Tt: TDecay.nb

File TDecay.nb, 21.7 KB (added by (none), 13 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[ 22013, 705]
14NotebookOptionsPosition[ 19831, 624]
15NotebookOutlinePosition[ 20189, 640]
16CellTagsIndexPosition[ 20146, 637]
17WindowFrame->Normal
18ContainsDynamic->False*)
19
20(* Beginning of Notebook Content *)
21Notebook[{
22
23Cell[CellGroupData[{
24Cell["\<\
25Tree-level decays of the top quark\
26\>", "Title",
27 CellChangeTimes->{{3.42892672627883*^9, 3.428926824323577*^9}, {
28 3.428937703319875*^9, 3.428937712432496*^9}, {3.4289403678900433`*^9,
29 3.428940370752344*^9}}],
30
31Cell[CellGroupData[{
32
33Cell["Input FeynCalc", "Subsection"],
34
35Cell[BoxData[
36 RowBox[{
37 RowBox[{"<<", "HighEnergyPhysics`fc`"}], ";"}]], "Input"]
38}, Open ]],
39
40Cell[CellGroupData[{
41
42Cell["t \[RightArrow] bW", "Section",
43 CellChangeTimes->{{3.4289377207239313`*^9, 3.428937731049849*^9}, {
44 3.428940376434594*^9, 3.428940384134904*^9}}],
45
46Cell[CellGroupData[{
47
48Cell["Kinematics 1->2", "Subsection",
49 CellChangeTimes->{{3.428926835790217*^9, 3.428926837886043*^9}}],
50
51Cell[BoxData[
52 RowBox[{"\[IndentingNewLine]",
53 RowBox[{
54 RowBox[{
55 RowBox[{
56 RowBox[{"ScalarProduct", "[",
57 RowBox[{"pt", ",", "pt"}], "]"}], "=",
58 RowBox[{"mt", "^", "2"}]}], ";"}], "\[IndentingNewLine]",
59 RowBox[{
60 RowBox[{
61 RowBox[{"ScalarProduct", "[",
62 RowBox[{"pb", ",", "pb"}], "]"}], "=", "0"}], ";"}],
63 "\[IndentingNewLine]",
64 RowBox[{
65 RowBox[{
66 RowBox[{"ScalarProduct", "[",
67 RowBox[{"pw", ",", "pw"}], "]"}], "=",
68 RowBox[{"mw", "^", "2"}]}], ";"}], "\[IndentingNewLine]",
69 RowBox[{
70 RowBox[{
71 RowBox[{"ScalarProduct", "[",
72 RowBox[{"pt", ",", "pb"}], "]"}], "=",
73 RowBox[{
74 RowBox[{
75 RowBox[{"mt", "^", "2"}], "/", "2"}], "-",
76 RowBox[{
77 RowBox[{"mw", "^", "2"}], "/", "2"}]}]}], ";"}], "\[IndentingNewLine]",
78
79 RowBox[{
80 RowBox[{
81 RowBox[{"ScalarProduct", "[",
82 RowBox[{"pt", ",", "pw"}], "]"}], "=",
83 RowBox[{
84 RowBox[{
85 RowBox[{"mt", "^", "2"}], "/", "2"}], "+",
86 RowBox[{
87 RowBox[{"mw", "^", "2"}], "/", "2"}]}]}], ";"}], "\[IndentingNewLine]",
88
89 RowBox[{
90 RowBox[{
91 RowBox[{"ScalarProduct", "[",
92 RowBox[{"pb", ",", "pw"}], "]"}], "=",
93 RowBox[{
94 RowBox[{
95 RowBox[{"mt", "^", "2"}], "/", "2"}], "-",
96 RowBox[{
97 RowBox[{"mw", "^", "2"}], "/", "2"}]}]}], ";"}],
98 "\[IndentingNewLine]"}]}]], "Input",
99 CellChangeTimes->{{3.4289268403011503`*^9, 3.428926946965074*^9}, {
100 3.428937810100576*^9, 3.428937873020487*^9}, {3.428938071207912*^9,
101 3.428938078071608*^9}, {3.428938213984881*^9, 3.428938224130307*^9}, {
102 3.4289384819556913`*^9, 3.428938484248788*^9}, {3.428939959216198*^9,
103 3.428939982716838*^9}, {3.4289400233100157`*^9, 3.428940028333314*^9}, {
