# WAsymm: WDecay.nb

File WDecay.nb, 14.5 KB (added by anonymous, 7 years ago) |
---|

Line | |
---|---|

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

2 | |

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

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

5 | |

6 | (* CreatedBy='Mathematica 6.0' *) |

7 | |

8 | (*CacheID: 234*) |

9 | (* Internal cache information: |

10 | NotebookFileLineBreakTest |

11 | NotebookFileLineBreakTest |

12 | NotebookDataPosition[ 145, 7] |

13 | NotebookDataLength[ 14703, 517] |

14 | NotebookOptionsPosition[ 12682, 441] |

15 | NotebookOutlinePosition[ 13040, 457] |

16 | CellTagsIndexPosition[ 12997, 454] |

17 | WindowFrame->Normal |

18 | ContainsDynamic->False*) |

19 | |

20 | (* Beginning of Notebook Content *) |

21 | Notebook[{ |

22 | |

23 | Cell[CellGroupData[{ |

24 | Cell[TextData[{ |

25 | "Calculation for ", |

26 | StyleBox[" ", "DisplayFormula"], |

27 | Cell[BoxData[ |

28 | FormBox[ |

29 | SuperscriptBox["W", "+"], TraditionalForm]]], |

30 | StyleBox["\[RightArrow] ", "DisplayFormula"], |

31 | Cell[BoxData[ |

32 | FormBox[ |

33 | SuperscriptBox["e", "+"], TraditionalForm]]], |

34 | " ", |

35 | Cell[BoxData[ |

36 | FormBox[ |

37 | SubscriptBox["\[Nu]", "e"], TraditionalForm]]] |

38 | }], "Title", |

39 | CellChangeTimes->{{3.42892672627883*^9, 3.428926824323577*^9}}], |

40 | |

41 | Cell[CellGroupData[{ |

42 | |

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

44 | |

45 | Cell[BoxData[ |

46 | RowBox[{ |

47 | RowBox[{"<<", "HighEnergyPhysics`fc`"}], ";"}]], "Input"] |

48 | }, Closed]], |

49 | |

50 | Cell[CellGroupData[{ |

51 | |

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

53 | |

54 | Cell[CellGroupData[{ |

55 | |

56 | Cell["Kinematics 1->2", "Subsubsection", |

57 | CellChangeTimes->{{3.428926835790217*^9, 3.428926837886043*^9}}], |

58 | |

59 | Cell[BoxData[ |

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

61 | RowBox[{ |

62 | RowBox[{ |

63 | RowBox[{ |

64 | RowBox[{"ScalarProduct", "[", |

65 | RowBox[{"P", ",", "P"}], "]"}], "=", "mw2"}], ";"}], |

66 | "\[IndentingNewLine]", |

67 | RowBox[{ |

68 | RowBox[{ |

69 | RowBox[{"ScalarProduct", "[", |

70 | RowBox[{"pe", ",", "pe"}], "]"}], "=", "0"}], ";"}], |

71 | "\[IndentingNewLine]", |

72 | RowBox[{ |

73 | RowBox[{ |

74 | RowBox[{"ScalarProduct", "[", |

75 | RowBox[{"p\[Nu]", ",", "p\[Nu]"}], "]"}], "=", "0"}], ";"}], |

76 | "\[IndentingNewLine]", |

77 | RowBox[{ |

78 | RowBox[{ |

79 | RowBox[{"ScalarProduct", "[", |

80 | RowBox[{"P", ",", "pe"}], "]"}], "=", |

81 | RowBox[{"mw2", "/", "2"}]}], ";"}], "\[IndentingNewLine]", |

82 | RowBox[{ |

83 | RowBox[{ |

84 | RowBox[{"ScalarProduct", "[", |

85 | RowBox[{"P", ",", "p\[Nu]"}], "]"}], "=", |

86 | RowBox[{"mw2", "/", "2"}]}], ";"}], "\[IndentingNewLine]", |

87 | RowBox[{ |

88 | RowBox[{ |

89 | RowBox[{"ScalarProduct", "[", |

90 | RowBox[{"pe", ",", "p\[Nu]"}], "]"}], "=", |

91 | RowBox[{"mw2", "/", "2"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input", |

