# B-L-SM: minimal_Zp.fr

File minimal_Zp.fr, 38.2 KB (added by L.Basso, 9 years ago) |
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1 | (***************************************************************************************************************) |

2 | (****** This is the FeynRules mod-file for the minimal Zp models ******) |

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

4 | (****** Author: L. Basso ******) |

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 = "minimal_Zp"; |

13 | |

14 | |

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

16 | Version -> "2.0", |

17 | Date -> "09-06-2011", |

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

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

20 | References -> {"L.~Basso, G.M.~Pruna and S.~Moretti, \"A Renormalisation Group Equation Study of the Scalar Sector of the Minimal B-L Extension of the Standard Model,\", Phys.,Rev. D 82, 055018 (2010) [arXiv:1004.3039 [hep-ph]]", "L.~Basso, G.M.~Pruna and S.~Moretti, \"A Theoretical constraints on the couplings of non-exotic minimal Z' bosons,\", JHEP 1108 122 (2011) [arXiv:1106.4762 [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 | |

46 | |

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

48 | |

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

65 | |

66 | |

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

68 | |

69 | M$InteractionOrderHierarchy = { |

70 | {QCD, 1}, |

71 | {QED, 2} |

72 | }; |

73 | |

74 | |

75 | (**************** Parameters *************) |

76 | |

77 | M$Parameters = { |

78 | |

79 | (* External parameters *) |

80 | |

81 | |

82 | \[Alpha]EWM1== { |

83 | ParameterType -> External, |

84 | BlockName -> BLINPUTS, |

85 | ParameterName -> aEWM1, |

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

87 | Value -> 127.9, |

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

89 | |

90 | Gf == { |

91 | ParameterType -> External, |

92 | BlockName -> BLINPUTS, |

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

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

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

96 | |

97 | \[Alpha]S == { |

98 | ParameterType -> External, |

99 | BlockName -> BLINPUTS, |

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

101 | ParameterName -> aS, |

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

103 | Value -> 0.1184, |

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

105 | |

106 | MW == { |

107 | ParameterType -> External, |

108 | BlockName -> BLINPUTS, |

109 | Value -> 80.292, |

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

111 | |

112 | MZp == { |

113 | ParameterType -> External, |

114 | BlockName -> BLINPUTS, |

115 | Value -> 1500.00, |

116 | Description -> "Zp mass"}, |

117 | |

118 | g1p == { |

119 | ParameterType -> External, |

120 | BlockName -> BLINPUTS, |

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

122 | Value -> 0.2, |

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

124 | |

125 | gt == { |

126 | ParameterType -> External, |

127 | BlockName -> BLINPUTS, |

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

129 | Value -> -0.1, |

130 | Description -> "Z-Zp mixing coupling"}, |

131 | |

132 | ymdo == { |

133 | ParameterType -> External, |

134 | BlockName -> YUKAWA, |

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

136 | OrderBlock -> {1}, |

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

138 | |

139 | |

140 | ymup == { |

141 | ParameterType -> External, |

142 | BlockName -> YUKAWA, |

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

144 | OrderBlock -> {2}, |

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

146 | |

147 | yms == { |

148 | ParameterType -> External, |

149 | BlockName -> YUKAWA, |

150 | Value -> 0.101, |

151 | OrderBlock -> {3}, |

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

153 | |

154 | ymc == { |

155 | ParameterType -> External, |

156 | BlockName -> YUKAWA, |

157 | Value -> 1.27, |

158 | OrderBlock -> {4}, |

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

160 | |

161 | ymb == { |

162 | ParameterType -> External, |

163 | BlockName -> YUKAWA, |

164 | Value -> 4.7, |

165 | OrderBlock -> {5}, |

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

167 | |

168 | ymt == { |

169 | ParameterType -> External, |

170 | BlockName -> YUKAWA, |

171 | Value -> 172.0, |

172 | OrderBlock -> {6}, |

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

174 | |

175 | yme == { |

176 | ParameterType -> External, |

177 | BlockName -> YUKAWA, |

178 | Value -> 0.000511, |

179 | OrderBlock -> {11}, |

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

181 | |

182 | ymmu == { |

183 | ParameterType -> External, |

184 | BlockName -> YUKAWA, |

185 | Value -> 0.1057, |

186 | OrderBlock -> {13}, |

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

188 | |

189 | ymtau == { |

190 | ParameterType -> External, |

191 | BlockName -> YUKAWA, |

192 | Value -> 1.777, |

193 | OrderBlock -> {15}, |

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

195 | |

196 | MH1 == { |

197 | ParameterType -> External, |

198 | BlockName -> BLINPUTS, |

199 | Value -> 120.00, |

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

201 | |

202 | MH2 == { |

203 | ParameterType -> External, |

204 | BlockName -> BLINPUTS, |

205 | Value -> 450.00, |

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

207 | |

208 | |

209 | Sa == { |

210 | ParameterType -> External, |

211 | BlockName -> BLINPUTS, |

212 | Value -> 0.1, |

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

214 | |

215 | sw2 == { |

216 | ParameterType -> External, |

217 | BlockName -> BLINPUTS, |

218 | Value -> 0.232, |

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

220 | |

221 | |

222 | |

223 | (* Internal Parameters *) |