104 3.428940095373877*^9, 3.428940115206889*^9}, {3.4289403078974743`*^9,
105 3.428940317454282*^9}, {3.4289403562310753`*^9, 3.428940356350072*^9}}]
106}, Open ]],
107
108Cell[CellGroupData[{
109
110Cell["Amplitude (1 diagram)", "Subsection",
111 CellChangeTimes->{{3.4289292421393127`*^9, 3.428929244675111*^9}}],
112
113Cell["The summed and averaged square matrix element", "Text",
114 CellChangeTimes->{{3.4289271420095243`*^9, 3.4289271454722757`*^9}, {
115 3.4289273354903717`*^9, 3.428927351049911*^9}, {3.4289275105378*^9,
116 3.42892751343362*^9}}],
117
118Cell[CellGroupData[{
119
120Cell[BoxData[
121 RowBox[{"M2", "=",
122 RowBox[{
123 RowBox[{"1", "/", "2"}],
124 RowBox[{
125 RowBox[{"(",
126 RowBox[{
127 RowBox[{"gw", "/", "2"}], "/",
128 RowBox[{"Sqrt", "[", "2", "]"}]}], ")"}], "^", "2"}], "Vtb2", " ",
129 RowBox[{"(",
130 RowBox[{
131 RowBox[{"-",
132 RowBox[{"MetricTensor", "[",
133 RowBox[{"mu", ",", "nu"}], "]"}]}], "+",
134 RowBox[{
135 RowBox[{"FV", "[",
136 RowBox[{"pw", ",", "mu"}], "]"}],
137 RowBox[{
138 RowBox[{"FV", "[",
139 RowBox[{"pw", ",", "nu"}], "]"}], "/",
140 RowBox[{"mw", "^", "2"}]}]}]}], ")"}],
141 RowBox[{"Tr", "[",
142 RowBox[{
143 RowBox[{"GSD", "[", "pb", "]"}], ".",
144 RowBox[{"GAD", "[", "mu", "]"}], ".",
145 RowBox[{"(",
146 RowBox[{"1", "-", "GA5"}], ")"}], ".",
147 RowBox[{"(",
148 RowBox[{
149 RowBox[{"GSD", "[", "pt", "]"}], "+", "mt"}], ")"}], ".",
150 RowBox[{"GAD", "[", "nu", "]"}], ".",
151 RowBox[{"(",
152 RowBox[{"1", "-", "GA5"}], ")"}]}], "]"}]}]}]], "Input",
153 CellChangeTimes->{{3.428927033246361*^9, 3.4289271401967373`*^9}, {
154 3.42892727787171*^9, 3.428927413135103*^9}, {3.4289274432481937`*^9,
155 3.4289274930463*^9}, {3.428929121395401*^9, 3.428929122088388*^9},
156 3.428929375657975*^9, {3.428929541763723*^9, 3.428929566521463*^9}, {
157 3.428937860468915*^9, 3.428937864548534*^9}, {3.4289380364317427`*^9,
158 3.428938062823503*^9}, {3.42893809477054*^9, 3.4289381246774197`*^9}, {
159 3.4289382285018063`*^9, 3.428938230286139*^9}, {3.4289401410610647`*^9,
160 3.428940262985488*^9}}],
161
162Cell[BoxData[
163 FormBox[
164 RowBox[{
165 FractionBox["1", "4"], " ",
166 SuperscriptBox["gw", "2"], " ", "Vtb2", " ",
167 RowBox[{"(",
168 RowBox[{
169 FractionBox[
170 RowBox[{
171 SuperscriptBox["pw", "mu"], " ",
172 SuperscriptBox["pw", "nu"]}],
173 SuperscriptBox["mw", "2"]], "-",
174 SuperscriptBox["g",
175 RowBox[{"mu", "nu"}]]}], ")"}], " ",
176 RowBox[{"(",
177 RowBox[{
178 RowBox[{
179 RowBox[{"-",
180 SuperscriptBox["g",
181 RowBox[{"mu", "nu"}]]}], " ",
182 SuperscriptBox["mt", "2"]}], "-",
183 RowBox[{"2", " ", "\[ImaginaryI]", " ",
184 SuperscriptBox["\[Epsilon]",
185 RowBox[{
186 FormBox[
187 FormBox["mu",
