# SILH: SILH.2.fr

File SILH.2.fr, 25.5 KB (added by degrande, 7 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->"08/02/2012" |

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

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

17 | Version -> "1.0", |

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] ] = Unfold[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 | (**************** Orders ****************) |

58 | |

59 | M$InteractionOrderHierarchy = { |

60 | {QCD, 1}, |

61 | {QED, 2}, |

62 | {NP,2} |

63 | } |

64 | |

65 | M$InteractionOrderLimit = { |

66 | {QCD, 99}, |

67 | {QED, 99}, |

68 | {NP,1} |

69 | } |

70 | |

71 | |

72 | (**************** Parameters *************) |

73 | |

74 | M$Parameters = { |

75 | |

76 | (* External SM parameters *) |

77 | |

78 | \[Alpha]EWM1== { |

79 | ParameterType -> External, |

80 | BlockName -> SMINPUTS, |

81 | ParameterName -> aEWM1, |

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

83 | Value -> 127.9, |

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

85 | |

86 | Gf == { |

87 | ParameterType -> External, |

88 | BlockName -> SMINPUTS, |

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

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

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

92 | |

93 | \[Alpha]S == { |

94 | ParameterType -> External, |

95 | BlockName -> SMINPUTS, |

96 | ParameterName -> aS, |

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

98 | Value -> 0.118, |

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

100 | |

101 | |

102 | ZM == { |

103 | ParameterType -> External, |

104 | BlockName -> SMINPUTS, |

105 | Value -> 91.188, |

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

107 | |

108 | |

109 | ymc == { |

110 | ParameterType -> External, |

111 | BlockName -> YUKAWA, |

112 | Value -> 1.42, |

113 | OrderBlock -> {4}, |

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

115 | |

116 | ymb == { |

117 | ParameterType -> External, |

118 | BlockName -> YUKAWA, |

119 | Value -> 4.7, |

120 | OrderBlock -> {5}, |

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

122 | |

123 | ymt == { |

124 | ParameterType -> External, |

125 | BlockName -> YUKAWA, |

126 | Value -> 174.3, |

127 | OrderBlock -> {6}, |

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

129 | |

130 | ymtau == { |

131 | ParameterType -> External, |

132 | BlockName -> YUKAWA, |

133 | Value -> 1.777, |

134 | OrderBlock -> {15}, |

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

136 | |

137 | |

138 | |

139 | (* External SILH Parameter *) |

140 | |

141 | frho =={ |

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

143 | ParameterType -> External, |

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

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

146 | |

147 | grho =={ |

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

149 | ParameterType -> External, |

150 | Value -> 1, |

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

152 | |

153 | cH =={ |

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

155 | ParameterType -> External, |

156 | Value -> 1, |

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

158 | |

159 | cT =={ |

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

161 | ParameterType -> External, |

162 | Value -> 1, |

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

164 | |

165 | c6 =={ |

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

167 | ParameterType -> External, |

168 | Value -> 1, |

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

170 | |

171 | cy =={ |

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

173 | ParameterType -> External, |

174 | Value -> 1, |

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

176 | |

177 | c6W =={ |

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

179 | ParameterType -> External, |

180 | Value -> 1, |

181 | InteractionOrder ->{QED,-3}}, |

182 | |

183 | cB =={ |

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

185 | ParameterType -> External, |

186 | Value -> 1, |

187 | InteractionOrder ->{QED,-3}}, |

188 | |

189 | cHW =={ |

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

191 | ParameterType -> External, |

192 | Value -> 1, |

193 | InteractionOrder ->{QED,-3}}, |

194 | |

195 | cHB =={ |

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

197 | ParameterType -> External, |

198 | Value -> 1, |

199 | InteractionOrder ->{QED,-3}}, |

200 | |

201 | cga =={ |

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

203 | ParameterType -> External, |

204 | Value -> 1, |

205 | InteractionOrder ->{QED,-5}}, |

206 | |

207 | cg =={ |

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

209 | ParameterType -> External, |

210 | Value -> 1, |

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

212 | |

213 | c2W =={ |

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

215 | ParameterType -> External, |

216 | Value -> 1}, |

217 | |

218 | c2B =={ |

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

220 | ParameterType -> External, |

221 | Value -> 1}, |

222 | |

223 | c2g =={ |

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

225 | ParameterType -> External, |

226 | Value -> 1}, |

227 | |

228 | c3W =={ |

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

230 | ParameterType -> External, |

231 | Value -> 1}, |

232 | |

233 | c3B =={ |

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

235 | ParameterType -> External, |

236 | Value -> 1}, |

237 | |

238 | |

239 | (* Internal Parameters *) |

240 | |

241 | \[Alpha]EW == { |

242 | ParameterType -> Internal, |

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

244 | ParameterName -> aEW, |

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

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

247 | |

248 | |

249 | MW == { |

250 | ParameterType -> Internal, |

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

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

253 | |

254 | sw2 == { |

255 | ParameterType -> Internal, |

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

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

258 | |

259 | ee == { |

260 | TeX -> e, |

261 | ParameterType -> Internal, |

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

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

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

265 | |

266 | cw == { |

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

268 | ParameterType -> Internal, |

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

