# SILH: SILH.fr

File SILH.fr, 24.3 KB (added by claudeduhr, 9 years ago) |
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1 | (***************************************************************************************************************) |

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

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

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

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

6 | (****** Only unitary gauge is implemented ******) |

7 | (****** Only the first order in \[Xi](see parameters) is implemented ******) |

8 | (***************************************************************************************************************) |

9 | |

10 | M$ModelName = "SILH"; |

11 | |

12 | |

13 | M$Information = {Authors -> {"C. Degrande"}, |

14 | Date->"12/06/2009" |

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

16 | Emails -> {"celine.degrande@uclouvain.be"}, |

17 | Version -> 1, |

18 | URLs->"http://feynrules.phys.ucl.ac.be/view/Main/SILH" |

19 | }; |

20 | |

21 | |

22 | (******* Index definitions ********) |

23 | |

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

25 | |

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

27 | |

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

29 | |

30 | IndexRange[ Index[SU2W] ] = Range[3] |

31 | |

32 | |

33 | IndexStyle[Colour, i] |

34 | |

35 | IndexStyle[Generation, f] |

36 | |

37 | IndexStyle[Gluon ,a] |

38 | |

39 | IndexStyle[SUW2 ,k] |

40 | |

41 | |

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

43 | |

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

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

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

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

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

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

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

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

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

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

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

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

56 | |

57 | |

58 | (**************** Parameters *************) |

59 | |

60 | M$Parameters = { |

61 | |

62 | (* External SM parameters *) |

63 | |

64 | \[Alpha]EWM1== { |

65 | ParameterType -> External, |

66 | BlockName -> SMINPUTS, |

67 | ParameterName -> aEWM1, |

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

69 | Value -> 127.9, |

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

71 | |

72 | Gf == { |

73 | ParameterType -> External, |

74 | BlockName -> SMINPUTS, |

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

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

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

78 | |

79 | \[Alpha]S == { |

80 | ParameterType -> External, |

81 | BlockName -> SMINPUTS, |

82 | ParameterName -> aS, |

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

84 | Value -> 0.118, |

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

86 | |

87 | |

88 | ZM == { |

89 | ParameterType -> External, |

90 | BlockName -> SMINPUTS, |

91 | Value -> 91.188, |

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

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 | |

124 | |

125 | (* External SILH Parameter *) |

126 | |

127 | frho =={ |

128 | TeX -> Subscript[f,\[Rho]], |

129 | ParameterType -> External, |

130 | Value -> 1 (*TeV*), |

131 | Description -> "sigma model scale"}, |

132 | |

133 | grho =={ |

134 | TeX -> Subscript[g,\[Rho]], |

135 | ParameterType -> External, |

136 | Value -> 1, |

137 | Description -> "sigma model coupling"}, |

138 | |

139 | cH =={ |

140 | TeX -> Subscript[c,H], |

141 | ParameterType -> External, |

142 | Value -> 1}, |

143 | |

144 | cT =={ |

145 | TeX -> Subscript[c,T], |

146 | ParameterType -> External, |

147 | Value -> 1}, |

148 | |

149 | c6 =={ |

150 | TeX -> Subscript[c,6], |

151 | ParameterType -> External, |

152 | Value -> 1}, |

153 | |

154 | cy =={ |

155 | TeX -> Subscript[c,y], |

156 | ParameterType -> External, |

157 | Value -> 1}, |

158 | |

159 | cW =={ |

160 | TeX -> Subscript[c,W], |

161 | ParameterType -> External, |

162 | Value -> 1}, |

163 | |

164 | cB =={ |

165 | TeX -> Subscript[c,B], |

166 | ParameterType -> External, |

167 | Value -> 1}, |

168 | |

169 | cHW =={ |

170 | TeX -> Subscript[c,HW], |

171 | ParameterType -> External, |

172 | Value -> 1}, |

173 | |

174 | cHB =={ |

175 | TeX -> Subscript[c,HB], |

176 | ParameterType -> External, |

177 | Value -> 1}, |

178 | |

179 | cga =={ |

180 | TeX -> Subscript[c,\[Gamma]], |

181 | ParameterType -> External, |

182 | Value -> 1}, |

183 | |

184 | cg =={ |

185 | TeX -> Subscript[c,g], |

