TypeIISeesaw: type_ii_v1.3.fr

File type_ii_v1.3.fr, 12.2 KB (added by MihaNemevsek, 7 months ago)

FeynRules Type II Seesaw model file with internal mD0

Line 
1(* ****************************************************************** *)
2(* *****                                                        ***** *)
3(* *****  FeynRules model file supplementing the reduced SM     ***** *)
4(* *****  with a type-II see-saw                                ***** *)
5(* *****                                                        ***** *)
6(* *****  Authors: Benjamin Fuks, Miha Nemevsek                 ***** *)
7(* *****                                                        ***** *)
8(* ****************************************************************** *)
9
10(* ************************** *)
11(* *****      Setup     ***** *)
12(* ************************** *)
13M$ModelName   = "TypeIISeesaw";
14M$Information = { Authors -> {"B. Fuks", "M.Nemevsek"}, Version -> "1.3", Date -> "25.11.2019" };
15FeynmanGauge  = True;
16
17
18(* ************************** *)
19(* *****  Change  log   ***** *)
20(* ************************** *)
21
22(* 25.09.19 - v1.0: first version                                                   *)
23(* 24.10.19 - v1.1: All scalar masses external.                                     *)
24(*                  Mixing relations are now exact.                                 *)
25(* 18.11.19 - v1.2: Changing the name of the LH block for vevD (cannot be vevd too) *)
26(* 25.11.19 - v1.3: mh, mDpp, mDp and lam_{D1,D2,hD1} are inputs, mD0, mchiD,
27                    lam_{hD2} and the mixings are outputs *)
28
29
30(* ************************** *)
31(* **** Particle classes **** *)
32(* ************************** *)
33M$ClassesDescription = {
34(* Fermions: physical fields *)
35  F[1] == {
36    ClassName -> vi, ClassMembers -> {v1,v2,v3}, Indices -> {Index[Generation]}, FlavorIndex -> Generation,
37    SelfConjugate -> True, Mass -> {Mvi, {Mv1, 0.05*^-9}, {Mv2, Internal}, {Mv3, Internal} }, Width -> 0,
38    PDG -> {12,14,16}
39  },
40
41  (* Fermions: unphysical fields *)
42  F[11] == {
43    ClassName -> LL, Unphysical -> True, Indices -> {Index[SU2D], Index[Generation]}, FlavorIndex -> SU2D,
44    SelfConjugate -> False, QuantumNumbers -> {Y->-1/2},
45    Definitions -> {
46      LL[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNS[ff,ff2] ProjM[sp1,sp2] vi[sp2,ff2]],
47      LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]]
48    }
49  },
50
51  (* Higgs: unphysical scalars  *)
52  S[11] == {
53    ClassName -> Phi, Unphysical -> True, Indices -> {Index[SU2D]}, FlavorIndex -> SU2D,
54    SelfConjugate -> False, QuantumNumbers -> {Y -> 1/2},
