# AnomalousGaugeCoupling: quartic.fr

File quartic.fr, 36.1 KB (added by eboli, 5 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 and anomalous quartic couplings"; |

13 | |

14 | |

15 | M$Information = {Authors -> {"N. Christensen", "C. Duhr", "modified by OJPE and MCGG"}, |

16 | Version -> "1.4", |

17 | Date -> "02. 06. 2009, last change 13. 08. 2012", |

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

19 | "USP", "Stony Brook"}, |

20 | Emails -> {"neil@pa.msu.edu", "claude.duhr@uclouvain.be", "eboli@fma.if.usp.br", |

21 | "concha@max2.physics.sunysb.edu"}, |

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

23 | |

24 | (* |

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

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

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

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

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

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

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

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

33 | Updated parameters to PDG 2010. |

34 | V1.4 Anomalous quartic gauge-boson couplings added by OJPE and MCGG |

35 | *) |

36 | |

37 | FeynmanGauge = True; |

38 | |

39 | (* FR$DSign=-1 *) |

40 | |

41 | (******* Index definitions ********) |

42 | |

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

44 | |

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

46 | |

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

48 | |

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

50 | |

51 | |

52 | IndexStyle[Colour, i] |

53 | |

54 | IndexStyle[Generation, f] |

55 | |

56 | IndexStyle[Gluon ,a] |

57 | |

58 | IndexStyle[SU2W ,k] |

59 | |

60 | |

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

62 | |

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

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

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

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

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

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

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

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

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

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

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

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

75 | |

76 | |

77 | (**************** Parameters *************) |

78 | |

79 | M$Parameters = { |

80 | |

81 | (* External parameters *) |

82 | |

83 | \[Alpha]EWM1== { |

84 | ParameterType -> External, |

85 | BlockName -> SMINPUTS, |

86 | ParameterName -> aEWM1, |

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

88 | Value -> 127.9, |

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

90 | |

91 | |

92 | Gf == { |

93 | ParameterType -> External, |

94 | BlockName -> SMINPUTS, |

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

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

97 | Value -> 1.16637 * 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 -> 0.1184, |

