# bo2020: HiggsGG-LO-mtfinite.nb

File HiggsGG-LO-mtfinite.nb, 35.9 KB (added by fabiomaltoni, 8 months ago) |
---|

Line | |
---|---|

1 | (* Content-type: application/vnd.wolfram.mathematica *) |

2 | |

3 | (*** Wolfram Notebook File ***) |

4 | (* http://www.wolfram.com/nb *) |

5 | |

6 | (* CreatedBy='Mathematica 8.0' *) |

7 | |

8 | (*CacheID: 234*) |

9 | (* Internal cache information: |

10 | NotebookFileLineBreakTest |

11 | NotebookFileLineBreakTest |

12 | NotebookDataPosition[ 157, 7] |

13 | NotebookDataLength[ 36654, 1171] |

14 | NotebookOptionsPosition[ 34232, 1082] |

15 | NotebookOutlinePosition[ 34664, 1099] |

16 | CellTagsIndexPosition[ 34621, 1096] |

17 | WindowFrame->Normal*) |

18 | |

19 | (* Beginning of Notebook Content *) |

20 | Notebook[{ |

21 | |

22 | Cell[CellGroupData[{ |

23 | Cell["Calculation for gg>H with full top mass dependence ", "Title", |

24 | CellChangeTimes->{{3.692444489003084*^9, 3.692444517685689*^9}}], |

25 | |

26 | Cell[CellGroupData[{ |

27 | |

28 | Cell["Input FeynCalc", "Subsection"], |

29 | |

30 | Cell[CellGroupData[{ |

31 | |

32 | Cell[BoxData[ |

33 | RowBox[{"<<", "FeynCalc`"}]], "Input", |

34 | CellChangeTimes->{3.692451954377186*^9}], |

35 | |

36 | Cell[BoxData[ |

37 | FormBox[ |

38 | RowBox[{ |

39 | StyleBox[ |

40 | RowBox[{"Get", "::", "noopen"}], "MessageName"], |

41 | RowBox[{ |

42 | ":", " "}], "\<\"Cannot open \ |

43 | \[NoBreak]\\!\\(\\*FormBox[\\\"\\\\\\\"FeynCalc`\\\\\\\"\\\", \ |

44 | TraditionalForm]\\)\[NoBreak]. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ |

45 | ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ |

46 | ButtonData:>\\\"paclet:ref/message/General/noopen\\\", ButtonNote -> \ |

47 | \\\"Get::noopen\\\"]\\)\"\>"}], TraditionalForm]], "Message", "MSG", |

48 | CellChangeTimes->{3.692511575152804*^9, 3.6925118342385178`*^9, |

49 | 3.6925130738099127`*^9, 3.6925170817600527`*^9, 3.692518106515353*^9}], |

50 | |

51 | Cell[BoxData[ |

52 | FormBox["$Failed", TraditionalForm]], "Output", |

53 | CellChangeTimes->{3.692511575155848*^9, 3.6925118342578897`*^9, |

54 | 3.6925130738166857`*^9, 3.692517081778297*^9, 3.692518106567068*^9}] |

55 | }, Open ]], |

56 | |

57 | Cell[CellGroupData[{ |

58 | |

59 | Cell[BoxData[ |

60 | RowBox[{"<<", |

61 | "\"\</Users/marcozaro/Physics/feyncalc-master/FeynCalc/fc.m\>\""}]], "Input"], |

62 | |

63 | Cell[CellGroupData[{ |

64 | |

65 | Cell[BoxData[ |

66 | FormBox[ |

67 | InterpretationBox[ |

68 | RowBox[{ |

69 | StyleBox["\<\"FeynCalc \"\>", "Text", |

70 | StripOnInput->False, |

71 | FontWeight->Bold], "\[InvisibleSpace]", |

72 | StyleBox["\<\"9.1.0 (development version). For help, use the \"\>", "Text", |

