Spin2: dm_s_spin2.fr

File dm_s_spin2.fr, 9.4 KB (added by degrande, 16 months ago)
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1(* **************************************************************************** *)
2(* *****                                                                  ***** *)
3(* *****  FeynRules model file: Simplified DM models                      ***** *)
4(* *****                        with a s-channel spin-2 mediator          ***** *)
5(* *****  Author: G. Das, C. Degrande, V. Hirschi, F. Maltoni and H. Shao ***** *)
6(* *****                                                                  ***** *)
7(* **************************************************************************** *)
8
9
10(* ************************** *)
11(* *****  Information   ***** *)
12(* ************************** *)
13M$ModelName = "DMsimp_s_spin2";
14
15M$Information = {
16 Authors      -> {"G. Das, C. Degrande, V. Hirschi, F. Maltoni, H. Shao"},
17 Institutions -> {"Saha Institute of Nuclear Physics, Durham University, Universite catholique de Louvain, CERN"},
18 Emails       -> {"celine.degrande@durham.ac.uk","goutam.das@saha.ac.in"},
19 URLs         -> "http://feynrules.irmp.ucl.ac.be/wiki/DMsimp/", 
20 References   -> {"G. Das et al., arXiv:1605.09359"},
21 Version      -> "1.0",
22 Date         -> "01.06.2016"
23};
24
25(* ************************** *)
26(* *****  Change  log   ***** *)
27(* ************************** *)
28
29(* 01.06.2016 v1.0 - release version. *)
30
31
32(***** Setting for interaction order (as e.g. used by MadGraph 5)  ******)
33
34M$InteractionOrderLimit = {
35 {DMT, 2}
36};
37
38M$InteractionOrderHierarchy = {
39 {QCD, 1}, {DMT, 2}, {QED, 2}
40};
41
42
43(* ************************** *)
44(* *****     Fields     ***** *)
45(* ************************** *)
46M$ClassesDescription = {
47
48F[7] == { ClassName -> Xd,
49          SelfConjugate -> False,
50          Mass -> {MXd, 10.},
51          Width -> 0,
52          PDG -> 5000521,
53          TeX -> Subscript[X,d],
54          FullName -> "Dirac DM" },
55
56T[1] == { ClassName -> Y2,
57          SelfConjugate -> True,
58          Symmetric -> True,
59          Mass -> {MY2, 1000.},
60          Width -> {WY2, 10.},
61          PDG -> 5000002,
62          TeX -> Subscript[Y,2],
63          FullName -> "Spin-2 mediator" }
64
65};
66
67
68(* ************************** *)
69(* *****   Parameters   ***** *)
70(* ************************** *) 
71M$Parameters = {
72
73 Lambda == { ParameterType -> External,
74             BlockName -> DMINPUTS,
75             TeX -> \[CapitalLambda],
76             Description -> "cut-off scale",
77             Value -> 1000.0},
78
79 gTg == {
80      ParameterType -> External,
81      InteractionOrder -> {DMT, 1},
82      BlockName -> DMINPUTS,
83      TeX -> Subscript[gT,g],
84      Description -> "g-Y2  coupling",
85      Value -> 1. },
86
87 gTw == {
88      ParameterType -> External,
89      InteractionOrder -> {DMT, 1},
90      BlockName -> DMINPUTS,
91      TeX -> Subscript[gT,W],
92      Description -> "W-Y2  coupling",
93      Value -> 1. },
94
95 gTb == {
96      ParameterType -> External,
97      InteractionOrder -> {DMT, 1},
98      BlockName -> DMINPUTS,
99      TeX -> Subscript[gT,B],
100      Description -> "B-Y2  coupling",
101      Value -> 1. },
102
103 gTq == {
104      ParameterType -> External,
105      InteractionOrder -> {DMT, 1},
106      BlockName -> DMINPUTS,
107      TeX -> Subscript[gT,q],
108      Description -> "q-Y2  coupling",
109      Value -> 1. },
110
111 gTq3 == {
112      ParameterType -> External,
113      InteractionOrder -> {DMT, 1},
114      BlockName -> DMINPUTS,
115      TeX -> Subscript[gT,q3],
116      Description -> "t-Y2  coupling",
117      Value -> 1. },
118
119 gTl == {
120      ParameterType -> External,
121      InteractionOrder -> {DMT, 1},
122      BlockName -> DMINPUTS,
123      TeX -> Subscript[gT,l],
124      Description -> "l-Y2  coupling",
125      Value -> 1. },
126     
127 gTh == {
128      ParameterType -> External,
129      InteractionOrder -> {DMT, 1},
130      BlockName -> DMINPUTS,
131      TeX -> Subscript[gT,h],
132      Description -> "h-Y2  coupling",
133      Value -> 1. },
134     
135 gTx == {
136      ParameterType -> External,
137      InteractionOrder -> {DMT, 1},
138      BlockName -> DMINPUTS,
139      TeX -> Subscript[gT,x],
140      Description -> "Xd-Y2  coupling",
141      Value -> 1. }       
142
143};
144
