2HDMold: 2HDM.nb

File 2HDM.nb, 18.8 KB (added by degrande, 5 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:
10NotebookFileLineBreakTest
11NotebookFileLineBreakTest
12NotebookDataPosition[       145,          7]
13NotebookDataLength[     19040,        553]
14NotebookOptionsPosition[     15640,        436]
15NotebookOutlinePosition[     16020,        453]
16CellTagsIndexPosition[     15977,        450]
17WindowFrame->Normal*)
18
19(* Beginning of Notebook Content *)
20Notebook[{
21Cell[BoxData[
22 RowBox[{"$FeynRulesPath", "=",
23  RowBox[{"SetDirectory", "[", "\"\<< path >\>\"", "]"}]}]], "Input",
24 CellChangeTimes->{{3.41265862251538*^9, 3.412658649947229*^9}, {
25  3.423415585782702*^9, 3.423415597189939*^9}, {3.4234163173467493`*^9,
26  3.4234163227881193`*^9}, {3.4499828019723682`*^9, 3.449982827416329*^9}, {
27  3.449995896987596*^9, 3.44999590156848*^9}, {3.453787194669977*^9,
28  3.4537871987493134`*^9}}],
29
30Cell[BoxData[
31 RowBox[{"<<", "FeynRules`"}]], "Input"],
32
33Cell[BoxData[
34 RowBox[{
35  RowBox[{"SetDirectory", "[",
36   RowBox[{"<", " ",
37    RowBox[{"model", " ", "path"}], " ", ">"}], "]"}], ";"}]], "Input",
38 CellChangeTimes->{{3.419073170860696*^9, 3.419073182827229*^9}, {
39  3.449995977371011*^9, 3.449995977737762*^9}, {3.449996062058289*^9,
40  3.449996073803035*^9}, {3.45378721864566*^9, 3.453787221979855*^9}}],
41
42Cell[CellGroupData[{
43
44Cell["The generic Two Higgs Doublet model", "Title",
45 CellChangeTimes->{{3.453787246659294*^9, 3.453787254056096*^9}}],
46
47Cell["We first load in the model-file", "Text",
48 CellChangeTimes->{{3.4537872570726023`*^9, 3.4537872575282097`*^9}}],
49
50Cell[BoxData[
51 RowBox[{"LoadModel", "[", "\"\<2HDM.fr\>\"", "]"}]], "Input",
52 CellChangeTimes->{{3.4022069973481913`*^9, 3.402207011768662*^9},
53   3.4022081212072697`*^9, {3.402208250379383*^9, 3.402208254043104*^9},
54   3.4027466057480917`*^9, {3.403240270135737*^9, 3.403240277228945*^9},
55   3.403266503388291*^9, {3.403267649630335*^9, 3.40326765417397*^9}, {
56   3.403269919787421*^9, 3.403269921965273*^9}, {3.403347551273425*^9,
57   3.403347555049163*^9}, 3.4044490490588417`*^9, {3.411744339876704*^9,
58   3.411744340012457*^9}, {3.4121886924550533`*^9, 3.412188699157571*^9},
59   3.412188808811866*^9, 3.4121888580521603`*^9, {3.412450464077868*^9,
60   3.412450464378695*^9}, {3.413715097460478*^9, 3.41371509757642*^9}, {
61   3.41440825334604*^9, 3.414408254159686*^9}, {3.41862573831756*^9,
62   3.4186257392223186`*^9}, {3.4190731862389174`*^9, 3.419073187003003*^9}, {
63   3.419073336802393*^9, 3.4190733374513063`*^9}, {3.4190828041801767`*^9,
64   3.4190828048079023`*^9}, {3.449996078731757*^9, 3.449996080402082*^9}}],
65
66Cell[BoxData[
67 RowBox[{"LoadRestriction", "[", "\"\<HiggsBasis.rst\>\"", "]"}]], "Input",
68 CellChangeTimes->{{3.45378777192177*^9, 3.45378778546101*^9}}],
69
70Cell["We can now read in the param_card", "Text",