73 | StripOnInput->False], "\[InvisibleSpace]", |

74 | StyleBox[ |

75 | TagBox[ |

76 | ButtonBox[ |

77 | RowBox[{"documentation", " ", "center"}], |

78 | BaseStyle->"Link", |

79 | ButtonData:>"paclet:FeynCalc/", |

80 | ButtonNote->"paclet:FeynCalc/"], |

81 | DisplayForm], "Text", |

82 | StripOnInput->False], "\[InvisibleSpace]", |

83 | StyleBox["\<\", check out the \"\>", "Text", |

84 | StripOnInput->False], "\[InvisibleSpace]", |

85 | StyleBox[ |

86 | TagBox[ |

87 | ButtonBox["wiki", |

88 | BaseStyle->"Hyperlink", |

89 | ButtonData:>{ |

90 | URL["https://github.com/FeynCalc/feyncalc/wiki"], None}, |

91 | ButtonNote->"https://github.com/FeynCalc/feyncalc/wiki"], |

92 | DisplayForm], "Text", |

93 | StripOnInput->False], "\[InvisibleSpace]", |

94 | StyleBox["\<\" or write to the \"\>", "Text", |

95 | StripOnInput->False], "\[InvisibleSpace]", |

96 | StyleBox[ |

97 | TagBox[ |

98 | ButtonBox[ |

99 | RowBox[{"mailing", " ", |

100 | RowBox[{"list", "."}]}], |

101 | BaseStyle->"Hyperlink", |

102 | ButtonData:>{ |

103 | URL["http://www.feyncalc.org/forum/"], None}, |

104 | ButtonNote->"http://www.feyncalc.org/forum/"], |

105 | DisplayForm], "Text", |

106 | StripOnInput->False]}], |

107 | SequenceForm[ |

108 | Style["FeynCalc ", "Text", Bold], |

109 | Style["9.1.0 (development version). For help, use the ", "Text"], |

110 | Style[ |

111 | DisplayForm[ |

112 | ButtonBox[ |

113 | "documentation center", BaseStyle -> "Link", ButtonData :> |

114 | "paclet:FeynCalc/", ButtonNote -> "paclet:FeynCalc/"]], "Text"], |

115 | Style[", check out the ", "Text"], |

116 | Style[ |

117 | DisplayForm[ |

118 | ButtonBox["wiki", ButtonData :> { |

119 | URL["https://github.com/FeynCalc/feyncalc/wiki"], None}, BaseStyle -> |

120 | "Hyperlink", ButtonNote -> |

121 | "https://github.com/FeynCalc/feyncalc/wiki"]], "Text"], |

122 | Style[" or write to the ", "Text"], |

123 | Style[ |

124 | DisplayForm[ |

125 | ButtonBox["mailing list.", ButtonData :> { |

126 | URL["http://www.feyncalc.org/forum/"], None}, BaseStyle -> |

127 | "Hyperlink", ButtonNote -> "http://www.feyncalc.org/forum/"]], "Text"]], |

128 | Editable->False], TraditionalForm]], "Print", |

129 | CellChangeTimes->{3.692511576512598*^9, 3.692511835506633*^9, |

130 | 3.692513076189733*^9, 3.6925170831289682`*^9, 3.692518108090785*^9}], |

131 | |

132 | Cell[BoxData[ |

133 | FormBox[ |

134 | InterpretationBox[ |

135 | RowBox[{ |

136 | StyleBox["\<\"See also the supplied \"\>", "Text", |

137 | StripOnInput->False], "\[InvisibleSpace]", |

138 | StyleBox[ |

139 | TagBox[ |

140 | ButtonBox[ |

141 | RowBox[{"examples", "."}], |

142 | BaseStyle->"Hyperlink", |

143 | ButtonFunction:>SystemOpen[ |

144 | FileNameJoin[{FeynCalc`$FeynCalcDirectory, "Examples"}]], |

145 | Evaluator->Automatic, |

146 | Method->"Preemptive"], |

147 | DisplayForm], "Text", |

148 | StripOnInput->False], "\[InvisibleSpace]", |

149 | StyleBox["\<\" If you use FeynCalc in your research, please cite\"\>", |

150 | "Text", |

151 | StripOnInput->False]}], |

152 | SequenceForm[ |

153 | Style["See also the supplied ", "Text"], |

154 | Style[ |

155 | DisplayForm[ |

156 | ButtonBox[ |

157 | "examples.", BaseStyle -> "Hyperlink", ButtonFunction :> SystemOpen[ |

158 | FileNameJoin[{FeynCalc`$FeynCalcDirectory, "Examples"}]], Evaluator -> |

159 | Automatic, Method -> "Preemptive"]], "Text"], |

160 | Style[" If you use FeynCalc in your research, please cite", "Text"]], |

161 | Editable->False], TraditionalForm]], "Print", |

162 | CellChangeTimes->{3.692511576512598*^9, 3.692511835506633*^9, |

163 | 3.692513076189733*^9, 3.6925170831289682`*^9, 3.692518108099052*^9}], |

164 | |

165 | Cell[BoxData[ |

166 | FormBox[ |

167 | StyleBox["\<\" \[Bullet] V. Shtabovenko, R. Mertig and F. Orellana, TUM-EFT \ |

168 | 71/15, arXiv:1601.01167\"\>", "Text", |

169 | StripOnInput->False], TraditionalForm]], "Print", |

170 | CellChangeTimes->{3.692511576512598*^9, 3.692511835506633*^9, |

171 | 3.692513076189733*^9, 3.6925170831289682`*^9, 3.6925181081053534`*^9}], |

172 | |

173 | Cell[BoxData[ |

174 | FormBox[ |

175 | StyleBox["\<\" \[Bullet] R. Mertig, M. B\[ODoubleDot]hm, and A. Denner, \ |

176 | Comput. Phys. Commun., 64, 345-359, 1991.\"\>", "Text", |

177 | StripOnInput->False], TraditionalForm]], "Print", |

178 | CellChangeTimes->{3.692511576512598*^9, 3.692511835506633*^9, |

179 | 3.692513076189733*^9, 3.6925170831289682`*^9, 3.6925181081130238`*^9}] |

180 | }, Open ]] |

181 | }, Open ]] |

182 | }, Open ]], |

183 | |

184 | Cell[CellGroupData[{ |

185 | |

186 | Cell["Preliminaries", "Subsection"], |

187 | |

188 | Cell[CellGroupData[{ |

189 | |

190 | Cell["Kinematics 2->1 ", "Subsubsection"], |

191 | |

192 | Cell[BoxData[ |

193 | RowBox[{"\[IndentingNewLine]", |

194 | RowBox[{ |

195 | RowBox[{ |

196 | RowBox[{ |

197 | RowBox[{"ScalarProduct", "[", |

198 | RowBox[{"q1", ",", "q1"}], "]"}], "=", "0"}], ";"}], |

199 | "\[IndentingNewLine]", |

200 | RowBox[{ |

201 | RowBox[{ |

202 | RowBox[{"ScalarProduct", "[", |

203 | RowBox[{"q2", ",", "q2"}], "]"}], "=", "0"}], ";"}], |

204 | "\[IndentingNewLine]", |

205 | RowBox[{ |

206 | RowBox[{ |

207 | RowBox[{"ScalarProduct", "[", |

208 | RowBox[{"q1", ",", "q2"}], "]"}], "=", |

209 | RowBox[{ |

210 | RowBox[{"mh", "^", "2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]", |

211 | RowBox[{ |

212 | RowBox[{ |

213 | RowBox[{"ScalarProduct", "[", |

214 | RowBox[{"q", ",", "q1"}], "]"}], "=", |

215 | RowBox[{ |

216 | RowBox[{"mh", "^", "2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]", |

217 | RowBox[{ |

218 | RowBox[{ |

219 | RowBox[{"ScalarProduct", "[", |

220 | RowBox[{"q", ",", "q2"}], "]"}], "=", |

221 | RowBox[{ |

222 | RowBox[{"mh", "^", "2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]", |

223 | RowBox[{ |

224 | RowBox[{ |

225 | RowBox[{"ScalarProduct", "[", |

226 | RowBox[{"q", ",", "q"}], "]"}], "=", |

227 | RowBox[{"mh", "^", "2"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", |

