# HiddenAbelianHiggsModel: Hidden.fr

File Hidden.fr, 22.3 KB (added by BenjF, 8 years ago) |
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1 | (***************************************************************************************************************) |

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

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

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

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

6 | (***************************************************************************************************************) |

7 | |

8 | M$ModelName = "Abelian_Higgs_Model"; |

9 | |

10 | |

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

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

13 | Institutions -> {"Universite catholique de Louvain (CP3)"}, |

14 | Emails -> {"claude.duhr@uclouvain.be"}, |

15 | Version -> "1.1", |

16 | References -> " J. D. Wells, \"How to Find a Hidden World at the Large Hadron Collider,\", [arXiv:0803.1243 [hep-ph]]", |

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

18 | |

19 | (* |

20 | v1.1: changed name for full Lagrangian from LSM to LHAHM |

21 | v1.2: Benj: the lambda parameter had the same name as the leptons, which was making the code crashing. |

22 | *) |

23 | |

24 | (* The U(1)X charge of the abelian Higgs is a free parameter *) |

25 | |

26 | qX = 1; |

27 | |

28 | |

29 | (******* Index definitions ********) |

30 | |

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

32 | |

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

34 | |

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

36 | |

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

38 | |

39 | |

40 | IndexStyle[Colour, i] |

41 | |

42 | IndexStyle[Generation, f] |

43 | |

44 | IndexStyle[Gluon ,a] |

45 | |

46 | IndexStyle[SUW2 ,k] |

47 | |

48 | |

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

50 | |

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

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

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

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

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

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

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

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

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

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

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

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

63 | |

64 | |

65 | (**************** Parameters *************) |

66 | |

67 | M$Parameters = { |

68 | |

69 | (* External parameters *) |

70 | |

71 | \[Alpha]EWM1== { |

72 | ParameterType -> External, |

73 | BlockName -> SMINPUTS, |

74 | ParameterName -> aEWM1, |

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

76 | Value -> 127.9, |

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

78 | |

79 | Gf == { |

80 | ParameterType -> External, |

81 | BlockName -> SMINPUTS, |

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

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

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

85 | |

86 | \[Alpha]S == { |

87 | ParameterType -> External, |

88 | BlockName -> SMINPUTS, |

89 | ParameterName -> aS, |

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

91 | Value -> 0.118, |

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

93 | |

94 | |

95 | ymc == { |

96 | ParameterType -> External, |

97 | BlockName -> YUKAWA, |

98 | Value -> 1.42, |

99 | OrderBlock -> {4}, |

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

101 | |

102 | ymb == { |

103 | ParameterType -> External, |

104 | BlockName -> YUKAWA, |

105 | Value -> 4.7, |

106 | OrderBlock -> {5}, |

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

108 | |

109 | ymt == { |

110 | ParameterType -> External, |

111 | BlockName -> YUKAWA, |

112 | Value -> 174.3, |

113 | OrderBlock -> {6}, |

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

115 | |

116 | ymtau == { |

117 | ParameterType -> External, |

118 | BlockName -> YUKAWA, |

119 | Value -> 1.777, |

120 | OrderBlock -> {15}, |

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

122 | |

123 | \[Lambda] == { |

124 | ParameterType -> External, |

125 | BlockName -> HIGGS, |

126 | ParameterName -> lam, |

127 | Value -> 0.42568, |

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

129 | Description -> "SM Higgs self-coupling"}, |

130 | |

131 | cabi == { |

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

133 | ParameterType -> External, |