71 CellChangeTimes->{{3.454001066602683*^9, 3.454001072540792*^9}}],
72
73Cell[BoxData[
74 RowBox[{
75  RowBox[{"ReadLHAFile", "[",
76   RowBox[{"Input", "\[Rule]", "\"\<param_card_FR.dat\>\""}], "]"}],
77  ";"}]], "Input",
78 CellChangeTimes->{{3.454001077554552*^9, 3.454001091308895*^9}}],
79
80Cell[CellGroupData[{
81
82Cell["The Lagrangian", "Section",
83 CellChangeTimes->{{3.411910065227421*^9, 3.411910071535137*^9},
84   3.4537872736095467`*^9}],
85
86Cell["\<\
87The full Lagrangian in unitary gauge can be accessed immediatly via\
88\>", "Text",
89 CellChangeTimes->{{3.411910016771447*^9, 3.411910062087528*^9}, {
90  3.411910094087652*^9, 3.411910096590087*^9}, {3.411910215381351*^9,
91  3.4119102162371798`*^9}, {3.453787355523837*^9, 3.4537873558028727`*^9}}],
92
93Cell[BoxData["L2HDM"], "Input",
94 CellChangeTimes->{{3.411910106011015*^9, 3.411910106351081*^9}, {
95  3.4537873576279984`*^9, 3.453787359226983*^9}}],
96
97Cell[CellGroupData[{
98
99Cell["Gauge sector", "Subsubsection",
100 CellChangeTimes->{{3.4119102216473637`*^9, 3.411910224608881*^9}}],
101
102Cell["\<\
103The part of the lagrangian representing the gauge sector can be accessed via\
104\>", "Text",
105 CellChangeTimes->{{3.4119101255458603`*^9, 3.411910192225008*^9}, {
106  3.411910235813308*^9, 3.4119102509651337`*^9}}],
107
108Cell[BoxData["LGauge"], "Input",
109 CellChangeTimes->{{3.411910181169772*^9, 3.411910184667088*^9}}]
110}, Open  ]],
111
112Cell[CellGroupData[{
113
114Cell["Scalar sector", "Subsubsection",
115 CellChangeTimes->{{3.4119102216473637`*^9, 3.411910224608881*^9}, {
116  3.411910274288354*^9, 3.41191027703699*^9}}],
117
118Cell["\<\
119The part of the lagrangian representing the scalar sector can be accessed via\
120\
121\>", "Text",
122 CellChangeTimes->{{3.4119101255458603`*^9, 3.411910192225008*^9}, {
123  3.411910235813308*^9, 3.4119102509651337`*^9}, {3.41191028690167*^9,
124  3.411910287709094*^9}}],
125
126Cell[BoxData["LHiggs"], "Input",
127 CellChangeTimes->{{3.411910181169772*^9, 3.411910184667088*^9}, {
128  3.411910290186841*^9, 3.411910292005392*^9}}]
129}, Open  ]],
130
131Cell[CellGroupData[{
132
133Cell["Fermion sector", "Subsubsection",
134 CellChangeTimes->{{3.4119102216473637`*^9, 3.411910224608881*^9}, {
135  3.4119103528868923`*^9, 3.411910357404933*^9}}],
136
137Cell["\<\
138The part of the lagrangian representing the fermion sector can be accessed via\
139\>", "Text",
140 CellChangeTimes->{{3.4119101255458603`*^9, 3.411910192225008*^9}, {
141  3.411910235813308*^9, 3.4119102509651337`*^9}, {3.4119103873434134`*^9,
142  3.411910388077118*^9}}],
143
144Cell[BoxData["LFermions"], "Input",
145 CellChangeTimes->{{3.411910181169772*^9, 3.411910184667088*^9}, {
146  3.411910379677638*^9, 3.4119103807255*^9}}]
147}, Open  ]],
148
149Cell[CellGroupData[{
150
151Cell["Yukawa sector", "Subsubsection",
152 CellChangeTimes->{{3.4119102216473637`*^9, 3.411910224608881*^9}, {
153  3.411910393742139*^9, 3.411910394852953*^9}}],
