HeavyN: heavyN_vSMEFTdim6.fr

File heavyN_vSMEFTdim6.fr, 15.6 KB (added by Richard Ruiz, 4 years ago)

.fr file for SM_HeavyN_vSMEFTdim6 (updated to include arXiv info)

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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(* At NLO, a subset of vSMEFT operators at dimension six were *)
14(* implemented in Cirigliano, et al. [arXiv:2105.11462] *)
15(* Please cite accordingly. *)
16(* *)
17(* Neutrino mass (mN) and mixing parameters (VlN) between heavy mass eigenstate and *)
18(* flavor eigenstates are taken to be independent, phenomenological parameters. *)
19(* Mixing parameters (VeN, VmuN, VtaN) are taken to be real. *)
20(* Wilson coefficients and vSMEFT cutoff scale are also real, independent parameters *)
21(* This allows for maximum flexibility and model independence when calculating *)
22(* rates. *)
23(* *)
24(* Feynman gauge is set to true. *)
25(* ********************************************************************************* *)
26
27(* ************************** *)
28(* ***** Information ***** *)
29(* ************************** *)
30M$ModelName = "SM_HeavyN_vSMEFTdim6";
31
32M$Information = {
33 Authors -> {"R. Ruiz"},
34 Version -> "2.5.branch1.2",
35 Date -> "2021 May 26",
36 Institutions -> {"IFJ PAN"},
37 Emails -> {"rruiz@ifj.edu.pl"},
38 References -> {"Atre, et al, JHEP0905, 030 (2009) [arXiv:0901.3589]",
39 "Alva, et al, JHEP1502, 072 (2015) [arXiv:1411.7305]",
40 "Degrande, et al, PRD [arXiv:1602.06957]",
41 "Cirigliano, et al, [arXiv:2105.11462]"},
42 URLs -> {"https://feynrules.irmp.ucl.ac.be/wiki/HeavyN"}
43};
44FeynmanGauge = True;
45
46
47(* ************************** *)
48(* ***** Change log ***** *)
49(* ************************** *)
50(* v1.1: Public release of LO model file *)
51(* v2.1: Added Goldstone couplings for Feynman Gauge and NLO implementation. *)
52(* v2.2: Corrected relative sign between Yukawa and gauge couplings. *)
53(* v2.5: Defined NuArray and NuMix for coupling to mesons. *)
54(* v2.5.branch1: branched from v2.5 to add dimension six operator *)
55(* v2.5.branch1.2: updated to include arXiv information *)
56
57IndexRange[Index[NuGeneration]] = Range[6];
58IndexStyle[NuGeneration, kk];
59
60(*IndexStyle[NuGeneration, ff1];*)
61(*IndexStyle[NuGeneration, ff2];*)
62
63
64(* ************************** *)
65(* ***** Parameters ***** *)
66(* ************************** *)
67M$Parameters = {
68 (* External Parameters *)
69
70 VeN1 == {
71 ParameterType -> External,
72 BlockName -> NUMIXING,
73 OrderBlock -> 1,
74 Value -> 1.0,
75 ComplexParameter -> False,
76 TeX -> Subscript[V,eN1],
77 Description -> "Mixing between ve flavor/gauge state and N1 mass state"
78 },
79
80 VeN2 == {
81 ParameterType -> External,
82 BlockName -> NUMIXING,
83 OrderBlock -> 2,
