TypeIISeesaw: type_ii_ih.fr

File type_ii_ih.fr, 13.0 KB (added by BenjF, 3 weeks ago)

version 1.1

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$ModelName   = "TypeII_IH";
14M$Information = { Authors -> {"B. Fuks"}, Version -> "1.1", Date -> "18.11.2019" };
15FeynmanGauge  = True;
16
17
18(* ************************** *)
19(* *****  Change  log   ***** *)
20(* ************************** *)
21
22(* 08.11.19 - v1.0: first version                                                   *)
23(* 18.11.19 - v1.1: Changing the name of the LH block for vevD (cannot be vevd too) *)
24
25
26(* ************************** *)
27(* **** Particle classes **** *)
28(* ************************** *)
29M$ClassesDescription = {
30(* Fermions: physical fields *)
31  F[1] == {
32    ClassName -> vi, ClassMembers -> {v1,v2,v3}, Indices -> {Index[Generation]}, FlavorIndex -> Generation,
33    SelfConjugate -> True, Mass -> {Mvi, {Mv1, Internal}, {Mv2, Internal}, {Mv3, 0.05*^-9} }, Width -> 0,
34    PDG -> {12,14,16}
35  },
36
37  (* Fermions: unphysical fields *)
38  F[11] == {
39    ClassName -> LL, Unphysical -> True, Indices -> {Index[SU2D], Index[Generation]}, FlavorIndex -> SU2D,
40    SelfConjugate -> False, QuantumNumbers -> {Y->-1/2},
41    Definitions -> {
42      LL[sp1_,1,ff_] :> Module[{sp2,ff2}, PMNS[ff,ff2] ProjM[sp1,sp2] vi[sp2,ff2]],
43      LL[sp1_,2,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]]
44    }
45  },
46
47  (* Higgs: unphysical scalars  *)
48  S[11] == {
49    ClassName -> Phi, Unphysical -> True, Indices -> {Index[SU2D]}, FlavorIndex -> SU2D,
50    SelfConjugate -> False, QuantumNumbers -> {Y -> 1/2},
51    Definitions -> {
52      Phi[1] -> vev/Sqrt[vev^2+2*vevD^2] GP - Sqrt[2] vevD/Sqrt[vev^2+2*vevD^2] DP,
53      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)
54    }
55  },
56  S[12] == {
57    ClassName -> hatD, Unphysical -> True, Indices-> {Index[SU2W]}, FlavorIndex->SU2W,
58    SelfConjugate -> False, QuantumNumbers -> {Y->1},
59    Definitions -> {
60      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) \
61         + 1/Sqrt[2] DPP,
62      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) \
63         + I/Sqrt[2] DPP,
64      hatD[3] -> Sqrt[2] vevD/Sqrt[vev^2+2*vevD^2] GP + vev/Sqrt[vev^2+2*vevD^2] DP
65    }
66  },
67
68  (* Higgs: physical scalars *)
69  S[4] == {
70    ClassName -> D0,  SelfConjugate -> True,  Mass -> {MD0, 500.}, Width -> {WD0, 1.017718*^-5}, PDG -> 44
71  },
72  S[5] == {
73    ClassName -> DP,  SelfConjugate -> False, Mass -> {MDP, 503.}, Width -> {WDP, 1.017090*^-5}, PDG -> 38,
74    ParticleName -> "D+",  AntiParticleName -> "D-",  QuantumNumbers -> {Q->1}
75  },
76  S[6] == {
77    ClassName -> DPP, SelfConjugate -> False, Mass -> {MDPP,502.}, Width -> {WDPP,1.011029*^-5}, PDG -> 61,
78    ParticleName -> "D++", AntiParticleName -> "D--", QuantumNumbers -> {Q->2}
79  },
80  S[7] == {
81    ClassName -> chi, SelfConjugate -> True,  Mass -> {Mchi,Internal}, Width -> {Wchi,1.017817*^-5}, PDG -> 62
82  }
83};
84
85