228 | CellChangeTimes->{{3.69245254913195*^9, 3.692452553746846*^9}}] |

229 | }, Open ]] |

230 | }, Open ]], |

231 | |

232 | Cell[CellGroupData[{ |

233 | |

234 | Cell["Amplitude (2 diagrams)", "Subsection"], |

235 | |

236 | Cell[CellGroupData[{ |

237 | |

238 | Cell[BoxData[ |

239 | RowBox[{"\[IndentingNewLine]", |

240 | RowBox[{ |

241 | RowBox[{"Amp", "=", |

242 | RowBox[{ |

243 | RowBox[{ |

244 | RowBox[{"(", |

245 | RowBox[{"-", "I"}], ")"}], |

246 | RowBox[{"(", |

247 | RowBox[{ |

248 | RowBox[{ |

249 | RowBox[{"(", |

250 | RowBox[{ |

251 | RowBox[{ |

252 | RowBox[{"-", |

253 | RowBox[{ |

254 | RowBox[{"(", |

255 | RowBox[{ |

256 | RowBox[{"-", "I"}], " ", "gs"}], ")"}], "^", "2"}]}], " ", |

257 | RowBox[{"(", |

258 | RowBox[{ |

259 | RowBox[{"-", " ", "I"}], " ", |

260 | RowBox[{"mt", " ", "/", "v"}]}], ")"}], " ", "*", " ", |

261 | RowBox[{"I", "^", "3"}], "*", |

262 | RowBox[{"deltaAB", "/", "2"}], "*", |

263 | RowBox[{"Tr", "[", |

264 | RowBox[{ |

265 | RowBox[{ |

266 | RowBox[{"(", |

267 | RowBox[{ |

268 | RowBox[{"GSD", "[", |

269 | RowBox[{"l", "+", "q1"}], "]"}], "+", "mt"}], ")"}], ".", |

270 | RowBox[{"GAD", "[", "mu", "]"}], ".", |

271 | RowBox[{"(", |

272 | RowBox[{ |

273 | RowBox[{"GSD", "[", "l", "]"}], "+", "mt"}], ")"}], ".", |

274 | RowBox[{"GAD", "[", "nu", "]"}], ".", |

275 | RowBox[{"(", |

276 | RowBox[{ |

277 | RowBox[{"GSD", "[", |

278 | RowBox[{"l", "-", "q2"}], "]"}], "+", "mt"}], ")"}]}], "+", |

279 | |

280 | RowBox[{ |

281 | RowBox[{"(", |

282 | RowBox[{ |

283 | RowBox[{"GSD", "[", |

284 | RowBox[{"l", "+", "q2"}], "]"}], "+", "mt"}], ")"}], ".", |

285 | RowBox[{"GAD", "[", "nu", "]"}], ".", |

286 | RowBox[{"(", |

287 | RowBox[{ |

288 | RowBox[{"GSD", "[", "l", "]"}], "+", "mt"}], ")"}], ".", |

289 | RowBox[{"GAD", "[", "mu", "]"}], ".", |

290 | RowBox[{"(", |

291 | RowBox[{ |

292 | RowBox[{"GSD", "[", |

293 | RowBox[{"l", "-", "q1"}], "]"}], "+", "mt"}], ")"}]}]}], |

294 | "]"}]}], " ", "//", "DiracSimplify"}], ")"}], "/.", " ", |

295 | RowBox[{ |

296 | RowBox[{"Pair", "[", |

297 | RowBox[{ |

298 | RowBox[{"Momentum", "[", "q2", "]"}], ",", |

299 | RowBox[{"LorentzIndex", "[", "nu", "]"}]}], "]"}], "\[Rule]", |

300 | "0"}]}], "/.", " ", |

301 | RowBox[{ |

302 | RowBox[{"Pair", "[", |

303 | RowBox[{ |

304 | RowBox[{"Momentum", "[", "q1", "]"}], ",", |

305 | RowBox[{"LorentzIndex", "[", "mu", "]"}]}], "]"}], "\[Rule]", |

306 | "0"}]}], ")"}]}], " ", "//", "Simplify"}]}], |

307 | "\[IndentingNewLine]"}]}]], "Input"], |

308 | |

309 | Cell[BoxData[ |

310 | FormBox[ |

311 | FractionBox[ |

312 | RowBox[{"2", " ", "\[ImaginaryI]", " ", "deltaAB", " ", |

313 | SuperscriptBox["gs", "2"], " ", |

314 | SuperscriptBox["mt", "2"], " ", |

315 | RowBox[{"(", |

316 | RowBox[{ |

317 | RowBox[{"-", |

318 | RowBox[{ |

319 | FormBox[ |

320 | SuperscriptBox["g", |

321 | RowBox[{ |

322 | FormBox[ |

323 | FormBox[ |

324 | FormBox["mu", |

325 | TraditionalForm], |

326 | TraditionalForm], |

327 | TraditionalForm], |

328 | FormBox[ |

329 | FormBox[ |

330 | FormBox["nu", |

331 | TraditionalForm], |

332 | TraditionalForm], |

333 | TraditionalForm]}]], |

334 | TraditionalForm], " ", |

335 | RowBox[{"(", |

336 | RowBox[{ |

337 | RowBox[{"2", " ", |

338 | SuperscriptBox[ |

339 | FormBox[ |

340 | FormBox["l", |

341 | TraditionalForm], |

342 | TraditionalForm], "2"]}], "+", |

343 | SuperscriptBox["mh", "2"], "-", |

344 | RowBox[{"2", " ", |

345 | SuperscriptBox["mt", "2"]}]}], ")"}]}]}], "+", |

346 | RowBox[{"8", " ", |

347 | FormBox[ |

348 | SuperscriptBox[ |

349 | FormBox[ |

350 | FormBox["l", |

351 | TraditionalForm], |

352 | TraditionalForm], |

353 | FormBox[ |

354 | FormBox[ |

355 | FormBox["mu", |

356 | TraditionalForm], |

357 | TraditionalForm], |

358 | TraditionalForm]], |

359 | TraditionalForm], " ", |

360 | FormBox[ |

361 | SuperscriptBox[ |

362 | FormBox[ |

363 | FormBox["l", |

364 | TraditionalForm], |

365 | TraditionalForm], |

366 | FormBox[ |

367 | FormBox[ |

368 | FormBox["nu", |

369 | TraditionalForm], |

370 | TraditionalForm], |

371 | TraditionalForm]], |

372 | TraditionalForm]}], "+", |

373 | RowBox[{"2", " ", |

374 | FormBox[ |

375 | SuperscriptBox[ |

376 | FormBox[ |

377 | FormBox["q2", |

378 | TraditionalForm], |

379 | TraditionalForm], |

380 | FormBox[ |

381 | FormBox[ |

382 | FormBox["mu", |

383 | TraditionalForm], |

384 | TraditionalForm], |

385 | TraditionalForm]], |

386 | TraditionalForm], " ", |

387 | FormBox[ |

388 | SuperscriptBox[ |

389 | FormBox[ |

390 | FormBox["q1", |

391 | TraditionalForm], |

392 | TraditionalForm], |

393 | FormBox[ |

394 | FormBox[ |

395 | FormBox["nu", |

396 | TraditionalForm], |

397 | TraditionalForm], |

398 | TraditionalForm]], |

399 | TraditionalForm]}], "-", |

400 | RowBox[{"2", " ", |

401 | FormBox[ |

402 | SuperscriptBox[ |

403 | FormBox[ |

404 | FormBox["q1", |

405 | TraditionalForm], |

406 | TraditionalForm], |

407 | FormBox[ |

408 | FormBox[ |

409 | FormBox["mu", |

410 | TraditionalForm], |

411 | TraditionalForm], |

412 | TraditionalForm]], |

413 | TraditionalForm], " ", |

414 | FormBox[ |

415 | SuperscriptBox[ |

416 | FormBox[ |

417 | FormBox["q2", |

418 | TraditionalForm], |

419 | TraditionalForm], |

420 | FormBox[ |

421 | FormBox[ |

422 | FormBox["nu", |

423 | TraditionalForm], |

424 | TraditionalForm], |

425 | TraditionalForm]], |

426 | TraditionalForm]}]}], ")"}]}], "v"], TraditionalForm]], "Output", |

427 | CellChangeTimes->{3.692452170263329*^9, 3.69245255666861*^9, |

