# Hillmodel: HillModel.fr

File HillModel.fr, 21.1 KB (added by claudeduhr, 7 years ago) |
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5 | (**************** This is the FeynRules model-file for the Hill model **************) |

6 | |

7 | M$ModelName = "HillModel"; |

8 | |

9 | M$Information = {Authors -> {"P. Aquino", "C. Duhr"}, |

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

11 | Emails -> {priscila@fma.if.usp.br, claude.duhr@uclouvain.be}, |

12 | Date -> "14. 06. 2009", |

13 | Version -> "1.0", |

14 | References -> "\"The minimal non-minimal Standard Model\", J.J. van der Bij, Phys.Lett.B636:56-59,2006, hep-ph/0603082", |

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

16 | |

17 | |

18 | FeynmanGauge=False; |

19 | |

20 | (******* Index definitions ********) |

21 | |

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

23 | |

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

25 | |

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

27 | |

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

29 | |

30 | |

31 | IndexStyle[Colour, i] |

32 | |

33 | IndexStyle[Generation, f] |

34 | |

35 | IndexStyle[Gluon ,a] |

36 | |

37 | |

38 | (**************** Parameters *************) |

39 | |

40 | M$Parameters = { |

41 | |

42 | (* External parameters *) |

43 | |

44 | \[Alpha]EW == { |

45 | ParameterType -> External, |

46 | BlockName -> SMINPUTS, |

47 | ParameterName -> aEW, |

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

49 | Value -> 1/132.50698, |

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

51 | |

52 | Gf == { |

53 | ParameterType -> External, |

54 | BlockName -> SMINPUTS, |

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

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

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

58 | |

59 | \[Alpha]S == { |

60 | ParameterType -> External, |

61 | BlockName -> SMINPUTS, |

62 | ParameterName -> aS, |

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

64 | Value -> 0.118, |

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

66 | |

67 | ZM == { |

68 | ParameterType -> External, |

69 | BlockName -> SMINPUTS, |

70 | Value -> 91.188, |

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

72 | |

73 | ymc == { |

74 | ParameterType -> External, |

75 | BlockName -> MGYUKAWA, |

76 | Value -> 1.42, |

77 | OrderBlock -> {4}, |

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

79 | |

80 | ymb == { |

81 | ParameterType -> External, |

82 | BlockName -> MGYUKAWA, |

83 | Value -> 4.7, |

84 | OrderBlock -> {5}, |

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

86 | |

87 | ymt == { |

88 | ParameterType -> External, |

89 | BlockName -> MGYUKAWA, |

90 | Value -> 174.3, |

91 | OrderBlock -> {6}, |

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

93 | |

94 | ymtau == { |

95 | ParameterType -> External, |

96 | BlockName -> MGYUKAWA, |

97 | Value -> 1.777, |

98 | OrderBlock -> {15}, |

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

100 | |

101 | ymm == { |

102 | Value -> 0.105}, |

103 | |

104 | (* Internal Parameters *) |

105 | |

106 | WM == { |

107 | ParameterType -> Internal, |

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

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

110 | |

111 | sw2 == { |

112 | ParameterType -> Internal, |

113 | Value -> 1-(WM/ZM)^2, |

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

115 | |

116 | ee == { |

117 | TeX -> e, |

118 | ParameterType -> Internal, |

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

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

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

122 | |

123 | cw == { |

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

125 | ParameterType -> Internal, |

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

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

128 | |

129 | sw == { |

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

131 | ParameterType -> Internal, |

132 | Value -> Sqrt[sw2], |

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

134 | |

135 | gw == { |

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

137 | ParameterType -> Internal, |

138 | Value -> ee / sw, |

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

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

141 | |

142 | g1 == { |

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

144 | ParameterType -> Internal, |

145 | Value -> ee / cw, |

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

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

148 | |

149 | gs == { |

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

151 | ParameterType -> Internal, |

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

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

154 | ParameterName -> G, |

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

156 | |

157 | v == { |

158 | ParameterType -> Internal, |

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

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

161 | |

162 | \[Lambda]0 == { |

163 | TeX -> Subscript[\[Lambda], 0], |

164 | Value -> 0.2, |

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

166 | ParameterName -> l0}, |

167 | |

168 | |

169 | yl == { |

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

171 | AllowSummation -> True, |

172 | ParameterType -> Internal, |

173 | ComplexParameter -> False, |

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

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

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

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

