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Cell[CellGroupData[{ Cell["Introduction", "Section", PageBreakAbove->True, CellTags->"Short Overview"], Cell[TextData[{ "FeynCalc 3.1 is a ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0 package for algebraic calculations in high energy physics. Tools are \ provided for Lorentz index contraction, Dirac algebra manipulation, color \ factor calculation, automatic Feynman rule derivation, general noncommutative \ algebra as well as various look-up tables for Feynman parameter integrals, \ Mellin transforms (e.g. all integrals - except 57,58 and 59, and correcting a \ minor misprint in 14) of Appendix 7 from ", ButtonBox["hep-ph/9810241", ButtonData:>{ URL[ "http://xxx.lanl.gov/abs/hep-ph/9810241"], None}, ButtonStyle->"Hyperlink"], " are tabulated in ", ButtonBox["Integrate2", ButtonData:>"Integrate2", ButtonStyle->"Hyperlink"], " , convolutions and Feynman rules. Furthermore special translation \ facilities are provided to change the FeynCalc syntax to and from FORM \ syntax. Optimized FORTRAN generation can be done with ", ButtonBox["Isolate", ButtonData:>"Isolate", ButtonStyle->"Hyperlink"], " and ", ButtonBox["Write2", ButtonData:>"Write2", ButtonStyle->"Hyperlink"], "." }], "Text"], Cell[TextData[{ "The more important functions for input of objects like ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["p", "\[Mu]"], ",", SuperscriptBox["\[Gamma]", "\[Nu]"], ",", SuperscriptBox["g", RowBox[{"\[Mu]", " ", "\[Nu]"}]], ",", " ", SuperscriptBox["\[CurlyEpsilon]", RowBox[{"\[Mu]", " ", "\[Nu]", " ", "\[Rho]", " ", "\[Sigma]"}]], ",", " ", RowBox[{"etc", "."}]}], TraditionalForm]]], " (abbreviations in parentheses) are: ", ButtonBox["DiracMatrix", ButtonData:>"DiracMatrix", ButtonStyle->"Hyperlink"], " (", ButtonBox["GA", ButtonData:>"GA", ButtonStyle->"Hyperlink"], "), ", ButtonBox["DiracSlash", ButtonData:>"DiracSlash", ButtonStyle->"Hyperlink"], " (", ButtonBox["GS", ButtonData:>"GS", ButtonStyle->"Hyperlink"], "), ", ButtonBox["FourVector", ButtonData:>"FourVector", ButtonStyle->"Hyperlink", ButtonNote->"FourVector"], " (", ButtonBox["FV", ButtonData:>"FV", ButtonStyle->"Hyperlink"], "), ", ButtonBox["LeviCivita", ButtonData:>"LeviCivita", ButtonStyle->"Hyperlink"], " (", ButtonBox["LC", ButtonData:>"LC", ButtonStyle->"Hyperlink"], "), ", ButtonBox["MetricTensor", ButtonData:>"MetricTensor", ButtonStyle->"Hyperlink"], " (", ButtonBox["MT", ButtonData:>"MT", ButtonStyle->"Hyperlink"], "), ", ButtonBox["Spinor", ButtonData:>"Spinor", ButtonStyle->"Hyperlink"], ", ", ButtonBox["SUNDelta", ButtonData:>"SUNDelta", ButtonStyle->"Hyperlink"], ", ", ButtonBox["SUNF", ButtonData:>"SUNF", ButtonStyle->"Hyperlink"], ", ", ButtonBox["ScalarProduct", ButtonData:>"ScalarProduct", ButtonStyle->"Hyperlink"], " (", ButtonBox["SP", ButtonData:>"SP", ButtonStyle->"Hyperlink"], "). 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The functions \ OneLoop and OneLoopSum for calculation of Standard Model (-like) 1-loop \ diagrams still work in FeynCalc 3.1 but they have not been developed much \ further compared to the FeynCalc 1.0 version. While ", ButtonBox["OneLoop", ButtonData:>"OneLoop", ButtonStyle->"Hyperlink"], " and OneLoopSum still work fine for self-energy, triangle and box diagrams \ not too complicated the reader should be aware of the package FormCalc which \ is more effective for the adventurous researcher calculating thousands of \ diagrams involving four external gauge bosons. Notice however that FormCalc \ does not reduce the Passarino-Veltman integrals to scalar integrals. Also \ FormCalc is limited to the 't Hooft Feynman gauge. 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For a description of TARCER see ", ButtonBox["hep-ph/9801383", ButtonData:>{ URL[ "http://xxx.lanl.gov/abs/hep-ph/9801383"], None}, ButtonStyle->"Hyperlink"], " or the published version in Computer Physics Communications 111 (1998) \ 265-273." }], "Text"], Cell["\<\ For more detailed information concerning FeynCalc functions you can \ investigate most of the source code in the FeynCalc directory in the \ HighEnergyPhysics directory. The location of the HighEnergyPhysics directory \ is stored upon installation in the fc.m file and you can get its value from \ the global variable $FeynCalcDirectory. A complete list of FeynCalc objects \ is stored in the variable $FeynCalcStuff. Not all functions are documented in \ this notebook. Some are either very special ones (e.g. for tools for 2-loop \ QCD diagrams originating in twist-2 OPE) or still experimental.