TypeIISeesaw: type_ii_v1.3.fr

File type_ii_v1.3.fr, 12.2 KB (added by Miha Nemevsek, 5 years ago)

FeynRules Type II Seesaw model file with internal mD0

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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