# B-L-SM: B-L.fr

File B-L.fr, 33.9 KB (added by L.Basso, 7 years ago) |
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1 | (***************************************************************************************************************) |

2 | (****** This is the FeynRules mod-file for the pure B-L model ******) |

3 | (****** ******) |

4 | (****** Authors: L. Basso, G. M. Pruna ******) |

5 | (****** ******) |

6 | (****** Choose whether Feynman gauge is desired. ******) |

7 | (****** If set to False, unitary gauge is assumed. ****) |

8 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***) |

9 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****) |

10 | (***************************************************************************************************************) |

11 | |

12 | M$ModelName = "B-L-FR"; |

13 | |

14 | |

15 | M$Information = {Authors -> {"L. Basso", "G. M. Pruna"}, |

16 | Version -> "1.1", |

17 | Date -> "27-10-2011", |

18 | Institutions -> {"University of Southampton, UK", "RAL-PPD, Didcot, UK", "Albert-Ludwigs-UniversitÃ€t Freiburg"}, |

19 | Emails -> {"lorenzo.basso@physik.uni-freiburg.de", "Giovanni_Marco.Pruna@tu-dresden.de"}, |

20 | References -> " L.~Basso, A.~Belyaev, S.~Moretti and C.~H.~Shepherd-Themistocleous, \"Phenomenology of the minimal B-L extension of the Standard model: Z' and neutrinos,\", Phys. Rev. D 80, 055030 (2009) [arXiv:0812.4313 [hep-ph]]", |