186 | ParameterType -> External, |

187 | Value -> 1}, |

188 | |

189 | c2W =={ |

190 | TeX -> Subscript[c,2W], |

191 | ParameterType -> External, |

192 | Value -> 1}, |

193 | |

194 | c2B =={ |

195 | TeX -> Subscript[c,2B], |

196 | ParameterType -> External, |

197 | Value -> 1}, |

198 | |

199 | c2g =={ |

200 | TeX -> Subscript[c,2g], |

201 | ParameterType -> External, |

202 | Value -> 1}, |

203 | |

204 | c3W =={ |

205 | TeX -> Subscript[c,3W], |

206 | ParameterType -> External, |

207 | Value -> 1}, |

208 | |

209 | c3B =={ |

210 | TeX -> Subscript[c,3B], |

211 | ParameterType -> External, |

212 | Value -> 1}, |

213 | |

214 | |

215 | (* Internal Parameters *) |

216 | |

217 | \[Alpha]EW == { |

218 | ParameterType -> Internal, |

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

220 | ParameterName -> aEW, |

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

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

223 | |

224 | |

225 | MW == { |

226 | ParameterType -> Internal, |

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

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

229 | |

230 | sw2 == { |

231 | ParameterType -> Internal, |

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

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

234 | |

235 | ee == { |

236 | TeX -> e, |

237 | ParameterType -> Internal, |

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

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

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

241 | |

242 | cw == { |

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

244 | ParameterType -> Internal, |

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

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

247 | |

248 | sw == { |

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

250 | ParameterType -> Internal, |

251 | Value -> Sqrt[sw2], |

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

253 | |

254 | gw == { |

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

256 | ParameterType -> Internal, |

257 | Value -> ee / sw, |

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

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

260 | |

261 | g1 == { |

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

263 | ParameterType -> Internal, |

264 | Value -> ee / cw, |

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

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

267 | |

268 | gs == { |

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

270 | ParameterType -> Internal, |

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

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

273 | ParameterName -> G, |

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

275 | |

276 | v == { |

277 | ParameterType -> Internal, |

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

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

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

281 | |

282 | \[Xi] == { |

283 | ParameterType -> Internal, |

284 | Value -> v^2/frho^2, |

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

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

287 | |

288 | \[Lambda] == { |

289 | ParameterType -> Internal, |

290 | Value -> MH^2/(2*v^2)(1+cH*\[Xi]-3/2 c6*\[Xi]), |

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

292 | ParameterName -> lam, |

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

294 | |

295 | muH == { |

296 | ParameterType -> Internal, |

297 | Value -> Sqrt[v^2 \[Lambda](1+3/4 c6 \[Xi])], |

298 | TeX -> \[Mu], |

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

300 | |

301 | |

302 | yl == { |

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

304 | AllowSummation -> True, |

305 | ParameterType -> Internal, |

306 | Value -> {yl[1] -> 0, yl[2] -> 0, yl[3] -> Sqrt[2] ymtau / v (1+cy/2\[Xi])}, |

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

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

309 | ComplexParameter -> False, |

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

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

312 | |

313 | yu == { |

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

315 | AllowSummation -> True, |

316 | ParameterType -> Internal, |

317 | Value -> {yu[1] -> 0, yu[2] -> Sqrt[2] ymc / v (1+cy/2\[Xi]), yu[3] -> Sqrt[2] ymt / v (1+cy/2\[Xi])}, |

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

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

320 | ComplexParameter -> False, |

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

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

323 | |

324 | yd == { |

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

326 | AllowSummation -> True, |

327 | ParameterType -> Internal, |

328 | Value -> {yd[1] -> 0, yd[2] -> 0, yd[3] -> Sqrt[2] ymb / v (1+cy/2\[Xi])}, |