134 | BlockName -> CKMBLOCK, |

135 | OrderBlock -> {1}, |

136 | Value -> 0.488, |

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

138 | |

139 | |

140 | (* New hidden external parameters *) |

141 | |

142 | \[Alpha]XM1 == { |

143 | ParameterType -> External, |

144 | BlockName -> HIDDEN, |

145 | ParameterName -> aXM1, |

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

147 | Value -> 127.9, |

148 | Description -> "Inverse of the U(1)X coupling constant"}, |

149 | |

150 | \[Eta] == { |

151 | ParameterType -> External, |

152 | BlockName -> HIDDEN, |

153 | ParameterName -> eta, |

154 | Value -> 0.01, |

155 | Description -> "U(1)X - U(1)Y mixing parameter"}, |

156 | |

157 | \[Rho] == { |

158 | ParameterType -> External, |

159 | BlockName -> HIDDEN, |

160 | ParameterName -> rho, |

161 | Value -> 0.010142, |

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

163 | Description -> "Abelian Higgs self-coupling"}, |

164 | |

165 | \[Kappa] == { |

166 | ParameterType -> External, |

167 | BlockName -> HIDDEN, |

168 | ParameterName -> kap, |

169 | Value -> 0.0977392, |

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

171 | Description -> "Coupling between the abelian and the SM Higgs"}, |

172 | |

173 | |

174 | (* Internal Parameters *) |

175 | |

176 | (* Weak Mixing *) |

177 | |

178 | cw == { |

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

180 | ParameterType -> Internal, |

181 | Value -> MW/MZ, |

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

183 | |

184 | sw == { |

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

186 | ParameterType -> Internal, |

187 | Value -> Sqrt[1-cw^2], |

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

189 | |

190 | (* Gauge couplings *) |

191 | |

192 | \[Alpha]EW == { |

193 | ParameterType -> Internal, |

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

195 | ParameterName -> aEW, |

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

197 | Description -> "Electroweak coupling constant"}, |

198 | |

199 | ee == { |

200 | TeX -> e, |

201 | ParameterType -> Internal, |

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

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

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

205 | |

206 | gw == { |

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

208 | ParameterType -> Internal, |

209 | Value -> ee / sw, |

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

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

212 | |

213 | g1 == { |

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

215 | ParameterType -> Internal, |

216 | Value -> ee / cw, |

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

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

219 | |

220 | gs == { |

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

222 | ParameterType -> Internal, |

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

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

225 | ParameterName -> G, |

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

227 | |

228 | \[Alpha]X == { |

229 | ParameterType -> Internal, |

230 | Value -> 1/\[Alpha]XM1, |

231 | ParameterName -> aX, |

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

233 | Description -> "U(1)X coupling contant"}, |

234 | |

235 | gX == { |

236 | TeX -> Subscript[g, X], |

237 | ParameterType -> Internal, |

238 | Value -> Sqrt[4 Pi \[Alpha]X], |

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

240 | Description -> "U(1)X coupling constant"}, |

241 | |

242 | (* New scales *) |

243 | |

244 | MZ0 == { |

245 | ParameterType -> Internal, |

246 | Value -> MZ, |

247 | Description -> "Z mass before mixing"}, |

248 | |

249 | MX =={ |

250 | ParameterType -> Internal, |

251 | Value -> MZp, |

252 | Description -> "X mass before mixing"}, |

253 | |

254 | \[CapitalDelta]Z =={ |

255 | ParameterType -> Internal, |

256 | Value -> MX^2/MZ0^2, |

257 | ParameterName -> DZ, |

258 | Description -> "Ratio of scales"}, |

259 | |

260 | |

261 | (* Higgs sector *) |

262 | |

263 | |

264 | |

265 | v == { |

266 | ParameterType -> Internal, |

267 | Value -> 1/Sqrt[Gf* Sqrt[2]], |

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

269 | Description -> "SM Higgs VEV"}, |

270 | |

271 | \[Xi] == { |

272 | ParameterType -> Internal, |

273 | Value -> MX/qX/gX, |

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

275 | ParameterName -> xi, |

276 | Description -> "Abelian Higgs VEV"}, |

277 | |

278 | MH1 == { |

279 | ParameterType -> Internal, |

280 | Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 - Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]], |