21 | URLs -> "http://feynrules.phys.ucl.ac.be/..."}; |

22 | |

23 | FeynmanGauge = True; |

24 | |

25 | |

26 | (******* Index definitions ********) |

27 | |

28 | IndexRange[ Index[Generation] ] = Range[3] |

29 | |

30 | IndexRange[ Index[Colour] ] = NoUnfold[Range[3]] |

31 | |

32 | IndexRange[ Index[Gluon] ] = NoUnfold[Range[8]] |

33 | |

34 | IndexRange[ Index[SU2W] ] = Unfold[Range[3]] |

35 | |

36 | |

37 | IndexStyle[Colour, i] |

38 | |

39 | IndexStyle[Generation, f] |

40 | |

41 | IndexStyle[Gluon ,a] |

42 | |

43 | IndexStyle[SU2W ,k] |

44 | |

45 | (******* Gauge parameters (for FeynArts) ********) |

46 | |

47 | GaugeXi[ V[1] ] = GaugeXi[A]; |

48 | GaugeXi[ V[2] ] = GaugeXi[Z]; |

49 | GaugeXi[ V[3] ] = GaugeXi[W]; |

50 | GaugeXi[ V[4] ] = GaugeXi[G]; |

51 | GaugeXi[ V[7] ] = GaugeXi[Zp]; |

52 | GaugeXi[ S[1] ] = 1; |

53 | GaugeXi[ S[2] ] = GaugeXi[Z]; |

54 | GaugeXi[ S[3] ] = GaugeXi[W]; |

55 | GaugeXi[ S[4] ] = 1; |

56 | GaugeXi[ S[5] ] = GaugeXi[Zp]; |

57 | GaugeXi[ U[1] ] = GaugeXi[A]; |

58 | GaugeXi[ U[2] ] = GaugeXi[Z]; |

59 | GaugeXi[ U[31] ] = GaugeXi[W]; |

60 | GaugeXi[ U[32] ] = GaugeXi[W]; |

61 | GaugeXi[ U[4] ] = GaugeXi[G]; |

62 | GaugeXi[ U[7] ] = GaugeXi[Zp]; |

63 | |

64 | (***** Setting for interaction order (as e.g. used by MadGraph 5) ******) |

65 | |

66 | M$InteractionOrderHierarchy = { |

67 | {QCD, 1}, |

68 | {QED, 2} |

69 | }; |

70 | |

71 | (**************** Parameters *************) |

72 | |

73 | M$Parameters = { |

74 | |

75 | (* External parameters *) |

76 | |

77 | \[Alpha]EWM1== { |

78 | ParameterType -> External, |

79 | BlockName -> BLINPUTS, |

80 | ParameterName -> aEWM1, |

81 | InteractionOrder -> {QED, -2}, |

82 | Value -> 127.9, |

83 | Description -> "Inverse of the electroweak coupling constant at Z-pole"}, |

84 | |

85 | Gf == { |

86 | ParameterType -> External, |

87 | BlockName -> BLINPUTS, |

88 | InteractionOrder -> {QED, 2}, |

89 | Value -> 1.16637 * 10^(-5), |

90 | Description -> "Fermi constant"}, |

91 | |

92 | \[Alpha]S == { |

93 | ParameterType -> External, |

94 | BlockName -> BLINPUTS, |

95 | TeX -> Subscript[\[Alpha], s], |

96 | ParameterName -> aS, |

97 | InteractionOrder -> {QCD, 2}, |

98 | Value -> 0.1184, |

99 | Description -> "Strong coupling constant at the Z pole."}, |

100 | |

101 | g1p == { |

102 | ParameterType -> External, |

103 | BlockName -> BLINPUTS, |

104 | InteractionOrder -> {QED, 1}, |

105 | Value -> 0.2, |

106 | Description -> "Zp coupling"}, |

107 | |

108 | MH1 == { |

109 | ParameterType -> External, |

110 | BlockName -> BLINPUTS, |

111 | Value -> 120.00, |

112 | Description -> "H1 mass"}, |

113 | |

114 | MH2 == { |

115 | ParameterType -> External, |

116 | BlockName -> BLINPUTS, |

117 | Value -> 450.00, |

118 | Description -> "H2 mass"}, |

119 | |

120 | |

121 | Sa == { |

122 | ParameterType -> External, |

123 | BlockName -> BLINPUTS, |

124 | Value -> 0.01, |

125 | Description -> "Sine of Higgses mixing angle"}, |

126 | |

127 | ymdo == { |

128 | ParameterType -> External, |

129 | BlockName -> YUKAWA, |

130 | Value -> 5.04*10^(-3), |

131 | OrderBlock -> {1}, |

132 | Description -> "Down Yukawa mass"}, |

133 | |

134 | |

135 | ymup == { |

136 | ParameterType -> External, |

137 | BlockName -> YUKAWA, |

138 | Value -> 2.55*10^(-3), |

139 | OrderBlock -> {2}, |

140 | Description -> "Up Yukawa mass"}, |

141 | |

142 | |

143 | yms == { |

144 | ParameterType -> External, |

145 | BlockName -> YUKAWA, |

146 | Value -> 0.101, |

147 | OrderBlock -> {3}, |

148 | Description -> "Strange Yukawa mass"}, |

149 | |

150 | ymc == { |

151 | ParameterType -> External, |

152 | BlockName -> YUKAWA, |

153 | Value -> 1.27, |

154 | OrderBlock -> {4}, |

155 | Description -> "Charm Yukawa mass"}, |

156 | |

157 | ymb == { |

158 | ParameterType -> External, |

159 | BlockName -> YUKAWA, |

160 | Value -> 4.7, |

161 | OrderBlock -> {5}, |

162 | Description -> "Bottom Yukawa mass"}, |

163 | |

164 | ymt == { |

165 | ParameterType -> External, |

166 | BlockName -> YUKAWA, |

167 | Value -> 172.0, |

168 | OrderBlock -> {6}, |

169 | Description -> "Top Yukawa mass"}, |

170 | |

171 | yme == { |

172 | ParameterType -> External, |

173 | BlockName -> YUKAWA, |

174 | Value -> 0.000511, |

175 | OrderBlock -> {11}, |

176 | Description -> "Electron Yukawa mass"}, |

177 | |

178 | ymmu == { |

179 | ParameterType -> External, |

180 | BlockName -> YUKAWA, |

181 | Value -> 0.1057, |

182 | OrderBlock -> {13}, |

183 | Description -> "Muon Yukawa mass"}, |

184 | |

185 | ymtau == { |

186 | ParameterType -> External, |

187 | BlockName -> YUKAWA, |

188 | Value -> 1.777, |

189 | OrderBlock -> {15}, |

190 | Description -> "Tau Yukawa mass"}, |

191 | |

192 | |

193 | sw2 == { |

194 | ParameterType -> External, |

195 | BlockName -> BLINPUTS, |

196 | Value -> 0.232, |

197 | Description -> "Squared Sin of the Weinberg angle"}, |

198 | |

199 | |

200 | (* Internal Parameters *) |

201 | |

202 | \[Alpha]EW == { |

203 | ParameterType -> Internal, |

204 | Value -> 1/\[Alpha]EWM1, |

205 | ParameterName -> aEW, |

206 | InteractionOrder -> {QED, 2}, |

207 | Description -> "Electroweak coupling contant"}, |

208 | |

209 | sw == { |

210 | TeX -> Subscript[s, w], |

211 | ParameterType -> Internal, |

212 | Value -> Sqrt[sw2], |

213 | Description -> "Sin of the Weinberg angle"}, |

214 | |

215 | |

216 | cw == { |

217 | TeX -> Subscript[c, w], |

218 | ParameterType -> Internal, |

219 | Value -> Sqrt[1 - sw^2], |

220 | Description -> "Cos of the Weinberg angle"}, |

221 | |

222 | MW == { |

223 | ParameterType -> Internal, |

224 | Value -> MZ * cw, |

225 | Description -> "W mass"}, |

226 | |

227 | |

228 | ee == { |

229 | TeX -> e, |

230 | ParameterType -> Internal, |

231 | Value -> Sqrt[4 Pi \[Alpha]EW], |

232 | InteractionOrder -> {QED, 1}, |

233 | Description -> "Electric coupling constant"}, |

234 | |

235 | |

236 | gw == { |

237 | TeX -> Subscript[g, w], |

238 | ParameterType -> Internal, |

239 | Value -> ee / sw, |

240 | InteractionOrder -> {QED, 1}, |

241 | Description -> "Weak coupling constant"}, |

242 | |

243 | g1 == { |

244 | TeX -> Subscript[g, 1], |

245 | ParameterType -> Internal, |

246 | Value -> ee / cw, |

247 | InteractionOrder -> {QED, 1}, |

248 | Description -> "U(1)Y coupling constant"}, |

249 | |

250 | gs == { |

251 | TeX -> Subscript[g, s], |

252 | ParameterType -> Internal, |

253 | Value -> Sqrt[4 Pi \[Alpha]S], |

254 | InteractionOrder -> {QCD, 1}, |

255 | ParameterName -> G, |

256 | Description -> "Strong coupling constant"}, |

257 | |

258 | |

259 | v == { |

260 | ParameterType -> Internal, |

261 | BlockName -> VEV, |

262 | Value -> 2*MW*sw/ee, |

263 | InteractionOrder -> {QED, -1}, |

264 | Description -> "H1 VEV"}, |

265 | |

266 | x == { |

267 | ParameterType -> Internal, |

268 | BlockName -> VEV, |

269 | Value -> MZp/(2*g1p), |

270 | InteractionOrder -> {QED, -1}, |

271 | Description -> "H2 VEV"}, |

272 | |

273 | |

274 | Ca == { |

275 | ParameterType -> Internal, |

276 | Value -> Sqrt[1-Sa^2], |

277 | ParameterName -> Ca, |

278 | Description -> "Cosine of Higgses mixing angle"}, |

279 | |

280 | yl == { |

281 | TeX -> Superscript[y, l], |

282 | Indices -> {Index[Generation]}, |

283 | AllowSummation -> True, |

284 | ParameterType -> Internal, |

285 | Value -> {yl[1] -> Sqrt[2] yme / v, yl[2] -> Sqrt[2] ymmu / v, yl[3] -> Sqrt[2] ymtau / v}, |

286 | ParameterName -> {yl[1] -> ye, yl[2] -> ym, yl[3] -> ytau}, |

287 | InteractionOrder -> {QED, 1}, |

288 | ComplexParameter -> False, |

289 | Description -> "Lepton Yukawa coupling"}, |

290 | |

291 | yu == { |

292 | Indices -> {Index[Generation]}, |

293 | AllowSummation -> True, |

294 | AllowSummation -> True, |

295 | ParameterType -> Internal, |

296 | Value -> {yu[1] -> Sqrt[2] ymup / v, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v}, |