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

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

331 | ComplexParameter -> False, |

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

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

334 | |

335 | cabi == { |

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

337 | ParameterType -> External, |

338 | BlockName -> CKMBLOCK, |

339 | OrderBlock -> {1}, |

340 | Value -> 0.488, |

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

342 | |

343 | CKM == { |

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

345 | TensorClass -> CKM, |

346 | Unitary -> True, |

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

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

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

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

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

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

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

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

355 | |

356 | mrho =={ |

357 | TeX -> Subscript[m,\[Rho]], |

358 | ParameterType -> Internal, |

359 | Value -> grho*frho, |

360 | Description -> "sigma model mass"} |

361 | } |

362 | |

363 | |

364 | (************** Gauge Groups ******************) |

365 | |

366 | M$GaugeGroups = { |

367 | |

368 | U1Y == { |

369 | Abelian -> True, |

370 | GaugeBoson -> B, |

371 | Charge -> Y, |

372 | CouplingConstant -> g1}, |

373 | |

374 | SU2L == { |

375 | Abelian -> False, |

376 | GaugeBoson -> Wi, |

377 | StructureConstant -> Eps, |

378 | CouplingConstant -> gw}, |

379 | |

380 | SU3C == { |

381 | Abelian -> False, |

382 | GaugeBoson -> G, |

383 | StructureConstant -> f, |

384 | SymmetricTensor -> dSUN, |

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

386 | CouplingConstant -> gs} |

387 | } |

388 | |

389 | (********* Particle Classes **********) |

390 | |

391 | M$ClassesDescription = { |

392 | |

393 | (********** Fermions ************) |

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

395 | F[1] == { |

396 | ClassName -> vl, |

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

398 | FlavorIndex -> Generation, |

399 | SelfConjugate -> False, |

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

401 | Mass -> 0, |

402 | Width -> 0, |

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

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

405 | PropagatorType -> S, |

406 | PropagatorArrow -> Forward, |

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

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

409 | |

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

411 | F[2] == { |

412 | ClassName -> l, |

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

414 | FlavorIndex -> Generation, |

415 | SelfConjugate -> False, |

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

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

418 | Width -> 0, |

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

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

421 | PropagatorType -> Straight, |

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

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

424 | PropagatorArrow -> Forward, |

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

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

427 | |

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

429 | F[3] == { |

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

431 | ClassName -> uq, |

432 | FlavorIndex -> Generation, |

433 | SelfConjugate -> False, |

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

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

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

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

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

439 | PropagatorType -> Straight, |

440 | PropagatorArrow -> Forward, |

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

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

443 | |

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

445 | F[4] == { |

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

447 | ClassName -> dq, |

448 | FlavorIndex -> Generation, |

449 | SelfConjugate -> False, |

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

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

452 | Width -> 0, |

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

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

455 | PropagatorType -> Straight, |

456 | PropagatorArrow -> Forward, |

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

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

459 | |

460 | (********** Ghosts **********) |

461 | U[1] == { |

462 | ClassName -> ghA, |

463 | SelfConjugate -> False, |

464 | Indices -> {}, |

465 | Ghost -> A, |

466 | Mass -> 0, |

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

468 | PropagatorLabel -> uA, |

469 | PropagatorType -> GhostDash, |

470 | PropagatorArrow -> Forward}, |

471 | |

472 | U[2] == { |

473 | ClassName -> ghZ, |

474 | SelfConjugate -> False, |

475 | Indices -> {}, |

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

477 | Ghost -> Z, |

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

479 | PropagatorLabel -> uZ, |

480 | PropagatorType -> GhostDash, |

481 | PropagatorArrow -> Forward}, |

482 | |

483 | U[31] == { |

484 | ClassName -> ghWp, |

485 | SelfConjugate -> False, |

486 | Indices -> {}, |

