TypeIISeesaw: type_ii.fr

File type_ii.fr, 13.2 KB (added by BenjF, 3 weeks ago)

version 1.2

Line 
1(* ****************************************************************** *)
2(* *****                                                        ***** *)
3(* *****  FeynRules model file supplementing the reduced SM     ***** *)
4(* *****  with a type-II see-saw                                ***** *)
5(* *****                                                        ***** *)
6(* *****  Author: Benjamin Fuks                                 ***** *)
7(* *****                                                        ***** *)
8(* ****************************************************************** *)
9
10(* ************************** *)
11(* *****      Setup     ***** *)
12(* ************************** *)
13M$ModelName   = "TypeII";
14M$Information = { Authors -> {"B. Fuks"}, Version -> "1.2", Date -> "18.11.2019" };
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
27
28(* ************************** *)
29(* **** Particle classes **** *)
30(* ************************** *)
31M$ClassesDescription = {
32(* Fermions: physical fields *)
33  F[1] == {
34    ClassName -> vi, ClassMembers -> {v1,v2,v3}, Indices -> {Index[Generation]}, FlavorIndex -> Generation,
35    SelfConjugate -> True, Mass -> {Mvi, {Mv1, 0.05*^-9}, {Mv2, Internal}, {Mv3, Internal} }, Width -> 0,
36    PDG -> {12,14,16}
37  },
38
39  (* Fermions: unphysical fields *)
40  F[11] == {
41    ClassName -> LL, Unphysical -> True, Indices -> {Index[SU2D], Index[Generation]}, FlavorIndex -> SU2D,
42    SelfConjugate -> False, QuantumNumbers -> {Y->-1/2},
43    Definitions -> {
44      LL[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNS[ff,ff2] ProjM[sp1,sp2] vi[sp2,ff2]],
45      LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]]
46    }
47  },
48
49  (* Higgs: unphysical scalars  *)
50  S[11] == {
51    ClassName -> Phi, Unphysical -> True, Indices -> {Index[SU2D]}, FlavorIndex -> SU2D,
52    SelfConjugate -> False, QuantumNumbers -> {Y -> 1/2},
53    Definitions -> {
54      Phi[1] -> vev/Sqrt[vev^2+2*vevD^2] GP - Sqrt[2] vevD/Sqrt[vev^2+2*vevD^2] DP,
55      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)
56    }
57  },
58  S[12] == {
59    ClassName -> hatD, Unphysical -> True, Indices-> {Index[SU2W]}, FlavorIndex->SU2W,
60    SelfConjugate -> False, QuantumNumbers -> {Y->1},
61    Definitions -> {
62      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) \
63         + 1/Sqrt[2] DPP,
64      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) \
65         + I/Sqrt[2] DPP,
66      hatD[3] -> Sqrt[2] vevD/Sqrt[vev^2+2*vevD^2] GP + vev/Sqrt[vev^2+2*vevD^2] DP
67    }
68  },
69
70  (* Higgs: physical scalars *)
71  S[4] == {
72    ClassName -> D0,  SelfConjugate -> True,  Mass -> {MD0, 500.}, Width -> {WD0, 1.017718*^-5}, PDG -> 44
73  },
74  S[5] == {
75    ClassName -> DP,  SelfConjugate -> False, Mass -> {MDP, 503.}, Width -> {WDP, 1.017090*^-5}, PDG -> 38,
76    ParticleName -> "D+",  AntiParticleName -> "D-",  QuantumNumbers -> {Q->1}
77  },
78  S[6] == {
79    ClassName -> DPP, SelfConjugate -> False, Mass -> {MDPP,502.}, Width -> {WDPP,1.011029*^-5}, PDG -> 61,
80    ParticleName -> "D++", AntiParticleName -> "D--", QuantumNumbers -> {Q->2}
81  },
82  S[7] == {