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

108 | |

109 | ymdo == { |

110 | ParameterType -> External, |

111 | BlockName -> YUKAWA, |

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

113 | OrderBlock -> {1}, |

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

115 | |

116 | |

117 | ymup == { |

118 | ParameterType -> External, |

119 | BlockName -> YUKAWA, |

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

121 | OrderBlock -> {2}, |

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

123 | |

124 | yms == { |

125 | ParameterType -> External, |

126 | BlockName -> YUKAWA, |

127 | Value -> 0.101, |

128 | OrderBlock -> {3}, |

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

130 | |

131 | |

132 | ymc == { |

133 | ParameterType -> External, |

134 | BlockName -> YUKAWA, |

135 | Value -> 1.27, |

136 | OrderBlock -> {4}, |

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

138 | |

139 | ymb == { |

140 | ParameterType -> External, |

141 | BlockName -> YUKAWA, |

142 | Value -> 4.7, |

143 | OrderBlock -> {5}, |

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

145 | |

146 | ymt == { |

147 | ParameterType -> External, |

148 | BlockName -> YUKAWA, |

149 | Value -> 172.0, |

150 | OrderBlock -> {6}, |

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

152 | |

153 | yme == { |

154 | ParameterType -> External, |

155 | BlockName -> YUKAWA, |

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

157 | OrderBlock -> {11}, |

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

159 | |

160 | ymm == { |

161 | ParameterType -> External, |

162 | BlockName -> YUKAWA, |

163 | Value -> 0.10566, |

164 | OrderBlock -> {13}, |

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

166 | |

167 | ymtau == { |

168 | ParameterType -> External, |

169 | BlockName -> YUKAWA, |

170 | Value -> 1.777, |

171 | OrderBlock -> {15}, |

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

173 | |

174 | cabi == { |

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

176 | ParameterType -> External, |

177 | BlockName -> CKMBLOCK, |

178 | Value -> 0.227736, |

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

180 | |

181 | (* OjpE *) |

182 | |

183 | FS0 == { |

184 | ParameterType -> External, |

185 | BlockName -> ANOINPUTS, |

186 | TeX -> Subscript[f, S0], |

187 | InteractionOrder -> {NP, 1}, |

188 | Value -> 1., |

189 | Description -> "L_S,0 coefficient"}, |

190 | |

191 | |

192 | FS1 == { |

193 | ParameterType -> External, |

194 | BlockName -> ANOINPUTS, |

195 | TeX -> Subscript[f, S1], |

196 | InteractionOrder -> {NP, 1}, |

197 | Value -> 1., |

198 | Description -> "L_S,1 coefficient"}, |

199 | |

200 | FM0 == { |

201 | ParameterType -> External, |

202 | BlockName -> ANOINPUTS, |

203 | TeX -> Subscript[f, M0], |

204 | InteractionOrder -> {NP, 1}, |

205 | Value -> 1., |

206 | Description -> "L_M,0 coefficient"}, |

207 | |

208 | FM1 == { |

209 | ParameterType -> External, |

210 | BlockName -> ANOINPUTS, |

211 | TeX -> Subscript[f, M1], |

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

213 | Value -> 1., |

214 | Description -> "L_M,1 coefficient"}, |

215 | |

216 | FM2 == { |

217 | ParameterType -> External, |

218 | BlockName -> ANOINPUTS, |

219 | TeX -> Subscript[f, M2], |

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

221 | Value -> 1., |

222 | Description -> "L_M,2 coefficient"}, |

223 | |

224 | FM3 == { |

225 | ParameterType -> External, |

226 | BlockName -> ANOINPUTS, |

227 | TeX -> Subscript[f, M3], |

228 | InteractionOrder -> {NP, 1}, |

229 | Value -> 1., |

230 | Description -> "L_M,3 coefficient"}, |

231 | |

232 | FM4 == { |

233 | ParameterType -> External, |

234 | BlockName -> ANOINPUTS, |

235 | TeX -> Subscript[f, M4], |

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

237 | Value -> 1., |

238 | Description -> "L_M,4 coefficient"}, |

239 | |

240 | FM5 == { |

241 | ParameterType -> External, |

242 | BlockName -> ANOINPUTS, |

243 | TeX -> Subscript[f, M5], |

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

245 | Value -> 1., |

246 | Description -> "L_M,5 coefficient"}, |

247 | |

248 | FM6 == { |

249 | ParameterType -> External, |

250 | BlockName -> ANOINPUTS, |

251 | TeX -> Subscript[f, M6], |

252 | InteractionOrder -> {NP, 1}, |

253 | Value -> 1., |

254 | Description -> "L_M,6 coefficient"}, |

255 | |

256 | FM7 == { |

257 | ParameterType -> External, |

258 | BlockName -> ANOINPUTS, |

259 | TeX -> Subscript[f, M7], |

260 | InteractionOrder -> {NP, 1}, |

261 | Value -> 1., |

262 | Description -> "L_M,7 coefficient"}, |

263 | |

264 | FT0 == { |

265 | ParameterType -> External, |

266 | BlockName -> ANOINPUTS, |

267 | TeX -> Subscript[f, T0], |

268 | InteractionOrder -> {NP, 1}, |

269 | Value -> 1., |

270 | Description -> "L_T,0 coefficient"}, |

271 | |

272 | FT1 == { |

273 | ParameterType -> External, |

274 | BlockName -> ANOINPUTS, |

275 | TeX -> Subscript[f, T1], |

276 | InteractionOrder -> {NP, 1}, |

277 | Value -> 1., |

278 | Description -> "L_T,1 coefficient"}, |

279 | |

280 | FT2 == { |

281 | ParameterType -> External, |

282 | BlockName -> ANOINPUTS, |

283 | TeX -> Subscript[f, T2], |

284 | InteractionOrder -> {NP, 1}, |

285 | Value -> 1., |

286 | Description -> "L_T,2 coefficient"}, |

287 | |

288 | FT3 == { |

289 | ParameterType -> External, |

290 | BlockName -> ANOINPUTS, |

291 | TeX -> Subscript[f, T3], |

292 | InteractionOrder -> {NP, 1}, |

293 | Value -> 1., |

294 | Description -> "L_T,3 coefficient"}, |

295 | |

296 | FT4 == { |

297 | ParameterType -> External, |