154
155Cell["\<\
156The part of the lagrangian representing the Yukawa sector can be accessed via\
157\
158\>", "Text",
159 CellChangeTimes->{{3.4119101255458603`*^9, 3.411910192225008*^9}, {
160  3.411910235813308*^9, 3.4119102509651337`*^9}, {3.411910399061659*^9,
161  3.411910400421185*^9}}],
162
163Cell[BoxData["LYukawa"], "Input",
164 CellChangeTimes->{{3.411910181169772*^9, 3.411910184667088*^9}, {
165  3.4119104032372026`*^9, 3.411910404165523*^9}}]
166}, Open  ]],
167
168Cell[CellGroupData[{
169
170Cell["Feynman Gauge", "Subsection",
171 CellChangeTimes->{{3.411910080775518*^9, 3.41191008414785*^9}, {
172  3.411910431304595*^9, 3.41191043361451*^9}}],
173
174Cell["\<\
175By default, SM lagrangian is loaded in unitary gauge. However, Feynman gauge \
176for the QCD sector (required for CalcHep for example) can be obtained via \
177\>", "Text",
178 CellChangeTimes->{{3.411910440565042*^9, 3.411910480762147*^9}, {
179  3.4537873808489027`*^9, 3.453787415736421*^9}}],
180
181Cell[BoxData[
182 RowBox[{
183  RowBox[{"FeynmanGauge", "=", "True"}], ";"}]], "Input",
184 CellChangeTimes->{{3.411910487433539*^9, 3.4119104927114267`*^9}}],
185
186Cell["\<\
187The full lagrangian in Feynman gauge can be accessed immediatly via\
188\>", "Text",
189 CellChangeTimes->{{3.411910016771447*^9, 3.411910062087528*^9}, {
190  3.411910094087652*^9, 3.411910096590087*^9}, {3.411910215381351*^9,
191  3.4119102162371798`*^9}, {3.411910436148773*^9, 3.411910437013105*^9}}],
192
193Cell[BoxData["L2HDM"], "Input",
194 CellChangeTimes->{{3.411910106011015*^9, 3.411910106351081*^9}, {
195  3.4537873968568993`*^9, 3.453787398534165*^9}}],
196
197Cell[CellGroupData[{
198
199Cell["Ghost sector", "Subsubsection",
200 CellChangeTimes->{{3.4119102216473637`*^9, 3.411910224608881*^9}, {
201  3.411910393742139*^9, 3.411910394852953*^9}, {3.4119106057673063`*^9,
202  3.411910606397141*^9}}],
203
204Cell["\<\
205The part of the lagrangian representing the ghost sector can be accessed via\
206\>", "Text",
207 CellChangeTimes->{{3.4119101255458603`*^9, 3.411910192225008*^9}, {
208  3.411910235813308*^9, 3.4119102509651337`*^9}, {3.411910399061659*^9,
209  3.411910400421185*^9}, {3.4119106110136833`*^9, 3.411910611661195*^9}}],
210
211Cell[BoxData["LGhost"], "Input",
212 CellChangeTimes->{{3.411910181169772*^9, 3.411910184667088*^9}, {
213  3.4119104032372026`*^9, 3.411910404165523*^9}, {3.411910615100849*^9,
214  3.411910615781582*^9}}]
215}, Open  ]]
216}, Open  ]]
217}, Open  ]],
218
219Cell[CellGroupData[{
220
221Cell["Checking the Lagrangian", "Section",
222 CellChangeTimes->{{3.4234156496121893`*^9, 3.423415657027569*^9}}],
223
224Cell[BoxData[
225 RowBox[{
226  RowBox[{"FeynmanGauge", "=", "True"}], ";"}]], "Input",
227 CellChangeTimes->{{3.4234159280429783`*^9, 3.423415934798614*^9}}],
228
229Cell[CellGroupData[{
230
231Cell["Checking hermiticity", "Subsection",
232 CellChangeTimes->{{3.4234156831783743`*^9, 3.423415689540821*^9}}],