83    ClassName -> chi, SelfConjugate -> True,  Mass -> {Mchi,Internal}, Width -> {Wchi,1.017817*^-5}, PDG -> 62
84  }
85};
86
87
88(* ************************** *)
89(* *****   Parameters   ***** *)
90(* ************************** *)
91M$Parameters = {
92  (* PMNS matrix *)
93  th12 == {
94    ParameterType -> External, Value -> 0.59, TeX -> Subscript[\[Theta], 12],
95    BlockName -> PMNS, OrderBlock -> 1, Description -> "Solar mixing angle - theta12"
96  },
97  th23 == {
98    ParameterType -> External, Value -> 0.87, TeX -> Subscript[\[Theta], 23],
99    BlockName -> PMNS, OrderBlock -> 2, Description -> "Atmospheric mixing angle - theta23"
100  },
101  th13 == {
102    ParameterType -> External, Value -> 0.15, TeX -> Subscript[\[Theta], 13],
103    BlockName -> PMNS, OrderBlock -> 3, Description -> "Reactor mixing angle - theta_13"
104  },
105  delCP == {
106    ParameterType -> External, Value -> 0 (* 3.8 *), TeX -> Subscript[\[Delta], CP],
107    BlockName -> PMNS, OrderBlock -> 4, Description -> "Leptonic Dirac CP phase"
108  },
109  phiM1 == {
110    ParameterType -> External, Value -> 0.0, TeX -> Subscript[\[Phi], 1],
111    BlockName -> PMNS, OrderBlock -> 5, Description -> "1st Majorana CP phase"
112  },
113  phiM2 == {
114    ParameterType -> External, Value -> 0.0, TeX -> Subscript[\[Phi], 2],
115    BlockName -> PMNS, OrderBlock -> 6, Description -> "2nd Majorana CP phase"
116  },
117
118  (* Neutrino mass differences *)
119  dmsq21 == {
120    ParameterType -> External, Value -> 7.39*^-23, TeX -> Subsuperscript["\[CapitalDelta]m",21,2],
121    BlockName -> MNU, OrderBlock -> 2, Description -> "Solar mass splitting squared"
122  },
123  dmsq31 == {
124    ParameterType -> External, Value -> 2.5*^-21, TeX -> Subsuperscript["\[CapitalDelta]m",31,2],
125    BlockName -> MNU, OrderBlock -> 3, Description -> "Atmospheric mass splitting squared"
126  },
127
128  (* PMNS mixing matrix defined from oscillation data *)
129  PMNS == {
130    ParameterType -> Internal, Indices -> {Index[Generation],Index[Generation]}, TeX -> Superscript[V, PMNS],
131    ComplexParameter -> True,
132    Value -> {
133        PMNS[1,1] ->  Cos[th12]*Cos[th13],
134        PMNS[1,2] ->  Cos[th13]*Sin[th12]*Exp[I/2 phiM1],
135        PMNS[1,3] ->  Sin[th13]*Exp[I (phiM2/2 - delCP)],
136        PMNS[2,1] -> -Cos[th23]*Sin[th12] - Cos[th12]*Sin[th13]*Sin[th23]*Exp[I delCP],
137        PMNS[2,2] ->  (Cos[th12]*Cos[th23] - Sin[th12]*Sin[th13]*Sin[th23]*Exp[I delCP])*Exp[I/2 phiM1],
138        PMNS[2,3] ->  Cos[th13]*Sin[th23]*Exp[I/2 phiM2],
139        PMNS[3,1] ->  Sin[th12]*Sin[th23] - Cos[th12]*Cos[th23]*Sin[th13]*Exp[I delCP],
140        PMNS[3,2] ->  (-Cos[th23]*Sin[th12]*Sin[th13]*Exp[I delCP] - Cos[th12]*Sin[th23])*Exp[I/2 phiM1],
141        PMNS[3,3] -> Cos[th13]*Cos[th23]*Exp[I/2 phiM2]
142    }
143  },
144
145  (* Higgs sector: external parameters *)
146  lamHD1 == {
147    ParameterType -> External, Value -> 0.10, InteractionOrder -> {QED,2},
148    BlockName -> QUARTICS, OrderBlock -> 1, TeX -> Subscript[\[Lambda], "h\[CapitalDelta]1"]
149  },
150  lamD1 == {
151    ParameterType -> External, Value -> 0.11, InteractionOrder -> {QED,2},
152    BlockName -> QUARTICS, OrderBlock -> 2, TeX  -> Subscript[\[Lambda], "\[CapitalDelta]1"]
153  },
154  vevD == {
