| 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[ 97158, 3262]
|
|---|
| 14 | NotebookOptionsPosition[ 90849, 3045]
|
|---|
| 15 | NotebookOutlinePosition[ 91347, 3064]
|
|---|
| 16 | CellTagsIndexPosition[ 91304, 3061]
|
|---|
| 17 | WindowFrame->Normal*)
|
|---|
| 18 |
|
|---|
| 19 | (* Beginning of Notebook Content *)
|
|---|
| 20 | Notebook[{
|
|---|
| 21 |
|
|---|
| 22 | Cell[CellGroupData[{
|
|---|
| 23 | Cell["gg \[Rule] H at NLO in the HEFT", "Title",
|
|---|
| 24 | PageWidth->PaperWidth,
|
|---|
| 25 | CellChangeTimes->{{3.6924444471962833`*^9, 3.6924444683925543`*^9}}],
|
|---|
| 26 |
|
|---|
| 27 | Cell[CellGroupData[{
|
|---|
| 28 |
|
|---|
| 29 | Cell["Input FeynCalc", "Subsection",
|
|---|
| 30 | PageWidth->PaperWidth],
|
|---|
| 31 |
|
|---|
| 32 | Cell[CellGroupData[{
|
|---|
| 33 |
|
|---|
| 34 | Cell[BoxData[
|
|---|
| 35 | RowBox[{"<<", "HighEnergyPhysics`fc`"}]], "Input",
|
|---|
| 36 | PageWidth->PaperWidth],
|
|---|
| 37 |
|
|---|
| 38 | Cell[BoxData[
|
|---|
| 39 | FormBox[
|
|---|
| 40 | RowBox[{
|
|---|
| 41 | StyleBox[
|
|---|
| 42 | RowBox[{"Get", "::", "noopen"}], "MessageName"],
|
|---|
| 43 | RowBox[{
|
|---|
| 44 | ":", " "}], "\<\"Cannot open \
|
|---|
| 45 | \[NoBreak]\\!\\(\\*FormBox[\\\"\\\\\\\"HighEnergyPhysics`fc`\\\\\\\"\\\", \
|
|---|
| 46 | TraditionalForm]\\)\[NoBreak]. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
|
|---|
| 47 | ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
|
|---|
| 48 | ButtonData:>\\\"paclet:ref/message/General/noopen\\\", ButtonNote -> \
|
|---|
| 49 | \\\"Get::noopen\\\"]\\)\"\>"}], TraditionalForm]], "Message", "MSG",
|
|---|
| 50 | CellChangeTimes->{3.6925155192937403`*^9, 3.6925217772912483`*^9,
|
|---|
| 51 | 3.69252240256242*^9, 3.692522450767223*^9}],
|
|---|
| 52 |
|
|---|
| 53 | Cell[BoxData[
|
|---|
| 54 | FormBox["$Failed", TraditionalForm]], "Output",
|
|---|
| 55 | CellChangeTimes->{3.6925217772943497`*^9, 3.692522402580044*^9,
|
|---|
| 56 | 3.6925224507858*^9}]
|
|---|
| 57 | }, Open ]],
|
|---|
| 58 |
|
|---|
| 59 | Cell[CellGroupData[{
|
|---|
| 60 |
|
|---|
| 61 | Cell[BoxData[
|
|---|
| 62 | RowBox[{"<<",
|
|---|
| 63 | "\"\</Users/marcozaro/Physics/feyncalc-master/FeynCalc/fc.m\>\""}]], "Input"],
|
|---|
| 64 |
|
|---|
| 65 | Cell[CellGroupData[{
|
|---|
| 66 |
|
|---|
| 67 | Cell[BoxData[
|
|---|
| 68 | FormBox[
|
|---|
| 69 | InterpretationBox[
|
|---|
| 70 | RowBox[{
|
|---|
| 71 | StyleBox["\<\"FeynCalc \"\>", "Text",
|
|---|
| 72 | StripOnInput->False,
|
|---|
| 73 | FontWeight->Bold], "\[InvisibleSpace]",
|
|---|
| 74 | StyleBox["\<\"9.1.0 (development version). For help, use the \"\>", "Text",
|
|---|
| 75 | StripOnInput->False], "\[InvisibleSpace]",
|
|---|
| 76 | StyleBox[
|
|---|
| 77 | TagBox[
|
|---|
| 78 | ButtonBox[
|
|---|
| 79 | RowBox[{"documentation", " ", "center"}],
|
|---|
| 80 | BaseStyle->"Link",
|
|---|
| 81 | ButtonData:>"paclet:FeynCalc/",
|
|---|
| 82 | ButtonNote->"paclet:FeynCalc/"],
|
|---|
| 83 | DisplayForm], "Text",
|
|---|
| 84 | StripOnInput->False], "\[InvisibleSpace]",
|
|---|
| 85 | StyleBox["\<\", check out the \"\>", "Text",
|
|---|
| 86 | StripOnInput->False], "\[InvisibleSpace]",
|
|---|
| 87 | StyleBox[
|
|---|
| 88 | TagBox[
|
|---|
| 89 | ButtonBox["wiki",
|
|---|
| 90 | BaseStyle->"Hyperlink",
|
|---|
| 91 | ButtonData:>{
|
|---|
| 92 | URL["https://github.com/FeynCalc/feyncalc/wiki"], None},
|
|---|
| 93 | ButtonNote->"https://github.com/FeynCalc/feyncalc/wiki"],
|
|---|
| 94 | DisplayForm], "Text",
|
|---|
| 95 | StripOnInput->False], "\[InvisibleSpace]",
|
|---|
| 96 | StyleBox["\<\" or write to the \"\>", "Text",
|
|---|
| 97 | StripOnInput->False], "\[InvisibleSpace]",
|
|---|
| 98 | StyleBox[
|
|---|
| 99 | TagBox[
|
|---|
| 100 | ButtonBox[
|
|---|
| 101 | RowBox[{"mailing", " ",
|
|---|
| 102 | RowBox[{"list", "."}]}],
|
|---|
| 103 | BaseStyle->"Hyperlink",
|
|---|
| 104 | ButtonData:>{
|
|---|
| 105 | URL["http://www.feyncalc.org/forum/"], None},
|
|---|
| 106 | ButtonNote->"http://www.feyncalc.org/forum/"],
|
|---|
| 107 | DisplayForm], "Text",
|
|---|
| 108 | StripOnInput->False]}],
|
|---|
| 109 | SequenceForm[
|
|---|
| 110 | Style["FeynCalc ", "Text", Bold],
|
|---|
| 111 | Style["9.1.0 (development version). For help, use the ", "Text"],
|
|---|
| 112 | Style[
|
|---|
| 113 | DisplayForm[
|
|---|
| 114 | ButtonBox[
|
|---|
| 115 | "documentation center", BaseStyle -> "Link", ButtonData :>
|
|---|
| 116 | "paclet:FeynCalc/", ButtonNote -> "paclet:FeynCalc/"]], "Text"],
|
|---|
| 117 | Style[", check out the ", "Text"],
|
|---|
| 118 | Style[
|
|---|
| 119 | DisplayForm[
|
|---|
| 120 | ButtonBox["wiki", ButtonData :> {
|
|---|
| 121 | URL["https://github.com/FeynCalc/feyncalc/wiki"], None}, BaseStyle ->
|
|---|
| 122 | "Hyperlink", ButtonNote ->
|
|---|
| 123 | "https://github.com/FeynCalc/feyncalc/wiki"]], "Text"],
|
|---|
| 124 | Style[" or write to the ", "Text"],
|
|---|
| 125 | Style[
|
|---|
| 126 | DisplayForm[
|
|---|
| 127 | ButtonBox["mailing list.", ButtonData :> {
|
|---|
| 128 | URL["http://www.feyncalc.org/forum/"], None}, BaseStyle ->
|
|---|
| 129 | "Hyperlink", ButtonNote -> "http://www.feyncalc.org/forum/"]], "Text"]],
|
|---|
| 130 | Editable->False], TraditionalForm]], "Print",
|
|---|
| 131 | CellChangeTimes->{3.692522403983714*^9, 3.692522452074922*^9}],
|
|---|
| 132 |
|
|---|
| 133 | Cell[BoxData[
|
|---|
| 134 | FormBox[
|
|---|
| 135 | InterpretationBox[
|
|---|
| 136 | RowBox[{
|
|---|
| 137 | StyleBox["\<\"See also the supplied \"\>", "Text",
|
|---|
| 138 | StripOnInput->False], "\[InvisibleSpace]",
|
|---|
| 139 | StyleBox[
|
|---|
| 140 | TagBox[
|
|---|
| 141 | ButtonBox[
|
|---|
| 142 | RowBox[{"examples", "."}],
|
|---|
| 143 | BaseStyle->"Hyperlink",
|
|---|
| 144 | ButtonFunction:>SystemOpen[
|
|---|
| 145 | FileNameJoin[{FeynCalc`$FeynCalcDirectory, "Examples"}]],
|
|---|
| 146 | Evaluator->Automatic,
|
|---|
| 147 | Method->"Preemptive"],
|
|---|
| 148 | DisplayForm], "Text",
|
|---|
| 149 | StripOnInput->False], "\[InvisibleSpace]",
|
|---|
| 150 | StyleBox["\<\" If you use FeynCalc in your research, please cite\"\>",
|
|---|
| 151 | "Text",
|
|---|
| 152 | StripOnInput->False]}],
|
|---|
| 153 | SequenceForm[
|
|---|
| 154 | Style["See also the supplied ", "Text"],
|
|---|
| 155 | Style[
|
|---|
| 156 | DisplayForm[
|
|---|
| 157 | ButtonBox[
|
|---|
| 158 | "examples.", BaseStyle -> "Hyperlink", ButtonFunction :> SystemOpen[
|
|---|
| 159 | FileNameJoin[{FeynCalc`$FeynCalcDirectory, "Examples"}]], Evaluator ->
|
|---|
| 160 | Automatic, Method -> "Preemptive"]], "Text"],
|
|---|
| 161 | Style[" If you use FeynCalc in your research, please cite", "Text"]],
|
|---|
| 162 | Editable->False], TraditionalForm]], "Print",
|
|---|
| 163 | CellChangeTimes->{3.692522403983714*^9, 3.69252245208001*^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->{3.692522403983714*^9, 3.692522452084078*^9}],
|
|---|
| 171 |
|
|---|
| 172 | Cell[BoxData[
|
|---|
| 173 | FormBox[
|
|---|
| 174 | StyleBox["\<\" \[Bullet] R. Mertig, M. B\[ODoubleDot]hm, and A. Denner, \
|
|---|
| 175 | Comput. Phys. Commun., 64, 345-359, 1991.\"\>", "Text",
|
|---|
| 176 | StripOnInput->False], TraditionalForm]], "Print",
|
|---|
| 177 | CellChangeTimes->{3.692522403983714*^9, 3.692522452087838*^9}]
|
|---|
| 178 | }, Open ]]
|
|---|
| 179 | }, Open ]],
|
|---|
| 180 |
|
|---|
| 181 | Cell[BoxData[
|
|---|
| 182 | RowBox[{
|
|---|
| 183 | RowBox[{"$LimitTo4", "=", "False"}], ";"}]], "Input",
|
|---|
| 184 | PageWidth->PaperWidth]
|
|---|
| 185 | }, Open ]],
|
|---|
| 186 |
|
|---|
| 187 | Cell[CellGroupData[{
|
|---|
| 188 |
|
|---|
| 189 | Cell["Virtual diagrams :preliminaries", "Section",
|
|---|
| 190 | PageWidth->PaperWidth],
|
|---|
| 191 |
|
|---|
| 192 | Cell[CellGroupData[{
|
|---|
| 193 |
|
|---|
| 194 | Cell["Kinematics", "Subsection",
|
|---|
| 195 | PageWidth->PaperWidth],
|
|---|
| 196 |
|
|---|
| 197 | Cell["\<\
|
|---|
| 198 | -----I take all momenta outgoing
|
|---|
| 199 |
|
|---|
| 200 | p1 + p2 + p3 = 0
|
|---|
| 201 |
|
|---|
| 202 | p1^2=0
|
|---|
| 203 | p2^2=0
|
|---|
| 204 | p3^3=Q^2
|
|---|
| 205 |
|
|---|
| 206 |
|
|---|
| 207 | \
|
|---|
| 208 | \>", "Text",
|
|---|
| 209 | PageWidth->PaperWidth],
|
|---|
| 210 |
|
|---|
| 211 | Cell[BoxData[{
|
|---|
| 212 | RowBox[{
|
|---|
| 213 | RowBox[{
|
|---|
| 214 | RowBox[{"ScalarProduct", "[",
|
|---|
| 215 | RowBox[{"p1", ",", "p1"}], "]"}], "=", "0"}],
|
|---|
| 216 | ";"}], "\[IndentingNewLine]",
|
|---|
| 217 | RowBox[{
|
|---|
| 218 | RowBox[{
|
|---|
| 219 | RowBox[{"ScalarProduct", "[",
|
|---|
| 220 | RowBox[{"p2", ",", "p2"}], "]"}], "=", "0"}],
|
|---|
| 221 | ";"}], "\[IndentingNewLine]",
|
|---|
| 222 | RowBox[{
|
|---|
| 223 | RowBox[{
|
|---|
| 224 | RowBox[{"ScalarProduct", "[",
|
|---|
| 225 | RowBox[{"p3", ",", "p3"}], "]"}], "=", "Q2"}],
|
|---|
| 226 | ";"}], "\[IndentingNewLine]",
|
|---|
| 227 | RowBox[{
|
|---|
| 228 | RowBox[{
|
|---|
| 229 | RowBox[{"ScalarProduct", "[",
|
|---|
| 230 | RowBox[{"p1", ",", "p3"}], "]"}], "=",
|
|---|
| 231 | RowBox[{
|
|---|
| 232 | RowBox[{"-", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 233 | RowBox[{
|
|---|
| 234 | RowBox[{
|
|---|
| 235 | RowBox[{"ScalarProduct", "[",
|
|---|
| 236 | RowBox[{"p1", ",", "p2"}], "]"}], "=",
|
|---|
| 237 | RowBox[{"Q2", "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 238 | RowBox[{
|
|---|
| 239 | RowBox[{
|
|---|
| 240 | RowBox[{"ScalarProduct", "[",
|
|---|
| 241 | RowBox[{"p2", ",", "p3"}], "]"}], "=",
|
|---|
| 242 | RowBox[{
|
|---|
| 243 | RowBox[{"-", " ", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 244 | RowBox[{
|
|---|
| 245 | RowBox[{
|
|---|
| 246 | RowBox[{"ScalarProduct", "[",
|
|---|
| 247 | RowBox[{"p1", ",", "e1"}], "]"}], "=", "0"}],
|
|---|
| 248 | ";"}], "\[IndentingNewLine]",
|
|---|
| 249 | RowBox[{
|
|---|
| 250 | RowBox[{
|
|---|
| 251 | RowBox[{"ScalarProduct", "[",
|
|---|
| 252 | RowBox[{"p2", ",", "e2"}], "]"}], "=", "0"}],
|
|---|
| 253 | ";"}], "\[IndentingNewLine]",
|
|---|
| 254 | RowBox[{
|
|---|
| 255 | RowBox[{
|
|---|
| 256 | RowBox[{"ScalarProduct", "[",
|
|---|
| 257 | RowBox[{"p1", ",", "e2"}], "]"}], "=", "0"}],
|
|---|
| 258 | ";"}], "\[IndentingNewLine]",
|
|---|
| 259 | RowBox[{
|
|---|
| 260 | RowBox[{
|
|---|
| 261 | RowBox[{
|
|---|
| 262 | RowBox[{"ScalarProduct", "[",
|
|---|
| 263 | RowBox[{"p2", ",", "e1"}], "]"}], "=", "0"}], ";"}],
|
|---|
| 264 | "\[IndentingNewLine]"}], "\[IndentingNewLine]",
|
|---|
| 265 | RowBox[{
|
|---|
| 266 | RowBox[{
|
|---|
| 267 | RowBox[{"ScalarProduct", "[",
|
|---|
| 268 | RowBox[{"p1", ",", "p1", ",",
|
|---|
| 269 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 270 | ";"}], "\[IndentingNewLine]",
|
|---|
| 271 | RowBox[{
|
|---|
| 272 | RowBox[{
|
|---|
| 273 | RowBox[{"ScalarProduct", "[",
|
|---|
| 274 | RowBox[{"p2", ",", "p2", ",",
|
|---|
| 275 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 276 | ";"}], "\[IndentingNewLine]",
|
|---|
| 277 | RowBox[{
|
|---|
| 278 | RowBox[{
|
|---|
| 279 | RowBox[{"ScalarProduct", "[",
|
|---|
| 280 | RowBox[{"p3", ",", "p3", ",",
|
|---|
| 281 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "Q2"}],
|
|---|
| 282 | ";"}], "\[IndentingNewLine]",
|
|---|
| 283 | RowBox[{
|
|---|
| 284 | RowBox[{
|
|---|
| 285 | RowBox[{"ScalarProduct", "[",
|
|---|
| 286 | RowBox[{"p1", ",", "p3", ",",
|
|---|
| 287 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=",
|
|---|
| 288 | RowBox[{
|
|---|
| 289 | RowBox[{"-", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 290 | RowBox[{
|
|---|
| 291 | RowBox[{
|
|---|
| 292 | RowBox[{"ScalarProduct", "[",
|
|---|
| 293 | RowBox[{"p1", ",", "p2", ",",
|
|---|
| 294 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=",
|
|---|
| 295 | RowBox[{"Q2", "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 296 | RowBox[{
|
|---|
| 297 | RowBox[{
|
|---|
| 298 | RowBox[{"ScalarProduct", "[",
|
|---|
| 299 | RowBox[{"p2", ",", "p3", ",",
|
|---|
| 300 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=",
|
|---|
| 301 | RowBox[{
|
|---|
| 302 | RowBox[{"-", " ", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 303 | RowBox[{
|
|---|
| 304 | RowBox[{
|
|---|
| 305 | RowBox[{"ScalarProduct", "[",
|
|---|
| 306 | RowBox[{"p1", ",", "e1", ",",
|
|---|
| 307 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 308 | ";"}], "\[IndentingNewLine]",
|
|---|
| 309 | RowBox[{
|
|---|
| 310 | RowBox[{
|
|---|
| 311 | RowBox[{"ScalarProduct", "[",
|
|---|
| 312 | RowBox[{"p2", ",", "e2", ",",
|
|---|
| 313 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 314 | ";"}], "\[IndentingNewLine]",
|
|---|
| 315 | RowBox[{
|
|---|
| 316 | RowBox[{
|
|---|
| 317 | RowBox[{"ScalarProduct", "[",
|
|---|
| 318 | RowBox[{"p1", ",", "e2", ",",
|
|---|
| 319 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 320 | ";"}], "\[IndentingNewLine]",
|
|---|
| 321 | RowBox[{
|
|---|
| 322 | RowBox[{
|
|---|
| 323 | RowBox[{"ScalarProduct", "[",
|
|---|
| 324 | RowBox[{"p2", ",", "e1", ",",
|
|---|
| 325 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 326 | ";"}], "\[IndentingNewLine]"}], "Input",
|
|---|
| 327 | PageWidth->PaperWidth]
|
|---|
| 328 | }, Open ]],
|
|---|
| 329 |
|
|---|
| 330 | Cell[CellGroupData[{
|
|---|
| 331 |
|
|---|
| 332 | Cell["Verteces and Propagators", "Subsection",
|
|---|
| 333 | PageWidth->PaperWidth],
|
|---|
| 334 |
|
|---|
| 335 | Cell[TextData[{
|
|---|
| 336 | StyleBox["GGG is the kinematic part of the three-gluon vtx (momenta \
|
|---|
| 337 | outgoing, clockwise ordering):\nVTX(ggg) = (-\[ImaginaryI] ",
|
|---|
| 338 | FontSize->14],
|
|---|
| 339 | Cell[BoxData[
|
|---|
| 340 | FormBox[
|
|---|
| 341 | SubscriptBox["g", "s"], TraditionalForm]],
|
|---|
| 342 | FontSize->14],
|
|---|
| 343 | StyleBox[" ) (\[ImaginaryI] ",
|
|---|
| 344 | FontSize->14],
|
|---|
| 345 | Cell[BoxData[
|
|---|
| 346 | FormBox[
|
|---|
| 347 | SuperscriptBox["f", "abc"], TraditionalForm]],
|
|---|
| 348 | FontSize->14],
|
|---|
| 349 | StyleBox[") GGG\nVTX(qqg) = ( -\[ImaginaryI] ",
|
|---|
| 350 | FontSize->14],
|
|---|
| 351 | Cell[BoxData[
|
|---|
| 352 | FormBox[
|
|---|
| 353 | SubscriptBox["g", "s"], TraditionalForm]],
|
|---|
| 354 | FontSize->14],
|
|---|
| 355 | ")",
|
|---|
| 356 | StyleBox[" ",
|
|---|
| 357 | FontSize->14],
|
|---|
| 358 | Cell[BoxData[
|
|---|
| 359 | FormBox[
|
|---|
| 360 | SubscriptBox[
|
|---|
| 361 | RowBox[{"(",
|
|---|
| 362 | SuperscriptBox["T", "a"], ")"}], "ij"], TraditionalForm]],
|
|---|
| 363 | FontSize->14],
|
|---|
| 364 | StyleBox[" ",
|
|---|
| 365 | FontSize->14],
|
|---|
| 366 | Cell[BoxData[
|
|---|
| 367 | FormBox[
|
|---|
| 368 | SuperscriptBox["\[Gamma]", "\[Mu]"], TraditionalForm]],
|
|---|
| 369 | FontSize->14],
|
|---|
| 370 | StyleBox["\nGluon Propagator= ",
|
|---|
| 371 | FontSize->14],
|
|---|
| 372 | Cell[BoxData[
|
|---|
| 373 | FormBox[
|
|---|
| 374 | FractionBox[
|
|---|
| 375 | StyleBox[
|
|---|
| 376 | RowBox[{
|
|---|
| 377 | RowBox[{"-", "\[ImaginaryI]"}], " ",
|
|---|
| 378 | SuperscriptBox["g", "\[Mu]\[Nu]"]}],
|
|---|
| 379 | FontSize->16],
|
|---|
| 380 | SuperscriptBox["p", "2"]], TraditionalForm]],
|
|---|
| 381 | FontSize->14],
|
|---|
| 382 | "\nQuark ",
|
|---|
| 383 | StyleBox["Propagator= ",
|
|---|
| 384 | FontSize->14],
|
|---|
| 385 | Cell[BoxData[
|
|---|
| 386 | FormBox[
|
|---|
| 387 | FractionBox[
|
|---|
| 388 | StyleBox[
|
|---|
| 389 | RowBox[{"\[ImaginaryI]", " "}],
|
|---|
| 390 | FontSize->16],
|
|---|
| 391 | OverscriptBox["p", "^"]], TraditionalForm]],
|
|---|
| 392 | FontSize->14]
|
|---|
| 393 | }], "Text",
|
|---|
| 394 | PageWidth->PaperWidth],
|
|---|
| 395 |
|
|---|
| 396 | Cell[BoxData[{
|
|---|
| 397 | RowBox[{
|
|---|
| 398 | RowBox[{
|
|---|
| 399 | RowBox[{"GGG", "[",
|
|---|
| 400 | RowBox[{
|
|---|
| 401 | "p1_", ",", "p2_", ",", "p3_", ",", "m1_", ",", "m2_", ",", "m3_"}],
|
|---|
| 402 | "]"}], ":=",
|
|---|
| 403 | RowBox[{
|
|---|
| 404 | RowBox[{
|
|---|
| 405 | RowBox[{"FV", "[",
|
|---|
| 406 | RowBox[{
|
|---|
| 407 | RowBox[{"p1", "-", "p2"}], ",", "m3"}], "]"}], " ",
|
|---|
| 408 | RowBox[{"MT", "[",
|
|---|
| 409 | RowBox[{"m1", ",", "m2"}], "]"}]}], "+",
|
|---|
| 410 | RowBox[{
|
|---|
| 411 | RowBox[{"FV", "[",
|
|---|
| 412 | RowBox[{
|
|---|
| 413 | RowBox[{"p2", "-", "p3"}], ",", "m1"}], "]"}], " ",
|
|---|
| 414 | RowBox[{"MT", "[",
|
|---|
| 415 | RowBox[{"m2", ",", "m3"}], "]"}]}], "+",
|
|---|
| 416 | RowBox[{
|
|---|
| 417 | RowBox[{"FV", "[",
|
|---|
| 418 | RowBox[{
|
|---|
| 419 | RowBox[{"p3", "-", "p1"}], ",", "m2"}], "]"}], " ",
|
|---|
| 420 | RowBox[{"MT", "[",
|
|---|
| 421 | RowBox[{"m1", ",", "m3"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 422 | RowBox[{
|
|---|
| 423 | RowBox[{
|
|---|
| 424 | RowBox[{"GGGD", "[",
|
|---|
| 425 | RowBox[{
|
|---|
| 426 | "p1_", ",", "p2_", ",", "p3_", ",", "m1_", ",", "m2_", ",", "m3_"}],