428 | 3.692452972716131*^9, 3.6924538156646147`*^9, 3.692510939269392*^9, |

429 | 3.692511576946205*^9, 3.692511835928535*^9, 3.692513076828374*^9, |

430 | 3.6925170835612497`*^9, 3.692518108761848*^9}] |

431 | }, Open ]] |

432 | }, Open ]], |

433 | |

434 | Cell[CellGroupData[{ |

435 | |

436 | Cell["Let's ask FeynCalc to do the tensor reduction", "Subsection"], |

437 | |

438 | Cell[CellGroupData[{ |

439 | |

440 | Cell[BoxData[ |

441 | RowBox[{"\[IndentingNewLine]", |

442 | RowBox[{ |

443 | RowBox[{ |

444 | RowBox[{"res", "=", |

445 | RowBox[{ |

446 | RowBox[{ |

447 | RowBox[{ |

448 | RowBox[{ |

449 | RowBox[{"1", "/", |

450 | RowBox[{ |

451 | RowBox[{"(", |

452 | RowBox[{"2", " ", "Pi"}], ")"}], "^", "4"}]}], "*", |

453 | RowBox[{"OneLoop", "[", |

454 | RowBox[{"l", ",", |

455 | RowBox[{ |

456 | RowBox[{ |

457 | RowBox[{"FAD", "[", |

458 | RowBox[{ |

459 | RowBox[{"{", |

460 | RowBox[{"l", ",", "mt"}], "}"}], ",", |

461 | RowBox[{"{", |

462 | RowBox[{ |

463 | RowBox[{"l", "+", "q1"}], ",", "mt"}], "}"}], ",", |

464 | RowBox[{"{", |

465 | RowBox[{ |

466 | RowBox[{"l", "-", "q2"}], ",", "mt"}], "}"}]}], "]"}], " ", |

467 | "Amp"}], "//", "Contract"}]}], "]"}]}], "//", "PaVeReduce"}], "//", |

468 | "Factor"}], "//", "Simplify"}]}], ";"}], "\[IndentingNewLine]", |

469 | RowBox[{"res", "=", |

470 | RowBox[{ |

471 | RowBox[{"(", |

472 | RowBox[{ |

473 | RowBox[{"res", "/.", " ", |

474 | RowBox[{ |

475 | RowBox[{"Pair", "[", |

476 | RowBox[{ |

477 | RowBox[{"Momentum", "[", "q2", "]"}], ",", |

478 | RowBox[{"LorentzIndex", "[", "nu", "]"}]}], "]"}], "\[Rule]", |

479 | "0"}]}], "/.", " ", |

480 | RowBox[{ |

481 | RowBox[{"Pair", "[", |

482 | RowBox[{ |

483 | RowBox[{"Momentum", "[", "q1", "]"}], ",", |

484 | RowBox[{"LorentzIndex", "[", "mu", "]"}]}], "]"}], "\[Rule]", |

485 | "0"}]}], " ", ")"}], "//", "Simplify"}]}]}]}]], "Input"], |

486 | |

487 | Cell[BoxData[ |

488 | FormBox[ |

489 | RowBox[{ |

490 | FractionBox["1", |

491 | RowBox[{"8", " ", |

492 | SuperscriptBox["\[Pi]", "2"], " ", |

493 | RowBox[{"(", |

494 | RowBox[{"D", "-", "2"}], ")"}], " ", |

495 | SuperscriptBox["mh", "2"], " ", "v"}]], |

496 | RowBox[{"deltaAB", " ", |

497 | SuperscriptBox["gs", "2"], " ", |

498 | SuperscriptBox["mt", "2"], " ", |

499 | RowBox[{"(", |

500 | RowBox[{ |

501 | RowBox[{ |

502 | SuperscriptBox["mh", "2"], " ", |

503 | FormBox[ |

504 | SuperscriptBox[ |

505 | OverscriptBox["g", "_"], |

506 | RowBox[{ |

507 | FormBox[ |

508 | FormBox[ |

509 | FormBox["mu", |

510 | TraditionalForm], |

511 | TraditionalForm], |

512 | TraditionalForm], |

513 | FormBox[ |

514 | FormBox[ |

515 | FormBox["nu", |

516 | TraditionalForm], |

517 | TraditionalForm], |

518 | TraditionalForm]}]], |

519 | TraditionalForm]}], "-", |

520 | RowBox[{"2", " ", |

521 | FormBox[ |

522 | SuperscriptBox[ |

523 | FormBox[ |

524 | OverscriptBox[ |

525 | FormBox["q2", |

526 | TraditionalForm], "_"], |

527 | TraditionalForm], |

528 | FormBox[ |

529 | FormBox[ |

530 | FormBox["mu", |

531 | TraditionalForm], |

532 | TraditionalForm], |

533 | TraditionalForm]], |

534 | TraditionalForm], " ", |

535 | FormBox[ |

536 | SuperscriptBox[ |

537 | FormBox[ |

538 | OverscriptBox[ |

539 | FormBox["q1", |

540 | TraditionalForm], "_"], |

541 | TraditionalForm], |

542 | FormBox[ |

543 | FormBox[ |

544 | FormBox["nu", |

545 | TraditionalForm], |

546 | TraditionalForm], |

547 | TraditionalForm]], |

548 | TraditionalForm]}]}], ")"}], " ", |

549 | RowBox[{"(", |

550 | RowBox[{ |

551 | RowBox[{"2", " ", |

552 | RowBox[{"(", |

553 | RowBox[{"D", "-", "4"}], ")"}], " ", |

554 | FormBox[ |

555 | RowBox[{ |

556 | SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", |

557 | RowBox[{ |

558 | SuperscriptBox["mh", "2"], ",", |

559 | SuperscriptBox["mt", "2"], ",", |

560 | SuperscriptBox["mt", "2"]}], ")"}], |

561 | TraditionalForm]}], "+", |

562 | RowBox[{ |

563 | RowBox[{"(", |

564 | RowBox[{ |

565 | RowBox[{ |

566 | RowBox[{"(", |

567 | RowBox[{"D", "-", "2"}], ")"}], " ", |

568 | SuperscriptBox["mh", "2"]}], "-", |

569 | RowBox[{"8", " ", |

570 | SuperscriptBox["mt", "2"]}]}], ")"}], " ", |

571 | FormBox[ |

572 | RowBox[{ |

573 | SubscriptBox["\<\"C\"\>", "\<\"0\"\>"], "(", |

574 | RowBox[{"0", ",", "0", ",", |

575 | SuperscriptBox["mh", "2"], ",", |

576 | SuperscriptBox["mt", "2"], ",", |

577 | SuperscriptBox["mt", "2"], ",", |

578 | SuperscriptBox["mt", "2"]}], ")"}], |

579 | TraditionalForm]}]}], ")"}]}]}], TraditionalForm]], "Output", |

580 | CellChangeTimes->{3.69245217851362*^9, 3.692452559992298*^9, |

581 | 3.692452977284349*^9, 3.692453819606213*^9, 3.692510960462818*^9, |

582 | 3.6925115775440702`*^9, 3.692511836507619*^9, 3.6925130777097187`*^9, |

583 | 3.692517084203616*^9, 3.6925181096158943`*^9}] |

584 | }, Open ]] |

585 | }, Open ]], |

586 | |

587 | Cell[CellGroupData[{ |

588 | |

589 | Cell["\<\ |

590 | The scalar integral C0 can be evaluated with the help of the Feynman \ |

591 | parameters (by hand), and the result is (\[Tau] = mh^2 / (4 mt^2):\ |

592 | \>", "Subsection", |

593 | CellChangeTimes->{{3.692515977056491*^9, 3.6925159820148697`*^9}, { |

594 | 3.692516016057069*^9, 3.69251602591861*^9}, {3.6925179204440413`*^9, |

595 | 3.692517920634293*^9}, {3.692520466725155*^9, 3.692520468165311*^9}, { |

596 | 3.692521738384965*^9, 3.692521741980186*^9}}], |

597 | |

598 | Cell["\<\ |

599 | c0x=-I/(16 Pi^2)*1/mt^2*Integrate[1/(1-4 \[Tau] x y),{y,0,1-x}, Assumptions \ |