\ \>", "Text"], Cell[TextData[{ "The ", Cell[BoxData[ FormBox[ SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], "scheme used in OneLoop is the naive one, i.e., ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"{", RowBox[{ SuperscriptBox["\[Gamma]", "5"], ",", SuperscriptBox["\[Gamma]", "\[Mu]"]}], ")"}], "=", "0"}], TraditionalForm]]], " in 4 and D dimensions. See also ", ButtonBox["ToLarin", ButtonData:>"ToLarin", ButtonStyle->"Hyperlink"] }], "Text"], Cell["The metric used is the one from Bjorken and Drell (+---).", "Text"], Cell[TextData[{ "For suggestions and bug reports please email the author: ", ButtonBox["rolf@mertig.com", ButtonData:>{ URL[ "mailto:rolf@mertig.com"], None}, ButtonStyle->"Hyperlink"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Start FeynCalc", "Section", CellTags->"Load FeynCalc"], Cell["\<\ This is only for timing purposes of this notebook and can be \ omitted in general.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"absolutestarttime", "=", RowBox[{"AbsoluteTime", "[", "]"}]}]], "Input"], Cell[BoxData[ FormBox["3.130269317`15.5162*^9", TraditionalForm]], "Output"] }, Open ]], Cell["This defines typesetting rules for q1 and q2:", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"q1", "/:", RowBox[{"MakeBoxes", "[", RowBox[{"q1", ",", "TraditionalForm"}], "]"}], ":=", RowBox[{"InterpretationBox", "[", RowBox[{ RowBox[{"SubscriptBox", "[", RowBox[{"q", ",", "1"}], "]"}], ",", "q1"}], "]"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"q2", "/:", RowBox[{"MakeBoxes", "[", RowBox[{"q2", ",", "TraditionalForm"}], "]"}], ":=", RowBox[{"InterpretationBox", "[", RowBox[{ RowBox[{"SubscriptBox", "[", RowBox[{"q", ",", "2"}], "]"}], ",", "q2"}], "]"}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"{", RowBox[{"q1", ",", "q2"}], "}"}]], "Input"], Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ InterpretationBox[ SubscriptBox["q", "1"], q1], ",", InterpretationBox[ SubscriptBox["q", "2"], q2]}], "}"}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"q1", ",", "q2"}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "By loading FeynCalc the setting of the default output format type is \ automatically set to TraditionalForm. 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Please send suggestions \ to me ...\ \>", "Commentary"], Cell[TextData[{ "The following subsections are examples from various areas of research or \ education. See also ", ButtonBox["www.feyncalc.com/examples", ButtonData:>{ URL[ "http://www.feyncalc.com/examples"], None}, ButtonStyle->"Hyperlink", ButtonNote->"http://www.feyncalc.com/examples"], "." }], "Text"], Cell[CellGroupData[{ Cell["Standard Model", "Subsection"], Cell[CellGroupData[{ Cell[TextData[{ "Tree level ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Gamma]", " ", "\[Gamma]"}], " ", "\[Rule]", " ", RowBox[{ SuperscriptBox["e", "+"], SuperscriptBox["e", "-"]}]}], TraditionalForm]]] }], "Subsubsection", CellTags->"Tree level"], Cell[TextData[{ "Tree level pair production ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Gamma]", " ", "\[Gamma]"}], " ", "\[Rule]", " ", RowBox[{ SuperscriptBox["e", "+"], SuperscriptBox["e", "-"]}]}], TraditionalForm]]] }], "Text"], Cell["Define typesetting rules for p1, p2, k1, k2", "Text"], Cell["\<\ p1/: MakeBoxes[p1, fmt_] := InterpretationBox[SubscriptBox[p, 1], \ p1]\ \>", "Input"], Cell["\<\ k1/: MakeBoxes[k1, fmt_] := InterpretationBox[SubscriptBox[k, 1], \ k1]\ \>", "Input"], Cell["\<\ p2/: MakeBoxes[p2, fmt_] := InterpretationBox[SubscriptBox[p, 2], \ p2]\ \>", "Input"], Cell["\<\ k2/: MakeBoxes[k2, fmt_] := InterpretationBox[SubscriptBox[k, 2], \ k2]\ \>", "Input"], Cell["Define slashes of external momenta to save future typing.