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

271 | |

272 | sw == { |

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

274 | ParameterType -> Internal, |

275 | Value -> Sqrt[sw2], |

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

277 | |

278 | gw == { |

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

280 | ParameterType -> Internal, |

281 | Value -> ee / sw, |

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

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

284 | |

285 | g1 == { |

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

287 | ParameterType -> Internal, |

288 | Value -> ee / cw, |

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

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

291 | |

292 | gs == { |

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

294 | ParameterType -> Internal, |

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

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

297 | ParameterName -> G, |

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

299 | |

300 | v == { |

301 | ParameterType -> Internal, |

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

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

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

305 | |

306 | Xi == { |

307 | TeX -> \[Xi], |

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

309 | ParameterType -> Internal, |

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

311 | Description -> "ratio of frho and the Higgs vev"}, |

312 | |

313 | \[Lambda] == { |

314 | ParameterType -> Internal, |

315 | Value -> MH^2/(2*v^2)(1+cH*Xi-3/2 c6*Xi), |

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

317 | ParameterName -> lam, |

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

319 | |

320 | muH == { |

321 | ParameterType -> Internal, |

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

323 | TeX -> \[Mu], |

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

325 | |

326 | |

327 | yl == { |

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

329 | AllowSummation -> True, |

330 | ParameterType -> Internal, |

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

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

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

334 | ComplexParameter -> False, |

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

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

337 | |

338 | yu == { |

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

340 | AllowSummation -> True, |

341 | ParameterType -> Internal, |

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

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

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

345 | ComplexParameter -> False, |

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

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

348 | |

349 | yd == { |

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

351 | AllowSummation -> True, |

352 | ParameterType -> Internal, |

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

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

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

356 | ComplexParameter -> False, |

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

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

359 | |

360 | cabi == { |

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

362 | ParameterType -> External, |

363 | BlockName -> CKMBLOCK, |

364 | OrderBlock -> {1}, |

365 | Value -> 0.488, |

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

367 | |

368 | CKM == { |

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

370 | TensorClass -> CKM, |

371 | Unitary -> True, |

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

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

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

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

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

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

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

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

380 | |

381 | mrho =={ |

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

383 | ParameterType -> Internal, |

384 | Value -> grho*frho, |

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

386 | } |

387 | |

388 | |

389 | (************** Gauge Groups ******************) |

390 | |

391 | M$GaugeGroups = { |

392 | |

393 | U1Y == { |

394 | Abelian -> True, |

395 | GaugeBoson -> B, |

396 | Charge -> Y, |

397 | CouplingConstant -> g1}, |

398 | |

399 | SU2L == { |

400 | Abelian -> False, |

401 | GaugeBoson -> Wi, |

402 | StructureConstant -> Eps, |

403 | CouplingConstant -> gw}, |

404 | |

405 | SU3C == { |

406 | Abelian -> False, |

407 | GaugeBoson -> G, |

408 | StructureConstant -> f, |

409 | SymmetricTensor -> dSUN, |

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

411 | CouplingConstant -> gs} |

412 | } |

413 | |

414 | (********* Particle Classes **********) |

415 | |

416 | M$ClassesDescription = { |

417 | |

418 | (********** Fermions ************) |

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

420 | F[1] == { |

421 | ClassName -> vl, |

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

423 | FlavorIndex -> Generation, |

424 | SelfConjugate -> False, |

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

426 | Mass -> 0, |

427 | Width -> 0, |

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

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

430 | PropagatorType -> S, |

431 | PropagatorArrow -> Forward, |

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

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

434 | |

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

436 | F[2] == { |

437 | ClassName -> l, |

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

439 | FlavorIndex -> Generation, |

440 | SelfConjugate -> False, |

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

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

443 | Width -> 0, |

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

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

446 | PropagatorType -> Straight, |

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

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

449 | PropagatorArrow -> Forward, |

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

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

452 | |

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