188 TraditionalForm],
189 TraditionalForm],
190 FormBox[
191 FormBox["nu",
192 TraditionalForm],
193 TraditionalForm],
194 FormBox["pb",
195 TraditionalForm],
196 FormBox["pt",
197 TraditionalForm]}]]}], "+",
198 RowBox[{
199 SuperscriptBox["mw", "2"], " ",
200 SuperscriptBox["g",
201 RowBox[{"mu", "nu"}]]}], "+",
202 RowBox[{"2", " ",
203 SuperscriptBox[
204 FormBox["pt",
205 TraditionalForm],
206 FormBox[
207 FormBox["mu",
208 TraditionalForm],
209 TraditionalForm]], " ",
210 SuperscriptBox[
211 FormBox["pb",
212 TraditionalForm],
213 FormBox[
214 FormBox["nu",
215 TraditionalForm],
216 TraditionalForm]]}], "+",
217 RowBox[{"2", " ",
218 SuperscriptBox[
219 FormBox["pb",
220 TraditionalForm],
221 FormBox[
222 FormBox["mu",
223 TraditionalForm],
224 TraditionalForm]], " ",
225 SuperscriptBox[
226 FormBox["pt",
227 TraditionalForm],
228 FormBox[
229 FormBox["nu",
230 TraditionalForm],
231 TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output",
232 CellChangeTimes->{
233 3.4289272789512367`*^9, 3.428927318445057*^9, {3.4289273534290743`*^9,
234 3.428927404797317*^9}, {3.4289274516566753`*^9, 3.42892749447148*^9},
235 3.4289291227183*^9, {3.428929370895793*^9, 3.428929376751039*^9},
236 3.428929567605669*^9, {3.428938112386113*^9, 3.428938125511932*^9},
237 3.4289382307430983`*^9, {3.428938486376433*^9, 3.4289384975076303`*^9},
238 3.428939015665769*^9, 3.428940263914661*^9, {3.428940301403697*^9,
239 3.428940318910907*^9}, 3.428940388164935*^9}]
240}, Open ]],
241
242Cell["We contract the Lorentz indices", "Text",
243 CellChangeTimes->{{3.42894027176694*^9, 3.4289402767919693`*^9}}],
244
245Cell[CellGroupData[{
246
247Cell[BoxData[
248 RowBox[{"M2", "=",
249 RowBox[{
250 RowBox[{"Contract", "[", "M2", "]"}], "//", "Simplify"}]}]], "Input",
251 CellChangeTimes->{{3.428940286320468*^9, 3.4289402931521072`*^9}, {
252 3.4289403938410273`*^9, 3.42894039536911*^9}}],
253
254Cell[BoxData[
255 FormBox[
256 FractionBox[
257 RowBox[{
258 SuperscriptBox["gw", "2"], " ",
259 RowBox[{"(",
260 RowBox[{
261 SuperscriptBox["mt", "4"], "+",
262 RowBox[{
263 SuperscriptBox["mw", "2"], " ",
264 SuperscriptBox["mt", "2"]}], "-",
265 RowBox[{"2", " ",
266 SuperscriptBox["mw", "4"]}]}], ")"}], " ", "Vtb2"}],
267 RowBox[{"4", " ",
268 SuperscriptBox["mw", "2"]}]], TraditionalForm]], "Output",
269 CellChangeTimes->{{3.428940293573032*^9, 3.428940320656869*^9}, {
270 3.428940389419715*^9, 3.4289403959046288`*^9}}]
271}, Open ]],
272
273Cell["We insert he definition of the Fermi constant, and x=mw/mt", "Text",
274 CellChangeTimes->{{3.428927552171399*^9, 3.428927561923086*^9}, {
275 3.4289404070234756`*^9, 3.428940412095091*^9}}],
276
277Cell[CellGroupData[{
278
279Cell[BoxData[
280 RowBox[{"M2", "=",
281 RowBox[{
282 RowBox[{
