# StandardModel: SM_old.fr

File SM_old.fr, 22.8 KB (added by BenjF, 6 years ago) |
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1 | (***************************************************************************************************************) |

2 | (****** This is the FeynRules mod-file for the Standard model ******) |

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

4 | (****** Authors: N. Christensen, 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 | M$ModelName = "Standard Model"; |

13 | |

14 | |

15 | M$Information = {Authors -> {"N. Christensen", "C. Duhr"}, |

16 | Version -> "1.3", |

17 | Date -> "02. 06. 2009", |

18 | Institutions -> {"Michigan State University", "Universite catholique de Louvain (CP3)"}, |

19 | Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be"}, |

20 | URLs -> "http://feynrules.phys.ucl.ac.be/view/Main/StandardModel"}; |

21 | |

22 | (* |

23 | V1.3 - Updated Top quark mass to 2010 PDG value (172 GeV) |

24 | V1.2 - Set FeynmanGauge=True as default. |

25 | Set Gluonic ghosts to be included in both gauges. |

26 | V1.1 - Fixed yukawa couplings in Feynman gauge. |

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

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

29 | V1.3 - Added yukawa couplings for all fermions for gauge invariance. |

30 | Added yukawa couplings for 1st generation fermions to Massless.rst. |

31 | Updated parameters to PDG 2010. |

32 | *) |

33 | |

34 | FeynmanGauge = True; |

35 | |

36 | |

37 | (******* Index definitions ********) |

38 | |

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

40 | |

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

42 | |

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

44 | |

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

46 | |

47 | |

48 | IndexStyle[Colour, i] |

49 | |

50 | IndexStyle[Generation, f] |

51 | |

52 | IndexStyle[Gluon ,a] |

53 | |

54 | IndexStyle[SU2W ,k] |

55 | |

56 | |

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

58 | |

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

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

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

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

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

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

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

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

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

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

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

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

71 | |

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

73 | |

74 | M$InteractionOrderHierarchy = { |

75 | {QCD, 1}, |

76 | {QED, 2} |

77 | }; |

78 | |

79 | |

80 | (**************** Parameters *************) |

81 | |

82 | M$Parameters = { |

83 | |

84 | (* External parameters *) |

85 | |

86 | \[Alpha]EWM1== { |

87 | ParameterType -> External, |

88 | BlockName -> SMINPUTS, |

89 | ParameterName -> aEWM1, |

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

91 | Value -> 127.9, |

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

93 | |

94 | Gf == { |

95 | ParameterType -> External, |

96 | BlockName -> SMINPUTS, |

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

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

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

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

101 | |

102 | \[Alpha]S == { |

103 | ParameterType -> External, |

104 | BlockName -> SMINPUTS, |

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

106 | ParameterName -> aS, |

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

108 | Value -> 0.1184, |

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

110 | |

111 | ymdo == { |

112 | ParameterType -> External, |

113 | BlockName -> YUKAWA, |

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

115 | OrderBlock -> {1}, |

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

117 | |

118 | |

119 | ymup == { |

120 | ParameterType -> External, |

121 | BlockName -> YUKAWA, |

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

123 | OrderBlock -> {2}, |

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

125 | |

126 | yms == { |

127 | ParameterType -> External, |

128 | BlockName -> YUKAWA, |

129 | Value -> 0.101, |

130 | OrderBlock -> {3}, |

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

132 | |

133 | |

134 | ymc == { |

135 | ParameterType -> External, |

136 | BlockName -> YUKAWA, |

137 | Value -> 1.27, |

138 | OrderBlock -> {4}, |

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

140 | |

141 | ymb == { |

142 | ParameterType -> External, |

143 | BlockName -> YUKAWA, |

144 | Value -> 4.7, |

145 | OrderBlock -> {5}, |

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

147 | |

148 | ymt == { |

149 | ParameterType -> External, |

150 | BlockName -> YUKAWA, |

151 | Value -> 172.0, |

152 | OrderBlock -> {6}, |

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

154 | |

155 | yme == { |

156 | ParameterType -> External, |

157 | BlockName -> YUKAWA, |

158 | Value -> 5.11*10^(-4), |

159 | OrderBlock -> {11}, |

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

161 | |

162 | ymm == { |

163 | ParameterType -> External, |

164 | BlockName -> YUKAWA, |

165 | Value -> 0.10566, |

166 | OrderBlock -> {13}, |

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

168 | |

169 | ymtau == { |

170 | ParameterType -> External, |

171 | BlockName -> YUKAWA, |

172 | Value -> 1.777, |

173 | OrderBlock -> {15}, |

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

175 | |

176 | cabi == { |

177 | TeX -> Subscript[\[Theta], c], |

178 | ParameterType -> External, |

179 | BlockName -> CKMBLOCK, |

180 | Value -> 0.227736, |

181 | Description -> "Cabibbo angle"}, |

182 | |

183 | |

184 | (* Internal Parameters *) |

185 | |

186 | \[Alpha]EW == { |

187 | ParameterType -> Internal, |

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

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

190 | ParameterName -> aEW, |

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

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

193 | |

194 | |

195 | MW == { |

196 | ParameterType -> Internal, |

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

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