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"{", RowBox[{"p1sl", ",", "p2sl", ",", "k1sl", ",", "k2sl"}], "}"}], "=", RowBox[{"DiracSlash", "/@", RowBox[{"{", RowBox[{"p1", ",", "p2", ",", "k1", ",", "k2"}], "}"}]}]}]], "Input"], Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ RowBox[{ FormBox["\<\"\[Gamma]\"\>", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox[ InterpretationBox[ SubscriptBox["p", "1"], p1], "TraditionalForm"]}], ",", RowBox[{ FormBox["\<\"\[Gamma]\"\>", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox[ InterpretationBox[ SubscriptBox["p", "2"], p2], "TraditionalForm"]}], ",", RowBox[{ FormBox["\<\"\[Gamma]\"\>", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox[ InterpretationBox[ SubscriptBox["k", "1"], k1], "TraditionalForm"]}], ",", RowBox[{ FormBox["\<\"\[Gamma]\"\>", "TraditionalForm"], "\[NoBreak]", "\[CenterDot]", "\[NoBreak]", FormBox[ InterpretationBox[ SubscriptBox["k", "2"], k2], "TraditionalForm"]}]}], "}"}], TraditionalForm]], "Output"] }, Open ]], Cell[TextData[{ "Kinematic definitions so that only ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["p", "1"], ".", SubscriptBox["k", "1"]}], TraditionalForm]]], ", ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["p", "1"], ".", SubscriptBox["k", "2"]}], TraditionalForm]]], " appear in final results. I.e., define ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["p", "1", "2"], "=", RowBox[{ SubsuperscriptBox["p", "2", "2"], "=", " ", SuperscriptBox["m", "2"]}]}], TraditionalForm]]], " ", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["k", "1", "2"], "=", RowBox[{ SubsuperscriptBox["k", "2", "2"], "=", " ", "0"}]}], TraditionalForm]]], " ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["k", "1"], "\[CenterDot]", SubscriptBox["k", "2"]}], " ", "=", " ", RowBox[{ RowBox[{ SubscriptBox["p", "1"], "\[CenterDot]", SubscriptBox["p", "2"]}], "+", SuperscriptBox["m", "2"]}]}], TraditionalForm]]], " ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["k", "1"], "\[CenterDot]", SubscriptBox["p", "2"]}], " ", "=", " ", RowBox[{ SubscriptBox["k", "2"], "\[CenterDot]", SubscriptBox["p", "1"]}]}], TraditionalForm]]], " ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["k", "2"], "\[CenterDot]", SubscriptBox["p", "2"]}], " ", "=", " ", RowBox[{ SubscriptBox["k", "1"], 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x)*x - 4*ln(x)*ln(1 - x)*ln(1 - x) + 4*ln(x)*ln(1 - x)*ln(1 - x)*x + 8*ln(x)*ln(1 - x)*ln(1 - x)*[1+x]^-1 - 8*ln(x)*ln(1 - x)*ln(1 + x) + 8*ln(x)*ln(1 - x)*ln(1 + x)*x + 16*ln(x)*ln(1 - x)*ln(1 + x)*[1+x]^-1 + 4/3*ln(x)*ln(1 + x)*x^-1 + 4*ln(x)*ln(1 + x)*x + 16/3*ln(x)*ln(1 + x)*x^2 + 8*ln(x)*ln(1 + x)*ln(1 + x)*x + 8*ln(x)*ln(1 + x)*ln(1 + x)*[1+x]^-1 - 6*ln(x)*ln(x) - 8/3*ln(x)*ln(x)*x^2 + 2*ln(x)*ln(x)*ln(1 - x) - 2*ln(x)*ln(x)*ln(1 - x)*x - 4*ln(x)*ln(x)*ln(1 - x)*[1+x]^-1 - 6*ln(x)*ln(x)*ln(1 + x) + 2*ln(x)*ln(x)*ln(1 + x)*x + 8*ln(x)*ln(x)*ln(1 + x)*[1+x]^-1 + ln(x)*ln(x)*ln(x) - ln(x)*ln(x)*ln(x)*x - 2*ln(x)*ln(x)*ln(x)*[1+x]^-1 + 4*ln(x)*Li2(1 - x) - 4*ln(x)*Li2(1 - x)*x - 8*ln(x)*Li2(1 - x)*[1+x]^-1 - 4*ln(x)*Li2( - x) + 4*ln(x)*Li2( - x)*x + 8*ln(x)*Li2( - x)*[1+x]^-1 - 4*Li2(1 - x) - 4*Li2(1 - x)*x + 4/3*Li2( - x)*x^-1 + 4*Li2( - x)*x + 16/3*Li2( - x)*x^2 + 8*Li3(1 - x) - 8*Li3(1 - x)*x - 16*Li3(1 - x)*[1+x]^-1 - 4*Li3( - x) - 4*Li3( - x)*x + 4*S12(1 - x) - 4*S12(1 - x)*x - 8*S12(1 - x)*[1+x]^-1 - 8*S12( - x) + 24*S12( - x)*x + 32*S12( - x)*[1+x]^-1 + 4*S12(x^2) - 4*S12(x^2)*x - 8*S12(x^2)*[1+x]^-1 ) + [(-1)^m]*O1*Cf^2 * ( + 82/3 + 12*x*Z2 + 4*x*Z3 - 82/3*x - 32/3*x^2*Z2 - 12*Z2 - 8*Z3*[1+x]^-1 + 12*Z3 + 16*ln(1 - x) - 16*ln(1 - x)*x + 16*ln(1 - x)*Li2(1 - x) - 16*ln(1 - x)*Li2(1 - x)*x - 32*ln(1 - x)*Li2(1 - x)*[1+x]^-1 - 16*ln(1 + x)*x*Z2 - 16*ln(1 + x)*Z2*[1+x]^-1 + 16*ln(1 + x)*Li2(1 - x) - 16*ln(1 + x)*Li2(1 - x)*x - 32*ln(1 + x)*Li2(1 - x)*[1+x]^-1 - 32*ln(1 + x)*Li2( - x)*x - 32*ln(1 + x)*Li2( - x)*[1+x]^-1 + 74/3*ln(x) + 50/3*ln(x)*x + 8*ln(x)*ln(1 - x) + 8*ln(x)*ln(1 - x)*x + 8*ln(x)*ln(1 - x)*ln(1 - x) - 8*ln(x)*ln(1 - x)*ln(1 - x)*x - 16*ln(x)*ln(1 - x)*ln(1 - x)*[1+x]^-1 + 16*ln(x)*ln(1 - x)*ln(1 + x) - 16*ln(x)*ln(1 - x)*ln(1 + x)*x - 32*ln(x)*ln(1 - x)*ln(1 + x)*[1+x]^-1 - 8/3*ln(x)*ln(1 + x)*x^-1 - 8*ln(x)*ln(1 + x)*x - 32/3*ln(x)*ln(1 + x)*x^2 - 16*ln(x)*ln(1 + x)*ln(1 + x)*x - 