283 RowBox[{"M2", "/.",
284 RowBox[{"gw", "\[Rule]",
285 RowBox[{"Sqrt", "[",
286 RowBox[{"Gf", " ", "8",
287 RowBox[{
288 RowBox[{"mw", "^", "2"}], " ", "/",
289 RowBox[{"Sqrt", "[", "2", "]"}]}]}], "]"}]}]}], "/.",
290 RowBox[{"mw", "\[Rule]",
291 RowBox[{"x", " ", "mt"}]}]}], "//", "Simplify"}]}]], "Input",
292 CellChangeTimes->{{3.428927568404044*^9, 3.42892758705121*^9}, {
293 3.4289381595073957`*^9, 3.4289381716760798`*^9}, {3.428940329450939*^9,
294 3.4289403469848347`*^9}, {3.428940417769717*^9, 3.428940437988619*^9},
295 3.428940474202092*^9}],
296
297Cell[BoxData[
298 FormBox[
299 RowBox[{
300 RowBox[{"-",
301 SqrtBox["2"]}], " ", "Gf", " ",
302 SuperscriptBox["mt", "4"], " ", "Vtb2", " ",
303 RowBox[{"(",
304 RowBox[{"x", "-", "1"}], ")"}], " ",
305 RowBox[{"(",
306 RowBox[{"x", "+", "1"}], ")"}], " ",
307 RowBox[{"(",
308 RowBox[{
309 RowBox[{"2", " ",
310 SuperscriptBox["x", "2"]}], "+", "1"}], ")"}]}],
311 TraditionalForm]], "Output",
312 CellChangeTimes->{
313 3.428927588058874*^9, 3.4289291256255703`*^9, 3.428929571106011*^9,
314 3.428938172246612*^9, 3.428938233053894*^9, 3.4289384978556747`*^9,
315 3.428939015694807*^9, 3.4289403476319036`*^9, {3.4289404226184263`*^9,
316 3.428940438583735*^9}, 3.428940474667651*^9}]
317}, Open ]]
318}, Open ]],
319
320Cell[CellGroupData[{
321
322Cell["Phase Space", "Subsection",
323 CellChangeTimes->{{3.4289292202493353`*^9, 3.428929221917066*^9}}],
324
325Cell["The two particle phase space is", "Text",
326 CellChangeTimes->{{3.4289286541859837`*^9, 3.428928662992796*^9}, {
327 3.428938253498197*^9, 3.428938253866067*^9}}],
328
329Cell[CellGroupData[{
330
331Cell[BoxData[
332 RowBox[{"d\[CapitalPhi]2", "=",
333 RowBox[{
334 RowBox[{
335 RowBox[{"(",
336 RowBox[{"2", "Pi"}], ")"}], "^", "4"}],
337 RowBox[{"\[Delta]", "[",
338 RowBox[{"pt", "-", "pb", "-", "pw"}], "]"}],
339 RowBox[{
340 RowBox[{
341 RowBox[{"d3pb", "/",
342 RowBox[{
343 RowBox[{"(",
344 RowBox[{"2", "Pi"}], ")"}], "^", "3"}]}], "/", "2"}], "/", "Eb"}],
345 " ",
346 RowBox[{
347 RowBox[{
348 RowBox[{"d3pw", "/",
349 RowBox[{
350 RowBox[{"(",
351 RowBox[{"2", "Pi"}], ")"}], "^", "3"}]}], "/", "2"}], "/",
352 "Ew"}]}]}]], "Input",
353 CellChangeTimes->{{3.428928668808182*^9, 3.428928748243292*^9}, {
354 3.4289288594542103`*^9, 3.428928869884198*^9}, {3.42893818360579*^9,
355 3.428938207781085*^9}, {3.4289382412163973`*^9, 3.4289382417010736`*^9}, {
356 3.428940498332073*^9, 3.428940511698041*^9}}],
357
358Cell[BoxData[
359 FormBox[
360 FractionBox[
361 RowBox[{"d3pb", " ", "d3pw", " ",
362 RowBox[{"\[Delta]", "(",
363 RowBox[{
364 RowBox[{"-", "pb"}], "+", "pt", "-", "pw"}], ")"}]}],
365 RowBox[{"16", " ", "Eb", " ", "Ew", " ",
366 SuperscriptBox["\[Pi]", "2"]}]], TraditionalForm]], "Output",