297 | ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt}, |

298 | InteractionOrder -> {QED, 1}, |

299 | ComplexParameter -> False, |

300 | Description -> "U-quark Yukawa coupling"}, |

301 | |

302 | yd == { |

303 | TeX -> Superscript[y, d], |

304 | Indices -> {Index[Generation]}, |

305 | AllowSummation -> True, |

306 | ParameterType -> Internal, |

307 | Value -> {yd[1] -> Sqrt[2] ymdo / v, yd[2] -> Sqrt[2] yms / v, yd[3] -> Sqrt[2] ymb / v}, |

308 | ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb}, |

309 | InteractionOrder -> {QED, 1}, |

310 | ComplexParameter -> False, |

311 | Description -> "D-quark Yukawa coupling"}, |

312 | |

313 | ynd == { |

314 | Indices -> {Index[Generation]}, |

315 | AllowSummation -> True, |

316 | ParameterType -> Internal, |

317 | Value -> {ynd[1] -> Sqrt[2*MnL1*MnH1]/v, |

318 | ynd[2] -> Sqrt[2*MnL2*MnH2]/v, |

319 | ynd[3] -> Sqrt[2*MnL3*MnH3]/v}, |

320 | ParameterName -> {ynd[1] -> ynd1, ynd[2] -> ynd2, ynd[3] -> ynd3}, |

321 | InteractionOrder -> {QED, 1}, |

322 | ComplexParameter -> False, |

323 | Description -> "Dirac neutrino Yukawa coupling"}, |

324 | |

325 | ynm == { |

326 | Indices -> {Index[Generation]}, |

327 | AllowSummation -> True, |

328 | ParameterType -> Internal, |

329 | Value -> {ynm[1] -> (MnH1-MnL1)/Sqrt[2]/x, |

330 | ynm[2] -> (MnH2-MnL2)/Sqrt[2]/x, |

331 | ynm[3] -> (MnH3-MnL3)/Sqrt[2]/x}, |

332 | ParameterName -> {ynm[1] -> ynm1, ynm[2] -> ynm2, ynm[3] -> ynm3}, |

333 | InteractionOrder -> {QED, 1}, |

334 | ComplexParameter -> False, |

335 | Description -> "Majorana neutrino Yukawa coupling"}, |

336 | |

337 | Mdd == { |

338 | Indices -> {Index[Generation]}, |

339 | AllowSummation -> True, |

340 | ParameterType -> Internal, |

341 | Value -> {Mdd[1] -> ynd1*v/Sqrt[2], |

342 | Mdd[2] -> ynd2*v/Sqrt[2], |

343 | Mdd[3] -> ynd3*v/Sqrt[2]}, |

344 | ParameterName -> {Mdd[1] -> Mdd1, |

345 | Mdd[2] -> Mdd2, |

346 | Mdd[3] -> Mdd3}, |

347 | ComplexParameter -> False, |

348 | Description -> "Neutrino Dirac Mass"}, |

349 | |

350 | s12 == { |

351 | TeX -> Subscript[S\[Theta], 12], |

352 | ParameterType -> External, |

353 | BlockName -> CKMBLOCK, |

354 | Value -> 0.221, |

355 | Description -> "Sin(theta_12), PDG-94"}, |

356 | |

357 | s23 == { |

358 | TeX -> Subscript[S\[Theta], 23], |

359 | ParameterType -> External, |

360 | BlockName -> CKMBLOCK, |

361 | Value -> 0.040, |

362 | Description -> "Sin(theta_23), PDG-94"}, |

363 | |

364 | s13 == { |

365 | TeX -> Subscript[S\[Theta], 13], |

366 | ParameterType -> External, |

367 | BlockName -> CKMBLOCK, |

368 | Value -> 0.0035, |

369 | Description -> "Sin(theta_13), PDG-94"}, |

370 | |

371 | c12 == { |

372 | TeX -> Subscript[C\[Theta], 12], |

373 | ParameterType -> Internal, |

374 | BlockName -> CKMBLOCK, |

375 | Value -> Sqrt[1-s12^2], |

376 | Description -> "Cos(theta_12)"}, |

377 | |

378 | c23 == { |

379 | TeX -> Subscript[C\[Theta], 23], |

380 | ParameterType -> Internal, |

381 | BlockName -> CKMBLOCK, |

382 | Value -> Sqrt[1-s23^2], |

383 | Description -> "Cos(theta_23)"}, |

384 | |

385 | c13 == { |

386 | TeX -> Subscript[C\[Theta], 13], |

387 | ParameterType -> Internal, |

388 | BlockName -> CKMBLOCK, |

389 | Value -> Sqrt[1-s13^2], |

390 | Description -> "Cos(theta_13)"}, |

391 | |

392 | CKM == { |

393 | Indices -> {Index[Generation], Index[Generation]}, |

394 | TensorClass -> CKM, |

395 | Unitary -> True, |

396 | Value -> {CKM[1,1] -> c12*c13, |

397 | CKM[1,2] -> s12*c13, |

398 | CKM[1,3] -> s13, |

399 | CKM[2,1] -> -s12*c23-c12*s23*s13, |

400 | CKM[2,2] -> c12*c23-s12*s23*s13, |

401 | CKM[2,3] -> s23*c13, |

402 | CKM[3,1] -> s12*s23-c12*c23*s13, |

403 | CKM[3,2] -> -c12*s23-s12*c23*s13, |

404 | CKM[3,3] -> c23*c13}, |

405 | Description -> "CKM-Matrix"}, |

406 | |

407 | San == { |

408 | Indices -> {Index[Generation]}, |

409 | AllowSummation -> True, |

410 | ParameterType -> Internal, |

411 | Value -> {San[1] -> -Sqrt[MnL1/(MnH1+MnL1)], |

412 | San[2] -> -Sin[ArcSin[2*Mdd2/Sqrt[4*Mdd2^2+(MnH2-MnL2)^2]]/2], |

413 | San[3] -> -Sin[ArcSin[2*Mdd3/Sqrt[4*Mdd3^2+(MnH3-MnL3)^2]]/2]}, |