298 | BlockName -> ANOINPUTS, |

299 | TeX -> Subscript[f, T4], |

300 | InteractionOrder -> {NP, 1}, |

301 | Value -> 1., |

302 | Description -> "L_T,4 coefficient"}, |

303 | |

304 | FT5 == { |

305 | ParameterType -> External, |

306 | BlockName -> ANOINPUTS, |

307 | TeX -> Subscript[f, T5], |

308 | InteractionOrder -> {NP, 1}, |

309 | Value -> 1., |

310 | Description -> "L_T,5 coefficient"}, |

311 | |

312 | FT6 == { |

313 | ParameterType -> External, |

314 | BlockName -> ANOINPUTS, |

315 | TeX -> Subscript[f, T6], |

316 | InteractionOrder -> {NP, 1}, |

317 | Value -> 1., |

318 | Description -> "L_T,6 coefficient"}, |

319 | |

320 | FT7 == { |

321 | ParameterType -> External, |

322 | BlockName -> ANOINPUTS, |

323 | TeX -> Subscript[f, T7], |

324 | InteractionOrder -> {NP, 1}, |

325 | Value -> 1., |

326 | Description -> "L_T,7 coefficient"}, |

327 | |

328 | FT8 == { |

329 | ParameterType -> External, |

330 | BlockName -> ANOINPUTS, |

331 | TeX -> Subscript[f, T8], |

332 | InteractionOrder -> {NP, 1}, |

333 | Value -> 1., |

334 | Description -> "L_T,8 coefficient"}, |

335 | |

336 | FT9 == { |

337 | ParameterType -> External, |

338 | BlockName -> ANOINPUTS, |

339 | TeX -> Subscript[f, T9], |

340 | InteractionOrder -> {NP, 1}, |

341 | Value -> 1., |

342 | Description -> "L_T,9 coefficient"}, |

343 | |

344 | (* ------------------------------------------------------- *) |

345 | |

346 | (* Internal Parameters *) |

347 | |

348 | \[Alpha]EW == { |

349 | ParameterType -> Internal, |

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

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

352 | ParameterName -> aEW, |

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

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

355 | |

356 | |

357 | MW == { |

358 | ParameterType -> Internal, |

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

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

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

362 | |

363 | sw2 == { |

364 | ParameterType -> Internal, |

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

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

367 | |

368 | ee == { |

369 | TeX -> e, |

370 | ParameterType -> Internal, |

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

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

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

374 | |

375 | cw == { |

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

377 | ParameterType -> Internal, |

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

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

380 | |

381 | sw == { |

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

383 | ParameterType -> Internal, |

384 | Value -> Sqrt[sw2], |

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

386 | |

387 | gw == { |

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

389 | ParameterType -> Internal, |

390 | Value -> ee / sw, |

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

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

393 | |

394 | g1 == { |

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

396 | ParameterType -> Internal, |

397 | Value -> ee / cw, |

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

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

400 | |

401 | gs == { |

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

403 | ParameterType -> Internal, |

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

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

406 | ParameterName -> G, |

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

408 | |

409 | |

410 | v == { |

411 | ParameterType -> Internal, |

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

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

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

415 | |

416 | \[Lambda] == { |

417 | ParameterType -> Internal, |

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

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

420 | ParameterName -> lam, |

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

422 | |

423 | muH == { |

424 | ParameterType -> Internal, |

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

426 | TeX -> \[Mu], |

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

428 | |

429 | |

430 | yl == { |

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

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

433 | AllowSummation -> True, |

434 | ParameterType -> Internal, |

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

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

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

438 | ComplexParameter -> False, |

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

440 | |

441 | yu == { |

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

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

444 | AllowSummation -> True, |

445 | ParameterType -> Internal, |

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

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

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

449 | ComplexParameter -> False, |

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

451 | |

452 | yd == { |

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

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

455 | AllowSummation -> True, |

456 | ParameterType -> Internal, |

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

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