|
|---|
| 427 | "]"}], ":=",
|
|---|
| 428 | RowBox[{
|
|---|
| 429 | RowBox[{
|
|---|
| 430 | RowBox[{"FVD", "[",
|
|---|
| 431 | RowBox[{
|
|---|
| 432 | RowBox[{"p1", "-", "p2"}], ",", "m3"}], "]"}], " ",
|
|---|
| 433 | RowBox[{"MTD", "[",
|
|---|
| 434 | RowBox[{"m1", ",", "m2"}], "]"}]}], "+",
|
|---|
| 435 | RowBox[{
|
|---|
| 436 | RowBox[{"FVD", "[",
|
|---|
| 437 | RowBox[{
|
|---|
| 438 | RowBox[{"p2", "-", "p3"}], ",", "m1"}], "]"}], " ",
|
|---|
| 439 | RowBox[{"MTD", "[",
|
|---|
| 440 | RowBox[{"m2", ",", "m3"}], "]"}]}], "+",
|
|---|
| 441 | RowBox[{
|
|---|
| 442 | RowBox[{"FVD", "[",
|
|---|
| 443 | RowBox[{
|
|---|
| 444 | RowBox[{"p3", "-", "p1"}], ",", "m2"}], "]"}], " ",
|
|---|
| 445 | RowBox[{"MTD", "[",
|
|---|
| 446 | RowBox[{"m1", ",", "m3"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 447 | RowBox[{
|
|---|
| 448 | RowBox[{
|
|---|
| 449 | RowBox[{"GGGG", "[",
|
|---|
| 450 | RowBox[{"m1_", ",", "m2_", ",", "m3_", ",", "m4_"}], "]"}], ":=",
|
|---|
| 451 | RowBox[{
|
|---|
| 452 | RowBox[{"2", " ",
|
|---|
| 453 | RowBox[{"MT", "[",
|
|---|
| 454 | RowBox[{"m1", ",", "m2"}], "]"}], " ",
|
|---|
| 455 | RowBox[{"MT", "[",
|
|---|
| 456 | RowBox[{"m3", ",", "m4"}], "]"}]}], "-",
|
|---|
| 457 | RowBox[{
|
|---|
| 458 | RowBox[{"MT", "[",
|
|---|
| 459 | RowBox[{"m1", ",", "m3"}], "]"}], " ",
|
|---|
| 460 | RowBox[{"MT", "[",
|
|---|
| 461 | RowBox[{"m2", ",", "m4"}], "]"}]}], "-",
|
|---|
| 462 | RowBox[{
|
|---|
| 463 | RowBox[{"MT", "[",
|
|---|
| 464 | RowBox[{"m1", ",", "m4"}], "]"}], " ",
|
|---|
| 465 | RowBox[{"MT", "[",
|
|---|
| 466 | RowBox[{"m2", ",", "m3"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 467 | RowBox[{
|
|---|
| 468 | RowBox[{
|
|---|
| 469 | RowBox[{"GGGGD", "[",
|
|---|
| 470 | RowBox[{"m1_", ",", "m2_", ",", "m3_", ",", "m4_"}], "]"}], ":=",
|
|---|
| 471 | RowBox[{
|
|---|
| 472 | RowBox[{"2", " ",
|
|---|
| 473 | RowBox[{"MTD", "[",
|
|---|
| 474 | RowBox[{"m1", ",", "m2"}], "]"}], " ",
|
|---|
| 475 | RowBox[{"MTD", "[",
|
|---|
| 476 | RowBox[{"m3", ",", "m4"}], "]"}]}], "-",
|
|---|
| 477 | RowBox[{
|
|---|
| 478 | RowBox[{"MTD", "[",
|
|---|
| 479 | RowBox[{"m1", ",", "m3"}], "]"}], " ",
|
|---|
| 480 | RowBox[{"MTD", "[",
|
|---|
| 481 | RowBox[{"m2", ",", "m4"}], "]"}]}], "-",
|
|---|
| 482 | RowBox[{
|
|---|
| 483 | RowBox[{"MTD", "[",
|
|---|
| 484 | RowBox[{"m1", ",", "m4"}], "]"}], " ",
|
|---|
| 485 | RowBox[{"MTD", "[",
|
|---|
| 486 | RowBox[{"m2", ",", "m3"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 487 | RowBox[{
|
|---|
| 488 | RowBox[{"PropQuark", "=", "I"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 489 | RowBox[{
|
|---|
| 490 | RowBox[{"PropGluon", " ", "=",
|
|---|
| 491 | RowBox[{"-", "I"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 492 | RowBox[{
|
|---|
| 493 | RowBox[{"vtx", "=",
|
|---|
| 494 | RowBox[{
|
|---|
| 495 | RowBox[{"-", "I"}], " ", "gs"}]}], ";"}]}], "Input",
|
|---|
| 496 | PageWidth->PaperWidth]
|
|---|
| 497 | }, Open ]],
|
|---|
| 498 |
|
|---|
| 499 | Cell[CellGroupData[{
|
|---|
| 500 |
|
|---|
| 501 | Cell["Born Matrix element ", "Subsection",
|
|---|
| 502 | PageWidth->PaperWidth],
|
|---|
| 503 |
|
|---|
| 504 | Cell[CellGroupData[{
|
|---|
| 505 |
|
|---|
| 506 | Cell[BoxData[{
|
|---|
| 507 | RowBox[{"factborn", "=", "gs2"}], "\[IndentingNewLine]",
|
|---|
| 508 | RowBox[{
|
|---|
| 509 | RowBox[{"Born", "=",
|
|---|
| 510 | RowBox[{
|
|---|
| 511 | RowBox[{"factborn",
|
|---|
| 512 | RowBox[{"(", " ",
|
|---|
| 513 | RowBox[{
|
|---|
| 514 | RowBox[{
|
|---|
| 515 | RowBox[{"MTD", "[",
|
|---|
| 516 | RowBox[{"mu", ",", "nu"}], "]"}], " ",
|
|---|
| 517 | RowBox[{"SPD", "[",
|
|---|
| 518 | RowBox[{"p1", ",", "p2"}], "]"}]}], "-",
|
|---|
| 519 | RowBox[{
|
|---|
| 520 | RowBox[{"FVD", "[",
|
|---|
| 521 | RowBox[{"p1", ",", "nu"}], "]"}], " ",
|
|---|
| 522 | RowBox[{"FVD", "[",
|
|---|
| 523 | RowBox[{"p2", ",", "mu"}], "]"}]}]}], ")"}], " ",
|
|---|
| 524 | RowBox[{"FVD", "[",
|
|---|
| 525 | RowBox[{"e1", ",", "mu"}], "]"}], " ",
|
|---|
| 526 | RowBox[{"FVD", "[",
|
|---|
| 527 | RowBox[{"e2", ",", "nu"}], "]"}]}], "//", "Contract"}]}],
|
|---|
| 528 | ";"}], "\[IndentingNewLine]",
|
|---|
| 529 | RowBox[{
|
|---|
| 530 | RowBox[{"Born4", "=",
|
|---|
| 531 | RowBox[{"Born", "/.", " ",
|
|---|
| 532 | RowBox[{"D", "\[Rule]", "4"}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 533 | RowBox[{"Born", "=", "Born"}]}], "Input",
|
|---|
| 534 | PageWidth->PaperWidth],
|
|---|
| 535 |
|
|---|
| 536 | Cell[BoxData[
|
|---|
| 537 | FormBox["gs2", TraditionalForm]], "Output",
|
|---|
| 538 | CellChangeTimes->{3.5426318223635883`*^9, 3.692515519604402*^9,
|
|---|
| 539 | 3.6925218211499767`*^9, 3.692522404445462*^9, 3.692522452532443*^9}],
|
|---|
| 540 |
|
|---|
| 541 | Cell[BoxData[
|
|---|
| 542 | FormBox[
|
|---|
| 543 | RowBox[{
|
|---|
| 544 | FractionBox["1", "2"], " ", "gs2", " ", "Q2", " ",
|
|---|
| 545 | RowBox[{"(",
|
|---|
| 546 | RowBox[{
|
|---|
| 547 | FormBox[
|
|---|
| 548 | FormBox["e1",
|
|---|
| 549 | TraditionalForm],
|
|---|
| 550 | TraditionalForm],
|
|---|
| 551 | FormBox["\<\"\[CenterDot]\"\>",
|
|---|
| 552 | TraditionalForm],
|
|---|
| 553 | FormBox[
|
|---|
| 554 | FormBox["e2",
|
|---|
| 555 | TraditionalForm],
|
|---|
| 556 | TraditionalForm]}], ")"}]}], TraditionalForm]], "Output",
|
|---|
| 557 | CellChangeTimes->{3.5426318223635883`*^9, 3.692515519604402*^9,
|
|---|
| 558 | 3.6925218211499767`*^9, 3.692522404445462*^9, 3.692522452550085*^9}]
|
|---|
| 559 | }, Open ]],
|
|---|
| 560 |
|
|---|
| 561 | Cell[CellGroupData[{
|
|---|
| 562 |
|
|---|
| 563 | Cell[BoxData[{
|
|---|
| 564 | RowBox[{"BornSq", "=",
|
|---|
| 565 | RowBox[{
|
|---|
| 566 | RowBox[{"Normal", "[",
|
|---|
| 567 | RowBox[{"Series", "[",
|
|---|
| 568 | RowBox[{
|
|---|
| 569 | RowBox[{
|
|---|
| 570 | RowBox[{"(", "\[IndentingNewLine]",
|
|---|
| 571 | RowBox[{
|
|---|
| 572 | RowBox[{
|
|---|
| 573 | RowBox[{
|
|---|
| 574 | RowBox[{"gs2", "^", "2"}], " ", "/",
|
|---|
| 575 | RowBox[{
|
|---|
| 576 | RowBox[{"(",
|
|---|
| 577 | RowBox[{"D", "-", "2"}], ")"}], "^", "2"}]}], "*",
|
|---|
| 578 | RowBox[{"(", " ",
|
|---|
| 579 | RowBox[{
|
|---|
| 580 | RowBox[{
|
|---|
| 581 | RowBox[{"MTD", "[",
|
|---|
| 582 | RowBox[{"mu", ",", "nu"}], "]"}], " ",
|
|---|
| 583 | RowBox[{"SPD", "[",
|
|---|
| 584 | RowBox[{"p1", ",", "p2"}], "]"}]}], "-",
|
|---|
| 585 | RowBox[{
|
|---|
| 586 | RowBox[{"FVD", "[",
|
|---|
| 587 | RowBox[{"p1", ",", "nu"}], "]"}], " ",
|
|---|
| 588 | RowBox[{"FVD", "[",
|
|---|
| 589 | RowBox[{"p2", ",", "mu"}], "]"}]}]}], ")"}],
|
|---|
| 590 | RowBox[{"(", " ",
|
|---|
| 591 | RowBox[{
|
|---|
| 592 | RowBox[{
|
|---|
| 593 | RowBox[{"MTD", "[",
|
|---|
| 594 | RowBox[{"mu", ",", "nu"}], "]"}], " ",
|
|---|
| 595 | RowBox[{"SPD", "[",
|
|---|
| 596 | RowBox[{"p1", ",", "p2"}], "]"}]}], "-",
|
|---|
| 597 | RowBox[{
|
|---|
| 598 | RowBox[{"FVD", "[",
|
|---|
| 599 | RowBox[{"p1", ",", "nu"}], "]"}], " ",
|
|---|
| 600 | RowBox[{"FVD", "[",
|
|---|
| 601 | RowBox[{"p2", ",", "mu"}], "]"}]}]}], ")"}]}], " ", "//",
|
|---|
| 602 | "Contract"}], ")"}], " ", "/.", " ",
|
|---|
| 603 | RowBox[{"D", "\[Rule]",
|
|---|
| 604 | RowBox[{"4", "-",
|
|---|
| 605 | RowBox[{"2", "e"}]}]}]}], ",",
|
|---|
| 606 | RowBox[{"{",
|
|---|
| 607 | RowBox[{"e", ",", "0", ",", "2"}], "}"}]}], "]"}], "]"}], "//",
|
|---|
| 608 | "Simplify"}]}], "\[IndentingNewLine]",
|
|---|
| 609 | RowBox[{
|
|---|
| 610 | RowBox[{"BornSq4", "=",
|
|---|
| 611 | RowBox[{"BornSq", "/.", " ",
|
|---|
| 612 | RowBox[{"e", "\[Rule]", "0"}]}]}], ";"}]}], "Input"],
|
|---|
| 613 |
|
|---|
| 614 | Cell[BoxData[
|
|---|
| 615 | FormBox[
|
|---|
| 616 | RowBox[{
|
|---|
| 617 | FractionBox["1", "8"], " ",
|
|---|
| 618 | RowBox[{"(",
|
|---|
| 619 | RowBox[{
|
|---|
| 620 | SuperscriptBox["e", "2"], "+", "e", "+", "1"}], ")"}], " ",
|
|---|
| 621 | SuperscriptBox["gs2", "2"], " ",
|
|---|
| 622 | SuperscriptBox["Q2", "2"]}], TraditionalForm]], "Output",
|
|---|
| 623 | CellChangeTimes->{3.542631822489691*^9, 3.692515519701975*^9,
|
|---|
| 624 | 3.6925218211943827`*^9, 3.692522404519568*^9, 3.6925224525920267`*^9}]
|
|---|
| 625 | }, Open ]]
|
|---|
| 626 | }, Open ]],
|
|---|
| 627 |
|
|---|
| 628 | Cell[CellGroupData[{
|
|---|
| 629 |
|
|---|
| 630 | Cell["\<\
|
|---|
| 631 | My Scalar Integrals
|
|---|
| 632 | The commented expression seems not to work on Mathematica 10 + FC9\
|
|---|
| 633 | \>", "Subsection",
|
|---|
| 634 | PageWidth->PaperWidth,
|
|---|
| 635 | CellChangeTimes->{{3.692521838667712*^9, 3.692521858834566*^9}}],
|
|---|
| 636 |
|
|---|
| 637 | Cell[BoxData[
|
|---|
| 638 | RowBox[{
|
|---|
| 639 | RowBox[{"(*",
|
|---|
| 640 | RowBox[{
|
|---|
| 641 | RowBox[{
|
|---|
| 642 | RowBox[{"subInt", "[", "expr_", "]"}], ":=",
|
|---|
| 643 | RowBox[{"expr", "/.", " ",
|
|---|
| 644 | RowBox[{"{", "\[IndentingNewLine]",
|
|---|
| 645 | RowBox[{
|
|---|
| 646 | RowBox[{
|
|---|
| 647 | RowBox[{"B0", "[", "x__", "]"}], "\[Rule]", " ",
|
|---|
| 648 | RowBox[{
|
|---|
| 649 | RowBox[{"DUPI", "/",
|
|---|
| 650 | RowBox[{"(",
|
|---|
| 651 | RowBox[{"I", " ",
|
|---|
| 652 | RowBox[{"Pi", "^", "2"}]}], ")"}]}], " ",
|
|---|
| 653 | RowBox[{"MyB0", "[", "x", "]"}]}]}], ",", "\[IndentingNewLine]",
|
|---|
| 654 | RowBox[{
|
|---|
| 655 | RowBox[{"C0", "[", "x__", "]"}], "\[Rule]", " ",
|
|---|
| 656 | RowBox[{
|
|---|
| 657 | RowBox[{"DUPI", "/",
|
|---|
| 658 | RowBox[{"(",
|
|---|
| 659 | RowBox[{"I", " ",
|
|---|
| 660 | RowBox[{"Pi", "^", "2"}]}], ")"}]}], " ",
|
|---|
| 661 | RowBox[{"MyC0", "[", "x", "]"}]}]}], ",", "\[IndentingNewLine]",
|
|---|
| 662 | RowBox[{
|
|---|
| 663 | RowBox[{"D0", "[", "x__", "]"}], "\[Rule]", " ",
|
|---|
| 664 | RowBox[{
|
|---|
| 665 | RowBox[{"DUPI", "/",
|
|---|
| 666 | RowBox[{"(",
|
|---|
| 667 | RowBox[{"I", " ",
|
|---|
| 668 | RowBox[{"Pi", "^", "2"}]}], ")"}]}], " ",
|
|---|
| 669 | RowBox[{"MyD0", "[", "x", "]"}]}]}]}], "}"}]}]}], ";"}], "*)"}],
|
|---|
| 670 | "\[IndentingNewLine]",
|
|---|
| 671 | RowBox[{
|
|---|
| 672 | RowBox[{
|
|---|
| 673 | RowBox[{
|
|---|
| 674 | RowBox[{"subInt", "[", "expr_", "]"}], " ", ":=", " ",
|
|---|
| 675 | RowBox[{"Simplify", "[",
|
|---|
| 676 | RowBox[{"expr", " ", "/.", " ",
|
|---|
| 677 | RowBox[{"{",
|
|---|
| 678 | RowBox[{
|
|---|
| 679 | RowBox[{
|
|---|
| 680 | RowBox[{
|
|---|
| 681 | RowBox[{"PaVe", "[",
|
|---|
| 682 | RowBox[{"x_", ",", "y_", ",", "z_"}], "]"}], " ", "/;", " ",
|
|---|
| 683 | RowBox[{
|
|---|
| 684 | RowBox[{"Length", "[",
|
|---|
| 685 | RowBox[{"Join", "[",
|
|---|
| 686 | RowBox[{"y", ",", "z"}], "]"}], "]"}], " ", "\[Equal]", " ",
|
|---|
| 687 | "6"}]}], "\[Rule]",
|
|---|
| 688 | RowBox[{
|
|---|
| 689 | RowBox[{"DUPI", "/",
|
|---|
| 690 | RowBox[{"(",
|
|---|
| 691 | RowBox[{"I", " ",
|
|---|
| 692 | RowBox[{"Pi", "^", "2"}]}], ")"}]}], "MyC0"}]}], ",",
|
|---|
| 693 | "\[IndentingNewLine]",
|
|---|
| 694 | RowBox[{
|
|---|
| 695 | RowBox[{
|
|---|
| 696 | RowBox[{"PaVe", "[",
|
|---|
| 697 | RowBox[{"x_", ",", "y_", ",", "z_"}], "]"}], " ", "/;", " ",
|
|---|
| 698 | RowBox[{
|
|---|
| 699 | RowBox[{"Length", "[",
|
|---|
| 700 | RowBox[{"Join", "[",
|
|---|
| 701 | RowBox[{"y", ",", "z"}], "]"}], "]"}], " ", "\[Equal]", " ",
|
|---|
| 702 | "3"}]}], "\[Rule]",
|
|---|
| 703 | RowBox[{
|
|---|
| 704 | RowBox[{"DUPI", "/",
|
|---|
| 705 | RowBox[{"(",
|
|---|
| 706 | RowBox[{"I", " ",
|
|---|
| 707 | RowBox[{"Pi", "^", "2"}]}], ")"}]}], "MyB0"}]}]}], " ", "}"}]}],
|
|---|
| 708 | "]"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 709 | RowBox[{
|
|---|
| 710 | RowBox[{"MyC0", "=",
|
|---|
| 711 | RowBox[{
|
|---|
| 712 | RowBox[{"(",
|
|---|
| 713 | RowBox[{"c\[CapitalGamma]", "*",
|
|---|
| 714 | RowBox[{"(",
|
|---|
| 715 | RowBox[{
|
|---|
| 716 | RowBox[{"2", "/",
|
|---|
| 717 | RowBox[{"e", "^", "2"}]}], "-",
|
|---|
| 718 | RowBox[{"Pi", "^", "2"}], "-",
|
|---|
| 719 | RowBox[{
|
|---|
| 720 | RowBox[{"2", "/", "e"}], "*",
|
|---|
| 721 | RowBox[{"Log", "[",
|
|---|
| 722 | RowBox[{"Q2", "/", "mu2"}], "]"}]}], "+",
|
|---|
| 723 | RowBox[{
|
|---|
| 724 | RowBox[{"Log", "[",
|
|---|
| 725 | RowBox[{"Q2", "/", "mu2"}], "]"}], "^", "2"}]}], ")"}]}], ")"}],
|
|---|
| 726 | "/",
|
|---|
| 727 | RowBox[{"(",
|
|---|
| 728 | RowBox[{"2", "*", "Q2"}], ")"}]}]}], ";", " ",
|
|---|
| 729 | RowBox[{"(*", " ",
|
|---|
| 730 | RowBox[{"this", " ", "is", " ",
|
|---|
| 731 | RowBox[{"C0", "[",
|
|---|
| 732 | RowBox[{"0", ",", "0", ",", "Q2", ",", "0", ",", "0", ",", "0"}],
|
|---|
| 733 | "]"}]}], "*)"}], "\[IndentingNewLine]",
|
|---|
| 734 | RowBox[{"MyB0", "=",
|
|---|
| 735 | RowBox[{"c\[CapitalGamma]", " ",
|
|---|
| 736 | RowBox[{"(",
|
|---|
| 737 | RowBox[{
|
|---|
| 738 | RowBox[{"1", "/", "e"}], "+", "2", "-",
|
|---|
| 739 | RowBox[{"Log", "[",
|
|---|
| 740 | RowBox[{"Q2", "/", "mu2"}], "]"}]}], ")"}]}]}], ";", " ",
|
|---|
| 741 | RowBox[{"(*", " ",
|
|---|
| 742 | RowBox[{
|
|---|
| 743 | RowBox[{"this", " ", "is", " ",
|
|---|
| 744 | RowBox[{"B0", "[",
|
|---|
| 745 | RowBox[{"Q2", ",", "0", ",", "0"}], "]"}]}], ",", " ",
|
|---|
| 746 | RowBox[{
|
|---|
| 747 | RowBox[{"B0", "[",
|
|---|
| 748 | RowBox[{"0", ",", "0", ",", "0"}], "]"}], " ", "is", " ",
|
|---|
| 749 | "automatically", " ", "discarded", " ", "by", " ", "FC", " ",
|
|---|
| 750 | RowBox[{"(",
|
|---|
| 751 | RowBox[{"it", " ", "is", " ", "0"}], ")"}]}]}], "*)"}],
|
|---|
| 752 | "\n"}]}]}]], "Input",
|
|---|
| 753 | PageWidth->PaperWidth,
|
|---|
| 754 | CellChangeTimes->{{3.692521981776946*^9, 3.692522061165731*^9},
|
|---|
| 755 | 3.692522128293076*^9, 3.692522194390325*^9, {3.692522247972107*^9,
|
|---|
| 756 | 3.6925223829969473`*^9}, {3.692522439712294*^9, 3.692522440039565*^9}, {
|
|---|
| 757 | 3.69252247672123*^9, 3.692522488719124*^9}}],
|
|---|
| 758 |
|
|---|
| 759 | Cell[BoxData[""], "Input"],
|
|---|
| 760 |
|
|---|
| 761 | Cell[BoxData[""], "Input"]
|
|---|
| 762 | }, Open ]]
|
|---|
| 763 | }, Open ]],
|
|---|
| 764 |
|
|---|
| 765 | Cell[CellGroupData[{
|
|---|
| 766 |
|
|---|
| 767 | Cell["CDR", "Section"],
|
|---|
| 768 |
|
|---|
| 769 | Cell[CellGroupData[{
|
|---|
| 770 |
|
|---|
| 771 | Cell["Vertex Diagram ", "Subsection",
|
|---|
| 772 | PageWidth->PaperWidth],
|
|---|
| 773 |
|
|---|
| 774 | Cell[CellGroupData[{
|
|---|
| 775 |
|
|---|
| 776 | Cell[BoxData[{
|
|---|
| 777 | RowBox[{
|
|---|
| 778 | RowBox[{"colorvtx", "=",
|
|---|
| 779 | RowBox[{
|
|---|
| 780 | RowBox[{
|
|---|
| 781 | RowBox[{"SUNF", "[",
|
|---|
| 782 | RowBox[{"b", ",", "x", ",", "y"}], "]"}],
|
|---|
| 783 | RowBox[{"SUNF", "[",
|
|---|
| 784 | RowBox[{"y", ",", "a", ",", "x"}], "]"}]}], " ", "//",
|
|---|
| 785 | "SUNSimplify"}]}], "\n"}], "\[IndentingNewLine]",
|
|---|
| 786 | RowBox[{
|
|---|
| 787 | RowBox[{"num", "=",
|
|---|
| 788 | RowBox[{
|
|---|
| 789 | RowBox[{
|
|---|
| 790 | RowBox[{"gs2", "^", "2"}], "*",
|
|---|
| 791 | RowBox[{"(",
|
|---|
| 792 | RowBox[{"-", "gs2"}], ")"}], "*", "I", "*", "\[IndentingNewLine]",
|
|---|
| 793 | RowBox[{"(", " ",
|
|---|
| 794 | RowBox[{
|
|---|
| 795 | RowBox[{
|
|---|
| 796 | RowBox[{"MTD", "[",
|
|---|
| 797 | RowBox[{"al", ",", "be"}], "]"}], " ",
|
|---|
| 798 | RowBox[{"SPD", "[",
|
|---|
| 799 | RowBox[{
|
|---|
| 800 | RowBox[{
|
|---|
| 801 | RowBox[{"-", "l"}], "+", "p1"}], ",",
|
|---|
| 802 | RowBox[{"p2", "+", "l"}]}], "]"}]}], "-", " ",
|
|---|
| 803 | RowBox[{
|
|---|
| 804 | RowBox[{"FVD", "[",
|
|---|
| 805 | RowBox[{
|
|---|
| 806 | RowBox[{
|
|---|
| 807 | RowBox[{"-", "l"}], "+", "p1"}], ",", "be"}], "]"}], " ",
|
|---|
| 808 | RowBox[{"FVD", "[",
|
|---|
| 809 | RowBox[{
|
|---|
| 810 | RowBox[{"p2", "+", "l"}], ",", "al"}], "]"}]}]}], ")"}], " ", "*",
|
|---|
| 811 | " ",
|
|---|
| 812 | RowBox[{"GGGD", "[",
|
|---|
| 813 | RowBox[{
|
|---|
| 814 | RowBox[{"-", "l"}], ",", "p1", ",",
|
|---|
| 815 | RowBox[{"l", "-", "p1"}], ",", "ro", ",", "mu", ",", "al"}], "]"}],
|
|---|
| 816 | "*", "\[IndentingNewLine]",
|
|---|
| 817 | RowBox[{"GGGD", "[",
|
|---|
| 818 | RowBox[{"p2", ",", "l", ",",
|
|---|
| 819 | RowBox[{
|
|---|
| 820 | RowBox[{"-", "l"}], "-", "p2"}], ",", "nu", ",", "ro", ",", "be"}],
|
|---|
| 821 | "]"}], "*",
|
|---|
| 822 | RowBox[{"(", " ",
|
|---|
| 823 | RowBox[{
|
|---|
| 824 | RowBox[{
|
|---|
| 825 | RowBox[{"MTD", "[",
|
|---|
| 826 | RowBox[{"mu", ",", "nu"}], "]"}], " ",
|
|---|
| 827 | RowBox[{"SPD", "[",
|
|---|
| 828 | RowBox[{"p1", ",", "p2"}], "]"}]}], "-",
|
|---|
| 829 | RowBox[{
|
|---|
| 830 | RowBox[{"FVD", "[",
|
|---|
| 831 | RowBox[{"p1", ",", "nu"}], "]"}], " ",
|
|---|
| 832 | RowBox[{"FVD", "[",
|
|---|
| 833 | RowBox[{"p2", ",", "mu"}], "]"}]}]}], ")"}]}], " ", "//",
|
|---|
| 834 | "Contract"}]}], ";"}], "\n",
|
|---|
| 835 | RowBox[{
|
|---|
| 836 | RowBox[{"dens", "=",
|
|---|
| 837 | RowBox[{"FAD", "[",
|
|---|