414 | ParameterName -> {San[1] -> San1, San[2] -> San2, San[3] -> San3}, |

415 | ComplexParameter -> False, |

416 | Description -> "Sin-array of neutrino mass-eigenstates"}, |

417 | |

418 | Can == { |

419 | Indices -> {Index[Generation]}, |

420 | AllowSummation -> True, |

421 | ParameterType -> Internal, |

422 | Value -> {Can[1] -> Sqrt[1-San1^2], |

423 | Can[2] -> Sqrt[1-San2^2], |

424 | Can[3] -> Sqrt[1-San3^2]}, |

425 | ParameterName -> {Can[1] -> Can1, Can[2] -> Can2, Can[3] -> Can3}, |

426 | ComplexParameter -> False, |

427 | Description -> "Cos-array of neutrino mass-eigenstates"}, |

428 | |

429 | |

430 | |

431 | |

432 | \[Lambda]1 == { |

433 | ParameterType -> Internal, |

434 | Value -> MH1^2 /(2*v^2)*Ca^2 + MH2^2 /(2*v^2)*Sa^2, |

435 | ParameterName -> lam1, |

436 | InteractionOrder -> {QED, 2}, |

437 | Description -> "Lambda 1"}, |

438 | |

439 | \[Lambda]2 == { |

440 | ParameterType -> Internal, |

441 | Value -> MH1^2 /(2*x^2)*Sa^2 + MH2^2 /(2*x^2)*Ca^2, |

442 | ParameterName -> lam2, |

443 | InteractionOrder -> {QED, 2}, |

444 | Description -> "Lambda 2"}, |

445 | |

446 | \[Lambda]3 == { |

447 | ParameterType -> Internal, |

448 | Value -> (MH2^2 - MH1^2)/(x*v)*Sa*Ca, |

449 | ParameterName -> lam3, |

450 | InteractionOrder -> {QED, 2}, |

451 | Description -> "Lambda 3, mixing parameter"}, |

452 | |

453 | mu2H1 == { |

454 | ParameterType -> Internal, |

455 | Value -> - \[Lambda]1 * v^2 - \[Lambda]3 /2 * x^2, |

456 | TeX -> m^2, |

457 | Description -> "Coefficient of the quadratic piece of the H1 potential"}, |

458 | |

459 | mu2H2 == { |

460 | ParameterType -> Internal, |

461 | Value -> - \[Lambda]3 /2 * v^2 - \[Lambda]2 * x^2, |

462 | TeX -> \[Mu]^2, |

463 | Description -> "Coefficient of the quadratic piece of the H2 potential"} |

464 | |

465 | } |

466 | |

467 | (************** Gauge Groups ******************) |

468 | |

469 | M$GaugeGroups = { |

470 | |

471 | U1BL == { |

472 | Abelian -> True, |

473 | GaugeBoson -> Bp, |

474 | Charge -> BL, |

475 | CouplingConstant -> g1p}, |

476 | |

477 | U1Y == { |

478 | Abelian -> True, |

479 | GaugeBoson -> B, |

480 | Charge -> Y, |

481 | CouplingConstant -> g1}, |

482 | |

483 | SU2L == { |

484 | Abelian -> False, |

485 | GaugeBoson -> Wi, |

486 | StructureConstant -> Eps, |

487 | CouplingConstant -> gw}, |

488 | |

489 | SU3C == { |

490 | Abelian -> False, |

491 | GaugeBoson -> G, |

492 | StructureConstant -> f, |

493 | SymmetricTensor -> dSUN, |

494 | Representations -> {T, Colour}, |

495 | CouplingConstant -> gs} |

496 | } |

497 | |

498 | (********* Particle Classes **********) |

499 | |

500 | M$ClassesDescription = { |

501 | |

502 | (********** Fermions ************) |

503 | |

504 | (* Mass-Eigenstate light neutrino: Q = 0, BL= -1 *) |

505 | |

506 | F[11] == { |

507 | ClassName -> nL, |

508 | ClassMembers -> {nL1, nL2, nL3}, |

509 | FlavorIndex -> Generation, |

510 | SelfConjugate -> True, |

511 | Indices -> {Index[Generation]}, |

512 | Mass -> {MnL, {MnL1, 10^(-9)}, {MnL2, 10^(-9)}, {MnL3, 10^(-9)}}, |

513 | Width -> 0, |

514 | PropagatorLabel -> {"nL", "nul1", "nul2", "nul3"}, |

515 | PropagatorType -> Straight, |

516 | ParticleName -> {"n1", "n2", "n3"}, |

517 | PropagatorArrow -> Forward, |

518 | PDG -> {12, 14, 16}, |

519 | FullName -> {"Light neutrino 1", "Light neutrino 2", "Light neutrino 3"} }, |

520 | |

521 | (* Mass-Eigenstate heavy neutrino: Q = 0, BL= -1 *) |

522 | |

523 | F[12] == { |

524 | ClassName -> nH, |

525 | ClassMembers -> {nH1, nH2, nH3}, |

526 | FlavorIndex -> Generation, |

527 | SelfConjugate -> True, |

528 | Indices -> {Index[Generation]}, |

529 | Mass -> {MnH, {MnH1, 200.00}, {MnH2, 200.00}, {MnH3, 200.00}}, |

530 | Width -> 10^(-13), |

531 | PropagatorLabel -> {"nH", "nuh1", "nuh2", "nuh3"}, |

532 | PropagatorType -> Straight, |

533 | ParticleName -> {"~n1", "~n2", "~n3"}, |

534 | PropagatorArrow -> Forward, |

535 | PDG -> {9910012, 9910014, 9910016}, |

536 | FullName -> {"Heavy neutrino 1", "Heavy neutrino 2", "Heavy neutrino 3"} }, |