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

200 | |

201 | sw2 == { |

202 | ParameterType -> Internal, |

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

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

205 | |

206 | ee == { |

207 | TeX -> e, |

208 | ParameterType -> Internal, |

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

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

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

212 | |

213 | cw == { |

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

215 | ParameterType -> Internal, |

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

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

218 | |

219 | sw == { |

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

221 | ParameterType -> Internal, |

222 | Value -> Sqrt[sw2], |

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

224 | |

225 | gw == { |

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

227 | ParameterType -> Internal, |

228 | Value -> ee / sw, |

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

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

231 | |

232 | g1 == { |

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

234 | ParameterType -> Internal, |

235 | Value -> ee / cw, |

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

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

238 | |

239 | gs == { |

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

241 | ParameterType -> Internal, |

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

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

244 | ParameterName -> G, |

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

246 | |

247 | |

248 | v == { |

249 | ParameterType -> Internal, |

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

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

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

253 | |

254 | \[Lambda] == { |

255 | ParameterType -> Internal, |

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

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

258 | ParameterName -> lam, |

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

260 | |

261 | muH == { |

262 | ParameterType -> Internal, |

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

264 | TeX -> \[Mu], |

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

266 | |

267 | |

268 | yl == { |

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

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

271 | AllowSummation -> True, |

272 | ParameterType -> Internal, |

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

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

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

276 | ComplexParameter -> False, |

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

278 | |

279 | yu == { |

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

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

282 | AllowSummation -> True, |

283 | ParameterType -> Internal, |

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

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

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

287 | ComplexParameter -> False, |

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

289 | |

290 | yd == { |

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

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

293 | AllowSummation -> True, |

294 | ParameterType -> Internal, |

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

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

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

298 | ComplexParameter -> False, |

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

300 | |

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

302 | CKM == { |

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

304 | TensorClass -> CKM, |

305 | Unitary -> True, |

306 | Value -> {CKM[1,1] -> Cos[cabi], |

307 | CKM[1,2] -> Sin[cabi], |

308 | CKM[1,3] -> 0, |

309 | CKM[2,1] -> -Sin[cabi], |

310 | CKM[2,2] -> Cos[cabi], |

311 | CKM[2,3] -> 0, |

312 | CKM[3,1] -> 0, |

313 | CKM[3,2] -> 0, |

314 | CKM[3,3] -> 1}, |

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

316 | } |

317 | |

318 | |

319 | (************** Gauge Groups ******************) |

320 | |

321 | M$GaugeGroups = { |

322 | |

323 | U1Y == { |

324 | Abelian -> True, |

325 | GaugeBoson -> B, |

326 | Charge -> Y, |

327 | CouplingConstant -> g1}, |

328 | |

329 | SU2L == { |

330 | Abelian -> False, |

331 | GaugeBoson -> Wi, |

332 | StructureConstant -> Eps, |

333 | CouplingConstant -> gw}, |

334 | |

335 | SU3C == { |

336 | Abelian -> False, |

337 | GaugeBoson -> G, |

338 | StructureConstant -> f, |

339 | SymmetricTensor -> dSUN, |

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

341 | CouplingConstant -> gs} |

342 | } |

343 | |

344 | (********* Particle Classes **********) |

345 | |

346 | M$ClassesDescription = { |

347 | |

348 | (********** Fermions ************) |

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

350 | F[1] == { |

351 | ClassName -> vl, |

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

353 | FlavorIndex -> Generation, |

354 | SelfConjugate -> False, |

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

356 | Mass -> 0, |

357 | Width -> 0, |

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

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

360 | PropagatorType -> S, |

361 | PropagatorArrow -> Forward, |

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

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

364 | |

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

366 | F[2] == { |

367 | ClassName -> l, |

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

369 | FlavorIndex -> Generation, |

370 | SelfConjugate -> False, |

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

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

373 | Width -> 0, |

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

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

376 | PropagatorType -> Straight, |

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

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

379 | PropagatorArrow -> Forward, |

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

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

382 | |