233
234Cell["The hermiticity of the Lagrangian can be checked via", "Text",
235 CellChangeTimes->{{3.423415694323595*^9, 3.423415707867804*^9}}],
236
237Cell[BoxData[
238 RowBox[{"CheckHermiticity", "[",
239  RowBox[{"L2HDM", ",",
240   RowBox[{"FlavorExpand", "\[Rule]", "SU2W"}]}], "]"}]], "Input",
241 CellChangeTimes->{{3.414763473002973*^9, 3.4147634845507174`*^9}, {
242  3.453787432047991*^9, 3.453787433215515*^9}}],
243
244Cell["\<\
245The same command can be applied to the flavor - expanded Lagrangian\
246\>", "Text",
247 CellChangeTimes->{{3.423415721582508*^9, 3.423415739787958*^9}}],
248
249Cell[BoxData[
250 RowBox[{"CheckHermiticity", "[",
251  RowBox[{"L2HDM", ",",
252   RowBox[{"FlavorExpand", "\[Rule]", "True"}]}], "]"}]], "Input",
253 CellChangeTimes->{{3.414763604111637*^9, 3.4147636044973803`*^9}, {
254  3.453787441615571*^9, 3.453787442614904*^9}}]
255}, Open  ]]
256}, Open  ]],
257
258Cell[CellGroupData[{
259
260Cell["Calculation of the Feynman rules", "Section",
261 CellChangeTimes->{{3.411910637332127*^9, 3.41191064360071*^9}}],
262
263Cell["\<\
264We will calculate now explicitly the Feynman rules for the 2HDM.\
265\>", "Text",
266 CellChangeTimes->{{3.41191064804084*^9, 3.411910672936666*^9}, {
267  3.453787483596156*^9, 3.453787484219084*^9}}],
268
269Cell[BoxData[
270 RowBox[{
271  RowBox[{"FeynmanGauge", "=", "False"}], ";"}]], "Input",
272 CellChangeTimes->{{3.411910674121689*^9, 3.4119106799564953`*^9}, {
273  3.4537874894123993`*^9, 3.453787489939929*^9}}],
274
275Cell[CellGroupData[{
276
277Cell["Gauge sector", "Subsection",
278 CellChangeTimes->{{3.411910690443768*^9, 3.411910692233274*^9}}],
279
280Cell[BoxData[
281 RowBox[{
282  RowBox[{"vertsGauge", "=",
283   RowBox[{"FeynmanRules", "[",
284    RowBox[{"LGauge", ",",
285     RowBox[{"FlavorExpand", "\[Rule]", "SU2W"}]}], "]"}]}], ";"}]], "Input",
286 CellChangeTimes->{
287  3.40274690437012*^9, {3.402746954727231*^9, 3.4027469691642714`*^9}, {
288   3.4032592998045692`*^9, 3.403259304564069*^9}, 3.403267976055098*^9, {
289   3.411910705212987*^9, 3.411910705553741*^9}, {3.423415993272615*^9,
290   3.42341600147605*^9}}]
291}, Open  ]],
292
293Cell[CellGroupData[{
294
295Cell["Higgs Sector", "Subsection",
296 CellChangeTimes->{3.404470070069872*^9}],
297
298Cell[BoxData[
299 RowBox[{
300  RowBox[{"vertsHiggs", "=",
301   RowBox[{"FeynmanRules", "[", "LHiggs", "]"}]}], ";"}]], "Input",
302 CellChangeTimes->{{3.411910728609757*^9, 3.41191072908109*^9}, {
303   3.423416009086747*^9, 3.423416012982971*^9}, 3.423416065626593*^9}]
304}, Open  ]],
305
306Cell[CellGroupData[{
307
308Cell["Matter sector", "Subsection"],
309
310Cell[BoxData[
311 RowBox[{
312  RowBox[{"vertsFermions", "=",
313   RowBox[{"FeynmanRules", "[", "LFermions", "]"}]}], ";"}]], "Input",
314 CellChangeTimes->{{3.402205118991502*^9, 3.4022051228508387`*^9},
315   3.402747846432675*^9, {3.4032613449872217`*^9, 3.403261349245253*^9}, {
