# FourthGeneration: 4Gen.fr

File 4Gen.fr, 22.7 KB (added by claudeduhr, 8 years ago) |
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1 | (***************************************************************************************************************) |

2 | (****** This is the FeynRules mod-file for the 4th generation model ******) |

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

4 | (****** Authors: C. Duhr ******) |

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 | |

13 | (* |

14 | This model is based on the SM implmentation of FeynRules, |

15 | and basically obtained by just increasing the range of the Index of type Generation from 3 to 4 |

16 | *) |

17 | |

18 | |

19 | |

20 | M$ModelName = "4th_Generation_Complex_CKM"; |

21 | |

22 | |

23 | |

24 | M$Information = {Authors -> {"C. Duhr"}, |

25 | Version -> "1.1", |

26 | Date -> "02. 11. 2010", |

27 | Institutions -> {"IPPP, Durham"}, |

28 | Emails -> {"claude.duhr@durham.ac.uk"}}; |

29 | |

30 | (*V1.1 - Fixed yukawa couplings in Feynman gauge. |

31 | Changed yd[n] CKM[n,m] to yd[m] CKM[n,m]. |

32 | Changed yu[n] Conjugate[CKM[m,n]] to yu[m] Conjugate[CKM[m,n]]. |

33 | *) |

34 | |

35 | FeynmanGauge = False; |

36 | |

37 | |

38 | (******* Index definitions ********) |

39 | |

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

41 | |

42 | IndexRange[ Index[QuarkGeneration] ] = Range[4] |

43 | |

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

45 | |

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

47 | |

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

49 | |

50 | |

51 | IndexStyle[Colour, i] |

52 | |

53 | IndexStyle[Generation, f] |

54 | |

55 | IndexStyle[QuarkGeneration, q] |

56 | |

57 | IndexStyle[Gluon ,a] |

58 | |

59 | IndexStyle[SU2W ,k] |

60 | |

61 | |

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

63 | |

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

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

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

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

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

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

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

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

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

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

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

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

76 | |

77 | |

78 | (**************** Parameters *************) |

79 | |

80 | M$Parameters = { |

81 | |

82 | (* External parameters *) |

83 | |

84 | \[Alpha]EWM1== { |

85 | ParameterType -> External, |

86 | BlockName -> SMINPUTS, |

87 | ParameterName -> aEWM1, |

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

89 | Value -> 127.9, |

90 | Description -> "Inverse of the electroweak coupling constant"}, |

91 | |

92 | Gf == { |

93 | ParameterType -> External, |

94 | BlockName -> SMINPUTS, |

95 | TeX -> Subscript[G, f], |

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

97 | Value -> 1.16639 * 10^(-5), |

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

99 | |

100 | \[Alpha]S == { |

101 | ParameterType -> External, |

102 | BlockName -> SMINPUTS, |

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

104 | ParameterName -> aS, |

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

106 | Value -> 0.1172, |

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

108 | |

109 | |

110 | ymc == { |

111 | ParameterType -> External, |

112 | BlockName -> YUKAWA, |

113 | Value -> 1.42, |

114 | OrderBlock -> {4}, |

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

116 | |

117 | ymb == { |

118 | ParameterType -> External, |

119 | BlockName -> YUKAWA, |

120 | Value -> 4.7, |

121 | OrderBlock -> {5}, |

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

123 | |

124 | ymbp == { |

125 | ParameterType -> External, |

126 | BlockName -> YUKAWA, |

127 | Value -> 500, |

128 | OrderBlock -> {7}, |

129 | Description -> "Bottom-prime Yukawa mass"}, |

130 | |

131 | ymt == { |

132 | ParameterType -> External, |

133 | BlockName -> YUKAWA, |

134 | Value -> 174.3, |

135 | OrderBlock -> {6}, |

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

137 | |

138 | ymtp == { |

139 | ParameterType -> External, |

140 | BlockName -> YUKAWA, |

141 | Value -> 700, |