454 | F[3] == { |

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

456 | ClassName -> uq, |

457 | FlavorIndex -> Generation, |

458 | SelfConjugate -> False, |

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

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

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

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

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

464 | PropagatorType -> Straight, |

465 | PropagatorArrow -> Forward, |

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

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

468 | |

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

470 | F[4] == { |

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

472 | ClassName -> dq, |

473 | FlavorIndex -> Generation, |

474 | SelfConjugate -> False, |

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

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

477 | Width -> 0, |

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

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

480 | PropagatorType -> Straight, |

481 | PropagatorArrow -> Forward, |

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

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

484 | |

485 | (********** Ghosts **********) |

486 | U[1] == { |

487 | ClassName -> ghA, |

488 | SelfConjugate -> False, |

489 | Indices -> {}, |

490 | Ghost -> A, |

491 | Mass -> 0, |

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

493 | PropagatorLabel -> uA, |

494 | PropagatorType -> GhostDash, |

495 | PropagatorArrow -> Forward}, |

496 | |

497 | U[2] == { |

498 | ClassName -> ghZ, |

499 | SelfConjugate -> False, |

500 | Indices -> {}, |

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

502 | Ghost -> Z, |

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

504 | PropagatorLabel -> uZ, |

505 | PropagatorType -> GhostDash, |

506 | PropagatorArrow -> Forward}, |

507 | |

508 | U[31] == { |

509 | ClassName -> ghWp, |

510 | SelfConjugate -> False, |

511 | Indices -> {}, |

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

513 | Ghost -> W, |

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

515 | PropagatorLabel -> uWp, |

516 | PropagatorType -> GhostDash, |

517 | PropagatorArrow -> Forward}, |

518 | |

519 | U[32] == { |

520 | ClassName -> ghWm, |

521 | SelfConjugate -> False, |

522 | Indices -> {}, |

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

524 | Ghost -> Wbar, |

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

526 | PropagatorLabel -> uWm, |

527 | PropagatorType -> GhostDash, |

528 | PropagatorArrow -> Forward}, |

529 | |

530 | U[4] == { |

531 | ClassName -> ghG, |

532 | SelfConjugate -> False, |

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

534 | Ghost -> G, |

535 | Mass -> 0, |

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

537 | PropagatorLabel -> uG, |

538 | PropagatorType -> GhostDash, |

539 | PropagatorArrow -> Forward}, |

540 | |

541 | U[5] == { |

542 | ClassName -> ghWi, |

543 | Unphysical -> True, |

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

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

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

547 | SelfConjugate -> False, |

548 | Ghost -> Wi, |

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

550 | FlavorIndex -> SU2W}, |

551 | |

552 | U[6] == { |

553 | ClassName -> ghB, |

554 | SelfConjugate -> False, |

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

556 | Indices -> {}, |

557 | Ghost -> B, |

558 | Unphysical -> True}, |

559 | |

560 | (************ Gauge Bosons ***************) |

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

562 | V[1] == { |

563 | ClassName -> A, |

564 | SelfConjugate -> True, |

565 | Indices -> {}, |

566 | Mass -> 0, |

567 | Width -> 0, |

568 | PropagatorLabel -> "a", |

569 | PropagatorType -> W, |

570 | PropagatorArrow -> None, |

571 | PDG -> 22, |

572 | FullName -> "Photon" }, |

573 | |

574 | V[2] == { |

575 | ClassName -> Z, |

576 | SelfConjugate -> True, |

577 | Indices -> {}, |

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

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

580 | PropagatorLabel -> "Z", |

581 | PropagatorType -> Sine, |

582 | PropagatorArrow -> None, |

583 | PDG -> 23, |

584 | FullName -> "Z" }, |

585 | |

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

587 | V[3] == { |

588 | ClassName -> W, |

589 | SelfConjugate -> False, |

590 | Indices -> {}, |

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

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

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

594 | PropagatorLabel -> "W", |

595 | PropagatorType -> Sine, |

596 | PropagatorArrow -> Forward, |

597 | ParticleName ->"W+", |

598 | AntiParticleName ->"W-", |

599 | PDG -> 24, |

600 | FullName -> "W" }, |

601 | |

602 | V[4] == { |

603 | ClassName -> G, |

604 | SelfConjugate -> True, |

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

606 | Mass -> 0, |

607 | Width -> 0, |

608 | PropagatorLabel -> G, |

609 | PropagatorType -> C, |

610 | PropagatorArrow -> None, |

611 | PDG -> 21, |

612 | FullName -> "G" }, |

613 | |

614 | V[5] == { |

615 | ClassName -> Wi, |

616 | Unphysical -> True, |

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

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

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

620 | SelfConjugate -> True, |

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

622 | FlavorIndex -> SU2W, |

623 | Mass -> 0, |

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

625 | |

626 | V[6] == { |

627 | ClassName -> B, |

628 | SelfConjugate -> True, |

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

630 | Indices -> {}, |

631 | Mass -> 0, |

632 | Unphysical -> True}, |

633 | |

634 | |

635 | (************ Scalar Fields **********) |

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

637 | S[1] == { |

638 | ClassName -> H, |

639 | SelfConjugate -> True, |

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

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

642 | PropagatorLabel -> "H", |

643 | PropagatorType -> D, |

644 | PropagatorArrow -> None, |

645 | PDG -> 25, |

646 | FullName -> "H" }, |

647 | |

648 | S[2] == { |

649 | ClassName -> phi, |

650 | SelfConjugate -> True, |

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

652 | Width -> Wphi, |

653 | PropagatorLabel -> "Phi", |

654 | PropagatorType -> D, |

655 | PropagatorArrow -> None, |

656 | ParticleName ->"phi0", |

