DMsimp: dm_s_spin2.fr

File dm_s_spin2.fr, 10.6 KB (added by mawatari, 3 years ago)

Main FR model file for spin2 v1.1

Line 
1(* **************************************************************************** *)
2(* *****                                                                  ***** *)
3(* *****  FeynRules model file: Simplified DM models                      ***** *)
4(* *****                        with an s-channel spin-2 mediator         ***** *)
5(* *****  Author: G. Das, C. Degrande, V. Hirschi, F. Maltoni and H. Shao ***** *)
6(* *****          K. Mawatari                                             ***** *)
7(* *****                                                                  ***** *)
8(* **************************************************************************** *)
9
10
11(* ************************** *)
12(* *****  Information   ***** *)
13(* ************************** *)
14M$ModelName = "DMsimp_s_spin2";
15
16M$Information = {
17 Authors      -> {"G. Das, C. Degrande, V. Hirschi, F. Maltoni, H. Shao, K. Mawatari"},
18 Institutions -> {"Saha Institute of Nuclear Physics, Durham University, Universite catholique de Louvain, CERN, LPSC Grenoble"},
19 Emails       -> {"celine.degrande@durham.ac.uk","goutam.das@saha.ac.in", "kentarou.mawatari@lpsc.in2p3.fr"},
20 URLs         -> "http://feynrules.irmp.ucl.ac.be/wiki/DMsimp/", 
21 References   -> {"G. Das et al., arXiv:1605.09359","S. Kraml et al., arXiv:1701.07008"},
22 Version      -> "1.1",
23 Date         -> "01.02.2017"
24};
25
26(* ************************** *)
27(* *****  Change  log   ***** *)
28(* ************************** *)
29
30(* 01.06.2016 v1.0 - release version. *)
31(* 01.02.2017 v1.1 - added Xc and Xv. *)
32
33
34(***** Setting for interaction order (as e.g. used by MadGraph 5)  ******)
35
36M$InteractionOrderLimit = {
37 {DMT, 2}
38};
39
40M$InteractionOrderHierarchy = {
41 {QCD, 1}, {DMT, 2}, {QED, 2}
42};
43
44
45(* ************************** *)
46(* *****     Fields     ***** *)
47(* ************************** *)
48M$ClassesDescription = {
49
50S[7] == { ClassName -> Xr,
51          SelfConjugate -> True,
52          Mass -> {MXr, 10.},
53          Width -> 0,
54          PDG -> 5000511,
55          Tex -> Subscript[X,r],
56          FullName -> "Real scalar DM" },
57
58F[7] == { ClassName -> Xd,
59          SelfConjugate -> False,
60          Mass -> {MXd, 10.},
61          Width -> 0,
62          PDG -> 5000521,
63          TeX -> Subscript[X,d],
64          FullName -> "Dirac DM" },
65
66V[7] == { ClassName -> Xv,
67          SelfConjugate -> True,
68          Mass -> {MXv, 10.},
69          Width -> 0,
70          PDG -> 5000531,
71          Tex -> Subscript[X,v],
72          FullNme -> "Vector DM" },
73
74T[1] == { ClassName -> Y2,
75          SelfConjugate -> True,
76          Symmetric -> True,
77          Mass -> {MY2, 1000.},
78          Width -> {WY2, 10.},
79          PDG -> 5000002,