367 CellChangeTimes->{{3.428928862716354*^9, 3.428928870072042*^9},
368 3.428929126861431*^9, 3.428929574710586*^9, {3.428938234752118*^9,
369 3.428938241930442*^9}, 3.428938501869619*^9, 3.4289390157281837`*^9,
370 3.428940513564455*^9}]
371}, Open ]],
372
373Cell["\<\
374Performing the integration over d3pb in the rest frame of the t gives\
375\>", "Text",
376 CellChangeTimes->{{3.428928749821361*^9, 3.428928784904477*^9}, {
377 3.4289288233373938`*^9, 3.428928824472897*^9}, {3.428938246362335*^9,
378 3.428938248774928*^9}, {3.428940519825862*^9, 3.428940522487805*^9}}],
379
380Cell[CellGroupData[{
381
382Cell[BoxData[
383 RowBox[{"PS", "=",
384 RowBox[{
385 RowBox[{
386 RowBox[{"1", "/", "4"}], "/",
387 RowBox[{
388 RowBox[{"(",
389 RowBox[{"2", "Pi"}], ")"}], "^", "2"}]}], " ",
390 RowBox[{"\[Delta]", "[",
391 RowBox[{"mt", "-", "Ew", " ", "-",
392 RowBox[{"Sqrt", "[",
393 RowBox[{
394 RowBox[{"Ew", "^", "2"}], "-",
395 RowBox[{"mw", "^", "2"}]}], "]"}]}], "]"}],
396 RowBox[{
397 RowBox[{"d3pw", "/", "Ew"}], "/",
398 RowBox[{"Sqrt", "[",
399 RowBox[{
400 RowBox[{"Ew", "^", "2"}], "-",
401 RowBox[{"mw", "^", "2"}]}], "]"}]}]}]}]], "Input",
402 CellChangeTimes->{{3.4289287922794847`*^9, 3.4289288819309*^9}, {
403 3.42893825962851*^9, 3.42893826484441*^9}, {3.428940495085102*^9,
404 3.42894049515322*^9}, {3.428940527217524*^9, 3.4289405731543007`*^9}}],
405
406Cell[BoxData[
407 FormBox[
408 FractionBox[
409 RowBox[{"d3pw", " ",
410 RowBox[{"\[Delta]", "(",
411 RowBox[{
412 RowBox[{"-", "Ew"}], "+", "mt", "-",
413 SqrtBox[
414 RowBox[{
415 SuperscriptBox["Ew", "2"], "-",
416 SuperscriptBox["mw", "2"]}]]}], ")"}]}],
417 RowBox[{"16", " ", "Ew", " ",
418 SqrtBox[
419 RowBox[{
420 SuperscriptBox["Ew", "2"], "-",
421 SuperscriptBox["mw", "2"]}]], " ",
422 SuperscriptBox["\[Pi]", "2"]}]], TraditionalForm]], "Output",
423 CellChangeTimes->{{3.428928849656254*^9, 3.428928882523725*^9},
424 3.428929068231016*^9, 3.428929127845537*^9, 3.428929574829381*^9,
425 3.42893826621164*^9, 3.428938504167341*^9, 3.4289386058116293`*^9,
426 3.4289386914875193`*^9, 3.4289390157737207`*^9, 3.428940573661015*^9, {
427 3.4289408529820642`*^9, 3.428940868212055*^9}, 3.4289409333227367`*^9}]
428}, Open ]],
429
430Cell["\<\
431Going to spherical coordinates, and usging pw dpw = Ew dEw, we get\
432\>", "Text",
433 CellChangeTimes->{{3.428928883567082*^9, 3.4289289264749002`*^9}, {
434 3.4289382922025423`*^9, 3.428938296218473*^9}, {3.4289406507943153`*^9,
435 3.428940654855733*^9}}],
436
437Cell[CellGroupData[{
438
439Cell[BoxData[
440 RowBox[{"PS", "=",
441 RowBox[{"PS", "/.", " ",
442 RowBox[{"d3pw", "\[Rule]",
443 RowBox[{"4", "Pi", " ",
444 RowBox[{"Sqrt", "[",
445 RowBox[{
446 RowBox[{"Ew", "^", "2"}], "-",
447 RowBox[{"mw", "^", "2"}]}], "]"}], "Ew", " ", "dEw"}]}]}]}]], "Input",