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

179 | |

180 | yu == { |

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

182 | AllowSummation -> True, |

183 | ParameterType -> Internal, |

184 | ComplexParameter -> False, |

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

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

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

188 | ComplexParameter -> False, |

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

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

191 | |

192 | yd == { |

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

194 | AllowSummation -> True, |

195 | ParameterType -> Internal, |

196 | ComplexParameter -> False, |

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

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

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

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

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

202 | |

203 | cabi == { |

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

205 | ParameterType -> External, |

206 | BlockName -> CKMBLOCK, |

207 | OrderBlock -> {1}, |

208 | Value -> 0.488, |

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

210 | |

211 | CKM == { |

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

213 | TensorClass -> CKM, |

214 | Unitary -> True, |

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

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

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

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

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

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

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

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

223 | |

224 | f1 == {Value -> 500, |

225 | TeX -> Subscript[f, 1], |

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

227 | |

228 | \[Lambda]1 == {Value -> 0.2, |

229 | TeX -> Subscript[\[Lambda], 1], |

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

231 | ParameterName -> l1}, |

232 | |

233 | tha == {Value -> 2.88, |

234 | TeX -> Subscript[\[Theta], a], |

235 | Description -> "Scalar mixing angle"}, |

236 | |

237 | ca == {ParameterType -> Internal, |

238 | Value -> Cos[tha], |

239 | TeX -> Subscript[c,a], |

240 | Description -> "Cos of the scalar mixing angle"}, |

241 | |

242 | sa == {ParameterType -> Internal, |

243 | Value -> Sin[tha], |

244 | TeX -> Subscript[s,a], |

245 | Description -> "Sin of the scalar mixing angle"} |

246 | } |

247 | |

248 | |

249 | (************** Gauge Groups ******************) |

250 | |

251 | M$GaugeGroups = { |

252 | |

253 | U1Y == { |

254 | Abelian -> True, |

255 | GaugeBoson -> B, |

256 | Charge -> Y, |

257 | CouplingConstant -> ee}, |

258 | |

259 | SU2L == { |

260 | Abelian -> False, |

261 | GaugeBoson -> Wi, |

262 | StructureConstant -> ep, |

263 | CouplingConstant -> gw, |

264 | Definitions -> {ep -> Eps}}, |

265 | |

266 | SU3C == { |

267 | Abelian -> False, |

268 | GaugeBoson -> G, |

269 | StructureConstant -> f, |

270 | DTerm -> dSUN, |

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

272 | CouplingConstant -> gs} |

273 | } |

274 | |

275 | (********* Particle Classes **********) |

276 | |

277 | M$ClassesDescription = { |

278 | |

279 | (*** Fermions ***) |

280 | |

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

282 | F[1] == { |

283 | ClassName -> vl, |

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

285 | FlavorIndex -> Generation, |

286 | SelfConjugate -> False, |

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

288 | Mass -> 0, |

289 | Width -> 0, |

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

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

292 | PropagatorType -> S, |

293 | PropagatorArrow -> Forward, |

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

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

296 | |

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

298 | F[2] == { |

299 | ClassName -> l, |

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

301 | FlavorIndex -> Generation, |

302 | SelfConjugate -> False, |

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

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

305 | Width -> 0, |

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

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

308 | PropagatorType -> Straight, |

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

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

311 | PropagatorArrow -> Forward, |

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

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

314 | |

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

316 | F[3] == { |

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

318 | ClassName -> uq, |

319 | FlavorIndex -> Generation, |

320 | SelfConjugate -> False, |

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

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

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

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

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

326 | PropagatorType -> Straight, |

327 | PropagatorArrow -> Forward, |

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

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

330 | |

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

332 | F[4] == { |

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

334 | ClassName -> dq, |

335 | FlavorIndex -> Generation, |

336 | SelfConjugate -> False, |

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

