[X1[mu],nu])
519        -kv5 Eps[mu,nu,rho,sig](Wbar[mu]del[W[nu],rho]-del[Wbar[mu],rho]W[nu])X1[sig]
520        +I kv4 Wbar[mu]W[nu](1/2)Eps[mu,nu,rho,sig](del[X1[sig],rho]-del[X1[rho],sig])
521);
522LZZ= -kv3 X1[mu]del[Z[mu],nu]Z[nu]- kv5 Eps[mu,nu,rho,sig]X1[mu]Z[nu]del[Z[sig],rho];
523
524(* LWW and LZZ based on the reference: K.Hagiwara et al, Nucl. Phys. B282 (1987) 253-307 *)
525(*****************************************************************************************)
526
527Ltot:= LSM + LF +LagRS + LG0 + LWW + LZZ + LGHD + LG2m;
528