281 | Description -> "Mass of H1"}, |

282 | |

283 | MH2 == { |

284 | ParameterType -> Internal, |

285 | Value -> Sqrt[\[Lambda] v^2 + \[Rho] \[Xi]^2 + Sqrt[(\[Lambda] v^2 - \[Rho] \[Xi]^2)^2 + \[Kappa]^2 v^2 \[Xi]^2]], |

286 | Description -> "Mass of H2"}, |

287 | |

288 | \[Mu]SM2 =={ |

289 | TeX -> Subsuperscript[\[Mu], SM, 2], |

290 | ParameterType -> Internal, |

291 | Value -> (\[Rho] v^2 + \[Kappa] \[Xi]^2)/2, |

292 | ParameterName -> muSM2, |

293 | Description -> "Quadratic SM potential term"}, |

294 | |

295 | \[Mu]H2 =={ |

296 | TeX -> Subsuperscript[\[Mu], H, 2], |

297 | ParameterType -> Internal, |

298 | Value -> (\[Kappa] v^2 + \[Lambda] \[Xi]^2)/2, |

299 | ParameterName -> muH2, |

300 | Description -> "Quadratic abelian potential term"}, |

301 | |

302 | (* Mixing parameters *) |

303 | |

304 | |

305 | \[Theta]a == { |

306 | TeX -> Subscript[\[Theta], \[Alpha]], |

307 | ParameterType -> Internal, |

308 | Value -> ArcTan[-2 sw \[Eta]/(1-sw^2 \[Eta]^2 -\[CapitalDelta]Z)]/2, |

309 | ParameterName -> alp, |

310 | Description -> "Mixing in the weak sector"}, |

311 | |

312 | ca == { |

313 | TeX -> Subscript[c, \[Alpha]], |

314 | ParameterType -> Internal, |

315 | Value -> Cos[\[Theta]a], |

316 | Description -> "Cosine of alp"}, |

317 | |

318 | sa == { |

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

320 | ParameterType -> Internal, |

321 | Value -> Sin[\[Theta]a], |

322 | Description -> "Sine of alp"}, |

323 | |

324 | \[Chi] == { |

325 | ParameterType -> Internal, |

326 | Value -> (Sqrt[1+4\[Eta]^2] - 1)/2/\[Eta], |

327 | ParameterName -> chi, |

328 | Description -> "kinetic mixing parameter"}, |

329 | |

330 | (* Higgs *) |

331 | |

332 | \[Theta]h == { |

333 | TeX -> Subscript[\[Theta], h], |

334 | ParameterType -> Internal, |

335 | Value -> ArcTan[\[Kappa] v \[Xi]/(\[Rho] \[Xi]^2 - \[Lambda] v^2)]/2, |

336 | ParameterName -> th, |

337 | Description -> "Mixing in the Higgs sector"}, |

338 | |

339 | ch == { |

340 | TeX -> Subscript[c, h], |

341 | ParameterType -> Internal, |

342 | Value -> Cos[\[Theta]h], |

343 | Description -> "Cosine of th"}, |

344 | |

345 | sh == { |

346 | TeX -> Subscript[s, h], |

347 | ParameterType -> Internal, |

348 | Value -> Sin[\[Theta]h], |

349 | Description -> "Sine of th"}, |

350 | |

351 | (* Yukawa sector *) |

352 | |

353 | yl == { |

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

355 | AllowSummation -> True, |

356 | ParameterType -> Internal, |

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

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

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

360 | ComplexParameter -> False, |

361 | Definitions -> {yl[1] -> 0, yl[2] ->0}, |

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

363 | |

364 | yu == { |

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

366 | AllowSummation -> True, |

367 | ParameterType -> Internal, |

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

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

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

371 | ComplexParameter -> False, |

372 | Definitions -> {yu[1] -> 0}, |

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

374 | |

375 | yd == { |

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

377 | AllowSummation -> True, |

378 | ParameterType -> Internal, |

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

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

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

382 | ComplexParameter -> False, |

383 | Definitions -> {yd[1] -> 0, yd[2] -> 0}, |

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

385 | |

386 | |

387 | CKM == { |

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

389 | TensorClass -> CKM, |

390 | Unitary -> True, |

391 | Definitions -> {CKM[3, 3] -> 1, |

392 | CKM[i_, 3] :> 0 /; i != 3, |

393 | CKM[3, i_] :> 0 /; i != 3}, |

394 | Value -> {CKM[1,2] -> Sin[cabi], |

395 | CKM[1,1] -> Cos[cabi], |

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

397 | CKM[2,2] -> Cos[cabi]}, |

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

399 | |

400 | |

401 | |

402 | } |

403 | |

404 | |

405 | (************** Gauge Groups ******************) |