600 | \[Rule] {\[Tau]<1, \[Tau]>0, x>0, x<1}]//Simplify; |

601 | c0 = Integrate[c0x, {x,0,1}, Assumptions \[Rule] {\[Tau]<1, \[Tau]>0}]; |

602 | c0FC=(2 Pi)^4/(I Pi^2) c0;\ |

603 | \>", "Input", |

604 | CellChangeTimes->{{3.692511045749646*^9, 3.692511049611127*^9}, { |

605 | 3.692511557857853*^9, 3.692511560335854*^9}, {3.69251225244053*^9, |

606 | 3.692512255516741*^9}, {3.69251503727313*^9, 3.692515038073168*^9}, { |

607 | 3.692515120413361*^9, 3.692515195614604*^9}, {3.6925155941637917`*^9, |

608 | 3.692515599171131*^9}, {3.692515651379901*^9, 3.69251568391683*^9}, { |

609 | 3.692515780222146*^9, 3.69251583934918*^9}, {3.692515875890379*^9, |

610 | 3.692515880441649*^9}, {3.692516835243518*^9, 3.692516838585149*^9}}] |

611 | }, Open ]], |

612 | |

613 | Cell[CellGroupData[{ |

614 | |

615 | Cell["\<\ |

616 | The scalar integral B0, we just need the 1/\[Epsilon] part, as it comes \ |

617 | multiplied by D-4)\ |

618 | \>", "Subsection", |

619 | CellChangeTimes->{{3.692515977056491*^9, 3.6925159820148697`*^9}, { |

620 | 3.692516016057069*^9, 3.69251602591861*^9}, {3.6925168604493313`*^9, |

621 | 3.692516890286077*^9}, {3.692520454657867*^9, 3.692520455316841*^9}}], |

622 | |

623 | Cell[BoxData[{ |

624 | RowBox[{ |

625 | RowBox[{"b01oeps", "=", |

626 | RowBox[{ |

627 | RowBox[{"I", " ", "/", |

628 | RowBox[{ |

629 | RowBox[{"(", |

630 | RowBox[{"4", " ", "Pi"}], ")"}], "^", "2"}]}], " ", |

631 | RowBox[{"2", "/", |

632 | RowBox[{"(", |

633 | RowBox[{"4", "-", "D"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", |

634 | RowBox[{ |

635 | RowBox[{"b0FC", "=", |

636 | RowBox[{ |

637 | RowBox[{ |

638 | RowBox[{ |

639 | RowBox[{"(", |

640 | RowBox[{"2", " ", "Pi"}], ")"}], "^", "4"}], "/", |

641 | RowBox[{"(", |

642 | RowBox[{"I", " ", |

643 | RowBox[{"Pi", "^", "2"}]}], ")"}]}], " ", "b01oeps"}]}], |

644 | ";"}]}], "Input", |

645 | CellChangeTimes->{{3.692516899350171*^9, 3.692517026300687*^9}, { |

646 | 3.692517146586252*^9, 3.692517151088367*^9}}] |

647 | }, Open ]], |

648 | |

649 | Cell[CellGroupData[{ |

650 | |

651 | Cell["\<\ |

652 | This is rather cumbersome, but it is just to replace FeynCalc\ |

653 | \[CloseCurlyQuote]s C0 and B0 functions with ours, as the commented (simpler) \ |

654 | expression seems not to work on Mathematica 10 + FC9\ |

655 | \>", "Subsection", |

656 | CellChangeTimes->{ |

657 | 3.692520284321138*^9, {3.692520319819466*^9, 3.692520379301304*^9}, { |

658 | 3.6925204827584248`*^9, 3.692520484348297*^9}}], |

659 | |

660 | Cell[BoxData[ |

661 | RowBox[{"(*", |

662 | RowBox[{ |

663 | RowBox[{"subint", "[", "expr_", "]"}], " ", ":=", " ", |

664 | RowBox[{"Simplify", "[", |

665 | RowBox[{"expr", " ", "/.", " ", |

666 | RowBox[{"{", |

667 | RowBox[{ |

668 | RowBox[{ |

669 | RowBox[{"C0", "[", "x_", "]"}], "\[Rule]", "c0FC"}], ",", " ", |

670 | RowBox[{"\[AliasDelimiter]", |

671 | RowBox[{ |

672 | RowBox[{ |

673 | RowBox[{ |

674 | RowBox[{ |

675 | RowBox[{ |

676 | RowBox[{"B0", "[", "x_", "]"}], "\[Rule]", "b0FC"}], " ", "}"}], |

677 | "]"}], ";"}], "*)"}]}]}]}]}]}]}]}]], "Input", |

678 | CellChangeTimes->{{3.692520387110497*^9, 3.6925204126273193`*^9}, { |

679 | 3.6925204890200253`*^9, 3.6925205027299833`*^9}}], |

680 | |

681 | Cell[BoxData[ |

682 | RowBox[{ |

683 | RowBox[{ |

684 | RowBox[{"subint", "[", "expr_", "]"}], " ", ":=", " ", |

685 | RowBox[{"Simplify", "[", |

686 | RowBox[{"expr", " ", "/.", " ", |

687 | RowBox[{"{", |

688 | RowBox[{ |

689 | RowBox[{ |

690 | RowBox[{ |

691 | RowBox[{"PaVe", "[", |

692 | RowBox[{"x_", ",", "y_", ",", "z_"}], "]"}], " ", "/;", " ", |

693 | RowBox[{ |

694 | RowBox[{"Length", "[", |

695 | RowBox[{"Join", "[", |

696 | RowBox[{"y", ",", "z"}], "]"}], "]"}], " ", "\[Equal]", " ", |

697 | "6"}]}], "\[Rule]", "c0FC"}], ",", "\[IndentingNewLine]", |

698 | RowBox[{ |

699 | RowBox[{ |

700 | RowBox[{"PaVe", "[", |

701 | RowBox[{"x_", ",", "y_", ",", "z_"}], "]"}], " ", "/;", " ", |

702 | RowBox[{ |

703 | RowBox[{"Length", "[", |

704 | RowBox[{"Join", "[", |

705 | RowBox[{"y", ",", "z"}], "]"}], "]"}], " ", "\[Equal]", " ", |

706 | "3"}]}], "\[Rule]", "b0FC"}]}], " ", "}"}]}], "]"}]}], |

707 | ";"}]], "Input", |

708 | CellChangeTimes->{{3.692511088650519*^9, 3.6925111026315603`*^9}, { |

709 | 3.69251122689157*^9, 3.692511251466298*^9}, {3.692511287165449*^9, |

710 | 3.692511390180458*^9}, {3.692511420580585*^9, 3.692511428562236*^9}, { |

711 | 3.692511486942605*^9, 3.692511501291944*^9}, {3.692511541963472*^9, |

712 | 3.692511544297491*^9}, {3.6925115908150187`*^9, 3.692511592571269*^9}, { |

713 | 3.69251164296789*^9, 3.692511663704157*^9}, {3.6925117165619698`*^9, |

714 | 3.692511817361938*^9}, 3.692511849421681*^9, {3.692512176273435*^9, |

715 | 3.692512189790781*^9}, {3.692513611230301*^9, 3.69251361647466*^9}, { |

716 | 3.692513648480934*^9, 3.6925136568424397`*^9}, {3.692513694800782*^9, |

717 | 3.692513702188364*^9}, {3.6925170421818333`*^9, 3.69251705299717*^9}, { |

718 | 3.6925172275141287`*^9, 3.6925172318887367`*^9}}], |

719 | |

720 | Cell[BoxData[""], "Input", |

721 | CellChangeTimes->{{3.692513736504738*^9, 3.69251374487772*^9}}] |

722 | }, Open ]], |

723 | |

724 | Cell[CellGroupData[{ |

725 | |

726 | Cell["\<\ |

727 | Let's take the mt->Infinity limit and see that the amplitude does not depend \ |