142 | OrderBlock -> {8}, |

143 | Description -> "Top-prime Yukawa mass"}, |

144 | |

145 | ymtau == { |

146 | ParameterType -> External, |

147 | BlockName -> YUKAWA, |

148 | Value -> 1.777, |

149 | OrderBlock -> {15}, |

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

151 | |

152 | |

153 | (* Internal Parameters *) |

154 | |

155 | \[Alpha]EW == { |

156 | ParameterType -> Internal, |

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

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

159 | ParameterName -> aEW, |

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

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

162 | |

163 | |

164 | MW == { |

165 | ParameterType -> Internal, |

166 | Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*\[Alpha]EW/Gf*MZ^2]], |

167 | TeX -> Subscript[M, W], |

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

169 | |

170 | sw2 == { |

171 | ParameterType -> Internal, |

172 | Value -> 1-(MW/MZ)^2, |

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

174 | |

175 | ee == { |

176 | TeX -> e, |

177 | ParameterType -> Internal, |

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

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

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

181 | |

182 | cw == { |

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

184 | ParameterType -> Internal, |

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

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

187 | |

188 | sw == { |

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

190 | ParameterType -> Internal, |

191 | Value -> Sqrt[sw2], |

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

193 | |

194 | gw == { |

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

196 | ParameterType -> Internal, |

197 | Value -> ee / sw, |

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

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

200 | |

201 | g1 == { |

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

203 | ParameterType -> Internal, |

204 | Value -> ee / cw, |

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

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

207 | |

208 | gs == { |

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

210 | ParameterType -> Internal, |

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

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

213 | ParameterName -> G, |

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

215 | |

216 | |

217 | v == { |

218 | ParameterType -> Internal, |

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

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

221 | Description -> "Higgs VEV"}, |

222 | |

223 | \[Lambda] == { |

224 | ParameterType -> Internal, |

225 | Value -> MH^2/(2*v^2), |

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

227 | ParameterName -> lam, |

228 | Description -> "Higgs quartic coupling"}, |

229 | |

230 | muH == { |

231 | ParameterType -> Internal, |

232 | Value -> Sqrt[v^2 \[Lambda]], |

233 | TeX -> \[Mu], |

234 | Description -> "Coefficient of the quadratic piece of the Higgs potential"}, |

235 | |

236 | |

237 | yl == { |

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

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

240 | AllowSummation -> True, |

241 | ParameterType -> Internal, |

242 | Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v}, |

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

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

245 | ComplexParameter -> False, |

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

247 | |

248 | yu == { |

249 | TeX -> Superscript[y, u], |

250 | Indices -> {Index[QuarkGeneration]}, |

251 | AllowSummation -> True, |

252 | ParameterType -> Internal, |

253 | Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v, yu[3] -> Sqrt[2] ymt / v, yu[4] -> Sqrt[2] ymtp / v}, |

254 | ParameterName -> {yu[1] -> yup, yu[2] -> yc, yu[3] -> yt, yu[4] -> ytp}, |

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

256 | ComplexParameter -> False, |

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

258 | |

259 | yd == { |

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

261 | Indices -> {Index[QuarkGeneration]}, |

262 | AllowSummation -> True, |

263 | ParameterType -> Internal, |

264 | Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v, yd[4] -> Sqrt[2] ymbp / v}, |