537 | |

538 | (* Left-handed neutrino: unphysical *) |

539 | F[13] == { |

540 | ClassName -> nF, |

541 | ClassMembers -> {nF1,nF2,nF3}, |

542 | FlavorIndex -> Generation, |

543 | SelfConjugate -> True, |

544 | Indices -> {Index[Generation]}, |

545 | Unphysical -> True, |

546 | Definitions -> {nF[s_,i_] -> Can[i] nL[s,i]-San[i] nH[s,i]}, |

547 | FullName -> {"Majorana LH component of Dirac neutrino 1", |

548 | "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} }, |

549 | |

550 | (* Right-handed neutrino: unphysical *) |

551 | F[14] == { |

552 | ClassName -> nR, |

553 | ClassMembers -> {nR1,nR2,nR3}, |

554 | FlavorIndex -> Generation, |

555 | SelfConjugate -> True, |

556 | Indices -> {Index[Generation]}, |

557 | Unphysical -> True, |

558 | Definitions -> {nR[s_,i_] -> San[i] nL[s,i]+Can[i] nH[s,i]}, |

559 | FullName -> {"Majorana LH component of Dirac neutrino 1", "Majorana LH component of Dirac neutrino 2", "Majorana LH component of Dirac neutrino 3"} }, |

560 | |

561 | |

562 | (* Flavour-eigenstate neutrino: unphysical *) |

563 | F[15] == { |

564 | ClassName -> vl, |

565 | ClassMembers -> {vle,vlm,vlt}, |

566 | FlavorIndex -> Generation, |

567 | SelfConjugate -> False, |

568 | Indices -> {Index[Generation]}, |

569 | QuantumNumbers -> {Q -> 0, LeptonNumber -> 1, BarionLepton -> -1}, |

570 | Unphysical -> True, |

571 | Definitions -> {vl[s_,i_] -> left[nF[s,i]]+right[nR[s,i]]}, |

572 | ParticleName -> {"nue", "num", "nut"}, |

573 | AntiParticleName -> {"nue-bar", "num-bar", "nut-bar"}, |

574 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"} }, |

575 | |

576 | |

577 | (* Leptons (electron): I_3 = -1/2, Q = -1, BL= -1 *) |

578 | F[2] == { |

579 | ClassName -> l, |

580 | ClassMembers -> {e, m, tt}, |

581 | FlavorIndex -> Generation, |

582 | SelfConjugate -> False, |

583 | Indices -> {Index[Generation]}, |

584 | Mass -> {Ml, {ME, 0.000511}, {MM, 0.1057}, {MTA, 1.777}}, |

585 | Width -> 0, |

586 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1, BarionLepton -> -1}, |