86(* ************************** *)
87(* *****   Parameters   ***** *)
88(* ************************** *)
89M$Parameters = {
90  (* PMNS matrix *)
91  th12 == {
92    ParameterType -> External, Value -> 0.59, TeX -> Subscript[\[Theta], 12],
93    BlockName -> PMNS, OrderBlock -> 1, Description -> "Solar mixing angle - theta12"
94  },
95  th23 == {
96    ParameterType -> External, Value -> 0.87, TeX -> Subscript[\[Theta], 23],
97    BlockName -> PMNS, OrderBlock -> 2, Description -> "Atmospheric mixing angle - theta23"
98  },
99  th13 == {
100    ParameterType -> External, Value -> 0.15, TeX -> Subscript[\[Theta], 13],
101    BlockName -> PMNS, OrderBlock -> 3, Description -> "Reactor mixing angle - theta_13"
102  },
103  delCP == {
104    ParameterType -> External, Value -> 0 (* 3.8 *), TeX -> Subscript[\[Delta], CP],
105    BlockName -> PMNS, OrderBlock -> 4, Description -> "Leptonic Dirac CP phase"
106  },
107  phiM1 == {
108    ParameterType -> External, Value -> 0.0, TeX -> Subscript[\[Phi], 1],
109    BlockName -> PMNS, OrderBlock -> 5, Description -> "1st Majorana CP phase"
110  },
111  phiM2 == {
112    ParameterType -> External, Value -> 0.0, TeX -> Subscript[\[Phi], 2],
113    BlockName -> PMNS, OrderBlock -> 6, Description -> "2nd Majorana CP phase"
114  },
115
116  (* Neutrino mass differences *)
117  dmsq21 == {
118    ParameterType -> External, Value -> 7.39*^-23, TeX -> Subsuperscript["\[CapitalDelta]m",21,2],
119    BlockName -> MNU, OrderBlock -> 2, Description -> "Solar mass splitting squared"
120  },
121  dmsq32 == {
122    ParameterType -> External, Value -> -2.5*^-21, TeX -> Subsuperscript["\[CapitalDelta]m",32,2],
123    BlockName -> MNU, OrderBlock -> 3, Description -> "Atmospheric mass splitting squared"
124  },
125
126  (* PMNS mixing matrix defined from oscillation data *)
127  PMNS == {
128    ParameterType -> Internal, Indices -> {Index[Generation],Index[Generation]}, TeX -> Superscript[V, PMNS],
129    ComplexParameter -> True,
130    Value -> {
131        PMNS[1,1] ->  Cos[th12]*Cos[th13],
132        PMNS[1,2] ->  Cos[th13]*Sin[th12]*Exp[I/2 phiM1],
133        PMNS[1,3] ->  Sin[th13]*Exp[I (phiM2/2 - delCP)],
134        PMNS[2,1] -> -Cos[th23]*Sin[th12] - Cos[th12]*Sin[th13]*Sin[th23]*Exp[I delCP],
135        PMNS[2,2] ->  (Cos[th12]*Cos[th23] - Sin[th12]*Sin[th13]*Sin[th23]*Exp[I delCP])*Exp[I/2 phiM1],
136        PMNS[2,3] ->  Cos[th13]*Sin[th23]*Exp[I/2 phiM2],
137        PMNS[3,1] ->  Sin[th12]*Sin[th23] - Cos[th12]*Cos[th23]*Sin[th13]*Exp[I delCP],
138        PMNS[3,2] ->  (-Cos[th23]*Sin[th12]*Sin[th13]*Exp[I delCP] - Cos[th12]*Sin[th23])*Exp[I/2 phiM1],
139        PMNS[3,3] -> Cos[th13]*Cos[th23]*Exp[I/2 phiM2]
140    }
141  },
142
143  (* Higgs sector: external parameters *)
144  lamHD1 == {
145    ParameterType -> External, Value -> 0.10, InteractionOrder -> {QED,2},
146    BlockName -> QUARTICS, OrderBlock -> 1, TeX -> Subscript[\[Lambda], "h\[CapitalDelta]1"]
147  },
148  lamD1 == {
149    ParameterType -> External, Value -> 0.11, InteractionOrder -> {QED,2},