84 Value -> 0.0,
85 ComplexParameter -> False,
86 TeX -> Subscript[V,eN2],
87 Description -> "Mixing between ve flavor/gauge state and N2 mass state"
88 },
89
90 VeN3 == {
91 ParameterType -> External,
92 BlockName -> NUMIXING,
93 OrderBlock -> 3,
94 Value -> 0.0,
95 ComplexParameter -> False,
96 TeX -> Subscript[V,eN3],
97 Description -> "Mixing between ve flavor/gauge state and N3 mass state"
98 },
99
100 VmuN1 == {
101 ParameterType -> External,
102 BlockName -> NUMIXING,
103 OrderBlock -> 4,
104 Value -> 0.0,
105 ComplexParameter -> False,
106 TeX -> Subscript[V,muN1],
107 Description -> "Mixing between vm flavor/gauge state and N1 mass state"
108 },
109
110 VmuN2 == {
111 ParameterType -> External,
112 BlockName -> NUMIXING,
113 OrderBlock -> 5,
114 Value -> 1.0,
115 ComplexParameter -> False,
116 TeX -> Subscript[V,muN2],
117 Description -> "Mixing between vm flavor/gauge state and N2 mass state"
118 },
119
120 VmuN3 == {
121 ParameterType -> External,
122 BlockName -> NUMIXING,
123 OrderBlock -> 6,
124 Value -> 0.0,
125 ComplexParameter -> False,
126 TeX -> Subscript[V,muN3],
127 Description -> "Mixing between vm flavor/gauge state and N3 mass state"
128 },
129
130 VtaN1 == {
131 ParameterType -> External,
132 BlockName -> NUMIXING,
133 OrderBlock -> 7,
134 Value -> 0.0,
135 ComplexParameter -> False,
136 TeX -> Subscript[V,taN1],
137 Description -> "Mixing between vt flavor/gauge state and N1 mass state"
138 },
139
140 VtaN2 == {
141 ParameterType -> External,
142 BlockName -> NUMIXING,
143 OrderBlock -> 8,
144 Value -> 0.0,
145 ComplexParameter -> False,
146 TeX -> Subscript[V,taN2],
147 Description -> "Mixing between vt flavor/gauge state and N2 mass state"
148 },
149
150 VtaN3 == {
151 ParameterType -> External,
152 BlockName -> NUMIXING,
153 OrderBlock -> 9,
154 Value -> 1.0,
155 ComplexParameter -> False,
156 TeX -> Subscript[V,taN3],
157 Description -> "Mixing between vt flavor/gauge state and N3 mass state"
158 },
159
160 (* vSMEFT Block *)
161 Lambda == {
162 ParameterType -> External,
163 BlockName -> vSMEFTBLOCK,
164 OrderBlock -> 1,
165 Value -> 1000.0,
166 ComplexParameter -> False,
167 InteractionOrder -> {QED,-1},
168 TeX -> \[CapitalLambda],
169 Description -> "EFT cutoff scale [GeV]"
170 },
171
172 CeN1 == {
173 ParameterType -> External,
174 BlockName -> vSMEFTBLOCK,
175 OrderBlock -> 2,
176 Value -> 1.0,
177 ComplexParameter -> False,
178 TeX -> Subscript[C,eN1],
179 Description -> "Wilson coeff. between ve flavor/gauge state and N1 mass state"
180 },
181
182 CeN2 == {
183 ParameterType -> External,
184 BlockName -> vSMEFTBLOCK,
185 OrderBlock -> 3,
186 Value -> 0.0,
187 ComplexParameter -> False,
188 TeX -> Subscript[C,eN2],
189 Description -> "Wilson coeff. between ve flavor/gauge state and N2 mass state"
190 },
191
192 CeN3 == {
