| 1 | (************** Content-type: application/mathematica **************
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| 2 |
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| 3 | Mathematica-Compatible Notebook
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| 4 |
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| 5 | This notebook can be used with any Mathematica-compatible
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| 6 | application, such as Mathematica, MathReader or Publicon. The data
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| 7 | for the notebook starts with the line containing stars above.
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| 8 |
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| 9 | To get the notebook into a Mathematica-compatible application, do
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| 10 | one of the following:
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| 12 | * Save the data starting with the line of stars above into a file
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| 13 | with a name ending in .nb, then open the file inside the
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| 14 | application;
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| 20 | sent directly in email or through ftp in text mode. Newlines can be
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| 21 | CR, LF or CRLF (Unix, Macintosh or MS-DOS style).
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| 22 |
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| 23 | NOTE: If you modify the data for this notebook not in a Mathematica-
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| 24 | compatible application, you must delete the line below containing
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| 25 | the word CacheID, otherwise Mathematica-compatible applications may
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| 26 | try to use invalid cache data.
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| 27 |
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| 28 | For more information on notebooks and Mathematica-compatible
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| 29 | applications, contact Wolfram Research:
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| 30 | web: http://www.wolfram.com
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| 31 | email: info@wolfram.com
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| 33 |
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| 34 | Notebook reader applications are available free of charge from
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| 35 | Wolfram Research.
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| 36 | *******************************************************************)
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| 37 |
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| 38 | (*CacheID: 232*)
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| 39 |
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| 40 |
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| 42 | NotebookFileLineBreakTest*)
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| 46 | (*WindowFrame->Normal*)
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| 47 |
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| 48 |
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| 49 |
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| 50 | Notebook[{
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| 51 |
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| 52 | Cell[CellGroupData[{
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| 53 | Cell[TextData[{
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| 54 | "Calculation for ",
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| 55 | StyleBox["gg > Higgs at LO with full top-mass dependence",
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| 56 | "DisplayFormula"]
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| 57 | }], "Title"],
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| 58 |
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| 59 | Cell[CellGroupData[{
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| 60 |
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| 61 | Cell["Input FeynCalc", "Subsection"],
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| 62 |
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| 63 | Cell[BoxData[
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| 64 | \(\(<< HighEnergyPhysics`fc`;\)\)], "Input"],
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| 65 |
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| 66 | Cell[TextData[{
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| 67 | StyleBox["FeynCalc",
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| 68 | FontWeight->"Bold"],
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| 69 | " ",
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| 70 | "4.1.0.3b",
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| 71 | " ",
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| 72 | " Evaluate ?FeynCalc for help or visit ",
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| 73 | ButtonBox["www.feyncalc.org",
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| 74 | ButtonData:>{
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| 75 | URL[ "http://www.feyncalc.org"], None},
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| 78 | }], "Text",
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| 92 | \(\(\(\[IndentingNewLine]\)\(\(ScalarProduct[q1, q1] =
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| 94 | \(ScalarProduct[q2, q2] = 0;\)\[IndentingNewLine]
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| 95 | \(ScalarProduct[q1, q2] = mh2/2;\)\[IndentingNewLine]
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| 96 | \(ScalarProduct[q, q1] = mh2/2;\)\[IndentingNewLine]
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| 97 | \(ScalarProduct[q, q2] = mh2/2;\)\[IndentingNewLine]
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| 98 | \(ScalarProduct[q, q] = mh2;\)\[IndentingNewLine]
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| 99 | \)\)\)], "Input"]
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| 103 | Cell[CellGroupData[{
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| 106 |
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| 107 | Cell[CellGroupData[{
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| 108 |
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| 109 | Cell[BoxData[
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| 110 | \(\(\(\[IndentingNewLine]\)\(\(Amp = \((\(-I\))\) \((\(\((\(-\((\(-I\)\ \
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| 111 | gs)\)^2\)\ \ \((\(-\ I\)\ mt\ /v)\)\ *\ I^3*deltaAB/2*
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| 112 | Tr[\((GSD[l + q1] + mt)\) .
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| 113 | GAD[mu] . \((GSD[l] + mt)\) .
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| 114 | GAD[nu] . \((GSD[l - q2] +
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| 115 | mt)\) + \((GSD[l + q2] + mt)\) .
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| 116 | GAD[nu] . \((GSD[l] + mt)\) .
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| 117 | GAD[mu] . \((GSD[l - q1] + mt)\)]\ //
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| 118 | DiracSimplify)\) /. \
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| 119 | Pair[Momentum[q2], LorentzIndex[nu]] \[Rule] 0\) /. \
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| 120 | Pair[Momentum[q1], LorentzIndex[mu]] \[Rule] 0)\)\ //
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| 205 | Cell[BoxData[
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| 208 | FAD[{l, mt}, {l + q1, mt}, {l - q2, mt}]\ Amp // Contract] //
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| 209 | PaVeReduce\) // Factor\) // Simplify;\)\[IndentingNewLine]
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| 210 | res = \((\(res /. \ Pair[Momentum[q2], LorentzIndex[nu]] \[Rule] 0\) /. \
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| 211 | Pair[Momentum[q1], LorentzIndex[mu]] \[Rule] 0\ )\) //
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| 257 |
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| 258 | Cell[CellGroupData[{
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| 259 |
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| 260 | Cell["\<\
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| 261 | The scalar integral C0, can be evaluated with the help of the \
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| 262 | Feynman parameters (by hand) and the result is:\
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| 263 | \>", "Subsection"],
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| 264 |
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| 265 | Cell["\<\
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| 266 | c0=-I/(16 Pi^2)*1/mt^2*Integrate[1/(1-4 \[Tau] x \
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| 267 | y),{x,0,1},{y,0,1-x}, Assumptions \[Rule] {\[Tau]<1}]//Simplify;
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| 268 | c0FC=(2 Pi)^4/(I Pi^2) c0;\
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| 270 | }, Closed]],
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| 271 |
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| 272 | Cell[CellGroupData[{
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| 273 |
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| 274 | Cell["\<\
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| 275 | Let's take the mt->Infinity limit and see that the amplitude does \
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| 276 | not depend on m_top:\
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| 277 | \>", "Subsection"],
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| 278 |
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| 279 | Cell[CellGroupData[{
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| 280 |
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| 281 | Cell[BoxData[
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| 282 | \(myamp =
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| 283 | Normal[Series[\(\(\(\((\
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| 284 | res\ /. \ C0[x__]\ \[Rule] c0FC // Simplify)\) /. \
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| 285 | gs^2\ \[Rule] \ as\ 4\ Pi\) /. \
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| 286 | mh2 \[Rule] mh^2\) /. \ \[Tau] \[Rule] \ \(mh^2/4\)/mt^2 //
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| 287 | PowerExpand\) // FullSimplify, {mt, Infinity, 4}]] //
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| 324 |
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| 325 | (*******************************************************************
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| 326 | Cached data follows. If you edit this Notebook file directly, not
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| 327 | using Mathematica, you must remove the line containing CacheID at
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| 328 | the top of the file. The cache data will then be recreated when
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| 329 | you save this file from within Mathematica.
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| 330 | *******************************************************************)
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| 331 |
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| 332 | (*CellTagsOutline
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| 333 | CellTagsIndex->{}
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| 334 | *)
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| 396 | *)
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| 397 |
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| 398 |
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| 399 |
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| 400 | (*******************************************************************
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| 401 | End of Mathematica Notebook file.
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| 402 | *******************************************************************)
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| 403 |
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