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

384 | F[3] == { |

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

386 | ClassName -> uq, |

387 | FlavorIndex -> Generation, |

388 | SelfConjugate -> False, |

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

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

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

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

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

394 | PropagatorType -> Straight, |

395 | PropagatorArrow -> Forward, |

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

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

398 | |

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

400 | F[4] == { |

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

402 | ClassName -> dq, |

403 | FlavorIndex -> Generation, |

404 | SelfConjugate -> False, |

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

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

407 | Width -> 0, |

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

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

410 | PropagatorType -> Straight, |

411 | PropagatorArrow -> Forward, |

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

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

414 | |

415 | (********** Ghosts **********) |

416 | U[1] == { |

417 | ClassName -> ghA, |

418 | SelfConjugate -> False, |

419 | Indices -> {}, |

420 | Ghost -> A, |

421 | Mass -> 0, |

422 | Width -> 0, |

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

424 | PropagatorLabel -> uA, |

425 | PropagatorType -> GhostDash, |

426 | PropagatorArrow -> Forward}, |

427 | |

428 | U[2] == { |

429 | ClassName -> ghZ, |

430 | SelfConjugate -> False, |

431 | Indices -> {}, |

432 | Mass -> {MZ, 91.1876}, |

433 | Width -> {WZ, Internal}, |

434 | Ghost -> Z, |

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

436 | PropagatorLabel -> uZ, |

437 | PropagatorType -> GhostDash, |

438 | PropagatorArrow -> Forward}, |

439 | |

440 | U[31] == { |

441 | ClassName -> ghWp, |

442 | SelfConjugate -> False, |

443 | Indices -> {}, |

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

445 | Width -> {WW, Internal}, |

446 | Ghost -> W, |

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

448 | PropagatorLabel -> uWp, |

449 | PropagatorType -> GhostDash, |

450 | PropagatorArrow -> Forward}, |

451 | |

452 | U[32] == { |

453 | ClassName -> ghWm, |

454 | SelfConjugate -> False, |

455 | Indices -> {}, |

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

457 | Width -> {WW, Internal}, |

458 | Ghost -> Wbar, |

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

460 | PropagatorLabel -> uWm, |

461 | PropagatorType -> GhostDash, |

462 | PropagatorArrow -> Forward}, |

463 | |

464 | U[4] == { |

465 | ClassName -> ghG, |

466 | SelfConjugate -> False, |

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

468 | Ghost -> G, |

469 | Mass -> 0, |

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

471 | PropagatorLabel -> uG, |

472 | PropagatorType -> GhostDash, |

473 | PropagatorArrow -> Forward}, |

474 | |

475 | U[5] == { |

476 | ClassName -> ghWi, |

477 | Unphysical -> True, |

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

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

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

481 | SelfConjugate -> False, |

482 | Ghost -> Wi, |

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

484 | FlavorIndex -> SU2W}, |

485 | |

486 | U[6] == { |

487 | ClassName -> ghB, |

488 | SelfConjugate -> False, |

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

490 | Indices -> {}, |

491 | Ghost -> B, |

492 | Unphysical -> True}, |

493 | |

494 | (************ Gauge Bosons ***************) |

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

496 | V[1] == { |

497 | ClassName -> A, |

498 | SelfConjugate -> True, |

499 | Indices -> {}, |

500 | Mass -> 0, |

501 | Width -> 0, |

502 | PropagatorLabel -> "a", |

503 | PropagatorType -> W, |

504 | PropagatorArrow -> None, |

505 | PDG -> 22, |

506 | FullName -> "Photon" }, |

507 | |

508 | V[2] == { |

509 | ClassName -> Z, |

510 | SelfConjugate -> True, |

511 | Indices -> {}, |

512 | Mass -> {MZ, 91.1876}, |

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

514 | PropagatorLabel -> "Z", |

515 | PropagatorType -> Sine, |

516 | PropagatorArrow -> None, |

517 | PDG -> 23, |

518 | FullName -> "Z" }, |

519 | |

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

521 | V[3] == { |

522 | ClassName -> W, |

523 | SelfConjugate -> False, |

524 | Indices -> {}, |

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

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

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

528 | PropagatorLabel -> "W", |

529 | PropagatorType -> Sine, |

530 | PropagatorArrow -> Forward, |

531 | ParticleName ->"W+", |

532 | AntiParticleName ->"W-", |

533 | PDG -> 24, |

534 | FullName -> "W" }, |

535 | |

536 | V[4] == { |

537 | ClassName -> G, |

538 | SelfConjugate -> True, |

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

540 | Mass -> 0, |

541 | Width -> 0, |

542 | PropagatorLabel -> G, |

543 | PropagatorType -> C, |

544 | PropagatorArrow -> None, |

545 | PDG -> 21, |

546 | FullName -> "G" }, |

547 | |

548 | V[5] == { |

549 | ClassName -> Wi, |

550 | Unphysical -> True, |

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

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

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

554 | SelfConjugate -> True, |

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

556 | FlavorIndex -> SU2W, |

557 | Mass -> 0, |

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

559 | |

560 | V[6] == { |

561 | ClassName -> B, |

562 | SelfConjugate -> True, |

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

564 | Indices -> {}, |

565 | Mass -> 0, |

566 | Unphysical -> True}, |

567 | |

568 | |

569 | (************ Scalar Fields **********) |

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

571 | S[1] == { |

572 | ClassName -> H, |

573 | SelfConjugate -> True, |

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

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

576 | PropagatorLabel -> "H", |

577 | PropagatorType -> D, |

578 | PropagatorArrow -> None, |

579 | PDG -> 25, |

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