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

460 | ComplexParameter -> False, |

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

462 | |

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

464 | CKM == { |

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

466 | TensorClass -> CKM, |

467 | Unitary -> True, |

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

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

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

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

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

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

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

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

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

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

478 | } |

479 | |

480 | |

481 | (************** Gauge Groups ******************) |

482 | |

483 | M$GaugeGroups = { |

484 | |

485 | U1Y == { |

486 | Abelian -> True, |

487 | GaugeBoson -> B, |

488 | Charge -> Y, |

489 | CouplingConstant -> g1}, |

490 | |

491 | SU2L == { |

492 | Abelian -> False, |

493 | GaugeBoson -> Wi, |

494 | StructureConstant -> Eps, |

495 | CouplingConstant -> gw}, |

496 | |

497 | SU3C == { |

498 | Abelian -> False, |

499 | GaugeBoson -> G, |

500 | StructureConstant -> f, |

501 | SymmetricTensor -> dSUN, |

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

503 | CouplingConstant -> gs} |

504 | } |

505 | |

506 | (********* Particle Classes **********) |

507 | |

508 | M$ClassesDescription = { |

509 | |

510 | (********** Fermions ************) |

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

512 | F[1] == { |

513 | ClassName -> vl, |

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

515 | FlavorIndex -> Generation, |

516 | SelfConjugate -> False, |

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

518 | Mass -> 0, |

519 | Width -> 0, |

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

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

522 | PropagatorType -> S, |

523 | PropagatorArrow -> Forward, |

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

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

526 | |

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

528 | F[2] == { |

529 | ClassName -> l, |

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

531 | FlavorIndex -> Generation, |

532 | SelfConjugate -> False, |

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

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

535 | Width -> 0, |

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

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

538 | PropagatorType -> Straight, |

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

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

541 | PropagatorArrow -> Forward, |

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

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

544 | |

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

546 | F[3] == { |

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

548 | ClassName -> uq, |

549 | FlavorIndex -> Generation, |

550 | SelfConjugate -> False, |

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

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

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

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

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

556 | PropagatorType -> Straight, |

557 | PropagatorArrow -> Forward, |

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

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

560 | |

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

562 | F[4] == { |

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

564 | ClassName -> dq, |

565 | FlavorIndex -> Generation, |

566 | SelfConjugate -> False, |

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

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

569 | Width -> 0, |

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

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

572 | PropagatorType -> Straight, |

573 | PropagatorArrow -> Forward, |

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

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

576 | |

577 | (********** Ghosts **********) |

578 | U[1] == { |

579 | ClassName -> ghA, |

580 | SelfConjugate -> False, |

581 | Indices -> {}, |

582 | Ghost -> A, |

583 | Mass -> 0, |

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

585 | PropagatorLabel -> uA, |

586 | PropagatorType -> GhostDash, |

587 | PropagatorArrow -> Forward}, |

588 | |

589 | U[2] == { |

590 | ClassName -> ghZ, |

591 | SelfConjugate -> False, |

592 | Indices -> {}, |

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

594 | Ghost -> Z, |

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

596 | PropagatorLabel -> uZ, |

597 | PropagatorType -> GhostDash, |

598 | PropagatorArrow -> Forward}, |

599 | |

600 | U[31] == { |

601 | ClassName -> ghWp, |

602 | SelfConjugate -> False, |

603 | Indices -> {}, |

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

605 | Ghost -> W, |

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

607 | PropagatorLabel -> uWp, |

608 | PropagatorType -> GhostDash, |

609 | PropagatorArrow -> Forward}, |

610 | |

611 | U[32] == { |

612 | ClassName -> ghWm, |

613 | SelfConjugate -> False, |

614 | Indices -> {}, |

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

616 | Ghost -> Wbar, |