16*ln(x)*ln(1 + x)*ln(1 + x)*[1+x]^-1 + 12*ln(x)*ln(x) + 16/3*ln(x)*ln(x)*x^2 - 4*ln(x)*ln(x)*ln(1 - x) + 4*ln(x)*ln(x)*ln(1 - x)*x + 8*ln(x)*ln(x)*ln(1 - x)*[1+x]^-1 + 12*ln(x)*ln(x)*ln(1 + x) - 4*ln(x)*ln(x)*ln(1 + x)*x - 16*ln(x)*ln(x)*ln(1 + x)*[1+x]^-1 - 2*ln(x)*ln(x)*ln(x) + 2*ln(x)*ln(x)*ln(x)*x + 4*ln(x)*ln(x)*ln(x)*[1+x]^-1 - 8*ln(x)*Li2(1 - x) + 8*ln(x)*Li2(1 - x)*x + 16*ln(x)*Li2(1 - x)*[1+x]^-1 + 8*ln(x)*Li2( - x) - 8*ln(x)*Li2( - x)*x - 16*ln(x)*Li2( - x)*[1+x]^-1 + 8*Li2(1 - x) + 8*Li2(1 - x)*x - 8/3*Li2( - x)*x^-1 - 8*Li2( - x)*x - 32/3*Li2( - x)*x^2 - 16*Li3(1 - x) + 16*Li3(1 - x)*x + 32*Li3(1 - x)*[1+x]^-1 + 8*Li3( - x) + 8*Li3( - x)*x - 8*S12(1 - x) + 8*S12(1 - x)*x + 16*S12(1 - x)*[1+x]^-1 + 16*S12( - x) - 48*S12( - x)*x - 64*S12( - x)*[1+x]^-1 - 8*S12(x^2) + 8*S12(x^2)*x + 16*S12(x^2)*[1+x]^-1 ) + [(-1)^m]*O2*Ca*Cf * ( + 8/3 - 8/3*x - 16/3*x^2*Z2 - 8/3*ln(x) + 16/3*ln(x)*x + 8/3*ln(x)*ln(1 + x)*x^-1 - 8*ln(x)*ln(1 + x)*x - 16/3*ln(x)*ln(1 + x)*x^2 + 8/3*ln(x)*ln(x)*x^2 + 8/3*Li2( - x)*x^-1 - 8*Li2( - x)*x - 16/3*Li2( - x)*x^2 ) + [(-1)^m]*O2*Cf^2 * ( - 16/3 + 16/3*x + 32/3*x^2*Z2 + 16/3*ln(x) - 32/3*ln(x)*x - 16/3*ln(x)*ln(1 + x)*x^-1 + 16*ln(x)*ln(1 + x)*x + 32/3*ln(x)*ln(1 + x)*x^2 - 16/3*ln(x)*ln(x)*x^2 - 16/3*Li2( - x)*x^-1 + 16*Li2( - x)*x + 32/3*Li2( - x)*x^2 ) + e^-2*delta*O1*Ca*Cf * ( - 22 ) + e^-2*delta*O1*Cf*Tf * ( + 8 ) + e^-2*delta*O1*Cf^2 * ( - 18 + 32*Z2 ) + e^-2*O1*Ca*Cf * ( + 44/3 + 44/3*x - 88/3*[(1-x)+]^-1 ) + e^-2*O1*Cf*Tf * ( - 16/3 - 16/3*x + 32/3*[(1-x)+]^-1 ) + e^-2*O1*Cf^2 * ( + 40 + 8*x - 48*[(1-x)+]^-1 + 32*ln(1 - x) + 32*ln(1 - x)*x - 64*ln(1 - x)*[(1-x)+]^-1 - 24*ln(x) - 24*ln(x)*x + 32*ln(x)*[1-x]^-1 ) + e^-1*delta*O1*Ca*Cf * ( + 325/6 - 44/3*Z2 - 12*Z3 ) + e^-1*delta*O1*Cf*Tf * ( - 58/3 + 16/3*Z2 ) + e^-1*delta*O1*Cf^2 * ( + 87/2 - 36*Z2 - 8*Z3 ) + e^-1*O1*Ca*Cf * ( - 158/9 + 4*x*Z2 + 22/9*x - 8*Z2*[(1-x)+]^-1 + 4*Z2 + 238/9*[(1-x)+]^-1 + 44/3*ln(1 - x) + 44/3*ln(1 - x)*x - 88/3*ln(1 - x)*[(1-x)+]^-1 + 34/3*ln(x) + 34/3*ln(x)*x - 44/3*ln(x)*[1-x]^-1 - 2*ln(x)*ln(x) - 2*ln(x)*ln(x)*x + 4*ln(x)*ln(x)*[1-x]^-1 ) + e^-1*O1*Cf*Tf * ( + 88/9 - 56/9*x - 56/9*[(1-x)+]^-1 - 16/3*ln(1 - x) - 16/3*ln(1 - x)*x + 32/3*ln(1 - x)*[(1-x)+]^-1 - 8/3*ln(x) - 8/3*ln(x)*x + 16/3*ln(x)*[1-x]^-1 ) + e^-1*O1*Cf^2 * ( - 40 - 4*x + 56*[(1-x)+]^-1 - 4*ln(1 - x) + 44*ln(1 - x)*x - 24*ln(1 - x)*[(1-x)+]^-1 + 24*ln(1 - x)*ln(1 - x) + 24*ln(1 - x)*ln(1 - x)*x - 48*ln(1 - x)*ln(1 - x)*[(1-x)+]^-1 + 36*ln(x) - 20*ln(x)*x - 36*ln(x)*[1-x]^-1 - 16*ln(x)*ln(1 - x)*[1-x]^-1 - 14*ln(x)*ln(x) - 14*ln(x)*ln(x)*x + 16*ln(x)*ln(x)*[1-x]^-1 - 8*Li2(1 - x) - 8*Li2(1 - x)*x ) + e^-1*O2*Ca*Cf * ( + 20/3 - 88/3*x ) + e^-1*O2*Cf*Tf * ( - 16/3 + 32/3*x ) + e^-1*O2*Cf^2 * ( - 16 - 8*x - 32*ln(1 - x)*x + 16*ln(x)*x ) + delta*O1*Ca*Cf * ( - 7081/72 + 301/18*Z2 + 49/5*Z2^2 + 28*Z3 ) + delta*O1*Cf*Tf * ( + 569/18 - 46/9*Z2 - 8*Z3 ) + delta*O1*Cf^2 * ( - 541/8 + 97/2*Z2 - 74/5*Z2^2 + 54*Z3 ) + O1*Ca*Cf * ( + 941/27 + 17/3*x*Z2 - 8*x*Z3 - 580/27*x - 16/3*x^2*Z2 - 24*x^2*Z3 - 28/3*Z2*[(1-x)+]^-1 - 1/3*Z2 + 12*Z3*[1-x]^-1 + 22*Z3*[(1-x)+]^-1 - 20*Z3 - 670/27*[(1-x)+]^-1 - 122/9*ln(1 - x) + 6*ln(1 - x)*x*Z2 - 32/9*ln(1 - x)*x + 8*ln(1 - x)*x^2*Z2 - 10*ln(1 - x)*Z2*[(1-x)+]^-1 + 2*ln(1 - x)*Z2 + 238/9*ln(1 - x)*[(1-x)+]^-1 + 22/3*ln(1 - x)*ln(1 - x) + 22/3*ln(1 - x)*ln(1 - x)*x - 44/3*ln(1 - x)*ln(1 - x)*[(1-x)+]^-1 + 2*ln(1 - x)*Li2(1 - x) - 2*ln(1 - x)*Li2(1 - x)*x + 8*ln(1 - x)*Li2(1 - x)*x^2 - 2*ln(1 - x)*Li2(1 - x)*[1-x]^-1 + 14/9*ln(x) - 2*ln(x)*x*Z2 + 176/9*ln(x)*x - 8*ln(x)*x^2*Z2 + 10*ln(x)*Z2*[1-x]^-1 - 6*ln(x)*Z2 + 101/9*ln(x)*[1-x]^-1 + 28/3*ln(x)*ln(1 - x) + 10/3*ln(x)*ln(1 - x)*x - 38/3*ln(x)*ln(1 - x)*[1-x]^-1 - 12*ln(x)*ln(1 + x) - 4/3*ln(x)*ln(1 + x)*x^-1 - 16*ln(x)*ln(1 + x)*x - 16/3*ln(x)*ln(1 + x)*x^2 + 47/6*ln(x)*ln(x) + 47/6*ln(x)*ln(x)*x + 8/3*ln(x)*ln(x)*x^2 - 11/3*ln(x)*ln(x)*[1-x]^-1 + ln(x)*ln(x)*ln(1 - x) - ln(x)*ln(x)*ln(1 - x)*x + 4*ln(x)*ln(x)*ln(1 - x)*x^2 - ln(x)*ln(x)*ln(1 - x)*[1-x]^-1 - ln(x)*ln(x)*ln(x) - ln(x)*ln(x)*ln(x)*x + 2*ln(x)*ln(x)*ln(x)*[1-x]^-1 + 8*ln(x)*Li2(1 - x) + 16*ln(x)*Li2(1 - x)*x^2 - 12*ln(x)*Li2(1 - x)*[1-x]^-1 + 8*ln(x)*Li2( - x) - 8*ln(x)*Li2( - x)*[1-x]^-1 - 12*Li2(1 - x)*x + 4*Li2(1 - x)*[1-x]^-1 - 12*Li2( - x) - 4/3*Li2( - x)*x^-1 - 16*Li2( - x)*x - 16/3*Li2( - x)*x^2 - 6*Li3(1 - x) + 6*Li3(1 - x)*x - 24*Li3(1 - x)*x^2 + 6*Li3(1 - x)*[1-x]^-1 - 16*Li3( - x) + 16*Li3( - x)*[1-x]^-1 + 14*S12(1 - x) - 6*S12(1 - x)*x + 24*S12(1 - x)*x^2 - 14*S12(1 - x)*[1-x]^-1 ) + O1*Cf*Tf * ( - 88/27 - 4/3*x*Z2 + 20/27*x + 8/3*Z2*[(1-x)+]^-1 - 4/3*Z2 + 128/27*[(1-x)+]^-1 + 88/9*ln(1 - x) - 56/9*ln(1 - x)*x - 56/9*ln(1 - x)*[(1-x)+]^-1 - 8/3*ln(1 - x)*ln(1 - x) - 8/3*ln(1 - x)*ln(1 - x)*x + 16/3*ln(1 - x)*ln(1 - x)*[(1-x)+]^-1 + 44/9*ln(x) - 28/9*ln(x)*x - 28/9*ln(x)*[1-x]^-1 - 8/3*ln(x)*ln(1 - x) - 8/3*ln(x)*ln(1 - x)*x + 16/3*ln(x)*ln(1 - x)*[1-x]^-1 - 2/3*ln(x)*ln(x) - 2/3*ln(x)*ln(x)*x + 4/3*ln(x)*ln(x)*[1-x]^-1 ) + O1*Cf^2 * ( + 188/3 - 4*x*Z2 - 24*x*Z3 + 4/3*x + 32/3*x^2*Z2 + 48*x^2*Z3 - 4*Z2*[(1-x)+]^-1 + 20*Z2 - 24*Z3*[1-x]^-1 + 24*Z3 - 56*[(1-x)+]^-1 - 38*ln(1 - x) + 8*ln(1 - x)*x*Z2 + 38*ln(1 - x)*x - 16*ln(1 - x)*x^2*Z2 - 8*ln(1 - x)*Z2*[(1-x)+]^-1 + 8*ln(1 - x)*Z2 + 28*ln(1 - x)*[(1-x)+]^-1 - 13*ln(1 - x)*ln(1 - x) + 31*ln(1 - x)*ln(1 - x)*x - 6*ln(1 - x)*ln(1 - x)*[(1-x)+]^-1 + 28/3*ln(1 - x)*ln(1 - x)*ln(1 - x) + 28/3*ln(1 - x)*ln(1 - x)*ln(1 - x)*x - 56/3*ln(1 - x)*ln(1 - x)*ln(1 - x)*[(1-x)+]^-1 - 12*ln(1 - x)*Li2(1 - x) + 4*ln(1 - x)*Li2(1 - x)*x - 16*ln(1 - x)*Li2(1 - x)*x^2 - 68/3*ln(x) - 14*ln(x)*x*Z2 - 68/3*ln(x)*x + 16*ln(x)*x^2*Z2 + 2*ln(x)*Z2 + 44*ln(x)*[1-x]^-1 - 6*ln(x)*ln(1 - x) + 34*ln(x)*ln(1 - x)*x - 20*ln(x)*ln(1 - x)*[1-x]^-1 + 6*ln(x)*ln(1 - x)*ln(1 - x) + 6*ln(x)*ln(1 - x)*ln(1 - x)*x - 20*ln(x)*ln(1 - x)*ln(1 - x)*[1-x]^-1 + 24*ln(x)*ln(1 + x) + 8/3*ln(x)*ln(1 + x)*x^-1 + 32*ln(x)*ln(1 + x)*x + 32/3*ln(x)*ln(1 + x)*x^2 + 11*ln(x)*ln(x) - 23*ln(x)*ln(x)*x - 16/3*ln(x)*ln(x)*x^2 - 15*ln(x)*ln(x)*[1-x]^-1 - 6*ln(x)*ln(x)*ln(1 - x) + 2*ln(x)*ln(x)*ln(1 - x)*x - 8*ln(x)*ln(x)*ln(1 - x)*x^2 - 4*ln(x)*ln(x)*ln(1 - x)*[1-x]^-1 - 5*ln(x)*ln(x)*ln(x) - 5*ln(x)*ln(x)*ln(x)*x + 16/3*ln(x)*ln(x)*ln(x)*[1-x]^-1 - 8*ln(x)*Li2(1 - x) + 24*ln(x)*Li2(1 - x)*x - 32*ln(x)*Li2(1 - x)*x^2 - 16*ln(x)*Li2(1 - x)*[1-x]^-1 - 16*ln(x)*Li2( - x) + 16*ln(x)*Li2( - x)*[1-x]^-1 - 24*Li2(1 - x) + 48*Li2(1 - x)*x - 4*Li2(1 - x)*[1-x]^-1 + 24*Li2( - x) + 8/3*Li2( - x)*x^-1 + 32*Li2( - x)*x + 32/3*Li2( - x)*x^2 + 20*Li3(1 - x) - 28*Li3(1 - x)*x + 48*Li3(1 - x)*x^2 + 32*Li3( - x) - 32*Li3( - x)*[1-x]^-1 - 8*S12(1 - x) + 56*S12(1 - x)*x - 48*S12(1 - x)*x^2 - 32*S12(1 - x)*[1-x]^-1 ) + O2*Ca*Cf * ( - 26/9 - 8*x*Z2 - 24*x*Z3 + 232/9*x + 16/3*x^2*Z2 + 24*x^2*Z3 + 4*Z2 - 16/3*ln(1 - x) + 8*ln(1 - x)*x*Z2 - 64/3*ln(1 - x)*x - 8*ln(1 - x)*x^2*Z2 + 8*ln(1 - x)*Li2(1 - x)*x - 8*ln(1 - x)*Li2(1 - x)*x^2 + 6*ln(x) - 8*ln(x)*x*Z2 - 28*ln(x)*x + 8*ln(x)*x^2*Z2 - 4*ln(x)*ln(1 - x) + 8*ln(x)*ln(1 - x)*x - 8/3*ln(x)*ln(1 + x)*x^-1 + 8*ln(x)*ln(1 + x)*x + 16/3*ln(x)*ln(1 + x)*x^2 - 8/3*ln(x)*ln(x)*x^2 + 4*ln(x)*ln(x)*ln(1 - x)*x - 4*ln(x)*ln(x)*ln(1 - x)*x^2 + 16*ln(x)*Li2(1 - x)*x - 16*ln(x)*Li2(1 - x)*x^2 - 8*Li2(1 - x) + 16*Li2(1 - x)*x - 8/3*Li2( - x)*x^-1 + 8*Li2( - x)*x + 16/3*Li2( - x)*x^2 - 24*Li3(1 - x)*x + 24*Li3(1 - x)*x^2 + 24*S12(1 - x)*x - 24*S12(1 - x)*x^2 ) + O2*Cf*Tf * ( - 8/9 - 32/9*x - 16/3*ln(1 - x) + 32/3*ln(1 - x)*x - 8/3*ln(x) + 16/3*ln(x)*x ) + O2*Cf^2 * ( - 32/3 + 16*x*Z2 + 48*x*Z3 - 16/3*x - 32/3*x^2*Z2 - 48*x^2*Z3 - 8*Z2 - 16*ln(1 - x)*x*Z2 - 44*ln(1 - x)*x + 16*ln(1 - x)*x^2*Z2 - 24*ln(1 - x)*ln(1 - x)*x - 16*ln(1 - x)*Li2(1 - x)*x + 16*ln(1 - x)*Li2(1 - x)*x^2 - 40/3*ln(x) + 16*ln(x)*x*Z2 + 68/3*ln(x)*x - 16*ln(x)*x^2*Z2 + 8*ln(x)*ln(1 - x) - 32*ln(x)*ln(1 - x)*x + 16/3*ln(x)*ln(1 + x)*x^-1 - 16*ln(x)*ln(1 + x)*x - 32/3*ln(x)*ln(1 + x)*x^2 + 12*ln(x)*ln(x)*x + 16/3*ln(x)*ln(x)*x^2 - 8*ln(x)*ln(x)*ln(1 - x)*x + 8*ln(x)*ln(x)*ln(1 - x)*x^2 - 32*ln(x)*Li2(1 - x)*x + 32*ln(x)*Li2(1 - x)*x^2 + 16*Li2(1 - x) - 48*Li2(1 - x)*x + 16/3*Li2( - x)*x^-1 - 16*Li2( - x)*x - 32/3*Li2( - x)*x^2 + 48*Li3(1 - x)*x - 48*Li3(1 - x)*x^2 - 48*S12(1 - x)*x + 48*S12(1 - x)*x^2 ) \"]//ReleaseHold;\ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Short", "[", "aqq", "]"}]], "Input"], Cell[BoxData[ FormBox[ TagBox[ RowBox[{ FractionBox[ RowBox[{"O1", " ", RowBox[{"(", RowBox[{ RowBox[{"32", " ", RowBox[{"\[Zeta]", "(", "2", ")"}]}], "-", "18"}], ")"}], " ", RowBox[{"\[Delta]", "(", FormBox[ RowBox[{"1", "-", "x"}], "TraditionalForm"], ")"}], " ", SubsuperscriptBox["C", "F", "2"]}], SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "2"]], "+", RowBox[{"\[LeftSkeleton]", "29", "\[RightSkeleton]"}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"], " ", SubscriptBox["C", "A"], " ", "O1", " ", RowBox[{"(", RowBox[{"\[LeftSkeleton]", "1", "\[RightSkeleton]"}], ")"}], " ", SubscriptBox["C", "F"]}]}], Short], TraditionalForm]], "Output"] }, Open ]], Cell["\<\ Comment: By default all bracketed FORM expressions are translated \ to a Hold[] expression.