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

582 | FullName -> "H" }, |

583 | |

584 | S[2] == { |

585 | ClassName -> phi, |

586 | SelfConjugate -> True, |

587 | Mass -> {MZ, 91.1876}, |

588 | Width -> Wphi, |

589 | PropagatorLabel -> "Phi", |

590 | PropagatorType -> D, |

591 | PropagatorArrow -> None, |

592 | ParticleName ->"phi0", |

593 | PDG -> 250, |

594 | FullName -> "Phi", |

595 | Goldstone -> Z }, |

596 | |

597 | S[3] == { |

598 | ClassName -> phi2, |

599 | SelfConjugate -> False, |

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

601 | Width -> Wphi2, |

602 | PropagatorLabel -> "Phi2", |

603 | PropagatorType -> D, |

604 | PropagatorArrow -> None, |

605 | ParticleName ->"phi+", |

606 | AntiParticleName ->"phi-", |

607 | PDG -> 251, |

608 | FullName -> "Phi2", |

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

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

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

612 | Goldstone -> W, |

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

614 | } |

615 | |

616 | |

617 | |

618 | |

619 | (*****************************************************************************************) |

620 | |

621 | (* SM Lagrangian *) |

622 | |

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

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

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

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

627 | |

628 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - |

629 | |

630 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* |

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

632 | |

633 | |

634 | (********************* Fermion Lagrangian terms*************************) |

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

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

637 | |

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

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

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

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

642 | |

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

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

645 | |

646 | LBright = |

647 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

648 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

649 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

650 | |

651 | LBleft = |

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

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

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

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

656 | |

657 | LWleft = ee/sw/2( |

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

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

660 | |

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

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

663 | |

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

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

666 | |

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

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

669 | ); |

670 | |

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

672 | |

673 | (******************** Higgs Lagrangian terms****************************) |

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

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

676 | |

677 | |

678 | |

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

680 | |

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

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

683 | |

684 | (*Y_phi=1*) |

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

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

687 | |

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

689 | |

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

691 | |

692 | |

693 | (*************** Yukawa Lagrangian***********************) |

694 | LYuk := If[FeynmanGauge, |

695 | |

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

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

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

699 | |

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

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

702 | |

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

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

705 | ], |

706 | |

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

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

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

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

711 | ] |

712 | ]; |

713 | |

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

715 | |

716 | |

717 | |

718 | (**************Ghost terms**************************) |

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

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

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

722 | |

723 | LGhost := If[FeynmanGauge, |

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

725 | |

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

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

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

729 | |

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

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

732 | |

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

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

735 | |

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

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

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

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

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

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

742 | |

743 | |

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

745 | LGhostG + LGhostWi + LGhostB + LGhostphi] |

746 | |

747 | , |

748 | |

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

750 | Block[{dBRSTG,LGhostG}, |

751 | |

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

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

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

755 | |

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

757 | LGhostG] |

758 | |

759 | ]; |

760 | |

761 | (*********Total SM Lagrangian*******) |

762 | LSM := LGauge + LHiggs + LFermions + LYukawa + LGhost; |