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

488 | Ghost -> W, |

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

490 | PropagatorLabel -> uWp, |

491 | PropagatorType -> GhostDash, |

492 | PropagatorArrow -> Forward}, |

493 | |

494 | U[32] == { |

495 | ClassName -> ghWm, |

496 | SelfConjugate -> False, |

497 | Indices -> {}, |

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

499 | Ghost -> Wbar, |

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

501 | PropagatorLabel -> uWm, |

502 | PropagatorType -> GhostDash, |

503 | PropagatorArrow -> Forward}, |

504 | |

505 | U[4] == { |

506 | ClassName -> ghG, |

507 | SelfConjugate -> False, |

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

509 | Ghost -> G, |

510 | Mass -> 0, |

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

512 | PropagatorLabel -> uG, |

513 | PropagatorType -> GhostDash, |

514 | PropagatorArrow -> Forward}, |

515 | |

516 | U[5] == { |

517 | ClassName -> ghWi, |

518 | Unphysical -> True, |

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

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

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

522 | SelfConjugate -> False, |

523 | Ghost -> Wi, |

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

525 | FlavorIndex -> SU2W}, |

526 | |

527 | U[6] == { |

528 | ClassName -> ghB, |

529 | SelfConjugate -> False, |

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

531 | Indices -> {}, |

532 | Ghost -> B, |

533 | Unphysical -> True}, |

534 | |

535 | (************ Gauge Bosons ***************) |

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

537 | V[1] == { |

538 | ClassName -> A, |

539 | SelfConjugate -> True, |

540 | Indices -> {}, |

541 | Mass -> 0, |

542 | Width -> 0, |

543 | PropagatorLabel -> "a", |

544 | PropagatorType -> W, |

545 | PropagatorArrow -> None, |

546 | PDG -> 22, |

547 | FullName -> "Photon" }, |

548 | |

549 | V[2] == { |

550 | ClassName -> Z, |

551 | SelfConjugate -> True, |

552 | Indices -> {}, |

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

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

555 | PropagatorLabel -> "Z", |

556 | PropagatorType -> Sine, |

557 | PropagatorArrow -> None, |

558 | PDG -> 23, |

559 | FullName -> "Z" }, |

560 | |

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

562 | V[3] == { |

563 | ClassName -> W, |

564 | SelfConjugate -> False, |

565 | Indices -> {}, |

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

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

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

569 | PropagatorLabel -> "W", |

570 | PropagatorType -> Sine, |

571 | PropagatorArrow -> Forward, |

572 | ParticleName ->"W+", |

573 | AntiParticleName ->"W-", |

574 | PDG -> 24, |

575 | FullName -> "W" }, |

576 | |

577 | V[4] == { |

578 | ClassName -> G, |

579 | SelfConjugate -> True, |

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

581 | Mass -> 0, |

582 | Width -> 0, |

583 | PropagatorLabel -> G, |

584 | PropagatorType -> C, |

585 | PropagatorArrow -> None, |

586 | PDG -> 21, |

587 | FullName -> "G" }, |

588 | |

589 | V[5] == { |

590 | ClassName -> Wi, |

591 | Unphysical -> True, |

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

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

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

595 | SelfConjugate -> True, |

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

597 | FlavorIndex -> SU2W, |

598 | Mass -> 0, |

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

600 | |

601 | V[6] == { |

602 | ClassName -> B, |

603 | SelfConjugate -> True, |

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

605 | Indices -> {}, |

606 | Mass -> 0, |

607 | Unphysical -> True}, |

608 | |

609 | |

610 | (************ Scalar Fields **********) |

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

612 | S[1] == { |

613 | ClassName -> H, |

614 | SelfConjugate -> True, |

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

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

617 | PropagatorLabel -> "H", |

618 | PropagatorType -> D, |

619 | PropagatorArrow -> None, |

620 | PDG -> 25, |

621 | FullName -> "H" }, |

622 | |

623 | S[2] == { |

624 | ClassName -> phi, |

625 | SelfConjugate -> True, |

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

627 | Width -> Wphi, |

628 | PropagatorLabel -> "Phi", |

629 | PropagatorType -> D, |

630 | PropagatorArrow -> None, |

631 | ParticleName ->"phi0", |

632 | PDG -> 250, |

633 | FullName -> "Phi", |

634 | Goldstone -> Z }, |

635 | |

636 | S[3] == { |

637 | ClassName -> phi2, |

638 | SelfConjugate -> False, |

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

640 | Width -> Wphi2, |

641 | PropagatorLabel -> "Phi2", |

642 | PropagatorType -> D, |

643 | PropagatorArrow -> None, |

644 | ParticleName ->"phi+", |

645 | AntiParticleName ->"phi-", |

646 | PDG -> 251, |

647 | FullName -> "Phi2", |

648 | Goldstone -> W, |

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

650 | |

651 | } |

652 | |

653 | (*Renomalisation*) |

654 | |

655 | Hbare = H(1-cH \[Xi]/2); |

656 | Bbare[mu_] := B[mu](1+cB sw^2/cw^2*MW^2/mrho^2+cga g1^2*gw^2/grho^2*\[Xi]/16/\[Pi]^2); |

657 | Wibare[mu_,i_] := Wi[mu,i](1+cW*MW^2/mrho^2); |

658 | g1bare = g1(1-cB sw^2/cw^2*MW^2/mrho^2-cga g1^2*gw^2/grho^2*\[Xi]/16/\[Pi]^2); |

659 | gwbare = gw(1-cW*MW^2/mrho^2); |

660 | Gbare[mu_,a_] := G[mu,a](1+cg gs^2*yu[Index[Generation,3]]^2/grho^2*\[Xi]/16/\[Pi]^2); |