| 838 | RowBox[{"l", ",",
|
|---|
| 839 | RowBox[{"p1", "-", "l"}], ",",
|
|---|
| 840 | RowBox[{"l", "+", "p2"}]}], "]"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 841 | RowBox[{
|
|---|
| 842 | RowBox[{"amp", "=",
|
|---|
| 843 | RowBox[{"CA", " ", "dens", "*", " ",
|
|---|
| 844 | RowBox[{"num", "/",
|
|---|
| 845 | RowBox[{
|
|---|
| 846 | RowBox[{"(",
|
|---|
| 847 | RowBox[{"D", "-", "2"}], ")"}], "^", "2"}]}]}]}], ";"}], "\n",
|
|---|
| 848 | RowBox[{"inte1", "=",
|
|---|
| 849 | RowBox[{
|
|---|
| 850 | RowBox[{
|
|---|
| 851 | RowBox[{"(",
|
|---|
| 852 | RowBox[{
|
|---|
| 853 | RowBox[{
|
|---|
| 854 | RowBox[{"(",
|
|---|
| 855 | RowBox[{
|
|---|
| 856 | RowBox[{
|
|---|
| 857 | RowBox[{"OneLoop", "[",
|
|---|
| 858 | RowBox[{"l", ",",
|
|---|
| 859 | RowBox[{"amp", "/", "DUPI"}]}], "]"}], "//", "PaVeReduce"}], "//",
|
|---|
| 860 | "Simplify"}], ")"}], "//", "Factor"}], "//", "Simplify"}], ")"}], "/.",
|
|---|
| 861 | " ",
|
|---|
| 862 | RowBox[{
|
|---|
| 863 | RowBox[{"B0", "[",
|
|---|
| 864 | RowBox[{"0", ",", "0", ",", "0"}], "]"}], "\[Rule]", "0"}]}], " ", "//",
|
|---|
| 865 | "Simplify"}]}]}], "Input",
|
|---|
| 866 | PageWidth->PaperWidth,
|
|---|
| 867 | CellChangeTimes->{{3.692522149415956*^9, 3.6925221619920483`*^9}, {
|
|---|
| 868 | 3.692522495640565*^9, 3.6925224959986963`*^9}}],
|
|---|
| 869 |
|
|---|
| 870 | Cell[BoxData[
|
|---|
| 871 | FormBox[
|
|---|
| 872 | RowBox[{
|
|---|
| 873 | SubscriptBox["C", "A"], " ",
|
|---|
| 874 | SuperscriptBox["\[Delta]",
|
|---|
| 875 | RowBox[{
|
|---|
| 876 | FormBox[
|
|---|
| 877 | FormBox["a",
|
|---|
| 878 | TraditionalForm],
|
|---|
| 879 | TraditionalForm],
|
|---|
| 880 | FormBox[
|
|---|
| 881 | FormBox["b",
|
|---|
| 882 | TraditionalForm],
|
|---|
| 883 | TraditionalForm]}]]}], TraditionalForm]], "Output",
|
|---|
| 884 | CellChangeTimes->{3.692522404810404*^9, 3.69252245267111*^9,
|
|---|
| 885 | 3.692522499089229*^9}],
|
|---|
| 886 |
|
|---|
| 887 | Cell[BoxData[
|
|---|
| 888 | FormBox[
|
|---|
| 889 | RowBox[{"-",
|
|---|
| 890 | FractionBox[
|
|---|
| 891 | RowBox[{
|
|---|
| 892 | SuperscriptBox["\[Pi]", "2"], " ",
|
|---|
| 893 | SuperscriptBox["gs2", "3"], " ",
|
|---|
| 894 | SuperscriptBox["Q2", "2"], " ",
|
|---|
| 895 | SubscriptBox["C", "A"], " ",
|
|---|
| 896 | RowBox[{"(",
|
|---|
| 897 | RowBox[{
|
|---|
| 898 | RowBox[{
|
|---|
| 899 | RowBox[{"(",
|
|---|
| 900 | RowBox[{
|
|---|
| 901 | RowBox[{"-",
|
|---|
| 902 | RowBox[{"20", " ",
|
|---|
| 903 | SuperscriptBox["D", "2"]}]}], "+",
|
|---|
| 904 | RowBox[{"73", " ", "D"}], "-", "52"}], ")"}], " ",
|
|---|
| 905 | FormBox[
|
|---|
| 906 | RowBox[{
|
|---|
| 907 | SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(",
|
|---|
| 908 | RowBox[{"Q2", ",", "0", ",", "0"}], ")"}],
|
|---|
| 909 | TraditionalForm]}], "+",
|
|---|
| 910 | RowBox[{"8", " ",
|
|---|
| 911 | RowBox[{"(",
|
|---|
| 912 | RowBox[{
|
|---|
| 913 | SuperscriptBox["D", "2"], "-",
|
|---|
| 914 | RowBox[{"3", " ", "D"}], "+", "2"}], ")"}], " ", "Q2", " ",
|
|---|
| 915 | FormBox[
|
|---|
| 916 | RowBox[{
|
|---|
| 917 | SubscriptBox["\<\"C\"\>", "\<\"0\"\>"], "(",
|
|---|
| 918 | RowBox[{"0", ",", "0", ",", "Q2", ",", "0", ",", "0", ",", "0"}],
|
|---|
| 919 | ")"}],
|
|---|
| 920 | TraditionalForm]}]}], ")"}]}],
|
|---|
| 921 | RowBox[{"16", " ",
|
|---|
| 922 | SuperscriptBox[
|
|---|
| 923 | RowBox[{"(",
|
|---|
| 924 | RowBox[{"D", "-", "2"}], ")"}], "2"], " ",
|
|---|
| 925 | RowBox[{"(",
|
|---|
| 926 | RowBox[{"D", "-", "1"}], ")"}], " ", "DUPI"}]]}],
|
|---|
| 927 | TraditionalForm]], "Output",
|
|---|
| 928 | CellChangeTimes->{3.692522404810404*^9, 3.69252245267111*^9,
|
|---|
| 929 | 3.6925225004402237`*^9}]
|
|---|
| 930 | }, Open ]],
|
|---|
| 931 |
|
|---|
| 932 | Cell[BoxData[""], "Input"]
|
|---|
| 933 | }, Open ]],
|
|---|
| 934 |
|
|---|
| 935 | Cell[CellGroupData[{
|
|---|
| 936 |
|
|---|
| 937 | Cell["4-gluon Diagram ", "Subsection",
|
|---|
| 938 | PageWidth->PaperWidth],
|
|---|
| 939 |
|
|---|
| 940 | Cell[CellGroupData[{
|
|---|
| 941 |
|
|---|
| 942 | Cell[BoxData[{
|
|---|
| 943 | RowBox[{
|
|---|
| 944 | RowBox[{"color", "=",
|
|---|
| 945 | RowBox[{
|
|---|
| 946 | RowBox[{
|
|---|
| 947 | RowBox[{"SUNF", "[",
|
|---|
| 948 | RowBox[{"b", ",", "c", ",", "y"}], "]"}],
|
|---|
| 949 | RowBox[{"SUNF", "[",
|
|---|
| 950 | RowBox[{"y", ",", "a", ",", "c"}], "]"}]}], " ", "//",
|
|---|
| 951 | "SUNSimplify"}]}], ";"}], "\n",
|
|---|
| 952 | RowBox[{
|
|---|
| 953 | RowBox[{"num", "=",
|
|---|
| 954 | RowBox[{
|
|---|
| 955 | RowBox[{
|
|---|
| 956 | RowBox[{"gs2", "^", "2"}], "*", "I", "*", " ", "gs2", "*",
|
|---|
| 957 | RowBox[{"(", " ",
|
|---|
| 958 | RowBox[{
|
|---|
| 959 | RowBox[{
|
|---|
| 960 | RowBox[{"MTD", "[",
|
|---|
| 961 | RowBox[{"ro", ",", "si"}], "]"}], " ",
|
|---|
| 962 | RowBox[{"SPD", "[",
|
|---|
| 963 | RowBox[{"l", ",",
|
|---|
| 964 | RowBox[{
|
|---|
| 965 | RowBox[{"-", "l"}], "+", "p1", "+", "p2"}]}], "]"}]}], "-", " ",
|
|---|
| 966 | RowBox[{
|
|---|
| 967 | RowBox[{"FVD", "[",
|
|---|
| 968 | RowBox[{"l", ",", "si"}], "]"}], " ",
|
|---|
| 969 | RowBox[{"FVD", "[",
|
|---|
| 970 | RowBox[{
|
|---|
| 971 | RowBox[{
|
|---|
| 972 | RowBox[{"-", "l"}], "+", "p1", "+", "p2"}], ",", "ro"}], "]"}]}]}],
|
|---|
| 973 | ")"}], " ", "*", " ",
|
|---|
| 974 | RowBox[{"GGGGD", "[",
|
|---|
| 975 | RowBox[{"nu", ",", "mu", ",", "ro", ",", "si"}], "]"}], " ", "*",
|
|---|
| 976 | RowBox[{"(", " ",
|
|---|
| 977 | RowBox[{
|
|---|
| 978 | RowBox[{
|
|---|
| 979 | RowBox[{"MTD", "[",
|
|---|
| 980 | RowBox[{"mu", ",", "nu"}], "]"}], " ",
|
|---|
| 981 | RowBox[{"SPD", "[",
|
|---|
| 982 | RowBox[{"p1", ",", "p2"}], "]"}]}], "-",
|
|---|
| 983 | RowBox[{
|
|---|
| 984 | RowBox[{"FVD", "[",
|
|---|
| 985 | RowBox[{"p1", ",", "nu"}], "]"}], " ",
|
|---|
| 986 | RowBox[{"FVD", "[",
|
|---|
| 987 | RowBox[{"p2", ",", "mu"}], "]"}]}]}], ")"}]}], " ", "//",
|
|---|
| 988 | "Contract"}]}], ";"}], "\n",
|
|---|
| 989 | RowBox[{
|
|---|
| 990 | RowBox[{"dens", "=",
|
|---|
| 991 | RowBox[{"FAD", "[",
|
|---|
| 992 | RowBox[{"l", ",",
|
|---|
| 993 | RowBox[{"l", "-", "p1", "-", "p2"}]}], "]"}]}], ";"}], "\n",
|
|---|
| 994 | RowBox[{
|
|---|
| 995 | RowBox[{"amp", "=",
|
|---|
| 996 | RowBox[{
|
|---|
| 997 | RowBox[{"CA", "/", "2"}], " ", "dens", "*",
|
|---|
| 998 | RowBox[{"num", "/",
|
|---|
| 999 | RowBox[{
|
|---|
| 1000 | RowBox[{"(",
|
|---|
| 1001 | RowBox[{"D", "-", "2"}], ")"}], "^", "2"}]}]}]}],
|
|---|
| 1002 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1003 | RowBox[{"inte2", "=",
|
|---|
| 1004 | RowBox[{
|
|---|
| 1005 | RowBox[{
|
|---|
| 1006 | RowBox[{"(",
|
|---|
| 1007 | RowBox[{
|
|---|
| 1008 | RowBox[{
|
|---|
| 1009 | RowBox[{"OneLoop", "[",
|
|---|
| 1010 | RowBox[{"l", ",",
|
|---|
| 1011 | RowBox[{"amp", "/", "DUPI"}]}], "]"}], "//", "PaVeReduce"}], "//",
|
|---|
| 1012 | "Simplify"}], ")"}], "//", "Factor"}], "//", "Simplify"}]}]}], "Input",
|
|---|
| 1013 | PageWidth->PaperWidth],
|
|---|
| 1014 |
|
|---|
| 1015 | Cell[BoxData[
|
|---|
| 1016 | FormBox[
|
|---|
| 1017 | RowBox[{"-",
|
|---|
| 1018 | FractionBox[
|
|---|
| 1019 | RowBox[{
|
|---|
| 1020 | SuperscriptBox["\[Pi]", "2"], " ",
|
|---|
| 1021 | RowBox[{"(",
|
|---|
| 1022 | RowBox[{
|
|---|
| 1023 | RowBox[{"2", " ", "D"}], "-", "3"}], ")"}], " ",
|
|---|
| 1024 | RowBox[{"(",
|
|---|
| 1025 | RowBox[{
|
|---|
| 1026 | RowBox[{"2", " ",
|
|---|
| 1027 | SuperscriptBox["D", "2"]}], "-",
|
|---|
| 1028 | RowBox[{"5", " ", "D"}], "+", "4"}], ")"}], " ",
|
|---|
| 1029 | SuperscriptBox["gs2", "3"], " ",
|
|---|
| 1030 | SuperscriptBox["Q2", "2"], " ",
|
|---|
| 1031 | SubscriptBox["C", "A"], " ",
|
|---|
| 1032 | FormBox[
|
|---|
| 1033 | RowBox[{
|
|---|
| 1034 | SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(",
|
|---|
| 1035 | RowBox[{"Q2", ",", "0", ",", "0"}], ")"}],
|
|---|
| 1036 | TraditionalForm]}],
|
|---|
| 1037 | RowBox[{"16", " ",
|
|---|
| 1038 | SuperscriptBox[
|
|---|
| 1039 | RowBox[{"(",
|
|---|
| 1040 | RowBox[{"D", "-", "2"}], ")"}], "2"], " ",
|
|---|
| 1041 | RowBox[{"(",
|
|---|
| 1042 | RowBox[{"D", "-", "1"}], ")"}], " ", "DUPI"}]]}],
|
|---|
| 1043 | TraditionalForm]], "Output",
|
|---|
| 1044 | CellChangeTimes->{3.5426318360589*^9, 3.692515521760001*^9,
|
|---|
| 1045 | 3.692521920374544*^9, 3.692522407076551*^9, 3.692522514659532*^9}]
|
|---|
| 1046 | }, Open ]]
|
|---|
| 1047 | }, Open ]],
|
|---|
| 1048 |
|
|---|
| 1049 | Cell[CellGroupData[{
|
|---|
| 1050 |
|
|---|
| 1051 | Cell["Sum the virtuals", "Subsection"],
|
|---|
| 1052 |
|
|---|
| 1053 | Cell[CellGroupData[{
|
|---|
| 1054 |
|
|---|
| 1055 | Cell[BoxData[
|
|---|
| 1056 | RowBox[{"\[IndentingNewLine]",
|
|---|
| 1057 | RowBox[{
|
|---|
| 1058 | RowBox[{"res1", "=", " ",
|
|---|
| 1059 | RowBox[{
|
|---|
| 1060 | RowBox[{
|
|---|
| 1061 | RowBox[{
|
|---|
| 1062 | RowBox[{
|
|---|
| 1063 | RowBox[{
|
|---|
| 1064 | RowBox[{"-", "1"}], "/", "2"}], "*", "\[IndentingNewLine]",
|
|---|
| 1065 | RowBox[{"Normal", "[",
|
|---|
| 1066 | RowBox[{"Series", "[",
|
|---|
| 1067 | RowBox[{
|
|---|
| 1068 | RowBox[{
|
|---|
| 1069 | RowBox[{
|
|---|
| 1070 | RowBox[{
|
|---|
| 1071 | RowBox[{
|
|---|
| 1072 | RowBox[{
|
|---|
| 1073 | RowBox[{"(", "inte1", ")"}], "/", "BornSq"}], "/", "I"}], "/",
|
|---|
| 1074 | RowBox[{
|
|---|
| 1075 | RowBox[{"(",
|
|---|
| 1076 | RowBox[{"mu2", "/", "Q2"}], ")"}], "^",
|
|---|
| 1077 | RowBox[{"(", "e", ")"}]}]}], " ", "/.", " ",
|
|---|
| 1078 | RowBox[{"D", "\[Rule]",
|
|---|
| 1079 | RowBox[{"4", "-",
|
|---|
| 1080 | RowBox[{"2", "e"}]}]}]}], "//", " ", "subInt"}], ",",
|
|---|
| 1081 | RowBox[{"{",
|
|---|
| 1082 | RowBox[{"e", ",", "0", ",", "0"}], "}"}]}], "]"}], "]"}]}], "//",
|
|---|
| 1083 | "Simplify"}], "//", "PowerExpand"}], "//", "Expand"}]}],
|
|---|
| 1084 | "\[IndentingNewLine]", "\[IndentingNewLine]",
|
|---|
| 1085 | RowBox[{"res2", "=", " ",
|
|---|
| 1086 | RowBox[{
|
|---|
| 1087 | RowBox[{
|
|---|
| 1088 | RowBox[{
|
|---|
| 1089 | RowBox[{
|
|---|
| 1090 | RowBox[{
|
|---|
| 1091 | RowBox[{"-", "1"}], "/", "2"}], "*", "\[IndentingNewLine]",
|
|---|
| 1092 | RowBox[{"Normal", "[",
|
|---|
| 1093 | RowBox[{"Series", "[",
|
|---|
| 1094 | RowBox[{
|
|---|
| 1095 | RowBox[{
|
|---|
| 1096 | RowBox[{
|
|---|
| 1097 | RowBox[{
|
|---|
| 1098 | RowBox[{
|
|---|
| 1099 | RowBox[{
|
|---|
| 1100 | RowBox[{"(", "inte2", ")"}], "/", "BornSq"}], "/", "I"}], "/",
|
|---|
| 1101 | RowBox[{
|
|---|
| 1102 | RowBox[{"(",
|
|---|
| 1103 | RowBox[{"mu2", "/", "Q2"}], ")"}], "^",
|
|---|
| 1104 | RowBox[{"(", "e", ")"}]}]}], " ", "/.", " ",
|
|---|
| 1105 | RowBox[{"D", "\[Rule]",
|
|---|
| 1106 | RowBox[{"4", "-",
|
|---|
| 1107 | RowBox[{"2", "e"}]}]}]}], "//", " ", "subInt"}], ",",
|
|---|
| 1108 | RowBox[{"{",
|
|---|
| 1109 | RowBox[{"e", ",", "0", ",", "0"}], "}"}]}], "]"}], "]"}]}], "//",
|
|---|
| 1110 | "Simplify"}], "//", "PowerExpand"}], "//", "Expand"}]}],
|
|---|
| 1111 | "\n"}]}]], "Input",
|
|---|
| 1112 | PageWidth->PaperWidth,
|
|---|
| 1113 | CellChangeTimes->{{3.54263188574975*^9, 3.542631902626193*^9}}],
|
|---|
| 1114 |
|
|---|
| 1115 | Cell[BoxData[
|
|---|
| 1116 | FormBox[
|
|---|
| 1117 | RowBox[{
|
|---|
| 1118 | RowBox[{"-",
|
|---|
| 1119 | FractionBox[
|
|---|
| 1120 | RowBox[{"c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1121 | SubscriptBox["C", "A"]}],
|
|---|
| 1122 | SuperscriptBox["e", "2"]]}], "+",
|
|---|
| 1123 | FractionBox[
|
|---|
| 1124 | RowBox[{"5", " ", "c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1125 | SubscriptBox["C", "A"]}],
|
|---|
| 1126 | RowBox[{"3", " ", "e"}]], "+",
|
|---|
| 1127 | RowBox[{
|
|---|
| 1128 | FractionBox["179", "72"], " ", "c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1129 | SubscriptBox["C", "A"]}], "+",
|
|---|
| 1130 | RowBox[{
|
|---|
| 1131 | FractionBox["1", "2"], " ",
|
|---|
| 1132 | SuperscriptBox["\[Pi]", "2"], " ", "c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1133 | SubscriptBox["C", "A"]}]}], TraditionalForm]], "Output",
|
|---|
| 1134 | CellChangeTimes->{
|
|---|
| 1135 | 3.542631840971065*^9, {3.542631900146366*^9, 3.542631903265226*^9},
|
|---|
| 1136 | 3.69251552178992*^9, 3.692521932580472*^9, {3.692522077916459*^9,
|
|---|
| 1137 | 3.692522101803856*^9}, 3.692522134521243*^9, 3.692522519476282*^9}],
|
|---|
| 1138 |
|
|---|
| 1139 | Cell[BoxData[
|
|---|
| 1140 | FormBox[
|
|---|
| 1141 | RowBox[{
|
|---|
| 1142 | RowBox[{"-",
|
|---|
| 1143 | FractionBox[
|
|---|
| 1144 | RowBox[{"5", " ", "c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1145 | SubscriptBox["C", "A"]}],
|
|---|
| 1146 | RowBox[{"3", " ", "e"}]]}], "-",
|
|---|
| 1147 | RowBox[{
|
|---|
| 1148 | FractionBox["179", "72"], " ", "c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1149 | SubscriptBox["C", "A"]}]}], TraditionalForm]], "Output",
|
|---|
| 1150 | CellChangeTimes->{
|
|---|
| 1151 | 3.542631840971065*^9, {3.542631900146366*^9, 3.542631903265226*^9},
|
|---|
| 1152 | 3.69251552178992*^9, 3.692521932580472*^9, {3.692522077916459*^9,
|
|---|
| 1153 | 3.692522101803856*^9}, 3.692522134521243*^9, 3.692522519526516*^9}]
|
|---|
| 1154 | }, Open ]],
|
|---|
| 1155 |
|
|---|
| 1156 | Cell[CellGroupData[{
|
|---|
| 1157 |
|
|---|
| 1158 | Cell[BoxData[
|
|---|
| 1159 | RowBox[{"\[IndentingNewLine]",
|
|---|
| 1160 | RowBox[{"res", "=", " ",
|
|---|
| 1161 | RowBox[{
|
|---|
| 1162 | RowBox[{
|
|---|
| 1163 | RowBox[{
|
|---|
| 1164 | RowBox[{
|
|---|
| 1165 | RowBox[{
|
|---|
| 1166 | RowBox[{"-", "1"}], "/", "2"}], "*", "\[IndentingNewLine]",
|
|---|
| 1167 | RowBox[{"Normal", "[",
|
|---|
| 1168 | RowBox[{"Series", "[",
|
|---|
| 1169 | RowBox[{
|
|---|
| 1170 | RowBox[{
|
|---|
| 1171 | RowBox[{
|
|---|
| 1172 | RowBox[{
|
|---|
| 1173 | RowBox[{
|
|---|
| 1174 | RowBox[{
|
|---|
| 1175 | RowBox[{"(",
|
|---|
| 1176 | RowBox[{"inte1", "+", "inte2"}], ")"}], "/", "BornSq"}], "/",
|
|---|
| 1177 | "I"}], "/",
|
|---|
| 1178 | RowBox[{
|
|---|
| 1179 | RowBox[{"(",
|
|---|
| 1180 | RowBox[{"mu2", "/", "Q2"}], ")"}], "^",
|
|---|
| 1181 | RowBox[{"(", "e", ")"}]}]}], " ", "/.", " ",
|
|---|
| 1182 | RowBox[{"D", "\[Rule]",
|
|---|
| 1183 | RowBox[{"4", "-",
|
|---|
| 1184 | RowBox[{"2", "e"}]}]}]}], "//", " ", "subInt"}], ",",
|
|---|
| 1185 | RowBox[{"{",
|
|---|
| 1186 | RowBox[{"e", ",", "0", ",", "0"}], "}"}]}], "]"}], "]"}]}], "//",
|
|---|
| 1187 | "Simplify"}], "//", "PowerExpand"}], "//", "Expand"}]}]}]], "Input",
|
|---|
| 1188 | PageWidth->PaperWidth],
|
|---|
| 1189 |
|
|---|
| 1190 | Cell[BoxData[
|
|---|
| 1191 | FormBox[
|
|---|
| 1192 | RowBox[{
|
|---|
| 1193 | RowBox[{
|
|---|
| 1194 | FractionBox["1", "2"], " ",
|
|---|
| 1195 | SuperscriptBox["\[Pi]", "2"], " ", "c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1196 | SubscriptBox["C", "A"]}], "-",
|
|---|
| 1197 | FractionBox[
|
|---|
| 1198 | RowBox[{"c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1199 | SubscriptBox["C", "A"]}],
|
|---|
| 1200 | SuperscriptBox["e", "2"]]}], TraditionalForm]], "Output",
|
|---|
| 1201 | CellChangeTimes->{3.542631840971065*^9, 3.692515521882228*^9,
|
|---|
| 1202 | 3.692522543770403*^9}]
|
|---|
| 1203 | }, Open ]]
|
|---|
| 1204 | }, Open ]],
|
|---|
| 1205 |
|
|---|
| 1206 | Cell[CellGroupData[{
|
|---|
| 1207 |
|
|---|
| 1208 | Cell["Add is the contribution from Hgg operator", "Subsection",
|
|---|
| 1209 | CellChangeTimes->{{3.692531754609666*^9, 3.692531767359894*^9}}],
|
|---|
| 1210 |
|
|---|
| 1211 | Cell[CellGroupData[{
|
|---|
| 1212 |
|
|---|
| 1213 | Cell[BoxData[{
|
|---|
| 1214 | RowBox[{
|
|---|
| 1215 | RowBox[{"add", "=",
|
|---|
| 1216 | RowBox[{
|
|---|
| 1217 | RowBox[{"1", "/", "2"}],
|
|---|
| 1218 | RowBox[{"(",
|
|---|
| 1219 | RowBox[{
|
|---|
| 1220 | RowBox[{"Normal", "[",
|
|---|
| 1221 | RowBox[{"Series", "[",
|
|---|
| 1222 | RowBox[{
|
|---|
| 1223 | RowBox[{"(",
|
|---|
| 1224 | RowBox[{
|
|---|
| 1225 | RowBox[{"(",
|
|---|
| 1226 | RowBox[{"1", "+", " ",
|
|---|
| 1227 | RowBox[{
|
|---|
| 1228 | RowBox[{
|
|---|
| 1229 | RowBox[{"19", "/", "4"}], "/", "\[Pi]"}], " ",
|
|---|
| 1230 | RowBox[{"gs2", "/",
|
|---|
| 1231 | RowBox[{"(",
|
|---|
| 1232 | RowBox[{"4", "\[Pi]"}], ")"}]}]}]}], " ", ")"}], "/",
|
|---|
| 1233 | RowBox[{"(",
|
|---|
| 1234 | RowBox[{"1", "+",
|
|---|
| 1235 | RowBox[{"2", " ",
|
|---|
| 1236 | RowBox[{
|
|---|
| 1237 | RowBox[{"gs2", "/",
|
|---|
| 1238 | RowBox[{"(",
|
|---|
| 1239 | RowBox[{"4", "\[Pi]"}], ")"}]}], "/", "\[Pi]"}]}]}], ")"}]}],
|
|---|
| 1240 | ")"}], ",",
|
|---|
| 1241 | RowBox[{"{",
|
|---|
| 1242 | RowBox[{"gs2", ",", "0", ",", "1"}], "}"}]}], "]"}], "]"}], "-",
|
|---|
| 1243 | "1"}], ")"}], "c\[CapitalGamma]", " ",
|
|---|
| 1244 | RowBox[{"CA", "/", "3"}], " ", "16",
|
|---|
| 1245 | RowBox[{"Pi", "^", "2"}]}]}], " ", ";"}], "\[IndentingNewLine]",
|
|---|
| 1246 | RowBox[{
|
|---|
| 1247 | RowBox[{"virt", "=",