150    BlockName -> QUARTICS, OrderBlock -> 2, TeX  -> Subscript[\[Lambda], "\[CapitalDelta]1"]
151  },
152  vevD == {
153    ParameterType -> External,  Value -> 1.0*^-7, InteractionOrder -> { QED,-1},
154    BlockName -> VEVDELTA, OrderBlock -> 1, TeX -> Subscript[v,\[CapitalDelta]]
155  },
156
157  (* Neutrino masses and Yukawas *)
158  Mv1 == { ParameterType -> Internal, Value -> Sqrt[Mv3^2 - dmsq32 - dmsq21], TeX -> Subscript[m, "\[Nu]1"] },
159  Mv2 == { ParameterType -> Internal, Value -> Sqrt[Mv3^2 - dmsq21], TeX -> Subscript[m, "\[Nu]2"] },
160  yDL == {
161    ParameterType -> Internal, Indices -> {Index[Generation], Index[Generation]},
162    InteractionOrder -> {QED, 1}, TeX -> Subscript[Y, \[CapitalDelta]], ComplexParameter -> True,
163    Value               -> {
164      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),
165      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),
166      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),
167
168      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),
169      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),
170      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),
171
172      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),
173      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),
174      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)
175    }
176  },
177
178  (* Higgs sector: internal parameters *)
179  mD2  == {
180   ParameterType -> Internal, Value -> MDPP^2 - lamHD1/2*vev^2 - lamD1*vevD^2,
181   TeX -> Subsuperscript[m,\[CapitalDelta],2]
182  },
183  lamHD2 == {
184   ParameterType -> Internal, TeX -> Subscript[ \[Lambda], "h\[CapitalDelta]2"], InteractionOrder -> {QED,2},
185   Value -> 2*(lamD1 - lamHD1 - (2*MDP^2)/(vev^2 + 2*vevD^2) -
186   (MD0^2 - 8*MDP^2 + 4*MDPP^2 + MH^2 + (lamD1 - lamHD1)*vev^2)/(vev^2 + 4*vevD^2)) -
187     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 +
188      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 -
189      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 -
190      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 -
191      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)*
192     (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 -
193      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 +
194      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 +
195      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 +
196      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 -
197      192*lamD1*MDP^2*vev^4*vevD^2 + 64*lamHD1*MDP^2*vev^4*vevD^2 + 128*lamD1*MDPP^2*vev^4*vevD^2 +
198      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 -
199      64*MD0^2*MH^2*vevD^4 - 128*MDPP^2*MH^2*vevD^4 + 128*lamD1*MD0^2*vev^2*vevD^4 -
200      384*lamD1*MDP^2*vev^2*vevD^4 + 128*lamHD1*MDP^2*vev^2*vevD^4 + 512*lamD1*MDPP^2*vev^2*vevD^4 +
201      128*lamD1*MH^2*vev^2*vevD^4 - 64*lamD1^2*vev^4*vevD^4 - 64*lamHD1^2*vev^4*vevD^4 +
202      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 -