92 | CellChangeTimes->{{3.4289268403011503`*^9, 3.428926946965074*^9}}] |

93 | }, Open ]] |

94 | }, Closed]], |

95 | |

96 | Cell[CellGroupData[{ |

97 | |

98 | Cell["Amplitude (1 diagram)", "Subsection", |

99 | CellChangeTimes->{{3.4289292421393127`*^9, 3.428929244675111*^9}}], |

100 | |

101 | Cell["The summed and averaged square matrix element", "Text", |

102 | CellChangeTimes->{{3.4289271420095243`*^9, 3.4289271454722757`*^9}, { |

103 | 3.4289273354903717`*^9, 3.428927351049911*^9}, {3.4289275105378*^9, |

104 | 3.42892751343362*^9}}], |

105 | |

106 | Cell[CellGroupData[{ |

107 | |

108 | Cell[BoxData[ |

109 | RowBox[{"M2", "=", |

110 | RowBox[{ |

111 | RowBox[{"1", "/", "3"}], |

112 | RowBox[{ |

113 | RowBox[{"(", |

114 | RowBox[{ |

115 | RowBox[{"gw", "/", "2"}], "/", |

116 | RowBox[{"Sqrt", "[", "2", "]"}]}], ")"}], "^", "2"}], |

117 | RowBox[{"Tr", "[", |

118 | RowBox[{ |

119 | RowBox[{"GSD", "[", "pe", "]"}], ".", |

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

121 | RowBox[{"(", |

122 | RowBox[{"1", "-", "GA5"}], ")"}], ".", |

123 | RowBox[{"GSD", "[", "p\[Nu]", "]"}], ".", |

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

125 | RowBox[{"(", |

126 | RowBox[{"1", "-", "GA5"}], ")"}]}], "]"}], |

127 | RowBox[{"(", |

128 | RowBox[{ |

129 | RowBox[{"-", |

130 | RowBox[{"MetricTensor", "[", |

131 | RowBox[{"mu", ",", "nu"}], "]"}]}], "+", |

132 | RowBox[{ |

133 | RowBox[{"FV", "[", |

134 | RowBox[{"P", ",", "mu"}], "]"}], |

135 | RowBox[{ |

136 | RowBox[{"FV", "[", |

137 | RowBox[{"P", ",", "nu"}], "]"}], "/", "mw2"}]}]}], ")"}]}]}]], "Input",\ |

138 | |

139 | CellChangeTimes->{{3.428927033246361*^9, 3.4289271401967373`*^9}, { |

140 | 3.42892727787171*^9, 3.428927413135103*^9}, {3.4289274432481937`*^9, |

141 | 3.4289274930463*^9}, {3.428929121395401*^9, 3.428929122088388*^9}, |

142 | 3.428929375657975*^9, {3.428929541763723*^9, 3.428929566521463*^9}}], |

143 | |

144 | Cell[BoxData[ |

145 | FormBox[ |

146 | RowBox[{ |

147 | FractionBox["1", "6"], " ", |

148 | SuperscriptBox["gw", "2"], " ", |

149 | RowBox[{"(", |

150 | RowBox[{ |

151 | FractionBox[ |

152 | RowBox[{ |

153 | SuperscriptBox["P", "mu"], " ", |

154 | SuperscriptBox["P", "nu"]}], "mw2"], "-", |

155 | SuperscriptBox["g", |

156 | RowBox[{"mu", "nu"}]]}], ")"}], " ", |

157 | RowBox[{"(", |

158 | RowBox[{ |

159 | RowBox[{ |

160 | RowBox[{"-", "2"}], " ", "\[ImaginaryI]", " ", |

161 | SuperscriptBox["\[Epsilon]", |

162 | RowBox[{ |

163 | FormBox[ |

164 | FormBox["mu", |

165 | TraditionalForm], |

166 | TraditionalForm], |

167 | FormBox[ |

168 | FormBox["nu", |

169 | TraditionalForm], |

170 | TraditionalForm], |

171 | FormBox["pe", |

172 | TraditionalForm], |

173 | FormBox["p\[Nu]", |

174 | TraditionalForm]}]]}], "-", |

175 | RowBox[{"mw2", " ", |

176 | SuperscriptBox["g", |

177 | RowBox[{"mu", "nu"}]]}], "+", |

178 | RowBox[{"2", " ", |

179 | SuperscriptBox[ |

180 | FormBox["p\[Nu]", |

181 | TraditionalForm], |

182 | FormBox[ |

183 | FormBox["mu", |

184 | TraditionalForm], |

185 | TraditionalForm]], " ", |

186 | SuperscriptBox[ |

187 | FormBox["pe", |

188 | TraditionalForm], |

189 | FormBox[ |

190 | FormBox["nu", |

191 | TraditionalForm], |

192 | TraditionalForm]]}], "+", |

193 | RowBox[{"2", " ", |

194 | SuperscriptBox[ |

195 | FormBox["pe", |

196 | TraditionalForm], |

197 | FormBox[ |

198 | FormBox["mu", |

199 | TraditionalForm], |

200 | TraditionalForm]], " ", |

201 | SuperscriptBox[ |

202 | FormBox["p\[Nu]", |

203 | TraditionalForm], |

204 | FormBox[ |

205 | FormBox["nu", |

206 | TraditionalForm], |

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

208 | CellChangeTimes->{ |

209 | 3.4289272789512367`*^9, 3.428927318445057*^9, {3.4289273534290743`*^9, |

210 | 3.428927404797317*^9}, {3.4289274516566753`*^9, 3.42892749447148*^9}, |

211 | 3.4289291227183*^9, {3.428929370895793*^9, 3.428929376751039*^9}, |

212 | 3.428929567605669*^9, 3.428938985716309*^9}] |

213 | }, Open ]], |

214 | |

215 | Cell["We contract the Lorentz indices", "Text", |

216 | CellChangeTimes->{{3.428927497453924*^9, 3.428927503026804*^9}}], |

217 | |

218 | Cell[CellGroupData[{ |

219 | |

220 | Cell[BoxData[ |

221 | RowBox[{"M2", "=", |

222 | RowBox[{"Contract", "[", "M2", "]"}]}]], "Input", |

223 | CellChangeTimes->{{3.428927540707325*^9, 3.42892754927673*^9}}], |

224 | |

225 | Cell[BoxData[ |

226 | FormBox[ |

227 | FractionBox[ |

228 | RowBox[{ |

229 | SuperscriptBox["gw", "2"], " ", "mw2"}], "3"], TraditionalForm]], "Output",\ |