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

339 | Width -> 0, |

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

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

342 | PropagatorType -> Straight, |

343 | PropagatorArrow -> Forward, |

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

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

346 | |

347 | (*** Gauge bosons ***) |

348 | |

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

350 | V[1] == { |

351 | ClassName -> A, |

352 | SelfConjugate -> True, |

353 | Indices -> {}, |

354 | Mass -> 0, |

355 | PropagatorLabel -> "a", |

356 | PropagatorType -> W, |

357 | PropagatorArrow -> None, |

358 | PDG -> 22, |

359 | FullName -> "Photon" }, |

360 | |

361 | V[2] == { |

362 | ClassName -> Z, |

363 | SelfConjugate -> True, |

364 | Indices -> {}, |

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

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

367 | PropagatorLabel -> "Z", |

368 | PropagatorType -> Sine, |

369 | PropagatorArrow -> None, |

370 | PDG -> 23, |

371 | FullName -> "Z" }, |

372 | |

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

374 | V[3] == { |

375 | ClassName -> W, |

376 | SelfConjugate -> False, |

377 | Indices -> {}, |

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

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

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

381 | PropagatorLabel -> "W", |

382 | PropagatorType -> Sine, |

383 | PropagatorArrow -> Forward, |

384 | ParticleName ->"W+", |

385 | AntiParticleName ->"W-", |

386 | PDG -> 24, |

387 | FullName -> "W" }, |

388 | |

389 | V[4] == { |

390 | ClassName -> G, |

391 | SelfConjugate -> True, |

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

393 | Mass -> 0, |

394 | PropagatorLabel -> {"G"}, |

395 | PropagatorType -> C, |

396 | PropagatorArrow -> None, |

397 | PDG -> 21, |

398 | FullName -> "G" }, |

399 | |

400 | V[5] == { |

401 | ClassName -> Wi, |

402 | Unphysical -> True, |

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

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

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

406 | SelfConjugate -> True, |

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

408 | FlavorIndex -> SU2W, |

409 | Mass -> 0, |

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

411 | |

412 | V[6] == { |

413 | ClassName -> B, |

414 | SelfConjugate -> True, |

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

416 | Indices -> {}, |

417 | Mass -> 0, |

418 | Unphysical -> True}, |

419 | |

420 | (*** Scalars ***) |

421 | |

422 | |

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

424 | |

425 | S[1] == { |

426 | ClassName -> h1, |

427 | SelfConjugate -> True, |

428 | Mass -> {Mh1, 78.5}, |

429 | Width -> {Wh1, 0.005}}, |

430 | |

431 | S[2] == { |

432 | ClassName -> h2, |

433 | SelfConjugate -> True, |

434 | Mass -> {Mh2, 326}, |

435 | Width -> {Wh2, 0.005}}, |

436 | |

437 | S[3] == { |

438 | ClassName -> H, |

439 | SelfConjugate -> True, |

440 | Unphysical -> True, |

441 | Definitions -> {H -> ca h1- sa h2}}, |

442 | |

443 | S[4] == { |

444 | ClassName -> h, |

445 | SelfConjugate -> True, |

446 | Unphysical -> True, |

447 | Definitions -> {h -> sa h1 +ca h2}}; |

448 | |

449 | S[5] == { |

450 | ClassName -> phi, |

451 | SelfConjugate -> True, |

452 | Mass -> {Mphi, 120}, |

453 | Width -> Wphi, |

454 | PropagatorLabel -> "Phi", |

455 | PropagatorType -> D, |

456 | PropagatorArrow -> None, |

457 | ParticleName ->"phi0", |

458 | PDG -> 250, |

459 | FullName -> "Phi", |

460 | Goldstone -> Z }, |

461 | |

462 | S[6] == { |

463 | ClassName -> phi2, |

464 | SelfConjugate -> False, |

465 | Mass -> {Mphi2, 120}, |

466 | Width -> Wphi2, |

467 | PropagatorLabel -> "Phi2", |

468 | PropagatorType -> D, |

469 | PropagatorArrow -> None, |

470 | ParticleName ->"phi+", |

471 | AntiParticleName ->"phi-", |

472 | PDG -> 251, |

473 | FullName -> "Phi2", |

474 | Goldstone -> W, |

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

476 | |

477 | |

478 | (********* Ghost Fields ****************)(********** Ghosts **********) |

479 | U[1] == { |

480 | ClassName -> ghA, |

481 | SelfConjugate -> False, |

482 | Indices -> {}, |

483 | Ghost -> A}, |

484 | |

485 | U[2] == { |

486 | ClassName -> ghZ, |

487 | SelfConjugate -> False, |

488 | Indices -> {}, |

489 | Ghost -> Z}, |

490 | |

491 | U[31] == { |

492 | ClassName -> ghWp, |

493 | SelfConjugate -> False, |

494 | Indices -> {}, |

495 | Ghost -> W, |

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

497 | |

498 | U[32] == { |

499 | ClassName -> ghWm, |

500 | SelfConjugate -> False, |

501 | Indices -> {}, |

502 | Ghost -> Wbar, |

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

504 | |

505 | U[4] == { |

506 | ClassName -> ghG, |

507 | SelfConjugate -> False, |

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

509 | Ghost -> G}, |

510 | |

511 | U[5] == { |

512 | ClassName -> ghWi, |

513 | Unphysical -> True, |

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

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

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

517 | SelfConjugate -> False, |

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

519 | FlavorIndex -> SU2W}, |

520 | |

521 | U[6] == { |

522 | ClassName -> ghB, |

523 | SelfConjugate -> False, |

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

525 | Indices -> {}, |

526 | Unphysical -> True} |

527 | |

528 | |

529 | } |

530 | |

531 | (*****************************************************************************************) |