224 | |

225 | \[Alpha]EW == { |

226 | ParameterType -> Internal, |

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

228 | TeX -> Subscript[\[Alpha], EW], |

229 | ParameterName -> aEW, |

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

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

232 | |

233 | |

234 | ee == { |

235 | TeX -> e, |

236 | ParameterType -> Internal, |

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

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

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

240 | |

241 | cw == { |

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

243 | ParameterType -> Internal, |

244 | Value -> Sqrt[1 - sw2], |

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

246 | |

247 | sw == { |

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

249 | ParameterType -> Internal, |

250 | Value -> Sqrt[sw2], |

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

252 | |

253 | gw == { |

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

255 | ParameterType -> Internal, |

256 | Value -> ee / sw, |

257 | Definitions -> {gw -> ee / sw}, |

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

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

260 | |

261 | g1 == { |

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

263 | ParameterType -> Internal, |

264 | Value -> ee / cw, |

265 | Definitions -> {g1 -> ee / cw}, |

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

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

268 | |

269 | gs == { |

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

271 | ParameterType -> Internal, |

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

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

274 | ParameterName -> G, |

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

276 | |

277 | v == { |

278 | ParameterType -> Internal, |

279 | BlockName -> VEV, |

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

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

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

283 | |

284 | |

285 | x == { |

286 | ParameterType -> Internal, |

287 | BlockName -> VEV, |

288 | Value -> MZp/(2*g1p)*Sqrt[1-gt^2*v^2/(4*MZp^2-v^2*(gw^2+g1^2))], |

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

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

291 | |

292 | |

293 | Ca == { |

294 | ParameterType -> Internal, |

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

296 | ParameterName -> Ca, |

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

298 | |

299 | |

300 | yl == { |

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

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

303 | AllowSummation -> True, |

304 | ParameterType -> Internal, |

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

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

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

308 | ComplexParameter -> False, |

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

310 | |

311 | yu == { |

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

313 | AllowSummation -> True, |

314 | AllowSummation -> True, |

315 | ParameterType -> Internal, |

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

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

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

319 | ComplexParameter -> False, |

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

321 | |

322 | yd == { |

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

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

325 | AllowSummation -> True, |

326 | ParameterType -> Internal, |

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

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

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

330 | ComplexParameter -> False, |

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

332 | |

333 | ynd == { |

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

335 | AllowSummation -> True, |

336 | ParameterType -> Internal, |

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

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

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

340 | ParameterName -> {ynd[1] -> ynd1, |

341 | ynd[2] -> ynd2, |

342 | ynd[3] -> ynd3}, |

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

344 | ComplexParameter -> False, |

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

346 | |

347 | ynm == { |

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

349 | AllowSummation -> True, |

350 | ParameterType -> Internal, |

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

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

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

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

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

356 | ComplexParameter -> False, |

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

358 | |

359 | Mdd == { |

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

361 | AllowSummation -> True, |

362 | ParameterType -> Internal, |

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

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

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

366 | ParameterName -> {Mdd[1] -> Mdd1, Mdd[2] -> Mdd2, Mdd[3] -> Mdd3}, |

367 | ComplexParameter -> False, |

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

369 | |

370 | s12 == { |

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

372 | ParameterType -> External, |

373 | BlockName -> CKMBLOCK, |

374 | Value -> 0.221, |

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

376 | |

377 | s23 == { |

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

379 | ParameterType -> External, |

380 | BlockName -> CKMBLOCK, |