55    Definitions -> {
56      Phi[1] -> vev/Sqrt[vev^2+2*vevD^2] GP - Sqrt[2] vevD/Sqrt[vev^2+2*vevD^2] DP,
57      Phi[2] -> 1/Sqrt[2](vev + cxi H - sxi D0 + I vev/Sqrt[vev^2+4*vevD^2] G0 - 2 I vevD/Sqrt[vev^2+4*vevD^2] chi)
58    }
59  },
60  S[12] == {
61    ClassName -> hatD, Unphysical -> True, Indices-> {Index[SU2W]}, FlavorIndex->SU2W,
62    SelfConjugate -> False, QuantumNumbers -> {Y->1},
63    Definitions -> {
64      hatD[1] -> 1/2 (vevD + sxi*H + cxi*D0 + 2 I vevD/Sqrt[vev^2+4*vevD^2] G0 + I vev/Sqrt[vev^2+4*vevD^2] chi) \
65         + 1/Sqrt[2] DPP,
66      hatD[2] -> -I/2 (vevD + sxi*H + cxi*D0 + 2 I vevD/Sqrt[vev^2+4*vevD^2] G0 + I vev/Sqrt[vev^2+4*vevD^2] chi) \
67         + I/Sqrt[2] DPP,
68      hatD[3] -> Sqrt[2] vevD/Sqrt[vev^2+2*vevD^2] GP + vev/Sqrt[vev^2+2*vevD^2] DP
69    }
70  },
71
72  (* Higgs: physical scalars *)
73  S[4] == {
74    ClassName -> D0,  SelfConjugate -> True,  Mass -> {MD0,Internal}, Width -> {WD0, 1.017718*^-5}, PDG -> 44
75  },
76  S[5] == {
77    ClassName -> DP,  SelfConjugate -> False, Mass -> {MDP, 503.}, Width -> {WDP, 1.017090*^-5}, PDG -> 38,
78    ParticleName -> "D+",  AntiParticleName -> "D-",  QuantumNumbers -> {Q->1}
79  },
80  S[6] == {
81    ClassName -> DPP, SelfConjugate -> False, Mass -> {MDPP,502.}, Width -> {WDPP,1.011029*^-5}, PDG -> 61,
82    ParticleName -> "D++", AntiParticleName -> "D--", QuantumNumbers -> {Q->2}
83  },
84  S[7] == {
85    ClassName -> chi, SelfConjugate -> True,  Mass -> {Mchi,Internal}, Width -> {Wchi,1.017817*^-5}, PDG -> 62
86  }
87};
88
89
90(* ************************** *)
91(* *****   Parameters   ***** *)
92(* ************************** *)
93M$Parameters = {
94  (* PMNS matrix *)
95  th12 == {
96    ParameterType -> External, Value -> 0.59, TeX -> Subscript[\[Theta], 12],
97    BlockName -> PMNS, OrderBlock -> 1, Description -> "Solar mixing angle - theta12"
98  },
99  th23 == {
100    ParameterType -> External, Value -> 0.87, TeX -> Subscript[\[Theta], 23],
101    BlockName -> PMNS, OrderBlock -> 2, Description -> "Atmospheric mixing angle - theta23"
102  },
103  th13 == {
104    ParameterType -> External, Value -> 0.15, TeX -> Subscript[\[Theta], 13],
105    BlockName -> PMNS, OrderBlock -> 3, Description -> "Reactor mixing angle - theta_13"
106  },
107  delCP == {
108    ParameterType -> External, Value -> 0 (* 3.8 *), TeX -> Subscript[\[Delta], CP],
109    BlockName -> PMNS, OrderBlock -> 4, Description -> "Leptonic Dirac CP phase"
110  },
111  phiM1 == {
112    ParameterType -> External, Value -> 0.0, TeX -> Subscript[\[Phi], 1],
113    BlockName -> PMNS, OrderBlock -> 5, Description -> "1st Majorana CP phase"
114  },