230 | |

231 | CellChangeTimes->{3.428927549552278*^9, 3.4289291245462008`*^9, |

232 | 3.4289293726684103`*^9, 3.428929569719249*^9, 3.428938985747068*^9}] |

233 | }, Open ]], |

234 | |

235 | Cell["We insert he definition of the Fermi constant", "Text", |

236 | CellChangeTimes->{{3.428927552171399*^9, 3.428927561923086*^9}}], |

237 | |

238 | Cell[CellGroupData[{ |

239 | |

240 | Cell[BoxData[ |

241 | RowBox[{"M2", "=", |

242 | RowBox[{"M2", "/.", |

243 | RowBox[{ |

244 | RowBox[{"gw", "^", "2"}], "\[Rule]", |

245 | RowBox[{"8", " ", "mw2", " ", |

246 | RowBox[{"Gf", "/", |

247 | RowBox[{"Sqrt", "[", "2", "]"}]}]}]}]}]}]], "Input", |

248 | CellChangeTimes->{{3.428927568404044*^9, 3.42892758705121*^9}}], |

249 | |

250 | Cell[BoxData[ |

251 | FormBox[ |

252 | RowBox[{ |

253 | FractionBox["4", "3"], " ", |

254 | SqrtBox["2"], " ", "Gf", " ", |

255 | SuperscriptBox["mw2", "2"]}], TraditionalForm]], "Output", |

256 | CellChangeTimes->{3.428927588058874*^9, 3.4289291256255703`*^9, |

257 | 3.428929571106011*^9, 3.428938985780642*^9}] |

258 | }, Open ]] |

259 | }, Closed]], |

260 | |

261 | Cell[CellGroupData[{ |

262 | |

263 | Cell["Phase Space", "Subsection", |

264 | CellChangeTimes->{{3.4289292202493353`*^9, 3.428929221917066*^9}}], |

265 | |

266 | Cell["The massless two particle phase space is", "Text", |

267 | CellChangeTimes->{{3.4289286541859837`*^9, 3.428928662992796*^9}}], |

268 | |

269 | Cell[CellGroupData[{ |

270 | |

271 | Cell[BoxData[ |

272 | RowBox[{"d\[CapitalPhi]2", "=", |

273 | RowBox[{ |

274 | RowBox[{ |

275 | RowBox[{"(", |

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

277 | RowBox[{"\[Delta]", "[", |

278 | RowBox[{"P", "-", "pe", "-", "p\[Nu]"}], "]"}], |

279 | RowBox[{ |

280 | RowBox[{ |

281 | RowBox[{"d3pe", "/", |

282 | RowBox[{ |

283 | RowBox[{"(", |

284 | RowBox[{"2", "Pi"}], ")"}], "^", "3"}]}], "/", "2"}], "/", "Ee"}], |

285 | " ", |

286 | RowBox[{ |

287 | RowBox[{ |

288 | RowBox[{"d3p\[Nu]", "/", |

289 | RowBox[{ |

290 | RowBox[{"(", |

291 | RowBox[{"2", "Pi"}], ")"}], "^", "3"}]}], "/", "2"}], "/", |

292 | "E\[Nu]"}]}]}]], "Input", |

293 | CellChangeTimes->{{3.428928668808182*^9, 3.428928748243292*^9}, { |

294 | 3.4289288594542103`*^9, 3.428928869884198*^9}}], |

295 | |

296 | Cell[BoxData[ |

297 | FormBox[ |

298 | FractionBox[ |

299 | RowBox[{"d3pe", " ", "d3p\[Nu]", " ", |

300 | RowBox[{"\[Delta]", "(", |

301 | RowBox[{"P", "-", "pe", "-", "p\[Nu]"}], ")"}]}], |

302 | RowBox[{"16", " ", "Ee", " ", "E\[Nu]", " ", |

303 | SuperscriptBox["\[Pi]", "2"]}]], TraditionalForm]], "Output", |

304 | CellChangeTimes->{{3.428928862716354*^9, 3.428928870072042*^9}, |

305 | 3.428929126861431*^9, 3.428929574710586*^9, 3.428938985810316*^9}] |

306 | }, Open ]], |

307 | |

308 | Cell["\<\ |

309 | Performing the integration over d3p\[Nu] in the rest frame of the W gives\ |