381 | Value -> 0.040, |

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

383 | |

384 | s13 == { |

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

386 | ParameterType -> External, |

387 | BlockName -> CKMBLOCK, |

388 | Value -> 0.0035, |

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

390 | |

391 | c12 == { |

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

393 | ParameterType -> Internal, |

394 | BlockName -> CKMBLOCK, |

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

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

397 | |

398 | c23 == { |

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

400 | ParameterType -> Internal, |

401 | BlockName -> CKMBLOCK, |

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

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

404 | |

405 | c13 == { |

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

407 | ParameterType -> Internal, |

408 | BlockName -> CKMBLOCK, |

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

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

411 | |

412 | CKM == { |

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

414 | TensorClass -> CKM, |

415 | Unitary -> True, |

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

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

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

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

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

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

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

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

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

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

426 | |

427 | San == { |

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

429 | AllowSummation -> True, |

430 | ParameterType -> Internal, |

431 | Value -> {San[1] -> Sin[ArcSin[-2*Mdd1/Sqrt[4*Mdd1^2+(MnH1-MnL1)^2]]/2], |

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

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

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

435 | ComplexParameter -> False, |

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

437 | |

438 | Can == { |

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

440 | AllowSummation -> True, |

441 | ParameterType -> Internal, |

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

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

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

445 | Definitions -> {Can[1]*San1-> Sa2n1/2, |

446 | Can[2]*San2-> Sa2n2/2, |

447 | Can[3]*San3-> Sa2n3/2, |

448 | Can[1]^2 -San1^2-> Ca2n1, |

449 | Can[2]^2 -San2^2-> Ca2n2, |

450 | Can[3]^2 -San3^2-> Ca2n3}, |

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

452 | ComplexParameter -> False, |

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

454 | |

455 | |

456 | |

457 | \[Lambda]1 == { |

458 | ParameterType -> Internal, |

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

460 | ParameterName -> lam1, |

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

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

463 | |

464 | \[Lambda]2 == { |

465 | ParameterType -> Internal, |

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

467 | ParameterName -> lam2, |

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

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

470 | |

471 | \[Lambda]3 == { |

472 | ParameterType -> Internal, |

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

474 | ParameterName -> lam3, |

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

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

477 | |

478 | mu2H1 == { |

479 | ParameterType -> Internal, |

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

481 | TeX -> m^2, |

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

483 | |

484 | mu2H2 == { |

485 | ParameterType -> Internal, |

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

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

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

489 | |

490 | |

491 | Sp2num == { |

492 | ParameterType -> Internal, |

493 | Value -> 2*gt*Sqrt[(ee/sw)^2+(ee/cw)^2]}, |

494 | |

495 | Cp2num == { |

496 | ParameterType -> Internal, |

497 | Value -> gt^2+16*(x/v)^2*g1p^2-(ee/sw)^2-(ee/cw)^2}, |

498 | |

499 | Sp == { |

500 | AllowSummation -> True, |

501 | ParameterType -> Internal, |

502 | Value -> Sin[ArcSin[Sp2num/Sqrt[Sp2num^2+Cp2num^2]]/2], |

503 | ComplexParameter -> False, |

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

505 | |

506 | Cp == { |

507 | AllowSummation -> True, |

508 | ParameterType -> Internal, |

509 | Value -> Sqrt[1-Sp^2], |

510 | ComplexParameter -> False, |

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

512 | |

513 | |

514 | Cn == { |

515 | ParameterType -> Internal, |

516 | ComplexParameter -> False, |

517 | Value -> (ee/sw)^2+(ee/cw)^2+gt^2+16*(x/v)^2*g1p^2}, |

518 | |

519 | Dn == { |

520 | ParameterType -> Internal, |

521 | ComplexParameter -> False, |

522 | Value -> 64*((ee/sw)^2+(ee/cw)^2)*g1p^2*v^2*x^2}, |

523 | |

524 | |

525 | MZ == { |

526 | ParameterType -> Internal, |

527 | Value -> Sqrt[(Cn*v^2-Sqrt[-Dn+v^4*Cn^2])/8], |

528 | Description -> "Z mass"}, |

529 | |

530 | S2gNum == { |

531 | ParameterType -> Internal, |

532 | ComplexParameter -> False, |

533 | Value -> 8*x/v*gt*g1p}, |

534 | |

535 | C2gNum == { |

536 | ParameterType -> Internal, |

537 | ComplexParameter -> False, |

538 | Value -> (ee/sw)^2+(ee/cw)^2+gt^2-16*(x/v)^2*g1p^2}, |

539 | |

540 | |

541 | sg == { |

542 | ParameterType -> Internal, |

543 | ComplexParameter -> False, |

544 | Value -> Sin[ArcSin[-S2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2], |