316   3.403266977133403*^9, 3.4032669793125563`*^9}, {3.411910788644576*^9,
317   3.411910789233307*^9}, {3.423416034294303*^9, 3.423416042739814*^9}}]
318}, Open  ]],
319
320Cell[CellGroupData[{
321
322Cell["Yukawa sector", "Subsection"],
323
324Cell[BoxData[
325 RowBox[{
326  RowBox[{"vertsYukawa", "=",
327   RowBox[{"FeynmanRules", "[", "LYukawa", "]"}]}], ";"}]], "Input",
328 CellChangeTimes->{{3.403266987858165*^9, 3.4032670026080303`*^9}, {
329  3.411910826105542*^9, 3.411910826777452*^9}, {3.423416089772278*^9,
330  3.423416095643961*^9}, {3.453787609095393*^9, 3.4537876092341127`*^9}}]
331}, Open  ]]
332}, Open  ]],
333
334Cell[CellGroupData[{
335
336Cell["Outputs and interfaces", "Section",
337 CellChangeTimes->{
338  3.411910944409371*^9, {3.412185514054689*^9, 3.412185517014236*^9}}],
339
340Cell[CellGroupData[{
341
342Cell["FeynArts output", "Subsection",
343 CellChangeTimes->{{3.411911000132907*^9, 3.411911005135379*^9}}],
344
345Cell["The FeynArts output for the 2HDM can be obtained via", "Text",
346 CellChangeTimes->{{3.411910955110715*^9, 3.4119109690877657`*^9}, {
347  3.411911062212926*^9, 3.4119110634765463`*^9}, {3.453787639896587*^9,
348  3.4537876423355713`*^9}}],
349
350Cell[BoxData[
351 RowBox[{"WriteFeynArtsOutput", "[",
352  RowBox[{"LGauge", ",", "LHiggs", ",", "LFermions", ",", "LYukawa", ",",
353   RowBox[{"FlavorExpand", "\[Rule]", "SU2W"}]}], "]"}]], "Input",
354 CellChangeTimes->{{3.411911018354619*^9, 3.4119110196967573`*^9}, {
355   3.412185470680571*^9, 3.412185480912915*^9}, {3.41245048911446*^9,
356   3.4124504892674522`*^9}, 3.414315634453483*^9, {3.423416180751266*^9,
357   3.423416182892613*^9}, 3.453787647041366*^9}]
358}, Open  ]],
359
360Cell[CellGroupData[{
361
362Cell["Sherpa output", "Subsection",
363 CellChangeTimes->{{3.4119110460271273`*^9, 3.411911049405038*^9}}],
364
365Cell["The Sherpa output for the 2HDM can be obtained via", "Text",
366 CellChangeTimes->{{3.411910955110715*^9, 3.4119109690877657`*^9}, {
367  3.411911059590749*^9, 3.4119110601885567`*^9}, {3.453787690392329*^9,
368  3.4537876910312977`*^9}}],
369
370Cell[BoxData[
371 RowBox[{"WriteSHOutput", "[",
372  RowBox[{"LGauge", ",", "LHiggs", ",", "LFermions", ",", "LYukawa"}],
373  "]"}]], "Input",
374 CellChangeTimes->{{3.4119110943383636`*^9, 3.41191110054212*^9}, {
375   3.412185455856553*^9, 3.412185456628922*^9}, {3.4143156544792233`*^9,
376   3.414315668290971*^9}, {3.423416222700699*^9, 3.423416235756197*^9},
377   3.453787694328566*^9}]
378}, Open  ]],
379
380Cell[CellGroupData[{
381
382Cell["MadGraph output", "Subsection",
383 CellChangeTimes->{{3.4119110460271273`*^9, 3.411911049405038*^9}, {
384  3.411911131666554*^9, 3.411911135984398*^9}}],
385
386Cell["The MadGraph output for the 2HDM can be obtained via", "Text",
387 CellChangeTimes->{{3.411910955110715*^9, 3.4119109690877657`*^9}, {
388  3.411911059590749*^9, 3.4119110601885567`*^9}, {3.41191113897644*^9,