661 | gsbare = gs(1-cg gs^2*yu[Index[Generation,3]]^2/grho^2*\[Xi]/16/\[Pi]^2); |

662 | |

663 | |

664 | (*****************************************************************************************) |

665 | |

666 | (* SM Lagrangian *) |

667 | |

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

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

670 | LGauge := Normal[Series[((-1/4 (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i2, i3] Wibare[mu, i2] Wibare[nu, i3])* |

671 | (del[Wibare[nu, i1], mu] - del[Wibare[mu, i1], nu] + gwbare Eps[i1, i4, i5] Wibare[mu, i4] Wibare[nu, i5]) - |

672 | |

673 | 1/4 (del[Bbare[nu], mu] - del[Bbare[mu], nu])^2 - |

674 | |

675 | 1/4 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a2, a3] Gbare[mu, a2] Gbare[nu, a3])* |

676 | (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a4, a5] Gbare[mu, a4] Gbare[nu, a5]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

677 | |

678 | |

679 | (********************* Fermion Lagrangian terms*************************) |

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

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

682 | |

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

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

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

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

687 | |

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

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

690 | |

691 | LBright = |

692 | -2g1bare Bbare[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

693 | 4/3*g1bare Bbare[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

694 | 2g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

695 | |

696 | LBleft = |

697 | -g1bare Bbare[mu]/2 vlbar.Ga[mu].ProjM.vl - (*Y_LL=-1*) |

698 | g1bare Bbare[mu]/2 lbar.Ga[mu].ProjM.l + (*Y_LL=-1*) |

699 | g1bare/3 Bbare[mu]/2 uqbar.Ga[mu].ProjM.uq + (*Y_QL=1/3*) |

700 | g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjM.dq ; (*Y_QL=1/3*) |

701 | |

702 | LWleft = gwbare/2( |

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

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

705 | |

706 | Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu](1+cW*MW^2/mrho^2) + |

707 | Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu](1+cW*MW^2/mrho^2) + |

708 | |

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

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

711 | |

712 | Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu](1+cW*MW^2/mrho^2) + |

713 | Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu](1+cW*MW^2/mrho^2) |

714 | ); |

715 | |

716 | Normal[Series[((Lkin + LQCD + LBright + LBleft + LWleft)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]]; |

717 | |

718 | (******************** Higgs Lagrangian terms****************************) |

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

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

721 | |

722 | Dc[f_, mu_] := del[f, mu] - I g1bare Bbare[mu]/2 f -I gwbare/2 (Wvec[mu].PMVec).f; |

723 | Dcbar[f_, mu_] := del[f, mu] + I g1bare Bbare[mu]/2 f + I gwbare/2 f.(Wvec[mu].PMVec); |

724 | |

725 | |

726 | |

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

728 | Wvec[mu_] := {Wibare[mu, 1], Wibare[mu, 2], Wibare[mu, 3]}; |

729 | |

730 | |

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

732 | |

733 | LHiggs := Normal[Series[(((Dcbar[Phibar, mu]).Dc[Phi, mu] - Vphi[Phi, Phibar])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

734 | |

735 | |

736 | (*************** Yukawa Lagrangian***********************) |

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

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

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

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

741 | ]; |

742 | |

743 | LYukawa := Normal[Series[((LYuk + HC[LYuk])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

744 | |

745 | |

746 | |

747 | (**************Ghost terms**************************) |

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

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

750 | (* where d_BRST G is BRST transform of the gauge fixing function. *)(*Not renormalized, only if FeynmanGauge*) |

751 | |

752 | LGhost := 0; |

753 | |

754 | (*********Total SM Lagrangian*******) |

755 | LSM := Normal[Series[((LGauge + LHiggs + LFermions + LYukawa + LGhost)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

756 | |

757 | |

758 | |

759 | (************** SILH LAGRANGIAN STARTING POINT ********************) |

760 | (** Better to introduce some useful short-hand notation here **) |

761 | |

762 | |

763 | HH = Phibar.Phi; |

764 | HDH[mu_] := (Phibar.Dc[Phi,mu] - Dcbar[Phibar,mu].Phi); |

765 | |

766 | FSWVec[mu_,nu_] := {FS[Wi,mu,nu,1],FS[Wi,mu,nu,2],FS[Wi,mu,nu,3]} |

767 | |

768 | DB[mu_] := del[FS[B,mu,nu],nu]; |

769 | |

770 | DG[mu_, a1_] := I del[del[G[nu, a1], mu],mu] - I del[del[G[mu, a1], nu],mu] + |