545 | Description -> "cosine of Z-Zp goldostone mixing angle"}, |

546 | |

547 | cg == { |

548 | ParameterType -> Internal, |

549 | ComplexParameter -> False, |

550 | Value -> Sqrt[1-sg^2], |

551 | Description -> "sine of Z-Zp goldstone mixing angle"} |

552 | (* Value -> Cos[ArcCos[-C2gNum/Sqrt[S2gNum^2+C2gNum^2]]/2], *) |

553 | } |

554 | |

555 | (************** Gauge Groups ******************) |

556 | |

557 | M$GaugeGroups = { |

558 | |

559 | U1BL == { |

560 | Abelian -> True, |

561 | GaugeBoson -> Bp, |

562 | Charge -> BL, |

563 | CouplingConstant -> g1p}, |

564 | |

565 | U1Y == { |

566 | Abelian -> True, |

567 | GaugeBoson -> B, |

568 | Charge -> Y, |

569 | CouplingConstant -> g1}, |

570 | |

571 | SU2L == { |

572 | Abelian -> False, |

573 | GaugeBoson -> Wi, |

574 | StructureConstant -> Eps, |

575 | CouplingConstant -> gw}, |

576 | |

577 | SU3C == { |

578 | Abelian -> False, |

579 | GaugeBoson -> G, |

580 | StructureConstant -> f, |

581 | SymmetricTensor -> dSUN, |

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

583 | CouplingConstant -> gs} |

584 | } |

585 | |

586 | (********* Particle Classes **********) |

587 | |

588 | M$ClassesDescription = { |

589 | |

590 | (********** Fermions ************) |

591 | |

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

593 | |

594 | F[11] == { |

595 | ClassName -> nL, |

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

597 | FlavorIndex -> Generation, |

598 | SelfConjugate -> True, |

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

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

601 | Width -> 0, |

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

603 | PropagatorType -> Straight, |

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

605 | PropagatorArrow -> Forward, |

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

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

608 | |

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

610 | |

611 | F[12] == { |

612 | ClassName -> nH, |

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

614 | FlavorIndex -> Generation, |

615 | SelfConjugate -> True, |

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

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

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

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

620 | PropagatorType -> Straight, |

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

622 | PropagatorArrow -> Forward, |

623 | PDG -> {9100012, 9100014, 9100016}, |

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

625 | |

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

627 | F[13] == { |

628 | ClassName -> nF, |

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

630 | FlavorIndex -> Generation, |

631 | SelfConjugate -> True, |

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

633 | Unphysical -> True, |

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

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

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

637 | |

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

639 | F[14] == { |

640 | ClassName -> nR, |

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

642 | FlavorIndex -> Generation, |

643 | SelfConjugate -> True, |

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

645 | Unphysical -> True, |

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

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

648 | |

649 | |

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

651 | F[15] == { |

652 | ClassName -> vl, |

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

654 | FlavorIndex -> Generation, |

655 | SelfConjugate -> False, |

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

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

658 | Unphysical -> True, |

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

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

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

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

663 | |

664 | |

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

666 | F[2] == { |

667 | ClassName -> l, |

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

669 | FlavorIndex -> Generation, |

670 | SelfConjugate -> False, |

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

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

673 | Width -> 0, |

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

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

676 | PropagatorType -> Straight, |

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

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

679 | PropagatorArrow -> Forward, |

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

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

682 | |

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

684 | F[3] == { |

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

686 | ClassName -> uq, |

687 | FlavorIndex -> Generation, |

688 | SelfConjugate -> False, |

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

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

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

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

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

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

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

696 | PropagatorType -> Straight, |

697 | PropagatorArrow -> Forward, |

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

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

700 | |

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

702 | F[4] == { |

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

704 | ClassName -> dq, |

705 | FlavorIndex -> Generation, |

706 | SelfConjugate -> False, |

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

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

709 | Width -> 0, |

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