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

618 | PropagatorLabel -> uWm, |

619 | PropagatorType -> GhostDash, |

620 | PropagatorArrow -> Forward}, |

621 | |

622 | U[4] == { |

623 | ClassName -> ghG, |

624 | SelfConjugate -> False, |

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

626 | Ghost -> G, |

627 | Mass -> 0, |

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

629 | PropagatorLabel -> uG, |

630 | PropagatorType -> GhostDash, |

631 | PropagatorArrow -> Forward}, |

632 | |

633 | U[5] == { |

634 | ClassName -> ghWi, |

635 | Unphysical -> True, |

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

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

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

639 | SelfConjugate -> False, |

640 | Ghost -> Wi, |

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

642 | FlavorIndex -> SU2W}, |

643 | |

644 | U[6] == { |

645 | ClassName -> ghB, |

646 | SelfConjugate -> False, |

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

648 | Indices -> {}, |

649 | Ghost -> B, |

650 | Unphysical -> True}, |

651 | |

652 | (************ Gauge Bosons ***************) |

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

654 | V[1] == { |

655 | ClassName -> A, |

656 | SelfConjugate -> True, |

657 | Indices -> {}, |

658 | Mass -> 0, |

659 | Width -> 0, |

660 | PropagatorLabel -> "a", |

661 | PropagatorType -> W, |

662 | PropagatorArrow -> None, |

663 | PDG -> 22, |

664 | FullName -> "Photon" }, |

665 | |

666 | V[2] == { |

667 | ClassName -> Z, |

668 | SelfConjugate -> True, |

669 | Indices -> {}, |

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

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

672 | PropagatorLabel -> "Z", |

673 | PropagatorType -> Sine, |

674 | PropagatorArrow -> None, |

675 | PDG -> 23, |

676 | FullName -> "Z" }, |

677 | |

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

679 | V[3] == { |

680 | ClassName -> W, |

681 | SelfConjugate -> False, |

682 | Indices -> {}, |

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

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

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

686 | PropagatorLabel -> "W", |

687 | PropagatorType -> Sine, |

688 | PropagatorArrow -> Forward, |

689 | ParticleName ->"W+", |

690 | AntiParticleName ->"W-", |

691 | PDG -> 24, |

692 | FullName -> "W" }, |

693 | |

694 | V[4] == { |

695 | ClassName -> G, |

696 | SelfConjugate -> True, |

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

698 | Mass -> 0, |

699 | Width -> 0, |

700 | PropagatorLabel -> G, |

701 | PropagatorType -> C, |

702 | PropagatorArrow -> None, |

703 | PDG -> 21, |

704 | FullName -> "G" }, |

705 | |

706 | V[5] == { |

707 | ClassName -> Wi, |

708 | Unphysical -> True, |

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

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

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

712 | SelfConjugate -> True, |

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

714 | FlavorIndex -> SU2W, |

715 | Mass -> 0, |

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

717 | |

718 | V[6] == { |

719 | ClassName -> B, |

720 | SelfConjugate -> True, |

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

722 | Indices -> {}, |

723 | Mass -> 0, |

724 | Unphysical -> True}, |

725 | |

726 | |

727 | (************ Scalar Fields **********) |

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

729 | S[1] == { |

730 | ClassName -> H, |

731 | SelfConjugate -> True, |

732 | Mass -> {MH, 125}, |

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

734 | PropagatorLabel -> "H", |

735 | PropagatorType -> D, |

736 | PropagatorArrow -> None, |

737 | PDG -> 25, |

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

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

740 | FullName -> "H" }, |

741 | |

742 | S[2] == { |

743 | ClassName -> phi, |

744 | SelfConjugate -> True, |

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

746 | Width -> Wphi, |

747 | PropagatorLabel -> "Phi", |

748 | PropagatorType -> D, |

749 | PropagatorArrow -> None, |

750 | ParticleName ->"phi0", |

751 | PDG -> 250, |

752 | FullName -> "Phi", |

753 | Goldstone -> Z }, |

754 | |

755 | S[3] == { |

756 | ClassName -> phi2, |

757 | SelfConjugate -> False, |

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

759 | Width -> Wphi2, |

760 | PropagatorLabel -> "Phi2", |

761 | PropagatorType -> D, |

762 | PropagatorArrow -> None, |

763 | ParticleName ->"phi+", |

764 | AntiParticleName ->"phi-", |

765 | PDG -> 251, |

766 | FullName -> "Phi2", |

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

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

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

770 | Goldstone -> W, |

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

772 | } |

773 | |

774 | |

775 | |

776 | |

777 | (*****************************************************************************************) |

778 | |

779 | (* SM Lagrangian *) |

780 | |

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

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

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

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

785 | |

786 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - |

787 | |

788 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* |

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

790 | |

791 | |

792 | (********************* Fermion Lagrangian terms*************************) |