657 | PDG -> 250, |

658 | FullName -> "Phi", |

659 | Goldstone -> Z }, |

660 | |

661 | S[3] == { |

662 | ClassName -> phi2, |

663 | SelfConjugate -> False, |

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

665 | Width -> Wphi2, |

666 | PropagatorLabel -> "Phi2", |

667 | PropagatorType -> D, |

668 | PropagatorArrow -> None, |

669 | ParticleName ->"phi+", |

670 | AntiParticleName ->"phi-", |

671 | PDG -> 251, |

672 | FullName -> "Phi2", |

673 | Goldstone -> W, |

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

675 | |

676 | } |

677 | |

678 | (*Renomalisation*) |

679 | |

680 | Hbare = H(1-cH Xi/2); |

681 | 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); |

682 | Wibare[mu_,i_] := Wi[mu,i](1+c6W*MW^2/mrho^2); |

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

684 | gwbare = gw(1-c6W*MW^2/mrho^2); |

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

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

687 | |

688 | |

689 | (*****************************************************************************************) |

690 | |

691 | (* SM Lagrangian *) |

692 | |

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

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

695 | 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])* |

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

697 | |

698 | 1/4 (del[Bbare[nu], mu] - del[Bbare[mu], nu])^2 - |

699 | |

700 | 1/4 (del[Gbare[nu, a1], mu] - del[Gbare[mu, a1], nu] + gsbare f[a1, a2, a3] Gbare[mu, a2] Gbare[nu, a3])* |

701 | (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}]]; |

702 | |

703 | |

704 | (********************* Fermion Lagrangian terms*************************) |

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

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

707 | |

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

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

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

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

712 | |

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

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

715 | |

716 | LBright = |

717 | -2g1bare Bbare[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

718 | 4/3*g1bare Bbare[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

719 | 2g1bare/3 Bbare[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

720 | |

721 | LBleft = |

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

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

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

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

726 | |

727 | LWleft = gwbare/2( |

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

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

730 | |

731 | Sqrt[2] vlbar.Ga[mu].ProjM.l W[mu](1+c6W*MW^2/mrho^2) + |

732 | Sqrt[2] lbar.Ga[mu].ProjM.vl Wbar[mu](1+c6W*MW^2/mrho^2) + |

733 | |

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

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

736 | |

737 | Sqrt[2] uqbar.Ga[mu].ProjM.CKM.dq W[mu](1+c6W*MW^2/mrho^2) + |

738 | Sqrt[2] dqbar.Ga[mu].ProjM.HC[CKM].uq Wbar[mu](1+c6W*MW^2/mrho^2) |

739 | ); |

740 | |

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

742 | |

743 | (******************** Higgs Lagrangian terms****************************) |

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

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

746 | |

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

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

749 | |

750 | |

751 | |

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

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

754 | |

755 | |

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

757 | |

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

759 | |

760 | |

761 | (*************** Yukawa Lagrangian***********************) |

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

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

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

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

766 | ]; |

767 | |

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

769 | |

770 | |

771 | |

772 | (**************Ghost terms**************************) |

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

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

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

776 | |

777 | LGhost := 0; |

778 | |

779 | (*********Total SM Lagrangian*******) |

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

781 | |

782 | |

783 | |

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

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

786 | |

787 | |

788 | HH = Phibar.Phi; |

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

790 | |

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

792 | |

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

794 | |

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

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

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

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

799 | |

800 | |

801 | (***************** SILH Lagrangian**************************) |

802 | |

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

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

805 | |

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

807 | |

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

809 | |

810 | |

811 | L6W := Normal[Series[((I c6W 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}]]; |

812 | |

813 | |

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

815 | |

816 | 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}]]; |

817 | |

818 | 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}]]; |

819 | |

820 | 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}]]; |

821 | |

822 | 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}]]; |

823 | |

824 | L62W := Normal[Series[((c2W gw^2/2/grho^2/mrho^2 (del[(1+c6W*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}]]; |

825 | |

826 | 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}]]; |

827 | |

828 | 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}]]; |

829 | |

830 | 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}]]; |

831 | |

832 | 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}]]; |

833 | |

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

835 | |

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

837 |