310 | \>", "Text", |

311 | CellChangeTimes->{{3.428928749821361*^9, 3.428928784904477*^9}, { |

312 | 3.4289288233373938`*^9, 3.428928824472897*^9}}], |

313 | |

314 | Cell[CellGroupData[{ |

315 | |

316 | Cell[BoxData[ |

317 | RowBox[{"PS", "=", |

318 | RowBox[{ |

319 | RowBox[{ |

320 | RowBox[{"1", "/", "4"}], "/", |

321 | RowBox[{ |

322 | RowBox[{"(", |

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

324 | RowBox[{"\[Delta]", "[", |

325 | RowBox[{"mw", "-", |

326 | RowBox[{"2", "Ee"}]}], "]"}], |

327 | RowBox[{"d3pe", "/", |

328 | RowBox[{"Ee", "^", "2"}]}]}]}]], "Input", |

329 | CellChangeTimes->{{3.4289287922794847`*^9, 3.4289288819309*^9}}], |

330 | |

331 | Cell[BoxData[ |

332 | FormBox[ |

333 | FractionBox[ |

334 | RowBox[{"d3pe", " ", |

335 | RowBox[{"\[Delta]", "(", |

336 | RowBox[{"mw", "-", |

337 | RowBox[{"2", " ", "Ee"}]}], ")"}]}], |

338 | RowBox[{"16", " ", |

339 | SuperscriptBox["Ee", "2"], " ", |

340 | SuperscriptBox["\[Pi]", "2"]}]], TraditionalForm]], "Output", |

341 | CellChangeTimes->{{3.428928849656254*^9, 3.428928882523725*^9}, |

342 | 3.428929068231016*^9, 3.428929127845537*^9, 3.428929574829381*^9, |

343 | 3.428938985844248*^9}] |

344 | }, Open ]], |

345 | |

346 | Cell["\<\ |

347 | Going to spherical coordinates, and usging pe dpe = Ee dEe, we get\ |

348 | \>", "Text", |

349 | CellChangeTimes->{{3.428928883567082*^9, 3.4289289264749002`*^9}}], |

350 | |

351 | Cell[CellGroupData[{ |

352 | |

353 | Cell[BoxData[ |

354 | RowBox[{"PS", "=", |

355 | RowBox[{ |

356 | RowBox[{"PS", "/.", |

357 | RowBox[{ |

358 | RowBox[{"\[Delta]", "[", |

359 | RowBox[{"mw", "-", |

360 | RowBox[{"2", "Ee"}]}], "]"}], "\[Rule]", |

361 | RowBox[{ |

362 | RowBox[{"1", "/", "2"}], |

363 | RowBox[{"\[Delta]", "[", |

364 | RowBox[{"Ee", "-", |

365 | RowBox[{"mw", "/", "2"}]}], "]"}]}]}]}], "/.", " ", |

366 | RowBox[{"d3pe", "\[Rule]", |

367 | RowBox[{"4", "Pi", " ", |

368 | RowBox[{"Ee", "^", "2"}], " ", "dEe"}]}]}]}]], "Input", |

369 | CellChangeTimes->{{3.4289289441444197`*^9, 3.428929022421103*^9}, |

370 | 3.428929070151713*^9}], |

371 | |

372 | Cell[BoxData[ |

373 | FormBox[ |

374 | FractionBox[ |

375 | RowBox[{"dEe", " ", |

376 | RowBox[{"\[Delta]", "(", |

377 | RowBox[{"Ee", "-", |

378 | FractionBox["mw", "2"]}], ")"}]}], |

379 | RowBox[{"8", " ", "\[Pi]"}]], TraditionalForm]], "Output", |

380 | CellChangeTimes->{3.428929025150517*^9, 3.428929070325218*^9, |

381 | 3.4289291311060667`*^9, 3.428929574875102*^9, 3.4289389858778963`*^9}] |