193 ParameterType -> External,
194 BlockName -> vSMEFTBLOCK,
195 OrderBlock -> 4,
196 Value -> 0.0,
197 ComplexParameter -> False,
198 TeX -> Subscript[C,eN3],
199 Description -> "Wilson coeff. between ve flavor/gauge state and N3 mass state"
200 },
201
202 CmuN1 == {
203 ParameterType -> External,
204 BlockName -> vSMEFTBLOCK,
205 OrderBlock -> 5,
206 Value -> 0.0,
207 ComplexParameter -> False,
208 TeX -> Subscript[C,muN1],
209 Description -> "Wilson coeff. between vm flavor/gauge state and N1 mass state"
210 },
211
212 CmuN2 == {
213 ParameterType -> External,
214 BlockName -> vSMEFTBLOCK,
215 OrderBlock -> 6,
216 Value -> 1.0,
217 ComplexParameter -> False,
218 TeX -> Subscript[C,muN2],
219 Description -> "Wilson coeff. between vm flavor/gauge state and N2 mass state"
220 },
221
222 CmuN3 == {
223 ParameterType -> External,
224 BlockName -> vSMEFTBLOCK,
225 OrderBlock -> 7,
226 Value -> 0.0,
227 ComplexParameter -> False,
228 TeX -> Subscript[C,muN3],
229 Description -> "Wilson coeff. between vm flavor/gauge state and N3 mass state"
230 },
231
232 CtaN1 == {
233 ParameterType -> External,
234 BlockName -> vSMEFTBLOCK,
235 OrderBlock -> 8,
236 Value -> 0.0,
237 ComplexParameter -> False,
238 TeX -> Subscript[C,taN1],
239 Description -> "Wilson coeff. between vt flavor/gauge state and N1 mass state"
240 },
241
242 CtaN2 == {
243 ParameterType -> External,
244 BlockName -> vSMEFTBLOCK,
245 OrderBlock -> 9,
246 Value -> 0.0,
247 ComplexParameter -> False,
248 TeX -> Subscript[C,taN2],
249 Description -> "Wilson coeff. between vt flavor/gauge state and N2 mass state"
250 },
251
252 CtaN3 == {
253 ParameterType -> External,
254 BlockName -> vSMEFTBLOCK,
255 OrderBlock -> 10,
256 Value -> 1.0,
257 ComplexParameter -> False,
258 TeX -> Subscript[C,taN3],
259 Description -> "Wilson coeff. between vt flavor/gauge state and N3 mass state"
260 },
261
262
263 (* Internal Parameters *)
264 gN == {
265 ParameterType -> Internal,
266 Definitions -> {gN->ee/sw},
267 InteractionOrder -> {NP,1},
268 TeX -> Subscript[g,N]
269 },
270 gvSMEFT == {
271 ParameterType -> Internal,
272 Definitions -> {gvSMEFT->ee*vev*vev/Lambda/Lambda/sw/2}
273 },
274
275(* ************************** *)
276(* ***** Containers ***** *)
277(* ************************** *)
278
279 PMNS == {
280 ParameterType -> Internal,
281 Indices -> {Index[Generation], Index[NuGeneration]},
282 Unitary -> False,
283 Value -> { PMNS[1,1]->1, PMNS[1,2]->0, PMNS[1,3]->0, PMNS[1,4]->VeN1, PMNS[1,5]->VeN2, PMNS[1,6]->VeN3,
284 PMNS[2,1]->0, PMNS[2,2]->1, PMNS[2,3]->0, PMNS[2,4]->VmuN1, PMNS[2,5]->VmuN2, PMNS[2,6]->VmuN3,
285 PMNS[3,1]->0, PMNS[3,2]->0, PMNS[3,3]->1, PMNS[3,4]->VtaN1, PMNS[3,5]->VtaN2, PMNS[3,6]->VtaN3},
286 TeX -> Subscript[V,PMNS],
287 Description -> "3x6 v-Nu Mixing Matrix"
288 },
289
