(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 14675, 479] NotebookOptionsPosition[ 13517, 433] NotebookOutlinePosition[ 13857, 448] CellTagsIndexPosition[ 13814, 445] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{"Quit", "[", "]"}]], "Input", CellChangeTimes->{{3.640805909205505*^9, 3.640805934217572*^9}, 3.6408084111310053`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"<<", "FeynCalc`"}]], "Input"], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{ StyleBox["\<\"FeynCalc \"\>", "Text", StripOnInput->False, FontWeight->Bold], "\[InvisibleSpace]", StyleBox["\<\"9.0.0. For help, type ?FeynCalc, use the \"\>", "Text", StripOnInput->False], "\[InvisibleSpace]", StyleBox[ TagBox[ ButtonBox[ RowBox[{"help", " ", "browser"}], BaseStyle->"AddOnsLink", ButtonData:>{"Short Overview", "intro"}, ButtonNote->"FeynCalc"], DisplayForm], "Text", StripOnInput->False], "\[InvisibleSpace]", StyleBox["\<\" or visit \"\>", "Text", StripOnInput->False], "\[InvisibleSpace]", StyleBox[ TagBox[ ButtonBox[ RowBox[{"www", ".", "feyncalc", ".", "org", "."}], BaseStyle->"Hyperlink", ButtonData:>{ URL["http://www.feyncalc.org/"], None}, ButtonNote->"http://www.feyncalc.org/"], DisplayForm], "Text", StripOnInput->False]}], SequenceForm[ Style["FeynCalc ", "Text", Bold], Style["9.0.0. For help, type ?FeynCalc, use the ", "Text"], Style[ DisplayForm[ ButtonBox[ "help browser", ButtonData :> {"Short Overview", "intro"}, BaseStyle -> "AddOnsLink", ButtonNote -> "FeynCalc"]], "Text"], Style[" or visit ", "Text"], Style[ DisplayForm[ ButtonBox["www.feyncalc.org.", ButtonData :> { URL["http://www.feyncalc.org/"], None}, BaseStyle -> "Hyperlink", ButtonNote -> "http://www.feyncalc.org/"]], "Text"]], Editable->False], TraditionalForm]], "Print", CellChangeTimes->{3.640808414611144*^9, 3.64080847632892*^9, 3.640808793709319*^9, 3.640808878425593*^9}] }, Open ]], Cell[BoxData[{ RowBox[{"ClearScalarProducts", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"bb", "=", "xx"}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"bb", ",", "p1"}], "]"}], "=", "0"}], ";", RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"bb", ",", "bb"}], "]"}], "=", "0"}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"p1", ",", "p1"}], "]"}], "=", RowBox[{"m", "^", "2"}]}], ";", RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"p2", ",", "p2"}], "]"}], "=", RowBox[{"m", "^", "2"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"p1", ",", "r"}], "]"}], "=", "0"}], ";", RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"bb", ",", "r"}], "]"}], "=", "0"}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"bb", ",", "p2"}], "]"}], "=", "0"}], ";", RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"r", ",", "p2"}], "]"}], "=", "1"}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"ScalarProduct", "[", RowBox[{"p1", ",", "p2"}], "]"}], "=", "0"}], ";"}], "\n", RowBox[{ RowBox[{"amp", "=", RowBox[{ RowBox[{"SPD", "[", RowBox[{"r", ",", "z"}], "]"}], " ", RowBox[{"SPD", "[", RowBox[{"bb", ",", "z"}], "]"}], " ", RowBox[{"SPD", "[", RowBox[{"p2", ",", "z"}], "]"}], " ", RowBox[{"SPD", "[", RowBox[{"p1", ",", "z"}], "]"}], " ", RowBox[{"FAD", "[", RowBox[{ RowBox[{"{", RowBox[{"z", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"p1", "+", "bb", "-", "z"}], ",", "m"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"p2", "-", "z"}], ",", "m"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"p1", "-", "z"}], ",", "m"}], "}"}]}], "]"}]}]}], ";"}]}], "Input", CellChangeTimes->{{3.640805912326272*^9, 3.640805998603587*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"OneLoop", "[", RowBox[{"z", ",", "amp"}], "]"}], "//", "PaVeReduce"}]], "Input"], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellChangeTimes->{3.640805966625101*^9, 3.6408060004728117`*^9, 3.640806098234682*^9, 3.6408078327337627`*^9, 3.640808093174629*^9, 3.640808479309299*^9, 3.640808796420051*^9, 