406 | |

407 | M$GaugeGroups = { |

408 | |

409 | U1Y == { |

410 | Abelian -> True, |

411 | GaugeBoson -> B, |

412 | Charge -> Y, |

413 | CouplingConstant -> g1}, |

414 | |

415 | U1X == { |

416 | Abelian -> True, |

417 | GaugeBoson -> X, |

418 | Charge -> QX, |

419 | CouplingConstant -> ee}, |

420 | |

421 | SU2L == { |

422 | Abelian -> False, |

423 | GaugeBoson -> Wi, |

424 | StructureConstant -> Eps, |

425 | CouplingConstant -> gw}, |

426 | |

427 | SU3C == { |

428 | Abelian -> False, |

429 | GaugeBoson -> G, |

430 | StructureConstant -> f, |

431 | SymmetricTensor -> dSUN, |

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

433 | CouplingConstant -> gs} |

434 | } |

435 | |

436 | (********* Particle Classes **********) |

437 | |

438 | M$ClassesDescription = { |

439 | |

440 | (********** Fermions ************) |

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

442 | F[1] == { |

443 | ClassName -> vl, |

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

445 | FlavorIndex -> Generation, |

446 | SelfConjugate -> False, |

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

448 | Mass -> 0, |

449 | Width -> 0, |

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

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

452 | PropagatorType -> S, |

453 | PropagatorArrow -> Forward, |

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

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

456 | |

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

458 | F[2] == { |

459 | ClassName -> l, |

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

461 | FlavorIndex -> Generation, |

462 | SelfConjugate -> False, |

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

464 | Mass -> {Ml, {ME, 0}, {MM, 0}, {MTA, 1.777}}, |

465 | Width -> 0, |

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

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

468 | PropagatorType -> Straight, |

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

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

471 | PropagatorArrow -> Forward, |

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

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

474 | |

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

476 | F[3] == { |

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

478 | ClassName -> uq, |

479 | FlavorIndex -> Generation, |

480 | SelfConjugate -> False, |

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

482 | Mass -> {Mu, {MU, 0}, {MC, 1.42}, {MT, 174.3}}, |

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

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

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

486 | PropagatorType -> Straight, |

487 | PropagatorArrow -> Forward, |

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

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

490 | |

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

492 | F[4] == { |

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

494 | ClassName -> dq, |

495 | FlavorIndex -> Generation, |

496 | SelfConjugate -> False, |

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

498 | Mass -> {Md, {MD, 0}, {MS, 0}, {MB, 4.7}}, |

499 | Width -> 0, |

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

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

502 | PropagatorType -> Straight, |

503 | PropagatorArrow -> Forward, |

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

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

506 | |

507 | (********** Ghosts **********) |

508 | |

509 | U[1] == { |

510 | ClassName -> ghG, |

511 | SelfConjugate -> False, |

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

513 | Ghost -> G, |

514 | Mass -> 0, |

515 | Width -> 0, |

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

517 | PropagatorLabel -> uG, |

518 | PropagatorType -> GhostDash, |

519 | PropagatorArrow -> Forward}, |

520 | |

521 | |

522 | (************ Gauge Bosons ***************) |

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

524 | V[1] == { |

525 | ClassName -> A, |

526 | SelfConjugate -> True, |

527 | Indices -> {}, |

528 | Mass -> 0, |

529 | Width -> 0, |

530 | PropagatorLabel -> "a", |