|
|---|
| 1248 | RowBox[{"add", "+", "res"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1249 | RowBox[{
|
|---|
| 1250 | RowBox[{"virt1", "=", "res1"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1251 | RowBox[{
|
|---|
| 1252 | RowBox[{
|
|---|
| 1253 | RowBox[{"virt2", "=", "res2"}], ";"}],
|
|---|
| 1254 | "\[IndentingNewLine]"}], "\[IndentingNewLine]", "add"}], "Input",
|
|---|
| 1255 | PageWidth->PaperWidth,
|
|---|
| 1256 | CellChangeTimes->{{3.5426319374668407`*^9, 3.542631949496957*^9},
|
|---|
| 1257 | 3.692522571042892*^9}],
|
|---|
| 1258 |
|
|---|
| 1259 | Cell[BoxData[
|
|---|
| 1260 | FormBox[
|
|---|
| 1261 | RowBox[{
|
|---|
| 1262 | FractionBox["11", "6"], " ", "c\[CapitalGamma]", " ", "gs2", " ",
|
|---|
| 1263 | SubscriptBox["C", "A"]}], TraditionalForm]], "Output",
|
|---|
| 1264 | CellChangeTimes->{3.5426318443159647`*^9, 3.542631976167509*^9,
|
|---|
| 1265 | 3.5426321214075212`*^9, 3.692515521927043*^9, 3.692522580645241*^9}]
|
|---|
| 1266 | }, Open ]],
|
|---|
| 1267 |
|
|---|
| 1268 | Cell[CellGroupData[{
|
|---|
| 1269 |
|
|---|
| 1270 | Cell[BoxData[{
|
|---|
| 1271 | RowBox[{
|
|---|
| 1272 | RowBox[{"virt", "=",
|
|---|
| 1273 | RowBox[{
|
|---|
| 1274 | RowBox[{"(",
|
|---|
| 1275 | RowBox[{
|
|---|
| 1276 | RowBox[{"(",
|
|---|
| 1277 | RowBox[{"virt", "*",
|
|---|
| 1278 | RowBox[{
|
|---|
| 1279 | RowBox[{"2", "/", "gs2"}], "/", "c\[CapitalGamma]"}]}], ")"}], "//",
|
|---|
| 1280 | "Expand"}], ")"}], "*",
|
|---|
| 1281 | FractionBox["as",
|
|---|
| 1282 | RowBox[{"2", "\[Pi]"}]], "c\[CapitalGamma]"}]}], " ",
|
|---|
| 1283 | RowBox[{"(*", " ",
|
|---|
| 1284 | RowBox[{"eq", " ", "39"}], "*)"}]}], "\[IndentingNewLine]",
|
|---|
| 1285 | RowBox[{
|
|---|
| 1286 | RowBox[{"virt1", "=",
|
|---|
| 1287 | RowBox[{
|
|---|
| 1288 | RowBox[{"(",
|
|---|
| 1289 | RowBox[{
|
|---|
| 1290 | RowBox[{"(",
|
|---|
| 1291 | RowBox[{"virt1", "*",
|
|---|
| 1292 | RowBox[{
|
|---|
| 1293 | RowBox[{"2", "/", "gs2"}], "/", "c\[CapitalGamma]"}]}], ")"}], "//",
|
|---|
| 1294 | "Expand"}], ")"}], "*",
|
|---|
| 1295 | FractionBox["as",
|
|---|
| 1296 | RowBox[{"2", "\[Pi]"}]], "c\[CapitalGamma]"}]}],
|
|---|
| 1297 | " "}], "\[IndentingNewLine]",
|
|---|
| 1298 | RowBox[{"virt2", "=",
|
|---|
| 1299 | RowBox[{
|
|---|
| 1300 | RowBox[{"(",
|
|---|
| 1301 | RowBox[{
|
|---|
| 1302 | RowBox[{"(",
|
|---|
| 1303 | RowBox[{"virt2", "*",
|
|---|
| 1304 | RowBox[{
|
|---|
| 1305 | RowBox[{"2", "/", "gs2"}], "/", "c\[CapitalGamma]"}]}], ")"}], "//",
|
|---|
| 1306 | "Expand"}], ")"}], "*",
|
|---|
| 1307 | FractionBox["as",
|
|---|
| 1308 | RowBox[{"2", "\[Pi]"}]], "c\[CapitalGamma]", " "}]}]}], "Input",
|
|---|
| 1309 | CellChangeTimes->{{3.542631852564522*^9, 3.542631853826531*^9}, {
|
|---|
| 1310 | 3.5426319547565536`*^9, 3.54263197179709*^9}, {3.5426320982454357`*^9,
|
|---|
| 1311 | 3.542632118569233*^9}, {3.692525395151532*^9, 3.692525397947733*^9}}],
|
|---|
| 1312 |
|
|---|
| 1313 | Cell[BoxData[
|
|---|
| 1314 | FormBox[
|
|---|
| 1315 | FractionBox[
|
|---|
| 1316 | RowBox[{"as", " ", "c\[CapitalGamma]", " ",
|
|---|
| 1317 | RowBox[{"(",
|
|---|
| 1318 | RowBox[{
|
|---|
| 1319 | RowBox[{"-",
|
|---|
| 1320 | FractionBox[
|
|---|
| 1321 | RowBox[{"2", " ",
|
|---|
| 1322 | SubscriptBox["C", "A"]}],
|
|---|
| 1323 | SuperscriptBox["e", "2"]]}], "+",
|
|---|
| 1324 | RowBox[{
|
|---|
| 1325 | SuperscriptBox["\[Pi]", "2"], " ",
|
|---|
| 1326 | SubscriptBox["C", "A"]}], "+",
|
|---|
| 1327 | FractionBox[
|
|---|
| 1328 | RowBox[{"11", " ",
|
|---|
| 1329 | SubscriptBox["C", "A"]}], "3"]}], ")"}]}],
|
|---|
| 1330 | RowBox[{"2", " ", "\[Pi]"}]], TraditionalForm]], "Output",
|
|---|
| 1331 | CellChangeTimes->{{3.542631848559409*^9, 3.54263185425035*^9}, {
|
|---|
| 1332 | 3.542631972325842*^9, 3.542631978338317*^9}, {3.542632099603859*^9,
|
|---|
| 1333 | 3.542632122724947*^9}, 3.692515521976563*^9, 3.692524472065591*^9}],
|
|---|
| 1334 |
|
|---|
| 1335 | Cell[BoxData[
|
|---|
| 1336 | FormBox[
|
|---|
| 1337 | FractionBox[
|
|---|
| 1338 | RowBox[{"as", " ", "c\[CapitalGamma]", " ",
|
|---|
| 1339 | RowBox[{"(",
|
|---|
| 1340 | RowBox[{
|
|---|
| 1341 | RowBox[{"-",
|
|---|
| 1342 | FractionBox[
|
|---|
| 1343 | RowBox[{"2", " ",
|
|---|
| 1344 | SubscriptBox["C", "A"]}],
|
|---|
| 1345 | SuperscriptBox["e", "2"]]}], "+",
|
|---|
| 1346 | FractionBox[
|
|---|
| 1347 | RowBox[{"10", " ",
|
|---|
| 1348 | SubscriptBox["C", "A"]}],
|
|---|
| 1349 | RowBox[{"3", " ", "e"}]], "+",
|
|---|
| 1350 | RowBox[{
|
|---|
| 1351 | SuperscriptBox["\[Pi]", "2"], " ",
|
|---|
| 1352 | SubscriptBox["C", "A"]}], "+",
|
|---|
| 1353 | FractionBox[
|
|---|
| 1354 | RowBox[{"179", " ",
|
|---|
| 1355 | SubscriptBox["C", "A"]}], "36"]}], ")"}]}],
|
|---|
| 1356 | RowBox[{"2", " ", "\[Pi]"}]], TraditionalForm]], "Output",
|
|---|
| 1357 | CellChangeTimes->{{3.542631848559409*^9, 3.54263185425035*^9}, {
|
|---|
| 1358 | 3.542631972325842*^9, 3.542631978338317*^9}, {3.542632099603859*^9,
|
|---|
| 1359 | 3.542632122724947*^9}, 3.692515521976563*^9, 3.69252447207027*^9}],
|
|---|
| 1360 |
|
|---|
| 1361 | Cell[BoxData[
|
|---|
| 1362 | FormBox[
|
|---|
| 1363 | FractionBox[
|
|---|
| 1364 | RowBox[{"as", " ", "c\[CapitalGamma]", " ",
|
|---|
| 1365 | RowBox[{"(",
|
|---|
| 1366 | RowBox[{
|
|---|
| 1367 | RowBox[{"-",
|
|---|
| 1368 | FractionBox[
|
|---|
| 1369 | RowBox[{"10", " ",
|
|---|
| 1370 | SubscriptBox["C", "A"]}],
|
|---|
| 1371 | RowBox[{"3", " ", "e"}]]}], "-",
|
|---|
| 1372 | FractionBox[
|
|---|
| 1373 | RowBox[{"179", " ",
|
|---|
| 1374 | SubscriptBox["C", "A"]}], "36"]}], ")"}]}],
|
|---|
| 1375 | RowBox[{"2", " ", "\[Pi]"}]], TraditionalForm]], "Output",
|
|---|
| 1376 | CellChangeTimes->{{3.542631848559409*^9, 3.54263185425035*^9}, {
|
|---|
| 1377 | 3.542631972325842*^9, 3.542631978338317*^9}, {3.542632099603859*^9,
|
|---|
| 1378 | 3.542632122724947*^9}, 3.692515521976563*^9, 3.692524472073923*^9}]
|
|---|
| 1379 | }, Open ]],
|
|---|
| 1380 |
|
|---|
| 1381 | Cell[BoxData["\[IndentingNewLine]"], "Input"],
|
|---|
| 1382 |
|
|---|
| 1383 | Cell[CellGroupData[{
|
|---|
| 1384 |
|
|---|
| 1385 | Cell[BoxData[
|
|---|
| 1386 | RowBox[{
|
|---|
| 1387 | RowBox[{
|
|---|
| 1388 | RowBox[{"32", "/", "256"}], "/", "3"}], "/",
|
|---|
| 1389 | RowBox[{
|
|---|
| 1390 | RowBox[{"(",
|
|---|
| 1391 | RowBox[{"1", "-", "e"}], ")"}], "^", "2"}]}]], "Input"],
|
|---|
| 1392 |
|
|---|
| 1393 | Cell[BoxData[
|
|---|
| 1394 | FormBox[
|
|---|
| 1395 | FractionBox["1",
|
|---|
| 1396 | RowBox[{"24", " ",
|
|---|
| 1397 | SuperscriptBox[
|
|---|
| 1398 | RowBox[{"(",
|
|---|
| 1399 | RowBox[{"1", "-", "e"}], ")"}], "2"]}]], TraditionalForm]], "Output"]
|
|---|
| 1400 | }, Open ]]
|
|---|
| 1401 | }, Open ]]
|
|---|
| 1402 | }, Open ]],
|
|---|
| 1403 |
|
|---|
| 1404 | Cell[CellGroupData[{
|
|---|
| 1405 |
|
|---|
| 1406 | Cell["The real contributions", "Section",
|
|---|
| 1407 | PageWidth->PaperWidth],
|
|---|
| 1408 |
|
|---|
| 1409 | Cell[CellGroupData[{
|
|---|
| 1410 |
|
|---|
| 1411 | Cell["Kinematics", "Subsection",
|
|---|
| 1412 | PageWidth->PaperWidth],
|
|---|
| 1413 |
|
|---|
| 1414 | Cell["\<\
|
|---|
| 1415 | -----I take all momenta outgoing
|
|---|
| 1416 |
|
|---|
| 1417 | p1 + p2 + p3 + p4 = 0
|
|---|
| 1418 |
|
|---|
| 1419 | p1^2=0
|
|---|
| 1420 | p2^2=0
|
|---|
| 1421 | p3^3=0
|
|---|
| 1422 | p4^2=mh^2
|
|---|
| 1423 |
|
|---|
| 1424 | -----invariants
|
|---|
| 1425 |
|
|---|
| 1426 | s = (p1 + p2)^2 = (p3 + p4)^2=2 p1.p2=mh^2+2 p3.p4
|
|---|
| 1427 | t = (p1 + p3)^2 = (p2+ p4)^2 =2 p1.p3=mh^2+2 p2.p4
|
|---|
| 1428 | u = (p2 + p3)^2 = (p1 + p4)^2=2 p1.p4+mh^2=+2 p2.p3
|
|---|
| 1429 |
|
|---|
| 1430 | s + t + u = mh^2
|
|---|
| 1431 |
|
|---|
| 1432 | \[Sigma]+\[Tau]+\[Upsilon]=1
|
|---|
| 1433 |
|
|---|
| 1434 | -----scalar products
|
|---|
| 1435 |
|
|---|
| 1436 | p1.p2=s/2
|
|---|
| 1437 | p1.p3=(t)/2
|
|---|
| 1438 | p1.p4= (u-mh^2)/2
|
|---|
| 1439 | p2.p3= (u)/2
|
|---|
| 1440 | p2.p4=(t-mh^2)/2
|
|---|
| 1441 | p3.p4=(s-mh^2)/2
|
|---|
| 1442 |
|
|---|
| 1443 | -----physical region for production p1+p2=-p3-p4
|
|---|
| 1444 |
|
|---|
| 1445 | s>(mh)^2 ;
|
|---|
| 1446 | t<0;
|
|---|
| 1447 | u<0;
|
|---|
| 1448 |
|
|---|
| 1449 | \
|
|---|
| 1450 | \>", "Text",
|
|---|
| 1451 | PageWidth->PaperWidth],
|
|---|
| 1452 |
|
|---|
| 1453 | Cell[BoxData[{
|
|---|
| 1454 | RowBox[{
|
|---|
| 1455 | RowBox[{
|
|---|
| 1456 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1457 | RowBox[{"p1", ",", "p1"}], "]"}], "=", "0"}],
|
|---|
| 1458 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1459 | RowBox[{
|
|---|
| 1460 | RowBox[{
|
|---|
| 1461 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1462 | RowBox[{"p2", ",", "p2"}], "]"}], "=", "0"}],
|
|---|
| 1463 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1464 | RowBox[{
|
|---|
| 1465 | RowBox[{
|
|---|
| 1466 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1467 | RowBox[{"p3", ",", "p3"}], "]"}], "=", "0"}],
|
|---|
| 1468 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1469 | RowBox[{
|
|---|
| 1470 | RowBox[{
|
|---|
| 1471 | RowBox[{
|
|---|
| 1472 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1473 | RowBox[{"q", ",", "p3"}], "]"}], "=",
|
|---|
| 1474 | RowBox[{"u", "/", "2"}]}], ";"}], " ",
|
|---|
| 1475 | RowBox[{"(*",
|
|---|
| 1476 | RowBox[{"q", "=",
|
|---|
| 1477 | RowBox[{"p2", "+", "p3"}]}], "*)"}]}], "\[IndentingNewLine]",
|
|---|
| 1478 | RowBox[{
|
|---|
| 1479 | RowBox[{
|
|---|
| 1480 | RowBox[{
|
|---|
| 1481 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1482 | RowBox[{"q", ",", "p2"}], "]"}], "=",
|
|---|
| 1483 | RowBox[{"u", "/", "2"}]}], ";"}], " ",
|
|---|
| 1484 | RowBox[{"(*",
|
|---|
| 1485 | RowBox[{"q", "=",
|
|---|
| 1486 | RowBox[{"p2", "+", "p3"}]}], "*)"}]}], "\[IndentingNewLine]",
|
|---|
| 1487 | RowBox[{
|
|---|
| 1488 | RowBox[{
|
|---|
| 1489 | RowBox[{
|
|---|
| 1490 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1491 | RowBox[{"q", ",", "q"}], "]"}], "=", "u"}], ";"}], " ",
|
|---|
| 1492 | RowBox[{"(*",
|
|---|
| 1493 | RowBox[{"q", "=",
|
|---|
| 1494 | RowBox[{"p2", "+", "p3"}]}], "*)"}]}], "\[IndentingNewLine]",
|
|---|
| 1495 | RowBox[{
|
|---|
| 1496 | RowBox[{
|
|---|
| 1497 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1498 | RowBox[{"p4", ",", "p4"}], "]"}], "=", "mh2"}],
|
|---|
| 1499 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1500 | RowBox[{
|
|---|
| 1501 | RowBox[{
|
|---|
| 1502 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1503 | RowBox[{"p1", ",", "p2"}], "]"}], "=",
|
|---|
| 1504 | RowBox[{"s", "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1505 | RowBox[{
|
|---|
| 1506 | RowBox[{
|
|---|
| 1507 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1508 | RowBox[{"p1", ",", "p3"}], "]"}], "=",
|
|---|
| 1509 | RowBox[{"t", "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1510 | RowBox[{
|
|---|
| 1511 | RowBox[{
|
|---|
| 1512 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1513 | RowBox[{"p1", ",", "p4"}], "]"}], "=",
|
|---|
| 1514 | RowBox[{
|
|---|
| 1515 | RowBox[{"(",
|
|---|
| 1516 | RowBox[{"u", "-", "mh2"}], ")"}], "/", "2"}]}],
|
|---|
| 1517 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1518 | RowBox[{
|
|---|
| 1519 | RowBox[{
|
|---|
| 1520 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1521 | RowBox[{"p2", ",", "p3"}], "]"}], "=",
|
|---|
| 1522 | RowBox[{"u", "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1523 | RowBox[{
|
|---|
| 1524 | RowBox[{
|
|---|
| 1525 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1526 | RowBox[{"p2", ",", "p4"}], "]"}], "=", " ",
|
|---|
| 1527 | RowBox[{
|
|---|
| 1528 | RowBox[{"(",
|
|---|
| 1529 | RowBox[{"t", "-", "mh2"}], ")"}], "/", "2"}]}],
|
|---|
| 1530 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1531 | RowBox[{
|
|---|
| 1532 | RowBox[{
|
|---|
| 1533 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1534 | RowBox[{"p3", ",", "p4"}], "]"}], "=",
|
|---|
| 1535 | RowBox[{
|
|---|
| 1536 | RowBox[{"(",
|
|---|
| 1537 | RowBox[{"s", "-", "mh2"}], ")"}], "/", "2"}]}], " ",
|
|---|
| 1538 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1539 | RowBox[{
|
|---|
| 1540 | RowBox[{
|
|---|
| 1541 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1542 | RowBox[{"p3", ",", "e3"}], "]"}], "=", "0"}], " ",
|
|---|
| 1543 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1544 | RowBox[{
|
|---|
| 1545 | RowBox[{
|
|---|
| 1546 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1547 | RowBox[{"p1", ",", "e1"}], "]"}], "=", "0"}], " ",
|
|---|
| 1548 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1549 | RowBox[{
|
|---|
| 1550 | RowBox[{
|
|---|
| 1551 | RowBox[{"ScalarProduct", "[",
|
|---|
| 1552 | RowBox[{"p2", ",", "e2"}], "]"}], "=", "0"}], " ",
|
|---|
| 1553 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1554 | RowBox[{
|
|---|
| 1555 | RowBox[{"s13", "=", "t"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1556 | RowBox[{
|
|---|
| 1557 | RowBox[{"s23", "=", "u"}], ";"}]}], "Input",
|
|---|
| 1558 | PageWidth->PaperWidth]
|
|---|
| 1559 | }, Open ]],
|
|---|
| 1560 |
|
|---|
| 1561 | Cell[CellGroupData[{
|
|---|
| 1562 |
|
|---|
| 1563 | Cell["Verteces and Propagators", "Subsection",
|
|---|
| 1564 | PageWidth->PaperWidth],
|
|---|
| 1565 |
|
|---|
| 1566 | Cell[TextData[{
|
|---|
| 1567 | StyleBox["GGG is the kinematic part of the three-gluon vtx (momenta \
|
|---|
| 1568 | outgoing, clockwise ordering):\nVTX(ggg) = (-\[ImaginaryI] ",
|
|---|
| 1569 | FontSize->14],
|
|---|
| 1570 | Cell[BoxData[
|
|---|
| 1571 | FormBox[
|
|---|
| 1572 | SubscriptBox["g", "s"], TraditionalForm]],
|
|---|
| 1573 | FontSize->14],
|
|---|
| 1574 | StyleBox[" ) (\[ImaginaryI] ",
|
|---|
| 1575 | FontSize->14],
|
|---|
| 1576 | Cell[BoxData[
|
|---|
| 1577 | FormBox[
|
|---|
| 1578 | SuperscriptBox["f", "abc"], TraditionalForm]],
|
|---|
| 1579 | FontSize->14],
|
|---|
| 1580 | StyleBox[") GGG\nVTX(qqg) = ( -\[ImaginaryI] ",
|
|---|
| 1581 | FontSize->14],
|
|---|
| 1582 | Cell[BoxData[
|
|---|
| 1583 | FormBox[
|
|---|
| 1584 | SubscriptBox["g", "s"], TraditionalForm]],
|
|---|
| 1585 | FontSize->14],
|
|---|
| 1586 | ")",
|
|---|
| 1587 | StyleBox[" ",
|
|---|
| 1588 | FontSize->14],
|
|---|
| 1589 | Cell[BoxData[
|
|---|
| 1590 | FormBox[
|
|---|
| 1591 | SubscriptBox[
|
|---|
| 1592 | RowBox[{"(",
|
|---|
| 1593 | SuperscriptBox["T", "a"], ")"}], "ij"], TraditionalForm]],
|
|---|
| 1594 | FontSize->14],
|
|---|
| 1595 | StyleBox[" ",
|
|---|
| 1596 | FontSize->14],
|
|---|
| 1597 | Cell[BoxData[
|
|---|
| 1598 | FormBox[
|
|---|
| 1599 | SuperscriptBox["\[Gamma]", "\[Mu]"], TraditionalForm]],
|
|---|
| 1600 | FontSize->14],
|
|---|
| 1601 | StyleBox["\nGluon Propagator= ",
|
|---|
| 1602 | FontSize->14],
|
|---|
| 1603 | Cell[BoxData[
|
|---|
| 1604 | FormBox[
|
|---|
| 1605 | FractionBox[
|
|---|
| 1606 | StyleBox[
|
|---|
| 1607 | RowBox[{
|
|---|
| 1608 | RowBox[{"-", "\[ImaginaryI]"}], " ",
|
|---|
| 1609 | SuperscriptBox["g", "\[Mu]\[Nu]"]}],
|
|---|
| 1610 | FontSize->16],
|
|---|
| 1611 | SuperscriptBox["p", "2"]], TraditionalForm]],
|
|---|
| 1612 | FontSize->14],
|
|---|
| 1613 | "\nQuark ",
|
|---|
| 1614 | StyleBox["Propagator= ",
|
|---|
| 1615 | FontSize->14],
|
|---|
| 1616 | Cell[BoxData[
|
|---|
| 1617 | FormBox[
|
|---|
| 1618 | FractionBox[
|
|---|
| 1619 | StyleBox[
|
|---|
| 1620 | RowBox[{"\[ImaginaryI]", " "}],
|
|---|
| 1621 | FontSize->16],
|
|---|
| 1622 | OverscriptBox["p", "^"]], TraditionalForm]],
|
|---|
| 1623 | FontSize->14]
|
|---|
| 1624 | }], "Text",
|
|---|
| 1625 | PageWidth->PaperWidth],
|
|---|
| 1626 |
|
|---|
| 1627 | Cell[BoxData[{
|
|---|
| 1628 | RowBox[{
|
|---|
| 1629 | RowBox[{
|
|---|
| 1630 | RowBox[{"GGGD", "[",
|
|---|
| 1631 | RowBox[{
|
|---|
| 1632 | "p1_", ",", "p2_", ",", "p3_", ",", "m1_", ",", "m2_", ",", "m3_"}],
|
|---|
| 1633 | "]"}], ":=",
|
|---|
| 1634 | RowBox[{
|
|---|
| 1635 | RowBox[{
|
|---|
| 1636 | RowBox[{"FourVector", "[",
|
|---|
| 1637 | RowBox[{
|
|---|
| 1638 | RowBox[{"p1", "-", "p2"}], ",", "m3", ",", " ",
|
|---|
| 1639 | RowBox[{"Dimension", " ", "\[Rule]", "D"}]}], "]"}], " ",
|
|---|
| 1640 | RowBox[{"MTD", "[",
|
|---|
| 1641 | RowBox[{"m1", ",", "m2"}], "]"}]}], "+",
|
|---|
| 1642 | RowBox[{
|
|---|
| 1643 | RowBox[{"FourVector", "[",
|
|---|
| 1644 | RowBox[{
|
|---|
| 1645 | RowBox[{"p2", "-", "p3"}], ",", "m1", ",", " ",
|
|---|
| 1646 | RowBox[{"Dimension", " ", "\[Rule]", " ", "D"}]}], "]"}], " ",
|
|---|
| 1647 | RowBox[{"MTD", "[",
|
|---|
| 1648 | RowBox[{"m2", ",", "m3"}], "]"}]}], "+",
|
|---|
| 1649 | RowBox[{
|
|---|
| 1650 | RowBox[{"FourVector", "[",
|
|---|
| 1651 | RowBox[{
|
|---|
| 1652 | RowBox[{"p3", "-", "p1"}], ",", "m2", ",", " ",
|
|---|
| 1653 | RowBox[{"Dimension", " ", "\[Rule]", " ", "D"}]}], "]"}], " ",
|
|---|
| 1654 | RowBox[{"MTD", "[",