3.6408088808518*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"OneLoop", "[", RowBox[{"z", ",", "amp", ",", RowBox[{"OneLoopSimplify", "\[Rule]", "True"}]}], "]"}]], "Input"], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellChangeTimes->{{3.6408059791239367`*^9, 3.6408060020685053`*^9}, 3.640806099615653*^9, 3.640807834988646*^9, 3.64080809564542*^9, 3.6408084818071003`*^9, 3.640808798987629*^9, 3.6408088834577637`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"TID", "[", RowBox[{"amp", ",", "z", ",", RowBox[{"UsePaVeBasis", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.64080602178262*^9, 3.640806052808414*^9}, { 3.64080813797127*^9, 3.640808219729398*^9}, {3.640808483066854*^9, 3.64080849796159*^9}, 3.640808787311816*^9}], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ FractionBox["1", "16"], " ", "\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["m", "2"], " ", FormBox[ TagBox[ FormBox[ RowBox[{ SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], ",", SuperscriptBox["m", "2"], ",", SuperscriptBox["m", "2"]}], ")"}], TraditionalForm], HoldForm], TraditionalForm]}], "+", RowBox[{ FractionBox["1", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", "2"], " ", "D", " ", FormBox[ RowBox[{ SubscriptBox["\<\"B\"\>", "\<\"001\"\>"], "(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], ",", SuperscriptBox["m", "2"], ",", SuperscriptBox["m", "2"]}], ")"}], TraditionalForm]}], "+", RowBox[{"2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", "2"], " ", FormBox[ RowBox[{ SubscriptBox["\<\"B\"\>", "\<\"001\"\>"], "(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], ",", SuperscriptBox["m", "2"], ",", SuperscriptBox["m", "2"]}], ")"}], TraditionalForm]}], "+", RowBox[{"2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["m", "2"], " ", FormBox[ RowBox[{ SubscriptBox["\<\"B\"\>", "\<\"111\"\>"], "(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], ",", SuperscriptBox["m", "2"], ",", SuperscriptBox["m", "2"]}], ")"}], TraditionalForm]}]}], ")"}]}], "+", FractionBox["1", RowBox[{"8", " ", RowBox[{"(", RowBox[{ SuperscriptBox[ FormBox["z", TraditionalForm], "2"], "-", SuperscriptBox["m", "2"]}], ")"}]}]]}], TraditionalForm]], "Output", CellChangeTimes->{{3.6408060351824083`*^9, 3.640806053614398*^9}, 3.640806101086027*^9, 3.640807837002489*^9, {3.640807892064226*^9, 3.64080791857451*^9}, 3.640808097741976*^9, 3.640808139578764*^9, { 3.640808170021019*^9, 3.640808220817603*^9}, {3.640808485216194*^9, 3.640808499292199*^9}, 3.640808801140398*^9, 3.640808885203537*^9}] }, Open ]], Cell[BoxData[ RowBox[{"Quit", "[", "]"}]], "Input", CellChangeTimes->{{3.640807976242114*^9, 3.6408079772651243`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"<<", "X`"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ FormBox["\<\"Package-X v1.0.1, by Hiren H. Patel\"\>", TraditionalForm]], "Print", CellChangeTimes->{3.6408079863162193`*^9, 3.640808282409474*^9, 3.64080874814913*^9, 3.640808805071157*^9, 3.640808887826305*^9}], Cell[BoxData[ FormBox["\<\"\\!\\(\\*TemplateBox[List[\\\"\\\\\\\"For more information, see \ the \\\\\\\"\\\", TagBox[ButtonBox[PaneSelectorBox[List[Rule[False, \ \\\"\\\\\\\"guide\\\\\\\"\\\"], Rule[True, StyleBox[\\\"\\\\\\\"guide\\\\\\\"\ \\\", List[\\\"HyperlinkActive\\\"]]]], \ Dynamic[CurrentValue[\\\"MouseOver\\\"]], Rule[BaseStyle, \ List[\\\"Hyperlink\\\"]], Rule[FrameMargins, 0], Rule[ImageSize, Automatic]], \ Rule[BaseStyle, \\\"Link\\\"], Rule[ButtonData, \\\"paclet:X/guide/PackageX\\\ \"], Rule[ButtonNote, \\\"paclet:X/guide/PackageX\\\"]], \ Function[Annotation[Slot[1], \\\"paclet:X/guide/PackageX\\\", \\\"Hyperlink\\\ \"]]]], \\\"RowDefault\\\"]\\)\"\>", TraditionalForm]], "Print", CellChangeTimes->{3.6408079863162193`*^9, 3.640808282409474*^9, 3.64080874814913*^9, 3.640808805071157*^9, 3.640808888715104*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ FractionBox["1", "8"], RowBox[{"(", RowBox[{ RowBox[{"D", " ", RowBox[{"pvB", "[", RowBox[{"1", ",", "1", ",", RowBox[{"2", RowBox[{"m", "^", "2"}]}], ",", "m", ",", "m"}], "]"}]}], "+", RowBox[{"2", RowBox[{"pvB", "[", RowBox[{"1", ",", "1", ",", RowBox[{"2", RowBox[{"m", "^", "2"}]}], ",", "m", ",", "m"}], "]"}]}], "+", RowBox[{"2", RowBox[{"m", "^", "2"}], " ", RowBox[{"pvB", "[", RowBox[{"0", ",", "3", ",", RowBox[{"2", RowBox[{"m", "^", "2"}]}], ",", "m", ",", "m"}], "]"}]}]}], ")"}]}], "+", RowBox[{ FractionBox["1", "16"], RowBox[{"m", "^", "2"}], RowBox[{"pvB", "[", RowBox[{"0", ",", "0", ",", RowBox[{"2", RowBox[{"m", "^", "2"}]}], ",", "m", ",", "m"}], "]"}]}], "+", RowBox[{ FractionBox["1", "8"], RowBox[{"pvA", "[", RowBox[{"0", ",", "m"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.640808045678872*^9, 3.640808046400549*^9}, { 3.640808291666419*^9, 3.640808291926302*^9}, {3.640808755988611*^9, 3.640808766909927*^9}}], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ FractionBox["1", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"D", " ", RowBox[{ SubscriptBox["B", RowBox[{ FormBox["\<\"0\"\>", TraditionalForm], FormBox["\<\"0\"\>", TraditionalForm], FormBox["\<\"1\"\>", TraditionalForm]}]], "(", FormBox[ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], TraditionalForm], ";", FormBox["m", TraditionalForm], ",", FormBox["m", TraditionalForm], ")"}]}], "+", RowBox[{"2", " ", RowBox[{ SubscriptBox["B", RowBox[{ FormBox["\<\"0\"\>", TraditionalForm], FormBox["\<\"0\"\>", TraditionalForm], FormBox["\<\"1\"\>", TraditionalForm]}]], "(", FormBox[ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], TraditionalForm], ";", FormBox["m", TraditionalForm], ",", FormBox["m", TraditionalForm], ")"}]}], "+", RowBox[{"2", " ", SuperscriptBox["m", "2"], " ", RowBox[{ SubscriptBox["B", RowBox[{ FormBox["\<\"1\"\>", TraditionalForm], FormBox["\<\"1\"\>", TraditionalForm], FormBox["\<\"1\"\>", TraditionalForm]}]], "(", FormBox[ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], TraditionalForm], ";", FormBox["m", TraditionalForm], ",", FormBox["m", TraditionalForm], ")"}]}]}], ")"}]}], "+", RowBox[{ FractionBox["1", "16"], " ", SuperscriptBox["m", "2"], " ", RowBox[{ SubscriptBox["B", "0"], "(", FormBox[ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], TraditionalForm], ";", FormBox["m", TraditionalForm], ",", FormBox["m", TraditionalForm], ")"}]}], "+", FractionBox[ RowBox[{ SubscriptBox["A", FormBox["\<\"0\"\>", TraditionalForm]], "(", FormBox["m", TraditionalForm], ")"}], "8"]}], TraditionalForm]], "Output", CellChangeTimes->{ 3.6408079938279943`*^9, 3.640808046788835*^9, 3.640808292754936*^9, { 3.640808749716763*^9, 3.640808767732814*^9}, 3.640808806222131*^9, 3.640808889434125*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"%", "/.", RowBox[{"D", "\[Rule]", RowBox[{"4", "-", RowBox[{"2", "\[Epsilon]"}]}]}]}], ")"}], "//", "LoopRefine"}]], "Input"], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellChangeTimes->{ 3.640808047316596*^9, 3.640808293400682*^9, {3.640808751821911*^9, 3.6408087686460447`*^9}, 3.6408088072569513`*^9}] }, Open ]] }, WindowSize->{1379, 957}, WindowMargins->{{Automatic, 500}, {-1, Automatic}}, FrontEndVersion->"10.0 for Linux x86 (64-bit) (September 9, 2014)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 146, 3, 32, "Input"], Cell[CellGroupData[{ Cell[729, 27, 53, 1, 32, "Input"], Cell[785, 30, 1684, 46, 28, "Print"] }, Open ]], Cell[2484, 79, 1988, 63, 187, "Input"], Cell[CellGroupData[{ Cell[4497, 146, 119, 3, 32, "Input"], Cell[4619, 151, 260, 4, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4916, 160, 142, 3, 32, "Input"], Cell[5061, 165, 269, 4, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5367, 174, 320, 6, 32, "Input"], Cell[5690, 182, 2432, 70, 63, "Output"] }, Open ]], Cell[8137, 255, 120, 2, 32, "Input"], Cell[CellGroupData[{ Cell[8282, 261, 46, 1, 32, "Input"], Cell[CellGroupData[{ Cell[8353, 266, 234, 4, 23, "Print"], Cell[8590, 272, 840, 12, 23, "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[9479, 290, 1168, 36, 62, "Input"], Cell[10650, 328, 2417, 85, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13104, 418, 195, 6, 32, "Input"], Cell[13302, 426, 199, 4, 31, "Output"] }, Open ]] } ] *) (* End of internal cache information *)