203      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)
204  },
205  lamD2 == {
206    ParameterType -> Internal, TeX  -> Subscript[\[Lambda], "\[CapitalDelta]2"], InteractionOrder -> {QED,2},
207    Value -> vev^2*MDP^2/(vevD^2(vev^2+2vevD^2)) - MDPP^2/vevD^2 - vev^2 lamHD2/(4 vevD^2)
208  },
209  muHD == {
210   ParameterType -> Internal, TeX -> Subscript[\[Mu], "h\[CapitalDelta]"], InteractionOrder -> {QED,2},
211   Value -> Sqrt[2]*vevD*(1/vev^2*(mD2+(lamHD1+lamHD2)/2*vev^2) + (lamD1+lamD2)*vevD^2/vev^2)
212  },
213  lamH == {
214    ParameterType -> Internal, TeX -> Subscript[\[Lambda],H], InteractionOrder -> {QED,2},
215    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))
216  },
217  muH2 == {
218    ParameterType -> Internal, TeX -> Superscript[Subscript[\[Mu],H],2],
219    Value -> lamH*vev^2 - vevD^2/(2 vev^2)*((lamHD1+lamHD2)*vev^2+4*mD2) - 2 vevD^4/vev^2*(lamD1+lamD2)
220  },
221
222  (* Internal masses and mixings *)
223  Mchi == {
224    ParameterType -> Internal, TeX -> Subscript[M,\[Chi]],
225    Value -> Sqrt[(vev^2+4 vevD^2)/vev^2 (MDPP^2 + lamHD2 vev^2/2 + lamD2 vevD^2)]
226  },
227  t2xi == {
228    ParameterType -> Internal, TeX -> Subscript[t,"2\[Xi]"],
229    Value -> (4*vev*vevD*(-4*MDP^2 + (2*lamHD1 + lamHD2)*(vev^2 + 2*vevD^2)))/
230      (-12*MDP^2*vev^2 + (vev^2 + 2*vevD^2)*(8*MDPP^2 + (8*lamH + lamHD2)*vev^2 - 8*lamD1*vevD^2))
231  },
232  cxi == {
233    ParameterType -> Internal, TeX -> Subscript[c,\[Xi]],
234    Value -> Cos[1/2 ArcTan[t2xi]]
235  },
236  sxi == {
237    ParameterType -> Internal, TeX -> Subscript[s,\[Xi]],
238    Value -> Sin[1/2 ArcTan[t2xi]]
239  }
240
241};
242
243
244(* ************************** *)
245(* *****   Lagrangian   ***** *)
246(* ************************** *)
247LScalar := \
248   DC[Phibar[ii],mu] DC[Phi[ii],mu] + DC[hatDbar[ii],mu] DC[hatD[ii],mu] \
249   + muH2 Phibar[ii]  Phi[ii]  \
250   - mD2  hatDbar[ii] hatD[ii] \
251   - lamH Phibar[ii] Phi[ii] Phibar[jj] Phi[jj] \
252   - lamD1 hatDbar[ii] hatD[ii] hatDbar[jj] hatD[jj] \
253   - lamD2 (hatDbar[ii] hatD[ii] hatDbar[jj] hatD[jj] - 1/2 hatDbar[ii] hatD[jj] hatDbar[ii] hatD[jj]) \
254   - lamHD1 Phibar[ii] Phi[ii] hatD[jj] hatDbar[jj] \
255   - lamHD2/2 (hatD[ii] hatDbar[ii] Phibar[jj] Phi[jj] + I Eps[ii,jj,mm] PauliSigma[mm,ip,jp] Phibar[ip] Phi[jp]
256        hatD[ii] hatDbar[jj] )  \
257   + muHD/Sqrt[2] Phibar[ii] hatD[mm] PauliSigma[mm,ii,jj] Phibar[jp] Eps[jj,jp] \
258   + muHD/Sqrt[2] Phi[jj] hatDbar[mm] PauliSigma[mm,ii,jj] Phi[jp] Eps[ii,jp];
259
260LYukawa := Block[{yuk},
261  yuk:=
262   - yd[ff2, ff3] CKM[ff1, ff2] QLbar[sp, ii, ff1, cc].dR [sp, ff3, cc] Phi[ii] \
263   - yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phi[ii] \
264   - Sum[yu[ff1, ff2] QLbar[sp, ii, ff1, cc].uR [sp, ff2, cc] Phibar[jj] Eps[ii, jj],{ii,2},{jj,2}] \
265   - Sum[yDL[ff1, ff2]/Sqrt[2] Eps[ip,ii] CC[LLbar][sp, ii, ff1].LL[sp, jj, ff2] hatD[mm] PauliSigma[mm,ip,jj],
266       {ii,2},{ip,2},{jj,2},{mm,3}];
267  yuk+HC[yuk]
268 ];
269
270LType2:= {LGauge, LFermions, LScalar, LYukawa, LGhost};
271