|
|---|
| 1655 | RowBox[{"m1", ",", "m3"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1656 | RowBox[{
|
|---|
| 1657 | RowBox[{
|
|---|
| 1658 | RowBox[{"H", "[",
|
|---|
| 1659 | RowBox[{"p1_", ",", "p2_", ",", "m1_", ",", "m2_"}], "]"}], ":=",
|
|---|
| 1660 | RowBox[{
|
|---|
| 1661 | RowBox[{
|
|---|
| 1662 | RowBox[{"MTD", "[",
|
|---|
| 1663 | RowBox[{"m1", ",", "m2"}], "]"}], " ",
|
|---|
| 1664 | RowBox[{"SPD", "[",
|
|---|
| 1665 | RowBox[{"p1", ",", "p2"}], "]"}]}], " ", "-", " ",
|
|---|
| 1666 | RowBox[{
|
|---|
| 1667 | RowBox[{"FourVector", "[",
|
|---|
| 1668 | RowBox[{"p1", ",", "m2", ",", " ",
|
|---|
| 1669 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "*",
|
|---|
| 1670 | "\[IndentingNewLine]", " ",
|
|---|
| 1671 | RowBox[{"FourVector", "[",
|
|---|
| 1672 | RowBox[{"p2", ",", "m1", ",", " ",
|
|---|
| 1673 | RowBox[{"Dimension", " ", "\[Rule]", "D"}]}], "]"}]}]}]}],
|
|---|
| 1674 | ";"}], "\[IndentingNewLine]",
|
|---|
| 1675 | RowBox[{
|
|---|
| 1676 | RowBox[{"PropQuark", "=", "I"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1677 | RowBox[{
|
|---|
| 1678 | RowBox[{"PropGluon", " ", "=",
|
|---|
| 1679 | RowBox[{"-", "I"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1680 | RowBox[{
|
|---|
| 1681 | RowBox[{"vtx", "=",
|
|---|
| 1682 | RowBox[{
|
|---|
| 1683 | RowBox[{"-", "I"}], " ", "gs"}]}], ";"}]}], "Input",
|
|---|
| 1684 | PageWidth->PaperWidth]
|
|---|
| 1685 | }, Open ]],
|
|---|
| 1686 |
|
|---|
| 1687 | Cell[CellGroupData[{
|
|---|
| 1688 |
|
|---|
| 1689 | Cell["Sum over the four Feynman diagrams", "Subsection"],
|
|---|
| 1690 |
|
|---|
| 1691 | Cell["\<\
|
|---|
| 1692 |
|
|---|
| 1693 | uno= - gs (-f123) GGGD[p1,p2,-p1-p2,m1,m2,mu] (-I MTD[mu,nu]/s) (I A) \
|
|---|
| 1694 | H[p3,p1+p2,m3,nu]//Contract;
|
|---|
| 1695 | tre= - gs (-f123) GGGD[p3,p1,-p3-p1,m3,m1,mu] (-I MTD[mu,nu]/t) (I A) \
|
|---|
| 1696 | H[p2,p1+p3,m2,nu]//Contract;
|
|---|
| 1697 | qua= - gs (-f123) GGGD[p2,p3,-p3-p2,m2,m3,mu] (-I MTD[mu,nu]/u) (I A) \
|
|---|
| 1698 | H[p1,p2+p3,m1,nu]//Contract;
|
|---|
| 1699 | due= - A gs (-f123) GGGD[p1,p2,p3,m1,m2,m3];
|
|---|
| 1700 | res=uno+due+tre+qua//ExpandScalarProduct;\
|
|---|
| 1701 | \>", "Input"]
|
|---|
| 1702 | }, Open ]],
|
|---|
| 1703 |
|
|---|
| 1704 | Cell[CellGroupData[{
|
|---|
| 1705 |
|
|---|
| 1706 | Cell["\<\
|
|---|
| 1707 | Now I have to square the amplitude. The sum is performed over the physical \
|
|---|
| 1708 | polarizations of the gluons:\
|
|---|
| 1709 | \>", "Subsection"],
|
|---|
| 1710 |
|
|---|
| 1711 | Cell["\<\
|
|---|
| 1712 | res1=res;
|
|---|
| 1713 | res2=res /. m1->m1p /. m2->m2p /. m3-> m3p;
|
|---|
| 1714 | tot=res1*(-MTD[m1,m1p]+(FVD[p1,m1] FVD[p2,m1p]+FVD[p1,m1p] \
|
|---|
| 1715 | FVD[p2,m1])/SPD[p1,p2])//Contract;
|
|---|
| 1716 | tot=tot*(-MTD[m2,m2p]+(FVD[p2,m2] FVD[p3,m2p]+FVD[p2,m2p] \
|
|---|
| 1717 | FVD[p3,m2])/SPD[p3,p2])//Contract;
|
|---|
| 1718 | tot=tot*(-MTD[m3,m3p]+(FVD[p1,m3] FVD[p3,m3p]+FVD[p1,m3p] \
|
|---|
| 1719 | FVD[p3,m3])/SPD[p3,p1])//Contract;
|
|---|
| 1720 | tot=tot*res2//Contract//Expand;\
|
|---|
| 1721 | \>", "Input"],
|
|---|
| 1722 |
|
|---|
| 1723 | Cell[CellGroupData[{
|
|---|
| 1724 |
|
|---|
| 1725 | Cell["\<\
|
|---|
| 1726 | Amp2=((tot//Contract//Factor)/. A-> as/3/Pi/v /. gs^2-> 4 Pi as/. f123^2-> 24 \
|
|---|
| 1727 | //Simplify)//Factor\
|
|---|
| 1728 | \>", "Input"],
|
|---|
| 1729 |
|
|---|
| 1730 | Cell[BoxData[
|
|---|
| 1731 | FormBox[
|
|---|
| 1732 | RowBox[{
|
|---|
| 1733 | FractionBox["1",
|
|---|
| 1734 | RowBox[{"3", " ", "\[Pi]", " ", "s", " ", "t", " ", "u", " ",
|
|---|
| 1735 | SuperscriptBox["v", "2"]}]],
|
|---|
| 1736 | RowBox[{"32", " ",
|
|---|
| 1737 | SuperscriptBox["as", "3"], " ",
|
|---|
| 1738 | RowBox[{"(",
|
|---|
| 1739 | RowBox[{
|
|---|
| 1740 | RowBox[{"D", " ",
|
|---|
| 1741 | SuperscriptBox["s", "4"]}], "+",
|
|---|
| 1742 | RowBox[{"2", " ", "D", " ",
|
|---|
| 1743 | SuperscriptBox["s", "3"], " ", "t"}], "+",
|
|---|
| 1744 | RowBox[{"2", " ", "D", " ",
|
|---|
| 1745 | SuperscriptBox["s", "3"], " ", "u"}], "+",
|
|---|
| 1746 | RowBox[{"3", " ", "D", " ",
|
|---|
| 1747 | SuperscriptBox["s", "2"], " ",
|
|---|
| 1748 | SuperscriptBox["t", "2"]}], "+",
|
|---|
| 1749 | RowBox[{"8", " ", "D", " ",
|
|---|
| 1750 | SuperscriptBox["s", "2"], " ", "t", " ", "u"}], "+",
|
|---|
| 1751 | RowBox[{"3", " ", "D", " ",
|
|---|
| 1752 | SuperscriptBox["s", "2"], " ",
|
|---|
| 1753 | SuperscriptBox["u", "2"]}], "+",
|
|---|
| 1754 | RowBox[{"2", " ", "D", " ", "s", " ",
|
|---|
| 1755 | SuperscriptBox["t", "3"]}], "+",
|
|---|
| 1756 | RowBox[{"8", " ", "D", " ", "s", " ",
|
|---|
| 1757 | SuperscriptBox["t", "2"], " ", "u"}], "+",
|
|---|
| 1758 | RowBox[{"8", " ", "D", " ", "s", " ", "t", " ",
|
|---|
| 1759 | SuperscriptBox["u", "2"]}], "+",
|
|---|
| 1760 | RowBox[{"2", " ", "D", " ", "s", " ",
|
|---|
| 1761 | SuperscriptBox["u", "3"]}], "+",
|
|---|
| 1762 | RowBox[{"D", " ",
|
|---|
| 1763 | SuperscriptBox["t", "4"]}], "+",
|
|---|
| 1764 | RowBox[{"2", " ", "D", " ",
|
|---|
| 1765 | SuperscriptBox["t", "3"], " ", "u"}], "+",
|
|---|
| 1766 | RowBox[{"3", " ", "D", " ",
|
|---|
| 1767 | SuperscriptBox["t", "2"], " ",
|
|---|
| 1768 | SuperscriptBox["u", "2"]}], "+",
|
|---|
| 1769 | RowBox[{"2", " ", "D", " ", "t", " ",
|
|---|
| 1770 | SuperscriptBox["u", "3"]}], "+",
|
|---|
| 1771 | RowBox[{"D", " ",
|
|---|
| 1772 | SuperscriptBox["u", "4"]}], "-",
|
|---|
| 1773 | RowBox[{"2", " ",
|
|---|
| 1774 | SuperscriptBox["s", "4"]}], "-",
|
|---|
| 1775 | RowBox[{"4", " ",
|
|---|
| 1776 | SuperscriptBox["s", "3"], " ", "t"}], "-",
|
|---|
| 1777 | RowBox[{"4", " ",
|
|---|
| 1778 | SuperscriptBox["s", "3"], " ", "u"}], "-",
|
|---|
| 1779 | RowBox[{"6", " ",
|
|---|
| 1780 | SuperscriptBox["s", "2"], " ",
|
|---|
| 1781 | SuperscriptBox["t", "2"]}], "-",
|
|---|
| 1782 | RowBox[{"20", " ",
|
|---|
| 1783 | SuperscriptBox["s", "2"], " ", "t", " ", "u"}], "-",
|
|---|
| 1784 | RowBox[{"6", " ",
|
|---|
| 1785 | SuperscriptBox["s", "2"], " ",
|
|---|
| 1786 | SuperscriptBox["u", "2"]}], "-",
|
|---|
| 1787 | RowBox[{"4", " ", "s", " ",
|
|---|
| 1788 | SuperscriptBox["t", "3"]}], "-",
|
|---|
| 1789 | RowBox[{"20", " ", "s", " ",
|
|---|
| 1790 | SuperscriptBox["t", "2"], " ", "u"}], "-",
|
|---|
| 1791 | RowBox[{"20", " ", "s", " ", "t", " ",
|
|---|
| 1792 | SuperscriptBox["u", "2"]}], "-",
|
|---|
| 1793 | RowBox[{"4", " ", "s", " ",
|
|---|
| 1794 | SuperscriptBox["u", "3"]}], "-",
|
|---|
| 1795 | RowBox[{"2", " ",
|
|---|
| 1796 | SuperscriptBox["t", "4"]}], "-",
|
|---|
| 1797 | RowBox[{"4", " ",
|
|---|
| 1798 | SuperscriptBox["t", "3"], " ", "u"}], "-",
|
|---|
| 1799 | RowBox[{"6", " ",
|
|---|
| 1800 | SuperscriptBox["t", "2"], " ",
|
|---|
| 1801 | SuperscriptBox["u", "2"]}], "-",
|
|---|
| 1802 | RowBox[{"4", " ", "t", " ",
|
|---|
| 1803 | SuperscriptBox["u", "3"]}], "-",
|
|---|
| 1804 | RowBox[{"2", " ",
|
|---|
| 1805 | SuperscriptBox["u", "4"]}]}], ")"}]}]}], TraditionalForm]], "Output",
|
|---|
| 1806 | CellChangeTimes->{3.6925262025482817`*^9}]
|
|---|
| 1807 | }, Open ]],
|
|---|
| 1808 |
|
|---|
| 1809 | Cell["\<\
|
|---|
| 1810 |
|
|---|
| 1811 | Amp2=Amp2 /. D->4-2e//Simplify;\
|
|---|
| 1812 | \>", "Input"],
|
|---|
| 1813 |
|
|---|
| 1814 | Cell[CellGroupData[{
|
|---|
| 1815 |
|
|---|
| 1816 | Cell[BoxData["Amp2"], "Input",
|
|---|
| 1817 | CellChangeTimes->{{3.692526234576797*^9, 3.6925262356483517`*^9}}],
|
|---|
| 1818 |
|
|---|
| 1819 | Cell[BoxData[
|
|---|
| 1820 | FormBox[
|
|---|
| 1821 | RowBox[{"-",
|
|---|
| 1822 | FractionBox[
|
|---|
| 1823 | RowBox[{"64", " ",
|
|---|
| 1824 | SuperscriptBox["as", "3"], " ",
|
|---|
| 1825 | RowBox[{"(",
|
|---|
| 1826 | RowBox[{
|
|---|
| 1827 | RowBox[{
|
|---|
| 1828 | RowBox[{"(",
|
|---|
| 1829 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1830 | SuperscriptBox["s", "4"]}], "+",
|
|---|
| 1831 | RowBox[{"2", " ",
|
|---|
| 1832 | RowBox[{"(",
|
|---|
| 1833 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1834 | SuperscriptBox["s", "3"], " ",
|
|---|
| 1835 | RowBox[{"(",
|
|---|
| 1836 | RowBox[{"t", "+", "u"}], ")"}]}], "+",
|
|---|
| 1837 | RowBox[{
|
|---|
| 1838 | SuperscriptBox["s", "2"], " ",
|
|---|
| 1839 | RowBox[{"(",
|
|---|
| 1840 | RowBox[{
|
|---|
| 1841 | RowBox[{"3", " ",
|
|---|
| 1842 | RowBox[{"(",
|
|---|
| 1843 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1844 | SuperscriptBox["t", "2"]}], "+",
|
|---|
| 1845 | RowBox[{"2", " ",
|
|---|
| 1846 | RowBox[{"(",
|
|---|
| 1847 | RowBox[{
|
|---|
| 1848 | RowBox[{"4", " ", "e"}], "-", "3"}], ")"}], " ", "t", " ", "u"}],
|
|---|
| 1849 | "+",
|
|---|
| 1850 | RowBox[{"3", " ",
|
|---|
| 1851 | RowBox[{"(",
|
|---|
| 1852 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1853 | SuperscriptBox["u", "2"]}]}], ")"}]}], "+",
|
|---|
| 1854 | RowBox[{"2", " ", "s", " ",
|
|---|
| 1855 | RowBox[{"(",
|
|---|
| 1856 | RowBox[{"t", "+", "u"}], ")"}], " ",
|
|---|
| 1857 | RowBox[{"(",
|
|---|
| 1858 | RowBox[{
|
|---|
| 1859 | RowBox[{
|
|---|
| 1860 | RowBox[{"(",
|
|---|
| 1861 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1862 | SuperscriptBox["t", "2"]}], "+",
|
|---|
| 1863 | RowBox[{
|
|---|
| 1864 | RowBox[{"(",
|
|---|
| 1865 | RowBox[{
|
|---|
| 1866 | RowBox[{"3", " ", "e"}], "-", "2"}], ")"}], " ", "t", " ", "u"}],
|
|---|
| 1867 | "+",
|
|---|
| 1868 | RowBox[{
|
|---|
| 1869 | RowBox[{"(",
|
|---|
| 1870 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1871 | SuperscriptBox["u", "2"]}]}], ")"}]}], "+",
|
|---|
| 1872 | RowBox[{
|
|---|
| 1873 | RowBox[{"(",
|
|---|
| 1874 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1875 | SuperscriptBox[
|
|---|
| 1876 | RowBox[{"(",
|
|---|
| 1877 | RowBox[{
|
|---|
| 1878 | SuperscriptBox["t", "2"], "+",
|
|---|
| 1879 | RowBox[{"t", " ", "u"}], "+",
|
|---|
| 1880 | SuperscriptBox["u", "2"]}], ")"}], "2"]}]}], ")"}]}],
|
|---|
| 1881 | RowBox[{"3", " ", "\[Pi]", " ", "s", " ", "t", " ", "u", " ",
|
|---|
| 1882 | SuperscriptBox["v", "2"]}]]}], TraditionalForm]], "Output",
|
|---|
| 1883 | CellChangeTimes->{3.692526236388625*^9}]
|
|---|
| 1884 | }, Open ]]
|
|---|
| 1885 | }, Open ]],
|
|---|
| 1886 |
|
|---|
| 1887 | Cell[CellGroupData[{
|
|---|
| 1888 |
|
|---|
| 1889 | Cell["Real Amplitude Squared in D dimensions", "Subsection",
|
|---|
| 1890 | PageWidth->PaperWidth],
|
|---|
| 1891 |
|
|---|
| 1892 | Cell[BoxData[
|
|---|
| 1893 | RowBox[{"\[IndentingNewLine]",
|
|---|
| 1894 | RowBox[{
|
|---|
| 1895 | RowBox[{
|
|---|
| 1896 | RowBox[{"Emme", "=",
|
|---|
| 1897 | RowBox[{
|
|---|
| 1898 | RowBox[{"1", "/", "s"}],
|
|---|
| 1899 | RowBox[{
|
|---|
| 1900 | RowBox[{
|
|---|
| 1901 | RowBox[{
|
|---|
| 1902 | RowBox[{"(",
|
|---|
| 1903 | RowBox[{
|
|---|
| 1904 | RowBox[{
|
|---|
| 1905 | RowBox[{"(",
|
|---|
| 1906 | RowBox[{
|
|---|
| 1907 | RowBox[{"mh2", "^", "4"}], "+",
|
|---|
| 1908 | RowBox[{"s", "^", "4"}], "+",
|
|---|
| 1909 | RowBox[{"t", "^", "4"}], "+",
|
|---|
| 1910 | RowBox[{"u", "^", "4"}]}], ")"}], " ",
|
|---|
| 1911 | RowBox[{"(",
|
|---|
| 1912 | RowBox[{"1", "-",
|
|---|
| 1913 | RowBox[{"2", " ", "e"}]}], ")"}]}], "+", " ",
|
|---|
| 1914 | RowBox[{
|
|---|
| 1915 | RowBox[{"e", "/", "2"}], " ",
|
|---|
| 1916 | RowBox[{
|
|---|
| 1917 | RowBox[{"(",
|
|---|
| 1918 | RowBox[{
|
|---|
| 1919 | RowBox[{"mh2", "^", "2"}], "+",
|
|---|
| 1920 | RowBox[{"s", "^", "2"}], "+",
|
|---|
| 1921 | RowBox[{"t", "^", "2"}], "+",
|
|---|
| 1922 | RowBox[{"u", "^", "2"}]}], ")"}], "^", "2"}]}]}], ")"}], "/",
|
|---|
| 1923 | "s"}], "/", "t"}], "/", "u"}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 1924 | RowBox[{
|
|---|
| 1925 | RowBox[{"RealD", "=",
|
|---|
| 1926 | RowBox[{"Emme", "/",
|
|---|
| 1927 | RowBox[{
|
|---|
| 1928 | RowBox[{"(",
|
|---|
| 1929 | RowBox[{"1", "-", "e"}], ")"}], "^", "2"}]}]}], ";"}],
|
|---|
| 1930 | "\[IndentingNewLine]",
|
|---|
| 1931 | RowBox[{
|
|---|
| 1932 | RowBox[{"Real4", "=",
|
|---|
| 1933 | RowBox[{"RealD", "/.", " ",
|
|---|
| 1934 | RowBox[{"e", "\[Rule]", "0"}]}]}], ";"}]}]}]], "Input",
|
|---|
| 1935 | PageWidth->PaperWidth],
|
|---|
| 1936 |
|
|---|
| 1937 | Cell[CellGroupData[{
|
|---|
| 1938 |
|
|---|
| 1939 | Cell[BoxData[
|
|---|
| 1940 | RowBox[{
|
|---|
| 1941 | RowBox[{
|
|---|
| 1942 | RowBox[{
|
|---|
| 1943 | RowBox[{"Amp2", "/", "s"}], " ", "-", " ",
|
|---|
| 1944 | RowBox[{"Emme", " ", "*", "64", " ",
|
|---|
| 1945 | RowBox[{
|
|---|
| 1946 | RowBox[{
|
|---|
| 1947 | RowBox[{
|
|---|
| 1948 | RowBox[{"as", "^", "3"}], " ", "/", " ", "3"}], "/", "Pi"}], " ", "/",
|
|---|
| 1949 | RowBox[{"v", "^", "2"}]}]}]}], " ", "/.",
|
|---|
| 1950 | RowBox[{"{",
|
|---|
| 1951 | RowBox[{"mh2", "\[Rule]",
|
|---|
| 1952 | RowBox[{"s", "+", "t", "+", "u"}]}], "}"}]}], "//",
|
|---|
| 1953 | "Simplify"}]], "Input",
|
|---|
| 1954 | CellChangeTimes->{{3.6925266643363037`*^9, 3.692526665304311*^9}, {
|
|---|
| 1955 | 3.692526755257955*^9, 3.692526892252841*^9}, {3.692526952170274*^9,
|
|---|
| 1956 | 3.69252696194454*^9}, {3.69252704067334*^9, 3.692527040832261*^9}}],
|
|---|
| 1957 |
|
|---|
| 1958 | Cell[BoxData[
|
|---|
| 1959 | FormBox[
|
|---|
| 1960 | FractionBox[
|
|---|
| 1961 | RowBox[{"64", " ",
|
|---|
| 1962 | SuperscriptBox["as", "3"], " ",
|
|---|
| 1963 | RowBox[{"(",
|
|---|
| 1964 | RowBox[{
|
|---|
| 1965 | RowBox[{
|
|---|
| 1966 | RowBox[{"(",
|
|---|
| 1967 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1968 | SuperscriptBox["s", "4"]}], "+",
|
|---|
| 1969 | RowBox[{"2", " ",
|
|---|
| 1970 | RowBox[{"(",
|
|---|
| 1971 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1972 | SuperscriptBox["s", "3"], " ",
|
|---|
| 1973 | RowBox[{"(",
|
|---|
| 1974 | RowBox[{"t", "+", "u"}], ")"}]}], "+",
|
|---|
| 1975 | RowBox[{
|
|---|
| 1976 | SuperscriptBox["s", "2"], " ",
|
|---|
| 1977 | RowBox[{"(",
|
|---|
| 1978 | RowBox[{
|
|---|
| 1979 | RowBox[{"3", " ",
|
|---|
| 1980 | RowBox[{"(",
|
|---|
| 1981 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1982 | SuperscriptBox["t", "2"]}], "+",
|
|---|
| 1983 | RowBox[{"2", " ",
|
|---|
| 1984 | RowBox[{"(",
|
|---|
| 1985 | RowBox[{
|
|---|
| 1986 | RowBox[{"4", " ", "e"}], "-", "3"}], ")"}], " ", "t", " ", "u"}],
|
|---|
| 1987 | "+",
|
|---|
| 1988 | RowBox[{"3", " ",
|
|---|
| 1989 | RowBox[{"(",
|
|---|
| 1990 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 1991 | SuperscriptBox["u", "2"]}]}], ")"}]}], "+",
|
|---|
| 1992 | RowBox[{"2", " ", "s", " ",
|
|---|
| 1993 | RowBox[{"(",
|
|---|
| 1994 | RowBox[{"t", "+", "u"}], ")"}], " ",
|
|---|
| 1995 | RowBox[{"(",
|
|---|
| 1996 | RowBox[{
|
|---|
| 1997 | RowBox[{
|
|---|
| 1998 | RowBox[{"(",
|
|---|
| 1999 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 2000 | SuperscriptBox["t", "2"]}], "+",
|
|---|
| 2001 | RowBox[{
|
|---|
| 2002 | RowBox[{"(",
|
|---|
| 2003 | RowBox[{
|
|---|
| 2004 | RowBox[{"3", " ", "e"}], "-", "2"}], ")"}], " ", "t", " ", "u"}],
|
|---|
| 2005 | "+",
|
|---|
| 2006 | RowBox[{
|
|---|
| 2007 | RowBox[{"(",
|
|---|
| 2008 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 2009 | SuperscriptBox["u", "2"]}]}], ")"}]}], "+",
|
|---|
| 2010 | RowBox[{
|
|---|
| 2011 | RowBox[{"(",
|
|---|
| 2012 | RowBox[{"e", "-", "1"}], ")"}], " ",
|
|---|
| 2013 | SuperscriptBox[
|
|---|
| 2014 | RowBox[{"(",
|
|---|
| 2015 | RowBox[{
|
|---|
| 2016 | SuperscriptBox["t", "2"], "+",
|
|---|
| 2017 | RowBox[{"t", " ", "u"}], "+",
|
|---|
| 2018 | SuperscriptBox["u", "2"]}], ")"}], "2"]}]}], ")"}]}],
|
|---|
| 2019 | RowBox[{"3", " ", "\[Pi]", " ",
|
|---|
| 2020 | SuperscriptBox["s", "2"], " ", "t", " ", "u", " ",
|
|---|
| 2021 | SuperscriptBox["v", "2"]}]], TraditionalForm]], "Output",
|
|---|
| 2022 | CellChangeTimes->{{3.692526794285302*^9, 3.6925268046529827`*^9}, {
|
|---|
| 2023 | 3.692526834935911*^9, 3.692526852357235*^9}, {3.692526953105447*^9,
|
|---|
| 2024 | 3.6925269622524967`*^9}, 3.692527041841333*^9}]
|
|---|
| 2025 | }, Open ]]
|
|---|
| 2026 | }, Open ]],
|
|---|
| 2027 |
|
|---|
| 2028 | Cell[CellGroupData[{
|
|---|
| 2029 |
|
|---|
| 2030 | Cell["Phase space in D dimensions", "Subsection",
|
|---|
| 2031 | PageWidth->PaperWidth],
|
|---|
| 2032 |
|
|---|
| 2033 | Cell[BoxData[
|
|---|
| 2034 | RowBox[{"\[IndentingNewLine]",
|
|---|
| 2035 | RowBox[{
|
|---|
| 2036 | RowBox[{
|
|---|
| 2037 | RowBox[{"PS", "=",
|
|---|
| 2038 | RowBox[{
|
|---|
| 2039 | FractionBox["1",
|
|---|
| 2040 | RowBox[{"8", "\[Pi]"}]],
|
|---|
| 2041 | SuperscriptBox[
|
|---|
| 2042 | RowBox[{"(",
|
|---|
| 2043 | FractionBox[
|
|---|
| 2044 | RowBox[{"4", " ", "\[Pi]", " "}], "mh2"], ")"}], "e"],
|
|---|
| 2045 | FractionBox["1",
|
|---|
| 2046 | RowBox[{"Gamma", "[",
|
|---|
| 2047 | RowBox[{"1", "-", "e"}], "]"}]], " ",
|
|---|
| 2048 | SuperscriptBox[
|
|---|
| 2049 | RowBox[{"(",
|
|---|
| 2050 | FractionBox["mh2", "s"], ")"}], "e"], " ",
|