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

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

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

714 | PropagatorType -> Straight, |

715 | PropagatorArrow -> Forward, |

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

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

718 | |

719 | |

720 | (********** Ghosts **********) |

721 | U[1] == { |

722 | ClassName -> ghA, |

723 | SelfConjugate -> False, |

724 | Indices -> {}, |

725 | Ghost -> A, |

726 | Mass -> 0, |

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

728 | PropagatorLabel -> uA, |

729 | PropagatorType -> GhostDash, |

730 | PropagatorArrow -> Forward}, |

731 | |

732 | U[2] == { |

733 | ClassName -> ghZ, |

734 | SelfConjugate -> False, |

735 | Indices -> {}, |

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

737 | Ghost -> Z, |

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

739 | PropagatorLabel -> uZ, |

740 | PropagatorType -> GhostDash, |

741 | PropagatorArrow -> Forward}, |

742 | |

743 | U[31] == { |

744 | ClassName -> ghWp, |

745 | SelfConjugate -> False, |

746 | Indices -> {}, |

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

748 | Ghost -> W, |

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

750 | PropagatorLabel -> uWp, |

751 | PropagatorType -> GhostDash, |

752 | PropagatorArrow -> Forward}, |

753 | |

754 | U[32] == { |

755 | ClassName -> ghWm, |

756 | SelfConjugate -> False, |

757 | Indices -> {}, |

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

759 | Ghost -> Wbar, |

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

761 | PropagatorLabel -> uWm, |

762 | PropagatorType -> GhostDash, |

763 | PropagatorArrow -> Forward}, |

764 | |

765 | U[4] == { |

766 | ClassName -> ghG, |

767 | SelfConjugate -> False, |

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

769 | Ghost -> G, |

770 | Mass -> 0, |

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

772 | PropagatorLabel -> uG, |

773 | PropagatorType -> GhostDash, |

774 | PropagatorArrow -> Forward}, |

775 | |

776 | U[5] == { |

777 | ClassName -> ghWi, |

778 | Unphysical -> True, |

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

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

781 | ghWi[3] -> cw*Cp ghZ + sw ghA - cw*Sp ghZp}, |

782 | SelfConjugate -> False, |

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

784 | FlavorIndex -> SU2W, |

785 | Ghost -> Wi}, |

786 | |

787 | U[6] == { |

788 | ClassName -> ghB, |

789 | SelfConjugate -> False, |

790 | Definitions -> {ghB -> -sw*Cp ghZ + cw ghA + sw*Sp ghZp}, |

791 | Indices -> {}, |

792 | Unphysical -> True, |

793 | Ghost -> B}, |

794 | |

795 | U[7] == { |

796 | ClassName -> ghZp, |

797 | SelfConjugate -> False, |

798 | Indices -> {}, |

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

800 | Ghost -> Zp, |

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

802 | PropagatorLabel -> uZp, |

803 | PropagatorType -> GhostDash, |

804 | PropagatorArrow -> Forward}, |

805 | |

806 | U[8] == { |

807 | ClassName -> ghBp, |

808 | SelfConjugate -> False, |

809 | Definitions -> {ghBp -> Sp ghZ + Cp ghZp}, |

810 | Indices -> {}, |

811 | Unphysical -> True, |

812 | Ghost -> Bp}, |

813 | |

814 | (************ Gauge Bosons ***************) |

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

816 | V[1] == { |

817 | ClassName -> A, |

818 | SelfConjugate -> True, |

819 | Indices -> {}, |

820 | Mass -> 0, |

821 | Width -> 0, |

822 | PropagatorLabel -> "a", |

823 | PropagatorType -> W, |

824 | PropagatorArrow -> None, |

825 | PDG -> 22, |

826 | FullName -> "Photon" }, |

827 | |

828 | V[2] == { |

829 | ClassName -> Z, |

830 | SelfConjugate -> True, |

831 | Indices -> {}, |

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

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

834 | PropagatorLabel -> "Z", |

835 | PropagatorType -> Sine, |

836 | PropagatorArrow -> None, |

837 | PDG -> 23, |

838 | FullName -> "Z" }, |

839 | |

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

841 | V[3] == { |

842 | ClassName -> W, |

843 | SelfConjugate -> False, |

844 | Indices -> {}, |

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

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

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

848 | PropagatorLabel -> "W", |

849 | PropagatorType -> Sine, |

850 | PropagatorArrow -> Forward, |

851 | ParticleName ->"W+", |

852 | AntiParticleName ->"W-", |

853 | PDG -> 24, |

854 | FullName -> "W" }, |

855 | |

856 | V[4] == { |

857 | ClassName -> G, |

858 | SelfConjugate -> True, |

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

860 | Mass -> 0, |

861 | Width -> 0, |

862 | PropagatorLabel -> G, |

863 | PropagatorType -> C, |

864 | PropagatorArrow -> None, |

865 | PDG -> 21, |

866 | FullName -> "G" }, |

867 | |

868 | V[5] == { |

869 | ClassName -> Wi, |

870 | Unphysical -> True, |

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

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

873 | Wi[mu_, 3] -> sw A[mu] + cw*Cp Z[mu] - cw*Sp Zp[mu]}, |

874 | SelfConjugate -> True, |

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

876 | FlavorIndex -> SU2W, |

877 | Mass -> 0, |

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

879 | |

880 | V[6] == { |

881 | ClassName -> B, |

882 | SelfConjugate -> True, |

883 | Definitions -> {B[mu_] -> cw A[mu] - sw*Cp Z[mu] + sw*Sp Zp[mu]}, |

884 | Indices -> {}, |

885 | Mass -> 0, |

886 | Unphysical -> True}, |

887 | |

888 | V[7] == { |

889 | ClassName -> Zp, |

890 | SelfConjugate -> True, |

891 | Indices -> {}, |

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

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

894 | PropagatorLabel -> "Zp", |

895 | PropagatorType -> Sine, |

896 | PropagatorArrow -> None, |

897 | PDG -> 9900032, |

898 | FullName -> "Zp" }, |

899 | |

900 | V[8] == { |

901 | ClassName -> Bp, |

902 | SelfConjugate -> True, |