531 | PropagatorType -> W, |

532 | PropagatorArrow -> None, |

533 | PDG -> 22, |

534 | FullName -> "Photon" }, |

535 | |

536 | V[21] == { |

537 | ClassName -> Z, |

538 | SelfConjugate -> True, |

539 | Indices -> {}, |

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

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

542 | PropagatorLabel -> "Z", |

543 | PropagatorType -> Sine, |

544 | PropagatorArrow -> None, |

545 | PDG -> 23, |

546 | FullName -> "Z" }, |

547 | |

548 | V[22] == { |

549 | ClassName -> Zp, |

550 | SelfConjugate -> True, |

551 | Indices -> {}, |

552 | Mass -> {MZp, 500}, |

553 | Width -> {WZp, 0.0008252}, |

554 | PropagatorLabel -> "Zp", |

555 | PropagatorType -> Sine, |

556 | PropagatorArrow -> None, |

557 | PDG -> 1023, |

558 | FullName -> "Zp" }, |

559 | |

560 | V[210] == { |

561 | ClassName -> Bp, |

562 | SelfConjugate -> True, |

563 | Unphysical -> True, |

564 | Indices -> {}, |

565 | Mass -> 0, |

566 | Width -> 0, |

567 | Definitions -> {Bp[mu_] :> cw A[mu] -sw ca Z[mu] + sw sa Zp[mu]}}, |

568 | |

569 | V[220] == { |

570 | ClassName -> Xp, |

571 | SelfConjugate -> True, |

572 | Unphysical -> True, |

573 | Indices -> {}, |

574 | Mass -> 0, |

575 | Width -> 0, |

576 | Definitions -> {Xp[mu_] :> sa Z[mu] + ca Zp[mu]}}, |

577 | |

578 | |

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

580 | V[3] == { |

581 | ClassName -> W, |

582 | SelfConjugate -> False, |

583 | Indices -> {}, |

584 | Mass -> {MW, 80.419}, |

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

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

587 | PropagatorLabel -> "W", |

588 | PropagatorType -> Sine, |

589 | PropagatorArrow -> Forward, |

590 | ParticleName ->"W+", |

591 | AntiParticleName ->"W-", |

592 | PDG -> 24, |

593 | FullName -> "W" }, |

594 | |

595 | V[4] == { |

596 | ClassName -> G, |

597 | SelfConjugate -> True, |

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

599 | Mass -> 0, |

600 | Width -> 0, |

601 | PropagatorLabel -> G, |

602 | PropagatorType -> C, |

603 | PropagatorArrow -> None, |

604 | PDG -> 21, |

605 | FullName -> "G" }, |

606 | |

607 | V[5] == { |

608 | ClassName -> Wi, |

609 | Unphysical -> True, |

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

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

612 | Wi[mu_, 3] -> -cw sa Zp[mu] + cw ca Z[mu] + sw A[mu]}, |

613 | SelfConjugate -> True, |

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

615 | FlavorIndex -> SU2W, |

616 | Mass -> 0, |

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

618 | |

619 | V[6] == { |

620 | ClassName -> B, |

621 | SelfConjugate -> True, |

622 | Definitions -> {B[mu_] -> Bp[mu] + \[Eta] Xp[mu]}, |

623 | Indices -> {}, |

624 | Mass -> 0, |

625 | Unphysical -> True}, |

626 | |

627 | V[61] == { |

628 | ClassName -> X, |

629 | SelfConjugate -> True, |

630 | Definitions -> {X[mu_] -> \[Chi] \[Eta] Xp[mu]}, |

631 | Indices -> {}, |

632 | Mass -> 0, |

633 | Unphysical -> True}, |

634 | |

635 | |

636 | |

637 | (************ Scalar Fields **********) |

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

639 | S[11] == { |

640 | ClassName -> h1, |

641 | SelfConjugate -> True, |

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

643 | Width -> {WH1, 0.00282299}, |

644 | PropagatorLabel -> "h1", |

645 | PropagatorType -> D, |

646 | PropagatorArrow -> None, |

647 | PDG -> 25, |

648 | FullName -> "h1" }, |

649 | |

650 | S[12] == { |

651 | ClassName -> h2, |

652 | SelfConjugate -> True, |

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

654 | Width -> {WH2, 5.23795}, |

655 | PropagatorLabel -> "h2", |

656 | PropagatorType -> D, |

657 | PropagatorArrow -> None, |

658 | PDG -> 35, |

659 | FullName -> "h2" }, |

660 | |

661 | S[110] == { |

662 | ClassName -> H, |

663 | SelfConjugate -> True, |

664 | Unphysical -> True, |

665 | Definitions -> {H -> ch h1 + sh h2}}, |

666 | |

667 | S[120] == { |

668 | ClassName -> phih, |

669 | SelfConjugate -> False, |

670 | Unphysical -> True, |

671 | Definitions -> {phih -> \[Xi]/Sqrt[2]-sh h1 + ch h2}} |

672 | } |

673 | |

674 | |

675 | |

676 | (*****************************************************************************************) |