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

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

795 | |

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

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

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

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

800 | |

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

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

803 | |

804 | LBright = |

805 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

806 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

807 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

808 | |

809 | LBleft = |

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

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

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

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

814 | |

815 | LWleft = ee/sw/2( |

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

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

818 | |

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

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

821 | |

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

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

824 | |

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

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

827 | ); |

828 | |

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

830 | |

831 | (******************** Higgs Lagrangian terms****************************) |

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

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

834 | |

835 | |

836 | |

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

838 | |

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

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

841 | |

842 | (*Y_phi=1*) |

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

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

845 | |

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

847 | |

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

849 | |

850 | |

851 | |

852 | |

853 | |

854 | (*************** Yukawa Lagrangian***********************) |

855 | LYuk := If[FeynmanGauge, |

856 | |

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

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

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

860 | |

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

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

863 | |

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

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

866 | ], |

867 | |

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

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

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

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

872 | ] |

873 | ]; |

874 | |

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

876 | |

877 | |

878 | |

879 | (**************Ghost terms**************************) |

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

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

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

883 | |

884 | LGhost := If[FeynmanGauge, |

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

886 | |

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

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

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

890 | |

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

892 | |

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

894 | |

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

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

897 | |

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

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

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

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

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

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

904 | |

905 | |

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

907 | LGhostG + LGhostWi + LGhostB + LGhostphi] |

908 | |

909 | , |

910 | |

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

912 | Block[{dBRSTG,LGhostG}, |

913 | |

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

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

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

917 | |

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

919 | LGhostG] |

920 | |

921 | ]; |

922 | |

923 | |

924 | (* anomalous quartic couplings as defined in PRD74, 073005 *) |

925 | |

926 | |

927 | (* S,0 *) |

928 | |

929 | LS0 := Block[{PMVec, WVec, Dc, Dcbar}, |

930 | |

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

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

933 | |

934 | (*Y_phi=1*) |

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

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

937 | |

938 | FS0 (Dcbar[Phibar, mu]). Dc[Phi, nu] (Dcbar[Phibar, mu]).Dc[Phi, nu] |

939 | |

940 | ]; |

941 | |

942 | (* S,1 *) |

943 | |

944 | LS1 := Block[{PMVec, WVec, Dc, Dcbar}, |

945 | |

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

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

948 | |

949 | (*Y_phi=1*) |

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

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

952 | |

953 | FS1 (Dcbar[Phibar, mu]). Dc[Phi, mu] (Dcbar[Phibar, nu]).Dc[Phi, nu] |

954 | |

955 | ]; |

956 | |

957 | |

958 | (* M,0 *) |

959 | |

960 | LM0 := Block[{PMVec, WVec, FSVec, Dc, Dcbar}, |

961 | |

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

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

964 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

965 | |

966 | (*Y_phi=1*) |

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

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

969 | |

970 | |

971 | FM0/4 (Dcbar[Phibar, alpha]).Dc[Phi, alpha] Tr[(FSvec[mu,nu].PMVec).(FSvec[mu,nu].PMVec)] |

972 | |

973 | ]; |

974 | |

975 | |

976 | (* M,1 *) |

977 | |

978 | LM1 := Block[{PMVec, WVec, FSvec, Dc, Dcbar}, |

979 | |

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

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

982 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

983 | |

984 | (*Y_phi=1*) |

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

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

987 | |

988 | |

989 | FM1/4 (Dcbar[Phibar, beta]).Dc[Phi, mu] Tr[(FSvec[mu,nu].PMVec).(FSvec[nu,beta].PMVec)] |

990 | |

991 | ]; |

992 | |

993 | |

994 | |

995 | (* M,2 *) |

996 | |

997 | LM2 := Block[{PMVec, WVec, Dc, Dcbar}, |

998 | |

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

1000 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1001 | |

1002 | (*Y_phi=1*) |

1003 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f; |

1004 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec); |

1005 | |

1006 | |

1007 | (* FM2 (Dcbar[Phibar, mu]).Dc[Phi, mu] FS[B,mu,nu] FS[B,mu,nu] *) |

1008 | |

1009 | FM2 (Dcbar[Phibar, beta]).Dc[Phi, beta] FS[B,mu,nu] FS[B,mu,nu] |

1010 | |

1011 | ]; |

1012 | |

1013 | (* M,3 *) |

1014 | |

1015 | LM3 := Block[{PMVec, WVec, Dc, Dcbar}, |

1016 | |

1017 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1018 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1019 | |