155    ParameterType -> External,  Value -> 1.0*^-7, InteractionOrder -> { QED,-1},
156    BlockName -> VEVDELTA, OrderBlock -> 1, TeX -> Subscript[v,\[CapitalDelta]]
157  },
158
159  (* Neutrino masses and Yukawas *)
160  Mv2 == { ParameterType -> Internal, Value -> Sqrt[Mv1^2 + dmsq21], TeX -> Subscript[m, "\[Nu]2"] },
161  Mv3 == { ParameterType -> Internal, Value -> Sqrt[Mv1^2 + dmsq31], TeX -> Subscript[m, "\[Nu]3"] },
162  yDL == {
163    ParameterType -> Internal, Indices -> {Index[Generation], Index[Generation]},
164    InteractionOrder -> {QED, 1}, TeX -> Subscript[Y, \[CapitalDelta]], ComplexParameter -> True,
165    Value               -> {
166      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),
167      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),
168      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),
169
170      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),
171      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),
172      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),
173
174      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),
175      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),
176      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)
177    }
178  },
179
180
181
182
183  (* Higgs sector: internal parameters *)
184  mD2  == {
185   ParameterType -> Internal, Value -> MDPP^2 - lamHD1/2*vev^2 - lamD1*vevD^2,
186   TeX -> Subsuperscript[m,\[CapitalDelta],2]
187  },
188  lamHD2 == {
189   ParameterType -> Internal, TeX -> Subscript[ \[Lambda], "h\[CapitalDelta]2"], InteractionOrder -> {QED,2},
190   Value -> 2*(lamD1 - lamHD1 - (2*MDP^2)/(vev^2 + 2*vevD^2) -
191   (MD0^2 - 8*MDP^2 + 4*MDPP^2 + MH^2 + (lamD1 - lamHD1)*vev^2)/(vev^2 + 4*vevD^2)) -
192     Sqrt[(-4*MD0^2*vev^6 + 24*MDP^2*vev^6 - 16*MDPP^2*vev^6 - 4*MH^2*vev^6 - 16*MD0^2*vev^4*vevD^2 +
193      80*MDP^2*vev^4*vevD^2 - 64*MDPP^2*vev^4*vevD^2 - 16*MH^2*vev^4*vevD^2 + 16*lamD1*vev^6*vevD^2 -
194      16*lamHD1*vev^6*vevD^2 - 16*MD0^2*vev^2*vevD^4 + 64*MDP^2*vev^2*vevD^4 - 64*MDPP^2*vev^2*vevD^4 -
195      16*MH^2*vev^2*vevD^4 + 64*lamD1*vev^4*vevD^4 - 64*lamHD1*vev^4*vevD^4 + 64*lamD1*vev^2*vevD^6 -
196      64*lamHD1*vev^2*vevD^6)^2 - 4*(-vev^8 - 8*vev^6*vevD^2 - 20*vev^4*vevD^4 - 16*vev^2*vevD^6)*
197     (48*MD0^2*MDP^2*vev^4 - 144*MDP^4*vev^4 - 32*MD0^2*MDPP^2*vev^4 + 192*MDP^2*MDPP^2*vev^4 -
198      64*MDPP^4*vev^4 - 16*MD0^2*MH^2*vev^4 + 48*MDP^2*MH^2*vev^4 - 32*MDPP^2*MH^2*vev^4 +
199      96*MD0^2*MDP^2*vev^2*vevD^2 - 64*MDP^4*vev^2*vevD^2 - 128*MD0^2*MDPP^2*vev^2*vevD^2 +
200      384*MDP^2*MDPP^2*vev^2*vevD^2 - 256*MDPP^4*vev^2*vevD^2 - 64*MD0^2*MH^2*vev^2*vevD^2 +
201      96*MDP^2*MH^2*vev^2*vevD^2 - 128*MDPP^2*MH^2*vev^2*vevD^2 + 32*lamD1*MD0^2*vev^4*vevD^2 -
202      192*lamD1*MDP^2*vev^4*vevD^2 + 64*lamHD1*MDP^2*vev^4*vevD^2 + 128*lamD1*MDPP^2*vev^4*vevD^2 +
203      32*lamD1*MH^2*vev^4*vevD^2 - 16*lamHD1^2*vev^6*vevD^2 - 128*MD0^2*MDPP^2*vevD^4 - 256*MDPP^4*vevD^4 -
204      64*MD0^2*MH^2*vevD^4 - 128*MDPP^2*MH^2*vevD^4 + 128*lamD1*MD0^2*vev^2*vevD^4 -
205      384*lamD1*MDP^2*vev^2*vevD^4 + 128*lamHD1*MDP^2*vev^2*vevD^4 + 512*lamD1*MDPP^2*vev^2*vevD^4 +
206      128*lamD1*MH^2*vev^2*vevD^4 - 64*lamD1^2*vev^4*vevD^4 - 64*lamHD1^2*vev^4*vevD^4 +