145(****************************************** Spin-2 ***************************************)
146
147(*** Defining the cov derivatives ***)
148
149covdelE[field_, mu_] :=
150  Module[{j, a},  del[field, mu]
151                 + 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]];
152
153covdelN[field_, mu_] :=
154  Module[{j, a}, del[field, mu] + I ee/cw B[mu]/2 ProjM.field - I ee/sw/2 ProjM.field Wi[mu,3]];
155
156(*** Defining the energy-momentum tensor T[mu,nu] ***)
157
158(* Fermions *)
159
160TFf[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] +
161                                  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] +
162                                 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];
163
164
165TFhb[mu_, nu_] :=   QLbar[ss, 2, 3, cc].Ga[mu, ss, ss1].DC[QL[ss1, 2, 3, cc], nu] -
166   DC[QLbar[ss, 2, 3, cc], mu].Ga[nu, ss, ss1].QL[ss1, 2, 3, cc] +
167   dRbar[ss, 3, cc].Ga[mu, ss, ss1].DC[dR[ss1, 3, cc], nu] -
168   DC[dRbar[ss, 3, cc], mu].Ga[nu, ss, ss1].dR[ss1, 3, cc];
169
170TFht[mu_, nu_] :=   QLbar[ss, 1, 3, cc].Ga[mu, ss, ss1].DC[QL[ss1, 1, 3, cc], nu] -
171   DC[QLbar[ss, 1, 3, cc], mu].Ga[nu, ss, ss1].QL[ss1, 1, 3, cc] +
172   uRbar[ss, 3, cc].Ga[mu, ss, ss1].DC[uR[ss1, 3, cc], nu] -
173   DC[uRbar[ss, 3, cc], mu].Ga[nu, ss, ss1].uR[ss1, 3, cc];
174
175TFlq[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]);
176
177TFt[mu_, nu_] := -ME[mu, nu] I/2 TFht[al, al] + I/4 ( TFht[mu, nu] + TFht[nu, mu]);
178
179feynmangaugerules =  If[Not[FeynmanGauge], {G0 | GP | GPbar -> 0}, {}];
180yuk =  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];
181yuk = yuk /. {CKM[a_, b_] Conjugate[CKM[a_, c_]] -> IndexDelta[b, c], CKM[b_, a_] Conjugate[CKM[c_, a_]] -> IndexDelta[b, c]};
182
183TYt[mu_, nu_] := -ME[mu, nu] (yuk + HC[yuk] /. feynmangaugerules)
184
185TFlep[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] +
186                                  lRbar[ss, ff].Ga[mu, ss, ss1].DC[lR[ss1, ff], nu] - DC[lRbar[ss, ff], mu].Ga[nu, ss, ss1].lR[ss1, ff] ;
187
188TFl[mu_, nu_] := -ME[mu, nu] I/2 TFlep[al, al] + I/4 ( TFlep[mu, nu] + TFlep[nu, mu]);
189
190
191(* Higgs *)
192
193Tscalar[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])
194
195(* Gauge bosons *)
196
197TGg[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];
198(*new lag for he weak sector before EWSB*)
199(*Careful to check the gauge fixing term coefficient*)
200TGB[mu_,nu_] := -ME[mu,nu](-1/4 FS[B,rho,sig]FS[B,rho,sig])-FS[B,mu,rho]FS[B,nu,rho];
201TGW[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];
202
203
204(* Gauge fixing term is here because Madgraph takes the Feynman gauge for massless gauge boson propagators *)
205(* and unitary gauge for massive gauge boson propagators. *)
206
207TGFg[mu_,nu_]:= -ME[mu,nu].( del[del[G[sig, a1], sig], rho].G[rho, a1] +
208                             1/2 del[G[rho, a1], rho].del[G[sig, a1], sig] ) +
209                 del[del[G[rho, a1], rho], mu].G[nu, a1] + del[del[G[rho, a1], rho], nu].G[mu, a1];
210
211TGFa[mu_,nu_]:= -ME[mu,nu].( del[del[A[sig], sig], rho].A[rho] +
212                             1/2 del[A[rho], rho].del[A[sig], sig] ) +
213                 del[del[A[rho], rho], mu].A[nu] + del[del[A[rho], rho], nu].A[mu];
214
215(** Ghost **)
216
217(*TGhost[mu_,nu_] := ( -ME[mu,nu].(DC[ghGbar,rho] DC[ghG,rho]) +
218                       DC[ghGbar,mu] DC[ghG,nu] + DC[ghGbar,nu] DC[ghG,mu] ); *)
219
220LQCDGhs = -ghGbar[ii].del[DC[ghG[ii], mu], mu];
221TGhost[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] )     );
222
223
224(*** Writing the lagrangian ***)
225
226L2f := -1/Lambda (gTq  TFlq[mu, nu] + gTq3 (TFt[mu, nu] + TYt[mu, nu]) +    gTl (TFl[mu, nu] + TYl[mu, nu])) Y2[mu, nu]
227L2v := -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];
228L2gh := -1/Lambda (gTg TGhost[mu,nu]              ) Y2[mu,nu];
229L2H  := -1/Lambda ExpandIndices[(gTh Tscalar[mu,nu]              )Y2[mu,nu],FlavorExpand->True] /. feynmangaugerules;
230
231(*** Writing the lagrangian ***)
232
233L2SM := L2f + L2v + L2gh + L2H;
234
235
236(**** DM sector ***)
237(* Fermions: q *)
238TFqX[mu_,nu_] := (-ME[mu,nu] ( I Xdbar.(Ga[rho].del[Xd, rho]) -1/2 del[I Xdbar.Ga[rho].Xd, rho]  ) +
239                (    I/2  Xdbar.Ga[mu].del[Xd, nu] - 1/4 I del[Xdbar.Ga[nu].Xd, mu] +
240                     I/2  Xdbar.Ga[nu].del[Xd, mu] - 1/4 I del[Xdbar.Ga[mu].Xd, nu] ));
241TYqX[mu_,nu_] := -ME[mu,nu] ( - MXd Xdbar.Xd );
242
243L2fX := -1/Lambda ( gTx (TFqX[mu,nu] + TYqX[mu,nu]) ) Y2[mu,nu]; 
244
245
246L2DM := L2fX + L2SM;