903 | Definitions -> {Bp[mu_] -> Sp Z[mu] + Cp Zp[mu]}, |

904 | Indices -> {}, |

905 | Unphysical -> True}, |

906 | |

907 | |

908 | (************ Scalar Fields **********) |

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

910 | S[1] == { |

911 | ClassName -> H1, |

912 | SelfConjugate -> True, |

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

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

915 | PropagatorLabel -> "H1", |

916 | PropagatorType -> D, |

917 | PropagatorArrow -> None, |

918 | PDG -> 9900025, |

919 | FullName -> "H1" }, |

920 | |

921 | S[2] == { |

922 | ClassName -> phiZ, |

923 | SelfConjugate -> True, |

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

925 | Width -> Wphi, |

926 | PropagatorLabel -> "PhiZ", |

927 | PropagatorType -> D, |

928 | PropagatorArrow -> None, |

929 | ParticleName ->"phiZ", |

930 | PDG -> 9900250, |

931 | FullName -> "PhiZ", |

932 | Goldstone -> Z }, |

933 | |

934 | S[3] == { |

935 | ClassName -> phi2, |

936 | SelfConjugate -> False, |

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

938 | Width -> Wphi2, |

939 | PropagatorLabel -> "Phi2", |

940 | PropagatorType -> D, |

941 | PropagatorArrow -> None, |

942 | ParticleName ->"phi+", |

943 | AntiParticleName ->"phi-", |

944 | PDG -> 9900251, |

945 | FullName -> "Phi2", |

946 | Goldstone -> W, |

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

948 | |

949 | S[4] == { |

950 | ClassName -> H2, |

951 | SelfConjugate -> True, |

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

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

954 | PropagatorLabel -> "H2", |

955 | PropagatorType -> D, |

956 | PropagatorArrow -> None, |

957 | PDG -> 9900026, |

958 | FullName -> "H2" }, |

959 | |

960 | S[5] == { |

961 | ClassName -> phiZp, |

962 | SelfConjugate -> True, |

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

964 | Width -> WphiZp, |

965 | PropagatorLabel -> "PhiZp", |

966 | PropagatorType -> D, |

967 | PropagatorArrow -> None, |

968 | ParticleName ->"phiZp", |

969 | PDG -> 9900252, |

970 | FullName -> "PhiZp", |

971 | Goldstone -> Zp }, |

972 | |

973 | S[6] == { |

974 | ClassName -> phi, |

975 | Unphysical -> True, |

976 | Definitions -> {phi -> cg phiZ - sg phiZp}, |

977 | SelfConjugate -> True}, |

978 | |

979 | S[7] == { |

980 | ClassName -> phip, |

981 | Unphysical -> True, |

982 | Definitions -> {phip -> sg phiZ + cg phiZp}, |

983 | SelfConjugate -> True}, |

984 | |

985 | S[8] == { |

986 | ClassName -> phic, |

987 | Unphysical -> True, |

988 | Definitions -> {phic[1] -> (phi2 + phi2bar)/Sqrt[2], |

989 | phic[2] -> (phi2bar - phi2)/Sqrt[2]/I}, |

990 | SelfConjugate -> False} |

991 | |

992 | } |

993 | |

994 | |

995 | (*****************************************************************************************) |

996 | |

997 | (* mZp Lagrangian *) |

998 | |

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

1000 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*) |

1001 | LGauge = -1/4 (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i2, i3] Wi[mu, i2] Wi[nu, i3])* |

1002 | (del[Wi[nu, i1], mu] - del[Wi[mu, i1], nu] + gw Eps[i1, i4, i5] Wi[mu, i4] Wi[nu, i5]) - |

1003 | |

1004 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[Bp[nu], mu] - del[Bp[mu], nu])^2 - |

1005 | |

1006 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* |

1007 | (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a4, a5] G[mu, a4] G[nu, a5]); |

1008 | |

1009 | |

1010 | (********************* Fermion Lagrangian terms*************************) |

1011 | (*Sign convention from Lagrangian in between Eq. (A.9) and Eq. (A.10) of Peskin & Schroeder.*) |

1012 | LFermions = Module[{Lkin, LQCD, LEWleft, LEWright}, |

1013 | |

1014 | Lkin = I uqbar.Ga[mu].del[uq, mu] + |

1015 | I dqbar.Ga[mu].del[dq, mu] + |

1016 | I lbar.Ga[mu].del[l, mu] + |

1017 | I left[anti[vl]].Ga[mu].del[left[vl],mu] + |

1018 | I right[anti[vl]].Ga[mu].del[right[vl],mu]; |

1019 | |

1020 | LQCD = gs (uqbar.Ga[mu].T[a].uq + |

1021 | dqbar.Ga[mu].T[a].dq)G[mu, a]; |

1022 | |

1023 | LBright = |

1024 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

1025 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

1026 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

1027 | |

1028 | LBleft = |

1029 | -ee/cw B[mu]/2 left[anti[vl]].Ga[mu].ProjM.vl - (*Y_LL=-1*) |

1030 | ee/cw B[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*) |

1031 | ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*) |

1032 | ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*) |

1033 | |

1034 | LWleft = ee/sw/2( |

1035 | left[anti[vl]].Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*) |

1036 | lbar.Ga[mu].ProjM.l Wi[mu, 3] + (* ( 0 -1 )*) |

1037 | |

1038 | Sqrt[2] left[anti[vl]].Ga[mu].ProjM.l W[mu] + |

1039 | Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu]+ |

1040 | |

1041 | uqbar.Ga[mu].ProjM.uq Wi[mu, 3] - (*sigma3 = ( 1 0 )*) |

1042 | dqbar.Ga[mu].ProjM.dq Wi[mu, 3] + (* ( 0 -1 )*) |

1043 | |

1044 | Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu] + |

1045 | Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu] |

1046 | ); |

1047 | |

1048 | LBpright = |

1049 | - g1p Bp[mu] right[anti[vl]].Ga[mu].ProjP.vl + (*Y_vlR=0, BL_vlR=-1*) |

1050 | (-1*gt -g1p) Bp[mu] lbar.Ga[mu].ProjP.l + (*Y_lR=-1, BL_lR=-1*) |

1051 | (2/3*gt + g1p/3) Bp[mu] uqbar.Ga[mu].ProjP.uq + (*Y_uR=2/3, BL_uR=1/3*) |

1052 | (-1/3*gt + g1p/3) Bp[mu] dqbar.Ga[mu].ProjP.dq; (*Y_dR=-1/3, BL_dR=1/3*) |

1053 | |

1054 | LBpleft = |

1055 | - (gt/2 + g1p) Bp[mu] left[anti[vl]].Ga[mu].ProjM.vl - (*Y_lL=-1/2, BL_vlL=-1*) |

1056 | (gt/2 + g1p) Bp[mu] lbar.Ga[mu].ProjM.l + (*Y_lL=-1/2, BL_lL=-1*) |

1057 | (gt/3/2 + g1p/3) Bp[mu] uqbar.Ga[mu].ProjM.uq + (*Y_qL=1/6, BL_uL=1/3*) |

1058 | (gt/3/2 + g1p/3) Bp[mu] dqbar.Ga[mu].ProjM.dq (*Y_qL=1/6, BL_dL=1/3*) |

1059 | ; |

1060 | |

1061 | Lkin + LQCD + LBright + LBleft + LWleft + LBpright + LBpleft ]; |

1062 | |

1063 | (******************** Higgs Lagrangian terms****************************) |