80          TeX -> Subscript[Y,2],
81          FullName -> "Spin-2 mediator" }
82
83};
84
85
86(* ************************** *)
87(* *****   Parameters   ***** *)
88(* ************************** *) 
89M$Parameters = {
90
91 Lambda == { ParameterType -> External,
92             BlockName -> DMINPUTS,
93             TeX -> \[CapitalLambda],
94             Description -> "cut-off scale",
95             Value -> 1000.0},
96
97 gTg == {
98      ParameterType -> External,
99      InteractionOrder -> {DMT, 1},
100      BlockName -> DMINPUTS,
101      TeX -> Subscript[gT,g],
102      Description -> "g-Y2  coupling",
103      Value -> 1. },
104
105 gTw == {
106      ParameterType -> External,
107      InteractionOrder -> {DMT, 1},
108      BlockName -> DMINPUTS,
109      TeX -> Subscript[gT,W],
110      Description -> "W-Y2  coupling",
111      Value -> 1. },
112
113 gTb == {
114      ParameterType -> External,
115      InteractionOrder -> {DMT, 1},
116      BlockName -> DMINPUTS,
117      TeX -> Subscript[gT,B],
118      Description -> "B-Y2  coupling",
119      Value -> 1. },
120
121 gTq == {
122      ParameterType -> External,
123      InteractionOrder -> {DMT, 1},
124      BlockName -> DMINPUTS,
125      TeX -> Subscript[gT,q],
126      Description -> "q-Y2  coupling",
127      Value -> 1. },
128
129 gTq3 == {
130      ParameterType -> External,
131      InteractionOrder -> {DMT, 1},
132      BlockName -> DMINPUTS,
133      TeX -> Subscript[gT,q3],
134      Description -> "t-Y2  coupling",
135      Value -> 1. },
136
137 gTl == {
138      ParameterType -> External,
139      InteractionOrder -> {DMT, 1},
140      BlockName -> DMINPUTS,
141      TeX -> Subscript[gT,l],
142      Description -> "l-Y2  coupling",
143      Value -> 1. },
144     
145 gTh == {
146      ParameterType -> External,
147      InteractionOrder -> {DMT, 1},
148      BlockName -> DMINPUTS,
149      TeX -> Subscript[gT,h],
150      Description -> "h-Y2  coupling",
151      Value -> 1. },
152     
153 gTXr == {
154      ParameterType -> External,
155      InteractionOrder -> {DMT, 1},
156      BlockName -> DMINPUTS,
157      TeX -> Subscript[gT,Xr],
158      Description -> "Xr-Y2  coupling",
159      Value -> 0. },
160
161 gTXd == {
162      ParameterType -> External,
163      InteractionOrder -> {DMT, 1},
164      BlockName -> DMINPUTS,
165      TeX -> Subscript[gT,Xd],
166      Description -> "Xd-Y2  coupling",
167      Value -> 1. },
168
169 gTXv == {
170      ParameterType -> External,
171      InteractionOrder -> {DMT, 1},
172      BlockName -> DMINPUTS,
173      TeX -> Subscript[gT,Xv],
174      Description -> "Xv-Y2  coupling",
175      Value -> 0. }
176
177};
178
179(****************************************** Spin-2 ***************************************)
180
181(*** Defining the cov derivatives ***)
182
183covdelE[field_, mu_] :=
184  Module[{j, a},  del[field, mu]