389  3.411911142024486*^9}, {3.45378770643867*^9, 3.453787706966777*^9}}],
390
391Cell[BoxData[
392 RowBox[{
393  RowBox[{"WriteMGOutput", "[",
394   RowBox[{"LGauge", ",", "LHiggs", ",", "LFermions", ",", "LYukawa"}], "]"}],
395   ";"}]], "Input",
396 CellChangeTimes->{{3.4119110943383636`*^9, 3.41191110054212*^9}, {
397   3.412185409690489*^9, 3.4121854352800217`*^9}, 3.453787697192544*^9}]
398}, Open  ]],
399
400Cell[CellGroupData[{
401
402Cell["CalcHep output", "Subsection",
403 CellChangeTimes->{{3.4119110460271273`*^9, 3.411911049405038*^9}, {
404  3.411911150323291*^9, 3.4119111515122623`*^9}}],
405
406Cell["\<\
407The CalcHep output for the 2HDM can be obtained via (Note that the QCD ghosts \
408are required in CalcHep!)\
409\>", "Text",
410 CellChangeTimes->{{3.411910955110715*^9, 3.4119109690877657`*^9}, {
411  3.411911059590749*^9, 3.4119110601885567`*^9}, {3.4119111540967712`*^9,
412  3.411911155096376*^9}, {3.4537877038388042`*^9, 3.45378773221243*^9}}],
413
414Cell[BoxData[{
415 RowBox[{
416  RowBox[{
417   RowBox[{"FeynmanGauge", "=", "True"}], ";"}],
418  "\[IndentingNewLine]"}], "\[IndentingNewLine]",
419 RowBox[{
420  RowBox[{"WriteCHOutput", "[",
421   RowBox[{
422   "LGauge", ",", "LHiggs", ",", "LFermions", ",", "LYukawa", ",", "LGhost",
423    ",",
424    RowBox[{"MaxExpressionLength", "\[Rule]", "800"}]}], "]"}],
425  ";"}]}], "Input",
426 CellChangeTimes->{{3.4119110943383636`*^9, 3.41191110054212*^9}, {
427   3.412185398898693*^9, 3.412185419919883*^9}, {3.414315699020526*^9,
428   3.41431570701153*^9}, 3.414315777726746*^9, {3.414316480328691*^9,
429   3.414316491307609*^9}, {3.4143165302100153`*^9, 3.414316531719597*^9},
430   3.423416262588552*^9, {3.453787700872117*^9, 3.453787701240477*^9}, {
431   3.45378773578975*^9, 3.453787756740387*^9}, {3.453788657465733*^9,
432   3.4537886587121067`*^9}, {3.453788732026514*^9, 3.453788732305941*^9}}]
433}, Open  ]]
434}, Open  ]]
435}, Open  ]]
436},
437WindowSize->{1280, 692},
438WindowMargins->{{0, Automatic}, {0, Automatic}},
439ShowSelection->True,
440Magnification->1.5,
441FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (November 10, 2008)",
442StyleDefinitions->"Default.nb"
443]
444(* End of Notebook Content *)
445
446(* Internal cache information *)
447(*CellTagsOutline
448CellTagsIndex->{}
449*)
450(*CellTagsIndex
451CellTagsIndex->{}
452*)
453(*NotebookFileOutline
454Notebook[{
455Cell[545, 20, 430, 7, 40, "Input"],
456Cell[978, 29, 54, 1, 40, "Input"],
457Cell[1035, 32, 358, 7, 40, "Input"],
458Cell[CellGroupData[{
459Cell[1418, 43, 118, 1, 114, "Title"],
460Cell[1539, 46, 117, 1, 39, "Text"],
461Cell[1659, 49, 1030, 14, 40, "Input"],
462Cell[2692, 65, 153, 2, 40, "Input"],
463Cell[2848, 69, 115, 1, 39, "Text"],
464Cell[2966, 72, 209, 5, 42, "Input"],
465Cell[CellGroupData[{
466Cell[3200, 81, 127, 2, 100, "Section"],
467Cell[3330, 85, 305, 5, 39, "Text"],
468Cell[3638, 92, 148, 2, 40, "Input"],
469Cell[CellGroupData[{