448 CellChangeTimes->{{3.4289289441444197`*^9, 3.428929022421103*^9},
449 3.428929070151713*^9, {3.4289382799967327`*^9, 3.428938290196628*^9}, {
450 3.428938584824209*^9, 3.428938599062233*^9}, {3.428940668498803*^9,
451 3.428940709969864*^9}}],
452
453Cell[BoxData[
454 FormBox[
455 FractionBox[
456 RowBox[{"dEw", " ",
457 RowBox[{"\[Delta]", "(",
458 RowBox[{
459 RowBox[{"-", "Ew"}], "+", "mt", "-",
460 SqrtBox[
461 RowBox[{
462 SuperscriptBox["Ew", "2"], "-",
463 SuperscriptBox["mw", "2"]}]]}], ")"}]}],
464 RowBox[{"4", " ", "\[Pi]"}]], TraditionalForm]], "Output",
465 CellChangeTimes->{
466 3.428929025150517*^9, 3.428929070325218*^9, 3.4289291311060667`*^9,
467 3.428929574875102*^9, 3.428938297415737*^9, 3.428938505065439*^9, {
468 3.428938600499318*^9, 3.428938606660725*^9}, {3.4289386861864023`*^9,
469 3.428938692218741*^9}, 3.4289390158068933`*^9, 3.4289407114162188`*^9, {
470 3.428940853812212*^9, 3.428940869000046*^9}, 3.42894093432963*^9}]
471}, Open ]],
472
473Cell["\<\
474Using the fact that
475
476\[Delta] (mt - Ew - Sqrt[Ew^2 - mw^2]) = 1/2 (1 - x^2) \[Delta] (Ew - (mt^2 + \
477mw^2)/2/mt)
478
479we get\
480\>", "Text",
481 CellChangeTimes->{{3.428940727592554*^9, 3.428940828727889*^9}}],
482
483Cell[CellGroupData[{
484
485Cell[BoxData[
486 RowBox[{"PS", " ", "=", " ",
487 RowBox[{"PS", " ", "/.", " ",
488 RowBox[{
489 RowBox[{"\[Delta]", "[",
490 RowBox[{"mt", "-", "Ew", "-",
491 RowBox[{"Sqrt", "[",
492 RowBox[{
493 RowBox[{"Ew", "^", "2"}], "-",
494 RowBox[{"mw", "^", "2"}]}], "]"}]}], "]"}], "->",
495 RowBox[{
496 RowBox[{"1", "/", "2"}], " ",
497 RowBox[{"(",
498 RowBox[{"1", "-",
499 RowBox[{"x", "^", "2"}]}], ")"}], " ",
500 RowBox[{"\[Delta]", "[",
501 RowBox[{"Ew", "-",
502 RowBox[{
503 RowBox[{
504 RowBox[{"(",
505 RowBox[{
506 RowBox[{"mt", "^", "2"}], "+",
507 RowBox[{"mw", "^", "2"}]}], ")"}], "/", "2"}], "/", "mt"}]}],
508 "]"}]}]}]}]}]], "Input",
509 CellChangeTimes->{{3.428940823713065*^9, 3.428940865439296*^9}}],
510
511Cell[BoxData[
512 FormBox[
513 FractionBox[
514 RowBox[{"dEw", " ",
515 RowBox[{"(",
516 RowBox[{"1", "-",
517 SuperscriptBox["x", "2"]}], ")"}], " ",
518 RowBox[{"\[Delta]", "(",
519 RowBox[{"Ew", "-",
520 FractionBox[
521 RowBox[{
522 SuperscriptBox["mt", "2"], "+",
523 SuperscriptBox["mw", "2"]}],
524 RowBox[{"2", " ", "mt"}]]}], ")"}]}],
525 RowBox[{"8", " ", "\[Pi]"}]], TraditionalForm]], "Output",
526 CellChangeTimes->{{3.4289408454932737`*^9, 3.428940870390575*^9},
527 3.428940936273623*^9}]
528}, Open ]],
529
530Cell["Performing the integration", "Text",
531 CellChangeTimes->{{3.428929031938621*^9, 3.428929037282918*^9}}],
532
533Cell[CellGroupData[{
534
535Cell[BoxData[
536 RowBox[{"PS", "=",
537 RowBox[{
538 RowBox[{"PS", "/.",