207      128*lamD1*MD0^2*vevD^6 + 512*lamD1*MDPP^2*vevD^6 + 128*lamD1*MH^2*vevD^6 - 256*lamD1^2*vev^2*vevD^6 -
208      64*lamHD1^2*vev^2*vevD^6 - 256*lamD1^2*vevD^8)]/(2*(vev^2 + 4*vevD^2)*(vev^3 + 2*vev*vevD^2)^2)
209  },
210  lamD2 == {
211    ParameterType -> Internal, TeX  -> Subscript[\[Lambda], "\[CapitalDelta]2"], InteractionOrder -> {QED,2},
212    Value -> vev^2*MDP^2/(vevD^2(vev^2+2vevD^2)) - MDPP^2/vevD^2 - vev^2 lamHD2/(4 vevD^2)
213  },
214  muHD == {
215   ParameterType -> Internal, TeX -> Subscript[\[Mu], "h\[CapitalDelta]"], InteractionOrder -> {QED,2},
216   Value -> Sqrt[2]*vevD*(1/vev^2*(mD2+(lamHD1+lamHD2)/2*vev^2) + (lamD1+lamD2)*vevD^2/vev^2)
217  },
218  lamH == {
219    ParameterType -> Internal, TeX -> Subscript[\[Lambda],H], InteractionOrder -> {QED,2},
220    Value -> MH^2/(2*vev^2) + 1/2 vevD^2/(vev^2 + 2 vevD^2) (-4*MDP^2 + (2*lamHD1+lamHD2)*(vev^2+2*vevD^2))^2/(12*MDP^2*vev^2-(vev^2+2*vevD^2)*(8*MDPP^2+4*MH^2+lamHD2*vev^2 - 8*lamD1*vevD^2))
221  },
222  muH2 == {
223    ParameterType -> Internal, TeX -> Superscript[Subscript[\[Mu],H],2],
224    Value -> lamH*vev^2 - vevD^2/(2 vev^2)*((lamHD1+lamHD2)*vev^2+4*mD2) - 2 vevD^4/vev^2*(lamD1+lamD2)
225  },
226
227  (* Internal masses and mixings *)
228  Mchi == {
229    ParameterType -> Internal, TeX -> Subscript[M,\[Chi]],
230    Value -> Sqrt[(vev^2+4 vevD^2)/vev^2 (MDPP^2 + lamHD2 vev^2/2 + lamD2 vevD^2)]
231  },
232  t2xi == {
233    ParameterType -> Internal, TeX -> Subscript[t,"2\[Xi]"],
234    Value -> (4*vev*vevD*(-4*MDP^2 + (2*lamHD1 + lamHD2)*(vev^2 + 2*vevD^2)))/
235      (-12*MDP^2*vev^2 + (vev^2 + 2*vevD^2)*(8*MDPP^2 + (8*lamH + lamHD2)*vev^2 - 8*lamD1*vevD^2))
236  },
237  cxi == {
238    ParameterType -> Internal, TeX -> Subscript[c,\[Xi]],
239    Value -> Cos[1/2 ArcTan[t2xi]]
240  },
241  sxi == {
242    ParameterType -> Internal, TeX -> Subscript[s,\[Xi]],
243    Value -> Sin[1/2 ArcTan[t2xi]]
244  }
245
246};
247
248
249(* ************************** *)
250(* *****   Lagrangian   ***** *)
251(* ************************** *)
252LScalar := \
253   DC[Phibar[ii],mu] DC[Phi[ii],mu] + DC[hatDbar[ii],mu] DC[hatD[ii],mu] \
254   + muH2 Phibar[ii]  Phi[ii]  \
255   - mD2  hatDbar[ii] hatD[ii] \
256   - lamH Phibar[ii] Phi[ii] Phibar[jj] Phi[jj] \
257   - lamD1 hatDbar[ii] hatD[ii] hatDbar[jj] hatD[jj] \
258   - lamD2 (hatDbar[ii] hatD[ii] hatDbar[jj] hatD[jj] - 1/2 hatDbar[ii] hatD[jj] hatDbar[ii] hatD[jj]) \
259   - lamHD1 Phibar[ii] Phi[ii] hatD[jj] hatDbar[jj] \
260   - lamHD2/2 (hatD[ii] hatDbar[ii] Phibar[jj] Phi[jj] + I Eps[ii,jj,mm] PauliSigma[mm,ip,jp] Phibar[ip] Phi[jp]
261        hatD[ii] hatDbar[jj] )  \
262   + muHD/Sqrt[2] Phibar[ii] hatD[mm] PauliSigma[mm,ii,jj] Phibar[jp] Eps[jj,jp] \
263   + muHD/Sqrt[2] Phi[jj] hatDbar[mm] PauliSigma[mm,ii,jj] Phi[jp] Eps[ii,jp];
264
265LYukawa := Block[{yuk},
266  yuk:=
267   - yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] \
268   - yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] \
269   - Sum[yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj],{ii,2},{jj,2}] \
270   - Sum[yDL[ff1, ff2]/Sqrt[2] Eps[ip,ii] CC[LLbar][sp, ii, ff1].LL[sp, jj, ff2] hatD[mm] PauliSigma[mm,ip,jj],
271       {ii,2},{ip,2},{jj,2},{mm,3}];
272  yuk+HC[yuk]
273 ];
274
275LType2:= {LGauge, LFermions, LScalar, LYukawa, LGhost};
276