|---|
| 2051 | SuperscriptBox[
|
|---|
| 2052 | RowBox[{"(",
|
|---|
| 2053 | RowBox[{"1", "-",
|
|---|
| 2054 | FractionBox["mh2", "s"]}], ")"}],
|
|---|
| 2055 | RowBox[{"1", "-",
|
|---|
| 2056 | RowBox[{"2", "e"}]}]], " ",
|
|---|
| 2057 | SuperscriptBox["v",
|
|---|
| 2058 | RowBox[{"-", "e"}]], " ",
|
|---|
| 2059 | SuperscriptBox[
|
|---|
| 2060 | RowBox[{"(", "omv", ")"}],
|
|---|
| 2061 | RowBox[{"-", "e"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2062 | RowBox[{
|
|---|
| 2063 | RowBox[{"substu", "=",
|
|---|
| 2064 | RowBox[{"{",
|
|---|
| 2065 | RowBox[{
|
|---|
| 2066 | RowBox[{"t", "\[Rule]", " ",
|
|---|
| 2067 | RowBox[{
|
|---|
| 2068 | RowBox[{"-", "s"}], " ",
|
|---|
| 2069 | RowBox[{"(",
|
|---|
| 2070 | RowBox[{"1", "-",
|
|---|
| 2071 | FractionBox["mh2", "s"]}], ")"}],
|
|---|
| 2072 | RowBox[{"(", "omv", ")"}]}]}], ",", " ",
|
|---|
| 2073 | RowBox[{"u", "\[Rule]", " ",
|
|---|
| 2074 | RowBox[{
|
|---|
| 2075 | RowBox[{"-", "s"}], " ",
|
|---|
| 2076 | RowBox[{"(",
|
|---|
| 2077 | RowBox[{"1", "-",
|
|---|
| 2078 | FractionBox["mh2", "s"]}], ")"}], "v"}]}], " ", ",",
|
|---|
| 2079 | RowBox[{"s", "\[Rule]", " ",
|
|---|
| 2080 | RowBox[{"mh2", "/", "z"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2081 | RowBox[{
|
|---|
| 2082 | RowBox[{"cGamma", "=",
|
|---|
| 2083 | RowBox[{
|
|---|
| 2084 | RowBox[{
|
|---|
| 2085 | RowBox[{"(",
|
|---|
| 2086 | RowBox[{"1", "/", "16"}], ")"}], "/",
|
|---|
| 2087 | RowBox[{"Pi", "^", "2"}]}], " ",
|
|---|
| 2088 | RowBox[{"mh2", "^",
|
|---|
| 2089 | RowBox[{"(",
|
|---|
| 2090 | RowBox[{"-", "e"}], ")"}]}],
|
|---|
| 2091 | RowBox[{
|
|---|
| 2092 | RowBox[{"(",
|
|---|
| 2093 | RowBox[{"4", " ", "Pi"}], ")"}], "^", "e"}], " ",
|
|---|
| 2094 | RowBox[{"Gamma", "[",
|
|---|
| 2095 | RowBox[{"1", "+", "e"}], "]"}], " ",
|
|---|
| 2096 | RowBox[{
|
|---|
| 2097 | RowBox[{
|
|---|
| 2098 | RowBox[{"Gamma", "[",
|
|---|
| 2099 | RowBox[{"1", "-", "e"}], "]"}], "^", "2"}], "/",
|
|---|
| 2100 | RowBox[{"Gamma", "[",
|
|---|
| 2101 | RowBox[{"1", "-",
|
|---|
| 2102 | RowBox[{"2", " ", "e"}]}], "]"}]}]}]}], ";"}], "\n",
|
|---|
| 2103 | RowBox[{
|
|---|
| 2104 | RowBox[{"pgg", "=",
|
|---|
| 2105 | RowBox[{"2",
|
|---|
| 2106 | RowBox[{"(",
|
|---|
| 2107 | RowBox[{
|
|---|
| 2108 | RowBox[{"z", " ",
|
|---|
| 2109 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2110 | RowBox[{"1", "/",
|
|---|
| 2111 | RowBox[{"(",
|
|---|
| 2112 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}], "+",
|
|---|
| 2113 | RowBox[{
|
|---|
| 2114 | RowBox[{"(",
|
|---|
| 2115 | RowBox[{"1", "-", "z"}], ")"}], "/", "z"}], "+",
|
|---|
| 2116 | RowBox[{"z",
|
|---|
| 2117 | RowBox[{"(",
|
|---|
| 2118 | RowBox[{"1", "-", "z"}], ")"}]}], "+",
|
|---|
| 2119 | RowBox[{
|
|---|
| 2120 | RowBox[{"11", "/", "12"}], " ",
|
|---|
| 2121 | RowBox[{"DeltaFunction", "[",
|
|---|
| 2122 | RowBox[{"1", "-", "z"}], "]"}]}]}], ")"}]}]}], ";"}],
|
|---|
| 2123 | "\[IndentingNewLine]",
|
|---|
| 2124 | RowBox[{
|
|---|
| 2125 | RowBox[{"s0", "=", "z"}], ";"}]}]}]], "Input",
|
|---|
| 2126 | PageWidth->PaperWidth]
|
|---|
| 2127 | }, Open ]],
|
|---|
| 2128 |
|
|---|
| 2129 | Cell[CellGroupData[{
|
|---|
| 2130 |
|
|---|
| 2131 | Cell["CDR", "Subsection",
|
|---|
| 2132 | PageWidth->PaperWidth],
|
|---|
| 2133 |
|
|---|
| 2134 | Cell[CellGroupData[{
|
|---|
| 2135 |
|
|---|
| 2136 | Cell[BoxData[{
|
|---|
| 2137 | RowBox[{
|
|---|
| 2138 | RowBox[{"intando", "=",
|
|---|
| 2139 | RowBox[{
|
|---|
| 2140 | RowBox[{"FullSimplify", "[",
|
|---|
| 2141 | RowBox[{
|
|---|
| 2142 | RowBox[{"FullSimplify", "[",
|
|---|
| 2143 | FractionBox[
|
|---|
| 2144 | RowBox[{"RealD", " ", "PS", " ", "c\[CapitalGamma]"}], "cGamma"],
|
|---|
| 2145 | "]"}], "//.", "\[InvisibleSpace]", "substu"}], "]"}], "/.",
|
|---|
| 2146 | "\[InvisibleSpace]",
|
|---|
| 2147 | RowBox[{"omv", "\[Rule]",
|
|---|
| 2148 | RowBox[{"1", "-", "v"}]}]}]}], ";"}], "\n",
|
|---|
| 2149 | RowBox[{"intando", "=",
|
|---|
| 2150 | FractionBox["intando",
|
|---|
| 2151 | SuperscriptBox[
|
|---|
| 2152 | RowBox[{"(",
|
|---|
| 2153 | RowBox[{"1", "-", "z"}], ")"}],
|
|---|
| 2154 | RowBox[{
|
|---|
| 2155 | RowBox[{
|
|---|
| 2156 | RowBox[{"-", "2"}], " ", "e"}], "-", "1"}]]]}]}], "Input"],
|
|---|
| 2157 |
|
|---|
| 2158 | Cell[BoxData[
|
|---|
| 2159 | FormBox[
|
|---|
| 2160 | RowBox[{"-",
|
|---|
| 2161 | RowBox[{
|
|---|
| 2162 | RowBox[{"(",
|
|---|
| 2163 | RowBox[{"c\[CapitalGamma]", " ",
|
|---|
| 2164 | SuperscriptBox[
|
|---|
| 2165 | RowBox[{"(",
|
|---|
| 2166 | FractionBox["1", "mh2"], ")"}], "e"], " ",
|
|---|
| 2167 | SuperscriptBox["mh2", "e"], " ", "\[Pi]", " ",
|
|---|
| 2168 | SuperscriptBox[
|
|---|
| 2169 | RowBox[{"(",
|
|---|
| 2170 | RowBox[{"1", "-", "v"}], ")"}],
|
|---|
| 2171 | RowBox[{
|
|---|
| 2172 | RowBox[{"-", "e"}], "-", "1"}]], " ",
|
|---|
| 2173 | SuperscriptBox["v",
|
|---|
| 2174 | RowBox[{
|
|---|
| 2175 | RowBox[{"-", "e"}], "-", "1"}]], " ",
|
|---|
| 2176 | SuperscriptBox["z", "e"], " ",
|
|---|
| 2177 | RowBox[{"(",
|
|---|
| 2178 | RowBox[{
|
|---|
| 2179 | RowBox[{"e", " ",
|
|---|
| 2180 | RowBox[{"(",
|
|---|
| 2181 | RowBox[{
|
|---|
| 2182 | RowBox[{"3", " ",
|
|---|
| 2183 | SuperscriptBox[
|
|---|
| 2184 | RowBox[{"(",
|
|---|
| 2185 | RowBox[{"1", "-", "v"}], ")"}], "4"], " ",
|
|---|
| 2186 | SuperscriptBox[
|
|---|
| 2187 | RowBox[{"(",
|
|---|
| 2188 | RowBox[{"z", "-", "1"}], ")"}], "4"]}], "+",
|
|---|
| 2189 | RowBox[{"3", " ",
|
|---|
| 2190 | SuperscriptBox["v", "4"], " ",
|
|---|
| 2191 | SuperscriptBox[
|
|---|
| 2192 | RowBox[{"(",
|
|---|
| 2193 | RowBox[{"z", "-", "1"}], ")"}], "4"]}], "-",
|
|---|
| 2194 | RowBox[{"2", " ",
|
|---|
| 2195 | SuperscriptBox["v", "2"], " ",
|
|---|
| 2196 | RowBox[{"(",
|
|---|
| 2197 | RowBox[{
|
|---|
| 2198 | SuperscriptBox["z", "2"], "+", "1"}], ")"}], " ",
|
|---|
| 2199 | SuperscriptBox[
|
|---|
| 2200 | RowBox[{"(",
|
|---|
| 2201 | RowBox[{"z", "-", "1"}], ")"}], "2"]}], "-",
|
|---|
| 2202 | RowBox[{"2", " ",
|
|---|
| 2203 | SuperscriptBox[
|
|---|
| 2204 | RowBox[{"(",
|
|---|
| 2205 | RowBox[{"1", "-", "v"}], ")"}], "2"], " ",
|
|---|
| 2206 | RowBox[{"(",
|
|---|
| 2207 | RowBox[{
|
|---|
| 2208 | RowBox[{
|
|---|
| 2209 | SuperscriptBox["v", "2"], " ",
|
|---|
| 2210 | SuperscriptBox[
|
|---|
| 2211 | RowBox[{"(",
|
|---|
| 2212 | RowBox[{"z", "-", "1"}], ")"}], "2"]}], "+",
|
|---|
| 2213 | SuperscriptBox["z", "2"], "+", "1"}], ")"}], " ",
|
|---|
| 2214 | SuperscriptBox[
|
|---|
| 2215 | RowBox[{"(",
|
|---|
| 2216 | RowBox[{"z", "-", "1"}], ")"}], "2"]}], "+",
|
|---|
| 2217 | RowBox[{"3", " ",
|
|---|
| 2218 | SuperscriptBox["z", "4"]}], "-",
|
|---|
| 2219 | RowBox[{"2", " ",
|
|---|
| 2220 | SuperscriptBox["z", "2"]}], "+", "3"}], ")"}]}], "-",
|
|---|
| 2221 | RowBox[{"2", " ",
|
|---|
| 2222 | RowBox[{"(",
|
|---|
| 2223 | RowBox[{
|
|---|
| 2224 | RowBox[{
|
|---|
| 2225 | SuperscriptBox[
|
|---|
| 2226 | RowBox[{"(",
|
|---|
| 2227 | RowBox[{"1", "-", "v"}], ")"}], "4"], " ",
|
|---|
| 2228 | SuperscriptBox[
|
|---|
| 2229 | RowBox[{"(",
|
|---|
| 2230 | RowBox[{"z", "-", "1"}], ")"}], "4"]}], "+",
|
|---|
| 2231 | RowBox[{
|
|---|
| 2232 | SuperscriptBox["v", "4"], " ",
|
|---|
| 2233 | SuperscriptBox[
|
|---|
| 2234 | RowBox[{"(",
|
|---|
| 2235 | RowBox[{"z", "-", "1"}], ")"}], "4"]}], "+",
|
|---|
| 2236 | SuperscriptBox["z", "4"], "+", "1"}], ")"}]}]}], ")"}], " ",
|
|---|
| 2237 | RowBox[{"\[CapitalGamma]", "(",
|
|---|
| 2238 | RowBox[{"1", "-",
|
|---|
| 2239 | RowBox[{"2", " ", "e"}]}], ")"}]}], ")"}], "/",
|
|---|
| 2240 | RowBox[{"(",
|
|---|
| 2241 | RowBox[{
|
|---|
| 2242 | SuperscriptBox[
|
|---|
| 2243 | RowBox[{"(",
|
|---|
| 2244 | RowBox[{"e", "-", "1"}], ")"}], "2"], " ",
|
|---|
| 2245 | SuperscriptBox[
|
|---|
| 2246 | RowBox[{"\[CapitalGamma]", "(",
|
|---|
| 2247 | RowBox[{"1", "-", "e"}], ")"}], "3"], " ",
|
|---|
| 2248 | RowBox[{"\[CapitalGamma]", "(",
|
|---|
| 2249 | RowBox[{"e", "+", "1"}], ")"}]}], ")"}]}]}],
|
|---|
| 2250 | TraditionalForm]], "Output"]
|
|---|
| 2251 | }, Open ]],
|
|---|
| 2252 |
|
|---|
| 2253 | Cell[BoxData[{
|
|---|
| 2254 | RowBox[{
|
|---|
| 2255 | RowBox[{"\[Sigma]r", "=",
|
|---|
| 2256 | RowBox[{
|
|---|
| 2257 | RowBox[{"Integrate", "[",
|
|---|
| 2258 | RowBox[{"intando", ",",
|
|---|
| 2259 | RowBox[{"{",
|
|---|
| 2260 | RowBox[{"v", ",", "0", ",", "1"}], "}"}], ",", " ",
|
|---|
| 2261 | RowBox[{"GenerateConditions", "\[Rule]", "False"}]}], "]"}], "//",
|
|---|
| 2262 | "PowerExpand"}]}], ";"}], "\n",
|
|---|
| 2263 | RowBox[{
|
|---|
| 2264 | RowBox[{"\[Sigma]r", "=",
|
|---|
| 2265 | RowBox[{
|
|---|
| 2266 | RowBox[{
|
|---|
| 2267 | RowBox[{"Normal", "[",
|
|---|
| 2268 | RowBox[{"Series", "[",
|
|---|
| 2269 | RowBox[{"\[Sigma]r", ",",
|
|---|
| 2270 | RowBox[{"{",
|
|---|
| 2271 | RowBox[{"e", ",", "0", ",", "1"}], "}"}]}], "]"}], "]"}], "//",
|
|---|
| 2272 | "Factor"}], "//", "FullSimplify"}]}], ";"}], "\n",
|
|---|
| 2273 | RowBox[{
|
|---|
| 2274 | RowBox[{"\[Sigma]r", " ", "=",
|
|---|
| 2275 | RowBox[{"\[Sigma]r", " ", "*",
|
|---|
| 2276 | RowBox[{"(",
|
|---|
| 2277 | RowBox[{
|
|---|
| 2278 | RowBox[{
|
|---|
| 2279 | FractionBox[
|
|---|
| 2280 | RowBox[{"-", "1"}],
|
|---|
| 2281 | RowBox[{"2", "e"}]],
|
|---|
| 2282 | RowBox[{"DeltaFunction", "[",
|
|---|
| 2283 | RowBox[{"1", "-", "z"}], "]"}]}], "+",
|
|---|
| 2284 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2285 | RowBox[{"1", "/",
|
|---|
| 2286 | RowBox[{"(",
|
|---|
| 2287 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}], "-",
|
|---|
| 2288 | RowBox[{"2", " ", "e", " ",
|
|---|
| 2289 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2290 | RowBox[{
|
|---|
| 2291 | RowBox[{"Log", "[",
|
|---|
| 2292 | RowBox[{"1", "-", "z"}], "]"}], "/",
|
|---|
| 2293 | RowBox[{"(",
|
|---|
| 2294 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}]}], ")"}]}]}], ";"}], "\n",
|
|---|
| 2295 | RowBox[{
|
|---|
| 2296 | RowBox[{"\[Sigma]r", "=",
|
|---|
| 2297 | RowBox[{
|
|---|
| 2298 | RowBox[{"Normal", "[",
|
|---|
| 2299 | RowBox[{"Series", "[",
|
|---|
| 2300 | RowBox[{
|
|---|
| 2301 | RowBox[{"\[Sigma]r", "/",
|
|---|
| 2302 | RowBox[{"(",
|
|---|
| 2303 | RowBox[{"1", "+", "e", "+",
|
|---|
| 2304 | RowBox[{"e", "^", "2"}]}], ")"}]}], ",",
|
|---|
| 2305 | RowBox[{"{",
|
|---|
| 2306 | RowBox[{"e", ",", "0", ",", "0"}], "}"}]}], "]"}], "]"}], "//",
|
|---|
| 2307 | "Expand"}]}], ";"}]}], "Input",
|
|---|
| 2308 | PageWidth->PaperWidth]
|
|---|
| 2309 | }, Open ]]
|
|---|
| 2310 | }, Open ]],
|
|---|
| 2311 |
|
|---|
| 2312 | Cell[CellGroupData[{
|
|---|
| 2313 |
|
|---|
| 2314 | Cell["Results", "Section"],
|
|---|
| 2315 |
|
|---|
| 2316 | Cell[CellGroupData[{
|
|---|
| 2317 |
|
|---|
| 2318 | Cell["Virtual+Real+Counterterms in CDR", "Subsection"],
|
|---|
| 2319 |
|
|---|
| 2320 | Cell[BoxData[{
|
|---|
| 2321 | RowBox[{
|
|---|
| 2322 | RowBox[{"\[Sigma]rn", "=",
|
|---|
| 2323 | RowBox[{
|
|---|
| 2324 | RowBox[{
|
|---|
| 2325 | RowBox[{
|
|---|
| 2326 | RowBox[{
|
|---|
| 2327 | RowBox[{"\[Sigma]r", "/", "c\[CapitalGamma]"}], "/", "\[Pi]"}], "/",
|
|---|
| 2328 | "2"}], " ", "CA"}], "-",
|
|---|
| 2329 | RowBox[{
|
|---|
| 2330 | RowBox[{"1", "/", "e"}], " ", "2", " ", "Pgg", " ", "z", " ", "CA"}],
|
|---|
| 2331 | "+",
|
|---|
| 2332 | RowBox[{
|
|---|
| 2333 | RowBox[{"1", "/", "e"}], " ", "2", " ", "pgg", " ", "z", " ", "CA"}]}]}],
|
|---|
| 2334 | ";"}], "\n",
|
|---|
| 2335 | RowBox[{
|
|---|
| 2336 | RowBox[{"\[Sigma]rn", "=",
|
|---|
| 2337 | RowBox[{"(",
|
|---|
| 2338 | RowBox[{
|
|---|
| 2339 | RowBox[{"(",
|
|---|
| 2340 | RowBox[{
|
|---|
| 2341 | RowBox[{"(",
|
|---|
| 2342 | RowBox[{
|
|---|
| 2343 | RowBox[{
|
|---|
| 2344 | RowBox[{"Coefficient", "[",
|
|---|
| 2345 | RowBox[{"\[Sigma]rn", ",",
|
|---|
| 2346 | RowBox[{"DeltaFunction", "[",
|
|---|
| 2347 | RowBox[{"1", "-", "z"}], "]"}]}], "]"}], "/.",
|
|---|
| 2348 | RowBox[{"z", "\[Rule]", "1"}]}], "//", "FullSimplify"}], ")"}], "*",
|
|---|
| 2349 | RowBox[{"DeltaFunction", "[",
|
|---|
| 2350 | RowBox[{"1", "-", "z"}], "]"}]}], ")"}], "+",
|
|---|
| 2351 | RowBox[{"(",
|
|---|
| 2352 | RowBox[{
|
|---|
| 2353 | RowBox[{"(",
|
|---|
| 2354 | RowBox[{"(",
|
|---|
| 2355 | RowBox[{
|
|---|
| 2356 | RowBox[{"Coefficient", "[",
|
|---|
| 2357 | RowBox[{"\[Sigma]rn", ",",
|
|---|
| 2358 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2359 | RowBox[{"1", "/",
|
|---|
| 2360 | RowBox[{"(",
|
|---|
| 2361 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}], "]"}], "//",
|
|---|
| 2362 | "FullSimplify"}], ")"}], ")"}],
|
|---|
| 2363 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2364 | RowBox[{"1", "/",
|
|---|
| 2365 | RowBox[{"(",
|
|---|
| 2366 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}], ")"}], "+",
|
|---|
| 2367 | RowBox[{"(",
|
|---|
| 2368 | RowBox[{
|
|---|
| 2369 | RowBox[{"(",
|
|---|
| 2370 | RowBox[{"(",
|
|---|
| 2371 | RowBox[{
|
|---|
| 2372 | RowBox[{"Coefficient", "[",
|
|---|
| 2373 | RowBox[{"\[Sigma]rn", ",",
|
|---|
| 2374 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2375 | RowBox[{
|
|---|
| 2376 | RowBox[{"Log", "[",
|
|---|
| 2377 | RowBox[{"1", "-", "z"}], "]"}], "/",
|
|---|
| 2378 | RowBox[{"(",
|
|---|
| 2379 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}], "]"}], "//",
|
|---|
| 2380 | "FullSimplify"}], ")"}], ")"}],
|
|---|
| 2381 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2382 | RowBox[{
|
|---|
| 2383 | RowBox[{"Log", "[",
|
|---|
| 2384 | RowBox[{"1", "-", "z"}], "]"}], "/",
|
|---|
| 2385 | RowBox[{"(",
|
|---|
| 2386 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}], ")"}], "+",
|
|---|
| 2387 | RowBox[{"(",
|
|---|
| 2388 | RowBox[{
|
|---|
| 2389 | RowBox[{
|
|---|
| 2390 | RowBox[{"\[Sigma]rn", "/.",
|
|---|
| 2391 | RowBox[{
|
|---|
| 2392 | RowBox[{"DeltaFunction", "[", "x_", "]"}], "\[Rule]", "0"}]}], "/.",
|
|---|
| 2393 | RowBox[{
|
|---|
| 2394 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2395 | RowBox[{
|
|---|
| 2396 | RowBox[{"Log", "[",
|
|---|
| 2397 | RowBox[{"1", "-", "z"}], "]"}], "/",
|
|---|
| 2398 | RowBox[{"(",
|
|---|
| 2399 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}], "\[Rule]", "0"}]}], "/.",
|
|---|
| 2400 | RowBox[{
|
|---|
| 2401 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2402 | RowBox[{"1", "/",
|
|---|
| 2403 | RowBox[{"(",
|
|---|
| 2404 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}], "\[Rule]", "0"}]}],
|
|---|
| 2405 | ")"}]}], ")"}]}], ";"}], "\n",
|
|---|
| 2406 | RowBox[{
|
|---|
| 2407 | RowBox[{"\[Sigma]rn", "=",
|
|---|
| 2408 | RowBox[{
|
|---|
| 2409 | RowBox[{
|
|---|
| 2410 | RowBox[{"(",
|
|---|
| 2411 | RowBox[{
|
|---|
| 2412 | RowBox[{"(",
|
|---|
| 2413 | RowBox[{"(",
|
|---|
| 2414 | RowBox[{
|
|---|
| 2415 | RowBox[{
|
|---|
| 2416 | RowBox[{"Coefficient", "[",
|
|---|
| 2417 | RowBox[{"\[Sigma]rn", ",",
|
|---|
| 2418 | RowBox[{
|
|---|
| 2419 | RowBox[{"1", "/", "e"}], " ",
|
|---|
| 2420 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2421 | RowBox[{"1", "/",
|
|---|
| 2422 | RowBox[{"(",
|
|---|
| 2423 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}]}], "]"}], "/",
|
|---|
| 2424 | RowBox[{"(",
|
|---|
| 2425 | RowBox[{"1", "-", "z"}], ")"}]}], "//", "FullSimplify"}], ")"}],
|
|---|
| 2426 | ")"}],
|
|---|
| 2427 | RowBox[{"1", "/", "e"}]}], ")"}], "+",
|
|---|
| 2428 | RowBox[{"(",
|
|---|
| 2429 | RowBox[{"\[Sigma]rn", "-",
|
|---|
| 2430 | RowBox[{
|
|---|
| 2431 | RowBox[{"Coefficient", "[",
|
|---|
| 2432 | RowBox[{"\[Sigma]rn", ",",
|
|---|
| 2433 | RowBox[{
|
|---|
| 2434 | RowBox[{"1", "/", "e"}], " ",
|
|---|
| 2435 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2436 | RowBox[{"1", "/",
|
|---|
| 2437 | RowBox[{"(",
|
|---|
| 2438 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}]}], "]"}],
|
|---|
| 2439 | RowBox[{"1", "/", "e"}], " ",
|
|---|
| 2440 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2441 | RowBox[{"1", "/",
|
|---|
| 2442 | RowBox[{"(",
|
|---|
| 2443 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}]}], ")"}]}], "//",
|
|---|
| 2444 | "Expand"}]}], ";"}]}], "Input",
|
|---|
| 2445 | PageWidth->PaperWidth],
|
|---|
| 2446 |
|
|---|
| 2447 | Cell[CellGroupData[{
|
|---|
| 2448 |
|
|---|
| 2449 | Cell[BoxData[
|
|---|
| 2450 | RowBox[{"divD", "=",
|
|---|
| 2451 | RowBox[{
|
|---|
| 2452 | RowBox[{"Coefficient", "[",
|
|---|
| 2453 | RowBox[{"\[Sigma]rn", ",",
|
|---|
| 2454 | RowBox[{"DeltaFunction", "[",
|
|---|
| 2455 | RowBox[{"1", "-", "z"}], "]"}]}], "]"}], "*",
|
|---|
| 2456 | RowBox[{
|
|---|
| 2457 | RowBox[{"as", "/", "2"}], "/", "\[Pi]"}], " ",
|
|---|
| 2458 | "c\[CapitalGamma]"}]}]], "Input"],
|
|---|
| 2459 |
|
|---|
| 2460 | Cell[BoxData[
|
|---|
| 2461 | FormBox[
|
|---|
| 2462 | FractionBox[
|
|---|
| 2463 | RowBox[{"as", " ", "c\[CapitalGamma]", " ",
|
|---|
| 2464 | RowBox[{"(",
|
|---|