539 RowBox[{
540 RowBox[{"dEw", " ",
541 RowBox[{"\[Delta]", "[",
542 RowBox[{"Ew", "-",
543 RowBox[{
544 RowBox[{
545 RowBox[{"(",
546 RowBox[{
547 RowBox[{"mt", "^", "2"}], "+",
548 RowBox[{"mw", "^", "2"}]}], ")"}], "/", "2"}], "/", "mt"}]}],
549 "]"}]}], "\[Rule]", "1"}]}], "/.",
550 RowBox[{"Ew", "\[Rule]",
551 RowBox[{
552 RowBox[{
553 RowBox[{"(",
554 RowBox[{
555 RowBox[{"mt", "^", "2"}], "+",
556 RowBox[{"mw", "^", "2"}]}], ")"}], "/", "2"}], "/",
557 "mt"}]}]}]}]], "Input",
558 CellChangeTimes->{{3.428929044586605*^9, 3.428929056603554*^9}, {
559 3.428938304472186*^9, 3.428938307564096*^9}, {3.428938621479186*^9,
560 3.428938627852805*^9}, {3.4289386823375387`*^9, 3.428938682419998*^9}, {
561 3.42894088870361*^9, 3.428940930891738*^9}}],
562
563Cell[BoxData[
564 FormBox[
565 FractionBox[
566 RowBox[{"1", "-",
567 SuperscriptBox["x", "2"]}],
568 RowBox[{"8", " ", "\[Pi]"}]], TraditionalForm]], "Output",
569 CellChangeTimes->{{3.428929056861126*^9, 3.428929071114458*^9},
570 3.4289291321148567`*^9, 3.428929574912538*^9, 3.428938307856097*^9,
571 3.428938506325878*^9, 3.4289386297502537`*^9, {3.4289386829460487`*^9,
572 3.428938694746279*^9}, 3.42893901583956*^9, {3.4289409036435966`*^9,
573 3.428940937548481*^9}}]
574}, Open ]]
575}, Open ]],
576
577Cell[CellGroupData[{
578
579Cell["Result", "Subsection",
580 CellChangeTimes->{{3.4289292627868023`*^9, 3.4289292633475027`*^9}}],
581
582Cell["The decay rate of the t then becomes", "Text",
583 CellChangeTimes->{{3.428929073874954*^9, 3.428929081291203*^9},
584 3.4289383237898083`*^9, 3.428940943883102*^9}],
585
586Cell[CellGroupData[{
587
588Cell[BoxData[
589 RowBox[{"\[CapitalGamma]", "=",
590 RowBox[{
591 RowBox[{
592 RowBox[{
593 RowBox[{"1", "/", "2"}], "/", "mt"}], " ", "PS", " ", "M2"}], "//",
594 "Simplify"}]}]], "Input",
595 CellChangeTimes->{{3.428929087038114*^9, 3.428929107627933*^9},
596 3.428929346599481*^9, {3.428938314727579*^9, 3.428938334043777*^9},
597 3.42893864433534*^9, 3.4289389462936773`*^9, {3.428940947099462*^9,
598 3.428940947409854*^9}}],
599
600Cell[BoxData[
601 FormBox[
602 FractionBox[
603 RowBox[{"Gf", " ",
604 SuperscriptBox["mt", "3"], " ", "Vtb2", " ",
605 SuperscriptBox[
606 RowBox[{"(",
607 RowBox[{
608 SuperscriptBox["x", "2"], "-", "1"}], ")"}], "2"], " ",
609 RowBox[{"(",
610 RowBox[{
611 RowBox[{"2", " ",
612 SuperscriptBox["x", "2"]}], "+", "1"}], ")"}]}],
613 RowBox[{"8", " ",
614 SqrtBox["2"], " ", "\[Pi]"}]], TraditionalForm]], "Output",
615 CellChangeTimes->{{3.428929108658009*^9, 3.428929133003119*^9},
616 3.4289293476527367`*^9, 3.4289295771229353`*^9, {3.428938319056734*^9,
617 3.4289383343919973`*^9}, 3.4289385085419197`*^9, {3.4289386319695272`*^9,
618 3.428938644554867*^9}, 3.428938696988208*^9, 3.428938947199583*^9,