265 | ParameterName -> {yd[1] -> ydo, yd[2] -> ys, yd[3] -> yb, yd[4] -> ybp}, |

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

267 | ComplexParameter -> False, |

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

269 | |

270 | (* N. B. : only Cabibbo mixing! *) |

271 | |

272 | |

273 | |

274 | RCKM == { |

275 | ParameterType -> External, |

276 | Indices -> {Index[QuarkGeneration], Index[QuarkGeneration]}, |

277 | BlockName -> RCKM, |

278 | ComplexParameter -> False, |

279 | Value -> {RCKM[1,1] :> 1, |

280 | RCKM[1,2] :> 0, |

281 | RCKM[1,3] :> 0, |

282 | RCKM[1,4] :> 0, |

283 | RCKM[2,1] :> 0, |

284 | RCKM[2,2] :> 0.99995, |

285 | RCKM[2,3] :> 0, |

286 | RCKM[2,4] :> 0.01, |

287 | RCKM[3,1] :> 0, |

288 | RCKM[3,2] :> -0.001, |

289 | RCKM[3,3] :> 0.995, |

290 | RCKM[3,4] :> 0.1, |

291 | RCKM[4,1] :> 0, |

292 | RCKM[4,2] :> -0.01, |

293 | RCKM[4,3] :> -0.1, |

294 | RCKM[4,4] :> 0.99495}, |

295 | Description -> "Real Part of the CKM matrix"}, |

296 | |

297 | ICKM == { |

298 | ParameterType -> External, |

299 | Indices -> {Index[QuarkGeneration], Index[QuarkGeneration]}, |

300 | BlockName -> ICKM, |

301 | ComplexParameter -> False, |

302 | Value -> {ICKM[1,1] :> 0, |

303 | ICKM[1,2] :> 0, |

304 | ICKM[1,3] :> 0, |

305 | ICKM[1,4] :> 0, |

306 | ICKM[2,1] :> 0, |

307 | ICKM[2,2] :> 0, |

308 | ICKM[2,3] :> 0, |

309 | ICKM[2,4] :> 0, |

310 | ICKM[3,1] :> 0, |

311 | ICKM[3,2] :> 0, |

312 | ICKM[3,3] :> 0, |

313 | ICKM[3,4] :> 0, |

314 | ICKM[4,1] :> 0, |

315 | ICKM[4,2] :> 0, |

316 | ICKM[4,3] :> 0, |

317 | ICKM[4,4] :> 0}, |

318 | Description -> "Imaginary Part of the CKM matrix"}, |

319 | |

320 | |

321 | |

322 | CKM == { |

323 | Indices -> {Index[QuarkGeneration], Index[QuarkGeneration]}, |

324 | Unitary -> True, |

325 | Value -> {CKM[i_,j_] :> RCKM[i,j] + I ICKM[i,j]}, |

326 | Description -> "CKM-Matrix"} |

327 | } |

328 | |

329 | |

330 | (************** Gauge Groups ******************) |

331 | |

332 | M$GaugeGroups = { |

333 | |

334 | U1Y == { |

335 | Abelian -> True, |

336 | GaugeBoson -> B, |

337 | Charge -> Y, |

338 | CouplingConstant -> g1}, |

339 | |

340 | SU2L == { |

341 | Abelian -> False, |

342 | GaugeBoson -> Wi, |

343 | StructureConstant -> Eps, |

344 | CouplingConstant -> gw}, |

345 | |

346 | SU3C == { |

347 | Abelian -> False, |

348 | GaugeBoson -> G, |

349 | StructureConstant -> f, |

350 | SymmetricTensor -> dSUN, |

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

352 | CouplingConstant -> gs} |

353 | } |

354 | |

355 | (********* Particle Classes **********) |

356 | |

357 | M$ClassesDescription = { |

358 | |

359 | (********** Fermions ************) |

360 | (* Leptons (neutrino): I_3 = +1/2, Q = 0 *) |

361 | F[1] == { |

362 | ClassName -> vl, |

363 | ClassMembers -> {ve,vm,vt}, |

364 | FlavorIndex -> Generation, |

365 | SelfConjugate -> False, |

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

367 | Mass -> 0, |

368 | Width -> 0, |

369 | QuantumNumbers -> {LeptonNumber -> 1}, |

370 | PropagatorLabel -> {"v", "ve", "vm", "vt"} , |

371 | PropagatorType -> S, |

372 | PropagatorArrow -> Forward, |

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

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

375 | |

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

377 | F[2] == { |

378 | ClassName -> l, |

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

380 | FlavorIndex -> Generation, |

381 | SelfConjugate -> False, |

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

383 | Mass -> {Ml, {Me, 5.11 * 10^(-4)}, {MM, 0.10566}, {MTA, 1.777}}, |

384 | Width -> 0, |

385 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1}, |

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

387 | PropagatorType -> Straight, |

388 | ParticleName -> {"e-", "m-", "tt-"}, |