185                 + 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]];
186
187covdelN[field_, mu_] :=
188  Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
189
190(*** Defining the energy-momentum tensor T[mu,nu] ***)
191
192(* Fermions *)
193
194TFf[mu_, nu_, ff_] :=   QLbar[ss, ii, ff, cc].Ga[mu, ss, ss1].DC[QL[ss1, ii, ff, cc], nu] -    DC[QLbar[ss, ii, ff, cc], mu].Ga[nu, ss, ss1].QL[ss1, ii, ff, cc] +
195                                  uRbar[ss, ff, cc].Ga[mu, ss, ss1].DC[uR[ss1, ff, cc], nu] - DC[uRbar[ss, ff, cc], mu].Ga[nu, ss, ss1].uR[ss1, ff, cc] +
196                                 dRbar[ss, ff, cc].Ga[mu, ss, ss1].DC[dR[ss1, ff, cc], nu] - DC[dRbar[ss, ff, cc], mu].Ga[nu, ss, ss1].dR[ss1, ff, cc];
197
198
199TFhb[mu_, nu_] :=   QLbar[ss, 2, 3, cc].Ga[mu, ss, ss1].DC[QL[ss1, 2, 3, cc], nu] -
200   DC[QLbar[ss, 2, 3, cc], mu].Ga[nu, ss, ss1].QL[ss1, 2, 3, cc] +
201   dRbar[ss, 3, cc].Ga[mu, ss, ss1].DC[dR[ss1, 3, cc], nu] -
202   DC[dRbar[ss, 3, cc], mu].Ga[nu, ss, ss1].dR[ss1, 3, cc];
203
204TFht[mu_, nu_] :=   QLbar[ss, 1, 3, cc].Ga[mu, ss, ss1].DC[QL[ss1, 1, 3, cc], nu] -
205   DC[QLbar[ss, 1, 3, cc], mu].Ga[nu, ss, ss1].QL[ss1, 1, 3, cc] +
206   uRbar[ss, 3, cc].Ga[mu, ss, ss1].DC[uR[ss1, 3, cc], nu] -
207   DC[uRbar[ss, 3, cc], mu].Ga[nu, ss, ss1].uR[ss1, 3, cc];
208
209TFlq[mu_, nu_] := -ME[mu, nu] I/2 TFf[al, al, 1] + I/4 ( TFf[mu, nu, 1] + TFf[nu, mu, 1]) - ME[mu, nu] I/2 TFf[al, al, 2] + I/4 ( TFf[mu, nu, 2] + TFf[nu, mu, 2])-ME[mu, nu] I/2 TFhb[al, al] + I/4 ( TFhb[mu, nu] + TFhb[nu, mu]);
210
211TFt[mu_, nu_] := -ME[mu, nu] I/2 TFht[al, al] + I/4 ( TFht[mu, nu] + TFht[nu, mu]);
212
213feynmangaugerules =  If[Not[FeynmanGauge], {G0 | GP | GPbar -> 0}, {}];
214yuk =  ExpandIndices[-yd[ff2, 3] CKM[3, ff2] QLbar[sp, ii, 3, cc].dR[sp, 3, cc] Phi[ii] - yu[3, 3] QLbar[sp, ii, 3, cc].uR[sp, 3, cc] Phibar[jj] Eps[ii, jj], FlavorExpand -> SU2D];
215yuk = yuk /. {CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
216
217TYt[mu_, nu_] := -ME[mu, nu] (yuk + HC[yuk] /. feynmangaugerules)
218
219TFlep[mu_, nu_] :=   LLbar[ss, ii, ff].Ga[mu, ss, ss1].DC[LL[ss1, ii, ff], nu] -    DC[LLbar[ss, ii, ff], mu].Ga[nu, ss, ss1].LL[ss1, ii, ff] +
220                                  lRbar[ss, ff].Ga[mu, ss, ss1].DC[lR[ss1, ff], nu] - DC[lRbar[ss, ff], mu].Ga[nu, ss, ss1].lR[ss1, ff] ;
221
222TFl[mu_, nu_] := -ME[mu, nu] I/2 TFlep[al, al] + I/4 ( TFlep[mu, nu] + TFlep[nu, mu]);
223
224TYl[mu_,nu_] := -ME[mu,nu] ( - MTA tabar.ta );
225
226(* Higgs *)
227
228Tscalar[mu_, nu_] := (2 DC[Phibar[ii], mu] DC[Phi[ii], nu]) - ME[mu, nu] (DC[Phibar[ii], rho] DC[Phi[ii], rho] + muH^2 Phibar[ii] Phi[ii] - lam Phibar[ii] Phi[ii] Phibar[jj] Phi[jj])
229
230(* Gauge bosons *)
231
232TGg[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];
233(*new lag for he weak sector before EWSB*)
234(*Careful to check the gauge fixing term coefficient*)
235TGB[mu_,nu_] := -ME[mu,nu](-1/4 FS[B,rho,sig]FS[B,rho,sig])-FS[B,mu,rho]FS[B,nu,rho];