728 | on m_top:\ |

729 | \>", "Subsection", |

730 | CellChangeTimes->{3.692520284321138*^9}], |

731 | |

732 | Cell[CellGroupData[{ |

733 | |

734 | Cell[BoxData[ |

735 | RowBox[{"myamp", "=", |

736 | RowBox[{ |

737 | RowBox[{"Normal", "[", |

738 | RowBox[{"Series", "[", |

739 | RowBox[{ |

740 | RowBox[{ |

741 | RowBox[{ |

742 | RowBox[{ |

743 | RowBox[{ |

744 | RowBox[{ |

745 | RowBox[{"(", " ", |

746 | RowBox[{"res", " ", "//", "Simplify"}], ")"}], "/.", " ", |

747 | RowBox[{ |

748 | RowBox[{"gs", "^", "2"}], " ", "\[Rule]", " ", |

749 | RowBox[{"as", " ", "4", " ", "Pi"}]}]}], "/.", " ", |

750 | RowBox[{"mh2", "\[Rule]", |

751 | RowBox[{"mh", "^", "2"}]}]}], "/.", " ", |

752 | RowBox[{"\[Tau]", "\[Rule]", " ", |

753 | RowBox[{ |

754 | RowBox[{ |

755 | RowBox[{"mh", "^", "2"}], "/", "4"}], "/", |

756 | RowBox[{"mt", "^", "2"}]}]}]}], "//", "PowerExpand"}], "//", |

757 | "FullSimplify"}], ",", |

758 | RowBox[{"{", |

759 | RowBox[{"mt", ",", "Infinity", ",", "4"}], "}"}]}], "]"}], "]"}], "//", |

760 | "Simplify"}]}]], "Input", |

761 | CellChangeTimes->{3.692511068164669*^9}], |

762 | |

763 | Cell[BoxData[ |

764 | FormBox[ |

765 | RowBox[{ |

766 | FractionBox["1", |

767 | RowBox[{"2", " ", "\[Pi]", " ", |

768 | RowBox[{"(", |

769 | RowBox[{"D", "-", "2"}], ")"}], " ", |

770 | SuperscriptBox["mh", "2"], " ", "v"}]], |

771 | RowBox[{"as", " ", "deltaAB", " ", |

772 | SuperscriptBox["mt", "2"], " ", |

773 | RowBox[{"(", |

774 | RowBox[{ |

775 | RowBox[{ |

776 | SuperscriptBox["mh", "2"], " ", |

777 | FormBox[ |

778 | SuperscriptBox[ |

779 | OverscriptBox["g", "_"], |

780 | RowBox[{ |

781 | FormBox[ |

782 | FormBox[ |

783 | FormBox["mu", |

784 | TraditionalForm], |

785 | TraditionalForm], |

786 | TraditionalForm], |

787 | FormBox[ |

788 | FormBox[ |

789 | FormBox["nu", |

790 | TraditionalForm], |

791 | TraditionalForm], |

792 | TraditionalForm]}]], |

793 | TraditionalForm]}], "-", |

794 | RowBox[{"2", " ", |

795 | FormBox[ |

796 | SuperscriptBox[ |

797 | FormBox[ |

798 | OverscriptBox[ |

799 | FormBox["q2", |

800 | TraditionalForm], "_"], |

801 | TraditionalForm], |

802 | FormBox[ |

803 | FormBox[ |

804 | FormBox["mu", |

805 | TraditionalForm], |

806 | TraditionalForm], |

807 | TraditionalForm]], |

808 | TraditionalForm], " ", |

809 | FormBox[ |

810 | SuperscriptBox[ |

811 | FormBox[ |

812 | OverscriptBox[ |

813 | FormBox["q1", |

814 | TraditionalForm], "_"], |

815 | TraditionalForm], |

816 | FormBox[ |

817 | FormBox[ |

818 | FormBox["nu", |

819 | TraditionalForm], |

820 | TraditionalForm], |

821 | TraditionalForm]], |

822 | TraditionalForm]}]}], ")"}], " ", |

823 | RowBox[{"(", |

824 | RowBox[{ |

825 | RowBox[{"2", " ", |

826 | RowBox[{"(", |

827 | RowBox[{"D", "-", "4"}], ")"}], " ", |

828 | FormBox[ |

829 | RowBox[{ |

830 | SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", |

831 | RowBox[{ |

832 | SuperscriptBox["mh", "2"], ",", |

833 | SuperscriptBox["mt", "2"], ",", |

834 | SuperscriptBox["mt", "2"]}], ")"}], |

835 | TraditionalForm]}], "+", |

836 | RowBox[{ |

837 | RowBox[{"(", |

838 | RowBox[{ |

839 | RowBox[{ |

840 | RowBox[{"(", |

841 | RowBox[{"D", "-", "2"}], ")"}], " ", |

842 | SuperscriptBox["mh", "2"]}], "-", |

843 | RowBox[{"8", " ", |

844 | SuperscriptBox["mt", "2"]}]}], ")"}], " ", |

845 | FormBox[ |

846 | RowBox[{ |

847 | SubscriptBox["\<\"C\"\>", "\<\"0\"\>"], "(", |

848 | RowBox[{"0", ",", "0", ",", |

849 | SuperscriptBox["mh", "2"], ",", |

850 | SuperscriptBox["mt", "2"], ",", |

851 | SuperscriptBox["mt", "2"], ",", |

852 | SuperscriptBox["mt", "2"]}], ")"}], |

853 | TraditionalForm]}]}], ")"}]}]}], TraditionalForm]], "Output", |

854 | CellChangeTimes->{{3.692511052510167*^9, 3.692511074721478*^9}, |

855 | 3.692511518596458*^9, {3.6925115780945807`*^9, 3.692511597069365*^9}, { |