389 | AntiParticleName -> {"e+", "m+", "tt+"}, |

390 | PropagatorArrow -> Forward, |

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

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

393 | |

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

395 | F[3] == { |

396 | ClassMembers -> {u, c, t, tp}, |

397 | ClassName -> uq, |

398 | FlavorIndex -> QuarkGeneration, |

399 | SelfConjugate -> False, |

400 | Indices -> {Index[QuarkGeneration], Index[Colour]}, |

401 | Mass -> {Mu, {MU, 2.55*10^(-3)}, {MC, 1.42}, {MT, 172}, {MTp, 700}}, |

402 | Width -> {0, 0, {WT, 1.4516}, {WTp, 14.109}}, |

403 | QuantumNumbers -> {Q -> 2/3}, |

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

405 | PropagatorType -> Straight, |

406 | PropagatorArrow -> Forward, |

407 | PDG -> {2, 4, 6, 8}, |

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

409 | |

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

411 | F[4] == { |

412 | ClassMembers -> {d, s, b, bp}, |

413 | ClassName -> dq, |

414 | FlavorIndex -> QuarkGeneration, |

415 | SelfConjugate -> False, |

416 | Indices -> {Index[QuarkGeneration], Index[Colour]}, |

417 | Mass -> {Md, {MD, 5.04*10^(-3)}, {MS, 0.104}, {MB, 4.7}, {MBp, 500}}, |

418 | Width -> {0,0,0,{WBp,0.28454}}, |

419 | QuantumNumbers -> {Q -> -1/3}, |

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

421 | PropagatorType -> Straight, |

422 | PropagatorArrow -> Forward, |

423 | PDG -> {1,3,5,7}, |

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

425 | |

426 | (********** Ghosts **********) |

427 | U[1] == { |

428 | ClassName -> ghA, |

429 | SelfConjugate -> False, |

430 | Indices -> {}, |

431 | Ghost -> A, |

432 | Mass -> 0, |

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

434 | PropagatorLabel -> uA, |

435 | PropagatorType -> GhostDash, |

436 | PropagatorArrow -> Forward}, |

437 | |

438 | U[2] == { |

439 | ClassName -> ghZ, |

440 | SelfConjugate -> False, |

441 | Indices -> {}, |

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

443 | Ghost -> Z, |

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

445 | PropagatorLabel -> uZ, |

446 | PropagatorType -> GhostDash, |

447 | PropagatorArrow -> Forward}, |

448 | |

449 | U[31] == { |

450 | ClassName -> ghWp, |

451 | SelfConjugate -> False, |

452 | Indices -> {}, |

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

454 | Ghost -> W, |

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

456 | PropagatorLabel -> uWp, |

457 | PropagatorType -> GhostDash, |

458 | PropagatorArrow -> Forward}, |

459 | |

460 | U[32] == { |

461 | ClassName -> ghWm, |

462 | SelfConjugate -> False, |

463 | Indices -> {}, |

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

465 | Ghost -> Wbar, |

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

467 | PropagatorLabel -> uWm, |

468 | PropagatorType -> GhostDash, |

469 | PropagatorArrow -> Forward}, |

470 | |

471 | U[4] == { |

472 | ClassName -> ghG, |

473 | SelfConjugate -> False, |

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

475 | Ghost -> G, |

476 | Mass -> 0, |

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

478 | PropagatorLabel -> uG, |

479 | PropagatorType -> GhostDash, |

480 | PropagatorArrow -> Forward}, |

481 | |

482 | U[5] == { |

483 | ClassName -> ghWi, |

484 | Unphysical -> True, |

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

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

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

488 | SelfConjugate -> False, |

489 | Ghost -> Wi, |

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

491 | FlavorIndex -> SU2W}, |

492 | |

493 | U[6] == { |

494 | ClassName -> ghB, |

495 | SelfConjugate -> False, |

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

497 | Indices -> {}, |

498 | Ghost -> B, |