587 | PropagatorLabel -> {"l", "e", "m", "tt"}, |

588 | PropagatorType -> Straight, |

589 | ParticleName -> {"e", "m", "l"}, |

590 | AntiParticleName -> {"E", "M", "L"}, |

591 | PropagatorArrow -> Forward, |

592 | PDG -> {11, 13, 15}, |

593 | FullName -> {"Electron", "Muon", "Tau"} }, |

594 | |

595 | (* Quarks (u): I_3 = +1/2, Q = +2/3, BL=1/3 *) |

596 | F[3] == { |

597 | ClassMembers -> {u, c, t}, |

598 | ClassName -> uq, |

599 | FlavorIndex -> Generation, |

600 | SelfConjugate -> False, |

601 | Indices -> {Index[Generation], Index[Colour]}, |

602 | Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.27}, {MT, 172.0}}, |

603 | Width -> {0, 0, {WT, 1.50833649}}, |

604 | QuantumNumbers -> {Q -> 2/3, BarionLepton -> 1/3}, |

605 | PropagatorLabel -> {"uq", "u", "c", "t"}, |

606 | ParticleName -> {"u", "c", "t"}, |

607 | AntiParticleName -> {"U", "C", "T"}, |

608 | PropagatorType -> Straight, |

609 | PropagatorArrow -> Forward, |

610 | PDG -> {2, 4, 6}, |

611 | FullName -> {"u-quark", "c-quark", "t-quark"}}, |

612 | |

613 | (* Quarks (d): I_3 = -1/2, Q = -1/3, BL=1/3 *) |

614 | F[4] == { |

615 | ClassMembers -> {d, s, b}, |

616 | ClassName -> dq, |

617 | FlavorIndex -> Generation, |

618 | SelfConjugate -> False, |

619 | Indices -> {Index[Generation], Index[Colour]}, |

620 | Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.101}, {MB, 4.7}}, |

621 | Width -> 0, |

622 | QuantumNumbers -> {Q -> -1/3, BarionLepton -> 1/3}, |

623 | ParticleName -> {"d", "s", "b"}, |

624 | AntiParticleName -> {"D", "S", "B"}, |

625 | PropagatorLabel -> {"dq", "d", "s", "b"}, |

626 | PropagatorType -> Straight, |

627 | PropagatorArrow -> Forward, |

628 | PDG -> {1,3,5}, |

629 | FullName -> {"d-quark", "s-quark", "b-quark"} }, |

630 | |

631 | |

632 | (********** Ghosts **********) |

633 | U[1] == { |

634 | ClassName -> ghA, |

635 | SelfConjugate -> False, |

636 | Indices -> {}, |

637 | Ghost -> A, |

638 | Mass -> 0, |

639 | QuantumNumbers -> {GhostNumber -> 1}, |

640 | PropagatorLabel -> uA, |

641 | PropagatorType -> GhostDash, |

642 | PropagatorArrow -> Forward}, |

643 | |

644 | U[2] == { |

645 | ClassName -> ghZ, |

646 | SelfConjugate -> False, |

647 | Indices -> {}, |

648 | Mass -> {MZ, Internal}, |

649 | Ghost -> Z, |

650 | QuantumNumbers -> {GhostNumber -> 1}, |

651 | PropagatorLabel -> uZ, |

652 | PropagatorType -> GhostDash, |

653 | PropagatorArrow -> Forward}, |

654 | |

655 | U[31] == { |

656 | ClassName -> ghWp, |

657 | SelfConjugate -> False, |

658 | Indices -> {}, |

659 | Mass -> {MW, Internal}, |

660 | Ghost -> W, |

661 | QuantumNumbers -> {Q-> 1, GhostNumber -> 1}, |

662 | PropagatorLabel -> uWp, |

663 | PropagatorType -> GhostDash, |

664 | PropagatorArrow -> Forward}, |

665 | |

666 | U[32] == { |

667 | ClassName -> ghWm, |

668 | SelfConjugate -> False, |

669 | Indices -> {}, |

670 | Mass -> {MW, Internal}, |

671 | Ghost -> Wbar, |

672 | QuantumNumbers -> {Q-> -1, GhostNumber -> 1}, |

673 | PropagatorLabel -> uWm, |

674 | PropagatorType -> GhostDash, |

675 | PropagatorArrow -> Forward}, |

676 | |

677 | U[4] == { |

678 | ClassName -> ghG, |

679 | SelfConjugate -> False, |

680 | Indices -> {Index[Gluon]}, |

681 | Ghost -> G, |

682 | Mass -> 0, |

683 | QuantumNumbers -> {GhostNumber -> 1}, |

684 | PropagatorLabel -> uG, |

685 | PropagatorType -> GhostDash, |

686 | PropagatorArrow -> Forward}, |

687 | |

688 | U[5] == { |

689 | ClassName -> ghWi, |

690 | Unphysical -> True, |

691 | Definitions -> {ghWi[1] -> (ghWp + ghWm)/Sqrt[2], |

692 | ghWi[2] -> (ghWm - ghWp)/Sqrt[2]/I, |

693 | ghWi[3] -> cw ghZ + sw ghA}, |

694 | SelfConjugate -> False, |

695 | Indices -> {Index[SU2W]}, |

696 | FlavorIndex -> SU2W, |

697 | Ghost -> Wi}, |

698 | |

699 | U[6] == { |

700 | ClassName -> ghB, |

701 | SelfConjugate -> False, |

702 | Definitions -> {ghB -> -sw ghZ + cw ghA}, |

703 | Indices -> {}, |

704 | Unphysical -> True, |

705 | Ghost -> B}, |

706 | |

707 | U[7] == { |

708 | ClassName -> ghZp, |

709 | SelfConjugate -> False, |

710 | Indices -> {}, |

711 | Mass -> {MZp, Internal}, |

712 | Ghost -> Zp, |

713 | QuantumNumbers -> {GhostNumber -> 1}, |

714 | PropagatorLabel -> uZp, |

715 | PropagatorType -> GhostDash, |

716 | PropagatorArrow -> Forward}, |

717 | |

718 | U[8] == { |

719 | ClassName -> ghBp, |

720 | SelfConjugate -> False, |

721 | Definitions -> {ghBp -> ghZp}, |

722 | Indices -> {}, |

723 | Unphysical -> True, |

724 | Ghost -> Bp}, |

725 | |

726 | (************ Gauge Bosons ***************) |

727 | (* Gauge bosons: Q = 0 *) |

728 | V[1] == { |

729 | ClassName -> A, |

730 | SelfConjugate -> True, |

731 | Indices -> {}, |

732 | Mass -> 0, |

733 | Width -> 0, |

734 | PropagatorLabel -> "a", |

735 | PropagatorType -> W, |

736 | PropagatorArrow -> None, |

737 | PDG -> 22, |

738 | FullName -> "Photon" }, |

739 | |

740 | V[2] == { |

741 | ClassName -> Z, |

742 | SelfConjugate -> True, |

743 | Indices -> {}, |

744 | Mass -> {MZ, 91.188}, |

745 | Width -> {WZ, 2.4952}, |

746 | PropagatorLabel -> "Z", |

747 | PropagatorType -> Sine, |

748 | PropagatorArrow -> None, |

749 | PDG -> 23, |

750 | FullName -> "Z" }, |

751 | |

752 | (* Gauge bosons: Q = -1 *) |

753 | V[3] == { |

754 | ClassName -> W, |

755 | SelfConjugate -> False, |

756 | Indices -> {}, |

757 | Mass -> {MW, Internal}, |

758 | Width -> {WW, 2.085}, |

759 | QuantumNumbers -> {Q -> 1}, |

760 | PropagatorLabel -> "W", |

761 | PropagatorType -> Sine, |

762 | PropagatorArrow -> Forward, |

763 | ParticleName ->"W+", |

764 | AntiParticleName ->"W-", |

765 | PDG -> 24, |

766 | FullName -> "W" }, |

767 | |

768 | V[4] == { |

769 | ClassName -> G, |

770 | SelfConjugate -> True, |

771 | Indices -> {Index[Gluon]}, |

772 | Mass -> 0, |

773 | Width -> 0, |

774 | PropagatorLabel -> G, |

775 | PropagatorType -> C, |

776 | PropagatorArrow -> None, |

777 | PDG -> 21, |

778 | FullName -> "G" }, |

779 | |

780 | V[5] == { |

781 | ClassName -> Wi, |

782 | Unphysical -> True, |