1020 | (*Y_phi=1*) |

1021 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f; |

1022 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec); |

1023 | |

1024 | |

1025 | |

1026 | FM3 (Dcbar[Phibar, mu]).Dc[Phi, beta] FS[B,mu,nu] FS[B,nu,beta] |

1027 | ]; |

1028 | |

1029 | |

1030 | (* M,4 *) |

1031 | |

1032 | LM4 := Block[{PMVec, WVec, FSVec, Dc, Dcbar}, |

1033 | |

1034 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1035 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1036 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1037 | |

1038 | (*Y_phi=1*) |

1039 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f; |

1040 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec); |

1041 | |

1042 | |

1043 | |

1044 | FM4/2 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).Dc[Phi, mu] FS[B,beta,nu] |

1045 | |

1046 | |

1047 | ]; |

1048 | |

1049 | (* M,5 *) |

1050 | |

1051 | LM5 := Block[{PMVec, WVec, FSVec, Dc, Dcbar}, |

1052 | |

1053 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1054 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1055 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1056 | |

1057 | (*Y_phi=1*) |

1058 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f; |

1059 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec); |

1060 | |

1061 | |

1062 | FM5/2 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).Dc[Phi, nu] FS[B,beta,mu] |

1063 | |

1064 | ]; |

1065 | |

1066 | |

1067 | (* M,6 *) |

1068 | |

1069 | LM6 :=Block[{PMVec, WVec, FSVec, Dc, Dcbar}, |

1070 | |

1071 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1072 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1073 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1074 | |

1075 | (*Y_phi=1*) |

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

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

1078 | |

1079 | |

1080 | FM6/4 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).(FSvec[beta,nu].PMVec).Dc[Phi, mu] |

1081 | |

1082 | ]; |

1083 | |

1084 | (* M,7 *) |

1085 | |

1086 | LM7 :=Block[{PMVec, WVec, FSVec, Dc, Dcbar}, |

1087 | |

1088 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1089 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1090 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1091 | |

1092 | (*Y_phi=1*) |

1093 | Dc[f_, mu_] := I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 (Wvec[mu].PMVec).f; |

1094 | Dcbar[f_, mu_] := -I del[f, mu] + ee/cw B[mu]/2 f + ee/sw/2 f.(Wvec[mu].PMVec); |

1095 | |

1096 | |

1097 | FM7/4 (Dcbar[Phibar, mu]).(FSvec[beta,nu].PMVec).(FSvec[beta,mu].PMVec).Dc[Phi, nu] |

1098 | |

1099 | ]; |

1100 | |

1101 | |

1102 | (* T,0 *) |

1103 | |

1104 | LT0 := Block[{PMVec, FSVec }, |

1105 | |

1106 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1107 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1108 | |

1109 | FT0/16 Tr[(FSvec[alpha,beta].PMVec).(FSvec[alpha,beta].PMVec)] Tr[(FSvec[mu,nu].PMVec).(FSvec[mu,nu].PMVec)] |

1110 | |

1111 | ]; |

1112 | |

1113 | (* T,1 *) |

1114 | |

1115 | LT1 := Block[{PMVec, FSVec}, |

1116 | |

1117 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1118 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1119 | |

1120 | FT1/16 Tr[(FSvec[alpha,nu].PMVec).(FSvec[mu,beta].PMVec)] Tr[(FSvec[mu,beta].PMVec).(FSvec[alpha,nu].PMVec)] |

1121 | |

1122 | ]; |

1123 | |

1124 | |

1125 | (* T,2 *) |

1126 | |

1127 | LT2 := Block[{PMVec, FSVec}, |

1128 | |

1129 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1130 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1131 | |

1132 | FT2/16 Tr[(FSvec[alpha,mu].PMVec).(FSvec[mu,beta].PMVec)] Tr[(FSvec[beta,nu].PMVec).(FSvec[nu,alpha].PMVec)] |

1133 | |

1134 | ]; |

1135 | |

1136 | (* T,3 identicaly zero!*) |

1137 | |

1138 | LT3 := Block[{PMVec, FSVec}, |

1139 | |

1140 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1141 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1142 | |