677 | |

678 | (* SM Lagrangian *) |

679 | |

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

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

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

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

684 | |

685 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - 1/4 (del[X[nu], mu] - del[X[mu], nu])^2 + |

686 | \[Chi]/2 (del[X[nu], mu] - del[X[mu], nu]) (del[B[nu], mu] - del[B[mu], nu]) - |

687 | |

688 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* |

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

690 | |

691 | |

692 | (********************* Fermion Lagrangian terms*************************) |

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

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

695 | |

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

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

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

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

700 | |

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

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

703 | |

704 | LBright = |

705 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

706 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

707 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

708 | |

709 | LBleft = |

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

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

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

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

714 | |

715 | LWleft = ee/sw/2( |

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

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

718 | |

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

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

721 | |

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

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

724 | |

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

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

727 | ); |

728 | |

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

730 | |

731 | (******************** Higgs Lagrangian terms****************************) |

732 | Phi := {0, (v + H)/Sqrt[2]}; |

733 | Phibar := {0, (v + H)/Sqrt[2]}; |

734 | |

735 | |

736 | |

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

738 | |

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

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

741 | |

742 | (*Y_phi=1*) |

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

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

745 | |

746 | Dc[phih, mu_] := del[phih, mu] -I gX qX X[mu] phih; |

747 | Dc[phihbar, mu_] := del[phihbar, mu] +I gX qX X[mu] phihbar; |

748 | |

749 | Vphi[Phi2SM_, Phi2H_] := -\[Mu]SM2 Phi2SM + \[Lambda] (Phi2SM)^2 - |

750 | \[Mu]H2 Phi2H + \[Rho] (Phi2H)^2 + |

751 | \[Kappa] (Phi2H) (Phi2SM) ; |

752 | |

753 | (* The value of qX is set at the beginning of the notebook *) |

754 | |

755 | (Dcbar[Phibar, mu]).Dc[Phi, mu] + Dc[phihbar,mu] Dc[phih, mu] - Vphi[Phibar.Phi, phihbar phih]]; |

756 | |

757 | |

758 | (*************** Yukawa Lagrangian***********************) |

759 | LYuk := Module[{s,r,n,m,i}, - |

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

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

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

763 | ] |

764 | |

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

766 | |

767 | |

768 | |

769 | (**************Ghost terms**************************) |

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

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

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

773 | |

774 | LGhost := |

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

776 | |

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

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

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

780 | |

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

782 | LGhostG] |

783 | |

784 | |

785 | (*********Total SM Lagrangian*******) |

786 | LHAHM := LGauge + LHiggs + LFermions + LYukawa + LGhost; |

787 | |

788 |