115  phiM2 == {
116    ParameterType -> External, Value -> 0.0, TeX -> Subscript[\[Phi], 2],
117    BlockName -> PMNS, OrderBlock -> 6, Description -> "2nd Majorana CP phase"
118  },
119
120  (* Neutrino mass differences *)
121  dmsq21 == {
122    ParameterType -> External, Value -> 7.39*^-23, TeX -> Subsuperscript["\[CapitalDelta]m",21,2],
123    BlockName -> MNU, OrderBlock -> 2, Description -> "Solar mass splitting squared"
124  },
125  dmsq31 == {
126    ParameterType -> External, Value -> 2.5*^-21, TeX -> Subsuperscript["\[CapitalDelta]m",31,2],
127    BlockName -> MNU, OrderBlock -> 3, Description -> "Atmospheric mass splitting squared"
128  },
129
130  (* PMNS mixing matrix defined from oscillation data *)
131  PMNS == {
132    ParameterType -> Internal, Indices -> {Index[Generation],Index[Generation]}, TeX -> Superscript[V, PMNS],
133    ComplexParameter -> True,
134    Value -> {
135        PMNS[1,1] ->  Cos[th12]*Cos[th13],
136        PMNS[1,2] ->  Cos[th13]*Sin[th12]*Exp[I/2 phiM1],
137        PMNS[1,3] ->  Sin[th13]*Exp[I (phiM2/2 - delCP)],
138        PMNS[2,1] -> -Cos[th23]*Sin[th12] - Cos[th12]*Sin[th13]*Sin[th23]*Exp[I delCP],
139        PMNS[2,2] ->  (Cos[th12]*Cos[th23] - Sin[th12]*Sin[th13]*Sin[th23]*Exp[I delCP])*Exp[I/2 phiM1],
140        PMNS[2,3] ->  Cos[th13]*Sin[th23]*Exp[I/2 phiM2],
141        PMNS[3,1] ->  Sin[th12]*Sin[th23] - Cos[th12]*Cos[th23]*Sin[th13]*Exp[I delCP],
142        PMNS[3,2] ->  (-Cos[th23]*Sin[th12]*Sin[th13]*Exp[I delCP] - Cos[th12]*Sin[th23])*Exp[I/2 phiM1],
143        PMNS[3,3] -> Cos[th13]*Cos[th23]*Exp[I/2 phiM2]
144    }
145  },
146
147  (* Higgs sector: external parameters *)
148  lamHD1 == {
149    ParameterType -> External, Value -> 0.10, InteractionOrder -> {QED,2},
150    BlockName -> QUARTICS, OrderBlock -> 1, TeX -> Subscript[\[Lambda], "h\[CapitalDelta]1"]
151  },
152  lamD1 == {
153    ParameterType -> External, Value -> 0.11, InteractionOrder -> {QED,2},
154    BlockName -> QUARTICS, OrderBlock -> 2, TeX  -> Subscript[\[Lambda], "\[CapitalDelta]1"]
155  },
156  lamD2 == {
157    ParameterType -> External, Value -> 0.15, InteractionOrder -> {QED,2},
158    BlockName -> QUARTICS, OrderBlock -> 2, TeX  -> Subscript[\[Lambda], "\[CapitalDelta]1"]
159  },
160  vevD == {
161    ParameterType -> External,  Value -> 1.0*^-7, InteractionOrder -> {QED,-1},
162    BlockName -> VEVDELTA, OrderBlock -> 1, TeX -> Subscript[v,\[CapitalDelta]]
163  },
164  (* Neutrino masses and Yukawas *)
165  Mv2 == { ParameterType -> Internal, Value -> Sqrt[Mv1^2 + dmsq21], TeX -> Subscript[m, "\[Nu]2"] },
166  Mv3 == { ParameterType -> Internal, Value -> Sqrt[Mv1^2 + dmsq31], TeX -> Subscript[m, "\[Nu]3"] },