856 | 3.6925116517937403`*^9, 3.692511666762609*^9}, 3.692511727680943*^9, |

857 | 3.692511836997037*^9, 3.6925121970051394`*^9, 3.692513126501425*^9, |

858 | 3.6925137048363113`*^9, 3.692517062946196*^9, 3.6925171054400797`*^9, |

859 | 3.692517156544361*^9, 3.692517246551955*^9, 3.692518130912465*^9}] |

860 | }, Open ]], |

861 | |

862 | Cell[CellGroupData[{ |

863 | |

864 | Cell[BoxData[ |

865 | RowBox[{"finalamp", " ", "=", " ", |

866 | RowBox[{ |

867 | RowBox[{ |

868 | RowBox[{"subint", "[", "myamp", "]"}], "/.", " ", |

869 | RowBox[{"{", |

870 | RowBox[{ |

871 | RowBox[{"D", "\[Rule]", "4"}], ",", " ", |

872 | RowBox[{ |

873 | RowBox[{"mt", "^", "2"}], "\[Rule]", |

874 | RowBox[{ |

875 | RowBox[{"mh", "^", "2"}], "/", |

876 | RowBox[{"(", |

877 | RowBox[{"4", "\[Tau]"}], ")"}]}]}]}], "}"}]}], " ", "//", |

878 | "Simplify"}]}]], "Input", |

879 | CellChangeTimes->{{3.692511396567629*^9, 3.69251140477779*^9}, { |

880 | 3.69251718353259*^9, 3.692517257077794*^9}, {3.692517912037135*^9, |

881 | 3.692517914900489*^9}, {3.6925179647563257`*^9, 3.692517976859829*^9}}], |

882 | |

883 | Cell[BoxData[ |

884 | FormBox[ |

885 | RowBox[{"-", |

886 | FractionBox[ |

887 | RowBox[{"as", " ", "deltaAB", " ", |

888 | RowBox[{"(", |

889 | RowBox[{ |

890 | RowBox[{ |

891 | RowBox[{"(", |

892 | RowBox[{"\[Tau]", "-", "1"}], ")"}], " ", |

893 | TemplateBox[{"2",FractionBox[ |

894 | RowBox[{"2", " ", "\[Tau]"}], |

895 | RowBox[{"\[Tau]", "+", |

896 | RowBox[{"\[ImaginaryI]", " ", |

897 | SqrtBox[ |

898 | RowBox[{ |

899 | RowBox[{"-", |

900 | RowBox[{"(", |

901 | RowBox[{"\[Tau]", "-", "1"}], ")"}]}], " ", |

902 | "\[Tau]"}]]}]}]]}, |

903 | "PolyLog"]}], "+", |

904 | RowBox[{ |

905 | RowBox[{"(", |

906 | RowBox[{"\[Tau]", "-", "1"}], ")"}], " ", |

907 | TemplateBox[{"2",FractionBox[ |

908 | RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Tau]"}], |

909 | RowBox[{ |

910 | RowBox[{"\[ImaginaryI]", " ", "\[Tau]"}], "+", |

911 | SqrtBox[ |

912 | RowBox[{ |

913 | RowBox[{"-", |

914 | RowBox[{"(", |

915 | RowBox[{"\[Tau]", "-", "1"}], ")"}]}], " ", |

916 | "\[Tau]"}]]}]]}, |

917 | "PolyLog"]}], "+", |

918 | RowBox[{"2", " ", "\[Tau]"}]}], ")"}], " ", |

919 | RowBox[{"(", |

920 | RowBox[{ |

921 | RowBox[{ |

922 | SuperscriptBox["mh", "2"], " ", |

923 | FormBox[ |

924 | SuperscriptBox[ |

925 | OverscriptBox["g", "_"], |

926 | RowBox[{ |

927 | FormBox[ |

928 | FormBox[ |

929 | FormBox["mu", |

930 | TraditionalForm], |

931 | TraditionalForm], |

932 | TraditionalForm], |

933 | FormBox[ |

934 | FormBox[ |

935 | FormBox["nu", |

936 | TraditionalForm], |

937 | TraditionalForm], |

938 | TraditionalForm]}]], |

939 | TraditionalForm]}], "-", |

940 | RowBox[{"2", " ", |

941 | FormBox[ |

942 | SuperscriptBox[ |

943 | FormBox[ |

944 | OverscriptBox[ |

945 | FormBox["q2", |

946 | TraditionalForm], "_"], |

947 | TraditionalForm], |

948 | FormBox[ |

949 | FormBox[ |

950 | FormBox["mu", |

951 | TraditionalForm], |

952 | TraditionalForm], |

953 | TraditionalForm]], |

954 | TraditionalForm], " ", |

955 | FormBox[ |

956 | SuperscriptBox[ |

957 | FormBox[ |

958 | OverscriptBox[ |

959 | FormBox["q1", |

960 | TraditionalForm], "_"], |

961 | TraditionalForm], |

962 | FormBox[ |

963 | FormBox[ |

964 | FormBox["nu", |

965 | TraditionalForm], |

966 | TraditionalForm], |

967 | TraditionalForm]], |

968 | TraditionalForm]}]}], ")"}]}], |

969 | RowBox[{"8", " ", "\[Pi]", " ", |

970 | SuperscriptBox["\[Tau]", "2"], " ", "v"}]]}], TraditionalForm]], "Output",\ |

971 | |

972 | CellChangeTimes->{{3.692511405202662*^9, 3.69251143518386*^9}, { |

973 | 3.6925115074304533`*^9, 3.69251151865038*^9}, {3.692511578190337*^9, |

974 | 3.692511597121833*^9}, {3.6925116546982393`*^9, 3.6925116668026123`*^9}, { |