532 | |

533 | (* SM Lagrangian *) |

534 | |

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

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

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

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

539 | |

540 | 1/4 (del[B[nu], mu] - del[B[mu], nu])^2 - |

541 | |

542 | 1/4 (del[G[nu, a1], mu] - del[G[mu, a1], nu] + gs f[a1, a2, a3] G[mu, a2] G[nu, a3])* |

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

544 | |

545 | |

546 | (********************* Fermion Lagrangian terms*************************) |

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

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

549 | |

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

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

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

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

554 | |

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

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

557 | |

558 | LBright = |

559 | -2ee/cw B[mu]/2 lbar.Ga[mu].ProjP.l + (*Y_lR=-2*) |

560 | 4ee/3/cw B[mu]/2 uqbar.Ga[mu].ProjP.uq - (*Y_uR=4/3*) |

561 | 2ee/3/cw B[mu]/2 dqbar.Ga[mu].ProjP.dq; (*Y_dR=-2/3*) |

562 | |

563 | LBleft = |

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

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

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

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

568 | |

569 | LWleft = ee/sw/2( |

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

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

572 | |

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

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

575 | |

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

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

578 | |

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

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

581 | ); |

582 | |

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

584 | |

585 | (******************** Higgs Lagrangian terms****************************) |

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

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

588 | |

589 | |

590 | |

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

592 | |

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

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

595 | |

596 | (*Y_phi=1*) |

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

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

599 | |

600 | Vphi[Phi_, Phibar_] := muH^2 Phibar.Phi + \[Lambda]0 (Phibar.Phi)^2; |

601 | |

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

603 | |

604 | (*The covariant derivative in terms of physical states is: *) |

605 | (* ( A + (cw^2-sw^2)/2cwsw Z 1/Sqrt[2]sw W+ ) *) |

606 | (* D phi = id phi + e ( ) phi *) |

607 | (* ( 1/Sqrt[2]sw W- -1/2cwsw Z ) *) |

608 | |

609 | (*From this we can determine the mixing term. *) |

610 | (* *) |

611 | (* L_mix = - MW ( W- dphi+ + W+ dphi- ) - MZ Z dphi0 *) |

612 | (* This term must be cancelled in the gauge fixing Lagrangian.*) |

613 | |

614 | |

615 | |

616 | (*************** Yukawa Lagrangian***********************) |

617 | LYuk := If[FeynmanGauge, |

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

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

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

621 | |

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

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

624 | |

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

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

627 | ], |

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

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

630 | |

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

632 | - |

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

634 | ] |

635 | ]; |

636 | |

637 | LYukawa := LYuk + HC[LYuk]/.HC[v]->v; |

638 | |

639 | |

640 | (************Gauge Fix terms*************************) |

641 | LGaugeFix := If[FeynmanGauge, |

642 | Block[{GFG,GFW,GFWbar,GFZ,GFA}, |

643 | |

644 | GFG[a_] := Module[{mu}, del[G[mu,a],mu] ]; |

645 | |

646 | GFW := Module[{mu}, del[W[mu],mu] + MW phi2 ]; |

647 | GFWbar := Module[{mu}, del[Wbar[mu],mu] + MW phi2bar ]; |

648 | |

649 | GFZ := Module[{mu}, del[Z[mu],mu] + MZ phi ]; |

650 | |

651 | GFA := Module[{mu}, del[A[mu],mu] ]; |

652 | |

653 | |

654 | - 1/2*GFG[a]GFG[a] - GFWbar*GFW - 1/2*GFZ^2 - 1/2*GFA^2 ] |

655 | |

656 | , 0]; |

657 | |

658 | (* We can determine the mixing term from this. *) |

659 | (* *) |

660 | (* L_mix = MW ( phi+ dW- + phi- dW+ ) + MZ phi0 dZ *) |

661 | (* This exactly cancels the mixing term from LHiggs. *) |

662 | |

663 | |

664 | |

665 | (**************Ghost terms**************************) |

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

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

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

669 | |

670 | LGhost := If[FeynmanGauge, |

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

672 | |

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

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

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

676 | |

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

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

679 | |

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

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

682 | |

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

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

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

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

687 | ( (v+H) + I phi) ghWmbar.ghWm ) - |

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

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

690 | |

691 | |

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

693 | LGhostG + LGhostWi + LGhostB + LGhostphi] |

694 | |

695 | , 0]; |

696 | |

697 | |

698 | (*************** Hill Lagrangian***********************) |

699 | |

700 | LHill := 1/2 del[h, mu]^2 - l1 (f1 (h + v^2/2/f1) - HC[Phi].Phi)^2; |

701 | |

702 | (*********Total SM Lagrangian*******) |

703 | Lag := LGauge + LHiggs + LFermions + LYukawa +LGhost + LGaugeFix+ LHill; |

704 |