619 3.42893901589124*^9, 3.428940948763257*^9}]
620}, Open ]]
621}, Open ]]
622}, Open ]]
623}, Open ]]
624},
625WindowSize->{710, 706},
626WindowMargins->{{Automatic, 230}, {Automatic, 4}},
627ShowSelection->True,
628FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (April 20, 2007)",
629StyleDefinitions->"Default.nb"
630]
631(* End of Notebook Content *)
632
633(* Internal cache information *)
634(*CellTagsOutline
635CellTagsIndex->{}
636*)
637(*CellTagsIndex
638CellTagsIndex->{}
639*)
640(*NotebookFileOutline
641Notebook[{
642Cell[CellGroupData[{
643Cell[590, 23, 224, 5, 76, "Title"],
644Cell[CellGroupData[{
645Cell[839, 32, 36, 0, 34, "Subsection"],
646Cell[878, 34, 83, 2, 27, "Input"]
647}, Open ]],
648Cell[CellGroupData[{
649Cell[998, 41, 154, 2, 67, "Section"],
650Cell[CellGroupData[{
651Cell[1177, 47, 103, 1, 34, "Subsection"],
652Cell[1283, 50, 1926, 54, 133, "Input"]
653}, Open ]],
654Cell[CellGroupData[{
655Cell[3246, 109, 111, 1, 34, "Subsection"],
656Cell[3360, 112, 228, 3, 26, "Text"],
657Cell[CellGroupData[{
658Cell[3613, 119, 1536, 40, 58, "Input"],
659Cell[5152, 161, 2321, 77, 48, "Output"]
660}, Open ]],
661Cell[7488, 241, 114, 1, 26, "Text"],
662Cell[CellGroupData[{
663Cell[7627, 246, 236, 5, 27, "Input"],
664Cell[7866, 253, 543, 16, 51, "Output"]
665}, Open ]],
666Cell[8424, 272, 191, 2, 26, "Text"],
667Cell[CellGroupData[{
668Cell[8640, 278, 640, 16, 27, "Input"],
669Cell[9283, 296, 683, 19, 39, "Output"]
670}, Open ]]
671}, Open ]],
672Cell[CellGroupData[{
673Cell[10015, 321, 101, 1, 34, "Subsection"],
674Cell[10119, 324, 164, 2, 26, "Text"],
675Cell[CellGroupData[{
676Cell[10308, 330, 832, 25, 27, "Input"],
677Cell[11143, 357, 528, 12, 48, "Output"]
678}, Open ]],
679Cell[11686, 372, 305, 5, 26, "Text"],
680Cell[CellGroupData[{
681Cell[12016, 381, 775, 22, 27, "Input"],
682Cell[12794, 405, 838, 21, 71, "Output"]
683}, Open ]],
684Cell[13647, 429, 260, 5, 26, "Text"],
685Cell[CellGroupData[{
686Cell[13932, 438, 523, 12, 27, "Input"],
687Cell[14458, 452, 716, 17, 61, "Output"]
688}, Open ]],
689Cell[15189, 472, 212, 8, 86, "Text"],
690Cell[CellGroupData[{
691Cell[15426, 484, 784, 24, 27, "Input"],
692Cell[16213, 510, 522, 16, 58, "Output"]
693}, Open ]],
694Cell[16750, 529, 108, 1, 26, "Text"],
695Cell[CellGroupData[{
696Cell[16883, 534, 890, 26, 27, "Input"],
697Cell[17776, 562, 468, 10, 48, "Output"]
698}, Open ]]
699}, Open ]],
700Cell[CellGroupData[{
701Cell[18293, 578, 98, 1, 34, "Subsection"],
702Cell[18394, 581, 168, 2, 26, "Text"],
703Cell[CellGroupData[{
704Cell[18587, 587, 423, 10, 27, "Input"],
705Cell[19013, 599, 766, 19, 55, "Output"]
706}, Open ]]
707}, Open ]]
708}, Open ]]
709}, Open ]]
710}
711]
712*)
713
714(* End of internal cache information *)