HeavyN: heavyN.fr

File heavyN.fr, 8.9 KB (added by Richard Ruiz, 9 years ago)

Heavy neutrino FeynRules model file in Feynman gauge.

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1(* ********************************************************************************* *)
2(* FeynRules Model file for a heavy neutrino extension of the Standard Model. *)
3(* Contains three massive Majorana neutrinos that couples to all SM leptons through *)
4(* mixing between the active (flavor) eigenstates and mass eigenstates. *)
5(* The Lagrangian is written in the Feynman Gauge. *)
6(* *)
7(* Contact author: R. Ruiz [richard.ruiz [at] durham.ac.uk] *)
8(* *)
9(* The Lagrangian is based on Atre, et. al. [arXiv:0901.3589]. *)
10(* At LO, the model was implemented in Alva, et. al. [arXiv:1411.7305]. *)
11(* At NLO, the model was implemented in Degrande, et al. [arXiv:1602.06957]. *)
12(* Both model files are extensions of default FeynRules SM model file. *)
13(* Please cite accordingly. *)
14(* *)
15(* Neutrino mass (mN) and mixing parameters (VlN) between heavy mass eigenstate and *)
16(* flavor eigenstates are taken to be independent, phenomenological parameters. *)
17(* Mixing parameters (VeN, VmuN, VtaN) are taken to be real. *)
18(* This allows for maximum flexibility and model independence when calculating *)
19(* rates. *)
20(* *)
21(* Feynman gauge is set to true. *)
22(* ********************************************************************************* *)
23
24(* ************************** *)
25(* ***** Information ***** *)
26(* ************************** *)
27M$ModelName = "SM_HeavyN";
28
29M$Information = {
30 Authors -> {"R. Ruiz"},
31 Version -> "2.2",
32 Date -> "27 June 2016",
33 Institutions -> {"IPPP / University of Durham"},
34 Emails -> {"richard.ruiz@durham.ac.uk"},
35 References -> {"Atre, et al, JHEP0905, 030 (2009) [arXiv:0901.3589]",
36 "Alva, et al, JHEP1502, 072 (2015) [arXiv:1411.7305]",
37 "Degrande, et al, [arXiv:1602.06957]"},
38 URLs -> {"https://feynrules.irmp.ucl.ac.be/wiki/HeavyN"}
39};
40FeynmanGauge = True;
41
42
43(* ************************** *)
44(* ***** Change log ***** *)
45(* ************************** *)
46(* v1.1: Public release of LO model file *)
47(* v2.1: Added Goldstone couplings for Feynman Gauge and NLO implementation *)
48(* v2.2: Corrected relative sign between Yukawa and gauge couplings. *)
49
50(* ************************** *)
51(* ***** Parameters ***** *)
52(* ************************** *)
53M$Parameters = {
54 (* External Parameters *)
55
56 VeN1 == {
57 ParameterType -> External,
58 BlockName -> NUMIXING,
59 OrderBlock -> 1,
60 Value -> 1.0,
61 ComplexParameter -> False,
62 TeX -> Subscript[V,eN1],
63 Description -> "Mixing between ve flavor/gauge state and N1 mass state"
64 },
65
66 VeN2 == {
67 ParameterType -> External,
68 BlockName -> NUMIXING,
69 OrderBlock -> 2,
70 Value -> 0.0,
71 ComplexParameter -> False,