499 | Unphysical -> True}, |

500 | |

501 | (************ Gauge Bosons ***************) |

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

503 | V[1] == { |

504 | ClassName -> A, |

505 | SelfConjugate -> True, |

506 | Indices -> {}, |

507 | Mass -> 0, |

508 | Width -> 0, |

509 | PropagatorLabel -> "a", |

510 | PropagatorType -> W, |

511 | PropagatorArrow -> None, |

512 | PDG -> 22, |

513 | FullName -> "Photon" }, |

514 | |

515 | V[2] == { |

516 | ClassName -> Z, |

517 | SelfConjugate -> True, |

518 | Indices -> {}, |

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

520 | Width -> {WZ, 2.44140351}, |

521 | PropagatorLabel -> "Z", |

522 | PropagatorType -> Sine, |

523 | PropagatorArrow -> None, |

524 | PDG -> 23, |

525 | FullName -> "Z" }, |

526 | |

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

528 | V[3] == { |

529 | ClassName -> W, |

530 | SelfConjugate -> False, |

531 | Indices -> {}, |

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

533 | Width -> {WW, 2.04759951}, |

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

535 | PropagatorLabel -> "W", |

536 | PropagatorType -> Sine, |

537 | PropagatorArrow -> Forward, |

538 | ParticleName ->"W+", |

539 | AntiParticleName ->"W-", |

540 | PDG -> 24, |

541 | FullName -> "W" }, |

542 | |

543 | V[4] == { |

544 | ClassName -> G, |

545 | SelfConjugate -> True, |

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

547 | Mass -> 0, |

548 | Width -> 0, |

549 | PropagatorLabel -> G, |

550 | PropagatorType -> C, |

551 | PropagatorArrow -> None, |

552 | PDG -> 21, |

553 | FullName -> "G" }, |

554 | |

555 | V[5] == { |

556 | ClassName -> Wi, |

557 | Unphysical -> True, |

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

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

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

561 | SelfConjugate -> True, |

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

563 | FlavorIndex -> SU2W, |

564 | Mass -> 0, |

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

566 | |

567 | V[6] == { |

568 | ClassName -> B, |

569 | SelfConjugate -> True, |

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

571 | Indices -> {}, |

572 | Mass -> 0, |

573 | Unphysical -> True}, |

574 | |

575 | |

576 | (************ Scalar Fields **********) |

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

578 | S[1] == { |

579 | ClassName -> H, |

580 | SelfConjugate -> True, |

581 | Mass -> {MH, 120}, |

582 | Width -> {WH, 0.00575308848}, |

583 | PropagatorLabel -> "H", |

584 | PropagatorType -> D, |

585 | PropagatorArrow -> None, |

586 | PDG -> 25, |

587 | TeXParticleName -> "\\phi", |

588 | TeXClassName -> "\\phi", |

589 | FullName -> "H" }, |

590 | |

591 | S[2] == { |

592 | ClassName -> phi, |

593 | SelfConjugate -> True, |

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

595 | Width -> Wphi, |

596 | PropagatorLabel -> "Phi", |

597 | PropagatorType -> D, |

598 | PropagatorArrow -> None, |

599 | ParticleName ->"phi0", |

600 | PDG -> 250, |

601 | FullName -> "Phi", |

602 | Goldstone -> Z }, |

603 | |

604 | S[3] == { |

605 | ClassName -> phi2, |

606 | SelfConjugate -> False, |

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

608 | Width -> Wphi2, |

609 | PropagatorLabel -> "Phi2", |

610 | PropagatorType -> D, |

611 | PropagatorArrow -> None, |

612 | ParticleName ->"phi+", |

613 | AntiParticleName ->"phi-", |

614 | PDG -> 251, |

615 | FullName -> "Phi2", |

616 | TeXClassName -> "\\phi^+", |

617 | TeXParticleName -> "\\phi^+", |

618 | TeXAntiParticleName -> "\\phi^-", |

619 | Goldstone -> W, |

620 | QuantumNumbers -> {Q -> 1}} |

621 | } |

622 | |

623 | |

624 | |

625 | |

626 | (*****************************************************************************************) |