382 | }, Open ]], |

383 | |

384 | Cell["Performing the integration", "Text", |

385 | CellChangeTimes->{{3.428929031938621*^9, 3.428929037282918*^9}}], |

386 | |

387 | Cell[CellGroupData[{ |

388 | |

389 | Cell[BoxData[ |

390 | RowBox[{"PS", "=", |

391 | RowBox[{"PS", "/.", |

392 | RowBox[{ |

393 | RowBox[{"dEe", " ", |

394 | RowBox[{"\[Delta]", "[", |

395 | RowBox[{"Ee", "-", |

396 | RowBox[{"mw", "/", "2"}]}], "]"}]}], "\[Rule]", "1"}]}]}]], "Input", |

397 | CellChangeTimes->{{3.428929044586605*^9, 3.428929056603554*^9}}], |

398 | |

399 | Cell[BoxData[ |

400 | FormBox[ |

401 | FractionBox["1", |

402 | RowBox[{"8", " ", "\[Pi]"}]], TraditionalForm]], "Output", |

403 | CellChangeTimes->{{3.428929056861126*^9, 3.428929071114458*^9}, |

404 | 3.4289291321148567`*^9, 3.428929574912538*^9, 3.4289389861836767`*^9}] |

405 | }, Open ]] |

406 | }, Closed]], |

407 | |

408 | Cell[CellGroupData[{ |

409 | |

410 | Cell["Result", "Subsection", |

411 | CellChangeTimes->{{3.4289292627868023`*^9, 3.4289292633475027`*^9}}], |

412 | |

413 | Cell["The decay rate of the W then becomes", "Text", |

414 | CellChangeTimes->{{3.428929073874954*^9, 3.428929081291203*^9}}], |

415 | |

416 | Cell[CellGroupData[{ |

417 | |

418 | Cell[BoxData[ |

419 | RowBox[{"\[CapitalGamma]", "=", |

420 | RowBox[{ |

421 | RowBox[{ |

422 | RowBox[{ |

423 | RowBox[{"1", "/", "2"}], "/", "mw"}], " ", "PS", " ", "M2"}], "/.", |

424 | RowBox[{"mw2", "\[Rule]", |

425 | RowBox[{"mw", "^", "2"}]}]}]}]], "Input", |

426 | CellChangeTimes->{{3.428929087038114*^9, 3.428929107627933*^9}, |

427 | 3.428929346599481*^9, 3.428938975232931*^9}], |

428 | |

429 | Cell[BoxData[ |

430 | FormBox[ |

431 | FractionBox[ |

432 | RowBox[{"Gf", " ", |

433 | SuperscriptBox["mw", "3"]}], |

434 | RowBox[{"6", " ", |

435 | SqrtBox["2"], " ", "\[Pi]"}]], TraditionalForm]], "Output", |

436 | CellChangeTimes->{{3.428929108658009*^9, 3.428929133003119*^9}, |

437 | 3.4289293476527367`*^9, 3.4289295771229353`*^9, 3.428938986228635*^9}] |

438 | }, Open ]] |

439 | }, Closed]] |

440 | }, Open ]] |

441 | }, |

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

443 | WindowMargins->{{Automatic, 230}, {Automatic, 4}}, |

444 | ShowSelection->True, |

445 | FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (April 20, 2007)", |

446 | StyleDefinitions->"Default.nb" |

447 | ] |

448 | (* End of Notebook Content *) |

449 | |

450 | (* Internal cache information *) |

451 | (*CellTagsOutline |

452 | CellTagsIndex->{} |

453 | *) |