783 | Definitions -> {Wi[mu_, 1] -> (W[mu] + Wbar[mu])/Sqrt[2], |

784 | Wi[mu_, 2] -> (Wbar[mu] - W[mu])/Sqrt[2]/I, |

785 | Wi[mu_, 3] -> cw Z[mu] + sw A[mu]}, |

786 | SelfConjugate -> True, |

787 | Indices -> {Index[SU2W]}, |

788 | FlavorIndex -> SU2W, |

789 | Mass -> 0, |

790 | PDG -> {1,2,3}}, |

791 | |

792 | V[6] == { |

793 | ClassName -> B, |

794 | SelfConjugate -> True, |

795 | Definitions -> {B[mu_] -> -sw Z[mu] + cw A[mu]}, |

796 | Indices -> {}, |

797 | Mass -> 0, |

798 | Unphysical -> True}, |

799 | |

800 | V[7] == { |

801 | ClassName -> Zp, |

802 | SelfConjugate -> True, |

803 | Indices -> {}, |

804 | Mass -> {MZp, 1500}, |

805 | Width -> {WZp, 80.00}, |

806 | PropagatorLabel -> "Zp", |

807 | PropagatorType -> Sine, |

808 | PropagatorArrow -> None, |

809 | PDG -> 9900032, |

810 | FullName -> "Zp" }, |

811 | |

812 | V[8] == { |

813 | ClassName -> Bp, |

814 | SelfConjugate -> True, |

815 | Definitions -> {Bp[mu_] -> Zp[mu]}, |

816 | Indices -> {}, |

817 | Unphysical -> True}, |

818 | |

819 | |

820 | (************ Scalar Fields **********) |

821 | (* physical Higgs: Q = 0 *) |

822 | S[1] == { |

823 | ClassName -> H1, |

824 | SelfConjugate -> True, |

825 | Mass -> {MH1, Internal}, |

826 | Width -> {WH1, 1.5}, |

827 | PropagatorLabel -> "H1", |

828 | PropagatorType -> D, |

829 | PropagatorArrow -> None, |

830 | PDG -> 9900025, |

831 | FullName -> "H1" }, |

832 | |

833 | S[2] == { |

834 | ClassName -> phi, |

835 | SelfConjugate -> True, |

836 | Mass -> {MZ, Internal}, |

837 | Width -> Wphi, |

838 | PropagatorLabel -> "Phi", |

839 | PropagatorType -> D, |

840 | PropagatorArrow -> None, |

841 | ParticleName ->"phi0", |

842 | PDG -> 9900250, |

843 | FullName -> "Phi", |

844 | Goldstone -> Z }, |

845 | |

846 | S[3] == { |

847 | ClassName -> phi2, |

848 | SelfConjugate -> False, |

849 | Mass -> {MW, Internal}, |

850 | Width -> Wphi2, |

851 | PropagatorLabel -> "Phi2", |

852 | PropagatorType -> D, |

853 | PropagatorArrow -> None, |

854 | ParticleName ->"phi+", |

855 | AntiParticleName ->"phi-", |

856 | PDG -> 9900251, |

857 | FullName -> "Phi2", |

858 | Goldstone -> W, |

859 | QuantumNumbers -> {Q -> 1}}, |

860 | |

861 | S[4] == { |

862 | ClassName -> H2, |

863 | SelfConjugate -> True, |

864 | Mass -> {MH2, Internal}, |

865 | Width -> {WH2, 10}, |

866 | PropagatorLabel -> "H2", |

867 | PropagatorType -> D, |

868 | PropagatorArrow -> None, |

869 | PDG -> 9900026, |

870 | FullName -> "H2" }, |

871 | |

872 | S[5] == { |

873 | ClassName -> phip, |

874 | SelfConjugate -> True, |

875 | Mass -> {MZp, Internal}, |

876 | Width -> Wphip, |

877 | PropagatorLabel -> "Phip", |

878 | PropagatorType -> D, |

879 | PropagatorArrow -> None, |

880 | ParticleName ->"phi0p", |

881 | PDG -> 9900252, |

882 | FullName -> "Phip", |

883 | Goldstone -> Zp } |

884 | |

885 | } |

886 | |

887 | |

888 | (*****************************************************************************************) |

889 | |

890 | (* SM Lagrangian *) |

891 | |

892 | (******************** Gauge F^2 Lagrangian terms*************************) |

893 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*) |

894 | LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])* |

895 | (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) - |

896 | |

897 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[Bp[nu], mu] - del[Bp[mu], nu])^2 - |

898 | |

899 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* |

900 | (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]); |

901 | |

902 | |

903 | (********************* Fermion Lagrangian terms*************************) |

904 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*) |

905 | LFermions := Module[{Lkin, LQCD, LEWleft, LEWright}, |

906 | |

907 | Lkin = I uqbar.Ga[mu].del[uq, mu] + |

908 | I dqbar.Ga[mu].del[dq, mu] + |

909 | I lbar.Ga[mu].del[l, mu] + |

910 | I left[anti[vl]].Ga[mu].del[left[vl],mu] + |

911 | I right[anti[vl]].Ga[mu].del[right[vl],mu]; |

912 | |

913 | LQCD = gs (uqbar.Ga[mu].T[a].uq + |

914 | dqbar.Ga[mu].T[a].dq)G[mu, a]; |

915 | |

916 | LBright = |

917 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

918 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

919 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

920 | |

921 | LBleft = |

922 | -ee/cw B[mu]/2 left[anti[vl]].Ga[mu].ProjM.vl - (*Y_LL=-1*) |

923 | ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*) |

924 | ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*) |

925 | ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*) |

926 | |

927 | LWleft = ee/sw/2( |

928 | left[anti[vl]].Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*) |

929 | lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*) |

930 | |

931 | Sqrt[2] left[anti[vl]].Ga[mu].ProjM.l W[mu] + |

932 | Sqrt[2] lbar.Ga[mu].ProjM.left[vl] Wbar[mu]+ |

933 | |

934 | uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*) |

935 | dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*) |

936 | |

937 | Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] + |

938 | Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu] |

939 | ); |

940 | |

941 | LBpright = |

942 | - g1p Bp[mu] anti[vl].Ga[mu].ProjP.right[vl] - (*BL_vlR=-1*) |

943 | g1p Bp[mu] lbar.Ga[mu].ProjP.l + (*BL_lR=-1*) |

944 | g1p/3 Bp[mu] uqbar.Ga[mu].ProjP.uq + (*BL_uR=1/3*) |

945 | g1p/3 Bp[mu] dqbar.Ga[mu].ProjP.dq; (*BL_dR=1/3*) |

946 | |

947 | LBpleft = |

948 | - g1p Bp[mu] anti[vl].Ga[mu].ProjM.left[vl] - (*BL_vlL=-1*) |

949 | g1p Bp[mu] lbar.Ga[mu].ProjM.l + (*BL_lL=-1*) |

950 | g1p/3 Bp[mu] uqbar.Ga[mu].ProjM.uq + (*BL_uL=1/3*) |

951 | g1p/3 Bp[mu] dqbar.Ga[mu].ProjM.dq (*BL_dL=1/3*) |

952 | ; |

953 | |

954 | Lkin + LQCD + LBright + LBleft + LWleft + LBpright + LBpleft ]; |

955 | |

956 | (******************** Higgs Lagrangian terms****************************) |

957 | Phi := If[FeynmanGauge, {-I phi2, (v + Ca*H1+Sa*H2 + I phi)/Sqrt[2]}, {0, (v + Ca*H1+Sa*H2)/Sqrt[2]}]; |