167  yDL == {
168    ParameterType -> Internal, Indices -> {Index[Generation], Index[Generation]},
169    InteractionOrder -> {QED, 1}, TeX -> Subscript[Y, \[CapitalDelta]], ComplexParameter -> True,
170    Value               -> {
171      yDL[1,1] -> Conjugate[PMNS[1,1]*PMNS[1,1]*Mv1+PMNS[1,2]*PMNS[1,2]*Mv2+PMNS[1,3]*PMNS[1,3]*Mv3]/(Sqrt[2]*vevD),
172      yDL[1,2] -> Conjugate[PMNS[1,1]*PMNS[2,1]*Mv1+PMNS[1,2]*PMNS[2,2]*Mv2+PMNS[1,3]*PMNS[2,3]*Mv3]/(Sqrt[2]*vevD),
173      yDL[1,3] -> Conjugate[PMNS[1,1]*PMNS[3,1]*Mv1+PMNS[1,2]*PMNS[3,2]*Mv2+PMNS[1,3]*PMNS[3,3]*Mv3]/(Sqrt[2]*vevD),
174
175      yDL[2,1] -> Conjugate[PMNS[2,1]*PMNS[1,1]*Mv1+PMNS[2,2]*PMNS[1,2]*Mv2+PMNS[2,3]*PMNS[1,3]*Mv3]/(Sqrt[2]*vevD),
176      yDL[2,2] -> Conjugate[PMNS[2,1]*PMNS[2,1]*Mv1+PMNS[2,2]*PMNS[2,2]*Mv2+PMNS[2,3]*PMNS[2,3]*Mv3]/(Sqrt[2]*vevD),
177      yDL[2,3] -> Conjugate[PMNS[2,1]*PMNS[3,1]*Mv1+PMNS[2,2]*PMNS[3,2]*Mv2+PMNS[2,3]*PMNS[3,3]*Mv3]/(Sqrt[2]*vevD),
178
179      yDL[3,1] -> Conjugate[PMNS[3,1]*PMNS[1,1]*Mv1+PMNS[3,2]*PMNS[1,2]*Mv2+PMNS[3,3]*PMNS[1,3]*Mv3]/(Sqrt[2]*vevD),
180      yDL[3,2] -> Conjugate[PMNS[3,1]*PMNS[2,1]*Mv1+PMNS[3,2]*PMNS[2,2]*Mv2+PMNS[3,3]*PMNS[2,3]*Mv3]/(Sqrt[2]*vevD),
181      yDL[3,3] -> Conjugate[PMNS[3,1]*PMNS[3,1]*Mv1+PMNS[3,2]*PMNS[3,2]*Mv2+PMNS[3,3]*PMNS[3,3]*Mv3]/(Sqrt[2]*vevD)
182    }
183  },
184
185  (* Higgs sector: internal parameters *)
186
187  mD2  == {
188   ParameterType -> Internal,
189   TeX -> Subsuperscript[m,\[CapitalDelta],2],
190   Value -> MDPP^2 - (lamhD1*vev^2)/2 - lamD1*vevD^2
191  },
192
193  lamHD2 == {
194   ParameterType -> Internal,
195   TeX -> Subscript[ \[Lambda], "h\[CapitalDelta]2"],
196   InteractionOrder -> {QED,2},
197   Value -> (4*(-MDPP^2 - lamD2*vevD^2 + MDP^2/(1 + (2*vevD^2)/vev^2)))/vev^2
198  },
199
200  lamH == {
201   ParameterType -> Internal,
202   TeX -> Subscript[\[Lambda],h],
203   InteractionOrder -> {QED,2},
204   Value -> (2*mD2*MH^2 - 2*MH^4 + (8*vevD^2*(mD2 + (lamD1 + lamD2)*vevD^2)^2)/vev^2 +
205  MH^2*vev^2*(lamhD1 + lamhD2 + (6*(lamD1 + lamD2)*vevD^2)/vev^2))/
206 (2*vev^2*(2*mD2 - 2*MH^2 + vev^2*(lamhD1 + lamhD2 + (6*(lamD1 + lamD2)*vevD^2)/vev^2)))
207  },
208
209  MD0 == {
210   ParameterType -> Internal,
211   TeX -> Subscript[M,Superscript[\[CapitalDelta],0]],
212   Value -> Sqrt[-((4*mD2^2*(1 + (4*vevD^2)/vev^2) + 4*mD2*vev^2*(lamhD1 + lamhD2 +
213      (2*(lamD1 + lamD2)*vevD^2*(3 + (4*vevD^2)/vev^2))/vev^2) +
214    vev^4*((lamhD1 + lamhD2)^2 + (12*(lamD1 + lamD2)*(lamhD1 + lamhD2)*vevD^2)/vev^2 +
215      (4*(lamD1 + lamD2)^2*vevD^4*(9 + (4*vevD^2)/vev^2))/vev^4) -
216    2*MH^2*(2*mD2 + vev^2*(lamhD1 + lamhD2 + (6*(lamD1 + lamD2)*vevD^2)/vev^2)))/