\ \>", "Commentary"], Cell[CellGroupData[{ Cell["FORM2FeynCalc[\"-[(-1)^m]\"]", "Input"], Cell[BoxData[ FormBox[ RowBox[{"-", RowBox[{"Hold", "(", SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"], ")"}]}], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "ReleaseHold"}]], "Input"], Cell[BoxData[ FormBox[ RowBox[{"-", SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"]}], TraditionalForm]], "Output"] }, Open ]], Cell["Calculate moments", "Text"], Cell["\<\ The first moment should be zero, which is verified by Integrate2 in \ a reasonable amount of time. The variable O2 can be set to zero since it is \ the coefficient of unphysical matrix elements.\ \>", "Text"], Cell[TextData[{ "This calculates for m=1 the integral ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubsuperscriptBox["\[Integral]", "0", RowBox[{"1", " "}]], " ", RowBox[{ SubsuperscriptBox[ StyleBox[ OverscriptBox[ StyleBox["A", FontSlant->"Plain"], "^"], FontSlant->"Plain"], "qq", RowBox[{"NS", ",", "PHYS"}]], " ", RowBox[{"\[DifferentialD]", "x"}]}]}], " "}], TraditionalForm]]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Timing", "[", RowBox[{"Integrate2", "[", RowBox[{ RowBox[{ RowBox[{"aqq", "/.", RowBox[{"m", "\[Rule]", "1"}]}], "/.", RowBox[{"O2", "\[Rule]", "0"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input"], Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ RowBox[{"18.6500000000000021`", " ", "Second"}], ",", "0"}], "}"}], TraditionalForm]], "Output"] }, Open ]], Cell["\<\ If you know that no partial fraction 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9*MW2**2*S + 2*S**3 - MW2**2*U - ", " & 4*MW2*S*U + 5*S**2*U + 3*S*U**2", " F(19)= 2*MW2**6 - 8*MW2**5*S + 12*MW2**4*S**2 - ", " & 8*MW2**3*S**3 + 2*MW2**2*S**4 - 2*MW2**5*T + ", " & 20*MW2**4*S*T - 36*MW2**3*S**2*T + 20*MW2**2*S**3*T - ", " & 2*MW2*S**4*T - 6*MW2**3*S*T**2 + 6*MW2**2*S**2*T**2 - ", " & 6*MW2*S**3*T**2 + 4*MW2*S**2*T**3 - S**2*T**4", " F(20)= -F(12)/(2D0*F(13)*F(14)) - ", " & (S**2*T**2*F(10)*F(15))/(2D0*F(14)**3) + ", " & (S**3*T**2*F(11)*F(15))/(2D0*F(14)**3) + ", " & (S**2*T*F(9)*F(15)**2)/F(14)**3 - ", " & (F(5)*F(16))/(2D0*F(13)**2*F(14)**2*F(15)) + ", " & (S*F(6)*F(17))/(2D0*F(14)**2*F(15)) + ", " & (F(7)*F(12)*F(18))/(2D0*F(13)**2*F(14)**2) - ", " & (F(8)*F(12)*F(19))/(2D0*F(13)**2*F(14)**3)", " d122res = F(20)"}]], TraditionalForm]], "Output"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"DeleteFile", "/@", RowBox[{"FileNames", "[", "\"\\"", "]"}]}], ";", RowBox[{"Clear", "[", RowBox[{"d122", ",", "se"}], "]"}], ";"}]], "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["PlusDistribution", "Subsection", CellTags->"PlusDistribution"], Cell[CellGroupData[{ Cell["Description", "Subsubsection"], Cell["\<\ PlusDistribution[1/(1-x)] denotes a distribution (in the sense of \ the \"+\" prescription).\ \>", "Text"], Cell[TextData[{ "See also: ", " ", ButtonBox["Integrate2", ButtonData:>"Integrate2", ButtonStyle->"Hyperlink", ButtonNote->"Integrate2"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Examples", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PlusDistribution", "[", RowBox[{"1", "/", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}], "]"}]], "Input"], Cell[BoxData[ FormBox[ SubscriptBox[ RowBox[{"(", FractionBox["1", RowBox[{"1", "-", "x"}]], ")"}], "+"], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PlusDistribution", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{"1", "-", "x"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}], "]"}]], "Input"], Cell[BoxData[ FormBox[ SubscriptBox[ RowBox[{"(", FractionBox[ RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}], RowBox[{"1", "-", "x"}]], ")"}], "+"], TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate2", "[", RowBox[{ RowBox[{"PlusDistribution", "[", RowBox[{"1", "/", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate2", "[", RowBox[{ RowBox[{"PlusDistribution", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{"1", "-", "x"}], "]"}], "/", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Integrate2", "[", RowBox[{ RowBox[{"PlusDistribution", "[", RowBox[{ RowBox[{ RowBox[{"Log", "[", RowBox[{"1", "-", "x"}], "]"}], "^", "2"}], "/", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PlusDistribution", "[", RowBox[{ RowBox[{"Log", "[", RowBox[{"x", " ", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}], "]"}], "/", RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}]}], "]"}]], "Input"], Cell[BoxData[ FormBox[ RowBox[{ FractionBox[ RowBox[{"log", "(", "x", ")"}], RowBox[{"1", "-", "x"}]], "+", SubscriptBox[ RowBox[{"(", FractionBox[ RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}], RowBox[{"1", "-", "x"}]], ")"}], "+"]}], TraditionalForm]], "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Polarization", "Subsection", CellTags->"Polarization"], Cell[CellGroupData[{ Cell["Description", "Subsubsection"], Cell["\<\ Polarization[k] = Polarization[k, I] is the head of a polarization \ momentum with (incoming) momentum k. 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StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.31, 0.62}, ColumnAlignments->{Left}, RowMinHeight->1.2}], Cell[StyleData["BottomBox", "Printout"], CellMargins->{{2, 0}, {0, -5}}, FontSize->10, Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->2.2}], Cell[StyleData["BottomBox", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, -5}}, FontFamily->"Palatino", FontSize->10, Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->2.2}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TopSpanBox"], CellFrame->{{0.5, 0.5}, {0, 0.5}}, CellMargins->{{11, 4}, {-2, 8}}, CellHorizontalScrolling->True, PageBreakBelow->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, StyleMenuListing->None, FontWeight->"Plain", Background->RGBColor[1, 0.6, 0.6], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.9, 0.03}, ColumnAlignments->{Left}}], Cell[StyleData["TopSpanBox", 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Background->GrayLevel[1], GridBoxOptions->{RowMinHeight->1.8}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Picture"], CellMargins->{{12, Inherited}, {0, 8}}, CellHorizontalScrolling->True], Cell[StyleData["Picture", "Printout"], CellMargins->{{2, Inherited}, {0, 8}}], Cell[StyleData["Picture", "EnhancedPrintout"], CellMargins->{{2, Inherited}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Caption"], CellMargins->{{12, 4}, {0, 2}}, PageBreakAbove->False, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["Caption", "Printout"], CellMargins->{{2, 4}, {2, 4}}, FontSize->7], Cell[StyleData["Caption", "EnhancedPrintout"], CellMargins->{{2, 4}, {2, 4}}, FontFamily->"Futura", FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Tables", "Section"], Cell[CellGroupData[{ Cell[StyleData["SingleRowTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, PageBreakWithin->False, AutoIndent->False, AutoSpacing->False, LineIndent->0, 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Cell["Contents and Index", "Section"], Cell[CellGroupData[{ Cell[StyleData["ContentsTitle"], CellMargins->{{10, 4}, {0, 18}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->26, FontWeight->"Bold"], Cell[StyleData["ContentsTitle", "Printout"], CellMargins->{{2, 0}, {0, 18}}, PageBreakBelow->False, FontSize->18], Cell[StyleData["ContentsTitle", "EnhancedPrintout"], CellMargins->{{2, 0}, {0, 18}}, PageBreakBelow->False, FontFamily->"Futura", FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ContentsSection"], CellMargins->{{20, 4}, {3, 18}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->12, FontWeight->"Bold"], Cell[StyleData["ContentsSection", "Printout"], CellMargins->{{12, 0}, {3, 18}}, PageBreakBelow->False, FontSize->11], Cell[StyleData["ContentsSection", "EnhancedPrintout"], CellMargins->{{12, 