627 | |

628 | (* SM Lagrangian *) |

629 | |

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

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

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

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

634 | |

635 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - |

636 | |

637 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* |

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

639 | |

640 | |

641 | (********************* Fermion Lagrangian terms*************************) |

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

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

644 | |

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

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

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

648 | I vlbar.Ga[mu].del[vl, mu]; |

649 | |

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

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

652 | |

653 | LBright = |

654 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

655 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

656 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

657 | |

658 | LBleft = |

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

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

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

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

663 | |

664 | LWleft = ee/sw/2( |

665 | vlbar.Ga[mu].ProjM.vl Wi[mu, 3] - (*sigma3 = ( 1 0 )*) |

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

667 | |

668 | Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu] + |

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

670 | |

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

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

673 | |

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

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

676 | ); |

677 | |

678 | Lkin + LQCD + LBright + LBleft + LWleft]; |

679 | |

680 | (******************** Higgs Lagrangian terms****************************) |

681 | Phi := If[FeynmanGauge, {-I phi2, (v + H + I phi)/Sqrt[2]}, {0, (v + H)/Sqrt[2]}]; |

682 | Phibar := If[FeynmanGauge, {I phi2bar, (v + H - I phi)/Sqrt[2]} ,{0, (v + H)/Sqrt[2]}]; |

683 | |

684 | |

685 | |

686 | LHiggs := Block[{PMVec, WVec, Dc, Dcbar, Vphi}, |

687 | |

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

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

690 | |

691 | (*Y_phi=1*) |

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

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

694 | |

695 | Vphi[Phi_, Phibar_] := -muH^2 Phibar.Phi + \[Lambda] (Phibar.Phi)^2; |

696 | |

697 | (Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar]]; |

698 | |

699 | |

700 | (*************** Yukawa Lagrangian***********************) |

701 | LYuk := If[FeynmanGauge, |

702 | |

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

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

705 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H +I phi)/Sqrt[2] - |

706 | |

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

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

709 | |

710 | yl[n] vlbar[s,n].ProjP[s,r].l[r,n] (-I phi2) - |

711 | yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H +I phi)/Sqrt[2] |

712 | ], |

713 | |

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

715 | yd[n] dqbar[s,n,i].ProjP[s,r].dq[r,n,i] (v+H)/Sqrt[2] - |

716 | yu[n] uqbar[s,n,i].ProjP[s,r].uq[r,n,i] (v+H)/Sqrt[2] - |

717 | yl[n] lbar[s,n].ProjP[s,r].l[r,n] (v+H)/Sqrt[2] |

718 | ] |

719 | ]; |

720 | |

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

722 | |

723 | |

724 | |

725 | (**************Ghost terms**************************) |

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

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

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

729 | |

730 | LGhost := If[FeynmanGauge, |

731 | Block[{dBRSTG,LGhostG,dBRSTWi,LGhostWi,dBRSTB,LGhostB}, |

732 | |

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

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

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

736 | |

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

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

739 | |

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

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

742 | |

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

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

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

746 | ee/(2*sw) MW ( ( (v+H) + I phi) ghWpbar.ghWp + ( (v+H) - I phi) ghWmbar.ghWm ) - |

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

748 | ee/(2*sw*cw) MZ (v+H) ghZbar.ghZ ; |

749 | |

750 | |

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

752 | LGhostG + LGhostWi + LGhostB + LGhostphi] |

753 | |

754 | , 0]; |

755 | |

756 | (*********Total SM Lagrangian*******) |

757 | L4Gen := LGauge + LHiggs + LFermions + LYukawa + LGhost; |