72 TeX -> Subscript[V,eN2],
73 Description -> "Mixing between ve flavor/gauge state and N2 mass state"
74 },
75
76 VeN3 == {
77 ParameterType -> External,
78 BlockName -> NUMIXING,
79 OrderBlock -> 3,
80 Value -> 0.0,
81 ComplexParameter -> False,
82 TeX -> Subscript[V,eN3],
83 Description -> "Mixing between ve flavor/gauge state and N3 mass state"
84 },
85
86 VmuN1 == {
87 ParameterType -> External,
88 BlockName -> NUMIXING,
89 OrderBlock -> 4,
90 Value -> 0.0,
91 ComplexParameter -> False,
92 TeX -> Subscript[V,muN1],
93 Description -> "Mixing between vm flavor/gauge state and N1 mass state"
94 },
95
96 VmuN2 == {
97 ParameterType -> External,
98 BlockName -> NUMIXING,
99 OrderBlock -> 5,
100 Value -> 1.0,
101 ComplexParameter -> False,
102 TeX -> Subscript[V,muN2],
103 Description -> "Mixing between vm flavor/gauge state and N2 mass state"
104 },
105
106 VmuN3 == {
107 ParameterType -> External,
108 BlockName -> NUMIXING,
109 OrderBlock -> 6,
110 Value -> 0.0,
111 ComplexParameter -> False,
112 TeX -> Subscript[V,muN3],
113 Description -> "Mixing between vm flavor/gauge state and N3 mass state"
114 },
115
116 VtaN1 == {
117 ParameterType -> External,
118 BlockName -> NUMIXING,
119 OrderBlock -> 7,
120 Value -> 0.0,
121 ComplexParameter -> False,
122 TeX -> Subscript[V,taN1],
123 Description -> "Mixing between vt flavor/gauge state and N1 mass state"
124 },
125
126 VtaN2 == {
127 ParameterType -> External,
128 BlockName -> NUMIXING,
129 OrderBlock -> 8,
130 Value -> 0.0,
131 ComplexParameter -> False,
132 TeX -> Subscript[V,taN2],
133 Description -> "Mixing between vt flavor/gauge state and N2 mass state"
134 },
135
136 VtaN3 == {
137 ParameterType -> External,
138 BlockName -> NUMIXING,
139 OrderBlock -> 9,
140 Value -> 1.0,
141 ComplexParameter -> False,
142 TeX -> Subscript[V,taN3],
143 Description -> "Mixing between vt flavor/gauge state and N3 mass state"
144 },
145
146 (* Internal Parameters *)
147 gN == {
148 ParameterType -> Internal,
149 Definitions -> {gN->ee/sw},
150 InteractionOrder -> {NP,1},
151 TeX -> Subscript[g,N]}
152};
153
154M$InteractionOrderHierarchy = {
155 {QCD,1},
156 {QED,2}
157};
158
159(* ************************** *)
160(* **** Particle classes **** *)
161(* ************************** *)
162M$ClassesDescription = {
163 (*Majorana Neutrino*)
164 F[131] == {
165 ClassName -> N1,
166 SelfConjugate -> True,
167 Mass -> {mN1,300.},
168 Width -> {WN1,0.303},
169 PropagatorLabel -> "N1",
170 PropagatorType -> Straight,
171 PropagatorArrow -> False,
172 ParticleName -> "N1",
173 PDG -> {9900012},
174 FullName -> "N1"},
175
176 F[132] == {
177 ClassName -> N2,
178 SelfConjugate -> True,
179 Mass -> {mN2,500.},
180 Width -> {WN2,1.50},
181 PropagatorLabel -> "N2",
182 PropagatorType -> Straight,
183 PropagatorArrow -> False,
184 ParticleName -> "N2",
185 PDG -> {9900014},
186 FullName -> "N2"},
187
188 F[133] == {
189 ClassName -> N3,