1064 | Phi := If[FeynmanGauge, {-I phi2, (v + Ca*H1+Sa*H2 + I phi)/Sqrt[2]}, {0, (v + Ca*H1+Sa*H2)/Sqrt[2]}]; |

1065 | Phibar := If[FeynmanGauge, {I phi2bar, (v + Ca*H1+Sa*H2 - I phi)/Sqrt[2]} ,{0, (v + Ca*H1+Sa*H2)/Sqrt[2]}]; |

1066 | |

1067 | Chi := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 + I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}]; |

1068 | Chibar := If[FeynmanGauge, {(x -Sa*H1+Ca*H2 - I phip)/Sqrt[2]}, {(x -Sa*H1+Ca*H2)/Sqrt[2]}]; |

1069 | |

1070 | LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphichi, Dcp, Dcpbar}, |

1071 | |

1072 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1073 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1074 | |

1075 | (*Y_phi=1/2*) |

1076 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + gt/2 Bp[mu] f + ee/sw/2 (Wvec[mu].PMVec).f; |

1077 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + gt/2 Bp[mu] f + ee/sw/2 f.(Wvec[mu].PMVec); |

1078 | |

1079 | (*BL_phi=2*) |

1080 | Dcp[f_, mu_] := I del[f, mu] + 2*g1p Bp[mu] f ; |

1081 | Dcpbar[f_, mu_] := -I del[f, mu] + 2*g1p Bp[mu] f ; |

1082 | |

1083 | Vphichi[Phi_, Phibar_, Chi_, Chibar_] := mu2H1 Phibar.Phi + mu2H2 Chibar.Chi + |

1084 | \[Lambda]1 (Phibar.Phi)^2 + \[Lambda]2 (Chibar.Chi)^2 + \[Lambda]3 (Phibar.Phi)*(Chibar.Chi); |

1085 | |

1086 | (Dcbar[Phibar, mu]).Dc[Phi, mu] + (Dcpbar[Chibar, mu]).Dcp[Chi, mu] - Vphichi[Phi, Phibar, Chi, Chibar] |

1087 | |

1088 | ]; |

1089 | |

1090 | |

1091 | |

1092 | (*************** Yukawa Lagrangian***********************) |

1093 | (*NOTE: Neutrino states have been expanded on the LH/RH components and the LH mass terms have been changed signs*) |

1094 | |

1095 | LYuk := If[FeynmanGauge, |

1096 | |

1097 | Module[{s,r,n,m,i}, - |

1098 | yd[m] CKM[n,m] uqbar[s,n,i].ProjP[s,r].dq[r,m,i] (-I phi2) - |

1099 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] - |

1100 | |

1101 | 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*) |

1102 | yu[m] Conjugate[CKM[m,n]] dqbar[s,n,i].ProjP[s,r].uq[r,m,i] ( I phi2bar) |

1103 | |

1104 | - yl[n] Can[n] anti[nL][s,n].ProjP[s,r].l[r,n] (-I phi2) |

1105 | + yl[n] San[n] anti[nH][s,n].ProjP[s,r].l[r,n] (-I phi2) |

1106 | |

1107 | - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2 +I phi)/Sqrt[2] + |

1108 | 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]+ |

1109 | 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]- |

1110 | |

1111 | ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2 - I phi)/Sqrt[2] |

1112 | |

1113 | - ynd[n] San[n] lbar[s,n].ProjP[s,r].nL[r,n] (I phi2bar) + |

1114 | ynd[n] Can[n] lbar[s,n].ProjP[s,r].nH[r,n] (I phi2bar) + |

1115 | |

1116 | 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]- |

1117 | 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]- |

1118 | |

1119 | ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2 + I phip)/Sqrt[2] |

1120 | |

1121 | |

1122 | ], |

1123 | |

1124 | Module[{s,r,n,m,i}, - |

1125 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2] - |

1126 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+Ca*H1+Sa*H2)/Sqrt[2] |

1127 | |

1128 | - yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2] + |

1129 | ynd[n] San[n] Can[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]+ |

1130 | ynd[n] San[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]- |

1131 | |

1132 | ynd[n] (Can[n] Can[n] - San[n] San[n]) anti[nL][s,n].ProjP[s,r].nH[r,n] (v+Ca*H1+Sa*H2)/Sqrt[2]+ |

1133 | |

1134 | |

1135 | |

1136 | ynm[n] San[n] San[n] anti[nL][s,n].ProjP[s,r].nL[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]- |

1137 | ynm[n] Can[n] Can[n] anti[nH][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2]- |

1138 | |

1139 | ynm[n] 2 San[n] Can[n] anti[nL][s,n].ProjP[s,r].nH[r,n] (x-Sa*H1+Ca*H2)/Sqrt[2] |

1140 | |

1141 | ] |

1142 | ]; |

1143 | |

1144 | LYukawa := LYuk + HC[LYuk]; |

1145 | |

1146 | |

1147 | |

1148 | (**************Ghost terms**************************) |

1149 | (* Now we need the ghost terms which are of the form: *) |

1150 | (* - g * antighost * d_BRST G *) |

1151 | (* where d_BRST G is BRST transform of the gauge fixing function. *) |

1152 | |

1153 | LGhost := If[FeynmanGauge, |

1154 | Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB, dBRSTBp, LGhostBp}, |