771 | I gs f[a1, a2, a3] (del[G[mu, a2],mu] G[nu, a3] + G[mu,a2] del[G[nu,a3],mu] + |

772 | ( g1 B[mu]/2 + gw/2 (Wvec[mu].PMatVec) + gs Ga[mu].T[a])) |

773 | (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3]); |

774 | |

775 | |

776 | (***************** SILH Lagrangian**************************) |

777 | |

778 | L6HT := Normal[Series[((cH/2/frho^2 del[HH,mu] del[HH,mu] + |

779 | cT/2/frho^2 HDH[mu] HDH[mu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

780 | |

781 | L6 := Normal[Series[((-c6 \[Lambda]/frho^2 HH^3)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

782 | |

783 | L6Y := Normal[Series[((-cy / frho^2 * HH * LYukawa)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

784 | |

785 | |

786 | L6W := Normal[Series[((I cW gw/2/mrho^2 (Phibar.PauliSigma[k].Dc[Phi,mu]-Dcbar[Phibar,mu].PauliSigma[k].Phi)*(del[FS[Wi,mu,nu,k],nu] + gw Eps[k1,k2,k] Wi[nu,k1] FS[Wi,mu,nu,k2]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

787 | |

788 | |

789 | L6B := Normal[Series[((I cB g1/2/mrho^2 HDH[mu] DB[mu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

790 | |

791 | L6HW := Normal[Series[((I cHW gw/16/Pi^2/frho^2 (HC[Dc[Phi,mu]].PauliSigma[i].Dc[Phi,nu]) FS[Wi,mu,nu,i])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

792 | |

793 | L6HB := Normal[Series[((I cHB g1/16/Pi^2/frho^2 (HC[Dc[Phi,mu]].Dc[Phi,nu]) FS[B,mu,nu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

794 | |

795 | L6Ga := Normal[Series[((cga g1^2/16/Pi^2/frho^2 gw^2/grho^2 HH FS[B,mu,nu] FS[B,mu,nu])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

796 | |

797 | L6G := Normal[Series[((cg gs^2/16/Pi^2/frho^2 yu[Index[Generation,3]]^2/grho^2 HH FS[G,mu,nu,a] FS[G,mu,nu,a])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

798 | |

799 | L62W := Normal[Series[((c2W gw^2/2/grho^2/mrho^2 (del[(1+cW*MW^2/mrho^2)FS[Wi,mu,nu,k],mu] + gw/2 Eps[k1,k2,k] Wi[mu,k1] FS[Wi,mu,nu,k2])*(del[FS[Wi,rho,nu,k],rho] + gw/2 Eps[k3,k4,k] Wi[rho,k3] FS[Wi,rho,nu,k4]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

800 | |

801 | L62B := Normal[Series[((c2B g1^2/2/grho^2/mrho^2 del[FS[B,nu, mu],mu] del[FS[B,nu, rho],rho])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

802 | |

803 | L62g := Normal[Series[((c2g gs^2/2/grho^2/mrho^2 (del[FS[G,mu,nu,a],mu] + gs f[a1,a2,a] G[mu,a1] FS[G,mu,nu,a2])*(del[FS[G,rho,nu,a],rho] + gs f[a3,a4,a] G[rho,a3] FS[G,rho,nu,a4]))//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

804 | |

805 | L63W := Normal[Series[((c3W gw^3/16/Pi^2/mrho^2 Eps[i,j,k] FS[Wi,mu,nu,i] FS[Wi,nu,rho,j] FS[Wi,rho,mu,k])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

806 | |

807 | L63g := Normal[Series[((c3g gs^3/16/Pi^2/mrho^2 f[a1,a2,a3] FS[G,mu,nu,a1] FS[G,nu,rho,a2] FS[G,rho,mu,a3])//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

808 | |

809 | Lvec := L62W + L62B + L62g + L63W + L63g; |

810 | |

811 | LSILH = Normal[Series[((L6HT + L6W + L6B + L6HW + L6HB + L6Ga + L6G + L6Y + L6)//.{mrho->grho*frho,frho->v/Sqrt[\[Xi]]}),{\[Xi],0,1}]]; |

812 |