454 | (*CellTagsIndex |

455 | CellTagsIndex->{} |

456 | *) |

457 | (*NotebookFileOutline |

458 | Notebook[{ |

459 | Cell[CellGroupData[{ |

460 | Cell[590, 23, 427, 15, 79, "Title"], |

461 | Cell[CellGroupData[{ |

462 | Cell[1042, 42, 36, 0, 34, "Subsection"], |

463 | Cell[1081, 44, 83, 2, 27, "Input"] |

464 | }, Closed]], |

465 | Cell[CellGroupData[{ |

466 | Cell[1201, 51, 35, 0, 26, "Subsection"], |

467 | Cell[CellGroupData[{ |

468 | Cell[1261, 55, 106, 1, 25, "Subsubsection"], |

469 | Cell[1370, 58, 1112, 33, 133, "Input"] |

470 | }, Open ]] |

471 | }, Closed]], |

472 | Cell[CellGroupData[{ |

473 | Cell[2531, 97, 111, 1, 26, "Subsection"], |

474 | Cell[2645, 100, 228, 3, 26, "Text"], |

475 | Cell[CellGroupData[{ |

476 | Cell[2898, 107, 1191, 34, 43, "Input"], |

477 | Cell[4092, 143, 1924, 68, 70, "Output"] |

478 | }, Open ]], |

479 | Cell[6031, 214, 113, 1, 26, "Text"], |

480 | Cell[CellGroupData[{ |

481 | Cell[6169, 219, 151, 3, 27, "Input"], |

482 | Cell[6323, 224, 269, 7, 70, "Output"] |

483 | }, Open ]], |

484 | Cell[6607, 234, 127, 1, 26, "Text"], |

485 | Cell[CellGroupData[{ |

486 | Cell[6759, 239, 295, 8, 27, "Input"], |

487 | Cell[7057, 249, 275, 7, 70, "Output"] |

488 | }, Open ]] |

489 | }, Closed]], |

490 | Cell[CellGroupData[{ |

491 | Cell[7381, 262, 101, 1, 26, "Subsection"], |

492 | Cell[7485, 265, 124, 1, 26, "Text"], |

493 | Cell[CellGroupData[{ |

494 | Cell[7634, 270, 696, 23, 27, "Input"], |

495 | Cell[8333, 295, 417, 9, 70, "Output"] |

496 | }, Open ]], |

497 | Cell[8765, 307, 214, 4, 26, "Text"], |

498 | Cell[CellGroupData[{ |

499 | Cell[9004, 315, 404, 13, 27, "Input"], |

500 | Cell[9411, 330, 450, 12, 70, "Output"] |

501 | }, Open ]], |

502 | Cell[9876, 345, 158, 3, 26, "Text"], |

503 | Cell[CellGroupData[{ |

504 | Cell[10059, 352, 569, 17, 27, "Input"], |

505 | Cell[10631, 371, 358, 9, 70, "Output"] |

506 | }, Open ]], |

507 | Cell[11004, 383, 108, 1, 26, "Text"], |

508 | Cell[CellGroupData[{ |

509 | Cell[11137, 388, 293, 8, 27, "Input"], |

510 | Cell[11433, 398, 245, 5, 70, "Output"] |

511 | }, Open ]] |

512 | }, Closed]], |

513 | Cell[CellGroupData[{ |

514 | Cell[11727, 409, 98, 1, 26, "Subsection"], |

515 | Cell[11828, 412, 118, 1, 26, "Text"], |

516 | Cell[CellGroupData[{ |

517 | Cell[11971, 417, 347, 9, 27, "Input"], |

518 | Cell[12321, 428, 321, 8, 52, "Output"] |

519 | }, Open ]] |

520 | }, Closed]] |

521 | }, Open ]] |

522 | } |

523 | ] |

524 | *) |

525 | |

526 | (* End of internal cache information *) |