1155 | |

1156 | (***********First the pure gauge piece.**********************) |

1157 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]]; |

1158 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu]; |

1159 | |

1160 | dBRSTWi[mu_,i_] := sw/ee Module[{i2, i3}, del[ghWi[i], mu] + ee/sw Eps[i,i2,i3] Wi[mu,i2] ghWi[i3] ]; |

1161 | LGhostWi := - ee/sw ghWibar[a].del[dBRSTWi[mu,a],mu]; |

1162 | |

1163 | dBRSTB[mu_] := cw/ee del[ghB, mu]; |

1164 | LGhostB := - ee/cw ghBbar.del[dBRSTB[mu],mu]; |

1165 | |

1166 | dBRSTBp[mu_] := 1/g1p del[ghBp, mu]; |

1167 | LGhostBp := - g1p ghBpbar.del[dBRSTBp[mu],mu]; |

1168 | |

1169 | (***********Next the piece from the scalar field.************) |

1170 | LGhostphi := |

1171 | (*- ee/(2*sw*cw) MW ( - I phi2 ( (cw^2-sw^2)ghWpbar.ghZ + 2sw*cw ghWpbar.ghA ) + |

1172 | I phi2bar ( (cw^2-sw^2)ghWmbar.ghZ + 2sw*cw ghWmbar.ghA ) ) - |

1173 | ee/(2*sw) MW ( ( (v+Ca*H1+Sa*H2) + I phi) ghWpbar.ghWp + |

1174 | ( (v+Ca*H1+Sa*H2) - I phi) ghWmbar.ghWm ) - |

1175 | I ee/(2*sw) MZ ( - phi2bar ghZbar.ghWp + phi2 ghZbar.ghWm ) - |

1176 | ee/(2*sw*cw) MZ (v+Ca*H1+Sa*H2) ghZbar.ghZ *) |

1177 | |

1178 | 1/4*gw*v (-gw*(v+Ca*H1+Sa*H2) ghWibar[1].ghWi[1] +g1 phic[2] ghWibar[1].ghB +gw phic[2] ghWibar[1].ghWi[3] -gw phi ghWibar[1].ghWi[2] + gt phic[2] ghWibar[1].ghBp) + |

1179 | 1/4*gw*v (-gw*(v+Ca*H1+Sa*H2) ghWibar[2].ghWi[2] -g1 phic[1] ghWibar[2].ghB -gw phic[1] ghWibar[2].ghWi[3] +gw phi ghWibar[2].ghWi[1] -gt phic[1] ghWibar[2].ghBp) + |

1180 | 1/4*gw*v (g1*(v+Ca*H1+Sa*H2) ghWibar[3].ghB -gw*(v+Ca*H1+Sa*H2) ghWibar[3].ghWi[3] +gw phic[1] ghWibar[3].ghWi[2] |

1181 | -gw phic[2] ghWibar[3].ghWi[1] +gt (v+Ca*H1+Sa*H2) ghWibar[3].ghBp ) + |

1182 | 1/4*g1*v (-g1*(v+Ca*H1+Sa*H2) ghBbar.ghB +gw*(v+Ca*H1+Sa*H2) ghBbar.ghWi[3] -gw phic[1] ghBbar.ghWi[2] +gw phic[2] ghBbar.ghWi[1] -gt*(v+Ca*H1+Sa*H2) ghBbar.ghBp) + |

1183 | 1/4*gt*v (-g1*(v+Ca*H1+Sa*H2) ghBpbar.ghB +gw*(v+Ca*H1+Sa*H2) ghBpbar.ghWi[3] -gw phic[1] ghBpbar.ghWi[2] +gw phic[2] ghBpbar.ghWi[1] -gt (v+Ca*H1+Sa*H2) ghBpbar.ghBp) - |

1184 | 4*g1p^2*x*(x-Sa*H1+Ca*H2) ghBpbar.ghBp |

1185 | ; |

1186 | |

1187 | (***********Now add the pieces together.********************) |

1188 | LGhostG + LGhostWi + LGhostB + LGhostphi + LGhostBp ] |

1189 | |

1190 | , |

1191 | |

1192 | (*If unitary gauge, only include the gluonic ghost.*) |

1193 | Block[{dBRSTG,LGhostG}, |

1194 | |

1195 | (***********First the pure gauge piece.**********************) |

1196 | dBRSTG[mu_,a_] := 1/gs Module[{a2, a3}, del[ghG[a], mu] + gs f[a,a2,a3] G[mu,a2] ghG[a3]]; |

1197 | LGhostG := - gs ghGbar[a].del[dBRSTG[mu,a],mu]; |

1198 | |

1199 | (***********Now add the pieces together.********************) |

1200 | LGhostG] |

1201 | |

1202 | ]; |

1203 | |

1204 | (*********Total SM Lagrangian*******) |

1205 | LmZp := LGauge + LHiggs + LFermions + LYukawa + LGhost; |