470Cell[3811, 98, 105, 1, 36, "Subsubsection"],
471Cell[3919, 101, 219, 4, 39, "Text"],
472Cell[4141, 107, 98, 1, 40, "Input"]
473}, Open  ]],
474Cell[CellGroupData[{
475Cell[4276, 113, 154, 2, 36, "Subsubsection"],
476Cell[4433, 117, 270, 6, 39, "Text"],
477Cell[4706, 125, 147, 2, 40, "Input"]
478}, Open  ]],
479Cell[CellGroupData[{
480Cell[4890, 132, 158, 2, 36, "Subsubsection"],
481Cell[5051, 136, 272, 5, 39, "Text"],
482Cell[5326, 143, 148, 2, 40, "Input"]
483}, Open  ]],
484Cell[CellGroupData[{
485Cell[5511, 150, 155, 2, 36, "Subsubsection"],
486Cell[5669, 154, 271, 6, 39, "Text"],
487Cell[5943, 162, 150, 2, 40, "Input"]
488}, Open  ]],
489Cell[CellGroupData[{
490Cell[6130, 169, 148, 2, 51, "Subsection"],
491Cell[6281, 173, 294, 5, 62, "Text"],
492Cell[6578, 180, 149, 3, 40, "Input"],
493Cell[6730, 185, 303, 5, 39, "Text"],
494Cell[7036, 192, 148, 2, 40, "Input"],
495Cell[CellGroupData[{
496Cell[7209, 198, 205, 3, 36, "Subsubsection"],
497Cell[7417, 203, 316, 5, 39, "Text"],
498Cell[7736, 210, 198, 3, 40, "Input"]
499}, Open  ]]
500}, Open  ]]
501}, Open  ]],
502Cell[CellGroupData[{
503Cell[7995, 220, 110, 1, 100, "Section"],
504Cell[8108, 223, 149, 3, 40, "Input"],
505Cell[CellGroupData[{
506Cell[8282, 230, 110, 1, 51, "Subsection"],
507Cell[8395, 233, 134, 1, 39, "Text"],
508Cell[8532, 236, 257, 5, 40, "Input"],
509Cell[8792, 243, 157, 3, 39, "Text"],
510Cell[8952, 248, 257, 5, 40, "Input"]
511}, Open  ]]
512}, Open  ]],
513Cell[CellGroupData[{
514Cell[9258, 259, 116, 1, 100, "Section"],
515Cell[9377, 262, 202, 4, 39, "Text"],
516Cell[9582, 268, 201, 4, 40, "Input"],
517Cell[CellGroupData[{
518Cell[9808, 276, 100, 1, 51, "Subsection"],
519Cell[9911, 279, 457, 10, 40, "Input"]
520}, Open  ]],
521Cell[CellGroupData[{
522Cell[10405, 294, 76, 1, 51, "Subsection"],
523Cell[10484, 297, 258, 5, 40, "Input"]
524}, Open  ]],
525Cell[CellGroupData[{
526Cell[10779, 307, 35, 0, 51, "Subsection"],
527Cell[10817, 309, 417, 7, 40, "Input"]
528}, Open  ]],
529Cell[CellGroupData[{
530Cell[11271, 321, 35, 0, 51, "Subsection"],
531Cell[11309, 323, 337, 6, 40, "Input"]
532}, Open  ]]
533}, Open  ]],
534Cell[CellGroupData[{
535Cell[11695, 335, 132, 2, 225, "Section"],
536Cell[CellGroupData[{
537Cell[11852, 341, 103, 1, 114, "Subsection"],
538Cell[11958, 344, 238, 3, 87, "Text"],
539Cell[12199, 349, 456, 7, 90, "Input"]
540}, Open  ]],
541Cell[CellGroupData[{
542Cell[12692, 361, 103, 1, 114, "Subsection"],
543Cell[12798, 364, 236, 3, 87, "Text"],
544Cell[13037, 369, 377, 7, 90, "Input"]
545}, Open  ]],
546Cell[CellGroupData[{
547Cell[13451, 381, 154, 2, 114, "Subsection"],
548Cell[13608, 385, 280, 3, 87, "Text"],
549Cell[13891, 390, 296, 6, 90, "Input"]
550}, Open  ]],
551Cell[CellGroupData[{
552Cell[14224, 401, 155, 2, 114, "Subsection"],
553Cell[14382, 405, 346, 6, 87, "Text"],
554Cell[14731, 413, 869, 18, 195, "Input"]
555}, Open  ]]
556}, Open  ]]
557}, Open  ]]
558}
559]
560*)
561
562(* End of internal cache information *)