958 | Phibar := If[FeynmanGauge, {I phi2bar, (v + Ca*H1+Sa*H2 - I phi)/Sqrt[2]} ,{0, (v + Ca*H1+Sa*H2)/Sqrt[2]}]; |

959 | |

960 | Chi := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 + I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}]; |

961 | Chibar := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 - I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}]; |

962 | |

963 | LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphichi, Dcp, Dcpbar}, |

964 | |

965 | PMVec = Table[PauliSigma[i], {i, 3}]; |

966 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

967 | |

968 | (*Y_phi=1/2*) |

969 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f; |

970 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec); |

971 | |

972 | (*BL_phi=2*) |

973 | Dcp[f_, mu_] := I del[f, mu] + 2*g1p Bp[mu] f ; |

974 | Dcpbar[f_, mu_] := -I del[f, mu] + 2*g1p Bp[mu] f ; |

975 | |

976 | Vphichi[Phi_, Phibar_, Chi_, Chibar_] := mu2H1 Phibar.Phi + mu2H2 Chibar.Chi + |

977 | \[Lambda]1 (Phibar.Phi)^2 + \[Lambda]2 (Chibar.Chi)^2 + \[Lambda]3 (Phibar.Phi)*(Chibar.Chi); |

978 | |

979 | (Dcbar[Phibar, mu]).Dc[Phi, mu] + (Dcpbar[Chibar, mu]).Dcp[Chi, mu] - Vphichi[Phi, Phibar, Chi, Chibar] |

980 | |

981 | ]; |

982 | |

983 | |

984 | (*************** Yukawa Lagrangian***********************) |

985 | (*NOTE: Neutrino states have been expanded on the LH/RH components and the LH mass terms have been changed signs*) |

986 | |

987 | LYuk := If[FeynmanGauge, |

988 | |

989 | Module[{s,r,n,m,i}, - |

990 | yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) - |

991 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] - |

992 | |

993 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2 -I phi)/Sqrt[2] + (*This sign from eps matrix*) |

994 | yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) |

995 | |

996 | - yl[n] Can[n] anti[nL][s,n].ProjP[s,r].l[r,n] (-I phi2) |

997 | + yl[n] San[n] anti[nH][s,n].ProjP[s,r].l[r,n] (-I phi2) |

998 | |

999 | - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] + |

1000 | ynd[n] San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]+ |

1001 | ynd[n] San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2]- |

1002 | |

1003 | ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (Ca*H1+Sa*H2 - I phi)/Sqrt[2] |

1004 | |

1005 | - ynd[n] San[n] lbar[s,n].ProjP[s,r].nL[r,n] (I phi2bar) + |

1006 | ynd[n] Can[n] lbar[s,n].ProjP[s,r].nH[r,n] (I phi2bar) + |

1007 | |

1008 | |

1009 | ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]- |

1010 | ynm[n] Can[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2]- |

1011 | |

1012 | ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (-Sa*H1+Ca*H2 + I phip)/Sqrt[2] |

1013 | |

1014 | |

1015 | ], |

1016 | |

1017 | Module[{s,r,n,m,i}, - |

1018 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2] - |

1019 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2] |

1020 | |

1021 | - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2] + |

1022 | ynd[n] San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]+ |

1023 | ynd[n] San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]- |

1024 | |

1025 | ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (Ca*H1+Sa*H2)/Sqrt[2]+ |

1026 | |

1027 | |

1028 | |

1029 | ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]- |

1030 | ynm[n] Can[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]- |

1031 | |

1032 | ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (-Sa*H1+Ca*H2)/Sqrt[2] |

1033 | |

1034 | ] |

1035 | ]; |

1036 | |

1037 | LYukawa := LYuk + HC[LYuk]; |

1038 | |

1039 | |

1040 | |

1041 | (**************Ghost terms**************************) |

1042 | (* Now we need the ghost terms which are of the form: *) |

1043 | (* - g * antighost * d_BRST G *) |

1044 | (* where d_BRST G is BRST transform of the gauge fixing function. *) |

1045 | |

1046 | LGhost := If[FeynmanGauge, |

1047 | Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB, dBRSTBp, LGhostBp}, |

1048 | |

1049 | (***********First the pure gauge piece.**********************) |

1050 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]]; |

1051 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu]; |

1052 | |

1053 | dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ]; |

1054 | LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu]; |

1055 | |

1056 | dBRSTB[mu_] := cw/ee del[ghB, mu]; |

1057 | LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu]; |

1058 | |

1059 | dBRSTBp[mu_] := 1/g1p del[ghBp, mu]; |

1060 | LGhostBp := - g1p ghBpbar.del[dBRSTBp[mu],mu]; |

1061 | |

1062 | (***********Next the piece from the scalar field.************) |

1063 | LGhostphi := - ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) + |

1064 | I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) - |

1065 | ee/(2*sw) MW ( ( (v+Ca*H1+Sa*H2) + I phi) ghWpbar.ghWp + |

1066 | ( (v+Ca*H1+Sa*H2) - I phi) ghWmbar.ghWm ) - |

1067 | I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) - |

1068 | ee/(2*sw*cw) MZ (v+Ca*H1+Sa*H2) ghZbar.ghZ - |

1069 | |

1070 | 2*g1p MZp (x-Sa*H1+Ca*H2) ghZpbar.ghZp ; |

1071 | |

1072 | |

1073 | (***********Now add the pieces together.********************) |

1074 | LGhostG + LGhostWi + LGhostB + LGhostphi + LGhostBp ] |

1075 | |

1076 | , |

1077 | |

1078 | (*If unitary gauge, only include the gluonic ghost.*) |

1079 | Block[{dBRSTG,LGhostG}, |

1080 | |

1081 | (***********First the pure gauge piece.**********************) |

1082 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]]; |

1083 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu]; |

1084 | |

1085 | (***********Now add the pieces together.********************) |

1086 | LGhostG] |

1087 | |

1088 | ]; |

1089 | |

1090 | (*********Total B-L Lagrangian*******) |

1091 | LBL := LGauge + LHiggs + LFermions + LYukawa + LGhost; |

1092 | |

1093 |