190 SelfConjugate -> True,
191 Mass -> {mN3,1000.},
192 Width -> {WN3,12.3},
193 PropagatorLabel -> "N3",
194 PropagatorType -> Straight,
195 PropagatorArrow -> False,
196 ParticleName -> "N3",
197 PDG -> {9900016},
198 FullName -> "N3"}
199};
200
201
202(* ************************** *)
203(* ***** Lagrangian ***** *)
204(* ************************** *)
205LNKin := I/2 N1bar[s1].Ga[v,s1,s2].del[N1[s2],v] - 1/2 mN1 N1bar[s1]N1[s1] \
206 + I/2 N2bar[s1].Ga[v,s1,s2].del[N2[s2],v] - 1/2 mN2 N2bar[s1]N2[s1] \
207 + I/2 N3bar[s1].Ga[v,s1,s2].del[N3[s2],v] - 1/2 mN3 N3bar[s1]N3[s1];
208
209(* Charge Current *)
210LNCCbare := gN/Sqrt[2] *( VeN1 * N1bar.W[m].ProjM[m].e \
211 + VmuN1 * N1bar.W[m].ProjM[m].mu \
212 + VtaN1 * N1bar.W[m].ProjM[m].ta ) \
213 + gN/Sqrt[2] *( VeN2 * N2bar.W[m].ProjM[m].e \
214 + VmuN2 * N2bar.W[m].ProjM[m].mu \
215 + VtaN2 * N2bar.W[m].ProjM[m].ta ) \
216 + gN/Sqrt[2] *( VeN3 * N3bar.W[m].ProjM[m].e \
217 + VmuN3 * N3bar.W[m].ProjM[m].mu \
218 + VtaN3 * N3bar.W[m].ProjM[m].ta );
219LNCC := LNCCbare + HC[LNCCbare];
220
221(* Neutral Current *)
222LNNCBare := 1/2 * gN/cw *( VeN1 * N1bar.Z[m].ProjM[m].ve \
223 + VmuN1 * N1bar.Z[m].ProjM[m].vm \
224 + VtaN1 * N1bar.Z[m].ProjM[m].vt ) \
225 + 1/2 * gN/cw *( VeN2 * N2bar.Z[m].ProjM[m].ve \
226 + VmuN2 * N2bar.Z[m].ProjM[m].vm \
227 + VtaN2 * N2bar.Z[m].ProjM[m].vt ) \
228 + 1/2 * gN/cw *( VeN3 * N3bar.Z[m].ProjM[m].ve \
229 + VmuN3 * N3bar.Z[m].ProjM[m].vm \
230 + VtaN3 * N3bar.Z[m].ProjM[m].vt );
231LNNC := LNNCBare + HC[LNNCBare];
232
233(* Higgs Interaction *)
234LNHbare := - gN*mN1/(2*MW) *( VeN1 * N1bar.ProjM.ve H \
235 + VmuN1 * N1bar.ProjM.vm H \
236 + VtaN1 * N1bar.ProjM.vt H ) \
237 - gN*mN2/(2*MW) *( VeN2 * N2bar.ProjM.ve H \
238 + VmuN2 * N2bar.ProjM.vm H \
239 + VtaN2 * N2bar.ProjM.vt H ) \
240 - gN*mN3/(2*MW) *( VeN3 * N3bar.ProjM.ve H \
241 + VmuN3 * N3bar.ProjM.vm H \
242 + VtaN3 * N3bar.ProjM.vt H );
243LNH := LNHbare + HC[LNHbare];
244
245(* Goldstone Interaction *)
246LNGbare := I *gN*mN1/(2*MW) *( VeN1 * vebar.ProjP.N1 G0 \
247 + VmuN1 * vmbar.ProjP.N1 G0 \
248 + VtaN1 * vtbar.ProjP.N1 G0) \
249 + I *gN*mN2/(2*MW) *( VeN2 * vebar.ProjP.N2 G0 \
250 + VmuN2 * vmbar.ProjP.N2 G0 \
251 + VtaN2 * vtbar.ProjP.N2 G0) \
252 + I *gN*mN3/(2*MW) *( VeN3 * vebar.ProjP.N3 G0 \
253 + VmuN3 * vmbar.ProjP.N3 G0 \
254 + VtaN3 * vtbar.ProjP.N3 G0) \
255 + I *gN*mN1/(Sqrt[2]*MW) *( VeN1 * ebar.ProjP.N1 GPbar \
256 + VmuN1 * mubar.ProjP.N1 GPbar \
257 + VtaN1 * tabar.ProjP.N1 GPbar) \
258 + I *gN*mN2/(Sqrt[2]*MW) *( VeN2 * ebar.ProjP.N2 GPbar \
259 + VmuN2 * mubar.ProjP.N2 GPbar \
260 + VtaN2 * tabar.ProjP.N2 GPbar) \
261 + I *gN*mN3/(Sqrt[2]*MW) *( VeN3 * ebar.ProjP.N3 GPbar \
262 + VmuN3 * mubar.ProjP.N3 GPbar \
263 + VtaN3 * tabar.ProjP.N3 GPbar);
264LNG := LNGbare + HC[LNGbare];
265
266(* Full N Lagrangian *)
267LN:= LNKin + LNCC + LNNC + LNH + LNG;
268
269(* Combine Lagrangian *)
270LFull := LSM + LN;