217   (-4*mD2 + 4*MH^2 - 2*vev^2*(lamhD1 + lamhD2 + (6*(lamD1 + lamD2)*vevD^2)/vev^2)))]
218  },
219
220  Mchi == {
221   ParameterType -> Internal,
222   TeX -> Subscript[M,\[Chi]],
223   Value -> Sqrt[(1 + (4*vevD^2)/vev^2)*(2*mD2 + vev^2*(lamhD1 + lamhD2 + (2*(lamD1 + lamD2)*vevD^2)/
224       vev^2))]/Sqrt[2]
225  },
226
227  muHD == {
228   ParameterType -> Internal,
229   TeX -> Subscript[\[Mu], "h\[CapitalDelta]"],
230   InteractionOrder -> {QED,2},
231   Value -> -((Sqrt[2]*vevD*(-2*MDP^2 + (MDPP^2 + lamD2*vevD^2)*(1 + (2*vevD^2)/vev^2)))/
232  (vev*(vev + (2*vevD^2)/vev)))
233  },
234
235  muH2 == {
236   ParameterType -> Internal,
237   TeX -> Superscript[Subscript[\[Mu],H],2],
238   Value -> lamH*vev^2 - (vevD^2*(4*mD2 + vev^2*(lamhD1 + lamhD2 + (4*(lamD1 + lamD2)*vevD^2)/vev^2)))/
239(2*vev^2)
240  },
241
242  t2xi == {
243   ParameterType -> Internal,
244   TeX -> Subscript[t,"2\[Xi]"],
245   Value -> (8*vevD*(mD2 + (lamD1 + lamD2)*vevD^2))/
246 (vev*(2*mD2 + vev^2*(-4*lamH + lamhD1 + lamhD2 + (6*(lamD1 + lamD2)*vevD^2)/vev^2)))
247  },
248
249  cxi == {
250    ParameterType -> Internal, TeX -> Subscript[c,\[Xi]],
251    Value -> Cos[1/2 ArcTan[t2xi]]
252  },
253
254  sxi == {
255    ParameterType -> Internal, TeX -> Subscript[s,\[Xi]],
256    Value -> Sin[1/2 ArcTan[t2xi]]
257  }
258};
259
260(* ************************** *)
261(* *****   Lagrangian   ***** *)
262(* ************************** *)
263LScalar := \
264   DC[Phibar[ii],mu] DC[Phi[ii],mu] + DC[hatDbar[ii],mu] DC[hatD[ii],mu] \
265   + muH2 Phibar[ii]  Phi[ii]  \
266   - mD2  hatDbar[ii] hatD[ii] \
267   - lamH Phibar[ii] Phi[ii] Phibar[jj] Phi[jj] \
268   - lamD1 hatDbar[ii] hatD[ii] hatDbar[jj] hatD[jj] \
269   - lamD2 (hatDbar[ii] hatD[ii] hatDbar[jj] hatD[jj] - 1/2 hatDbar[ii] hatD[jj] hatDbar[ii] hatD[jj]) \
270   - lamHD1 Phibar[ii] Phi[ii] hatD[jj] hatDbar[jj] \
271   - lamHD2/2 (hatD[ii] hatDbar[ii] Phibar[jj] Phi[jj] + I Eps[ii,jj,mm] PauliSigma[mm,ip,jp] Phibar[ip] Phi[jp]
272        hatD[ii] hatDbar[jj] )  \
273   + muHD/Sqrt[2] Phibar[ii] hatD[mm] PauliSigma[mm,ii,jj] Phibar[jp] Eps[jj,jp] \
274   + muHD/Sqrt[2] Phi[jj] hatDbar[mm] PauliSigma[mm,ii,jj] Phi[jp] Eps[ii,jp];
275
276LYukawa := Block[{yuk},
277  yuk:=
278   - yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] \
279   - yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] \
280   - Sum[yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj],{ii,2},{jj,2}] \
281   - Sum[yDL[ff1, ff2]/Sqrt[2] Eps[ip,ii] CC[LLbar][sp, ii, ff1].LL[sp, jj, ff2] hatD[mm] PauliSigma[mm,ip,jj],
282       {ii,2},{ip,2},{jj,2},{mm,3}];
283  yuk+HC[yuk]
284 ];
285
286LType2:= {LGauge, LFermions, LScalar, LYukawa, LGhost};
287