290 numass == {
291 ParameterType -> Internal,
292 Indices -> {Index[NuGeneration], Index[NuGeneration]},
293 Value -> {
294 numass[1,1]->0, numass[1,2]->0, numass[1,3]->0, numass[1,4]->0, numass[1,5]->0, numass[1,6]->0,
295 numass[2,1]->0, numass[2,2]->0, numass[2,3]->0, numass[2,4]->0, numass[2,5]->0, numass[2,6]->0,
296 numass[3,1]->0, numass[3,2]->0, numass[3,3]->0, numass[3,4]->0, numass[3,5]->0, numass[3,6]->0,
297 numass[4,1]->0, numass[4,2]->0, numass[4,3]->0, numass[4,4]->mN1, numass[4,5]->0, numass[4,6]->0,
298 numass[5,1]->0, numass[5,2]->0, numass[5,3]->0, numass[5,4]->0, numass[5,5]->mN2, numass[5,6]->0,
299 numass[6,1]->0, numass[6,2]->0, numass[6,3]->0, numass[6,4]->0, numass[6,5]->0, numass[6,6]->mN3},
300 InteractionOrder -> {QED, 0},
301 TeX -> Superscript[M, vN],
302 Description -> "Neutrino mass matrix"
303 }
304
305};
306
307
308M$InteractionOrderHierarchy = {
309 {QCD,1},
310 {QED,2}
311};
312
313
314(* ************************** *)
315(* **** Particle classes **** *)
316(* ************************** *)
317M$ClassesDescription = {
318 (*Majorana Neutrino*)
319 F[131] == {
320 ClassName -> N1,
321 SelfConjugate -> True,
322 Mass -> {mN1,300.},
323 Width -> {WN1,0.303},
324 PropagatorLabel -> "N1",
325 PropagatorType -> Straight,
326 PropagatorArrow -> False,
327 ParticleName -> "N1",
328 PDG -> {9900012},
329 FullName -> "N1"
330 },
331
332 F[132] == {
333 ClassName -> N2,
334 SelfConjugate -> True,
335 Mass -> {mN2,500.},
336 Width -> {WN2,1.50},
337 PropagatorLabel -> "N2",
338 PropagatorType -> Straight,
339 PropagatorArrow -> False,
340 ParticleName -> "N2",
341 PDG -> {9900014},
342 FullName -> "N2"
343 },
344
345 F[133] == {
346 ClassName -> N3,
347 SelfConjugate -> True,
348 Mass -> {mN3,1000.},
349 Width -> {WN3,12.3},
350 PropagatorLabel -> "N3",
351 PropagatorType -> Straight,
352 PropagatorArrow -> False,
353 ParticleName -> "N3",
354 PDG -> {9900016},
355 FullName -> "N3"
356 },
357
358 (* auxiliary container *)
359 F[140] == {
360 ClassName -> vNu,
361 Unphysical -> True,
362 Indices -> {Index[NuGeneration]},
363 FlavorIndex -> NuGeneration,
364 SelfConjugate -> False,
365 Definitions -> {vNu[sp1_,1]->ve[sp1],
366 vNu[sp1_,2]->vm[sp1],
367 vNu[sp1_,3]->vt[sp1],
368 vNu[sp1_,4]->N1[sp1],
369 vNu[sp1_,5]->N2[sp1],
370 vNu[sp1_,6]->N3[sp1]}
371 }
372
373};
374
375(* ************************** *)
376(* ***** Lagrangian ***** *)
377(* ************************** *)
378LNKin := I/2 N1bar[s1].Ga[v,s1,s2].del[N1[s2],v] - 1/2 mN1 N1bar[s1]N1[s1] \
379 + I/2 N2bar[s1].Ga[v,s1,s2].del[N2[s2],v] - 1/2 mN2 N2bar[s1]N2[s1] \
380 + I/2 N3bar[s1].Ga[v,s1,s2].del[N3[s2],v] - 1/2 mN3 N3bar[s1]N3[s1];
381
382(* Charge Current *)
383LNCCbare := gN/Sqrt[2] *( VeN1 * N1bar.W[m].ProjM[m].e \
384 + VmuN1 * N1bar.W[m].ProjM[m].mu \