0}, {3, 18}}, PageBreakBelow->False, FontFamily->"Futura", FontSize->11] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Contents"], CellMargins->{{21, 4}, {0, 8}}, StyleMenuListing->None], Cell[StyleData["Contents", "Printout"], CellMargins->{{13, 0}, {0, 8}}], Cell[StyleData["Contents", "EnhancedPrintout"], CellMargins->{{13, 0}, {0, 8}}, FontFamily->"Palatino", FontSize->11] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Index"], CellMargins->{{21, 4}, {0, 0}}, ParagraphIndent->-48, StyleMenuListing->None], Cell[StyleData["Index", "Printout"], CellMargins->{{13, 0}, {0, 0}}, FontSize->10], Cell[StyleData["Index", "EnhancedPrintout"], CellMargins->{{13, 0}, {0, 0}}, FontFamily->"Palatino", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["IndexSubentry"], CellMargins->{{36, 4}, {0, 0}}, ParagraphIndent->-48, StyleMenuListing->None], Cell[StyleData["IndexSubentry", "Printout"], CellMargins->{{24, 0}, {0, 0}}, FontSize->10], Cell[StyleData["IndexSubentry", "EnhancedPrintout"], CellMargins->{{24, 0}, {0, 0}}, FontFamily->"Palatino", FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Browser Emulation", 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Cell[CellGroupData[{ Cell[StyleData["Category1"], ShowCellBracket->False, ShowGroupOpenCloseIcon->True, CellMargins->{{12, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 50}, FontSize->16, FontWeight->"Bold"], Cell[StyleData["Category1", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Category2"], ShowCellBracket->False, ShowGroupOpenCloseIcon->True, CellMargins->{{85, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 60}, FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 0.500008]], Cell[StyleData["Category2", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Category3"], ShowCellBracket->False, ShowGroupOpenCloseIcon->True, CellMargins->{{157, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 70}, FontSize->12, FontWeight->"Bold", FontColor->RGBColor[0.2, 0, 0.4]], Cell[StyleData["Category3", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Category4"], ShowCellBracket->False, ShowGroupOpenCloseIcon->True, CellMargins->{{230, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 80}, FontWeight->"Bold", FontColor->RGBColor[0, 0.300008, 0.4]], Cell[StyleData["Category4", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[CellGroupData[{ Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->8, FontWeight->"Bold"], Cell[StyleData["Header", "Printout"]], Cell[StyleData["Header", "EnhancedPrintout"], FontFamily->"Futura"] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontSlant->"Plain"], Cell[StyleData["Footer", "Printout"]], Cell[StyleData["Footer", "EnhancedPrintout"], FontFamily->"Futura"] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->8, FontWeight->"Bold"], Cell[StyleData["PageNumber", "Printout"]], Cell[StyleData["PageNumber", "EnhancedPrintout"], FontFamily->"Futura"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Printout"], FontSize->11, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}], Cell[StyleData["Hyperlink", "EnhancedPrintout"], FontFamily->"Palatino", FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Printout"], FontSize->11, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}], Cell[StyleData["MainBookLink", "EnhancedPrintout"], FontFamily->"Palatino", FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}], Cell[StyleData["AddOnsLink", "EnhancedPrintout"], FontFamily->"WRICourier", FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}], Cell[StyleData["RefGuideLink", "EnhancedPrintout"], FontFamily->"WRICourier", FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->11, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}], Cell[StyleData["GettingStartedLink", "EnhancedPrintout"], FontFamily->"Palatino", FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->11, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}], Cell[StyleData["OtherInformationLink", "EnhancedPrintout"], FontFamily->"Palatino", FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]] }, Open ]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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