236TGW[mu_,nu_] := -ME[mu,nu](-1/4 FS[Wi,rho,sig,ii]FS[Wi,rho,sig,ii])-FS[Wi,mu,rho,ii]FS[Wi,nu,rho,ii];
237
238
239(* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators *)
240(* and unitary gauge for massive gauge boson propagators. *)
241
242TGFg[mu_,nu_]:= -ME[mu,nu].( del[del[G[sig, a1], sig], rho].G[rho, a1] +
243                             1/2 del[G[rho, a1], rho].del[G[sig, a1], sig] ) +
244                 del[del[G[rho, a1], rho], mu].G[nu, a1] + del[del[G[rho, a1], rho], nu].G[mu, a1];
245
246TGFa[mu_,nu_]:= -ME[mu,nu].( del[del[A[sig], sig], rho].A[rho] +
247                             1/2 del[A[rho], rho].del[A[sig], sig] ) +
248                 del[del[A[rho], rho], mu].A[nu] + del[del[A[rho], rho], nu].A[mu];
249
250(** Ghost **)
251
252(*TGhost[mu_,nu_] := ( -ME[mu,nu].(DC[ghGbar,rho] DC[ghG,rho]) +
253                       DC[ghGbar,mu] DC[ghG,nu] + DC[ghGbar,nu] DC[ghG,mu] ); *)
254
255LQCDGhs = -ghGbar[ii].del[DC[ghG[ii], mu], mu];
256TGhost[mu_,nu_] := -ME[mu,nu](ExpandIndices[ LQCDGhs , FlavorExpand->SU2W]) + ( del[ghGbar[a], mu].(del[ghG[a], nu] - gs f[a,b,c] G[nu,c] ghG[b] ) +   del[ghGbar[a], nu].(del[ghG[a], mu] - gs f[a,b,c] G[mu,c] ghG[b] )     );
257
258
259(*** Writing the lagrangian ***)
260
261L2f := -1/Lambda (gTq  TFlq[mu, nu] + gTq3 (TFt[mu, nu] + TYt[mu, nu]) +    gTl (TFl[mu, nu] + TYl[mu, nu])) Y2[mu, nu]
262L2v := -1/Lambda ExpandIndices[ ( gTg (TGg[mu,nu]+TGFg[mu,nu]) + gTw TGW[mu,nu] + gTb TGB[mu,nu] + (gTb cw^2 + gTw sw^2) TGFa[mu,nu]) Y2[mu,nu],FlavorExpand->True];
263L2gh := -1/Lambda (gTg TGhost[mu,nu]              ) Y2[mu,nu];
264L2H  := -1/Lambda ExpandIndices[(gTh Tscalar[mu,nu]              )Y2[mu,nu],FlavorExpand->True] /. feynmangaugerules;
265
266(*** Writing the lagrangian ***)
267
268L2SM := L2f + L2v + L2gh + L2H;
269
270
271(**** DM sector ***)
272(* Real Scalars: r *)
273TSrX[mu_,nu_] := -1/2 ME[mu,nu] (del[Xr, rho] del[Xr, rho] - MXr MXr Xr Xr ) +
274                  del[Xr, mu] del[Xr, nu];
275
276L2rX := -1/Lambda ( gTXr TSrX[mu,nu] Y2[mu,nu] );
277
278(* Fermions: q *)
279TFqX[mu_,nu_] := -ME[mu,nu] I Xdbar.(Ga[rho].del[Xd, rho]) +
280                  1/2 ME[mu,nu] del[I Xdbar.Ga[rho].Xd, rho] +
281                  I/2  Xdbar.Ga[mu].del[Xd, nu] - 1/4 I del[Xdbar.Ga[nu].Xd, mu] +
282                  I/2  Xdbar.Ga[nu].del[Xd, mu] - 1/4 I del[Xdbar.Ga[mu].Xd, nu];
283TYqX[mu_,nu_] := -ME[mu,nu] ( - MXd Xdbar.Xd );
284
285L2fX := -1/Lambda ( gTXd (TFqX[mu,nu] + TYqX[mu,nu]) ) Y2[mu,nu]; 
286
287(* Vectors: v *)
288TVvX[mu_,nu_] := -ME[mu,nu] ( -1/4 FS[Xv,sig,rho] FS[Xv,sig,rho] +
289                              +1/2 MXv MXv Xv[rho] Xv[rho] ) +             
290                  FS[Xv,mu,rho] FS[Xv,rho,nu] +
291                  MXv MXv Xv[mu] Xv[nu];
292
293L2vX := -1/Lambda ( gTXv TVvX[mu,nu] Y2[mu,nu] );
294               
295
296L2DM := L2rX + L2fX + L2vX + L2SM;