385 + VtaN1 * N1bar.W[m].ProjM[m].ta ) \
386 + gN/Sqrt[2] *( VeN2 * N2bar.W[m].ProjM[m].e \
387 + VmuN2 * N2bar.W[m].ProjM[m].mu \
388 + VtaN2 * N2bar.W[m].ProjM[m].ta ) \
389 + gN/Sqrt[2] *( VeN3 * N3bar.W[m].ProjM[m].e \
390 + VmuN3 * N3bar.W[m].ProjM[m].mu \
391 + VtaN3 * N3bar.W[m].ProjM[m].ta );
392LNCC := LNCCbare + HC[LNCCbare];
393
394(* Charge Current at dimension six*)
395LNRHbare := gvSMEFT/Sqrt[2] *( CeN1 * N1bar.W[m].ProjP[m].e \
396 + CmuN1 * N1bar.W[m].ProjP[m].mu \
397 + CtaN1 * N1bar.W[m].ProjP[m].ta )*(1 + 2/vev * H + 1/vev/vev * H H) \
398 + gvSMEFT/Sqrt[2] *( CeN2 * N2bar.W[m].ProjP[m].e \
399 + CmuN2 * N2bar.W[m].ProjP[m].mu \
400 + CtaN2 * N2bar.W[m].ProjP[m].ta )*(1 + 2/vev * H + 1/vev/vev * H H) \
401 + gvSMEFT/Sqrt[2] *( CeN3 * N3bar.W[m].ProjP[m].e \
402 + CmuN3 * N3bar.W[m].ProjP[m].mu \
403 + CtaN3 * N3bar.W[m].ProjP[m].ta )*(1 + 2/vev * H + 1/vev/vev * H H) ;
404LND6 := LNRHbare + HC[LNRHbare];
405
406(* Neutral Current *)
407LNNCBare := 1/2 * gN/cw *( VeN1 * N1bar.Z[m].ProjM[m].ve \
408 + VmuN1 * N1bar.Z[m].ProjM[m].vm \
409 + VtaN1 * N1bar.Z[m].ProjM[m].vt ) \
410 + 1/2 * gN/cw *( VeN2 * N2bar.Z[m].ProjM[m].ve \
411 + VmuN2 * N2bar.Z[m].ProjM[m].vm \
412 + VtaN2 * N2bar.Z[m].ProjM[m].vt ) \
413 + 1/2 * gN/cw *( VeN3 * N3bar.Z[m].ProjM[m].ve \
414 + VmuN3 * N3bar.Z[m].ProjM[m].vm \
415 + VtaN3 * N3bar.Z[m].ProjM[m].vt );
416LNNC := LNNCBare + HC[LNNCBare];
417
418(* Higgs Interaction *)
419LNHbare := - gN*mN1/(2*MW) *( VeN1 * N1bar.ProjM.ve H \
420 + VmuN1 * N1bar.ProjM.vm H \
421 + VtaN1 * N1bar.ProjM.vt H ) \
422 - gN*mN2/(2*MW) *( VeN2 * N2bar.ProjM.ve H \
423 + VmuN2 * N2bar.ProjM.vm H \
424 + VtaN2 * N2bar.ProjM.vt H ) \
425 - gN*mN3/(2*MW) *( VeN3 * N3bar.ProjM.ve H \
426 + VmuN3 * N3bar.ProjM.vm H \
427 + VtaN3 * N3bar.ProjM.vt H );
428LNH := LNHbare + HC[LNHbare];
429
430(* Goldstone Interaction *)
431LNGbare := I *gN*mN1/(2*MW) *( VeN1 * vebar.ProjP.N1 G0 \
432 + VmuN1 * vmbar.ProjP.N1 G0 \
433 + VtaN1 * vtbar.ProjP.N1 G0) \
434 + I *gN*mN2/(2*MW) *( VeN2 * vebar.ProjP.N2 G0 \
435 + VmuN2 * vmbar.ProjP.N2 G0 \
436 + VtaN2 * vtbar.ProjP.N2 G0) \
437 + I *gN*mN3/(2*MW) *( VeN3 * vebar.ProjP.N3 G0 \
438 + VmuN3 * vmbar.ProjP.N3 G0 \
439 + VtaN3 * vtbar.ProjP.N3 G0) \
440 + I *gN*mN1/(Sqrt[2]*MW) *( VeN1 * ebar.ProjP.N1 GPbar \
441 + VmuN1 * mubar.ProjP.N1 GPbar \
442 + VtaN1 * tabar.ProjP.N1 GPbar) \
443 + I *gN*mN2/(Sqrt[2]*MW) *( VeN2 * ebar.ProjP.N2 GPbar \
444 + VmuN2 * mubar.ProjP.N2 GPbar \
445 + VtaN2 * tabar.ProjP.N2 GPbar) \
446 + I *gN*mN3/(Sqrt[2]*MW) *( VeN3 * ebar.ProjP.N3 GPbar \
447 + VmuN3 * mubar.ProjP.N3 GPbar \
448 + VtaN3 * tabar.ProjP.N3 GPbar);
449LNG := LNGbare + HC[LNGbare];
450
451(* Full N Lagrangian *)
452LN:= LNKin + LNCC + LNNC + LNH + LNG + LND6;
453
454(* Combine Lagrangian *)
455LFull := LSM + LN;