975 | 3.6925117277323923`*^9, 3.692511780284226*^9}, {3.6925118370505447`*^9, |

976 | 3.69251185243128*^9}, 3.6925119259368773`*^9, 3.692512199011361*^9, |

977 | 3.6925131301000423`*^9, 3.6925136429395638`*^9, 3.6925137086067123`*^9, |

978 | 3.692517105499065*^9, 3.692517156624544*^9, 3.692517191590906*^9, { |

979 | 3.692517246612756*^9, 3.692517257431817*^9}, 3.692517978839405*^9, |

980 | 3.69251813100445*^9}] |

981 | }, Open ]], |

982 | |

983 | Cell[CellGroupData[{ |

984 | |

985 | Cell[BoxData[ |

986 | RowBox[{"finalampEFT", "=", |

987 | RowBox[{"Limit", "[", |

988 | RowBox[{"finalamp", ",", " ", |

989 | RowBox[{"\[Tau]", "->", " ", "0"}]}], "]"}]}]], "Input", |

990 | CellChangeTimes->{{3.6925172739166203`*^9, 3.692517329921995*^9}}], |

991 | |

992 | Cell[BoxData[ |

993 | FormBox[ |

994 | RowBox[{"-", |

995 | FractionBox[ |

996 | RowBox[{"as", " ", "deltaAB", " ", |

997 | RowBox[{"(", |

998 | RowBox[{ |

999 | RowBox[{ |

1000 | SuperscriptBox["mh", "2"], " ", |

1001 | FormBox[ |

1002 | SuperscriptBox[ |

1003 | OverscriptBox["g", "_"], |

1004 | RowBox[{ |

1005 | FormBox[ |

1006 | FormBox[ |

1007 | FormBox["mu", |

1008 | TraditionalForm], |

1009 | TraditionalForm], |

1010 | TraditionalForm], |

1011 | FormBox[ |

1012 | FormBox[ |

1013 | FormBox["nu", |

1014 | TraditionalForm], |

1015 | TraditionalForm], |

1016 | TraditionalForm]}]], |

1017 | TraditionalForm]}], "-", |

1018 | RowBox[{"2", " ", |

1019 | FormBox[ |

1020 | SuperscriptBox[ |

1021 | FormBox[ |

1022 | OverscriptBox[ |

1023 | FormBox["q2", |

1024 | TraditionalForm], "_"], |

1025 | TraditionalForm], |

1026 | FormBox[ |

1027 | FormBox[ |

1028 | FormBox["mu", |

1029 | TraditionalForm], |

1030 | TraditionalForm], |

1031 | TraditionalForm]], |

1032 | TraditionalForm], " ", |

1033 | FormBox[ |

1034 | SuperscriptBox[ |

1035 | FormBox[ |

1036 | OverscriptBox[ |

1037 | FormBox["q1", |

1038 | TraditionalForm], "_"], |

1039 | TraditionalForm], |

1040 | FormBox[ |

1041 | FormBox[ |

1042 | FormBox["nu", |

1043 | TraditionalForm], |

1044 | TraditionalForm], |

1045 | TraditionalForm]], |

1046 | TraditionalForm]}]}], ")"}]}], |

1047 | RowBox[{"6", " ", "\[Pi]", " ", "v"}]]}], TraditionalForm]], "Output", |

1048 | CellChangeTimes->{{3.6925173203674393`*^9, 3.69251733165294*^9}, |

1049 | 3.692517993143227*^9, 3.6925181320293016`*^9}] |

1050 | }, Open ]], |

1051 | |

1052 | Cell[BoxData[""], "Input"], |

1053 | |

1054 | Cell[CellGroupData[{ |

1055 | |

1056 | Cell[BoxData[ |

1057 | RowBox[{"Integrate", "[", |

1058 | RowBox[{ |

1059 | RowBox[{ |

1060 | RowBox[{"(", |

1061 | RowBox[{"1", "-", |

1062 | RowBox[{"4", " ", "x", " ", "y"}]}], ")"}], "/", |

1063 | RowBox[{"(", |

1064 | RowBox[{"1", "-", |

1065 | RowBox[{"\[Tau]", " ", "x", " ", "y"}]}], ")"}]}], ",", |

1066 | RowBox[{"{", |

1067 | RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", |

1068 | RowBox[{"{", |

1069 | RowBox[{"y", ",", "0", ",", |

1070 | RowBox[{"1", "-", "x"}]}], "}"}], ",", " ", |

1071 | RowBox[{"Assumptions", " ", "\[Rule]", " ", |

1072 | RowBox[{"{", |

1073 | RowBox[{"\[Tau]", "==", "0"}], "}"}]}]}], "]"}]], "Input", |

1074 | CellChangeTimes->{{3.542627525077577*^9, 3.542627611656934*^9}}], |

1075 | |

1076 | Cell[BoxData[ |

1077 | FractionBox["1", "3"]], "Output", |

1078 | CellChangeTimes->{{3.542627586138248*^9, 3.542627615440257*^9}}] |

1079 | }, Open ]] |

1080 | }, Open ]] |

1081 | }, Open ]] |

1082 | }, |

1083 | WindowSize->{710, 706}, |

1084 | WindowMargins->{{148, Automatic}, {Automatic, 0}}, |

1085 | PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}}, |

1086 | FrontEndVersion->"10.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (June 27, \ |

1087 | 2014)", |

1088 | StyleDefinitions->"Default.nb" |

1089 | ] |

1090 | (* End of Notebook Content *) |

1091 | |

1092 | (* Internal cache information *) |

1093 | (*CellTagsOutline |

1094 | CellTagsIndex->{} |

1095 | *) |

1096 | (*CellTagsIndex |

1097 | CellTagsIndex->{} |

1098 | *) |

1099 | (*NotebookFileOutline |

1100 | Notebook[{ |

1101 | Cell[CellGroupData[{ |

1102 | Cell[579, 22, 134, 1, 148, "Title"], |

1103 | Cell[CellGroupData[{ |

1104 | Cell[738, 27, 36, 0, 44, "Subsection"], |

1105 | Cell[CellGroupData[{ |

1106 | Cell[799, 31, 95, 2, 28, "Input"], |

1107 | Cell[897, 35, 616, 13, 24, "Message"], |

1108 | Cell[1516, 50, 199, 3, 30, "Output"] |

1109 | }, Open ]], |

1110 | Cell[CellGroupData[{ |

1111 | Cell[1752, 58, 109, 2, 28, "Input"], |

1112 | Cell[CellGroupData[{ |

1113 | Cell[1886, 64, 2461, 65, 44, "Print"], |

1114 | Cell[4350, 131, 1202, 31, 25, "Print"], |

1115 | Cell[5555, 164, 331, 6, 26, "Print"], |

1116 | Cell[5889, 172, 345, 6, 26, "Print"] |

1117 | }, Open ]] |

1118 | }, Open ]] |

1119 | }, Open ]], |

1120 | Cell[CellGroupData[{ |

1121 | Cell[6295, 185, 35, 0, 44, "Subsection"], |

1122 | Cell[CellGroupData[{ |

1123 | Cell[6355, 189, 41, 0, 35, "Subsubsection"], |

1124 | Cell[6399, 191, 1192, 36, 148, "Input"] |

1125 | }, Open ]] |

1126 | }, Open ]], |

1127 | Cell[CellGroupData[{ |

1128 | Cell[7640, 233, 44, 0, 44, "Subsection"], |

1129 | Cell[CellGroupData[{ |

1130 | Cell[7709, 237, 2570, 69, 182, "Input"], |

1131 | Cell[10282, 308, 3319, 121, 52, "Output"] |

1132 | }, Open ]] |

1133 | }, Open ]], |

1134 | Cell[CellGroupData[{ |

1135 | Cell[13650, 435, 67, 0, 44, "Subsection"], |

1136 | Cell[CellGroupData[{ |

1137 | Cell[13742, 439, 1534, 45, 131, "Input"], |

1138 | Cell[15279, 486, 2896, 96, 76, "Output"] |

1139 | }, Open ]] |

1140 | }, Open ]], |

1141 | Cell[CellGroupData[{ |

1142 | Cell[18224, 588, 429, 7, 69, "Subsection"], |

1143 | Cell[18656, 597, 748, 12, 59, "Input"] |

1144 | }, Open ]], |

1145 | Cell[CellGroupData[{ |

1146 | Cell[19441, 614, 335, 6, 69, "Subsection"], |

1147 | Cell[19779, 622, 697, 23, 46, "Input"] |

1148 | }, Open ]], |

1149 | Cell[CellGroupData[{ |

1150 | Cell[20513, 650, 368, 7, 94, "Subsection"], |

1151 | Cell[20884, 659, 677, 19, 28, "Input"], |

1152 | Cell[21564, 680, 1720, 37, 63, "Input"], |

1153 | Cell[23287, 719, 91, 1, 28, "Input"] |

1154 | }, Open ]], |

1155 | Cell[CellGroupData[{ |

1156 | Cell[23415, 725, 160, 4, 69, "Subsection"], |

1157 | Cell[CellGroupData[{ |

1158 | Cell[23600, 733, 952, 27, 97, "Input"], |

1159 | Cell[24555, 762, 3019, 96, 76, "Output"] |

1160 | }, Open ]], |

1161 | Cell[CellGroupData[{ |

1162 | Cell[27611, 863, 653, 17, 28, "Input"], |

1163 | Cell[28267, 882, 3231, 97, 71, "Output"] |

1164 | }, Open ]], |

1165 | Cell[CellGroupData[{ |

1166 | Cell[31535, 984, 231, 5, 28, "Input"], |

1167 | Cell[31769, 991, 1608, 57, 53, "Output"] |

1168 | }, Open ]], |

1169 | Cell[33392, 1051, 26, 0, 28, "Input"], |

1170 | Cell[CellGroupData[{ |

1171 | Cell[33443, 1055, 632, 18, 46, "Input"], |

1172 | Cell[34078, 1075, 114, 2, 48, "Output"] |

1173 | }, Open ]] |

1174 | }, Open ]] |

1175 | }, Open ]] |

1176 | } |

1177 | ] |

1178 | *) |

1179 |