1143 | FT3/8 Tr[(FSvec[alpha,mu].PMVec).(FSvec[mu,beta].PMVec).(FSvec[nu,alpha].PMVec)] FS[B, beta, nu] |

1144 | |

1145 | ]; |

1146 | |

1147 | |

1148 | (* T,4: identicaly zero *) |

1149 | |

1150 | LT4 := Block[{PMVec, FSVec}, |

1151 | |

1152 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1153 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1154 | |

1155 | |

1156 | FT4/8 Tr[(FSvec[alpha,mu].PMVec).(FSvec[alpha, mu].PMVec).(FSvec[beta, nu].PMVec)] FS[B, beta, nu] |

1157 | |

1158 | ]; |

1159 | |

1160 | |

1161 | (* T,5 *) |

1162 | |

1163 | LT5 := Block[{PMVec, FSVec}, |

1164 | |

1165 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1166 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1167 | |

1168 | |

1169 | FT5/4 Tr[(FSvec[mu,nu].PMVec).(FSvec[mu, nu].PMVec)] FS[B, beta, alpha] FS[B, beta, alpha] |

1170 | |

1171 | ]; |

1172 | |

1173 | |

1174 | (* T,6 *) |

1175 | |

1176 | LT6 := Block[{PMVec, FSVec}, |

1177 | |

1178 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1179 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1180 | |

1181 | FT6/4 Tr[(FSvec[alpha,nu].PMVec).(FSvec[mu, beta].PMVec)] FS[B, mu, beta] FS[B, alpha, nu] |

1182 | |

1183 | ]; |

1184 | |

1185 | |

1186 | (* T,7 *) |

1187 | |

1188 | LT7 := Block[{PMVec, FSVec}, |

1189 | |

1190 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1191 | FSvec[mu_,nu_] := {FS[Wi, mu, nu, 1], FS[Wi, mu, nu, 2], FS[Wi, mu, nu, 3]}; |

1192 | |

1193 | FT7/4 Tr[(FSvec[alpha, mu].PMVec).(FSvec[mu, beta].PMVec)] FS[B, beta, nu] FS[B, nu, alpha] |

1194 | |

1195 | ]; |

1196 | |

1197 | |

1198 | (* T,8: *) |

1199 | |

1200 | LT8 := Block[{PMVec, WVec}, |

1201 | |

1202 | PMVec = Table[PauliSigma[i], {i, 3}]; |

1203 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1204 | |

1205 | |

1206 | FT8 (del[B[nu], mu] - del[B[mu], nu] )* |

1207 | (del[B[nu], mu] - del[B[mu], nu] )* |

1208 | (del[B[beta], alpha] - del[B[alpha], beta] )* |

1209 | (del[B[beta], alpha] - del[B[alpha], beta] ) |

1210 | |

1211 | ]; |

1212 | |

1213 | (* T,9: *) |

1214 | |

1215 | LT9 := Block[{PMVec, WVec}, |

1216 | |

1217 | PMVec = Table[PauliSigma[i], {I, 3}]; |

1218 | Wvec[mu_] := {Wi[mu, 1], Wi[mu, 2], Wi[mu, 3]}; |

1219 | |

1220 | FT9 FS[B, mu, nu] FS[B, nu, alpha] FS[B, alpha, beta] FS[B, beta, mu] |

1221 | |

1222 | ]; |

1223 | |

1224 | |

1225 | (* ------------------------------------------------------- *) |

1226 | |

1227 | |

1228 | (*********Total SM Lagrangian in the unitary gauge*******) |

1229 | |

1230 | LSM := LGauge + LHiggs + LFermions + LYukawa ; |

1231 | |

1232 | LQS = LS0 + LS1; |

1233 | |

1234 | LQM = LM0 + LM1 + LM2 + LM3 + LM4 + LM5 + LM6 + LM7; |

1235 | |

1236 | LQT = LT0 + LT1 + LT2 + LT3 + LT4 + LT5 + LT6 + LT7 + LT8 + LT9; |

1237 | |

1238 | LQuartic := LSM + LQS + LQM + LQT; |

1239 | |

1240 | |

1241 | |

1242 | |

1243 |