| 2465 | RowBox[{
|
|---|
| 2466 | FractionBox[
|
|---|
| 2467 | RowBox[{"11", " ",
|
|---|
| 2468 | SubscriptBox["C", "A"]}],
|
|---|
| 2469 | RowBox[{"3", " ", "e"}]], "+",
|
|---|
| 2470 | FractionBox[
|
|---|
| 2471 | RowBox[{"2", " ",
|
|---|
| 2472 | SubscriptBox["C", "A"]}],
|
|---|
| 2473 | SuperscriptBox["e", "2"]], "-",
|
|---|
| 2474 | FractionBox[
|
|---|
| 2475 | RowBox[{
|
|---|
| 2476 | SuperscriptBox["\[Pi]", "2"], " ",
|
|---|
| 2477 | SubscriptBox["C", "A"]}], "3"]}], ")"}]}],
|
|---|
| 2478 | RowBox[{"2", " ", "\[Pi]"}]], TraditionalForm]], "Output"]
|
|---|
| 2479 | }, Open ]],
|
|---|
| 2480 |
|
|---|
| 2481 | Cell[CellGroupData[{
|
|---|
| 2482 |
|
|---|
| 2483 | Cell[BoxData[
|
|---|
| 2484 | RowBox[{"UVC", "=", " ",
|
|---|
| 2485 | RowBox[{
|
|---|
| 2486 | RowBox[{"1", "/", "e"}], " ", "4", "*",
|
|---|
| 2487 | FractionBox[
|
|---|
| 2488 | RowBox[{"-", "11"}], "6"], "CA", " ",
|
|---|
| 2489 | FractionBox["as",
|
|---|
| 2490 | RowBox[{"4", "\[Pi]"}]], "c\[CapitalGamma]", " "}]}]], "Input"],
|
|---|
| 2491 |
|
|---|
| 2492 | Cell[BoxData[
|
|---|
| 2493 | FormBox[
|
|---|
| 2494 | RowBox[{"-",
|
|---|
| 2495 | FractionBox[
|
|---|
| 2496 | RowBox[{"11", " ", "as", " ",
|
|---|
| 2497 | SubscriptBox["C", "A"], " ", "c\[CapitalGamma]"}],
|
|---|
| 2498 | RowBox[{"6", " ", "e", " ", "\[Pi]"}]]}], TraditionalForm]], "Output"]
|
|---|
| 2499 | }, Open ]],
|
|---|
| 2500 |
|
|---|
| 2501 | Cell[CellGroupData[{
|
|---|
| 2502 |
|
|---|
| 2503 | Cell[BoxData[
|
|---|
| 2504 | RowBox[{
|
|---|
| 2505 | RowBox[{"(",
|
|---|
| 2506 | RowBox[{
|
|---|
| 2507 | RowBox[{
|
|---|
| 2508 | RowBox[{
|
|---|
| 2509 | RowBox[{
|
|---|
| 2510 | RowBox[{"(",
|
|---|
| 2511 | RowBox[{"divD", "+", "UVC"}], ")"}], "/", "as"}], "/",
|
|---|
| 2512 | "c\[CapitalGamma]"}], " ", "2", " ", "\[Pi]"}], "//", "Expand"}], ")"}],
|
|---|
| 2513 | " ", "as", " ",
|
|---|
| 2514 | RowBox[{
|
|---|
| 2515 | RowBox[{"c\[CapitalGamma]", "/", "2"}], "/", "\[Pi]"}]}]], "Input"],
|
|---|
| 2516 |
|
|---|
| 2517 | Cell[BoxData[
|
|---|
| 2518 | FormBox[
|
|---|
| 2519 | FractionBox[
|
|---|
| 2520 | RowBox[{"as", " ", "c\[CapitalGamma]", " ",
|
|---|
| 2521 | RowBox[{"(",
|
|---|
| 2522 | RowBox[{
|
|---|
| 2523 | FractionBox[
|
|---|
| 2524 | RowBox[{"2", " ",
|
|---|
| 2525 | SubscriptBox["C", "A"]}],
|
|---|
| 2526 | SuperscriptBox["e", "2"]], "-",
|
|---|
| 2527 | FractionBox[
|
|---|
| 2528 | RowBox[{
|
|---|
| 2529 | SuperscriptBox["\[Pi]", "2"], " ",
|
|---|
| 2530 | SubscriptBox["C", "A"]}], "3"], "+",
|
|---|
| 2531 | FractionBox[
|
|---|
| 2532 | SubscriptBox["C", "A"], "3"]}], ")"}]}],
|
|---|
| 2533 | RowBox[{"2", " ", "\[Pi]"}]], TraditionalForm]], "Output"]
|
|---|
| 2534 | }, Open ]],
|
|---|
| 2535 |
|
|---|
| 2536 | Cell[BoxData[
|
|---|
| 2537 | RowBox[{
|
|---|
| 2538 | RowBox[{"sally", "=",
|
|---|
| 2539 | RowBox[{
|
|---|
| 2540 | RowBox[{"as", "/", "\[Pi]"}], " ",
|
|---|
| 2541 | RowBox[{"(",
|
|---|
| 2542 | RowBox[{
|
|---|
| 2543 | RowBox[{
|
|---|
| 2544 | RowBox[{
|
|---|
| 2545 | RowBox[{"-", "11"}], "/", "2"}], " ",
|
|---|
| 2546 | RowBox[{
|
|---|
| 2547 | RowBox[{"(",
|
|---|
| 2548 | RowBox[{"1", "-", "z"}], ")"}], "^", "3"}]}], "+",
|
|---|
| 2549 | RowBox[{"6", " ",
|
|---|
| 2550 | RowBox[{"(",
|
|---|
| 2551 | RowBox[{"1", "+",
|
|---|
| 2552 | RowBox[{"z", "^", "4"}], "+",
|
|---|
| 2553 | RowBox[{
|
|---|
| 2554 | RowBox[{"(",
|
|---|
| 2555 | RowBox[{"1", "-", "z"}], ")"}], "^", "4"}]}], ")"}], " ",
|
|---|
| 2556 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2557 | RowBox[{
|
|---|
| 2558 | RowBox[{"Log", "[",
|
|---|
| 2559 | RowBox[{"1", "-", "z"}], "]"}], "/",
|
|---|
| 2560 | RowBox[{"(",
|
|---|
| 2561 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}], "-",
|
|---|
| 2562 | RowBox[{"6", " ",
|
|---|
| 2563 | RowBox[{"(",
|
|---|
| 2564 | RowBox[{
|
|---|
| 2565 | RowBox[{
|
|---|
| 2566 | RowBox[{"z", "^", "2"}], " ",
|
|---|
| 2567 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2568 | RowBox[{"1", "/",
|
|---|
| 2569 | RowBox[{"(",
|
|---|
| 2570 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}]}], "+",
|
|---|
| 2571 | RowBox[{"(",
|
|---|
| 2572 | RowBox[{"1", "-", "z"}], ")"}], "+",
|
|---|
| 2573 | RowBox[{
|
|---|
| 2574 | RowBox[{"z", "^", "2"}],
|
|---|
| 2575 | RowBox[{"(",
|
|---|
| 2576 | RowBox[{"1", "-", "z"}], ")"}]}]}], ")"}],
|
|---|
| 2577 | RowBox[{"Log", "[", "z", "]"}]}]}], ")"}]}]}], ";"}]], "Input"],
|
|---|
| 2578 |
|
|---|
| 2579 | Cell[BoxData[
|
|---|
| 2580 | RowBox[{
|
|---|
| 2581 | RowBox[{
|
|---|
| 2582 | RowBox[{"(",
|
|---|
| 2583 | RowBox[{
|
|---|
| 2584 | RowBox[{
|
|---|
| 2585 | RowBox[{
|
|---|
| 2586 | RowBox[{
|
|---|
| 2587 | RowBox[{
|
|---|
| 2588 | RowBox[{"(",
|
|---|
| 2589 | RowBox[{
|
|---|
| 2590 | RowBox[{"\[Sigma]rn", "*",
|
|---|
| 2591 | RowBox[{
|
|---|
| 2592 | RowBox[{"as", "/", "2"}], "/", "\[Pi]"}]}], "/.",
|
|---|
| 2593 | RowBox[{
|
|---|
| 2594 | RowBox[{"DeltaFunction", "[", "x_", "]"}], "\[Rule]", "0"}]}],
|
|---|
| 2595 | ")"}], "-", "sally"}], "/.",
|
|---|
| 2596 | RowBox[{"CA", "\[Rule]", "3"}]}], "/.",
|
|---|
| 2597 | RowBox[{"Pgg", "\[Rule]", "0"}]}], "//", "Expand"}], "//",
|
|---|
| 2598 | "Simplify"}], ")"}], "/.",
|
|---|
| 2599 | RowBox[{
|
|---|
| 2600 | RowBox[{"PlusDistribution", "[",
|
|---|
| 2601 | RowBox[{"1", "/",
|
|---|
| 2602 | RowBox[{"(",
|
|---|
| 2603 | RowBox[{"1", "-", "z"}], ")"}]}], "]"}], "\[Rule]",
|
|---|
| 2604 | RowBox[{"1", "/",
|
|---|
| 2605 | RowBox[{"(",
|
|---|
| 2606 | RowBox[{"1", "-", "z"}], ")"}]}]}]}], "//", "Factor"}]], "Input"]
|
|---|
| 2607 | }, Open ]]
|
|---|
| 2608 | }, Open ]],
|
|---|
| 2609 |
|
|---|
| 2610 | Cell[CellGroupData[{
|
|---|
| 2611 |
|
|---|
| 2612 | Cell["Gluon initiated process", "Section",
|
|---|
| 2613 | PageWidth->PaperWidth],
|
|---|
| 2614 |
|
|---|
| 2615 | Cell[CellGroupData[{
|
|---|
| 2616 |
|
|---|
| 2617 | Cell["Kinematics for the Born", "Subsection",
|
|---|
| 2618 | PageWidth->PaperWidth],
|
|---|
| 2619 |
|
|---|
| 2620 | Cell["\<\
|
|---|
| 2621 | -----I take all momenta outgoing
|
|---|
| 2622 |
|
|---|
| 2623 | p1 + p2 + p3 = 0
|
|---|
| 2624 |
|
|---|
| 2625 | p1^2=0
|
|---|
| 2626 | p2^2=0
|
|---|
| 2627 | p3^3=Q^2
|
|---|
| 2628 |
|
|---|
| 2629 |
|
|---|
| 2630 | \
|
|---|
| 2631 | \>", "Text",
|
|---|
| 2632 | PageWidth->PaperWidth],
|
|---|
| 2633 |
|
|---|
| 2634 | Cell[BoxData[{
|
|---|
| 2635 | RowBox[{
|
|---|
| 2636 | RowBox[{
|
|---|
| 2637 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2638 | RowBox[{"p1", ",", "p1"}], "]"}], "=", "0"}],
|
|---|
| 2639 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2640 | RowBox[{
|
|---|
| 2641 | RowBox[{
|
|---|
| 2642 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2643 | RowBox[{"p2", ",", "p2"}], "]"}], "=", "0"}],
|
|---|
| 2644 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2645 | RowBox[{
|
|---|
| 2646 | RowBox[{
|
|---|
| 2647 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2648 | RowBox[{"p3", ",", "p3"}], "]"}], "=", "Q2"}],
|
|---|
| 2649 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2650 | RowBox[{
|
|---|
| 2651 | RowBox[{
|
|---|
| 2652 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2653 | RowBox[{"p1", ",", "p3"}], "]"}], "=",
|
|---|
| 2654 | RowBox[{
|
|---|
| 2655 | RowBox[{"-", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2656 | RowBox[{
|
|---|
| 2657 | RowBox[{
|
|---|
| 2658 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2659 | RowBox[{"p1", ",", "p2"}], "]"}], "=",
|
|---|
| 2660 | RowBox[{"Q2", "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2661 | RowBox[{
|
|---|
| 2662 | RowBox[{
|
|---|
| 2663 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2664 | RowBox[{"p2", ",", "p3"}], "]"}], "=",
|
|---|
| 2665 | RowBox[{
|
|---|
| 2666 | RowBox[{"-", " ", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2667 | RowBox[{
|
|---|
| 2668 | RowBox[{
|
|---|
| 2669 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2670 | RowBox[{"p1", ",", "e1"}], "]"}], "=", "0"}],
|
|---|
| 2671 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2672 | RowBox[{
|
|---|
| 2673 | RowBox[{
|
|---|
| 2674 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2675 | RowBox[{"p2", ",", "e2"}], "]"}], "=", "0"}],
|
|---|
| 2676 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2677 | RowBox[{
|
|---|
| 2678 | RowBox[{
|
|---|
| 2679 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2680 | RowBox[{"p1", ",", "e2"}], "]"}], "=", "0"}],
|
|---|
| 2681 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2682 | RowBox[{
|
|---|
| 2683 | RowBox[{
|
|---|
| 2684 | RowBox[{
|
|---|
| 2685 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2686 | RowBox[{"p2", ",", "e1"}], "]"}], "=", "0"}], ";"}],
|
|---|
| 2687 | "\[IndentingNewLine]"}], "\[IndentingNewLine]",
|
|---|
| 2688 | RowBox[{
|
|---|
| 2689 | RowBox[{
|
|---|
| 2690 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2691 | RowBox[{"p1", ",", "p1", ",",
|
|---|
| 2692 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 2693 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2694 | RowBox[{
|
|---|
| 2695 | RowBox[{
|
|---|
| 2696 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2697 | RowBox[{"p2", ",", "p2", ",",
|
|---|
| 2698 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 2699 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2700 | RowBox[{
|
|---|
| 2701 | RowBox[{
|
|---|
| 2702 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2703 | RowBox[{"p3", ",", "p3", ",",
|
|---|
| 2704 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "Q2"}],
|
|---|
| 2705 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2706 | RowBox[{
|
|---|
| 2707 | RowBox[{
|
|---|
| 2708 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2709 | RowBox[{"p1", ",", "p3", ",",
|
|---|
| 2710 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=",
|
|---|
| 2711 | RowBox[{
|
|---|
| 2712 | RowBox[{"-", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2713 | RowBox[{
|
|---|
| 2714 | RowBox[{
|
|---|
| 2715 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2716 | RowBox[{"p1", ",", "p2", ",",
|
|---|
| 2717 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=",
|
|---|
| 2718 | RowBox[{"Q2", "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2719 | RowBox[{
|
|---|
| 2720 | RowBox[{
|
|---|
| 2721 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2722 | RowBox[{"p2", ",", "p3", ",",
|
|---|
| 2723 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=",
|
|---|
| 2724 | RowBox[{
|
|---|
| 2725 | RowBox[{"-", " ", "Q2"}], "/", "2"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2726 | RowBox[{
|
|---|
| 2727 | RowBox[{
|
|---|
| 2728 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2729 | RowBox[{"p1", ",", "e1", ",",
|
|---|
| 2730 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 2731 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2732 | RowBox[{
|
|---|
| 2733 | RowBox[{
|
|---|
| 2734 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2735 | RowBox[{"p2", ",", "e2", ",",
|
|---|
| 2736 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 2737 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2738 | RowBox[{
|
|---|
| 2739 | RowBox[{
|
|---|
| 2740 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2741 | RowBox[{"p1", ",", "e2", ",",
|
|---|
| 2742 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 2743 | ";"}], "\[IndentingNewLine]",
|
|---|
| 2744 | RowBox[{
|
|---|
| 2745 | RowBox[{
|
|---|
| 2746 | RowBox[{"ScalarProduct", "[",
|
|---|
| 2747 | RowBox[{"p2", ",", "e1", ",",
|
|---|
| 2748 | RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "=", "0"}],
|
|---|
| 2749 | ";"}], "\[IndentingNewLine]"}], "Input",
|
|---|
| 2750 | PageWidth->PaperWidth]
|
|---|
| 2751 | }, Open ]],
|
|---|
| 2752 |
|
|---|
| 2753 | Cell[CellGroupData[{
|
|---|
| 2754 |
|
|---|
| 2755 | Cell["Real Amplitude", "Subsection",
|
|---|
| 2756 | PageWidth->PaperWidth],
|
|---|
| 2757 |
|
|---|
| 2758 | Cell[BoxData[{
|
|---|
| 2759 | RowBox[{
|
|---|
| 2760 | RowBox[{"Emme", "=",
|
|---|
| 2761 | RowBox[{"CF", " ",
|
|---|
| 2762 | RowBox[{"1", "/", "s"}],
|
|---|
| 2763 | RowBox[{
|
|---|
| 2764 | RowBox[{"(",
|
|---|
| 2765 | RowBox[{
|
|---|
| 2766 | RowBox[{"(",
|
|---|
| 2767 | RowBox[{
|
|---|
| 2768 | RowBox[{"s", "^", "2"}], "+",
|
|---|
| 2769 | RowBox[{"u", "^", "2"}]}], ")"}], " ", "-",
|
|---|
| 2770 | RowBox[{"e", " ",
|
|---|
| 2771 | RowBox[{
|
|---|
| 2772 | RowBox[{"(",
|
|---|
| 2773 | RowBox[{"s", "+", "u"}], ")"}], "^", "2"}]}]}], ")"}], "/",
|
|---|
| 2774 | "t"}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2775 | RowBox[{
|
|---|
| 2776 | RowBox[{"RealD", "=",
|
|---|
| 2777 | RowBox[{"Emme", "/",
|
|---|
| 2778 | RowBox[{"(",
|
|---|
| 2779 | RowBox[{"1", "-", "e"}], ")"}]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2780 | RowBox[{
|
|---|
| 2781 | RowBox[{"Real4", "=",
|
|---|
| 2782 | RowBox[{"RealD", "/.", " ",
|
|---|
| 2783 | RowBox[{"e", "\[Rule]", "0"}]}]}], ";"}]}], "Input"]
|
|---|
| 2784 | }, Open ]],
|
|---|
| 2785 |
|
|---|
| 2786 | Cell[CellGroupData[{
|
|---|
| 2787 |
|
|---|
| 2788 | Cell["Integration over the phase space in D dimensions", "Subsection",
|
|---|
| 2789 | PageWidth->PaperWidth],
|
|---|
| 2790 |
|
|---|
| 2791 | Cell[BoxData[{
|
|---|
| 2792 | RowBox[{
|
|---|
| 2793 | RowBox[{"PS", "=",
|
|---|
| 2794 | RowBox[{
|
|---|
| 2795 | FractionBox["1",
|
|---|
| 2796 | RowBox[{"8", "\[Pi]"}]],
|
|---|
| 2797 | SuperscriptBox[
|
|---|
| 2798 | RowBox[{"(",
|
|---|
| 2799 | FractionBox[
|
|---|
| 2800 | RowBox[{"4", " ", "\[Pi]", " "}], "mh2"], ")"}], "e"],
|
|---|
| 2801 | FractionBox["1",
|
|---|
| 2802 | RowBox[{"Gamma", "[",
|
|---|
| 2803 | RowBox[{"1", "-", "e"}], "]"}]], " ",
|
|---|
| 2804 | SuperscriptBox[
|
|---|
| 2805 | RowBox[{"(",
|
|---|
| 2806 | FractionBox["mh2", "s"], ")"}], "e"], " ",
|
|---|
| 2807 | SuperscriptBox[
|
|---|
| 2808 | RowBox[{"(",
|
|---|
| 2809 | RowBox[{"1", "-",
|
|---|
| 2810 | FractionBox["mh2", "s"]}], ")"}],
|
|---|
| 2811 | RowBox[{"1", "-",
|
|---|
| 2812 | RowBox[{"2", "e"}]}]], " ",
|
|---|
| 2813 | SuperscriptBox["v",
|
|---|
| 2814 | RowBox[{"-", "e"}]], " ",
|
|---|
| 2815 | SuperscriptBox[
|
|---|
| 2816 | RowBox[{"(",
|
|---|
| 2817 | RowBox[{"1", "-", "v"}], ")"}],
|
|---|
| 2818 | RowBox[{"-", "e"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2819 | RowBox[{
|
|---|
| 2820 | RowBox[{"substu", "=",
|
|---|
| 2821 | RowBox[{"{",
|
|---|
| 2822 | RowBox[{
|
|---|
| 2823 | RowBox[{"t", "\[Rule]", " ",
|
|---|
| 2824 | RowBox[{
|
|---|
| 2825 | RowBox[{"-", "s"}], " ",
|
|---|
| 2826 | RowBox[{"(",
|
|---|
| 2827 | RowBox[{"1", "-",
|
|---|
| 2828 | FractionBox["mh2", "s"]}], ")"}],
|
|---|
| 2829 | RowBox[{"(",
|
|---|
| 2830 | RowBox[{"1", "-", "v"}], ")"}]}]}], ",", " ",
|
|---|
| 2831 | RowBox[{"u", "\[Rule]", " ",
|
|---|
| 2832 | RowBox[{
|
|---|
| 2833 | RowBox[{"-", "s"}], " ",
|
|---|
| 2834 | RowBox[{"(",
|
|---|
| 2835 | RowBox[{"1", "-",
|
|---|
| 2836 | FractionBox["mh2", "s"]}], ")"}], "v"}]}], " ", ",",
|
|---|
| 2837 | RowBox[{"s", "\[Rule]", " ",
|
|---|
| 2838 | RowBox[{"mh2", "/", "z"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 2839 | RowBox[{
|
|---|
| 2840 | RowBox[{"cGamma", "=",
|
|---|
| 2841 | RowBox[{
|
|---|
| 2842 | RowBox[{
|
|---|
| 2843 | RowBox[{"(",
|
|---|
| 2844 | RowBox[{"1", "/", "16"}], ")"}], "/",
|
|---|
| 2845 | RowBox[{"Pi", "^", "2"}]}], " ",
|
|---|
| 2846 | RowBox[{"mh2", "^",
|
|---|
| 2847 | RowBox[{"(",
|
|---|
| 2848 | RowBox[{"-", "e"}], ")"}]}],
|
|---|
| 2849 | RowBox[{
|
|---|
| 2850 | RowBox[{"(",
|
|---|
| 2851 | RowBox[{"4", " ", "Pi"}], ")"}], "^", "e"}], " ",
|
|---|
| 2852 | RowBox[{"Gamma", "[",
|
|---|
| 2853 | RowBox[{"1", "+", "e"}], "]"}], " ",
|
|---|
| 2854 | RowBox[{
|
|---|
| 2855 | RowBox[{
|
|---|
| 2856 | RowBox[{"Gamma", "[",
|
|---|
| 2857 | RowBox[{"1", "-", "e"}], "]"}], "^", "2"}], "/",
|
|---|
| 2858 | RowBox[{"Gamma", "[",
|
|---|
| 2859 | RowBox[{"1", "-",
|
|---|
| 2860 | RowBox[{"2", " ", "e"}]}], "]"}]}]}]}], ";"}], "\n",
|
|---|
| 2861 | RowBox[{
|
|---|
| 2862 | RowBox[{"pgq", "=",
|
|---|
| 2863 | RowBox[{
|
|---|
| 2864 | RowBox[{"CF",
|
|---|
| 2865 | RowBox[{
|
|---|
| 2866 | RowBox[{"(",
|
|---|
| 2867 | RowBox[{
|
|---|
| 2868 | SuperscriptBox[
|
|---|
| 2869 | RowBox[{"(",
|
|---|
| 2870 | RowBox[{"1", "-", "z"}], ")"}], "2"], "+", "1"}], ")"}], "/",
|
|---|
| 2871 | "z"}]}], " ", "//", "Factor"}]}],
|
|---|
| 2872 | ";"}], "\[IndentingNewLine]"}], "Input",
|
|---|
| 2873 | PageWidth->PaperWidth],
|
|---|
| 2874 |
|
|---|
| 2875 | Cell[CellGroupData[{
|
|---|
| 2876 |
|
|---|
| 2877 | Cell["dim-reg", "Subsubsection",
|
|---|
| 2878 | PageWidth->PaperWidth],
|
|---|
| 2879 |
|
|---|
| 2880 | Cell[CellGroupData[{
|
|---|
| 2881 |
|
|---|
| 2882 | Cell[BoxData[{
|
|---|
| 2883 | RowBox[{
|
|---|
| 2884 | RowBox[{"\[Sigma]r", "=",
|
|---|
| 2885 | RowBox[{
|
|---|
| 2886 | RowBox[{"Integrate", "[",
|
|---|
| 2887 | RowBox[{
|
|---|
| 2888 | RowBox[{
|
|---|
| 2889 | RowBox[{
|
|---|
| 2890 | RowBox[{"(",
|
|---|
| 2891 | RowBox[{
|
|---|
| 2892 | RowBox[{"RealD", " ", "PS", " ",
|
|---|
| 2893 | RowBox[{"c\[CapitalGamma]", "/", "cGamma"}]}], " ", "//",
|
|---|
| 2894 | "Simplify"}], ")"}], "//.", " ", "substu"}], "//", "Expand"}], ",",
|
|---|
| 2895 | RowBox[{"{",
|
|---|
| 2896 | RowBox[{"v", ",", "0", ",", "1"}], "}"}], ",", " ",
|
|---|
| 2897 | RowBox[{"GenerateConditions", "\[Rule]", "False"}]}], "]"}], "//",
|
|---|
| 2898 | "Simplify"}]}], ";"}], "\n",
|
|---|
| 2899 | RowBox[{
|
|---|
| 2900 | RowBox[{"\[Sigma]r", "=",
|
|---|
| 2901 | RowBox[{
|
|---|
| 2902 | RowBox[{
|
|---|
| 2903 | RowBox[{"Normal", "[",
|
|---|
| 2904 | RowBox[{"Series", "[",
|
|---|
| 2905 | RowBox[{
|
|---|
| 2906 | RowBox[{"\[Sigma]r", "/",
|
|---|
| 2907 | RowBox[{"(",
|
|---|
| 2908 | RowBox[{"1", "+", " ", "e"}], ")"}]}], ",",
|
|---|
| 2909 | RowBox[{"{",
|
|---|
| 2910 | RowBox[{"e", ",", "0", ",", "0"}], "}"}]}], "]"}], "]"}], "/.", " ",
|
|---|
| 2911 | RowBox[{
|
|---|
| 2912 | RowBox[{"gs", "^", "2"}], " ", "\[Rule]", " ",
|
|---|
| 2913 | RowBox[{"as", " ", "4", " ", "\[Pi]"}]}]}], " ", "//",
|
|---|
| 2914 | "FullSimplify"}]}], ";"}], "\n",
|
|---|
| 2915 | RowBox[{
|
|---|
| 2916 | RowBox[{"\[Sigma]r", "=",
|
|---|
| 2917 | RowBox[{
|
|---|
| 2918 | RowBox[{
|
|---|
| 2919 | RowBox[{
|
|---|
| 2920 | RowBox[{
|
|---|
| 2921 | RowBox[{"-", "\[Sigma]r"}], "/", "c\[CapitalGamma]"}], "/", "\[Pi]"}],
|
|---|
| 2922 | "/", "2"}], "-",
|
|---|
| 2923 | RowBox[{
|
|---|
| 2924 | RowBox[{"1", "/", "e"}], " ", "z", " ", "Pgq"}], " ", "+",
|
|---|
| 2925 | RowBox[{
|
|---|
| 2926 | RowBox[{"1", "/", "e"}], " ", "z", " ", "pgq"}]}]}], ";"}], "\n",
|
|---|
| 2927 | RowBox[{"\[Sigma]r", "=",
|
|---|
| 2928 | RowBox[{
|
|---|
| 2929 | RowBox[{"\[Sigma]r", "//", "PowerExpand"}], "//", "Expand"}]}]}], "Input",
|
|---|
| 2930 | PageWidth->PaperWidth],
|
|---|
| 2931 |
|
|---|
| 2932 | Cell[BoxData[
|
|---|
| 2933 | FormBox[
|
|---|
| 2934 | RowBox[{
|
|---|
| 2935 | RowBox[{"-",
|
|---|
| 2936 | RowBox[{
|
|---|
| 2937 | FractionBox["1", "2"], " ",
|
|---|
| 2938 | SuperscriptBox["z", "2"], " ",
|
|---|
| 2939 | SubscriptBox["C", "F"]}]}], "+",
|
|---|
| 2940 | RowBox[{"2", " ",
|
|---|
| 2941 | SuperscriptBox["z", "2"], " ",
|
|---|
| 2942 | SubscriptBox["C", "F"], " ",
|
|---|
| 2943 | RowBox[{"log", "(",
|
|---|
| 2944 | RowBox[{"1", "-", "z"}], ")"}]}], "-",
|
|---|
| 2945 | RowBox[{
|
|---|
| 2946 | SuperscriptBox["z", "2"], " ",
|
|---|
| 2947 | SubscriptBox["C", "F"], " ",
|
|---|
| 2948 | RowBox[{"log", "(", "z", ")"}]}], "+",
|
|---|
| 2949 | RowBox[{"3", " ", "z", " ",
|
|---|
| 2950 | SubscriptBox["C", "F"]}], "-",
|
|---|
| 2951 | RowBox[{"4", " ", "z", " ",
|
|---|
| 2952 | SubscriptBox["C", "F"], " ",
|
|---|
| 2953 | RowBox[{"log", "(",
|
|---|
| 2954 | RowBox[{"1", "-", "z"}], ")"}]}], "+",
|
|---|
| 2955 | RowBox[{"2", " ", "z", " ",
|
|---|
| 2956 | SubscriptBox["C", "F"], " ",
|
|---|
| 2957 | RowBox[{"log", "(", "z", ")"}]}], "+",
|
|---|
| 2958 | RowBox[{"4", " ",
|
|---|
| 2959 | SubscriptBox["C", "F"], " ",
|
|---|
| 2960 | RowBox[{"log", "(",
|
|---|
| 2961 | RowBox[{"1", "-", "z"}], ")"}]}], "-",
|
|---|
| 2962 | RowBox[{"2", " ",
|
|---|
| 2963 | SubscriptBox["C", "F"], " ",
|
|---|
| 2964 | RowBox[{"log", "(", "z", ")"}]}], "-",
|
|---|
| 2965 | FractionBox[
|
|---|
| 2966 | RowBox[{"3", " ",
|
|---|
| 2967 | SubscriptBox["C", "F"]}], "2"], "-",
|
|---|
| 2968 | FractionBox[
|
|---|
| 2969 | RowBox[{"Pgq", " ", "z"}], "e"]}], TraditionalForm]], "Output",
|
|---|
| 2970 | CellChangeTimes->{3.6925287222347727`*^9}]
|
|---|
| 2971 | }, Open ]],
|
|---|
| 2972 |
|
|---|
| 2973 | Cell[CellGroupData[{
|
|---|
| 2974 |
|
|---|
| 2975 | Cell[BoxData[{
|
|---|
| 2976 | RowBox[{"sally", "=",
|
|---|
| 2977 | RowBox[{"2", "*",
|
|---|
| 2978 | RowBox[{"(",
|
|---|
| 2979 | RowBox[{
|
|---|
| 2980 | RowBox[{
|
|---|
| 2981 | RowBox[{"-", " ",
|
|---|
| 2982 | RowBox[{"(",
|
|---|
| 2983 | RowBox[{"1", "-", "z"}], ")"}]}], " ",
|
|---|
| 2984 | RowBox[{
|
|---|
| 2985 | RowBox[{"(",
|
|---|
| 2986 | RowBox[{"7", "-",
|
|---|
| 2987 | RowBox[{"3", "z"}]}], ")"}], "/", "3"}]}], " ", "+",
|
|---|
| 2988 | RowBox[{
|
|---|
| 2989 | RowBox[{"1", "/", "2"}], " ", "z", " ", "pgq", " ",
|
|---|
| 2990 | RowBox[{"(",
|
|---|
| 2991 | RowBox[{"1", "+",
|
|---|
| 2992 | RowBox[{"2",
|
|---|
| 2993 | RowBox[{"Log", "[",
|
|---|
| 2994 | RowBox[{"1", "-", "z"}], "]"}]}], "-",
|
|---|
| 2995 | RowBox[{"Log", "[", "z", "]"}]}], ")"}]}]}],
|
|---|
| 2996 | ")"}]}]}], "\[IndentingNewLine]",
|
|---|
| 2997 | RowBox[{
|
|---|
| 2998 | RowBox[{"(",
|
|---|
| 2999 | RowBox[{
|
|---|
| 3000 | RowBox[{
|
|---|
| 3001 | RowBox[{"(",
|
|---|
| 3002 | RowBox[{"\[Sigma]r", "-", " ", "sally"}], ")"}], "/.", " ",
|
|---|
| 3003 | RowBox[{"CF", "->",
|
|---|
| 3004 | RowBox[{"4", "/", "3"}]}]}], "/.", " ",
|
|---|
| 3005 | RowBox[{"Pgq", "\[Rule]", "0"}]}], ")"}], "//", "Simplify"}]}], "Input"],
|
|---|
| 3006 |
|
|---|
| 3007 | Cell[BoxData[
|
|---|
| 3008 | FormBox[
|
|---|
| 3009 | RowBox[{"2", " ",
|
|---|
| 3010 | RowBox[{"(",
|
|---|
| 3011 | RowBox[{
|
|---|
| 3012 | RowBox[{
|
|---|
| 3013 | FractionBox["1", "2"], " ",
|
|---|
| 3014 | RowBox[{"(",
|
|---|
| 3015 | RowBox[{
|
|---|
| 3016 | SuperscriptBox["z", "2"], "-",
|
|---|
| 3017 | RowBox[{"2", " ", "z"}], "+", "2"}], ")"}], " ",
|
|---|
| 3018 | SubscriptBox["C", "F"], " ",
|
|---|
| 3019 | RowBox[{"(",
|
|---|
| 3020 | RowBox[{
|
|---|
| 3021 | RowBox[{"2", " ",
|
|---|
| 3022 | RowBox[{"log", "(",
|
|---|
| 3023 | RowBox[{"1", "-", "z"}], ")"}]}], "-",
|
|---|
| 3024 | RowBox[{"log", "(", "z", ")"}], "+", "1"}], ")"}]}], "+",
|
|---|
| 3025 | RowBox[{
|
|---|
| 3026 | FractionBox["1", "3"], " ",
|
|---|
| 3027 | RowBox[{"(",
|
|---|
| 3028 | RowBox[{"7", "-",
|
|---|
| 3029 | RowBox[{"3", " ", "z"}]}], ")"}], " ",
|
|---|
| 3030 | RowBox[{"(",
|
|---|
| 3031 | RowBox[{"z", "-", "1"}], ")"}]}]}], ")"}]}],
|
|---|
| 3032 | TraditionalForm]], "Output",
|
|---|
| 3033 | CellChangeTimes->{3.692528722627721*^9}],
|
|---|
| 3034 |
|
|---|
| 3035 | Cell[BoxData[
|
|---|
| 3036 | FormBox["0", TraditionalForm]], "Output",
|
|---|
| 3037 | CellChangeTimes->{3.6925287226323357`*^9}]
|
|---|
| 3038 | }, Open ]],
|
|---|
| 3039 |
|
|---|
| 3040 | Cell[BoxData[""], "Input"]
|
|---|
| 3041 | }, Open ]]
|
|---|
| 3042 | }, Open ]]
|
|---|
| 3043 | }, Open ]]
|
|---|
| 3044 | }, Open ]]
|
|---|
| 3045 | },
|
|---|
| 3046 | WindowSize->{1049, 665},
|
|---|
| 3047 | WindowMargins->{{98, Automatic}, {Automatic, 0}},
|
|---|
| 3048 | PrintingCopies->1,
|
|---|
| 3049 | PrintingPageRange->{Automatic, Automatic},
|
|---|
| 3050 | PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
|
|---|
| 3051 | FrontEndVersion->"10.4 for Mac OS X x86 (32-bit, 64-bit Kernel) (February 25, \
|
|---|
| 3052 | 2016)",
|
|---|
| 3053 | StyleDefinitions->"Default.nb"
|
|---|
| 3054 | ]
|
|---|
| 3055 | (* End of Notebook Content *)
|
|---|
| 3056 |
|
|---|
| 3057 | (* Internal cache information *)
|
|---|
| 3058 | (*CellTagsOutline
|
|---|
| 3059 | CellTagsIndex->{}
|
|---|
| 3060 | *)
|
|---|
| 3061 | (*CellTagsIndex
|
|---|
| 3062 | CellTagsIndex->{}
|
|---|
| 3063 | *)
|
|---|
| 3064 | (*NotebookFileOutline
|
|---|
| 3065 | Notebook[{
|
|---|
| 3066 | Cell[CellGroupData[{
|
|---|
| 3067 | Cell[579, 22, 142, 2, 148, "Title"],
|
|---|
| 3068 | Cell[CellGroupData[{
|
|---|
| 3069 | Cell[746, 28, 60, 1, 44, "Subsection"],
|
|---|
| 3070 | Cell[CellGroupData[{
|
|---|
| 3071 | Cell[831, 33, 89, 2, 28, "Input"],
|
|---|
| 3072 | Cell[923, 37, 603, 13, 24, "Message"],
|
|---|
| 3073 | Cell[1529, 52, 151, 3, 30, "Output"]
|
|---|
| 3074 | }, Open ]],
|
|---|
| 3075 | Cell[CellGroupData[{
|
|---|
| 3076 | Cell[1717, 60, 109, 2, 28, "Input"],
|
|---|
| 3077 | Cell[CellGroupData[{
|
|---|
| 3078 | Cell[1851, 66, 2390, 64, 25, "Print"],
|
|---|
| 3079 | Cell[4244, 132, 1130, 30, 25, "Print"],
|
|---|
| 3080 | Cell[5377, 164, 258, 5, 26, "Print"],
|
|---|
| 3081 | Cell[5638, 171, 272, 5, 26, "Print"]
|
|---|
| 3082 | }, Open ]]
|
|---|
| 3083 | }, Open ]],
|
|---|
| 3084 | Cell[5937, 180, 103, 3, 28, "Input"]
|
|---|
| 3085 | }, Open ]],
|
|---|
| 3086 | Cell[CellGroupData[{
|
|---|
| 3087 | Cell[6077, 188, 74, 1, 64, "Section"],
|
|---|
| 3088 | Cell[CellGroupData[{
|
|---|
| 3089 | Cell[6176, 193, 56, 1, 44, "Subsection"],
|
|---|
| 3090 | Cell[6235, 196, 171, 12, 201, "Text"],
|
|---|
| 3091 | Cell[6409, 210, 3591, 116, 386, "Input"]
|
|---|
| 3092 | }, Open ]],
|
|---|
| 3093 | Cell[CellGroupData[{
|
|---|
| 3094 | Cell[10037, 331, 70, 1, 44, "Subsection"],
|
|---|
| 3095 | Cell[10110, 334, 1432, 59, 170, "Text"],
|
|---|
| 3096 | Cell[11545, 395, 3106, 100, 301, "Input"]
|
|---|
| 3097 | }, Open ]],
|
|---|
| 3098 | Cell[CellGroupData[{
|
|---|
| 3099 | Cell[14688, 500, 66, 1, 44, "Subsection"],
|
|---|
| 3100 | Cell[CellGroupData[{
|
|---|
| 3101 | Cell[14779, 505, 939, 28, 148, "Input"],
|
|---|
| 3102 | Cell[15721, 535, 195, 3, 28, "Output"],
|
|---|
| 3103 | Cell[15919, 540, 525, 17, 47, "Output"]
|
|---|
| 3104 | }, Open ]],
|
|---|
| 3105 | Cell[CellGroupData[{
|
|---|
| 3106 | Cell[16481, 562, 1716, 49, 80, "Input"],
|
|---|
| 3107 | Cell[18200, 613, 397, 10, 47, "Output"]
|
|---|
| 3108 | }, Open ]]
|
|---|
| 3109 | }, Open ]],
|
|---|
| 3110 | Cell[CellGroupData[{
|
|---|
| 3111 | Cell[18646, 629, 206, 5, 94, "Subsection"],
|
|---|
| 3112 | Cell[18855, 636, 4351, 120, 352, "Input"],
|
|---|
| 3113 | Cell[23209, 758, 26, 0, 28, "Input"],
|
|---|
| 3114 | Cell[23238, 760, 26, 0, 28, "Input"]
|
|---|
| 3115 | }, Open ]]
|
|---|
| 3116 | }, Open ]],
|
|---|
| 3117 | Cell[CellGroupData[{
|
|---|
| 3118 | Cell[23313, 766, 22, 0, 64, "Section"],
|
|---|
| 3119 | Cell[CellGroupData[{
|
|---|
| 3120 | Cell[23360, 770, 61, 1, 44, "Subsection"],
|
|---|
| 3121 | Cell[CellGroupData[{
|
|---|
| 3122 | Cell[23446, 775, 2964, 92, 267, "Input"],
|
|---|
| 3123 | Cell[26413, 869, 398, 15, 33, "Output"],
|
|---|
| 3124 | Cell[26814, 886, 1373, 42, 56, "Output"]
|
|---|
| 3125 | }, Open ]],
|
|---|
| 3126 | Cell[28202, 931, 26, 0, 28, "Input"]
|
|---|
| 3127 | }, Open ]],
|
|---|
| 3128 | Cell[CellGroupData[{
|
|---|
| 3129 | Cell[28265, 936, 62, 1, 44, "Subsection"],
|
|---|
| 3130 | Cell[CellGroupData[{
|
|---|
| 3131 | Cell[28352, 941, 2218, 71, 233, "Input"],
|
|---|
| 3132 | Cell[30573, 1014, 984, 30, 56, "Output"]
|
|---|
| 3133 | }, Open ]]
|
|---|
| 3134 | }, Open ]],
|
|---|
| 3135 | Cell[CellGroupData[{
|
|---|
| 3136 | Cell[31606, 1050, 38, 0, 44, "Subsection"],
|
|---|
| 3137 | Cell[CellGroupData[{
|
|---|
| 3138 | Cell[31669, 1054, 2077, 58, 233, "Input"],
|
|---|
| 3139 | Cell[33749, 1114, 872, 22, 50, "Output"],
|
|---|
| 3140 | Cell[34624, 1138, 579, 14, 48, "Output"]
|
|---|
| 3141 | }, Open ]],
|
|---|
| 3142 | Cell[CellGroupData[{
|
|---|
| 3143 | Cell[35240, 1157, 1039, 30, 131, "Input"],
|
|---|
| 3144 | Cell[36282, 1189, 441, 12, 50, "Output"]
|
|---|
| 3145 | }, Open ]]
|
|---|
| 3146 | }, Open ]],
|
|---|
| 3147 | Cell[CellGroupData[{
|
|---|
| 3148 | Cell[36772, 1207, 129, 1, 44, "Subsection"],
|
|---|
| 3149 | Cell[CellGroupData[{
|
|---|
| 3150 | Cell[36926, 1212, 1506, 44, 199, "Input"],
|
|---|
| 3151 | Cell[38435, 1258, 299, 6, 47, "Output"]
|
|---|
| 3152 | }, Open ]],
|
|---|
| 3153 | Cell[CellGroupData[{
|
|---|
| 3154 | Cell[38771, 1269, 1345, 41, 118, "Input"],
|
|---|
| 3155 | Cell[40119, 1312, 730, 20, 59, "Output"],
|
|---|
| 3156 | Cell[40852, 1334, 851, 24, 59, "Output"],
|
|---|
| 3157 | Cell[41706, 1360, 635, 17, 59, "Output"]
|
|---|
| 3158 | }, Open ]],
|
|---|
| 3159 | Cell[42356, 1380, 45, 0, 46, "Input"],
|
|---|
| 3160 | Cell[CellGroupData[{
|
|---|
| 3161 | Cell[42426, 1384, 171, 6, 28, "Input"],
|
|---|
| 3162 | Cell[42600, 1392, 181, 6, 52, "Output"]
|
|---|
| 3163 | }, Open ]]
|
|---|
| 3164 | }, Open ]]
|
|---|
| 3165 | }, Open ]],
|
|---|
| 3166 | Cell[CellGroupData[{
|
|---|
| 3167 | Cell[42842, 1405, 65, 1, 64, "Section"],
|
|---|
| 3168 | Cell[CellGroupData[{
|
|---|
| 3169 | Cell[42932, 1410, 56, 1, 44, "Subsection"],
|
|---|
| 3170 | Cell[42991, 1413, 701, 37, 676, "Text"],
|
|---|
| 3171 | Cell[43695, 1452, 3054, 105, 318, "Input"]
|
|---|
| 3172 | }, Open ]],
|
|---|
| 3173 | Cell[CellGroupData[{
|
|---|
| 3174 | Cell[46786, 1562, 70, 1, 44, "Subsection"],
|
|---|
| 3175 | Cell[46859, 1565, 1432, 59, 170, "Text"],
|
|---|
| 3176 | Cell[48294, 1626, 1942, 57, 233, "Input"]
|
|---|
| 3177 | }, Open ]],
|
|---|
| 3178 | Cell[CellGroupData[{
|
|---|
| 3179 | Cell[50273, 1688, 57, 0, 44, "Subsection"],
|
|---|
| 3180 | Cell[50333, 1690, 419, 10, 104, "Input"]
|
|---|
| 3181 | }, Open ]],
|
|---|
| 3182 | Cell[CellGroupData[{
|
|---|
| 3183 | Cell[50789, 1705, 137, 3, 44, "Subsection"],
|
|---|
| 3184 | Cell[50929, 1710, 396, 10, 104, "Input"],
|
|---|
| 3185 | Cell[CellGroupData[{
|
|---|
| 3186 | Cell[51350, 1724, 124, 3, 29, "Input"],
|
|---|
| 3187 | Cell[51477, 1729, 2906, 76, 98, "Output"]
|
|---|
| 3188 | }, Open ]],
|
|---|
| 3189 | Cell[54398, 1808, 57, 3, 44, "Input"],
|
|---|
| 3190 | Cell[CellGroupData[{
|
|---|
| 3191 | Cell[54480, 1815, 98, 1, 28, "Input"],
|
|---|
| 3192 | Cell[54581, 1818, 2131, 64, 56, "Output"]
|
|---|
| 3193 | }, Open ]]
|
|---|
| 3194 | }, Open ]],
|
|---|
| 3195 | Cell[CellGroupData[{
|
|---|
| 3196 | Cell[56761, 1888, 84, 1, 44, "Subsection"],
|
|---|
| 3197 | Cell[56848, 1891, 1388, 43, 131, "Input"],
|
|---|
| 3198 | Cell[CellGroupData[{
|
|---|
| 3199 | Cell[58261, 1938, 652, 17, 28, "Input"],
|
|---|
| 3200 | Cell[58916, 1957, 2228, 66, 56, "Output"]
|
|---|
| 3201 | }, Open ]]
|
|---|
| 3202 | }, Open ]],
|
|---|
| 3203 | Cell[CellGroupData[{
|
|---|
| 3204 | Cell[61193, 2029, 73, 1, 44, "Subsection"],
|
|---|
| 3205 | Cell[61269, 2032, 2906, 93, 260, "Input"]
|
|---|
| 3206 | }, Open ]],
|
|---|
| 3207 | Cell[CellGroupData[{
|
|---|
| 3208 | Cell[64212, 2130, 49, 1, 44, "Subsection"],
|
|---|
| 3209 | Cell[CellGroupData[{
|
|---|
| 3210 | Cell[64286, 2135, 636, 20, 92, "Input"],
|
|---|
| 3211 | Cell[64925, 2157, 3179, 92, 109, "Output"]
|
|---|
| 3212 | }, Open ]],
|
|---|
| 3213 | Cell[68119, 2252, 1760, 55, 240, "Input"]
|
|---|
| 3214 | }, Open ]]
|
|---|
| 3215 | }, Open ]],
|
|---|
| 3216 | Cell[CellGroupData[{
|
|---|
| 3217 | Cell[69928, 2313, 26, 0, 64, "Section"],
|
|---|
| 3218 | Cell[CellGroupData[{
|
|---|
| 3219 | Cell[69979, 2317, 55, 0, 44, "Subsection"],
|
|---|
| 3220 | Cell[70037, 2319, 4178, 125, 369, "Input"],
|
|---|
| 3221 | Cell[CellGroupData[{
|
|---|
| 3222 | Cell[74240, 2448, 301, 9, 28, "Input"],
|
|---|
| 3223 | Cell[74544, 2459, 551, 18, 64, "Output"]
|
|---|
| 3224 | }, Open ]],
|
|---|
| 3225 | Cell[CellGroupData[{
|
|---|
| 3226 | Cell[75132, 2482, 244, 7, 49, "Input"],
|
|---|
| 3227 | Cell[75379, 2491, 222, 6, 48, "Output"]
|
|---|
| 3228 | }, Open ]],
|
|---|
| 3229 | Cell[CellGroupData[{
|
|---|
| 3230 | Cell[75638, 2502, 359, 12, 28, "Input"],
|
|---|
| 3231 | Cell[76000, 2516, 493, 16, 64, "Output"]
|
|---|
| 3232 | }, Open ]],
|
|---|
| 3233 | Cell[76508, 2535, 1311, 41, 63, "Input"],
|
|---|
| 3234 | Cell[77822, 2578, 845, 27, 46, "Input"]
|
|---|
| 3235 | }, Open ]]
|
|---|
| 3236 | }, Open ]],
|
|---|
| 3237 | Cell[CellGroupData[{
|
|---|
| 3238 | Cell[78716, 2611, 66, 1, 64, "Section"],
|
|---|
| 3239 | Cell[CellGroupData[{
|
|---|
| 3240 | Cell[78807, 2616, 69, 1, 44, "Subsection"],
|
|---|
| 3241 | Cell[78879, 2619, 171, 12, 201, "Text"],
|
|---|
| 3242 | Cell[79053, 2633, 3591, 116, 386, "Input"]
|
|---|
| 3243 | }, Open ]],
|
|---|
| 3244 | Cell[CellGroupData[{
|
|---|
| 3245 | Cell[82681, 2754, 60, 1, 44, "Subsection"],
|
|---|
| 3246 | Cell[82744, 2757, 738, 25, 63, "Input"]
|
|---|
| 3247 | }, Open ]],
|
|---|
| 3248 | Cell[CellGroupData[{
|
|---|
| 3249 | Cell[83519, 2787, 94, 1, 44, "Subsection"],
|
|---|
| 3250 | Cell[83616, 2790, 2373, 82, 212, "Input"],
|
|---|
| 3251 | Cell[CellGroupData[{
|
|---|
| 3252 | Cell[86014, 2876, 56, 1, 35, "Subsubsection"],
|
|---|
| 3253 | Cell[CellGroupData[{
|
|---|
| 3254 | Cell[86095, 2881, 1586, 48, 165, "Input"],
|
|---|
| 3255 | Cell[87684, 2931, 1212, 38, 48, "Output"]
|
|---|
| 3256 | }, Open ]],
|
|---|
| 3257 | Cell[CellGroupData[{
|
|---|
| 3258 | Cell[88933, 2974, 925, 30, 46, "Input"],
|
|---|
| 3259 | Cell[89861, 3006, 792, 26, 48, "Output"],
|
|---|
| 3260 | Cell[90656, 3034, 100, 2, 28, "Output"]
|
|---|
| 3261 | }, Open ]],
|
|---|
| 3262 | Cell[90771, 3039, 26, 0, 28, "Input"]
|
|---|
| 3263 | }, Open ]]
|
|---|
| 3264 | }, Open ]]
|
|---|
| 3265 | }, Open ]]
|
|---|
| 3266 | }, Open ]]
|
|---|
| 3267 | }
|
|---|
| 3268 | ]
|
|---|
| 3269 | *)
|
|---|
| 3270 |
|
|---|